Topology

All occurrences

Where it appears in the corpus (767)

1. #01

   Ethics of the Real: Kant and Lacan · Alenka Zupančič · p.211

   Ethics and Tragedy in Psychoanalysis > Oedipus, or the Outcast of the Signifier > What shall we do with Oedipus?

   Theoretical move: The passage argues that Oedipus' topological unlocatability in *Oedipus at Colonus* — his literal impossibility of being 'situated' — enacts his status as a remainder/outcast that is ultimately transformed into a sublime object through the mechanism of the Other's mirror: the lack constitutive of the sublime is restored by showing Oedipus' disappearance only through its effect on the king of Athens, converting the abject leftover into an agalma.

   The messenger who describes the miraculous death - or, rather, disappearance - of Oedipus stresses its topological aspect

2. #02

   Marxist Film Theory and Fight Club · Anna Kornbluh · p.62

   <span id="page-6-0"></span>**[ACKNOWLEDGMENTS](#page-5-0)** > **Creative labor** > **Critique as practice**

   Theoretical move: The passage argues that ideology critique is best understood not as external demystification but as immanent, symptomatic practice—reading for the internal gaps and shadows of representation—and that cinema's projective technology makes it a privileged site for this dialectical procedure, which aims not merely to evaluate cultural products but to produce situated knowledge capable of precipitating social transformation.

   It has a complicated topology: the logics are not extraneous outsides of the text but dimly perceptible insides.

3. #03

   The Interpretation of Dreams · Sigmund Freud

   **(B) REGRESSION**

   Theoretical move: Freud constructs a topographical model of the psychic apparatus as a sequence of Ψ-systems (Pcpt, Mnem, consciousness, motility) to explain how dream-work transforms thoughts into perceptual images via regression, establishing the foundational architecture that separates perception from memory and both from consciousness.

   The idea which is placed at our disposal is one of psychic locality… The psychic locality, then, corresponds to a place within such an apparatus in which one of the primary elements of the picture comes into existence.

4. #04

   The Interpretation of Dreams · Sigmund Freud

   **(F) THE UNCONSCIOUS AND CONSCIOUSNESS—REALITY**

   Theoretical move: Freud argues that the unconscious is the foundational stratum of all psychic life—larger than and prior to consciousness—and that it operates as two functionally distinct systems (Ucs. and Pcs.), thereby replacing a topographic/spatial model with a dynamic-energetic one while positioning consciousness as merely a sensory organ for psychic qualities rather than the seat of the psychic.

   We described the relations of the two systems to each other and to consciousness by saying that the system Prec. is like a screen between the system Unc. and consciousness.

5. #05

   Capitalism and Desire: The Psychic Cost of Free Markets · Todd McGowan · p.150

   A More Tolerable Infi nity

   Theoretical move: McGowan argues that Hegel's concept of the "true infinite" (self-limiting, circular) constitutes a more radical anticapitalist critique than Marx's, because it poses an internal limit that capitalism—structurally committed to the "bad infinite" of endless expansion—cannot subsume; this true infinite shares the structure of the psychoanalytic subject.

   The image of progression in infinity is the straight line; the infinite is only at the two limits of this line… As true infinite, bent back upon itself, its image becomes the circle.

6. #06

   Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache' · Derek Hook, Calum Neill & Stijn Vanheule (eds.) · p.36

   [The Freudian Thing, or the Meaning of the Return to Freud in Psychoanalysis](#ch05.xhtml_tocbook-part-003) > Interlude

   Theoretical move: Lacan's critique of ego psychology, prosecuted through a prosopopoeia of a talking lectern, demonstrates that the ego-psychological ego—conceived as an autonomous, synthetic function—collapses into an inert object indistinguishable from a piece of furniture, and that it is the Symbolic (speech/parole) alone, not ego-level consciousness or perception, that truly distinguishes the analysand's psyche from inanimate things.

   the ego-level sentient awareness appealed to by his philosophical enemies is, in fact, reducible to 'a topological phenomenon,' namely, the surface(s) of an asubjective spatial 'pure exteriority'

7. #07

   Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache' · Derek Hook, Calum Neill & Stijn Vanheule (eds.) · p.174

   [On a Question Prior to Any Possible Treatment of Psychosis](#ch05.xhtml_tocbook-part-007) > I. Toward Freud

   Theoretical move: The passage argues that psychotic hallucinations—both 'code phenomena' (autonomous neologisms) and 'message phenomena' (disrupted signifying chains)—are not symptomatic of an underlying illness but ARE the structure itself, revealing the subject's relationship to the signifier as mapped by the Graph of Desire; the subject is constituted as an effect of signifier-to-signifier reference, not of any neurological or imaginary substrate.

   In making use of topology Lacan isn't arguing for a parallel between these phenomena and specific patterns in brain functioning (452, 6). Instead, Lacan's graph aims at being consistent with the logic outlined by Freud concerning productions of the unconscious

8. #08

   Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache' · Derek Hook, Calum Neill & Stijn Vanheule (eds.)

   [The Direction of the Treatment and the Principles of its Power](#ch05.xhtml_tocbook-part-008) > II. What is the place of interpretation?

   Theoretical move: Lacan uses the Rat Man and Ernst Kris cases to demonstrate that correct analytic interpretation operates through the Symbolic frame (the signifier, the Other, the paternal function) rather than through ego-level defense analysis; the ego-analysts' surface-to-depth model systematically misses desire by subordinating it to drives and defenses, requiring instead a topology that locates desire at the level of speech and the signifier.

   a different topology is needed 'if we are not to be mistaken as to the place of desire'

9. #09

   Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache' · Derek Hook, Calum Neill & Stijn Vanheule (eds.) · p.257

   [Remarks on Daniel Lagache’s Presentation: “Psychoanalysis and Personality Structure”](#ch05.xhtml_tocbook-part-009) > I. Structure and the subject

   Theoretical move: Lacan's commentary on Lagache's paper argues that structure must be understood in strictly formal, linguistic-mathematical terms (not naturalistic or organismic ones), such that signifying structure is not an abstract beyond but actively functions in the real—shaping organisms, producing the barred subject, and establishing the priority of the Other's discourse over any putative being-in-itself of the child.

   we should learn to 'think in terms of a topology that is necessitated by structure alone' (544, 3).

10. #10

    Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache' · Derek Hook, Calum Neill & Stijn Vanheule (eds.) · p.271

    [Remarks on Daniel Lagache’s Presentation: “Psychoanalysis and Personality Structure”](#ch05.xhtml_tocbook-part-009) > II. Where is id?

    Theoretical move: Lacan argues that negation (Verneinung/Bejahung) is not a logical operation but a structural one grounded in the signifying chain: the "failed negation" of the French 'ne' exemplifies how repression and the return of the repressed are identical, and how the subject of desire emerges precisely from the space carved out between the statement and enunciation by this structural capacity for one signifier to replace another — making lack, not fusion or adaptation, the founding condition of both subject and objective reality.

    Here we are perhaps beginning to see what Lacan had in mind when he called for the creation of a new 'transcendental aesthetic' or a new topology for the subject.

11. #11

    Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache' · Derek Hook, Calum Neill & Stijn Vanheule (eds.)

    [Remarks on Daniel Lagache’s Presentation: “Psychoanalysis and Personality Structure”](#ch05.xhtml_tocbook-part-009) > Concluding remarks

    Theoretical move: The passage argues that negation—made possible only by linguistic/symbolic structure—is the central theoretical theme of Lacan's Lagache essay, functioning as the mechanism through which lack is introduced into the real and through which the subject of desire emerges.

    some more detailed topological explorations

12. #12

    Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache' · Derek Hook, Calum Neill & Stijn Vanheule (eds.)

    [Remarks on Daniel Lagache’s Presentation: “Psychoanalysis and Personality Structure”](#ch05.xhtml_tocbook-part-009) > III. On the ideals of the person

    Theoretical move: The passage argues that the ego functions as a structural misrecognition-faculty — a lens that distorts rather than corrects — and that the proper distinction between the ideal ego and ego-ideal (as well as the difference between Verwerfung/foreclosure and repression) requires a topological-optical model rather than behavioral observation, demonstrating how the symbolic and imaginary registers differently shape (intra)subjective structure.

    Lacan proposes a way to get at the proper structure and functions of the ego-ideal and ideal ego by using a model he developed in the first year of his seminar: one that is expressly about... 'the relations between the ideal ego and the ego-ideal'

13. #13

    Embracing the Void: Rethinking the Origin of the Sacred · Richard Boothby · p.80

    Rethinking Religion (or, What Is the Sacred?) > The Worship of Force

    Theoretical move: Boothby argues that archaic Greek religion—its temple architecture, ritual sacrifice, and pantheon—can be read through Lacan's framework as a structural apparatus for staging the Real: the temple encloses the void of the Thing, sacrifice reenacts the birth of the signifier (the "murder of the thing"), and the gods themselves are modes by which the Real is revealed, not simply screened.

    In both the vase and the temple, we have an envelope of stone that encloses a primal vacancy.

14. #14

    Enjoying What We Don't Have: The Political Project of Psychoanalysis · Todd McGowan · p.295

    I > Th e Case of the Missing Signifi er > Th e Feminine Signifi er Isn't

    Theoretical move: The passage argues that the "missing signifier" of the feminine is not an external absence to be filled but an internal torsion within the signifying structure itself; authentic psychoanalytic politics consists not in expanding inclusion but in male subjects identifying with this internal void, thereby revealing that the divide between male and female subjectivity is a division within the subject rather than between subjects.

    psychoanalytic thought off ers us a unique vision of this signifi er as nothing but an internal torsion within the signifying structure.

15. #15

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part29.xhtml_ncx_173"></span><span id="9781134780112_Part29.xhtml_page_0195"></span>***S*** > <span id="9781134780112_Part29.xhtml_ncx_194"></span>**Structure**

    Theoretical move: The passage systematically traces Lacan's evolving concept of 'structure' from early social/affective relations through Saussurean linguistics and structuralism to topology, while establishing Clinical Structures (neurosis, psychosis, perversion) as the definitive nosographic framework grounded in discrete subject-positions relative to the Other rather than collections of symptoms.

    By the 1970s, topology has replaced language as the principal paradigm of structure for Lacan. He now argues that topology is not a mere metaphor for structure; it is that structure itself.

16. #16

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part25.xhtml_ncx_134"></span><span id="9781134780112_Part25.xhtml_page_0151"></span>***O*** > <span id="9781134780112_Part25.xhtml_ncx_140"></span>**Order**

    Theoretical move: The passage establishes the RSI triad (Real, Symbolic, Imaginary) as Lacan's fundamental classification system for psychoanalytic theory, arguing that their profound heterogeneity is held together by structural interdependence, illustrated topologically through the Borromean Knot.

    Lacan explores this question of what the three orders have in common by means of the topology of the BORROMEAN KNOT in his 1974–5 seminar.

17. #17

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part25.xhtml_ncx_134"></span><span id="9781134780112_Part25.xhtml_page_0151"></span>***O*** > <span id="9781134780112_Part25.xhtml_ncx_139"></span>**Optical model**

    Theoretical move: The optical model serves as a provisional didactic apparatus that illustrates how the symbolic order structures the imaginary, and distinguishes the ideal ego (real image) from the ego-ideal (symbolic guide governing the mirror's angle), before Lacan replaces optical models with topology to escape imaginary capture.

    Lacan soon replaces optical images with topological figures which are intended to prevent imaginary capture (see TOPOLOGY).

18. #18

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part19.xhtml_ncx_87"></span><span id="9781134780112_Part19.xhtml_page_0105"></span>***I*** > <span id="9781134780112_Part19.xhtml_ncx_90"></span><span id="9781134780112_Part19.xhtml_page_0108"></span>**imaginary**

    Theoretical move: The Imaginary order is defined not as mere illusion but as a structurally necessary, symbolically conditioned register whose basis is the mirror-stage ego-formation; the passage argues that reducing psychoanalysis to the imaginary (identification with the analyst, dual relationship) betrays the symbolic essence of analytic work, and that the only therapeutic purchase on the imaginary comes through its translation into the symbolic.

    Lacan's use of topological figures, which cannot be represented in the imagination, to explore the structure of the unconscious (see TOPOLOGY)

19. #19

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part29.xhtml_ncx_173"></span><span id="9781134780112_Part29.xhtml_page_0195"></span>***S*** > <span id="9781134780112_Part29.xhtml_ncx_189"></span>***sinthome***

    Theoretical move: The passage traces the theoretical evolution from Lacan's linguistic conception of the symptom (as signifier/ciphered message) to the topological concept of the *sinthome* as an unanalysable kernel of jouissance that serves as a fourth Borromean ring binding RSI, with Joyce's writing as the exemplary case of *sinthome*-as-suppléance in the absence of the paternal function.

    The theoretical shift from linguistics to topology which marks the final period of Lacan's work constitutes the true status of the sinthome as unanalysable...Topological theory is not conceived of as merely another kind of representational account, but as a form of writing, a praxis aiming to figure that which escapes the imaginary.

20. #20

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part23.xhtml_ncx_113"></span><span id="9781134780112_Part23.xhtml_page_0132"></span>***M*** > <span id="9781134780112_Part23.xhtml_ncx_117"></span>**mathematics**

    Theoretical move: Lacan's turn to mathematics as a formalising tool for psychoanalysis is not an attempt to produce a metalanguage or escape linguistic ambiguity, but rather to generate multiple effects of sense while foreclosing imaginary intuitive understanding, positioning mathematics as the ideal of scientific discourse complementary to—not replacing—the linguistic approach to the Symbolic.

    The branches of mathematics which Lacan uses most are ALGEBRA and TOPOLOGY, although there are also incursions into set theory and number theory.

21. #21

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part15.xhtml_ncx_57"></span><span id="9781134780112_Part15.xhtml_page_0075"></span>***E*** > <span id="9781134780112_Part15.xhtml_ncx_65"></span><span id="9781134780112_Part15.xhtml_page_0083"></span>**extimacy**

    Theoretical move: Extimacy (extimité) is introduced as a Lacanian neologism that deconstructs the inside/outside opposition, showing that the Real, the unconscious, and the Other are structurally both interior and exterior to the subject, with this topology expressed paradigmatically in the Torus and Möbius Strip.

    The structure of extimacy is perfectly expressed in the topology of the TORUS and of the MOEBIUS STRIP.

22. #22

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part06.xhtml_ncx_5"></span><span id="9781134780112_Part06.xhtml_page_0010"></span>***Preface***

    Theoretical move: This preface to an introductory dictionary of Lacanian psychoanalysis establishes its methodological framework: Lacan's discourse constitutes a unique, topologically structured language whose terms are mutually defining, and the dictionary form—itself a synchronic, self-referential, metonymic system—is the appropriate vehicle for exploring it, while the preface also theorises the dangers of ignoring the diachronic evolution of Lacan's concepts.

    each term is sustained only in its topological relation with the others.

23. #23

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part26.xhtml_ncx_142"></span><span id="9781134780112_Part26.xhtml_page_0161"></span>***P*** > <span id="9781134780112_Part26.xhtml_ncx_160"></span>**psychosis**

    Theoretical move: The passage establishes the Lacanian theory of psychosis as a clinical structure defined by foreclosure of the Name-of-the-Father, producing a hole in the symbolic order and imprisoning the subject in the imaginary; it further articulates the later reformulation via the Borromean Knot and the role of the sinthome as a fourth ring.

    In the 1970s Lacan reformulates his approach to psychosis around the notion of the BORROMEAN KNOT. The three rings in the knot represent the three orders.

24. #24

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part29.xhtml_ncx_173"></span><span id="9781134780112_Part29.xhtml_page_0195"></span>***S*** > <span id="9781134780112_Part29.xhtml_ncx_174"></span>**sadism/masochism**

    Theoretical move: The passage makes two related theoretical moves: (1) it establishes Lacan's reversal of Freud's sadism/masochism hierarchy by grounding both in the invocatory drive, making masochism primary and sadism a disavowal of it; (2) it articulates the concept of 'scene' as the frame distinguishing acting out (remaining within the symbolic) from passage to the act (exit from the symbolic into the real via identification with objet petit a).

    Freud emphasised that this concept of locality is not to be confused with physical locality or anatomical locality, and Lacan takes this as a justification for his own use of TOPOLOGY.

25. #25

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part30.xhtml_ncx_202"></span><span id="9781134780112_Part30.xhtml_page_0231"></span>***T*** > <span id="9781134780112_Part30.xhtml_ncx_205"></span><span id="9781134780112_Part30.xhtml_page_0234"></span> **topology**

    Theoretical move: Topology is argued to be not merely a metaphor for structure but structure itself in Lacan's framework, privileging the function of the cut as a non-intuitive, purely intellectual means of expressing the symbolic order and distinguishing continuous from discontinuous transformations in psychoanalytic treatment.

    Lacan argues that topology is not simply a metaphorical way of expressing the concept of structure; it is structure itself (Lacan, 1973b).

26. #26

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part30.xhtml_ncx_202"></span><span id="9781134780112_Part30.xhtml_page_0231"></span>***T*** > <span id="9781134780112_Part30.xhtml_ncx_206"></span>**torus**

    Theoretical move: The torus, as a topological figure, is deployed by Lacan to illustrate two structural features of the subject: its decentred, ex-centric nature, and the collapse of the inside/outside distinction that grounds the concept of extimacy.

    The torus is one of the figures that Lacan analyses in his study of TOPOLOGY.

27. #27

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part23.xhtml_ncx_113"></span><span id="9781134780112_Part23.xhtml_page_0132"></span>***M*** > <span id="9781134780112_Part23.xhtml_ncx_125"></span>**moebius Strip**

    Theoretical move: The Möbius strip, as a topological figure, is deployed by Lacan to dissolve binary oppositions (inside/outside, signifier/signified, etc.) by demonstrating that apparently discrete terms are in fact continuous, and to model the possibility of traversing the fantasy without a localizable crossing point.

    The moebius strip is one of the figures studied by Lacan in his use of TOPOLOGY.

28. #28

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part30.xhtml_ncx_202"></span><span id="9781134780112_Part30.xhtml_page_0231"></span>***T*** > <span id="9781134780112_Part30.xhtml_ncx_207"></span><span id="9781134780112_Part30.xhtml_page_0236"></span>**training**

    Theoretical move: Lacan abolishes the IPA distinction between therapeutic and training analysis, arguing that all analyses are potentially training analyses, and that the formation of the analyst is an ongoing, subject-transforming process irreducible to institutional certification.

    Lacan's public seminar which is filled with incursions into philosophy, topology, logic, literature and linguistics—all of which Lacan regards as essential to the training of analysts.

29. #29

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part29.xhtml_ncx_173"></span><span id="9781134780112_Part29.xhtml_page_0195"></span>***S*** > <span id="9781134780112_Part29.xhtml_ncx_180"></span><span id="9781134780112_Part29.xhtml_page_0203"></span>**Seminar**

    Theoretical move: This passage is a bibliographic and historical entry on Lacan's Seminar, tracing its institutional history, the oral-to-written transmission problem, and providing a complete chronological index of all twenty-seven annual seminars — functioning as reference material rather than advancing a theoretical argument.

    XXVI | 1978-9 | Topology and time.

30. #30

    An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

    <span id="9781134780112_Part29.xhtml_ncx_173"></span><span id="9781134780112_Part29.xhtml_page_0195"></span>***S*** > <span id="9781134780112_Part29.xhtml_ncx_176"></span>**Schema L**

    Theoretical move: Schema L is Lacan's first and most sustained diagrammatic formalization of psychoanalytic structure, demonstrating that the symbolic relation between the Other and the subject is always partially blocked by the imaginary axis, while also representing the decentered subject stretched across four structural loci; it is positioned as the originary quaternary from which all subsequent schemata derive, and as the precursor to Lacan's mature topological work.

    The schemata can be seen as Lacan's first incursion into the field of TOPOLOGY.

31. #31

    Seminar I · Freud's Papers on Technique · Jacques Lacan · p.81

    **vn**

    Theoretical move: Lacan introduces the "inverted bouquet" optical apparatus as a model for understanding the articulation of the imaginary, symbolic, and real — arguing that the mirror stage requires supplementation by a structural optics that distinguishes real from virtual images, and that the juncture of symbolic and imaginary is constitutive of what we call "reality."

    Optical images possess a peculiar diversity - some of them are purely subjective, these are the ones we call virtual, whereas others are real, namely in some respects, behave like objects and can be taken for such.

32. #32

    Seminar I · Freud's Papers on Technique · Jacques Lacan · p.145

    **XI**

    Theoretical move: Lacan deploys the optical schema to articulate the structural difference between the Ideal Ego (Idealich) and the Ego-Ideal (Ichideal): the imaginary is regulated by the symbolic (governed by the voice/speech of the Other), and love/transference are theorised as perturbations of that symbolic regulation—love confusing the two registers, transference exploiting the same imaginary mechanism but within the analytic symbolic frame.

    Think of the mirror as a pane of glass. You'll see yourself in the glass and you'll see the objects beyond it. That's exactly how it is - it's a coincidence between certain images and the real.

33. #33

    Seminar I · Freud's Papers on Technique · Jacques Lacan · p.168

    **Xffl**

    Theoretical move: Lacan distinguishes méconnaissance (misrecognition) from simple ignorance by arguing that misrecognition presupposes a correlative knowledge behind it, and uses this distinction to pivot from ego-psychology's conception of the ego as a synthesising function toward a Lacanian account of the ego as fundamentally imaginary and constituted through the specular/linguistic relation to the other.

    That's why I've led you step by step to the optical schema we've started to construct here.

34. #34

    Seminar I · Freud's Papers on Technique · Jacques Lacan · p.272

    **XXI**

    Theoretical move: Lacan argues that language/speech introduces a "hole in the real" that opens the dimension of being, and it is only within this dimension—not the real itself—that the three orders (symbolic, imaginary, real) and the three fundamental passions of transference (love, hate, ignorance) can be inscribed; analysis is therefore the realisation of being through speech, not the reconstitution of a narcissistic image.

    There must be a minimal law in that, which geometry here only embodies, namely that, if, in the plane of the real, you detach a shutter which moves into a third dimension, the minimum number of shutters you need to construct something solid is two.

35. #35

    Seminar I · Freud's Papers on Technique · Jacques Lacan · p.143

    **XI**

    Theoretical move: Lacan uses the animal ethology of Gestalt-governed sexual behaviour (stickleback dance) as a contrast case to argue that in the human animal, the imaginary function is radically disordered — no image adequately releases sexual behaviour — which is precisely why the mirror apparatus (real image/spherical mirror schema) is needed to theorise how the ego-ideal operates at the joint of the imaginary and the symbolic, and how this bears on the question of the end of analysis.

    Let's get the little apparatus going, the one I have been showing you these last few sessions... the physical phenomenon of the real image, which can be produced by the spherical mirror

36. #36

    Seminar I · Freud's Papers on Technique · Jacques Lacan · p.154

    **xn**

    Theoretical move: Lacan uses the mirror-apparatus schema to articulate how the imaginary specular dialectic introduces the death drive as a structural (not merely biological) dimension of human libido, and then extends this via Freud's 'Metapsychological Supplement to the Theory of Dreams' to show how topographical and temporal regression correspond to shifts in the plane of reflection, with narcissism functioning as the libidinal complement of the egoism of the dream.

    this mode of functioning allows us to see what was always Freud's idea, namely the possible correlations between the notion of topographical regression and the regression he called zeitlich-Entwicklungsgeschichte

37. #37

    Seminar X · Anxiety · Jacques Lacan · p.249

    **x** > **THE MOUTH AND THE EYE**

    Theoretical move: Lacan develops a topological inversion between the anxiety-point and the point of desire across the oral and phallic/scopic levels: at the oral level anxiety is located at the Other (the mother's body) while desire is secured in the fantasy-relation to the partial object; at the phallic level this is strictly reversed, with orgasm itself functioning as the anxiety-point's homologue. The eye is then introduced as the new partial object (objet a) whose structure of mirage and exclusion from transcendental aesthetics anchors this topology.

    this is what we are permitted to structure in a more articulated fashion... You can see this here on the blackboard. Here is the level S of the subject, who, in our diagram of the vase reflected in the mirror of the Other

38. #38

    Seminar X · Anxiety · Jacques Lacan · p.105

    BookX Anxiety > *NOT WITHOUT HAVING IT*

    Theoretical move: Lacan advances a catalogue of partial objects (objet petit a) as pre-symbolic, non-shareable objects whose entry into the field of exchange signals anxiety, while simultaneously arguing that the partial object's synchronic function in transference has been systematically neglected — a neglect that explains Freud's limit at castration and the post-analytic failures in sexual function. Topological surfaces (cross-cap, Möbius strip) are then deployed to distinguish the specular (imaginary) object from objet petit a.

    Here then is the impact and the scope of these topological considerations… the problem has to be posed in the topological terms of pure surface.

39. #39

    Seminar X · Anxiety · Jacques Lacan · p.188

    **x** > **XIII APHORISMS ON LOVE**

    Theoretical move: Lacan advances a series of aphorisms on the love-desire-jouissance relation, arguing that anxiety mediates between desire and jouissance, that sadism and masochism are not reversible but constitute a fourfold structure each concealing the other's true aim, and that "only love allows jouissance to condescend to desire" — with castration functioning as the structural impasse that governs the encounter between the sexes.

    One passes from one to the other by rotating it 90 degrees, and not through any symmetry or inversion.

40. #40

    Seminar X · Anxiety · Jacques Lacan · p.65

    BookX Anxiety > **v** > **THAT WHICH DECEIVES**

    Theoretical move: Lacan argues that the dimension of the Other is structurally irreducible across all approaches to anxiety—experimental (Pavlov, Goldstein), philosophical, and analytic—and that the illusion of self-transparent consciousness (Selbstbewusstsein / Subject Supposed to Know) is precisely what blocks recognition of this, while the uncanny marks the point where specular identification fails and anxiety's structural void becomes legible.

    This topology will only have value if you can find the clues it gives you confirmed by whatever approach might have been taken to the phenomenon of anxiety, by any serious study, whatever its presuppositions may be.

41. #41

    Seminar X · Anxiety · Jacques Lacan · p.49

    BookX Anxiety > **FROM THE COSMOS TO THE** *UNHEIMLICHE*

    Theoretical move: By tracing Hamlet's two modes of identification—with the specular image i(a) and with the lost object a—Lacan distinguishes the imaginary register from a remainder that escapes specularization, using the cross-cap topology to show that minus-phi (the phallus as lack) and objet petit a share a status irreducible to the specular image, thereby framing anxiety as the privileged passageway between cosmism and the object of desire.

    I tried last year to articulate this for you with a figure borrowed from the ambiguous domain of topology, which planes the imaginary data right down and teases out a kind of trans-space

42. #42

    Seminar X · Anxiety · Jacques Lacan · p.245

    **x** > **THE MOUTH AND THE EYE**

    Theoretical move: Lacan argues that the oral drive must be re-examined to show that the anxiety-point (located at the level of the mother/Other) and the point of desire (located at the mamma as partial object) are structurally distinct and non-coincident, with the mamma functioning as an 'amboceptive' object internal to the child's own sphere — thereby reframing the castration complex not as a dead end but as misread through an oral reduction that only metaphorically displaces it.

    The cut is made between what is going to become the individual who will be cast into the outside world and his envelopes, which are parts of himself... The separation occurs within this unity, the unit of the egg.

43. #43

    Seminar X · Anxiety · Jacques Lacan · p.30

    BookX Anxiety > **ANXIETY, SIGN OF DESIRE**

    Theoretical move: Lacan argues that analytic teaching cannot rest on mere cataloguing or analogical methods, but must operate through a "function of the key" — the signifying function — grounded in the unary trait as the primordial signifier that precedes the subject and justifies any ideal of straightforwardness in teaching.

    The key is a thing which unlocks and which, in unlocking, functions. The key is the form according to which the signifying function as such operates or not.

44. #44

    Seminar X · Anxiety · Jacques Lacan · p.163

    **x** > **PUNCTUATIONS ON DESIRE**

    Theoretical move: Lacan argues that anxiety arises not from Hegelian mutual recognition (where the Other acknowledges or misrecognizes me) but from a temporal dimension in which the Other's desire puts my very Being in question by targeting me as the cause of desire (as *objet a*) rather than as its object — a structure that also defines the operative dimension of analytic transference.

    you have to start off from the experience of love... to situate the topology into which this transference can be inscribed.

45. #45

    Seminar X · Anxiety · Jacques Lacan · p.121

    BookX Anxiety > **VIII**

    Theoretical move: The passage argues that the *passage à l'acte* is constituted by the subject's absolute identification with *objet a* — her reduction to and ejection from the scene as that object — and that this structural logic, rather than tactlessness or countertransference, explains why Freud himself enacts a *dropping* (passage à l'acte in reverse) when he terminates the treatment of the young homosexual woman. The topology of *a* in the mirror of the Other is shown to illuminate both hypnosis and obsessional doubt as different modalities of the object's structural invisibility to the subject.

    Of course he hasn't got the elements of my topology at his disposal, but you can't put it more clearly

46. #46

    Seminar X · Anxiety · Jacques Lacan · p.142

    **x** > **ON A LACK THAT IS IRREDUCIBLE TO THE SIGNIFIER**

    Theoretical move: Lacan argues that anxiety points to a radical, irreducible lack that cannot be symbolized or compensated by the signifier; using topological figures (torus, cross-cap, Möbius strip) he demonstrates that this structural fault—prior to and constitutive of the signifier itself—cannot be filled by negation, cancellation, or symbolization, distinguishing it categorically from privation and absence.

    If I made you do so much topology last year, it was precisely to suggest that the function of the hole is not univocal.

47. #47

    Seminar X · Anxiety · Jacques Lacan · p.112

    BookX Anxiety > **VIII**

    Theoretical move: The passage reframes Objet petit a not as the intentional object *of* desire (in the phenomenological/Husserlian sense) but as the *cause* of desire that lies *behind* it, prior to any internalization; this reconfiguration is then used to distinguish the structural positions of sadism and masochism as different modes of identification with the object.

    The topological function that I have presented you with allows for a plain formulation of what needs to be introduced to clear up this enigma, namely, it is the notion of an outside that stands prior to a certain internalization.

48. #48

    Seminar X · Anxiety · Jacques Lacan · p.263

    **x** > **THE VOICE OF YAHWEH**

    Theoretical move: Lacan introduces the Voice as a new form of objet petit a — separated, not reducible to phonemic opposition — by way of the shofar, which he deploys to distinguish the vocal dimension from the scopic, and to show that while the mirror-stage/eye level produces a closed image with no remainder, the voice opens the question of the big Other's memory (and thus repetition) in a dimension irreducible to space and the specular.

    Where this separated object is inserted, to which domain it is to be attached not within the inside/outside contrast, whose inadequacy you get a clear inkling of here, but within the reference to the Other

49. #49

    Seminar X · Anxiety · Jacques Lacan · p.129

    BookX Anxiety > *PASSAGE* **A** *L'ACTE* **AND ACTING-OUT** > Second table of division

    Theoretical move: The passage distinguishes the *passage à l'acte* from acting-out by locating the former on the side of the maximally barred subject who falls off the stage of the Other into the world, while developing the pre-specular logic of objects *a* as remainder and their relation to anxiety, ideal ego constitution, and depersonalization in psychosis.

    what you might call, if you like, topological metaphors - but I think it takes things further in so far as they introduce the possibility of a nonspecularizable form in the structure of certain of these objects.

50. #50

    Seminar X · Anxiety · Jacques Lacan · p.131

    BookX Anxiety > *PASSAGE* **A** *L'ACTE* **AND ACTING-OUT** > Second table of division

    Theoretical move: Lacan articulates the structural distinction between acting-out and passage à l'acte by anchoring both to the object a and its cut-relation to the Other: acting-out is essentially a monstration (wild transference) that shows the a as cause of desire to the Other, while the symptom is self-sufficient jouissance that only requires interpretation through established transference. The originary cut is relocated from birth-separation to the embryonic envelopes, grounding a topological account of a as off-cut.

    you will see just how tangible is the analogy between what is detached from these envelopes with the cut of the embryo and the separation, on the cross-cap, of a certain enigmatic a

51. #51

    Seminar X · Anxiety · Jacques Lacan · p.107

    BookX Anxiety > *NOT WITHOUT HAVING IT*

    Theoretical move: By demonstrating that the cross-cap, once the Objet petit a is separated off, leaves a Möbius strip with no specular image, Lacan argues that the introduction of object a into the world of objects dissolves the stable specular image (ideal ego) and produces the uncanny double — topologically grounding the relation between a, the imaginary, and the Real.

    Add a in the form of a cross-cap. Then separate off, in this cross-cap, the small a object I've put in your hands. It remains, attached to i(a), a surface that joins up as does a Möbius strip.

52. #52

    Seminar X · Anxiety · Jacques Lacan · p.294

    **xx** > **XXI PIAGET'S TAP**

    Theoretical move: Lacan argues that the objet petit a functions not as the object of desire but as its *cause*, and that this causal function — first legible in the structure of obsessional neurosis — is the primordial "shadow" or metaphor from which the philosophical category of cause derives; grasping the a as cause of desire is what orients the analysis of transference beyond the circle of transference neurosis.

    In the topological shapes I drew up for you here last year… The topological dimension, whose symbolic handling transcends space, evoked for many of you a fair number of shapes that are presentified for us by the diagrams of the embryo's development.

53. #53

    Seminar X · Anxiety · Jacques Lacan · p.216

    **x** > **xv**

    Theoretical move: Lacan uses the topology of vessels (the pot of castration as minus-phi, the Klein bottle as the structure of objet a) to argue that anxiety arises not from castration itself but from the way the object a comes to half-fill the hollow of primordial castration via the desire of the Other; circumcision is then read as a ritual embodiment of this topological structure, instituting a normative relation between subject, objet a, and the big Other.

    All we have to do is make two opposite points on the rim of the vessel join up by turning the surfaces inside out as we go along, so that they join up as they do on the Mobius band, and we're looking at a vessel that allows us to pass with the greatest of ease from the inner face to the outer face without ever having to go over the rim.

54. #54

    Seminar X · Anxiety · Jacques Lacan · p.62

    BookX Anxiety > **BEYOND CASTRATION ANXIETY**

    Theoretical move: Lacan pivots the classical Freudian account of castration anxiety from anxiety-as-signal-of-lack to anxiety-as-presence-of-the-object, demonstrating through the neurotic/pervert contrast and the exhaustion of demand that it is not the absence but the imminence of the object that generates anxiety, and that castration only appears at the far limit of demand's regressive cycle.

    This has to be understood topologically. But not being able to push things much farther today...

55. #55

    Seminar X · Anxiety · Jacques Lacan · p.335

    **xx** > **ON A CIRCLE THAT IS IRREDUCIBLE TO A POINT**

    Theoretical move: The passage argues that the obsessional's desire is structurally circular and irreducible — sustained as impossible by circling through oral, anal, phallic, scopic, and vociferous registers without ever closing on itself — and that this topology (figured as a circle on a torus that cannot be contracted to a point) explains the obsessional's relation to symptom, acting-out, passage à l'acte, idealized love, and narcissistic image-maintenance.

    the circle of the obsessional's desire is precisely one of those circles that can never be reduced to a point owing to their topological place on the torus

56. #56

    Seminar X · Anxiety · Jacques Lacan · p.286

    **xx** > **WHAT COMES IN THROUGH THE EAR**

    Theoretical move: The passage argues that the voice, as object a, is not assimilated but incorporated (Einverleibung), functioning not as sonorous resonance in physical space but as what resonates ex nihilo in the void of the Other — thereby linking the voice-object to anxiety, the desire of the Other, and ultimately to sacrifice as the capture of the Other in the web of desire.

    something in the organic form strikes us as bearing a certain resemblance to those primary, trans-spatial, topological givens that led us to take an interest in the most elementary shape of the formation — which is both created and creative — of a void

57. #57

    Seminar X · Anxiety · Jacques Lacan · p.14

    BookX Anxiety > **ANXIETY IN THE NET OF SIGNIFIERS**

    Theoretical move: Lacan opens Seminar X by positioning anxiety as the nodal concept that will retroactively knot together the key terms of his previous disquisitions (fantasy, the Graph of Desire, the desire of the Other, the subject's relation to the signifier), insisting anxiety is not locatable at the centre of seriousness/care/expectation but rather escapes that encirclement — and distinguishing the Lacanian approach from existentialist (Kierkegaard, Heidegger, Sartre) treatments of anxiety.

    the little topological surface to which I devoted so much of last year, that of the cross-cap

58. #58

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.106

    THE LINE AND LIGHT

    Theoretical move: Lacan positions the eye as a privileged partial object among those central to analytic experience, grounding its theoretical significance in its evolutionary primacy and linking it to a triangular optical schema that structures the subject's relation to the visual field.

    Last time, I think I said enough to enable you to grasp the interest of this small, very simple triangular schema that I have reproduced at the top of the blackboard.

59. #59

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.110

    THE LINE AND LIGHT > THE LINE AND LIGHT

    Theoretical move: Through the anecdote of the sardine can, Lacan distinguishes the geometral point of geometric optics (the subject's viewpoint) from the point of light at which "everything that looks at me is situated," thereby introducing the Gaze as irreducible to the subject's own visual perspective—the subject is always already seen from a point it cannot master.

    What you have here is the first example of this functioning of interlacing, intersection, chiasma, which I pointed out above, and which structures the whole of this domain.

60. #60

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.211

    FROM LOVE TO THE LIBIDO > THE TRANSFERENCE AND THE DRIVE

    Theoretical move: Lacan argues that the drive, in its turning inside-out through the erogenous zone, always seeks something that responds in the Other; and he prepares to introduce the lamella-myth (via Aristophanes in Plato's Symposium) to articulate the drive's 'false organ' as the only graspable pole in the domain of sexuality.

    the drive, in this turning inside out represented by its pocket, invaginating through the erogenous zone

61. #61

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.120

    WHAT IS A PICTURE?

    Theoretical move: Lacan positions the gaze as the form taken by the objet a in the field of the visible, situating it at the intersection of two triangular schemas—one locating the geometral subject of representation and the other constituting the subject as picture—thereby grounding the scopic drive within the broader logic of the central lack of desire.

    I have drawn the two triangular systems that I have already introduced

62. #62

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.286

    IN YOU MORE THAN YOU > IN YOU MORE THAN YOU

    Theoretical move: Lacan uses the topological figure of a surface crossing itself (cross-cap/Möbius-type surface) to argue that the line of self-intersection symbolizes identification, and then critiques any conception of analysis that terminates in identification with the analyst as eliding the true motive force of analysis — insisting there is a "beyond" to identification.

    one must abstract oneself from three-dimensional space, since it is a question here only of a topological reality that is limited to the function of a surface.

63. #63

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.170

    SEXUALITY IN THE DEFILES OF THE SIGNIFIER > SEXUALITY

    Theoretical move: Lacan argues that hallucination is only possible through the sexualization of objects (not mere need-satisfaction), and that the reality/pleasure principle opposition is grounded in desexualization; furthermore, transference reveals the weight of sexual reality running beneath the discourse of demand, which he begins to map topologically via the interior 8 figure.

    I tried to draw on the blackboard the topology of the subject according to a sign that I once called the interior 8.

64. #64

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.259

    FROM INTERPRETATION TO THE TRANSFERENCE

    Theoretical move: Lacan draws a structural distinction between projection and introjection by assigning them to different orders — the symbolic and the imaginary respectively — arguing that the intuitive, unreflective use of psychoanalytic vocabulary (identification, idealization, projection, introjection) is the primary source of theoretical confusion, and that language itself has a fundamental topology that pre-orients the speaking subject.

    man is orientated in the fundamental topology of language, which is very different from the

65. #65

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.100

    THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > ANAMORPHOSIS

    Theoretical move: Lacan argues that the privilege of the Gaze is grounded in its structural entanglement with Desire, and uses anamorphosis as an exemplary topology to demonstrate how the domain of vision is integrated into the field of desire—with the Cartesian subject of objectivity displaced by a subject sustaining itself in desire.

    In my seminar, I have made great use of the function of anamorphosis, in so far as it is an exemplary structure.

66. #66

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.186

    THE DECONSTRUCTION OF THE DRIVE > THE DECONSTRUCTION OF THE DRIVE

    Theoretical move: Lacan formalizes the Drang (thrust) of the drive through a topological-mathematical analogy drawn from vector calculus and potential energy fields, arguing that the drive's constancy is defined not by physiological variation but by its relation to a rim-like structure (gap/béance) — what he calls the Quelle — which maintains a constant flux across any surface it subtends.

    crosses a certain surface—which is simply what I call the gap (béance), from the fact that it is defined by a rim-like structure—is, for the same surface, a constant.

67. #67

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.228

    THE SUBJECT AND THE OTHER: ALIENATION > ALIENATION

    Theoretical move: Lacan articulates the "lethal factor" within the alienating vel (freedom or death) as a Hegelian moment of Terror, then pivots to introduce the second operation—separation—grounded in set-theoretic intersection, which completes the subject's circular relation to the Other and opens the field of transference.

    It is situated precisely in that same lunula in which you find the form of the gap, the rim.

68. #68

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.179

    THE DECONSTRUCTION OF THE DRIVE > THE TRANSFERENCE AND THE DRIVE

    Theoretical move: Lacan distinguishes the Freudian drive (Trieb) from any biological need or organismic totality, grounding it instead in a topological surface field (the Real-Ich/nervous system) defined by constant force (konstante Kraft) rather than momentary impulse — a move that separates drive from need and opens the terrain of libidinal energy as potential energy.

    I am stressing the surface characteristics of this field by treating it topologically, and in trying to show you how taking it in the form of a surface responds to all the needs of its handling.

69. #69

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.101

    THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > OF THE GAZE

    Theoretical move: Lacan distinguishes between geometral (perspectival) vision—a point-by-point mapping of space reconstructible even by a blind man—and sight proper, arguing that the Cartesian subject coincides with the geometral point of perspective but that this correspondence does not capture what is genuinely at stake in the gaze.

    That which is of the mode of the image in the field of vision is therefore reducible to the simple schema that enables us to establish anamorphosis, that is to say, to the relation of an image, in so far as it is linked to a surface, with a certain point that we shall call the 'geometral' point.

70. #70

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.194

    THE PARTIAL DRIVE AND ITS CIRCUIT > THE PARTIAL DRIVE AND ITS CIRCUIT

    Theoretical move: The partial drive achieves satisfaction not by attaining a biologically defined reproductive aim but through the self-enclosed circuit of its own return to the erogenous zone; the distinction between 'aim' (way taken) and 'goal' (terminal end) is used to redefine drive satisfaction as the loop itself rather than any external terminus.

    a circuit formed by the curve of this rising and redescending arrow that crosses, Drang as it is in its origin, the surface constituted by what I defined last time as the rim

71. #71

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.171

    SEXUALITY IN THE DEFILES OF THE SIGNIFIER > THE TRANSFERENCE AND THE DRIVE

    Theoretical move: Lacan uses the topology of the cross-cap to redefine desire not as the overlap between the field of demand/unconscious and sexual reality, but as the void at their junction — a "line of desire" — and then pivots to argue that the operative desire in transference is ultimately the analyst's desire, grounding this through a re-reading of the Anna O. case that distinguishes the sign (symptom, something for someone) from the signifier (representing a subject for another signifier).

    This surface belongs to another whose topology I have described to my pupils at various times... This surface is a Möbius surface, and its outside continues its inside.

72. #72

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.97

    THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > OF THE GAZE

    Theoretical move: Lacan pivots from Merleau-Ponty's phenomenology of vision toward a psychoanalytic account of the gaze, arguing that the topology of consciousness (figured as the inside-out glove) reveals how the illusion of self-seeing is structurally undone by the gaze, and that psychoanalysis—by treating consciousness as irremediably limited—opens a new dimension irreducible to the philosophical tradition.

    the note concerning what he calls the turning inside-out of the finger of a glove … that consciousness, in its illusion of seeing itself seeing itself, finds its basis in the inside-out structure of the gaze.

73. #73

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.196

    THE PARTIAL DRIVE AND ITS CIRCUIT > THE PARTIAL DRIVE AND ITS CIRCUIT

    Theoretical move: Lacan articulates the partial drive as a headless subject whose circuit (modeled on Freud's Schub) returns around a rim-object, and argues that the topological unity between the gaps of the drive apparatus and the gaps of the signifying chain is what enables the drive to function within the unconscious—while carefully distinguishing drive structure from perversion.

    it is because of the topological unity of the gaps in play, that the drive assumes its role in the functioning of the unconscious.

74. #74

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.221

    THE SUBJECT AND THE OTHER: ALIENATION > THE FIELD OF THE OTHER

    Theoretical move: The passage argues that the drive's essential structure — its circular return to the subject rather than simple object-directedness — is irreducible to love or well-being, and that the subject's realization in the signifier depends on a constitutive gap in its relation to the Other, theorized topologically as the function of the rim.

    This structure is based on what I first called the function of the cut and which is now articulated, in the development of my discourse, as the topological function of the rim.

75. #75

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.104

    THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > QUESTIONS AND ANSWERS

    Theoretical move: Lacan insists that the gaze cannot be grounded in Sartrean reflexive consciousness but must be understood through the dialectic of desire, and that all terms in his discourse—subject, real, gaze—are defined only through their topological relations to one another, not in themselves.

    they are to be understood in their relation to one another, and that they have a topological definition—subject and real are to be situated on either side of the split.

76. #76

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.159

    ANALYSIS AND TRUTH OR THE CLOSURE OF THE UNCONSCIOUS > THE TRANSFERENCE AND THE DRIVE

    Theoretical move: Lacan reverses the traditional topology of the unconscious — from a closed interior reservoir (double sack) to an open structure (hoop net) — to argue that the subject is constituted in the space of the Other, such that the locus from which the subject sees, speaks, and desires is not interior but external, with the unconscious closing through an obturating effect rather than being an innate enclosure.

    I therefore reverse the topology of the traditional imagery by presenting to you the following schema.

77. #77

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.109

    THE LINE AND LIGHT > OF THE GAZE

    Theoretical move: Lacan displaces the classical philosophical dialectic of appearance/being—grounded in geometral, rectilinear vision—by relocating the essence of the visual relation in the point of irradiation and the play of light, thereby preparing a model of the gaze as an irreducibly ambiguous, non-geometral relation between subject and light.

    owing to the rupture of space that underlies our very perception, what makes us perceive it as a cube

78. #78

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.121

    WHAT IS A PICTURE? > OF THE GAZE

    Theoretical move: Lacan displaces the philosophical problem of representation (surface/phenomenon vs. beyond/noumenon) by locating the gaze as an external instrument that constitutes the subject in the visible field, producing a foundational splitting of being rather than a Kantian epistemological limit.

    The two triangles are here superimposed, as in fact they are in the functioning of the scopic register.

79. #79

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.111

    THE LINE AND LIGHT > OF THE GAZE

    Theoretical move: Lacan argues that the subject is not the sovereign geometral point of perspective but is itself caught in the gaze—light looks at me, the picture is painted *in* my eye yet I am not *in* the picture—introducing the screen as the opaque mediation between picture and gaze that undoes mastery and replaces geometral space with an ambiguous, irrecuperable depth of field.

    something of another nature than geometral, optical space, something that plays an exactly reverse role

80. #80

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.250

    OF THE SUBJECT WHO IS SUPPOSED TO KNOW, OF THE FIRST DYAD, AND OF THE GOOD > OF THE SUBJECT WHO IS SUPPOSED TO KNOW

    Theoretical move: Lacan argues that desire and "not wanting to desire" are structurally identical (like a Möbius strip), and that this paradox is precisely the site where the analyst's desire functions as the essential pivot through which the subject's desire—constituted as desire of the Other—is both approached and indefinitely deferred in its recognition, rendering aphanisis an irreducible obstacle rather than a resolvable impasse.

    I will illustrate it for you next time with a small topological drawing that has already been on the blackboard

81. #81

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.218

    THE SUBJECT AND THE OTHER: ALIENATION

    Theoretical move: Lacan defends the structural (linguistic) account of the unconscious against charges of neglecting sexual dynamics, by re-articulating those dynamics through the topology of the subject/Other division and the partiality of the drive, thereby integrating libidinal force into a structuralist framework rather than opposing it.

    From this I have deduced a topology intended to account for the constitution of the subject.

82. #82

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.37

    THE FREUDIAN UNCONSCIOUS AND OURS > THE UNCONSCIOUS AND REPETITION

    Theoretical move: Lacan distinguishes 'cause' from deterministic law by locating cause precisely where a chain breaks down—where there is a gap, something that "doesn't work"—and argues that the Freudian unconscious is situated at exactly this point: the gap between cause and effect through which neurosis reaches a harmony with a Real that may itself be undetermined.

    I am not handling this topology very skilfully, because I do not have time—I have simply jumped into the deep end.

83. #83

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.185

    THE DECONSTRUCTION OF THE DRIVE > QUESTIONS AND ANSWERS

    Theoretical move: Lacan defers but acknowledges the economic point of view (energetics, constant force vs. variation) as a valid theoretical concern for understanding the drive, hinting that a reference to energetics in a limited system — where each point is characterized in terms of potential energy — will illuminate the discontinuous combinatory structure of the drive.

    In a limited system, there is a certain way of inscribing each defined point, as characterized in terms of potential energy

84. #84

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.176

    THE DECONSTRUCTION OF THE DRIVE

    Theoretical move: Lacan frames the drive (Trieb) as the fourth fundamental concept of psychoanalysis, insisting that Freud's specific use of the term constituted a radical conceptual break that is obscured by the term's prior history in psychology, physiology, and physics — a concealment that allows misreadings to invoke drive against Lacan's own doctrine of the unconscious.

    This topology is intended to give you some notion of the location of the point of disjuncture and conjuncture, of union and frontier, that can be occupied only by the desire of the analyst.

85. #85

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.197

    THE PARTIAL DRIVE AND ITS CIRCUIT > THE TRANSFERENCE AND THE DRIVE

    Theoretical move: In perversion, and specifically voyeurism, the subject is not absent but rather precisely placed within the drive's circuit: the object of the scopic drive (the gaze) is the lost object refound through the introduction of the Other, and what is sought is not the phallus but its absence — making absence itself the constitutive object of the scopic drive's aim.

    this is what my topology on the blackboard cannot show you, but can allow you to admit—the loop turns around itself; it is a missile

86. #86

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.108

    THE LINE AND LIGHT > THE LINE AND LIGHT

    Theoretical move: Lacan uses the figure of the blind man navigating geometral space by thread alone to argue that the geometral-optical structuring of space—reducible to homological point-to-point correspondences—does not capture what light itself provides, thereby marking the insufficiency of geometral optics for a theory of vision and setting up the need for another dimension beyond linear perspective.

    all that is needed is a stretched thread. This is why the blind man would be able to follow all our demonstrations

87. #87

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.60

    OF THE NETWORK OF SIGNIFIERS > OF THE NETWORK OF SIGNIFIERS

    Theoretical move: Lacan maps the subject of the unconscious onto Freud's optical/topographical schema (from the letter to Fliess and the seventh chapter of The Interpretation of Dreams), arguing that the network of signifiers—not chance—is what constitutes the subject, and that the place of the Other is situated in the interval between perception and consciousness.

    And how is a network mapped? One goes back and forth over one's ground, one crosses one's path

88. #88

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.199

    THE PARTIAL DRIVE AND ITS CIRCUIT > QUESTIONS AND ANSWERS

    Theoretical move: Lacan articulates the object of the drive as a "headless subjectification" — a structure without a subject — and links this topological formulation to the Freudian account of how repression of libido under the pleasure principle paradoxically enables the very development of the mental apparatus, including the capacity for attention (Aufmerksamkeit).

    a bone, a structure, an outline, which represents one side of the topology. The other side is that which is responsible for the fact that a subject, through his relations with the signifier, is a subject-with-holes (sujet troué).

89. #89

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.105

    THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > OF THE GAZE

    Theoretical move: Lacan distinguishes topology as a proper mapping of analytic experience (not merely a metaphor or expository device), and reaffirms that the gaze is not reducible to the eye, using Holbein's anamorphosis as the exemplary case where the gaze appears in a de-subjectivized, uncanny form.

    It is the mapping of the topology proper to our experience as analysts, which may later be taken in a metaphysical perspective.

90. #90

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.103

    THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > OF THE GAZE

    Theoretical move: Through the analysis of Holbein's anamorphic skull in *The Ambassadors*, Lacan argues that the geometral dimension of the gaze is not vision as such but a partial field that renders visible the subject's annihilation and the phallic function of lack—the gaze thus operates as the site where the subject is undone rather than constituted.

    that strange, suspended, oblique object in the foreground... from some angles appears to be flying through the air, at others to be tilted

91. #91

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.163

    ANALYSIS AND TRUTH OR THE CLOSURE OF THE UNCONSCIOUS > THE TRANSFERENCE AND THE DRIVE

    Theoretical move: Lacan differentiates his schema from Freud's ego-as-lens model by insisting that what is at stake in his own topology is not the ego (i(a)) but the objet petit a itself, marking a structural divergence between ego-centred and desire/drive-centred frameworks.

    you can see the difference—if I had wanted to put the ego somewhere, I would have written i(a). Whereas for me, here, it is the a that is in question.

92. #92

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.285

    IN YOU MORE THAN YOU > TO CONCLUDE

    Theoretical move: The analyst must maintain a precise distance between the point where the subject sees himself as lovable and the point where objet petit a causes the subject as lack; this gap, which the petit a never crosses, is what makes transference operable and can be topologized as an internal eight (cross-cap) surface.

    the function of the transference may be topologized in the form that I have already produced in my seminar on Identification—namely, the form that I have called on occasion the internal eight

93. #93

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.146

    PRESENCE OF THE ANALYST > PRESENCE OF THE ANALYST

    Theoretical move: Lacan argues that transference is a moment of closure against the unconscious, and that the analyst's interpretive intervention must be directed at the split subject itself (the "beauty behind the shutters") rather than a presumed healthy ego-part; this reframes transference as a topological knot requiring topology to adequately conceptualize it.

    this is why we must treat it as what it is, namely, a knot… It is a knot, and it prompts us to account for it—as I have been doing for several years—by considerations of topology.

94. #94

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.260

    FROM INTERPRETATION TO THE TRANSFERENCE > FROM INTERPRETATION TO THE TRANSFERENCE

    Theoretical move: Lacan maps Freud's ego-topology onto a schema of Lust/Unlust fields, arguing that what resists homeostasis is inscribed in the ego as non-ego (fremde Objekt), thereby grounding psychoanalytic clinical tact in an implicit topology of subject and real rather than in naïve scientific realism.

    they are referring when using each of the terms I have just listed...they frequently make adequate use of them, with the same spontaneity as the ordinary man uses ordinary speech...harmonize them with the evidence of a topology that I have already introduced here

95. #95

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.272

    FROM INTERPRETATION TO THE TRANSFERENCE > FROM INTERPRETATION TO THE TRANSFERENCE

    Theoretical move: Lacan distinguishes two forms of identification operative in transference — one anchored in the ego ideal (narcissistic, specular) and one introduced by separation and centred on the objet a as topological object — and argues that it is the signifier's entry into human life that makes sex capable of bringing death into presence, collapsing the life/death drive distinction into a single articulation at the level of the unconscious signification of sex.

    that object whose very reality is purely topological, of that object around which the drive moves, of that object that rises in a bump, like the wooden darning egg in the material which, in analysis, you are darning

96. #96

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.89

    THE SPLIT BETWEEN THE EYE AND THE GAZE > OF THE GAZE

    Theoretical move: Lacan introduces the concept of "the stain" as the pre-subjective, autonomous function of the gaze that pre-exists and governs vision, arguing that this function always escapes the reflective self-sufficiency of consciousness (the "seeing oneself seeing oneself"), and that narcissism's imaginary satisfaction is precisely what occludes this irreducible gaze-function within the scopic field.

    This much we can map of this topology, which last time we worked out for ourselves on the basis of that which appears from the position of the subject when he accedes to the imaginary forms offered him by the dream

97. #97

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.224

    THE SUBJECT AND THE OTHER: ALIENATION > ALIENATION

    Theoretical move: Lacan introduces the losange (◇) as a topological algorithm that supports the two operations of alienation and separation, showing it functions as a "rim" that articulates the subject's relation to the Other in both the fantasy matheme ($◇a) and the demand/drive node ($◇D), grounding subjectivity in the dependence on the signifier.

    there is no topology that does not have to be supported by some artifice—it is precisely the result of the fact that the subject depends on the signifier

98. #98

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.162

    ANALYSIS AND TRUTH OR THE CLOSURE OF THE UNCONSCIOUS > ANALYSIS AND TRUTH

    Theoretical move: The passage advances the claim that topological thinking—specifically the notion of surfaces that are simultaneously inside and outside—is uniquely necessary for conceptualizing the unconscious, and introduces the object as an 'obturator' (a partial, not merely passive, blocking function) as the key to understanding transference at the correct level.

    In everything concerning topology one must always be very careful to avoid attributing it with any kind of Gestalt function.

99. #99

    Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.120

    WHAT IS A PICTURE?

    Theoretical move: Lacan identifies the gaze as the specific form taken by objet petit a in the scopic field, establishing it as the object that symbolizes the central lack of desire, and introduces the two-triangle schema to show how the geometral subject is turned into a picture—subordinating geometral representation to the scopic drive.

    I have drawn the two triangular systems that I have already introduced

100. #100

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.121

     WHAT IS A PICTURE? > OF THE GAZE

     Theoretical move: In the scopic field, the subject is constituted not as a knowing consciousness but as a picture under an exterior gaze; Lacan displaces the Kantian problem of representation by grounding subjectivity in a primordial splitting imposed by the gaze, not in the subject's transcendental categories.

     The two triangles are here superimposed, as in fact they are in the functioning of the scopic register.

101. #101

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.37

     THE FREUDIAN UNCONSCIOUS AND OURS > THE UNCONSCIOUS AND REPETITION

     Theoretical move: Lacan distinguishes cause from deterministic law by arguing that cause is always marked by a gap or indefiniteness, and it is precisely at this gap—where cause does not fully determine its effect—that the Freudian unconscious is situated; the unconscious is not what mechanically produces neurosis but what reveals the gap through which neurosis reaches toward a non-determined real.

     I am not handling this topology very skilfully, because I do not have time—I have simply jumped into the deep end

102. #102

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.49

     OF THE SUBJECT OF CERTAINTY > THE UNCONSCIOUS AND REPETITION

     Theoretical move: Lacan argues that the status of the unconscious is ethical rather than ontic, using Freud's placement of the 'burning child' dream to show that the unconscious opens onto a beyond—a reality that exceeds the pleasure principle—and links this to the Name-of-the-Father as the structure that couples desire with the law through inherited sin (Hamlet/Oedipus).

     that which we see emerging at other points designated by the Freudian topology

103. #103

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.60

     OF THE NETWORK OF SIGNIFIERS > OF THE NETWORK OF SIGNIFIERS

     Theoretical move: The passage uses Freud's optical model (from Letter 52 to Fliess and The Interpretation of Dreams) to argue that the subject of the unconscious is constituted in the interval between perception and consciousness—the locus of the Other—and that mapping the signifying network (rather than spatial anatomy) is the only method of knowing the subject's existence.

     And how is a network mapped? One goes back and forth over one's ground, one crosses one's path... it is crosschecked in such a way that it escapes chance.

104. #104

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.89

     THE SPLIT BETWEEN THE EYE AND THE GAZE > OF THE GAZE

     Theoretical move: The passage introduces the concept of "the stain" as that which pre-exists the seen and identifies it with the gaze as a function that necessarily escapes the self-reflexive grasp of consciousness, thereby exposing the insufficiency of any account of vision grounded in imaginary self-satisfaction or narcissism.

     This much we can map of this topology, which last time we worked out for ourselves on the basis of that which appears from the position of the subject when he accedes to the imaginary forms offered him by the dream

105. #105

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.97

     THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > OF THE GAZE

     Theoretical move: The passage pivots from Merleau-Ponty's phenomenology of vision toward a psychoanalytic reframing: the gaze is not grounded in a self-seeing consciousness but in a structural inversion (the glove turned inside-out) that exposes consciousness as irremediably limited—setting up the Lacanian displacement of the visual field from the subject to the object.

     the note concerning what he calls the turning inside-out of the finger of a glove … consciousness, in its illusion of seeing itself seeing itself, finds its basis in the inside-out structure of the gaze

106. #106

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.100

     THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > ANAMORPHOSIS

     Theoretical move: Lacan argues that the gaze is privileged within the field of desire, and uses anamorphosis as a structural exemplar to show how the geometral/flat dimension of optics—inaugurated alongside Cartesian subjectivity—reveals the way vision is integrated into desire by distorting and then restoring the image depending on the subject's position.

     What does a simple, non-cylindrical anamorphosis consist of? Suppose there is a portrait on this flat piece of paper... you would obtain a figure enlarged and distorted according to the lines of what may be called a perspective.

107. #107

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.101

     THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > OF THE GAZE

     Theoretical move: Lacan distinguishes the geometral (point-by-point optical correspondence that grounds perspective and the Cartesian subject) from vision/sight proper, arguing that geometral space is reconstructible by a blind man and therefore does not capture what is genuinely at stake in the scopic field — thus opening the gap between the eye and the gaze.

     that which is of the mode of the image in the field of vision is therefore reducible to the simple schema that enables us to establish anamorphosis, that is to say, to the relation of an image, in so far as it is linked to a surface, with a certain point that we shall call the 'geometral' point.

108. #108

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.103

     THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > OF THE GAZE

     Theoretical move: Through a reading of Holbein's anamorphic skull in *The Ambassadors*, Lacan argues that the geometral dimension of the gaze—irreducible to vision—functions as a symbolic appearance of the phallic ghost and the lack, and that anamorphosis makes visible the subject's own annihilation, the death drive inscribed at the heart of the scopic field.

     from some angles appears to be flying through the air, at others to be tilted

109. #109

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.104

     THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > QUESTIONS AND ANSWERS

     Theoretical move: Lacan insists that the gaze is not grounded in the reflexive consciousness of the Sartrean other but in the dialectic of desire, and that his key terms (subject, real, gaze) have no intrinsic content but acquire meaning only through their topological relations to one another — with subject and real situated on either side of the split held open by fantasy.

     they are to be understood in their relation to one another, and that they have a topological definition — subject and real are to be situated on either side of the split

110. #110

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.105

     THE SPLIT BETWEEN THE EYE AND THE GAZE > ANAMORPHOSIS > OF THE GAZE

     Theoretical move: Lacan clarifies that topology is not merely expository but maps the proper structure of analytic experience, and distinguishes the gaze from the eye by invoking Holbein's anamorphosis as the exemplary case where the gaze confronts the subject with its own uncanny image.

     It is the mapping of the topology proper to our experience as analysts, which may later be taken in a metaphysical perspective.

111. #111

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.106

     THE LINE AND LIGHT

     Theoretical move: Lacan situates the eye as a privileged partial object among those central to psychoanalytic experience, tracing its appearance back to the earliest forms of life, and introduces a triangular optical schema to frame the relation between subject, organ, and the gaze.

     this small, very simple triangular schema that I have reproduced at the top of the blackboard

112. #112

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.107

     THE LINE AND LIGHT > OF THE GAZE

     Theoretical move: The passage argues that anamorphosis—exemplified by Holbein's skull—reveals how the geometral dimension of vision operates not as realistic reproduction but as a trap that captures the subject, disclosing an enigmatic relation between the gaze, desire, and the subject's own nothingness (death).

     The little schema also allows me to remark that certain optics allow that which concerns vision to escape.

113. #113

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.108

     THE LINE AND LIGHT > THE LINE AND LIGHT

     Theoretical move: Lacan uses the geometral/optical model to argue that light, despite appearing to be the ground of vision, is not what the geometral thread actually depends on—the thread precedes light, meaning the visible cannot be reduced to geometry alone, and vision's structure remains fundamentally labyrinthine and elusive.

     There is not a single one of the divisions, a single one of the double sides that the function of vision presents, that is not manifested to us as a labyrinth. As we begin to distinguish its various fields, we always perceive more and more the extent to which they intersect.

114. #114

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.109

     THE LINE AND LIGHT > OF THE GAZE

     Theoretical move: Lacan displaces the classical philosophical treatment of perception—which operates on geometral, rectilinear vision—by insisting that the essence of the gaze lies not in the straight line but in the point of light, irradiation, and refraction, thereby exposing the ambiguity of the subject's relation to light that underpins his two-triangle schema of the gaze.

     Indeed, you see this on the schema of the two triangles

115. #115

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.113

     THE LINE AND LIGHT > OF THE GAZE

     Theoretical move: Lacan uses the phenomena of mimicry to introduce the subject as "stain" in the visual field, arguing that the subject cannot be adequately grounded in an "absolute overview" (as rationalist-teleological accounts require), and that mimicry—exceeding mere adaptation—opens onto the properly phenomenal dimension where the subject's relation to the Gaze can be theorized.

     We are here in space panes extra parks [partes extra partes], which always provides such an objection to the apprehension to the object.

116. #116

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.123

     WHAT IS A PICTURE? > OF THE GAZE

     Theoretical move: Lacan argues that the picture's central field is structurally absent—replaced by a hole that reflects the pupil/gaze—such that the subject of the geometral plane is elided before the picture; this is why the picture does not operate in the register of representation but rather in the field of desire.

     rediscovering in the picture what is, strictly speaking, composition, the lines dividing the surfaces created by the painter, vanishing traces, lines of force, frames (bâtis) in which the image finds its status

117. #117

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.146

     PRESENCE OF THE ANALYST > PRESENCE OF THE ANALYST

     Theoretical move: The passage argues that the transference is not a moment of ego-alliance but a moment of closure against the unconscious, and that interpretation must address the split subject directly through this closure — reconceiving transference as a topological knot rather than a therapeutic lever on a "healthy part" of the subject.

     we must treat it as what it is, namely, a knot… It is a knot, and it prompts us to account for it—as I have been doing for several years—by considerations of topology.

118. #118

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.159

     ANALYSIS AND TRUTH OR THE CLOSURE OF THE UNCONSCIOUS > THE TRANSFERENCE AND THE DRIVE

     Theoretical move: By replacing the traditional imagery of the unconscious as a closed inner reservoir (the double sack) with a topological figure of the hoop net, Lacan reframes the unconscious as constituted through its opening/orifice and its relation to the Other, arguing that the subject constitutes itself—sees itself, speaks, and forms desire—from the locus of the Other rather than from an interior self-image.

     I therefore reverse the topology of the traditional imagery by presenting to you the following schema.

119. #119

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.162

     ANALYSIS AND TRUTH OR THE CLOSURE OF THE UNCONSCIOUS > ANALYSIS AND TRUTH

     Theoretical move: Lacan advances the topology of the unconscious by arguing that it is structurally inside the subject yet can only be realized outside, in the locus of the Other, and introduces the object as an "obturator" to figure this inside/outside structure—pointing toward the eye as a coming illustration of this topological object.

     In everything concerning topology one must always be very careful to avoid attributing it with any kind of Gestalt function.

120. #120

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.170

     SEXUALITY IN THE DEFILES OF THE SIGNIFIER > SEXUALITY

     Theoretical move: Lacan argues that hallucination is possible only through the sexualization of objects, not through a simple re-presentation of need; reality is defined as desexualized in Freud's two principles, and transference restores the weight of sexual reality beneath the discourse of demand. This is mapped topologically via the "interior 8" figure placing libido at the junction of its lobes.

     I tried to draw on the blackboard the topology of the subject according to a sign that I once called the interior 8.

121. #121

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.171

     SEXUALITY IN THE DEFILES OF THE SIGNIFIER > THE TRANSFERENCE AND THE DRIVE

     Theoretical move: By deploying the cross-cap topology, Lacan argues that the apparent overlap between the field of the unconscious and sexual reality is not an intersection but a void, and that desire names the line of junction between demand and sexuality—a topology that reframes transference not around the patient's desire but around the desire of the analyst. The passage also uses the Breuer/Anna O. case to sharpen the distinction between sign (symptom, body, sexuality) and signifier (representing a subject for another signifier).

     This surface is a Mcthius surface, and its outside continues its inside. There is a second necessity that emerges from this figure, that is, that it must, in order to close its curve, traverse at some point the preceding surface

122. #122

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.174

     SEXUALITY IN THE DEFILES OF THE SIGNIFIER > SEXUALITY

     Theoretical move: Lacan uses a critical review of early analysts' (Abraham, Ferenczi, Nunberg) countertransferential positions to pivot toward a topological account of how the subject accommodates its image around the objet petit a via a mirror-shutter mechanism, illustrating how desire structures the analytic field rather than the analyst's psychology.

     In order to conjugate the schema of the net with those I have made in response to a psychologizing theory of the psychoanalytic personality, you have only to turn the obturator I referred to earlier into a camera shutter, except that it would be a mirror.

123. #123

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.176

     THE DECONSTRUCTION OF THE DRIVE

     Theoretical move: Lacan introduces the Drive as the fourth fundamental concept of psychoanalysis, arguing that Freud's specific use of 'Trieb' is so novel that it conceals its prior history, and that misappropriations of the term (even against Lacan's own doctrine) stem from treating it as a mere 'radical given' rather than a rigorously theorized concept.

     This topology is intended to give you some notion of the location of the point of disjuncture and conjuncture, of union and frontier, that can be occupied only by the desire of the analyst.

124. #124

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.179

     THE DECONSTRUCTION OF THE DRIVE > THE TRANSFERENCE AND THE DRIVE

     Theoretical move: Lacan argues that Freud's Trieb (drive) is categorically distinct from biological need (hunger, thirst) and from momentary impulse-force; it is a constant force (konstante Kraft) operating on a topological surface field anchored in the nervous system (Real-Ich), not in the organism as a whole—a move that separates the drive from any naturalistic or organismic reading.

     I am stressing the surface characteristics of this field by treating it topologically, and in trying to show you how taking it in the form of a surface responds to all the needs of its handling.

125. #125

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.184

     THE DECONSTRUCTION OF THE DRIVE > THE DECONSTRUCTION OF THE DRIVE

     Theoretical move: Lacan argues that the drive is not a natural instinct oriented toward a biological end but a "montage" in the surrealist sense—a heterogeneous, reversible assemblage of Drang, object, aim, and source, whose very paradoxicality distinguishes it structurally from instinct.

     only in those points that are differentiated for us by their rimlike structure

126. #126

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.186

     THE DECONSTRUCTION OF THE DRIVE > THE DECONSTRUCTION OF THE DRIVE

     Theoretical move: Lacan uses the mathematical concept of flux (from vector calculus and potential energy) to argue that the Drang (thrust) of the drive is characterized by a constant maintained across variable rim-like structures — the gap/béance — thereby grounding the drive's constancy topologically rather than physiologically.

     crosses a certain surface—which is simply what I call the gap (béance), from the fact that it is defined by a rim-like structure

127. #127

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.194

     THE PARTIAL DRIVE AND ITS CIRCUIT > THE PARTIAL DRIVE AND ITS CIRCUIT

     Theoretical move: The passage argues that the partial drive's satisfaction consists not in reaching a biological end-goal (reproduction) but in the circular itinerary of the drive itself — the loop that departs from and returns to the erogenous rim — distinguishing 'aim' as path/circuit from 'goal' as terminal end-point, and grounding this in Freud's auto-erotic metaphor of the self-kissing mouth.

     a circuit formed by the curve of this rising and redescending arrow that crosses, Drang as it is in its origin, the surface constituted by what I defined last time as the rim

128. #128

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.196

     THE PARTIAL DRIVE AND ITS CIRCUIT > THE PARTIAL DRIVE AND ITS CIRCUIT

     Theoretical move: The passage argues that the drive's structure is topologically homologous to the structure of the unconscious: both are organised around a rim/gap that the drive must circumnavigate, with the object (objet petit a) serving as the sole guarantor of consistency, and this shared topology is what allows the drive to function within the unconscious—while insisting that the drive itself is not perversion.

     the drive assumes its role in the functioning of the unconscious... it is because of the topological unity of the gaps in play

129. #129

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.197

     THE PARTIAL DRIVE AND ITS CIRCUIT > THE TRANSFERENCE AND THE DRIVE

     Theoretical move: In perversion, and specifically voyeurism, the scopic drive's circuit completes itself not by seeing the phallus but by encountering its absence; the gaze functions as the lost object that is refound through shame when the Other intervenes, making the object-cause of desire constitutively the absence of the phallus rather than its presence.

     this is what my topology on the blackboard cannot show you, but can allow you to admit—the loop turns around itself

130. #130

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.199

     THE PARTIAL DRIVE AND ITS CIRCUIT > QUESTIONS AND ANSWERS

     Theoretical move: The passage argues that the object of the drive must be understood topologically as a "headless subjectification" distinct from both the subject-with-holes constituted by the signifier and the objects of fantasy and desire, while also linking the repression of libido under the pleasure principle to the very development of the mental apparatus (including attention/Aufmerksamkeit).

     a bone, a structure, an outline, which represents one side of the topology. The other side is that which is responsible for the fact that a subject, through his relations with the signifier, is a subject-with-holes (sujet troué).

131. #131

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.202

     FROM LOVE TO THE LIBIDO

     Theoretical move: Lacan redefines the libido not as a fluid or diffuse energy but as an organ—both a bodily part and an instrument—thereby shifting the conceptual ground from energetics to topology, and uses an analogy (the bladder rather than Plato's cave) to reframe the unconscious away from depth-metaphors.

     The unconscious is much more like the bladder

132. #132

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.205

     FROM LOVE TO THE LIBIDO > THE TRANSFERENCE AND THE DRIVE

     Theoretical move: Lacan critiques the ego-psychological reading of Freud's "Real-Ich" and autoerotism by showing that the infant is never indifferent to its perceptual field, thereby distinguishing the structure of love (tied to the gesamt Ich and the pleasure principle as a homeostatic surface) from the structure of the drive.

     The filtering from stimulation to discharge is the apparatus, the dome, to be circumscribed on a sphere, in which is defined at first what he calls the stage of the Real-Ich.

133. #133

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.218

     THE SUBJECT AND THE OTHER: ALIENATION

     Theoretical move: Lacan defends his structural approach against charges of neglecting sexual dynamics by arguing that the topology of subject/Other division already accounts for drive dynamics, with the partial drive situated on the side of the living being called to subjectivity — thereby integrating sexuality into a structuralist framework rather than opposing the two.

     From this I have deduced a topology intended to account for the constitution of the subject.

134. #134

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.221

     THE SUBJECT AND THE OTHER: ALIENATION > THE FIELD OF THE OTHER

     Theoretical move: The passage argues that the drive's logic — its circular return upon the subject — is irreducible to ambivalence or well-being, and that the subject's realization is produced through a structural gap in its signifying dependence on the Other, grounded topologically in the function of the rim/cut.

     what I first called the function of the cut and which is now articulated, in the development of my discourse, as the topological function of the rim.

135. #135

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.224

     THE SUBJECT AND THE OTHER: ALIENATION > ALIENATION

     Theoretical move: Lacan introduces the lozange (losange) as a topological algorithm unifying the two fundamental operations of subject/Other relation—alienation and separation—showing how it functions as the formal support for both the fantasy formula ($<>a) and the demand/drive node ($<>D), with the vel of the lower half marking the first operation (alienation).

     there is no topology that does not have to be supported by some artifice—it is precisely the result of the fact that the subject depends on the signifier

136. #136

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.226

     THE SUBJECT AND THE OTHER: ALIENATION > ALIENATION

     Theoretical move: The vel of alienation is articulated as a logical operation of joining (union) rather than addition: whichever term the subject chooses—being or meaning—one element necessarily disappears, such that the subject is constitutively split between non-meaning (being eclipsed by the signifier) and meaning deprived of the unconscious.

     I apologize if I am being naive in reminding you of this, but it is in order to give you the notion that this vel that I will try to articulate for you is supported only on the logical form of joining.

137. #137

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.228

     THE SUBJECT AND THE OTHER: ALIENATION > ALIENATION

     Theoretical move: Lacan introduces the 'lethal factor' within the alienating vel (freedom or death) to demonstrate that alienation necessarily involves a death-structured choice, and then pivots to announce the second dialectical operation—separation—grounded in set-theoretic intersection rather than union, which will generate the field of transference.

     It is situated precisely in that same lunula in which you find the form of the gap, the rim.

138. #138

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.250

     OF THE SUBJECT WHO IS SUPPOSED TO KNOW, OF THE FIRST DYAD, AND OF THE GOOD > OF THE SUBJECT WHO IS SUPPOSED TO KNOW

     Theoretical move: The passage argues that desire's defensive structure ("not wanting to desire" = "wanting not to desire") is structurally identical to desire itself, forming a Möbius-like loop; and that the analyst's desire functions as the pivotal axis that transforms the patient's demand into transference, while "man's desire is the desire of the Other" entails an irreducible alienation that constitutively prevents the subject's desire from ever being fully recognized.

     I will illustrate it for you next time with a small topological drawing that has already been on the blackboard

139. #139

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.259

     FROM INTERPRETATION TO THE TRANSFERENCE

     Theoretical move: Lacan distinguishes identification, idealization, projection, and introjection by anchoring them topologically in different orders (symbolic vs. imaginary), arguing that intuitive "common" usage of these terms is the root of theoretical misapprehension, and that language orients the speaking subject in a fundamental topology that exceeds everyday understanding.

     man is orientated in the fundamental topology of language, which is very different from the

140. #140

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.260

     FROM INTERPRETATION TO THE TRANSFERENCE > FROM INTERPRETATION TO THE TRANSFERENCE

     Theoretical move: Lacan argues that ordinary language implicitly encodes a topology that psychoanalysts deploy spontaneously, and grounds Freud's distinction between Ich, Lust/Unlust, and the 'foreign body' (fremde Objekt) within that topology — showing how the non-ego is not the vast Real but a specific inscribed negation seated in the lunula between two overlapping fields.

     implies the enveloping topology in which the subject recognizes himself when he speaks spontaneously.

141. #141

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.272

     FROM INTERPRETATION TO THE TRANSFERENCE > FROM INTERPRETATION TO THE TRANSFERENCE

     Theoretical move: Lacan distinguishes two axes of identification—the ego ideal (narcissistic, sustaining the transference) and the objet a (topological, linked to the drive and separation)—and argues that the life/death drive distinction is valid only insofar as all sexual drives are articulated at the level of unconscious signification, where sex necessarily makes present death as a signifier.

     of that object whose very reality is purely topological

142. #142

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.285

     IN YOU MORE THAN YOU > TO CONCLUDE

     Theoretical move: The analyst's management of transference must maintain the gap between the subject as lovable and the subject as caused by objet petit a, and this topological structure — the "internal eight" or cross-cap — formalizes the irreducibility of that gap: the petit a never crosses it, remaining as the unswallowable object stuck in the gullet of the signifier.

     the function of the transference may be topologized in the form that I have already produced in my seminar on Identification—namely, the form that I have called on occasion the internal eight, that double curve

143. #143

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.286

     IN YOU MORE THAN YOU > IN YOU MORE THAN YOU

     Theoretical move: Lacan uses the topology of a surface folding back on itself (the cross-cap/Möbius-type structure) to argue that the line of self-intersection symbolises identification, and then moves to critique analyses that define their termination as identification with the analyst, insisting there is a "beyond" to identification that constitutes the true motive force of analysis.

     one must abstract oneself from three-dimensional space, since it is a question here only of a topological reality that is limited to the function of a surface.

144. #144

     Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.304

     IN YOU MORE THAN YOU > TO CONCLUDE

     Theoretical move: This passage is a back-matter index for Seminar XI, listing key concepts and page references; it is non-substantive for theoretical extraction purposes, functioning purely as a navigational apparatus.

     topology, 22, 34, 74, 8g—go, 131, 144, 147, 155—6, i6i, 164, 181—2, 184, 203, 206, 209, 235, 244—5, 257, 270—1

145. #145

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.30

     But let us continue .

     Theoretical move: Lacan introduces the Klein bottle as a topological model isomorphic with the Möbius strip's one-sided surface, arguing that this figure concretely illustrates the structural property of the signifier—namely that its inside and outside communicate without abolition of closure—thereby grounding the linguistic relation between signifier and signified (front/back) in topology rather than substance.

     I am going to introduce today, introduce one of these shapes, one of these topological shapes, one of these shapes founded on the surface

146. #146

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.68

     **Seminar 5: Wednesday 13 January 1965** > **Seminar 6: Wednesday 20 January 1965**

     Theoretical move: Lacan advances the problem of identification by critiquing the topological naïveté of Euler circles and replacing them with a more rigorous topology (Klein bottle, Möbius surface, torus) in which the subject's structure is homologous to the mathematical derivation of number from zero — the signifier represents the subject for another signifier just as the zero grounds the series of whole numbers, making identification inseparable from the subject's constitutive lack.

     I tried to capture identification in a topology, in a sort of bundle, a collection of threads more simple than all of those whose twists and turns the labyrinth of modern logic bears witness to

147. #147

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.162

     **Seminar 12: Wednesday 17 March 1965**

     Theoretical move: Using Munch's *The Scream* as a theoretical figure, Lacan argues that silence is not the ground of the scream but is caused by it—paralleling the structure of the big Other as a holed, divided surface—and uses this to articulate how the o-object emerges as a remainder/residue in the operation of demand, structuring fantasy, desire, and transference around an irreducible cut.

     this silence, confused by me with this space enclosed by the surface, and of itself, by itself unexplorable, which constitutes the original structure that I have tried to image for you at the level of the Klein bottle.

148. #148

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.13

     http://www.lacaninireland.com > **Seminar 2: Wednesday 9 December 1964**

     Theoretical move: Lacan argues that the topology of surfaces (Möbius strip, cross-cap, torus) is not merely illustrative but structurally necessary for theorising the relationship of the signifier to the subject—specifically, that the signifier cannot signify itself except by reduplicated self-crossing, a property directly readable from the Möbius strip's topological behaviour.

     three years ago in a seminar on identification, I was led to the necessity of a certain topology which appeared to me to impose itself, to arise from that very experience which is the most particular

149. #149

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.95

     **Seminar 8: Wednesday 3 February 1965**

     Theoretical move: Lacan uses the optical model of the inverted bouquet to distinguish the non-specularisable status of objet petit a from the body-image and ideal ego, arguing that the impasses of identification at the end of analysis can only be resolved by orienting the work around the o-object rather than settling for identification to the analyst as a rectification of the ego ideal.

     We are trying to propose a shape and, make no mistake, a topology essential for psychoanalytic praxis.

150. #150

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.138

     **Seminar 10: Wednesday 3 March 1965**

     Theoretical move: The passage argues that the genesis of the subject is grounded in the logic of zero and one (lack and its filling), but that analytic experience always reveals an irreducible remainder—the objet petit a—which escapes both the demand-axis and the transference-axis, requiring topological figures (Klein bottle, Möbius strip) rather than Cartesian coordinates to capture the subject's divided structure and its relation to truth/castration.

     This is what is called, in topology, the connectivity number. This is the usage and the privilege of what I am trying to bring into play before you... the Klein bottle to be a part of a cutting point, a cut, a single one

151. #151

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.276

     **Seminar 20: Wednesday 26 May 1965**

     Theoretical move: Through a student presentation (Kaufmann) tracing the mythological figure of Polyphemus across Greek and later texts, the passage argues that the progressive revelation of Galatea in the myth discloses the structure of phantasy as positioned in a one-dimensional space of approach and flight, while simultaneously linking the Sophist's problem of negation (ouc vs. mais) to the distinction between phonetic identity and differential signification—a distinction the one-eyed Cyclops structurally cannot make.

     This gives us the phantasy as situating itself in a onedimensional space which is divided between approaching and fleeing. And this again precisely would have to be put into relationship with the angler.

152. #152

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.91

     **Seminar 7: Wednesday 27 January 1965** > PRESENTATION BY Mr YVES DUROUX

     Theoretical move: Duroux's presentation of Frege's successor operation—grounded in a double negation (zero defined contradictorily, one following via contradictory contradiction)—is offered by Lacan as the formal mathematical analogue for the subject's relation to the signifier: the passage from zero to one figures the logic by which the subject emerges through negation, anticipating Miller's forthcoming articulation of suture.

     I gave in connection with these questions a Moebius strip, it must now be twisted.

153. #153

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.44

     **Seminar 4: Wednesday 6 January 1965**

     Theoretical move: Lacan uses the Klein bottle as a topological model to demonstrate the structural logic of the subject's relation to signification: the suture between inner and outer spheres reveals how the subject is deceived by the apparent reflexivity of consciousness, and proper names are introduced as a test case showing that signifiers cannot be reduced to mere denotation without meaning.

     It is here that we see the value of this little model that in different shapes, but in reality always the same ones, I am discussing before you... my Moebius strip, my Klein bottle from the last time, this is what is involved.

154. #154

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.292

     **PRESENTATION BY MONSIEUR MILNER**

     Theoretical move: Lacan argues that the psychoanalyst is structurally excluded from the Real by his position and technique, and that this exclusion—symptomatically mirrored in logic's reduction of reference to truth/falsity (Frege)—necessitates organizing a new logic around three irreducible terms (knowledge, subject, sex) in order to situate sense, meaning, and the subject's division within analytic experience.

     the three distinct edges of knowledge, the subject, and sex allow us to situate in their relationship, at their place, this something which is going to make appear to us a certain paradox

155. #155

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.258

     **Seminar 19: Wednesday 19 May 1965** > (18) In other words let us deceive ourselves together.

     Theoretical move: The analyst's desire is theorized not as a counterforce to the patient's defensiveness but as a ruse that inhabits the patient's own defensive structure—occupying the pole of sexual reality's impossibility—so that what constitutes the analysand's original fantasy can be separated out and the objet petit a revealed as the substitute for the missing sexual relationship; this operation is articulated through the Möbius strip topology of the unexpected.

     this outline of the para-Eulerian structuring that I tried to give you as necessary at least for certain concepts, namely the inverted eight, a little portion whose external field is this Moebius strip

156. #156

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.27

     **Seminar 3 : Wednesday 16 December 1964**

     Theoretical move: Lacan argues that the transmission of psychoanalytic experience cannot be grounded in ego-ideal identification or immanent developmental schemas (à la Piaget), but must be seized at the level of structure—specifically the structure of language as a topology that is irreducible to any instrumental or biunivocal logic, implicating the subject as such.

     it is not for nothing that there occur in my discourse elements of metaphor which are so singular... as those of knot, which bring us back to what already the last time I brought in here, in this little model that I brought to you in the shape of the Moebius strip, by reminding you of the importance of something which is of the order of topology.

157. #157

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.146

     **Seminar 11: Wednesday 10 March 1965**

     Theoretical move: Lacan uses the topology of the Möbius strip, Klein bottle, and cross-cap to argue that the subject's structure is constituted by the cut rather than by any intrinsic disposition of parts, and that the field of unpleasure (the objet a, death drive) necessarily traverses the interior of the pleasure-principle field — thereby providing a topological rather than purely dialectical solution to the impasse of 'Beyond the Pleasure Principle'.

     what relationship there is between this subject of the cut and this image, and you are going to see this image at the limit of the image - for in fact it is not one - that I am trying here to make present, with certain mathematical references such as those that are called topological

158. #158

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.38

     But let us continue .

     Theoretical move: Language does not merely represent the real but actively enters and structures it, making topology the necessary accompaniment to any structural discovery; this is illustrated through the Virgilian two-gates-of-dream figure, which maps the split between truth (horn) and captivating error (ivory/ego-as-subsistent-soul).

     we are included, implicated in a rigorous and coherent topology, so that every discovery, every decisive door pushed at a point of this structure, must be accompanied by the mapping out in a strict exploration, by the definite indication of the point where the other opening is

159. #159

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.62

     **Seminar 5: Wednesday 13 January 1965** > (10) [Various noises] You see that we are in a police state!

     Theoretical move: Lacan uses the topology of the Klein bottle and its non-orientability to ground a structural account of the subject and language — specifically Identification — that supersedes the crude imaginary of Freud's second topology (ego-ideal, superego), while simultaneously critiquing Russell's theory of types/metalanguage as an evasion of the real problems of language and the subject.

     we have a different aspect, a completely different one which is presented by the loop through which each one of the turns, which up to the present bound themselves to one another

160. #160

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.226

     **Seminar 15: Wednesday 7 April 1965**

     Theoretical move: Lacan distinguishes the signifier from the sign by locating its function on the side of the emitter rather than the receiver, arguing that the signifier's representation of a subject for another signifier necessarily bars and divides that subject — and uses this structure to differentiate the clinical positions of psychosis, neurosis, and perversion with respect to a message's gap and the desire of the Other.

     Because of the fact that I was delayed, I cannot show you today on the Klein bottle itself that these are the fields that this first step determines

161. #161

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.58

     **Seminar 5: Wednesday 13 January 1965** > (10) [Various noises] You see that we are in a police state!

     Theoretical move: Lacan argues that the topological surface (specifically the Klein bottle) provides the most adequate schema for the divided subject constituted under language, and maps the three dimensions of Logical Time (instant of seeing, time to comprehend, moment to conclude) onto the subject's experience at the locus of the Other, showing how Demand circulates on this surface and requires an additional dimension—time as three-dimensional space—to escape indefinite self-enclosure.

     we are not called on to bring into play a schema which is not at all extended but which is akin to it properly speaking, the topological schema.

162. #162

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.301

     **Seminar 22: Wednesday 9 June 1965.**

     Theoretical move: Lacan argues that the Cartesian cogito founds the modern subject by displacing truth onto the big Other (God), thereby inaugurating a science of accumulative knowledge severed from truth; psychoanalysis, precisely because it works at the split (Entzweiung) between "I think" and "I am," is the practice that can finally articulate the radical relationship between truth and knowledge — a relationship structured topologically, as in the Möbius strip.

     this Moebius strip is realised just as well by a strip of paper folded three times in a certain way.

163. #163

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.77

     **Seminar 5: Wednesday 13 January 1965** > **Seminar 6: Wednesday 20 January 1965**

     Theoretical move: Lacan uses the figure of Socrates to triangulate the voice as objet petit a, the structure of desire (including its link to the impossible), and the syllogism's topological deception, thereby re-framing the death drive not as a wish for death but as the structural condition that articulates desire, identification, demand, and transference around an irreducible gap.

     a topological trait - in any case, and however these two circles are articulated, which undoubtedly do not overlap, disjointed as they are by the whole force of the topological reversion around which I make turn to-day the operation of my discourse

164. #164

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.262

     **Seminar 20: Wednesday 26 May 1965**

     Theoretical move: Leclaire argues that the analyst's position is irreducible—and perhaps inconceivable—because, unlike the logician who must suture discourse by assigning zero to the concept of non-identity-to-itself in order to save Truth, the analyst refuses suture: by remaining attuned to radical (sexual) difference and the non-identical-to-itself, the analyst occupies no fixed place and listens rather than constructs, making the analytic position structurally incompatible with any discourse that closes on truth.

     if Miller... situates himself, for his part, in order to speak to us, at a point of a topology of two dimensions, neither opened nor closed, thus neither outside nor inside

165. #165

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.206

     **Seminar 14: Wednesday 31 March 1965**

     Theoretical move: Through the clinical case of Philip (Leclaire's analysand), Lacan articulates the drive's circuit as a loop around a gap in the body, where "pure difference" (exquisite/acid fringe of sweetness) functions as the irreducible kernel of desire; the ejaculatory formula Poord'jeli is analysed as a vocal signifier that mimes and masters this circuit, connecting the drive's reversal to the sacred incantatory dimension of the Voice.

     I leave you, starting from this little sketch, which could be easily drawn on the blackboard by a double loop, to imagine the possible games in the variety of senses

166. #166

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.302

     **Seminar 22: Wednesday 9 June 1965.**

     Theoretical move: The passage argues that the asymmetry of sexual difference — irreducible to any symmetrical dyadic opposition — is precisely what the subject encounters as the Objet petit a: every time the subject reaches toward truth, what is found is transformed into the o-object, which stands as the veiled third term linking subject to knowledge through the symptom rather than through certainty.

     if you wish, on the upper right-hand side of this triangular structure, there is a symmetry. The two foldings of the paper are carried out in a way that is symmetrical with respect to the one which appears at the surface.

167. #167

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.21

     All men are mortal Socrates is a man Therefore Socrates is mortal

     Theoretical move: Lacan argues that the impossibility of metalanguage (demonstrated through Russell's own reductio) grounds the irreducibly precarious position of the subject in language, and that this same impossibility produces the structural incommunicability of psychoanalytic experience—communicable only through non-sense rather than master-words or codified sense.

     the whole topology that we are trying to develop is completely vain and futile

168. #168

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.67

     **Seminar 5: Wednesday 13 January 1965** > (10) [Various noises] You see that we are in a police state!

     Theoretical move: Lacan argues that the Freudian slip (parapraxis) operates not through any diffuse or motor stumbling but through a phonematic substitution at the level of the proper name, where the Name-of-the-Father functions as the structural pivot linking desire (including the desire to kill the father and Oedipal desire) to signification — and proposes that the desire of the analyst, topologically defined in relation to identification, must be the axis of analytic treatment.

     the way that we have to define, topologically, what is involved in analysis which is quite obviously the picking out of desire... we ought to know how to define this desire topologically in relationship with this pass, this phenomenon which for its part is undoubtedly linked in a certain way... to identification.

169. #169

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.114

     **Seminar 9: Wednesday 24 February 1965** > **Presentation by Jacques-Alain Miller**

     Theoretical move: Miller introduces the "logic of the signifier" as an archaeology of logic itself—one that precedes and prescribes logical law rather than following it—and argues, through a close reading of Frege's *Grundlagen*, that the excluded psychological subject reappears as a structural function (suture) necessary to the genesis of number, thereby grounding Lacanian theory in formal logic.

     This openness depends on the fact that, not being situated on its inside, one is not for all that rejected into its outside, if it is true that at a certain point, which escapes from a topology restricted to two dimensions, their convergence takes place.

170. #170

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.48

     **Seminar 4: Wednesday 6 January 1965**

     Theoretical move: Lacan uses topology (Klein bottle, Möbius strip) to argue that the structural properties of surfaces are independent of their immersion in three-dimensional intersubjective space, and then extends this logic to the proper name: the proper name functions not as a classificatory endpoint (contra Lévi-Strauss) but as a movable signifier that marks irreplaceability and lack, designed to "fill holes" in the signifying structure — a function illustrated through Freud's forgetting of the name Signorelli.

     a topological surface is something which requires the distinction between two kinds of these properties, the properties inherent to the surface, and the properties that it takes on from the fact that you put this surface into what is, for its part, real three-dimensional space.

171. #171

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.126

     **Seminar 9: Wednesday 24 February 1965** > **Presentation by Jacques-Alain Miller**

     Theoretical move: Miller's presentation argues that the subject's emergence as representation in the signifying chain is necessarily correlative to its vanishing—a circular temporal structure in which the subject is simultaneously the origin of the signifier and excluded by it—and uses this logic to critique Aulagnier's notion of 'insertion' as neglecting the dimension of aphanisis, while grounding desire's pseudo-infinity and alienation in the metonymic function of the objet petit a.

     What Dr Lacan explained to us right at the beginning of this year, what he tried to do, was to situate in a unique topology the relationships that obtain in the space of language

172. #172

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.16

     http://www.lacaninireland.com > **Seminar 2: Wednesday 9 December 1964**

     Theoretical move: Lacan deploys topological figures—the Möbius strip, cross-cap, and internal eight—to argue that these surfaces can replace Euler circles (extensional logic of classes) in formalising the logic of the signifying chain, suggesting topology offers a richer structural account of syllogistic relationships than classical set-theoretic diagrams.

     the division of the field that this structure can contribute: if we compare the Moebius surface to the surface which completes it in the cross-cap

173. #173

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.308

     **Seminar 22: Wednesday 9 June 1965.** > **Seminar 23: Wednesday 16 June 1965**

     Theoretical move: Lacan argues that the Real is constituted through the impossible — not as a condition of possibility (the Kantian-psychological error) but as the remainder produced when the possible is negated — and links this structure to the triad of subject, knowledge, and sex via the topology of the Möbius strip and the concept of Entzweiung, grounding the analytic relationship to the symptom in this splitting.

     I thought I ought to inscribe in the topological schema whose importance or timeliness I will have to come back to later, as being marked by the fact that the structure of this topology being that of a surface such that its front comes in a way, as one might say, to conjoin itself to what is after all its opposite, namely its back.

174. #174

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.142

     **Seminar 11: Wednesday 10 March 1965**

     Theoretical move: Lacan argues that the frustration-centered analytic theory of demand obscures the Freudian foundation of desire and sexuality, and that only the rigorous reference to language as signifying structure (demonstrated via mathematics' own "everything must be said" imperative and the impossibility of metalanguage) can ground the subject between zero and one — a subject who does not use language but arises from it, first appearing as privation before entering demand.

     this misfortunate little bottle, called the Klein bottle that I am putting before you this year, it seems, it seems that for the mathematicians themselves who busy themselves in this domain, which is rather new

175. #175

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.310

     **Seminar 22: Wednesday 9 June 1965.** > **Seminar 23: Wednesday 16 June 1965**

     Theoretical move: The passage argues that the topological structure of the Möbius strip, Klein bottle, cross-cap, and projective plane is not mere formal play but indexes the subjective positions of being: specifically, the o-object (objet petit a) is identified as the topological element that closes the cross-cap/projective plane, and its function is to cover over the Entzweiung (division) of the subject, making fantasy the fallacious conjuncture of that division with the o-object, while castration names the fundamental relation of the subject to sex/truth.

     There is then no escape from this topology; the triad, and it is curious that people did not see this until a certain epoque, the triad implies this topology of the Moebius strip.

176. #176

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.99

     **Seminar 8: Wednesday 3 February 1965**

     Theoretical move: Lacan argues that desire, understood topologically through the Klein bottle as a cut that reveals an a-cosmic surface, exposes the fundamental inadequacy of ego-psychological and developmental object-relations approaches to transference: the analyst risks being "deceived" (not merely deceiving) by reducing the structure of the subject to a normative developmental history of needs and traumatic incidence, thereby foreclosing the properly Freudian dimension of desire and the unconscious.

     the key that we are trying to give with this topology, is what is involved when desire arms itself

177. #177

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.72

     **Seminar 5: Wednesday 13 January 1965** > **Seminar 6: Wednesday 20 January 1965**

     Theoretical move: Lacan uses the topology of the Klein bottle—contrasted with the ordinary torus and the Euler circle—to demonstrate that the two halves of a predicative proposition (subject-term and predicate-term, e.g. "Socrates" / "is mortal") are topologically non-homogeneous, thereby grounding a structural critique of the classical syllogism and showing that the function of the proper name (nomination) cannot be treated as equivalent to membership in a universal class.

     Here in the Klein bottle what do we see happening? I already told you the last time and the schema that I have drawn for you today already shows it to you.

178. #178

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.106

     **Seminar 8: Wednesday 3 February 1965**

     Theoretical move: Lacan argues that the o-object (objet petit a) is the hiding place of the Other's desire, not merely a register of demand or transference identification, and that failing to distinguish desire from demand leads to a clinical impasse — illustrated through a case where the analyst remains captive to a decade-long identificatory grip because she reduces the symptom to oral demand rather than grasping the dimension of desire.

     the desire of the Other, in this radical field where the desire of the subject is irreducibly, not tied into him, but precisely constituted by this torsion that my bottle here tries to represent for you.

179. #179

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.18

     All men are mortal Socrates is a man Therefore Socrates is mortal

     Theoretical move: Lacan uses the Socrates syllogism and the linguistics of the proper name to argue that logical form is grounded in—not prior to—language and the signifier; the passage turns on the claim that grammatical/linguistic structure is constitutively primary over logic, and that the child's early use of the signifier (illustrated by Darwin's 'quack' example) already enacts the fundamental function of denomination, connecting cry, name, and monetary exchange as the two extreme poles of signifier-function.

     I spoke earlier about Dante and his topology that is finally illustrated in his great poem... it is not because for him everything about substance and being pivots around what is called the point, what is at the same time the point of expansion and of vanishing of this sphere.

180. #180

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.57

     **Seminar 5: Wednesday 13 January 1965**

     Theoretical move: Lacan justifies his topological models (Klein bottle, Möbius strip, cross-cap, torus) as the necessary formal apparatus for grasping the subject as a surface, aligning this with Hegel's Phenomenology and its loop of Absolute Knowing, and connecting both to the analytic concept of the Subject Supposed to Know as the structural foundation of transference.

     it forms part of a family - it is not at all alone - it is associated with what I called on occasion, evoking them more or less for your usage, the torus and the cross-cap

181. #181

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.34

     But let us continue .

     Theoretical move: Lacan uses the topological construction of the Klein bottle — built step by step from sphere to blastula to inside-out surface — to argue that the Cartesian cogito marks the historical rupture with cosmological (microcosm/macrocosm) thinking, and that psychoanalysis inherits this rupture, revealing the "other scene" (Unheimlich) as the locus where inside and outside are sutured into continuity rather than correspondence.

     it is starting from this discovery that the supposedly pre-established pact of the signifier with some thing being broken... it is starting from the moment where we introduce here a different suture, and one which I called elsewhere an essential buttoning point, which is the one that here opens up a hole, and thanks to which the structure of the Klein bottle is then, and only then, established

182. #182

     Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.222

     **Seminar 15: Wednesday 7 April 1965**

     Theoretical move: Lacan argues that nomination is not arbitrary convention but a memorial act carrying topological structure, and uses the proper name (via Leclaire's 'poord"jeli') as a paradigm for the suture function of the signifier—showing how the obsessional's clinical specificity is marked by an 'exquisite difference' caught in a suture, while Topology (Möbius strip/Klein bottle) models the torsion inherent in both language and living bodies.

     this Moebius strip which reduplicated gives the Klein bottle... this fabric, this surface which is the one on which I am trying to draw for you the topology of the signifier

183. #183

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.285

     **PRESENTATION BY JACQUES-ALAIN MILLER**

     Theoretical move: Miller defends his concept of suture as a structural (not merely psychoanalytic) category that describes how a subject is produced in discourse through the articulation of an apparent chain and a dissimulated chain, arguing against Leclaire's reduction of his theoretical discourse to the position of an analysand's speech, and insisting that the signifier's identity is constituted at its root by the non-identical-to-itself, i.e., by lack.

     I am trying to highlight the functions of a different point which is not the reduction of a circle but of this little interior eight.

184. #184

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.162

     **Seminar 12: Wednesday 17 March 1965**

     Theoretical move: Using Munch's *The Scream* as a topological illustration, Lacan argues that silence is not mere absence of speech but the structural correlate of the voice-as-object (objet petit a), such that the scream *causes* silence rather than silence grounding the scream; this models the Möbius/Klein bottle topology of demand, from whose cut the objet petit a falls as remainder—the origin of desire, fantasy, and transference.

     the model, sketched out in this way, for silence, and you have sensed, confused by me with this space enclosed by the surface, and of itself, by itself unexplorable, which constitutes the original structure that I have tried to image for you at the level of the Klein bottle

185. #185

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.302

     **Seminar 22: Wednesday 9 June 1965.**

     Theoretical move: The passage argues that sexual difference introduces an irreducible asymmetry into any dialectic of being and number, and that this asymmetry is what drives analytic experience to posit the objet petit a as the subject's inevitable substitute for truth — wherever the subject reaches his truth, he transforms it into the o-object, making the objet petit a the structural locus of the real beyond knowledge.

     The two foldings of the paper are carried out in a way that is symmetrical with respect to the one which appears at the surface... it is in a non-symmetrical fashion that the folding is produced.

186. #186

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.55

     **Seminar 5: Wednesday 13 January 1965**

     Theoretical move: Lacan justifies his use of topological models (Klein bottle, Möbius strip, torus, cross-cap) as theoretically necessary — not merely illustrative — by arguing that the subject must be conceived as a surface, and that this topological thinking finds its philosophical parallel in Hegel's Phenomenology, whose loop of absolute knowledge illuminates the analytic concept of the subject supposed to know and transference.

     it is associated with what I called on occasion, evoking them more or less for your usage, the torus and the cross-cap, with this fundamental introduction of what can distinguish one and the other in so far as there intervenes or not this particular surface that is knotted in a specific fashion to itself

187. #187

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.21

     All men are mortal Socrates is a man Therefore Socrates is mortal

     Theoretical move: Lacan uses Russell's *Principia Mathematica* and the theory of metalanguages as a foil to assert the foundational thesis that there is no metalanguage—every logical or structural discourse presupposes the primary use of language—and situates this thesis as the precondition for psychoanalytic practice, positioning the analyst not as a subject supposed to know but as one who risks themselves at the place of the subject's lack.

     the whole topology that we are trying to develop is completely vain and futile

188. #188

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.222

     **Seminar 15: Wednesday 7 April 1965**

     Theoretical move: Lacan argues that nomination is not arbitrary but a memorial act tied to the function of the signifier, and uses the topology of the Möbius strip / Klein bottle to model how proper names and sutures operate differently across clinical structures (neurosis, psychosis, perversion), with the obsessional's relation to the 'exquisite difference' as the paradigm case.

     This fabric, this surface which is the one on which I am trying to draw for you the topology of the signifier, if I give it this year this shape from the history of mathematical thinking, then of logic

189. #189

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.95

     **Seminar 8: Wednesday 3 February 1965**

     Theoretical move: The passage argues that the end of analysis cannot be reduced to identification with the analyst (rectification of the ego ideal) but must reckon with the non-specularizable objet petit a, which centres specularization without itself being visible in the mirror — thereby positing two irreducible poles (ego ideal and objet a) that govern identificatory processes and determine the impasses of analytic experience.

     We are trying to propose a shape and, make no mistake, a topology essential for psychoanalytic praxis.

190. #190

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.68

     **Seminar 5: Wednesday 13 January 1965** > **Seminar 6: Wednesday 20 January 1965**

     Theoretical move: Lacan argues that Euler's circles, while pedagogically seductive, conceal the essential topological complexity of identification; by drawing on mathematical logic's discovery that zero (lack) grounds the whole number series, he establishes a structural homology between the genesis of number and the movement of the subject from signifier to signifier, grounding identification in topology (the Klein bottle / Möbius surface) rather than in classical set-theoretic extension/comprehension.

     I tried to capture identification in a topology, in a sort of bundle, a collection of threads more simple than all of those whose twists and turns the labyrinth of modern logic bears witness to

191. #191

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.301

     **Seminar 22: Wednesday 9 June 1965.**

     Theoretical move: Lacan argues that the Cartesian cogito installs a constitutive split (Entzweiung) between the subject of sense and the subject of being, and that this division—wherein the subject is what is *lacking* to accumulated scientific knowledge—is precisely what psychoanalysis radicalises: the unconscious is an "I think" that knows without knowing it, and truth returns not through confrontation with knowledge but through the stumbling intervals of discourse, the symptom being its privileged site.

     this Moebius strip is realised just as well by a strip of paper folded three times in a certain way.

192. #192

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.138

     **Seminar 10: Wednesday 3 March 1965**

     Theoretical move: The passage argues that subjective constitution is not exhausted by the demand-Other dyad: the primordial "genesis of one from zero" (filling of a void/lack) always leaves an irreducible residue — the objet petit a — which escapes both demand and transference, and whose topology is best captured by the cut on the Klein bottle yielding a Möbius strip, thereby grounding the legitimacy of analytic operation in confronting this remainder rather than identifying with the analyst.

     the privilege of what I am trying to bring into play before you... the Klein bottle to be a part of a cutting point, a cut, a single one... to allow it to develop into a single Moebius strip.

193. #193

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.58

     **Seminar 5: Wednesday 13 January 1965** > (10) [Various noises] You see that we are in a police state!

     Theoretical move: Lacan argues that subjective structure is best apprehended topologically—via surfaces (Klein bottle, torus) rather than volume—and maps the three moments of Logical Time (instant of seeing, time to comprehend, moment to conclude) onto a three-dimensional temporal field structured by the Other, through which demand, transference, and identification are articulated as inscriptions on that surface.

     whether already in this schize, in this division, we are not called on to bring into play a schema which is not at all extended but which is akin to it properly speaking, the topological schema.

194. #194

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.99

     **Seminar 8: Wednesday 3 February 1965**

     Theoretical move: Lacan uses the topology of the Klein bottle to theorise desire as a "good cut" that reveals the a-cosmic, non-orientable surface of the subject, and then pivots to critique the object-relational/developmental reduction of transference, arguing that the analyst risks being deceived when transference is interpreted merely as a reproduction of parental experience rather than as a structural positioning of the subject at the locus of the Other.

     the key that we are trying to give with this topology, is what is involved when desire arms itself

195. #195

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.30

     But let us continue .

     Theoretical move: Lacan introduces topology—specifically the Klein bottle—as a structural model for the signifier's relation to the signified, arguing that just as the Klein bottle has only one face (its inside communicating completely with its outside), the signifier's material and semantic dimensions are not opposed but continuous surfaces, thus replacing naive realism or substantialist accounts of meaning with a topological, combinatory account.

     I am going to introduce today, introduce one of these shapes, one of these topological shapes, one of these shapes founded on the surface

196. #196

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.126

     **Seminar 9: Wednesday 24 February 1965** > **Presentation by Jacques-Alain Miller**

     Theoretical move: Miller's presentation argues that the subject's insertion into the signifying chain is necessarily correlative to its vanishing — a circular, non-linear temporal logic — and that alienation is properly grounded in the division of the subject (not in consciousness), while the o-object, functioning as metonymy and as the logic of number (zero/one), structures the pseudo-infinity of desire.

     What Dr Lacan explained to us right at the beginning of this year... was to situate in a unique topology the relationships that obtain in the space of language, the circumscriptions of the logical field, of the linguistic field and of the analytic field.

197. #197

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.17

     All men are mortal Socrates is a man Therefore Socrates is mortal

     Theoretical move: The passage argues that the proper name cannot be reduced to a merely designatory function but opens onto the question of the signifier's relation to death (via the syllogism and the Death Drive), and further that language—as the primary, grammatically structured maternal tongue—is prior to and not reducible to logic or conceptual thought, as demonstrated through Dante, Vygotsky vs. Piaget, and Darwin's child-language example in which the signifier's mobility (from cry to monetary unit) reveals the two poles structuring language: the cry and money.

     I spoke earlier about Dante and his topology that is finally illustrated in his great poem.

198. #198

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.142

     **Seminar 11: Wednesday 10 March 1965**

     Theoretical move: Lacan argues that the analytic technique, grounded in language and the signifier, must take mathematics as its guiding reference precisely because mathematics demonstrates that there is no metalanguage—every formal construction must be accompanied by common discourse—and that the subject is best located in the interval between zero and one, as a "shadow of the number," a figure of privation that precedes its constitution in demand.

     this misfortunate little bottle, called the Klein bottle that I am putting before you this year...it seems that this little bottle has not in effect...delivered up all its mysteries

199. #199

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.13

     http://www.lacaninireland.com > **Seminar 2: Wednesday 9 December 1964**

     Theoretical move: Lacan advances the thesis that the relationship of the signifier to the subject requires a non-Euclidean topology — specifically the Möbius strip — to account for the impossibility of the signifier signifying itself except by self-reduplication, thereby grounding the gap between the signifier's functioning and the production of meaning in a topological structure rather than a linear or spherical spatial intuition.

     three years ago in a seminar on identification... I was led to the necessity of a certain topology which appeared to me to impose itself

200. #200

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.48

     **Seminar 4: Wednesday 6 January 1965**

     Theoretical move: Lacan uses topology (Klein bottle, Möbius strip) to argue that the proper name is not a classificatory terminus but a movable function tied to lack: the subject is named not qua individual but qua something that can be absent, making the proper name a shutter that covers over a hole in the signifying structure—a point illustrated through Freud's forgetting of "Signorelli."

     a topological surface is something which requires the distinction between two kinds of these properties, the properties inherent to the surface, and the properties that it takes on from the fact that you put this surface into what is, for its part, real three-dimensional space.

201. #201

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.114

     **Seminar 9: Wednesday 24 February 1965** > **Presentation by Jacques-Alain Miller**

     Theoretical move: Miller's presentation argues that what Frege's logical genesis of number actually stages—despite its explicit exclusion of the psychological subject—is the operation of a non-psychological subject as a structural function: the function of identity that transforms things into objects and units is precisely the logic of the signifier, which precedes and prescribes formal logic rather than falling under it.

     the Freudian field is not representable as a closed surface... not being situated on its inside, one is not for all that rejected into its outside, if it is true that at a certain point, which escapes from a topology restricted to two dimensions, their convergence takes place.

202. #202

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.146

     **Seminar 11: Wednesday 10 March 1965**

     Theoretical move: Lacan uses the topological properties of the Möbius strip, Klein bottle, and cross-cap to argue that the subject's structure—its non-orientability, the function of the cut, and the relation between the subject, the big Other, and objet petit a—cannot be captured by classical set-theoretic (Eulerian) distinctions, and that the field of unpleasure (objet a, death drive) necessarily traverses the interior of the field of pleasure rather than standing opposed to it from outside.

     what relationship there is between this subject of the cut and this image, and you are going to see this image at the limit of the image - for in fact it is not one - that I am trying here to make present, with certain mathematical references such as those that are called topological

203. #203

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.309

     **Seminar 22: Wednesday 9 June 1965.** > **Seminar 23: Wednesday 16 June 1965**

     Theoretical move: The passage argues that the topological structure of the Möbius strip, cross-cap, and Klein bottle formally captures the subjective position of being, and that the objet petit a—conceived as a topological "rag" completing the cross-cap—is the operative term that closes the Entzweiung of the subject, enabling the passage from alienation to separation and grounding the structure of fantasy as a fallacious suturing of the subject's division over the real.

     There is then no escape from this topology; the triad, and it is curious that people did not see this until a certain epoque, the triad implies this topology of the Moebius strip.

204. #204

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.308

     **Seminar 22: Wednesday 9 June 1965.** > **Seminar 23: Wednesday 16 June 1965**

     Theoretical move: Lacan argues that the Real is constituted precisely by the impossible (what cannot be), positioning this against the Cartesian-Kantian project of grounding knowledge in conditions of possibility; the Freudian discovery returns what Descartes foreclosed by offloading eternal truths onto divine arbitrariness, and the three poles of subject, knowledge, and sexed being—articulated through Entzweiung and the Möbius strip topology—structure the fundamental psychoanalytic dialectic.

     I thought I ought to inscribe in the topological schema whose importance or timeliness I will have to come back to later, as being marked by the fact that the structure of this topology being that of a surface such that its front comes in a way, as one might say, to conjoin itself to what is after all its opposite, namely its back.

205. #205

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.276

     **Seminar 20: Wednesday 26 May 1965**

     Theoretical move: Through a student presentation tracing the Polyphemus myth across Greek and later texts, the seminar advances the theoretical argument that fantasy (phantasy) emerges as a structural element tied to signifying differentiation (the distinction between identity-negation and differential negation, *ouc* vs. *mais*), the problem of the one-eyed subject's inability to distinguish reflection from representation, and the relationship between the Letter/writing and arithmetic — all converging on the topology of fantasy as situated in a one-dimensional space of approach and flight.

     the phantasy as situating itself in a one-dimensional space which is divided between approaching and fleeing.

206. #206

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.16

     http://www.lacaninireland.com > **Seminar 2: Wednesday 9 December 1964**

     Theoretical move: Lacan uses the topological comparison between the Möbius strip and the cross-cap to argue that these surfaces can illuminate logical and syllogistic relationships more adequately than classical Euler-circle set logic, positioning topology as a formal language for the signifying chain.

     the division of the field that this structure can contribute: if we compare the Moebius surface to the surface which completes it in the cross-cap

207. #207

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.105

     **Seminar 8: Wednesday 3 February 1965**

     Theoretical move: Lacan uses a clinical vignette of a borderline patient treated for ten years to argue that the analyst's error was reducing the patient's symptomatology to demand (and its oral regression) rather than locating the properly structural dimension of desire—specifically, that desire is constituted by its torsion toward the Other's desire, and that the objet petit a is the site where the desire of the Other dwells, not a relation between two egos.

     the desire of the subject is irreducibly, not tied into him, but precisely constituted by this torsion that my bottle here tries to represent for you.

208. #208

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.67

     **Seminar 5: Wednesday 13 January 1965** > (10) [Various noises] You see that we are in a police state!

     Theoretical move: Lacan argues that the Freudian slip (parapraxis) is not merely a motor accident but a phonematic substitution that traces desire back to the Name-of-the-Father as the structural axis of both repression and identification, and that analysis must topologically define the desire of the analyst in relation to this pass through identification.

     the way that we have to define, topologically, what is involved in analysis... we ought to know how to define this desire topologically in relationship with this pass, this phenomenon which for its part is undoubtedly linked in a certain way... to identification.

209. #209

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.207

     **Seminar 14: Wednesday 31 March 1965**

     Theoretical move: Lacan uses the clinical case of Philip (Leclaire's analysand) to theorise how the circuit of sense—anchored by pure difference, the gap of the body, and the dehiscence of the other body—produces desire, the drive, and the object voice, culminating in the Shemah prayer as a limit-case where the signifier, jouissance, and the sacred converge around an invocatory formula.

     the very figure of the loop around, no doubt, some nothings of the formula itself... this could be easily drawn on the blackboard by a double loop.

210. #210

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.27

     **Seminar 3 : Wednesday 16 December 1964**

     Theoretical move: Lacan dismantles psychological and Piagetian models of intelligence by showing that language is not the instrument of intelligence but its constitutive difficulty, and pivots to the claim that the subject is only a subject by being implicated in structure—thereby grounding analytic transmission not in ego-ideal identification but in the topology of the signifier.

     elements of metaphor which are so singular, so unnoticed perhaps but also so striking, if we retain them, as those of knot, which bring us back to what already the last time I brought in here, in this little model that I brought to you in the shape of the Moebius strip, by reminding you of the importance of something which is of the order of topology.

211. #211

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.262

     **Seminar 20: Wednesday 26 May 1965**

     Theoretical move: Leclaire argues that the analyst's position is irreducible and even inconceivable within logical discourse because, unlike the logician, the analyst does not suture — does not close the gap in discourse by assigning zero to the concept of non-identity-to-itself — but instead remains open to radical (sexual) difference, castration, and death, occupying no fixed place in the topology of discourse.

     if Miller... situates himself, for his part, in order to speak to us, at a point of a topology of two dimensions, neither opened nor closed, thus neither outside nor inside, I agree

212. #212

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.40

     **Seminar 4: Wednesday 6 January 1965**

     Theoretical move: Lacan argues that psychoanalysis lacks genuine theoretical comprehension of its own experience (transference, identification, symptom), and locates the foundational discovery of the unconscious in Freud's analysis of the Signorelli forgetting — where what disappears is not a repressed content but phonemes, establishing that the unconscious operates at the level of signifying material rather than meaning.

     a certain knot of signs to signs... something installed in the subjective, which cannot in any way be resolved by reasonable and logical dialogue

213. #213

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.62

     **Seminar 5: Wednesday 13 January 1965** > (10) [Various noises] You see that we are in a police state!

     Theoretical move: Lacan argues that topological analysis of the Klein bottle/false torus grounds a theory of the 'structural unconscious' that surpasses Freud's second topology and its crudely imagistic concepts (ego-ideal, superego), while simultaneously demonstrating that language is non-orientable and cannot be mastered by any metalanguage—a critique directed at Russell's theory of types and its attempt to resolve the liar paradox through hierarchical meta-languages.

     we are dealing with an orientable reality... the circuits that are carried out in it can be located as nonorientable

214. #214

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.45

     **Seminar 4: Wednesday 6 January 1965**

     Theoretical move: Lacan uses the Klein bottle as a topological model to argue that the proper name is not a pure denotation without meaning but rather carries a surplus of signifying effects, and that topology—not imagination—is the correct framework for understanding the structure of the subject, the unconscious, and the point of suture between interior and exterior.

     It is not so easy to operate, here, with these topological models. It is no easier for me than for you.

215. #215

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.38

     But let us continue .

     Theoretical move: Language does not mirror reality but constitutes it operationally: by entering the real and creating structure within it, language enables a rigorous topology in which every structural discovery entails a corresponding opening elsewhere — a logic illustrated by Virgil's two gates of dream (horn/truth vs. ivory/error).

     we are included, implicated in a rigorous and coherent topology, so that every discovery, every decisive door pushed at a point of this structure, must be accompanied by the mapping out in a strict exploration, by the definite indication of the point where the other opening is

216. #216

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.34

     But let us continue .

     Theoretical move: Lacan uses the topological construction of the Klein bottle to displace the cosmological microcosm/macrocosm schema, arguing that what Descartes' cogito inaugurates—and what psychoanalysis radicalises—is a suturing that connects inside to outside in a non-orientable way, breaking the pre-established parallelism between subject and world that grounds classical psychology and cosmological thinking.

     it is starting from this discovery that the supposedly pre-established pact of the signifier with some thing being broken... it is established that it is from this rupture... that a science can be inscribed

217. #217

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.226

     **Seminar 15: Wednesday 7 April 1965**

     Theoretical move: Lacan uses the example of the "alone at five o'clock" love-sign to demonstrate that the signifier (unlike the sign) represents a subject for another signifier — not from the side of the receiver but from the side of the emitter — and deploys this to differentiate the clinical structures (psychosis, neurosis, perversion) by how each relates to the gap structured in a signifying message.

     Because of the fact that I was delayed, I cannot show you today on the Klein bottle itself that these are the fields that this first step determines.

218. #218

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.258

     **Seminar 19: Wednesday 19 May 1965** > (18) In other words let us deceive ourselves together.

     Theoretical move: The analyst's desire operates not as the imposition of knowledge onto the analysand but as a structural ruse that separates the analysand's defensiveness—directed not against the analyst but against the reality of sexual difference—into an ever-purer form of fantasy, with the objet petit a standing in for the impossible real of the sexual relation; the unexpected (figured topologically via the Möbius strip) is proposed as the operative mode of analytic desire against the field of anxious expectation.

     this outline of the para-Eulerian structuring that I tried to give you as necessary at least for certain concepts, namely the inverted eight, a little portion whose external field is this Moebius strip

219. #219

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.72

     **Seminar 5: Wednesday 13 January 1965** > **Seminar 6: Wednesday 20 January 1965**

     Theoretical move: Lacan deploys the topology of the Klein bottle to demonstrate that identification is structurally non-homogeneous: the circuit of demand, when traced on a Klein bottle rather than a torus, is necessarily reflected and reversed, showing that the two halves of any predicative proposition ("all men" / "are mortal"; "Socrates" / "is mortal") occupy non-equivalent fields — thereby grounding a structural critique of classical syllogistic logic and revealing the irreducible function of the proper name and the speaking subject.

     This figure, then, with its intuitive appeal, I intend it to allow you to grasp the coherence that there is at this point if we define it, determine it as circumscribing the conditions, the favours, but also the ambiguities and thus the lures of identification

220. #220

     Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.77

     **Seminar 5: Wednesday 13 January 1965** > **Seminar 6: Wednesday 20 January 1965**

     Theoretical move: Lacan uses the figure of Socrates to articulate the structural relationship between Voice as objet petit a, Desire, Demand, Transference, and the Death Drive, arguing that the syllogism "Socrates is mortal / all men are mortal" is a topological lure whose deceptive diameter maps onto the function of transference as the link between identification, demand, and the indeterminate subject of the unconscious.

     I will only highlight my punctuation of today around a topological trait - in any case, and however these two circles are articulated, which undoubtedly do not overlap

221. #221

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.256

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: The passage argues that the analytic dialectic cannot be confined to demand and the maternal Other (as in object-relations approaches), but must pass through desire and ultimately jouissance; castration is reinterpreted not merely as the Oedipal prohibition but as the barrier of desire that bars the subject from jouissance — and the Hegelian master/slave dialectic is criticised for falsely attributing jouissance to the master, revealing it as a mirage.

     with the look, there enters into play, still complete, a topology that I described and which cannot be gone back on, which is the one which justifies the existence of the screen.

222. #222

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.238

     **Seminar 19: Wednesday 25 May 1966**

     Theoretical move: Lacan reads Velázquez's Las Meninas as a structural demonstration of the Gaze and the Objet petit a: the Infanta figures the central 'slit' (phallus-as-object) around which the picture's whole economy of vision is organised, and the Cross-cap topology is invoked to show how the fall of the object (the painter's look) simultaneously produces the barred subject and installs the empty Other as the support of truth.

     I apologise to those who are not used to handling what I earlier advanced in the order of my topology, namely, this tiny object called the cross-cap or the projective plane

223. #223

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.120

     **Seminar 9: 2 February 1966**

     Theoretical move: Lacan positions the analytic experience as requiring the analyst to occupy a Pyrrhonian/sceptical stance toward truth, introduces the Subject Supposed to Know as the patient's trap for the analyst's epistemological drive, and pivots toward Pascal's Wager as a structural model for the subject's relationship to infinity, the real, and the impossibility of enjoying truth.

     which I am trying, with the resources of an elementary topology, to valorise for you as regards what we can take from it at the level of our articulations.

224. #224

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.91

     Dr Lacan

     Theoretical move: Lacan uses Dante's *Divine Comedy* as a topological witness that anticipates the psychoanalytic function of the objet petit a (as the gaze/look), arguing that the medieval opposition of knowledge and truth (doctrine of the double truth) prefigures the split that modern science inherits, and that the poet—through his projection of cosmological knowledge into the field of "final ends"—inadvertently maps the edge-topology that links the word-in-the-Other to the emergence of the o-object, concretely illustrated by the conjunction of the liar and the counterfeiter in Hell.

     Our topology here, in the sense that I understand it, that I manipulate it, that I introduce you to it has no other function than to allow there to be mapped out these transformations of the relationships of knowledge and of truth.

225. #225

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.182

     **Seminar 16: Wednesday 4 May 1966**

     Theoretical move: Lacan argues that topology—specifically projective geometry—provides the non-metaphorical, combinatorial foundation for the subject's relation to extension and signification, displacing the classical unifying subject (grounded in Cartesian homogeneous space) in favour of a structural account where the screen, the signifier, and the combinatorial replace imaginary unity and representational resemblance.

     It is a matter, for us, of situating our topology; to situate ourselves, we analysts, as acting in it.

226. #226

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.81

     **Seminar 6: Wednesday 12 January 1966**

     Theoretical move: Lacan uses the topology of the Möbius strip and its cuts to furnish a structural (non-metaphorical) account of the barred subject ($) and its relation to the non-specular objet a, arguing that the strip resulting from cutting a Möbius strip is applicable to the torus and models the subject, while the discal residue from cutting the projective plane models the o-object as non-specular.

     What good was it for me to have hammered out for years the difference between the real, the imaginary and the symbolic which you have now seen incarnated, I think that you sense this, that earlier in my successive spheres, you have seen the way the imaginary finds its place there.

227. #227

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.230

     **Seminar 19: Wednesday 25 May 1966**

     Theoretical move: Lacan uses Velázquez's *Las Meninas* to distinguish the picture from the mirror and to argue that the scopic field reveals the subject's constitutive division: the picture is not representation but the *Vorstellungsrepresentanz* (representative of the representation), and the Objet petit a occupies the interval between the plane of fantasy and the picture-plane, which is the only genuine *Dasein* of the divided subject.

     This topology which is inscribed in projective geometry and the surfaces of the analysis situs, is not to be taken, as in the case of the optical models in Freud, under the heading of metaphor but indeed as representing the structure itself.

228. #228

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.223

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: Lacan, in dialogue with Foucault, argues that the scopic drive and its object (the gaze as objet petit a) cannot be reduced to a physics of the visual field; instead, the screen—not light—is the founding structure of analytic experience, and fantasy must be understood as the "representative of representation," linking the scopic world to the divided subject and to the unthought that psychoanalysis makes thinkable.

     There is a certain Pappus' theorem which is found in a surprising fashion to be exactly inscribed in the theorems of Pascal and of Brianchon, those on the rectilinearity of the colinearity of the meeting points of a certain hexagon in so far as this hexagon is inscribed in a conic.

229. #229

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.253

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan argues that topology is not an optional supplement to psychoanalytic formation but its very substance — the 'stuff into which the analyst cuts' — and uses the mathematician's disclosure that mathematical discourse conceals its own referent to illuminate the structural parallel with the psychoanalyst's position, where the unconscious (Urverdrangung) prevents any direct saying of what is spoken about; jouissance, caught in the net of language/the signifier, is identified as the hidden dimension that grounds desire and that only topology can begin to approach.

     topology is the very stuff into which he cuts (*taille*), whether he knows it or does not know it, it does not matter whether he opens a book on topology or not, from the moment that he does psychoanalysis, this is the stuff into which he cuts

230. #230

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.175

     Mademoiselle Grazien

     Theoretical move: Lacan uses the topology of the torus and Klein bottle to theorize jouissance as structurally analogous to the symptom, arguing that orgasm is merely one privileged surface-point of jouissance rather than its essence; this allows him to critique "psychoanalytic mysticism" around female orgasm, reframe aphanisis as the fading of the subject (not desire), and follow Jones's account of the father-daughter couple to argue that feminine sexuality resolves into the woman taking the place of the objet petit a.

     I do not reject the word system on condition that you describe as system the fashion in which I systematise things and which is precisely made up of topological references.

231. #231

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.268

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan argues that the o-object (objet petit a) must be understood not merely at the level of demand (breast, faeces) but through desire and jouissance, where castration is the barrier that projects jouissance onto the murdered father as an Oedipal mirage — a move that corrects what Lacan identifies as the Hegelian error of attributing jouissance to the master rather than understanding its structural unavailability to any subject.

     with the look, there enters into play, still complete, a topology that I described and which cannot be gone back on, which is the one which justifies the existence of the screen

232. #232

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.152

     **Seminar 14: Wednesday 20 April 1966**

     Theoretical move: Lacan uses a condensed summary of his previous seminar's work to argue that the being of the subject is constituted through a suture of lack—grounded in Frege's arithmetic, the Cartesian cogito's torsion, and the signifier's relation to negativity—and that only psychoanalysis, by engaging the symptom as a being of truth rather than bandaging the wound of the subject's split, can genuinely confront what science, philosophy, and social critique merely suture over.

     it is the topology of this torsion that must be carried out… The divine bottle is the Klein bottle. Not everyone can make emerge from its neck what is in its lining.

233. #233

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.224

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: Lacan develops a projective-geometry account of the subject's inscription in the visual field, arguing that perspective's two "subject poles" (the vanishing point and the point at infinity) articulate the split subject's double presence/absence within the picture-plane, and that the painting (exemplified by Las Meninas) functions as a "trap for the look" precisely because the picture-within-the-picture saturates reality while the objet petit a—the falling, ungraspable element—is what the painter is really aiming to capture.

     what is called the vanishing point and that, therefore, the first presence of the subject point in the figure plane is any point whatsoever on the horizon line

234. #234

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.272

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan inverts the Hegelian master/slave dialectic by arguing that jouissance remains with the slave, not the master, and uses this to reframe castration as the operation that introduces a negative sign onto the phallus—making possible the (always asymmetric) encounter between masculine and feminine jouissance. He then previews the tripartite RSI framework and the 'logic of fantasy' as the conceptual architecture needed to account for the subject's relation to desire, jouissance, and the real.

     it is much more, I am trying, I solicit, I summon from you so that you may identify yourselves to what one could call in mathematical language the tor (t.o.r.) factor which means what there is in the real... this real bears witness to a certain torsion.

235. #235

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.219

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: Lacan corrects Audouard's misreading of his topology of the scopic drive by insisting that the "plane of the look" cannot project onto the picture plane in a geometrically reciprocal (intersubjective) way, and uses this correction to clarify that the drive's structure is a topological circuit around the o-object (objet petit a), not an optical reciprocity between subject and image.

     this constancy of the Drang can only be developed by supposing that it emanates from a surface and the fact that it is supported on a constant edge, finally assures, as one might say, the vectorial constancy of the Drang.

236. #236

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.211

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: Lacan uses Velázquez's *Las Meninas* — read in parallel with Foucault's analysis — as a topological support for articulating the structure of representation, the gaze, and the narcissism of the mirror, with Green's intervention yoking the picture's spatial planes to fantasy, the primal scene, and the "bar of repression," thereby making the painting do theoretical work on the intersection of vision, subjectivity, and projective geometry.

     the relationship between the picture and the mirror, what one and the other not alone illustrate for us or represent for us, but truly represent as a structure of representation

237. #237

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.51

     IV - IDENTITY AND NON-IDENTITYTO ONESELF: THE DEATH DRIVE

     Theoretical move: The passage stages a theoretical confrontation between a framework centred on frustration, narcissism, and the pleasure/reality principle duality (Stein's position) and Lacan's alternative, which reorders the analytic situation around lack, the subject supposed to know, and the signifier/signified distinction—arguing that frustration is not the terminal category of analysis and that the symbolic dimension is being systematically underweighted in current analytic theory.

     You will see that with the last topological notations that I have given you, it is going to appear quite clear that the difference between what I have contributed as an articulation

238. #238

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.72

     **Seminar 6: Wednesday 12 January 1966**

     Theoretical move: Lacan argues that psychoanalytic theory, grounded in topology (specifically the torus and Möbius strip), is structurally distinct from myth and demonstrates its scientific character precisely through this topological self-demonstration; simultaneously, the modern neurotic is constituted as the "representative of truth" at the historical juncture where science, by suturing the subject's gaps, paradoxically excludes the very truth that the neurotic embodies in speech and language.

     this is what is meant by the topological investigation which is the one that I am pursuing here, that I am taking up today, from the last time where I stopped it, on the structure of the torus

239. #239

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.197

     **Seminar 17: Wednesday 11 May 1966**

     Theoretical move: Lacan argues that the analyst's subjectivity is constitutively split, and that the institutional stabilisation of the "knower's" status (whether teacher, doctor, or analyst) tends to occlude this division through specular misrecognition; the analyst must maintain the divided position as a living practice rather than merely as theoretical knowledge, and perspective geometry is invoked to illustrate how the scopic drive and the objet petit a structure this irreducible split.

     A coherent geometry, establishing a perfect demonstrative rigour, which has nothing in common with metric geometry, namely, on condition of admitting what is happening in what I call today the perspective ground

240. #240

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.206

     **Seminar 17: Wednesday 11 May 1966**

     Theoretical move: Lacan reads Velázquez's *Las Meninas* as a structural demonstration of the gaze: the painting-within-the-painting operates as a *Vorstellungsrepräsentanz* that reveals how pictorial representation does not represent but rather stages (en représentation), and Velázquez's self-insertion as the looking subject (sujet regardant) marks the point where the subject is captured by the gaze, designating the space in front of the picture as the topological site of the viewing subject.

     Well then, it is something quite striking whose value cannot, in my opinion, be mapped out except from what I introduced to you in this topological structure.

241. #241

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.110

     Another question.

     Theoretical move: The passage records a seminar discussion in which Lacan and interlocutors (Conté, Melman, Audouard) interrogate Stein's theoretical articles on psychoanalytic treatment, centering on whether the analyst's word can function as objet petit a, and identifying the absence of the big Other as the critical gap in Stein's articulation of narcissism, desire, transference, and truth.

     what will follow topologically which, this year teaches you to situate the function of the o-object

242. #242

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.228

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: Lacan uses a close reading of Velázquez's *Las Meninas* and a Balthus painting to articulate the structural formula of the scopic drive — "You do not see me from where I am looking at you" — and to argue that unconscious fantasy is not a visible object but a constitutive *frame* (bâti) whose three pieces (two subjects and one objet a) are never simultaneously available to view.

     unconscious phantasy depends on a frame, and it is this frame that I do not despair, not only of making familiar to those who listen to me but of making it get under their skin

243. #243

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.19

     **Seminar 3: Wednesday 15 December 1965**

     Theoretical move: Lacan argues that the subject must be grasped topologically—not as a mere metaphorical "hole in the real" but as constituted through the cut on a surface, whereby the fall of the objet petit a is structurally inseparable from the division of the subject; two-dimensional topology (rather than three-dimensional intuition) is proposed as the privileged formal apparatus for capturing the impossible structure of the subject.

     No void, no fall of the o-object that a primordial anxiety is able to account for, and I am going to try to make you sense it by topological considerations.

244. #244

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.186

     **Seminar 16: Wednesday 4 May 1966**

     Theoretical move: Lacan uses projective geometry—specifically the structure of the projective plane as a cross-cap, the horizon line at infinity, and the duality between points and lines—to argue that the topology of vision reveals that what gives consistency to the visual-signifying world is an envelope structure (not indefinite extension), and that this same structure grounds the fantasy as the loss of the gaze-as-objet petit a and the division of the subject.

     what ought to reveal, materialise for us, the topology from which it results that something is produced in the construction of vision which is nothing other than what gives us the basis and the support of the phantasy

245. #245

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.191

     **Seminar 16: Wednesday 4 May 1966**

     Theoretical move: Lacan uses the geometry of perspective — specifically the vanishing point and the "other eye" (point of the looking subject) — to derive a topological apparatus for the subject's split ($), arguing that these two points together locate the Objet petit a as what divides the subject-as-seeing from the subject-as-looking, and that this projective-geometric construction is the rigorous foundation for the structure of Fantasy.

     It is a novelty to introduce it in this way, to find in it the topology of \$, with respect to which it must now be known where we situate the (o).

246. #246

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.200

     **Seminar 17: Wednesday 11 May 1966**

     Theoretical move: Lacan uses projective geometry to establish that every perspective structure contains two subject points—not one—and then maps this duality onto the scopic fantasy, identifying the elided "window" (opening/split) as the site of the objet petit a, while illustrating the argument through Velázquez's Las Meninas and distinguishing his reading from Foucault's by centring the inverted canvas as the structurally decisive element.

     the structure of the projective plane in its purely topological shape, namely, under the envelope of the cross-cap

247. #247

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.78

     **Seminar 6: Wednesday 12 January 1966**

     Theoretical move: Lacan argues that the psychoanalytic concept of the objet petit a—hidden in the 'suture of the subject' within modern logic—is what classical and modern logic fails to articulate when it reduces truth to bivalent truth-value; the Möbius strip and projective plane topology are introduced as the structural alternative to the spherical cosmology underpinning both idealism and naïve realism in theories of knowledge.

     It is here that there is introduced the structure of the projective plane in so far as this surface is different one and allows us to respond differently to what is cut out as object and as subject.

248. #248

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.261

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan inverts the Hegelian master/slave dialectic by locating jouissance on the side of the slave, then uses this inversion to ground a critique of Freudian obscurantism around feminine jouissance, the phallic function as negativity, and the three registers (imaginary/symbolic/real) as orientating instruments for a forthcoming 'logic of phantasy'.

     the tor (t.o.r.) factor which means what there is in the real... this real bears witness to a certain torsion. This torsion is not the ananke that Freud speaks of

249. #249

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.12

     **Seminar 2: Wednesday 8 December 1965**

     Theoretical move: Lacan argues that both the scientific object and the psychoanalytic object (objet petit a) are structurally constituted as lack/hole, and that the subject of science is defined by a cut homologous to Dedekind's cut; the antinomy between "saving truth" (science) and "enjoying truth" (epistemological drive/jouissance) is structured by the same alienation schema as "your money or your life," such that the objet petit a is always the excluded intersection-term of this forced choice.

     Such a structure is necessary for a cut to determine the field, on the one hand of the subject as it is necessitated as subject of science and on the other hand, the hole where there originates a certain style of the object

250. #250

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.15

     **Seminar 3: Wednesday 15 December 1965**

     Theoretical move: Lacan argues that the topological and mathematical structures he introduces (the circle/disc, the cut, the Klein bottle, torus, etc.) are not merely illustrative but are themselves signifiers that constitute the subject through lack—the historical "obstacles" in mathematics (negative numbers, imaginaries) are not failures of intuition but structural moments of the subject's constitutive lack as produced by the signifier.

     these figures called the Klein bottle, the projective plane, the torus find themselves, as compared to what is the structure of our habitual co-ordinates of intuition, in such an upsetting position that it is really necessary to practice them.

251. #251

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.64

     **Seminar 5: Wednesday 5 January 1966**

     Theoretical move: Lacan argues that the Cartesian-Aristotelian reduction of body to homogeneous three-dimensional extension is a fundamental epistemological deception, and proposes that the topological structure of two-dimensional surfaces (sphere, cylinder, torus) with holes—rather than metric spherical space—can provide a non-punctual, non-specular account of the divided subject and its relation to the real.

     we are able to give to space, to the extension of the real a different structure than that of the three-dimensional sphere... we take a step backwards. We do not hope to break through the rakia in three dimensions. Perhaps by being satisfied with two.

252. #252

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.276

     there are normal perverts,

     Theoretical move: Lacan uses the Möbius strip's double-circuit topology to argue that the Oedipus Complex has two equivalent articulations — the generative drama of the law and the drama of the desire to know — and proposes that only through the objet petit a can the castration complex be rigorously formalized, a task he defers to the following year's seminar.

     the Moebius strip only really connects up with itself when two circuits have been made

253. #253

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.264

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan argues that topology is not an optional supplement to psychoanalytic training but its very operative 'stuff' — the medium in which the analyst cuts the subject — and uses the mathematician's structural concealment of his object as a foil to show that the analyst's non-saying differs because an irreducible unconscious (Urverdrängung) prevents knowledge, while jouissance, caught in the net of language as sexual jouissance, is the hidden ground that desire defends against, pointing toward the death drive as the only genuine philosophical question.

     topology is the very stuff into which he cuts (*taille*), whether he knows it or does not know it, it does not matter whether he opens a book on topology or not, from the moment that he does psychoanalysis, this is the stuff into which he cuts

254. #254

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.5

     **Seminar 2: Wednesday 8 December 1965**

     Theoretical move: Lacan articulates the theoretical stakes of the "subject as cut" — the split between truth and knowledge, Wirklichkeit and Realität — and grounds his structuralism in topology (Möbius strip, cross-cap, Graph of Desire), arguing that the analyst's position is defined by, and must accommodate, this constitutive cut rather than escaping it through subjectivist laxity.

     this network structure for example has one advantage it is precisely that of belonging... to a topological world, which means that the connections are not lost because the shape is distortable, flexible, elastic

255. #255

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.208

     **Seminar 17: Wednesday 11 May 1966**

     Theoretical move: Through a close reading of Velázquez's Las Meninas, Lacan dismantles standard interpretations (mirror-of-painter, king-and-queen as sitters) to argue that the painting's structural logic turns on the opposition window/mirror: the window as the painter's empty place of return versus the mirror as the royal couple's omniscient gaze—a gaze that functions like Descartes' God, guaranteeing the subject's world, and whose obverse is the television screen as the modern correlate of the relation between subject and objet petit a.

     the strict difference there is between a mirror and the window; two terms precisely which structurally have no relationship... I put forward, in opposition to this obvious impossibility, that what is the essential in what is indicated by this picture is this function of the window.

256. #256

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.67

     **Seminar 5: Wednesday 5 January 1966**

     Theoretical move: Lacan uses topological figures—the torus, the cross-cap, and the Möbius strip—to argue that the subject is constitutively divided (not primordially unified), and that the Objet petit a as "truth-value" is the irreducible object that makes possible the world of objects and the subject's relation to it; the disc produced by cutting the cross-cap stands in a position of necessary crossing with the Möbius strip, which in turn figures the divided subject.

     to show you what constitutes, properly speaking, the discovery of this topology which is absolutely essential to allow us to conceive of the link which exists between this furrow of the subject

257. #257

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.96

     Dr Lacan

     Theoretical move: Lacan uses Dante's poetic structure—particularly the Narcissus/mirror motif and the figure of Beatrice in courtly love—to argue that the objet petit a (o-object) is non-specular: it appears as an image of nothing, and this structure of sublimation (where jouissance is withdrawn) establishes a privileged equilibrium between truth and knowledge that poetic construction can illuminate more directly than psychoanalytic theory alone.

     a thousand terms which designate for us topological references... the Klein bottle, will allow there to be structured in a decisive fashion what I mean here about the relationship of the subject to the other.

258. #258

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.134

     **Seminar 10: Wednesday 9 February 1966**

     Theoretical move: Lacan reads Pascal's Wager as a topological model of the fantasy structure: the infinite field of the big Other, barred and reduced to pure alternation of existence/non-existence, is what causes the Objet petit a to 'fall' as the real cause of desire—and this structural logic defines the analyst's position as the partner who 'knows he is nothing', enabling the object to fall from the opaque field of belief/dream.

     I want to clearly illuminate the topology of what I am designating here.

259. #259

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.242

     **Seminar 20: Wednesday 1 June 1966**

     Theoretical move: Lacan articulates the objet petit a as a topological structure (hole) that is "represented" precisely by not being representable, and reframes his entire method as a second circuit around Freud's teaching—not a mere return to sources but a non-orientable, Möbius-strip-like redoubling that transforms meaning through structure rather than reduplication.

     the o-object is a topological structure, the one that I imaged for you by the figures of the torus, the cross-cap, the mitre, even the Klein bottle

260. #260

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.148

     **Seminar 12: Wednesday 23 March 1966**

     Theoretical move: Lacan reconstructs, for an American audience, the foundational articulation between demand and desire, the splitting of the subject, and the topology of the torus as the structural support (*upokeimenon*) of desire — arguing that desire is not desire for jouissance but the barrier that keeps the subject at a calculated distance from it, and that this duplicity of desire with respect to demand grounds everything called ambivalence in analysis.

     topology is going to teach us to make function this sort of turning [inside-out, back-to-front] (retournement) which is properly the one that I will try to display… at the level of the structure of the torus

261. #261

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.7

     **Seminar 2: Wednesday 8 December 1965**

     Theoretical move: Lacan uses the vase-as-hole (the mustard pot) as a structural model for the symbolic order and the object of science, arguing that the material cause is the hole itself rather than any positive substance, and that science becomes possible precisely when the object is approached as lacking—a move that also grounds the distinction between the signifier's phonematic and logical poles in a new graph.

     there is right at the bottom ... a new little graph which I am giving you as an object of reflection which is properly speaking useful in order to grasp the relationships of what I called and continue to make function as the signifier

262. #262

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.62

     **Seminar 5: Wednesday 5 January 1966**

     Theoretical move: Lacan reframes the objet petit a as a "waste object" of the Real that is constitutively invisible within the specular/imaginary order, and retroactively shows that his notation i(o) at the Mirror Stage already encoded this object at the heart of identificatory alienation — making the o-object the central thread running from the Mirror Stage through topology, and abolishing a naive epistemology grounded in perception-consciousness.

     in the year when I traced out on the blackboard the first uses of these shapes (formes) to which I am now going to come in topology and in which I tried to inscribe for the edification of my listeners

263. #263

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.156

     **Seminar 14: Wednesday 20 April 1966**

     Theoretical move: Lacan argues that the analyst's implication in the symptom is not a relativist epistemological problem solvable by expanding the subject's knowledge; instead, a radical topological recasting is required—one that replaces the sphere-topology of classical knowledge (Plato's cave/sun) with an encounter with what language produces as a real, corporeal effect (the o-object), irreducible to any imaginary mirage or metalanguage.

     except precisely [by] what we would call a little bit more than very great precautions except for the radical, structural, absolutely total recasting of the topology of the question

264. #264

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.249

     **Seminar 20: Wednesday 1 June 1966**

     Theoretical move: Lacan advances the topology of the Objet petit a by demonstrating that the scopic and invocatory objects occupy a dimension beyond demand/frustration theories of neurosis, and introduces the hyperboloid of revolution as a topological figure that models the structural relationship between subject (S) and o-object, pointing toward a group-structure combinatorial of partial objects culminating in castration.

     we can see why it takes on, in topology itself, this privileged function, since, when all is said and done, to whatever combinatorial reduction we can push these topological shapes... it seems that there remains in them some residues of what, perhaps falsely, one calls the intuitive, and what is properly this o-object that I call the look.

265. #265

     Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.22

     **Seminar 3: Wednesday 15 December 1965**

     Theoretical move: Lacan argues that the Möbius strip provides the topological model for the divided subject: its essential property is that the cut IS the strip itself, meaning that subjectivity is constituted through division rather than unity. By showing how the cross-cap (projective plane) decomposes into a Möbius strip plus a spherical flap, and by introducing the torus and Klein bottle as further structural supports, Lacan grounds the relationships between subject, Objet petit a, demand, desire, and the Other in rigorous topological terms.

     I am caught between explaining something to you in an incorrect fashion or not explaining it to you at all; here we have a tangible example of one of these subjective impasses which are precisely what we base ourselves on.

266. #266

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.67

     **Seminar 5: Wednesday 5 January 1966**

     Theoretical move: Lacan uses topological figures—the torus, cross-cap, and Möbius strip—to demonstrate that the structure of the subject is necessarily split/divided, that the relation between demand and desire has a formal topology (at least two demands per desire and vice versa), and that the objet petit a functions as the 'truth-value' grounding the entire world of objects, thereby replacing any notion of primordial autoerotic unity with an irreducible openness at the heart of the subject.

     it is important to go further before I leave you. Namely, to show you what constitutes, properly speaking, the discovery of this topology which is absolutely essential to allow us to conceive of the link which exists between this furrow of the subject

267. #267

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.250

     **Seminar 20: Wednesday 1 June 1966**

     Theoretical move: Lacan uses the topology of the hyperboloid of revolution to illustrate the structural relationship between the subject (S) and the objet petit a, arguing that the o-object can only function within a group structure that permits negative values, which ultimately grounds the Freudian dimension of desire and castration.

     it is certainly remarkable that at the surface of what is obtained by such a revolution one can trace the series of straight lines which have as a property to go off to infinity.

268. #268

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.78

     **Seminar 6: Wednesday 12 January 1966**

     Theoretical move: Lacan argues that truth cannot be sutured by mere logical truth-value (alethes) or empirical reference, and that the o-object (objet petit a) — hidden in the suture of the subject within modern logic — is precisely what reveals the true secret of the connection between truth and knowledge; the projective plane and Möbius strip are then introduced as topological figures adequate to this subject-object structure, against the inadequate spherical cosmology that underlies both idealism and false realism.

     It is here that there is introduced the structure of the projective plane in so far as this surface is different one and allows us to respond differently to what is cut out as object and as subject.

269. #269

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.80

     **Seminar 6: Wednesday 12 January 1966**

     Theoretical move: Lacan establishes the Möbius strip and its topological transformations (cutting, doubling, the toric strip, the projective plane, and the discal residue) as the structural support for the barred subject ($) and the non-specular objet petit a, arguing that the conjunction of identity and difference proper to subjectivity can only be rigorously grounded in these topological—not metaphorical—structures, and that distinctions between real and imaginary reversal depend entirely on which surface-structure is in play.

     I point out to you that if the Moebius strip is itself the effect of a cut in another kind of surface, which to facilitate things for you I did not introduce otherwise, and that I earlier called the projective plane

270. #270

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.222

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: Lacan argues that the scopic drive's structure cannot be reduced to a physics of vision; the o-object (look/gaze) is a "representative of representation" (Freud's term) rather than a transparent window on reality, and projective geometry (Desargues, Pappus, Pascal) supplies a structural model for how fantasy mediates the divided subject's relation to the real — a move Lacan develops in direct dialogue with Foucault's *Les Mots et les Choses*.

     There is a certain Pappus' theorem which is found in a surprising fashion to be exactly inscribed in the theorems of Pascal and of Brianchon

271. #271

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.22

     **Seminar 3: Wednesday 15 December 1965**

     Theoretical move: Lacan argues that the Möbius strip, Cross-cap (projective plane), torus, and Klein bottle are not mere illustrations but structural supports for the constitution of the divided subject: the cut that divides the Möbius strip IS the Möbius strip, making division constitutive of subjectivity rather than secondary to it, and thereby grounding the relationship between demand, desire, and the Other in rigorous topological terms.

     I am going to put forward here something that is strictly speaking incorrect from the point of view of topology. Nevertheless, this is not going to worry us for I am caught between explaining something to you in an incorrect fashion or not explaining it to you at all.

272. #272

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.237

     **Seminar 19: Wednesday 25 May 1966**

     Theoretical move: Lacan uses Velázquez's *Las Meninas* as a visual matheme for the structural relationship between the gaze, the mirror, the Objet petit a, the Ideal Ego, and the field of the big Other: the painting is not a representation but a "trap for the look," and the royal couple's invisible gaze from the mirror-position enacts the function of the big Other in the narcissistic/specular relationship, while the o-object (objet petit a) remains irreducibly non-specular and therefore haunts the schema from outside it.

     It is a metaphor, of course, a metaphor which is applied... thanks to a spherical mirror a real image can be produced of an object hidden under what I call a little board.

273. #273

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.230

     **Seminar 19: Wednesday 25 May 1966**

     Theoretical move: Lacan distinguishes the picture from the mirror by theorising the picture as the "representative of the representation" (Vorstellungsrepräsentanz): the scopic field of the picture inscribes both the Objet petit a and the division of the subject through projective topology, where the subject's "there" (Dasein) is not a presence but the gap/interval between two parallel planes — the picture-plane and the fantasy-window — in which the object a falls.

     This topology which is inscribed in projective geometry and the surfaces of the analysis situs, is not to be taken, as in the case of the optical models in Freud, under the heading of metaphor but indeed as representing the structure itself.

274. #274

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.20

     **Seminar 3: Wednesday 15 December 1965**

     Theoretical move: Lacan advances the argument that topology—specifically two-dimensional surface theory—provides the structural model for the subject's constitution through the fall of the objet petit a, where the cut on a surface (not a metaphorical void in the real) is what determines the division of the subject; Bejahung/Verneinung, the phallus as attribute, and Stoic *ptosis* are marshalled to show that the subject is the effect of a structural cut, not merely a hole in the real.

     No void, no fall of the o-object that a primordial anxiety is able to account for, and I am going to try to make you sense it by topological considerations.

275. #275

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.253

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan argues that topology is not an optional supplement for the psychoanalyst but the very material into which the psychoanalytic operation cuts, and that jouissance—placed on the hither side of the big Other and caught in the net of subjective topology as sexual jouissance—is the irreducible, unsayable dimension that language/desire both defends against and compels us to question, linking the emergence of the signifier to the individual's relation to jouissance via Freud's death drive.

     topology is the very stuff into which he cuts (*taille*), whether he knows it or does not know it, it does not matter whether he opens a book on topology or not, from the moment that he does psychoanalysis, this is the stuff into which he cuts, into which he cuts the subject of the psychoanalytic operation.

276. #276

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.219

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: Lacan corrects a seminar participant's (Audouard's) attempt to reconstruct projective geometry of the gaze, using the error to clarify the topology of the scopic drive: the ground/look-plane cannot project onto the figure-plane along a horizon line but only along the line at infinity of the picture, and the drive's structure must be understood as a topological circuit around the objet petit a, not as an intersubjective reciprocity between two perspectives.

     the constancy of the Drang can only be developed by supposing that it emanates from a surface and the fact that it is supported on a constant edge, finally assures, as one might say, the vectorial constancy of the Drang.

277. #277

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.148

     **Seminar 12: Wednesday 23 March 1966**

     Theoretical move: Lacan recounts his American seminars as an occasion to condense his core theoretical moves—distinguishing demand from desire, grounding the splitting of the subject in the unconscious, locating sexuality as desire-to-know, and announcing that topology (torus, cross-cap, Klein bottle) will provide the structural substance for showing how one demand generates a duplicity of desire.

     topology is going to teach us to make function this sort of turning [inside-out, back-to-front] (retournement)… at the level of the structure of the torus

278. #278

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.227

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: By reading Velázquez's *Las Meninas* through Desargues' projective geometry, Lacan identifies the painter's "subject point" as structurally split between the vanishing point (the horizon) and a point at infinity outside the picture, such that the picture-within-the-picture functions as objet petit a — the representative of representation that can never be seized in the mirror, only in the gaze-trap the picture sets for the viewer.

     this is a properly structural and strictly scopic interpretation

279. #279

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.242

     **Seminar 20: Wednesday 1 June 1966**

     Theoretical move: Lacan argues that the objet petit a is a topological structure identifiable with the "hole" in surfaces like the torus, cross-cap, and Klein bottle—not a represented object but the very condition of representation—and frames his entire method as a second circuit of Freud's own Möbius-like path, where repetition transforms rather than reduplicates, culminating in the division of the subject.

     I spoke about topological elements, and topological elements in which in short, I have not, up to the present, in an explicit fashion, completely highlighted where to put this o-object.

280. #280

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.191

     **Seminar 16: Wednesday 4 May 1966**

     Theoretical move: Lacan develops a projective-geometric account of the subject's split by identifying two distinct points in perspective construction — the vanishing point (subject qua seeing) and the 'point of the looking subject' (which falls in the gap between subject and picture plane) — and argues that this topology of two points, with objet petit a placed between them, furnishes a rigorous visual figure for the fantasy and for the division of the subject ($).

     it is a novelty to introduce it in this way, to find in it the topology of \$, with respect to which it must now be known where we situate the (o)

281. #281

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.62

     **Seminar 5: Wednesday 5 January 1966**

     Theoretical move: Lacan argues that the objet petit a, as a "waste object" of the Real, is the hidden structural core of both identification (the ego as i(o)) and analytic practice, and that its invisibility is constitutive — tied to the illusory sovereignty of the visual/perceptual world — while topology (the cross-cap, torus) is introduced not as analogy but as the proper structure of reality itself.

     what I tried to inscribe for the edification of my listeners and to indicate to them what was to be extracted from them in terms of resonance, as an analogy, to introduce them to what I must now show them as being properly the structure of reality, and not some simply the figure.

282. #282

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.110

     Another question.

     Theoretical move: The passage stages a seminar discussion in which participants (Conté, Melman, Lacan) critically interrogate Stein's theoretical framework, converging on the argument that his account of the analyst's word, narcissism, desire, and predication remains incomplete precisely because it lacks a structural reference to the big Other as the third locus from which the subject receives his own word — a lacuna that collapses the treatment into a dual imaginary game between analyst and patient.

     what will follow topologically which, this year teaches you to situate the function of the o-object

283. #283

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.156

     **Seminar 14: Wednesday 20 April 1966**

     Theoretical move: Lacan argues that the analyst's implication in the symptom is not a relativist problem resolvable by expanding the subject's perspective, but requires a radical topological recasting; moreover, the psychoanalytic novelty lies in language producing real, corporeal effects that precede and exceed conscious apprehension, with the objet petit a re-introduced through a self-referential puzzle about writing to show that the o-object is a structural effect of language, not an imaginary mirage.

     except precisely [by] what we would call a little bit more than very great precautions except for the radical, structural, absolutely total recasting of the topology of the question

284. #284

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.175

     Mademoiselle Grazien

     Theoretical move: Lacan uses topology (torus, Klein bottle) to theorise jouissance as structurally coextensive with the body and irreducible to orgasm, and then pivots to Jones's concept of aphanisis and the father-daughter couple to argue that feminine subjective impasse culminates in the woman being forced to occupy the position of objet petit a — a move that exposes what Riviere named womanliness as masquerade.

     I do not reject the word system on condition that you describe as system the fashion in which I systematise things and which is precisely made up of topological references.

285. #285

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.51

     IV - IDENTITY AND NON-IDENTITYTO ONESELF: THE DEATH DRIVE

     Theoretical move: The passage stages a debate between a frustration-based model of analytic treatment (Stein's) and Lacan's structural alternative, pivoting on the claim that 'lack' is more fundamental than 'frustration', and that transference is grounded in the Subject Supposed to Know rather than in the analyst's representative function of reality — while Melman's intervention presses toward the primacy of the signifier/signified distinction over mere content of speech.

     with the last topological notations that I have given you, it is going to appear quite clear that the difference between what I have contributed as an articulation and what is precisely received in this order

286. #286

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.257

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan argues that the o-object of demand (breast, faeces) must be distinguished from the objects of desire (gaze, voice) and jouissance (linked to castration), and that castration is not reducible to the Oedipus myth's prohibition but marks the bar between the subject and jouissance — a bar that IS desire itself; further, the Hegelian master/slave dialectic fundamentally misreads jouissance by assuming that renunciation entails its loss.

     with the look, there enters into play, still complete, a topology that I described… which justifies the existence of the screen

287. #287

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.6

     **Seminar 2: Wednesday 8 December 1965**

     Theoretical move: Lacan argues that the subject must be rigorously understood as a "cut" (not a subjectivist position), and uses this to articulate the analyst's impossible-but-necessary position; he connects the Möbius strip and cross-cap as topological figures that make the constituting cut of the subject graspable, while distinguishing Wirklichkeit (realizable analytic relation) from Realität (the impossible Real that determines failure).

     this network structure for example has one advantage it is precisely that of belonging - almost to the first word, world but I use it quickly to make myself understood - to a topological world, which means that the connections are not lost because the shape is distortable, flexible, elastic.

288. #288

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.272

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan inverts the Hegelian master/slave dialectic by locating jouissance on the side of the slave, then reframes castration not as a prohibitive structure but as the operation of negativing the phallus so that desire and jouissance can be articulated across sexual difference — a move he introduces as preliminary to the 'logic of phantasy' and organises around three registers (imaginary, symbolic, real/torsion).

     this real bears witness to a certain torsion. This torsion is not the ananke that Freud speaks of, for ananke and logos are both of the order of the symbolic.

289. #289

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.134

     **Seminar 10: Wednesday 9 February 1966**

     Theoretical move: Lacan reads Pascal's Wager through the topology of the cross-cap and the barred Other to argue that the wager's stake is precisely the Objet petit a as cause of desire: wagering on God's existence installs the big Other under the bar (marking its non-existence as condition), and this structural move—not religious faith—is what psychoanalysis must reckon with to define the analyst's position relative to the subject's fantasy.

     I want to clearly illuminate the topology of what I am designating here.

290. #290

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.239

     **Seminar 19: Wednesday 25 May 1966**

     Theoretical move: Lacan uses Velázquez's *Las Meninas* to demonstrate how the Objet petit a (the Infanta as the 'girl = phallus', the slit, the hidden central object) structures the field of vision, showing that the subject is constituted by the cut of the object on the cross-cap, while the function of the Other as 'blind vision' (an empty, void Other) supports the truth of representation without itself seeing — with direct consequences for the end of analysis as the subject's encounter with the o-object.

     I apologise to those who are not used to handling what I earlier advanced in the order of my topology, namely, this tiny object called the cross-cap or the projective plane

291. #291

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.91

     Dr Lacan

     Theoretical move: Lacan uses Dante's *Divine Comedy* as a privileged site to show how the o-object (the gaze) emerges at the intersection of knowledge and truth within the pre-scientific philosophical tradition, arguing that the medieval doctrine of the double truth anticipates the topological distinction between open and closed sets, and that Dante, qua poet, unconsciously articulates the structure of the o-object—particularly through the mirror of Narcissus—at the very limit between knowledge and truth.

     Our topology here, in the sense that I understand it, that I manipulate it, that I introduce you to it has no other function than to allow there to be mapped out these transformations of the relationships of knowledge and of truth.

292. #292

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.96

     Dr Lacan

     Theoretical move: The passage argues that the objet petit a is non-specular — it appears as an image of nothing — and that courtly love (as in Dante's poetic construction) uniquely structures the relationship between the subject, the ego ideal, the o-object, and jouissance, thereby grounding psychoanalytic theory of sublimation in a topological framework.

     in a thousand terms of the field thus defined... we find a thousand terms which designate for us topological references... the Klein bottle, will allow there to be structured in a decisive fashion what I mean here about the relationship of the subject to the other.

293. #293

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.200

     **Seminar 17: Wednesday 11 May 1966**

     Theoretical move: Lacan uses projective geometry to argue that perspective structure necessarily contains two subject-points (not one), and that the elided "window" or opening between them is the structural site of the objet petit a in the scopic field — a topology he then illustrates via Velázquez's Las Meninas, reading the painting's face-down canvas as a figure for the division of the subject and the drive's Möbius-strip circuit.

     the structure of the projective plane in its purely topological shape, namely, under the envelope of the cross-cap. It is this something holed in this structure which, precisely, allows there to be introduced the irruption on which there is going to depend... the production of the division of the subject.

294. #294

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.12

     **Seminar 2: Wednesday 8 December 1965**

     Theoretical move: Lacan establishes a structural homology between the scientific object (defined as lack/hole, measurable only through the cut) and the objet petit a in psychoanalysis, showing that both the subject of science and the o-object are constituted through alienation—a forced choice in which something is always lost, either truth-as-jouissance or science-as-knowledge.

     Such a structure is necessary for a cut to determine the field, on the one hand of the subject as it is necessitated as subject of science and on the other hand, the hole where there originates a certain style of the object.

295. #295

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.120

     **Seminar 9: 2 February 1966**

     Theoretical move: Lacan uses the analytic situation — where every demand is necessarily disappointed — to critique masochism as a hasty diagnostic label, introduces the analyst as Subject Supposed to Know whose epistemological drive toward truth is itself caught in the law of disappointed demand, and pivots to Pascal's Wager as a structural model for the subject who must wager on truth while initially renouncing access to it in a Pyrrhonian suspension.

     which I am trying, with the resources of an elementary topology, to valorise for you as regards what we can take from it at the level of our articulations

296. #296

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.264

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan argues that topology is not an optional supplement to psychoanalytic training but its very operative material, and uses the structural parallel between mathematical discourse (which speaks what it cannot name) and psychoanalytic discourse (which cannot name what it speaks about due to the irreducible unconscious) to re-ground the function of language, desire, and jouissance as the hidden field from which the subject withdraws its object.

     topology is the very stuff into which he cuts (taille), whether he knows it or does not know it, it does not matter whether he opens a book on topology or not, from the moment that he does psychoanalysis

297. #297

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.211

     **Seminar 18: Wednesday 18 May 1966**

     Theoretical move: The passage stages an intersection between Lacan's ongoing seminar work on projective geometry, the mirror, and subjectivity of vision, and Foucault's analysis of Las Meninas, using the painting as a shared object that allows Lacan to articulate how the structure of representation in the picture illuminates narcissism, the gaze, and fantasy—culminating in Green's suggestion that the picture's fascination-effect is tied to the primal scene and the structure of fantasy.

     the really essential form of modern geometry, remains not simply unknown by you but particularly opaque, and, of course, I was able to see the effect of this when I tried to bring you some of it by these figures, very simple and exemplary figures

298. #298

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.9

     **Seminar 2: Wednesday 8 December 1965**

     Theoretical move: Lacan grounds the symbolic order in the primacy of the hole (lack/void) over presence, arguing that the object of science, the vase as symbolic creation, and energetics all converge on the same structural point: what matters is not what fills the void but the void itself — a thesis that links the subject of science (Descartes/Frege) to the functioning of the signifier and forecloses any meta-language.

     with a very particular intention... the people who put them in the tombs made a hole in the centre. Which proves to you that it is indeed from the angle of the hole that you have to seek the material cause.

299. #299

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.15

     **Seminar 3: Wednesday 15 December 1965**

     Theoretical move: Lacan argues that topological figures (Klein bottle, projective plane, torus) and the function of the cut/writing are not mere intuitive aids but index the constitutive structural lack of the subject produced by the signifier — a lack whose diverse historical forms (negative number, imaginary number) are not reducible to intuitive impurity but to the signifier's constitution of the subject.

     these figures called the Klein bottle, the projective plane, the torus find themselves, as compared to what is the structure of our habitual co-ordinates of intuition, in such an upsetting position that it is really necessary to practice them

300. #300

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.246

     **Seminar 20: Wednesday 1 June 1966**

     Theoretical move: The passage argues that the structure of the subject necessarily bears the mark of a gap or wound that "full objectification" forecloses, and that the objet petit a—specifically as it appears in the scopic field and in oral/anal dialectics—is not the object of need-satisfaction but the cause of desire, which emerges only when the subject's demand is articulated in relation to the desire of the Other.

     the criteria of the structure in so far as they respond to these exigencies, given what is being tackled, namely, the structure of the subject

301. #301

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.197

     **Seminar 17: Wednesday 11 May 1966**

     Theoretical move: The passage advances the argument that the analyst's subjective division (the split between 'I think' and 'I am') is not merely a piece of knowledge but a structural position that must be inhabited in practice, and that the scopic perspective construction—particularly the horizon line and the dual vanishing points—serves as a geometric illustration of how the objet petit a functions within the divided subject's visual relationship to the world.

     There is a German edition... I recalled that, in the relationship which is described as projective which is established between the plane of what one could call the picture and the plane of what... we will call the ground plane (le sol perspective), there are fundamental linear correspondences

302. #302

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.205

     **Seminar 17: Wednesday 11 May 1966**

     Theoretical move: Lacan reads Velázquez's *Las Meninas* as a structural demonstration of the Vorstellungsrepräsentanz: the picture-within-the-picture does not represent but rather *presentifies* the window-space of the gaze, showing that what constitutes the picture in its essence is not representation but the capture of the looking subject (sujet regardant) — a topology that introduces the dialectic of the subject via the scopic drive.

     it is something quite striking whose value cannot, in my opinion, be mapped out except from what I introduced to you in this topological structure.

303. #303

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.65

     **Seminar 5: Wednesday 5 January 1966**

     Theoretical move: Lacan argues that the classical philosophical reduction of the body and the real to three-dimensional homogeneous (spherical) extension is a fundamental deception about the subject and knowledge; by drawing on topology (the sphere, the cut, the hole, the cylinder, the torus), he proposes that a two-dimensional, edge-based topological structure—rather than metric space—is the proper framework for articulating the divided subject and its inscription in the real.

     We do not hope to break through the rakia in three dimensions. Perhaps by being satisfied with two… let us try to grasp the frontier as being what is really the essence of our business.

304. #304

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.261

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan argues that the Hegelian master/slave dialectic fails to explain social cohesion, whereas Freud's account grounds it in the homosexual bond and the prohibition of feminine jouissance; this leads to a recasting of castration not as prohibition but as the operation by which the phallus receives a negative sign, enabling the (non-)relationship between masculine and feminine jouissance — a problem Lacan frames as requiring a logic of fantasy and introduces through three registers (imaginary/symbolic/real) oriented around negativity and torsion.

     this real bears witness to a certain torsion... This torsion is the very one that we are trying to grasp in our field

305. #305

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.267

     **Seminar 21: Wednesday 8 June 1966**

     Theoretical move: Lacan argues that the object of demand (the o-object as bodily appurtenance recovered from the field of the Other) must be distinguished from the object of jouissance, and that castration is properly understood not through the Oedipus myth of incest prohibition alone, but as the barrier that bars the subject from jouissance—a barrier that is desire itself—thereby exposing the Hegelian error of attributing jouissance to the master in the Master/Slave dialectic.

     how, with the look, there enters into play, still complete, a topology that I described and which cannot be gone back on, which is the one which justifies the existence of the screen

306. #306

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.182

     **Seminar 16: Wednesday 4 May 1966**

     Theoretical move: Lacan argues that topology — specifically projective geometry — provides a non-metaphorical, combinatorial foundation for situating the subject, replacing the classical unified-point subject (grounded in Cartesian extension/thought dualism) with a structural account in which the screen, signification, and the subject's relation to extension are all rigorously formalised without appeal to intuitive or metrical geometry.

     It is a matter, for us, of situating our topology; to situate ourselves, we analysts, as acting in it.

307. #307

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.186

     **Seminar 16: Wednesday 4 May 1966**

     Theoretical move: Lacan uses projective geometry—specifically the topology of the projective plane and its cross-cap representation—to argue that the structure of vision is not one of indefinite extension but of an "envelope" structure, and that this structure grounds the phantasy by producing both a loss (the gaze as lost object, objet petit a) and a division of the subject; perspective's horizon line is the visible sign of this topological knotting.

     What is involved in what are opposed as field of vision and as look precisely at the level of this topology?

308. #308

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.72

     **Seminar 6: Wednesday 12 January 1966**

     Theoretical move: Lacan argues that psychoanalytic theory, grounded in topology (the torus, then the Möbius strip), distinguishes itself from myth by demonstrating its scientific structure; simultaneously, the modern neurotic—as the subject of science—is constituted as the one in whom truth speaks, making psychoanalytic praxis the structural complement (though not of a homogeneous order) of the neurotic symptom.

     this is what is meant by the topological investigation which is the one that I am pursuing here, that I am taking up today, from the last time where I stopped it, on the structure of the torus

309. #309

     Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.152

     **Seminar 14: Wednesday 20 April 1966**

     Theoretical move: Lacan reads a condensed summary of Seminar XIII, arguing that the being of the subject is constituted as the suture of a lack grounded in the Fregean one/zero relation and the cogito's torsion, and that psychoanalysis alone—unlike philosophy or social critique—can genuinely confront the wound of this lack, precisely because the analyst's being is implicated in it as a being of knowledge encountering the symptom as a being of truth.

     it is the topology of this torsion that must be carried out... The divine bottle is the Klein bottle. Not everyone can make emerge from its neck what is in its lining.

310. #310

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.47

     the smallest whole number which is not written on this board > KLEIN GROUP

     Theoretical move: Lacan deploys the Klein group as a four-term topological structure to ground Metaphor and the logic of the Unconscious, arguing that the formula of metaphor (signifying substitution) shares the same structural cell as the Klein group, and that this structure supports the claim that there is no Universe of discourse — a formal condition for the subject of the unconscious that is co-extensive with, yet irreducible to, the Cartesian cogito.

     the functioning of a group structured in this way … which to function, as you see, can be satisfied with four elements, which are represented here on the network which supports it by the vertices

311. #311

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.131

     the smallest whole number which is not written on this board > acting-out

     Theoretical move: Lacan formalizes the sexual act through the harmonic "mean and extreme ratio" (golden ratio logic), mapping the relation between the subject (small o), the mother as unifying One (capital O), and castration (minus phi) as the fundamental lack structurally inscribed in any subjective realization of the sexual act — thereby grounding sublimation and acting-out as proportional variants within the same signifying quadrangle organized by repetition.

     Let us suppose that we are going to have this signifying relation supported by the simplest support, the one that we have already given to the double loop of repetition: a simple line.

312. #312

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.12

     **Seminar 1: Wednesday 16 November 1966**

     Theoretical move: Lacan argues that because no signifier can signify itself, language cannot constitute a closed set—there is no Universe of discourse—which defeats any 'reduced language' account of the unconscious and grounds the necessity of distinguishing the One (which repeats to establish itself) from totality, thereby locating the foundational lack constitutive of the subject.

     requires us, at the origin, to distinguish very severely… the One from the totality… to distinguish this One from the countable One

313. #313

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.16

     the smallest whole number which is not written on this board

     Theoretical move: Lacan advances the axiom that "no signifier can signify itself" as the founding structural principle of the Universe of discourse, and demonstrates—through a self-referential paradox of writing—that this axiom introduces a constitutive gap or exclusion within that very Universe, raising the question of whether what the axiom specifies can itself be said.

     let us take arbitrarily the usage of a little sign which serves in this logic which is founded on writing, this W in which you will recognise the shape… of my diamond, in a way with its hat knocked off… which serves, this W, to designate, in the logic of sets, exclusion.

314. #314

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.129

     the smallest whole number which is not written on this board > acting-out

     Theoretical move: Lacan positions sublimation as the fourth term in a structural table alongside repetition, passage à l'acte, and acting-out, arguing that sublimation — defined via Freud's *zielgehemmt* — is the conceptual locus for understanding the satisfaction (*Befriedigung*) that underwrites repetition, while simultaneously critiquing ego-psychology's (Hartmann's) energetics framework for inverting and obscuring this problem; he then anchors sublimation's solution in the proposition that the act is a signifier, with the sexual act as the paradigmatic case whose repetition traces the oedipal scene.

     a signifier which is repeated, even though it happens in a single gesture, for topological reasons which make possible the existence of the double loop created by a single cut

315. #315

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.180

     the smallest whole number which is not written on this board > **Seminar 17: Wednesday 19 April 1967**

     Theoretical move: Lacan uses the golden ratio (φ) as a mathematical support to argue that sublimation cannot close the gap between even and odd power series—between the sexes—thereby demonstrating that there is no sexual relation at the level of the signifier, and condemning the psychoanalytic myth of primary narcissism/fusion as the foundation of libidinal economy.

     the incommensurable which circumscribes least quickly the intervals in which it can be localised … the one which demands most operations

316. #316

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.107

     the smallest whole number which is not written on this board > **Seminar 10: Wednesday 1 February 1967**

     Theoretical move: Lacan uses the formula *cogito ergo Es* to reframe the Freudian *Es* (Id) not as a variant ego but as a function grounded in the barred Other, arguing that the real Freudian discovery is an *object* (not a thought-system) whose status is identical with structure insofar as structure is real — illustrated topologically by the Möbius strip transforming into a torus.

     you will recognise once again the Moebius strip, the Moebius cut in two in so far as this does not divide it… to obtain this something which is perfectly closed, which has an inside and an outside and which is the fourth figure, which is here that of a torus.

317. #317

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.179

     the smallest whole number which is not written on this board > **Seminar 17: Wednesday 19 April 1967**

     Theoretical move: Lacan argues that jouissance-value—not truth—is the primary currency of the unconscious economy and of any discourse, including analytic discourse; this reframes the relation between truth, the unconscious, and the analyst's desire, while grounding the objet petit a topologically as the "setting" of the subject produced by the cut of repetition in the projective plane.

     the cut of the double loop, in this tiny mental object that is called the projective plane, cuts these two elements which are, respectively, the Moebius strip which, for us, figures as a support of the subject, and the ring which necessarily remains.

318. #318

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.77

     the smallest whole number which is not written on this board > **Seminar 7: Wednesday 11 January 1967**

     Theoretical move: The passage advances a structural account of the subject's division by mapping the Id (as grammatical/thinking structure) against the Unconscious (as non-existence, the 'I am not'), showing how these two fields do not overlap but rather eclipse each other—and that their intersection is mediated by the objet petit a, which emerges as the operator of alienation, while castration is recast as the failure of any Bedeutung to cover sexual difference.

     If the two circles, the two fields that we have opposed as representing the two terms … these two terms are opposed as constituting different relationships of the I in thinking and existence

319. #319

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.114

     the smallest whole number which is not written on this board > **Seminar 11: Wednesday 15 February 1967**

     Theoretical move: Lacan argues that analytic knowledge "passes into the real" via the same mechanism as Verwerfung (foreclosure): what is rejected in the symbolic reappears in the real. He then grounds this in a rigorous reading of Freudian repetition (Wiederholungszwang), demonstrating that repetition is irreducible to the pleasure principle, necessarily entails a lost object, and constitutes the subject through a retroactive, non-reflexive logical structure rather than a simple return to sameness.

     The graph - as one might say - of this function, I think that you all have seen passing the shape that I gave as an intuitive, imaginative support of this topology of return

320. #320

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.102

     the smallest whole number which is not written on this board > **Seminar 9: Wednesday 25 January 1967**

     Theoretical move: Lacan uses Freud's meta-commentary on dream-function (the preconscious desire to sleep, "it is only a dream") and the Zhuangzi butterfly-dream to argue that the I is structurally constituted as a *stain* in the visual field—inseparable from the gaze/objet petit a—and that topology is the only rigorous framework for articulating the o-object's relationship to the subject's loss and repetition.

     it is because this field has a structure, let us say: what we have already put forward under the term of *topology*.

321. #321

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.21

     the smallest whole number which is not written on this board > A B C D.

     Theoretical move: Lacan uses the logical paradox of the catalogue-of-catalogues (Russell's paradox) to demonstrate that the closure of any signifying chain necessarily generates an 'additional One' (Un en plus) — an uncountable surplus signifier that is nowhere in the chain yet designates the chain as a whole. This structure, illustrated through topology (the torus), the biblical Mene-Tekel-Parsin, and Mallarmé's absolute Book, grounds Lacan's theory of repetition: what repetition seeks is precisely what the mark effaces, because the first mark cannot be reduplicated without losing what it originally marked.

     what you find of it, for example, in the structure of the torus, being quite obvious that by buckling on the torus a certain number of circuits... there appearing at the same time this third required for these two to buckle together

322. #322

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.139

     the smallest whole number which is not written on this board > **Seminar 13: Wednesday 1 March 1967**

     Theoretical move: Lacan uses the golden number (φ, "small o") and the mathematics of the mean and extreme ratio to theorise the sexual relation: the subject enters genital union as a "product" (objet petit a), and the irreducible remainder generated by the division of the subject by the Other (the small o that cannot be eliminated) both limits jouissance and founds the "phantom of the gift" that constitutes feminine love.

     the remarkable properties of this small o … the mean and extreme ratio … allow us to comprehend something about what is involved in genital satisfaction

323. #323

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.31

     the smallest whole number which is not written on this board > **Seminar 4: Wednesday 7 December 1966**

     Theoretical move: Lacan uses Miller's Boole-derived formalization (centered on the elision of the self-signifying signifier, figured as (-1)) as a confirmatory framework for grounding the logic of fantasy, while insisting that psychoanalytic interpretation operates on the structure of a network/lattice—not subject to the "ex falso sequitur quod libet" objection—and that the criterion of truth is irreducible to reality, as demonstrated by the Wolfman case where truth is verified through the symptom as a signifying articulation.

     the function of sets … what is centred on the function of sets

324. #324

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.46

     the smallest whole number which is not written on this board > **Seminar 5: Wednesday 14 December 1966**

     Theoretical move: Lacan uses the question "what links the Écrits?" to argue that the thread running through his work is the critique of the formula "Me, I am me" — the illusion of self-identical ego — and then pivots to introduce the Klein group as a structural (rather than identificatory) framework for approaching the subject, showing that structure, not intuitive ego-identity, is the proper ground for psychoanalytic questions.

     It is the same Klein that I mentioned in connection with the bottle, called by that name.

325. #325

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.153

     the smallest whole number which is not written on this board > **Seminar 14: Wednesday 8 March 1967**

     Theoretical move: Lacan introduces acting-out as the structural representative of the deficient representation of the psychoanalytic act: because the analytic intervention misreads or inadequately articulates what is at stake (as in Kris's ego-psychological "surface" intervention), the patient enacts/stages what was not properly interpreted, bringing the oral object-a "on a plate." This positions acting-out as the inverse shadow of the analytic act, and advances the argument that the psychoanalytic act is structurally non-sexual yet topologically related to the sexual act via the analytic couch.

     In the topological order, there is something I have noticed, but it is really a problem: that the myths make very little of it. And, nevertheless, the bed is something that has to do with the sexual act.

326. #326

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.255

     the smallest whole number which is not written on this board > **Seminar 23: Wednesday 14 June 1967**

     Theoretical move: Lacan argues that perversion is structurally intelligible as the attempt to reconnect jouissance and the body that have been disjuncted by the signifying intervention constitutive of the subject, with the objet petit a (small o) serving as the topological and structural key to this reconnection, while the sadistic act paradigmatically illustrates how the perverse subject, in Verleugnung, becomes the instrument of a jouissance located in the Other rather than knowing itself as the subject of that jouissance.

     I chose this little model … this little model of incommensurable division par excellence, of this small o… which is defined by the One over o equals One plus o

327. #327

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.235

     the smallest whole number which is not written on this board > **Seminar 21: Wednesday 31 May 1967**

     Theoretical move: The passage argues that jouissance as a third function is topologically located at the locus of objet petit a, and that perversion—unlike neurosis or the master/slave dialectic—constitutes an experimental, subject-driven inquiry into jouissance by seeking the partial objects that escape signifying alienation; sadism and masochism are reframed as researches along the path of the sexual act rather than natural gender attributes.

     It is precisely through this that we are given the locus, the topology of what is involved in jouissance.

328. #328

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.115

     the smallest whole number which is not written on this board > **Seminar 11: Wednesday 15 February 1967**

     Theoretical move: Lacan argues that the topological figure of the double loop (inverted eight/Möbius strip) provides the structural model for both repetition and alienation, showing how the "additional One" (Un-en-plus) generated by the retroactive return of repetition fractures the Other and the subject alike, and that the act emerges precisely at the point where the passage à l'acte of alienation and repetition intersect on these non-orientable surfaces.

     Note that this is the most radical topological form and that it is necessary to introduce what, in Freud, is put forward in these polymorphous forms that are known under the term of regression

329. #329

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.137

     the smallest whole number which is not written on this board > **Seminar 13: Wednesday 1 March 1967**

     Theoretical move: Lacan introduces the "mean and extreme ratio" (golden ratio) as the mathematical model for the structure of the sexual relation, arguing that subjective satisfaction in the sexual act cannot be grounded in homeostatic/pleasure-principle models nor in complementarity (key-and-lock), but requires a third term (phallus/castration, child-phallus equivalence) whose structural logic is captured by this uniquely determined, incommensurable proportion—linking repetition, the division of the Other, and the problem of the object.

     the relation which posits, at the start, the equality of the relation of the smaller to the larger - the equality, I am saying, of this relation - to the relation of the larger to the sum of the two.

330. #330

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.121

     the smallest whole number which is not written on this board > **Seminar 11: Wednesday 15 February 1967**

     Theoretical move: The Act is defined not as motor discharge but as the intrinsic repetition of the signifier upon itself—a double loop that constitutes the subject as pure division; its effects are measured topologically by the mutation of surface produced by the cut, and Verleugnung is specifically identified as the rubric for the ambiguity that results from these effects.

     what results from the act in terms of change of surface … if after the act, the surface is of a different structure in such a case … here is something that is going to propose for us models to distinguish what is involved in terms of the incidence of the act … in the mutations of the subject.

331. #331

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.210

     the smallest whole number which is not written on this board > **Seminar 19: Wednesday 10 May 1967**

     Theoretical move: Lacan argues that the sexual act constitutes the founding impossibility (the "holed One") from which all truth, symptom, and signification emerge, while identifying the big Other not with spirit but with the body as the primary site of inscription — thereby grounding the Symbolic in a Real that cannot be formally proved.

     in the way in which I symbolise it when I make it operate on what is called 'the projective plane', I am claiming not to *construct a metaphor*, but, properly speaking, to speak about *the real support* of what is involved

332. #332

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.158

     the smallest whole number which is not written on this board > **Seminar 14: Wednesday 8 March 1967**

     Theoretical move: Lacan uses the golden number (mean and extreme ratio) as a matheme to distinguish the sexual act—where lack is structurally elided—from sublimation, which starts from lack, reproduces it iteratively, and arrives at a final cut strictly equal to the initiating lack; Fantasy ($ ◇ a) is then re-situated as the relation between objet a and the barred subject in the field of sexual satisfaction.

     someone who asked to intervene about what I put forward at least since the beginning of the month of January, about this topology, the one which comprises the four terms of alienation as well as those of repetition

333. #333

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.215

     the smallest whole number which is not written on this board > **Seminar 19: Wednesday 10 May 1967**

     Theoretical move: The passage argues that the subject is constituted precisely as the cut between the field of the One and the field of the Other (the unconscious), with topology—surface defined by its edge, volume defined by its cutting—providing the structural model; the Other is ultimately revealed to be the Other of objet petit a, whose incommensurability generates every question of measure.

     There is, as regards the signifier, namely, for the structure, no other support - of a surface, for example - than the hole that it constitutes by its edge… There is no other support for the body than the sharp edge that presides over its cutting up. These are topological truths.

334. #334

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.6

     **Seminar 1: Wednesday 16 November 1966**

     Theoretical move: The passage argues that the subject originates through the cut — topologically modeled on the cross-cap/projective plane — whereby the o-object is separated and Urverdrängung (primal repression) is defined as what a signifier represents for another signifier; the barred subject emerges only in alienated form, and desire is re-formulated not as the essence of man but as the essence of reality, displacing Spinoza's anthropology into a strictly structural, a-theological account.

     Everything that refers - in the surfaces that I talked about before you, in a series going from the projective plan to the Klein bottle - to what one could call extrinsic properties… are not properties of the surfaces: it is in a third dimension that they take on their function.

335. #335

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.170

     the smallest whole number which is not written on this board > **Seminar 16: Wednesday 12 April 1967**

     Theoretical move: Lacan argues that the absence of the sexual act is not a secret but a structural necessity announced by the unconscious itself, and that the Objet petit a — formalized as the "golden number" — functions as the incommensurable third term that both generates the sexual dyad and prevents its closure, articulating the impossibility of the sexual relationship through logical and mathematical formalization (Boolean algebra, imaginary numbers, the golden number).

     If we want to inscribe in a proper way this one and the other in the form of the intersection of Boole's algebra, this means this little lune of spatial overlapping.

336. #336

     Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.196

     the smallest whole number which is not written on this board > **Seminar 17: Wednesday 19 April 1967**

     Theoretical move: Lacan advances the thesis that there is no sexual relation by showing that the field between the small o (objet petit a) and the big Other is structured as a hole — not a unifying One — and that identification (ego ideal/ideal ego) operates in this gap; the Oedipus myth is then mobilised to demonstrate that jouissance itself is constitutively bound to rottenness and the hole, not to any unitive fullness.

     I drew two lines: one dotted and then continuous, drawn simply to mark that the small o is equal in the first part to the external small o, and that there is this remainder of o2

337. #337

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.102

     the smallest whole number which is not written on this board > **Seminar 9: Wednesday 25 January 1967**

     Theoretical move: Lacan uses Freud's theory of the preconscious as the agency that 'knows' one is asleep—and Zhuangzi's butterfly dream—to argue that the 'I am only dreaming' move masks the reality of the gaze, establishing the Objet petit a (as gaze/stain) as constitutively correlated with the I, and positioning topology as the rigorous framework for articulating the o-object's structure via cutting operations on surfaces.

     this field has a structure, let us say: what we have already put forward under the term of topology… it is in so far as we will come to articulate in it certain effects of cutting that we will know something about these vanishing points that we can describe as little o-objects

338. #338

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.276

     the smallest whole number which is not written on this board > **Seminar 24: Wednesday 21 June 1967**

     Theoretical move: Lacan distinguishes the function of fantasy in neurosis from its function in perversion by mapping clinical structures onto spatial metaphors (bedroom, toilet, boudoir, wardrobe, parlour, bog, analyst's office), culminating in the claim that the analyst's office is the site where the sexual act is presented as foreclosure (Verwerfung), thereby anticipating the seminar on the psychoanalytic act.

     these questions of the arrangements of logic are very important

339. #339

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.153

     the smallest whole number which is not written on this board > **Seminar 14: Wednesday 8 March 1967**

     Theoretical move: By introducing the concept of acting-out via the Kris case and the English etymology of 'to act out', Lacan argues that acting-out is a response to an inadequate or failed analytic intervention—specifically, a deficient representation of the psychoanalytic act itself—thereby linking the structure of acting-out to the inexact position of the analytic act relative to repression and the symptom.

     In the topological order, there is something I have noticed, but it is really a problem: that the myths make very little of it. And, nevertheless, the bed is something that has to do with the sexual act.

340. #340

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.47

     the smallest whole number which is not written on this board > KLEIN GROUP

     Theoretical move: Lacan argues that the Klein group's four-term structure provides the formal skeleton for both the metaphor/repression formula and the unconscious-as-language thesis, and that S(Ø)—the signifier of the barred Other—marks the constitutive 'One too many' that replaces the absent Universe of discourse, linking the logical structure of the subject to the Cartesian cogito.

     If we start again from structure… the functioning of a group structured in this way… which to function, as you see, can be satisfied with four elements… Note that there is no difference between this figure and the one that I sketch in here rapidly

341. #341

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.21

     the smallest whole number which is not written on this board > A B C D.

     Theoretical move: Lacan uses set-theoretic paradoxes (Russell, catalogue of catalogues) and topological structures (torus, edge) to argue that the closure of a signifying chain necessarily generates an "additional One" (Un en plus) — a surplus signifier that is uncountable within the chain yet constitutes the very condition of repetition, lack, and writing; this is then grounded in the Mene Tekel Parsin narrative as an archaic theory of the subject.

     what you find of it, for example, in the structure of the torus, being quite obvious that by buckling on the torus a certain number of circuits... It is enough to make two of them to see there appearing at the same time this third required for these two to buckle together

342. #342

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.146

     the smallest whole number which is not written on this board > **Seminar 14: Wednesday 8 March 1967**

     Theoretical move: Lacan argues that psychoanalytic theory systematically effaces the structural character of the sexual act as a *cut* (an act in the strong sense), substituting a discourse of relational adequacy ('genital stage', 'tenderness') that evades the irreducible discordance and failure built into that act; he introduces the 'psychoanalytic act' as a distinct concept requiring its own structural formalization, in contrast to—and as a corrective upon—the sexual act it takes as its reference point.

     the ternarity that was provided for me by the proportion of the golden number... I extract, believe me, all the same, not without knowing the ramifications of what I am using in the totality of mathematical theory

343. #343

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.5

     **Seminar 1: Wednesday 16 November 1966**

     Theoretical move: Lacan opens Seminar XIV by introducing "the logic of phantasy" as a formal project: the matheme $◇a is posed as a logical relation between the barred subject and the objet petit a, with the diamond (poinçon) encoding biconditional implication (if and only if), and fantasy's structural surface—identified as desire and reality in seamless continuity—is topologically modeled via the cross-cap and Möbius strip, displacing the imaginary register in favor of a properly logical determination.

     Let us call them the bubble and we will see what motivates, to what the existence of bubbles is attached in the real. This surface which I call bubble has properly speaking two names: desire and reality.

344. #344

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.114

     the smallest whole number which is not written on this board > **Seminar 11: Wednesday 15 February 1967**

     Theoretical move: Lacan argues that the Freudian Wiederholungszwang constitutes the logical foundation of the subject, irreducible to the pleasure principle, by demonstrating that repetition produces a lost object retroactively—the originating situation is lost as origin by the very fact of being repeated—and that this structure, grounded in the unary trait, is what allows analytic knowledge to pass into the real via Verwerfung.

     the shape that I gave as an intuitive, imaginative support of this topology of return, for it to solidify the part … namely, its retroactive effect

345. #345

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.16

     the smallest whole number which is not written on this board

     Theoretical move: Lacan deploys the paradox of self-reference (the smallest whole number not written on the board) to establish a foundational axiom for his theory of the signifier: that no signifier can signify itself. This axiom, when introduced into the Universe of discourse, generates a structural gap — a specification that simultaneously belongs to and threatens to exceed the totality of what can be said — linking the logic of writing, the Graph of Desire, and the structure of the unconscious as language.

     this W in which you will recognise the shape (these games are not perhaps purely accidental) of my diamond, in a way with its hat knocked off, that has been opened up like a little box, and which serves, this W, to designate, in the logic of sets, exclusion.

346. #346

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.137

     the smallest whole number which is not written on this board > **Seminar 13: Wednesday 1 March 1967**

     Theoretical move: Lacan argues that the sexual act cannot be modeled on organic satisfaction or simple complementarity (key/lock), but requires a structural, mathematical account of the "measure and proportion" implicit in repetition — introducing the Golden Ratio (mean and extreme ratio) as the formal analogue for the third element (phallus/castration) that structures the sexual relation, linking this to the incommensurable and to objet petit a.

     I remind you that this anharmonic relation was something we already had to evoke last year as fundamental to any structure described as projective

347. #347

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.45

     the smallest whole number which is not written on this board > **Seminar 5: Wednesday 14 December 1966**

     Theoretical move: Lacan uses the "Me, I am me" formula as the unifying thread of the Écrits—from the Mirror Stage to the Subversion of the Subject—to argue that naive ego-identity (moi = moi) is the obstacle to psychoanalytic inquiry, and then pivots to the Klein group as a formal structure that can approach questions of identity and negation from outside the field of intuitive identification.

     I am going to make for you here the schema of what is called a group … the Klein group, in as much as it is a group defined by a certain number of operations.

348. #348

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.139

     the smallest whole number which is not written on this board > **Seminar 13: Wednesday 1 March 1967**

     Theoretical move: Lacan deploys the mathematical structure of the golden ratio (objet petit a as mean and extreme ratio) to theorize sexual difference and genital satisfaction: the irreducible remainder (small o / objet petit a) produced in the subject's confrontation with the maternal unity of "one flesh" is what structures jouissance, phallus, and love as the gift of what one does not have — with detumescence as the illusory elimination of remainder, and feminine love as causa sui arising from giving what one lacks.

     I am indeed obliged, for the sake of honesty, to say that this small o relation is what is called the golden number … Let us see now some of the remarkable properties of this small o

349. #349

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.12

     **Seminar 1: Wednesday 16 November 1966**

     Theoretical move: Lacan argues that the unconscious cannot be reduced to a "language of reduced language" (analogy-based metaphor) because no signifier can signify itself, which entails—via Russell's paradox / set-theoretic axiom of specification—that there is no closed universe of discourse, and that the One of the subject must be distinguished from countable totality, grounding the constitutive lack of the subject.

     requires us, at the origin, to distinguish very severely… the One from the totality… to distinguish this One from the countable One

350. #350

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.121

     the smallest whole number which is not written on this board > **Seminar 11: Wednesday 15 February 1967**

     Theoretical move: The passage defines the Act as structurally equivalent to repetition-in-a-single-stroke (the double loop of the signifier), grounded in the topology of the Möbius strip cut; it argues that the act constitutes the subject as pure division (Repräsentanz), and that Verleugnung names the ambiguity produced by the act's effects, distinguishing the act from mere motor performance, imitation, and acting-out.

     what results from the act in terms of change of surface ... if after the act, the surface is of a different structure in such a case, if it is of a still different structure in another one or even if in certain cases it may not change

351. #351

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.180

     the smallest whole number which is not written on this board > **Seminar 17: Wednesday 19 April 1967**

     Theoretical move: Lacan uses the golden number (φ) as a mathematical support to argue that sublimation cannot achieve a perfect 'One' or sexual relation—a gap always remains between even and odd power series—and then leverages this to attack the psychoanalytic myth of primary narcissism and the 'unitive' fantasy, asserting that the subject is 'measured by sex' as by a unit, not fused with it, and that no analytic sense can be given to 'masculine' or 'feminine' as signifiers.

     I already indicated to you as I could, for want of being able to give you - this would certainly take us too far - the most modern and the strictest mathematical theory of it

352. #352

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.77

     the smallest whole number which is not written on this board > **Seminar 7: Wednesday 11 January 1967**

     Theoretical move: Lacan articulates the structural relationship between the Id (Es) and the unconscious as two non-overlapping fields defined by complementary negations ("I am not thinking" and "I am not"), arguing that their mutual eclipsing produces, on one side, the o-object as the truth of alienation's structure, and on the other, castration as the incapacity of any Bedeutung to cover sexual difference—with the drive's grammatical montage (as read through "A Child is Being Beaten") serving as the hinge for this demonstration.

     If the two circles, the two fields that we have opposed as representing the two terms... these two terms are opposed as constituting different relationships of the I in thinking and existence, it is because when one looks more closely at the circles in which this has now been circumscribed

353. #353

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.6

     **Seminar 1: Wednesday 16 November 1966**

     Theoretical move: Through topological figures (cross-cap, projective plane) and set-theoretic logic (Euler circles), Lacan argues that the subject originates not as a pre-given entity but is *engendered* by the signifier through a primary cut; the objet petit a is the first "Bedeutung" — the residue of the subject's alienation from the Other — and desire is redefined as the essence of *reality* rather than of man, displacing Spinoza's formula into a properly psychoanalytic, a-theological one.

     Everything that refers - in the surfaces that I talked about before you, in a series going from the projective plan to the Klein bottle - to what one could call extrinsic properties… most of what seems most evident to you when I image these surfaces, are not properties of the surfaces: it is in a third dimension that they take on their function.

354. #354

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.170

     the smallest whole number which is not written on this board > **Seminar 16: Wednesday 12 April 1967**

     Theoretical move: Lacan argues that the absence of the sexual act is not a secret but an open cry of the unconscious, and develops this through the mathematical-logical structure of Objet petit a as the "golden number" — showing that in the sexual dyad, the difference (small o) cannot resolve into a dyad but rather loops back to produce o itself, thereby formalizing why a third term (the phallus/partial object) is always required and the sexual act structurally fails to unite the sexed subjects.

     If we want to inscribe in a proper way this one and the other in the form of the intersection of Boole's algebra, this means this little lune of spatial overlapping.

355. #355

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.179

     the smallest whole number which is not written on this board > **Seminar 17: Wednesday 19 April 1967**

     Theoretical move: Lacan argues that jouissance-value is the foundational economy of the unconscious, and that the unconscious speaks of sex without necessarily saying the truth about it — establishing a structural gap between speaking and saying that conditions the analyst's position and explains the psychoanalyst's constitutive resistance to his own discourse.

     the cut of the double loop, in this tiny mental object that is called the *projective plane*, cuts these two elements which are, respectively, the Moebius strip which, for us, figures as a support of the subject, and the ring which necessarily remains of it

356. #356

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.255

     the smallest whole number which is not written on this board > **Seminar 23: Wednesday 14 June 1967**

     Theoretical move: Lacan deploys the golden-ratio schema of objet petit a to articulate how perversion attempts to reconnect the body and jouissance that the signifying intervention (the subject-function) necessarily disjoins — with the sadist as the exemplary figure who, in Verleugnung, becomes the instrument of jouissance rather than its master, ultimately revealing that jouissance can only be located in the 'outside-the-body' part that is the o-object.

     A schema which it would be easy to show - even though in a purely metaphorical fashion - can represent rather well what, in the sexual act can be presented for us

357. #357

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.129

     the smallest whole number which is not written on this board > acting-out

     Theoretical move: Lacan installs sublimation as the fourth term of a structural quartet (alongside repetition, passage à l'acte, and acting-out), arguing that sublimation names the locus of fundamental satisfaction (Befriedigung) internal to repetition, and that the act is constitutively signifying—a repeating signifier that establishes and restructures the subject, with the sexual act exemplifying this structure by repeating the Oedipal scene.

     It is a signifier which is repeated, even though it happens in a single gesture, for topological reasons which make possible the existence of the double loop created by a single cut.

358. #358

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.235

     the smallest whole number which is not written on this board > **Seminar 21: Wednesday 31 May 1967**

     Theoretical move: Lacan argues that jouissance as a third function is topologically located at the locus of objet petit a — the partial objects that escape signifying domination — and uses the master/slave dialectic to demonstrate that jouissance subsists on the side of the slave, not the master; perversion is then recast as a systematic, subject-driven inquiry into this residual jouissance of the Other, while sadism and masochism are reframed as researches along the path of the sexual relation rather than natural gendered dispositions.

     It is precisely through this that we are given the locus, the topology of what is involved in jouissance.

359. #359

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.215

     the smallest whole number which is not written on this board > **Seminar 19: Wednesday 10 May 1967**

     Theoretical move: The passage argues that the subject is constituted precisely by the gap between the field of the One and the field of the Other (the unconscious), such that the subject is always a structural degree below its body; this topological account displaces both Eros-as-unity fantasies and Cartesian soul/body dualism, and repositions objet petit a (small o) as the incommensurable origin from which all questions of measure arise.

     It is enough to reflect on the fact that there is... as regards the signifier, namely, for the structure, no other support - of a surface, for example - than the hole that it constitutes by its edge... every possible development of what is called an algebra of edges, requires the following.

360. #360

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.115

     the smallest whole number which is not written on this board > **Seminar 11: Wednesday 15 February 1967**

     Theoretical move: The passage establishes that the topological figure of the double loop (inverted eight) is the structural ground of both repetition and alienation, and uses this topology to argue that the Other is inherently "fractured" (barred), that the subject's division is ineradicable from truth, and that the Act emerges as the logical consequence of alienation's passage through the topology of repetition.

     this is the most radical topological form... it cannot have its function as edge on just any surface whatsoever

361. #361

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.210

     the smallest whole number which is not written on this board > **Seminar 19: Wednesday 10 May 1967**

     Theoretical move: Lacan argues that the sexual act is constitutively impossible (there is no sexual act), yet it remains the sole ground of truth; the symptom is the knot at the hole of the 'One', the Other is identified with the body as the primordial locus of inscription, and all truth—including ideology and perception—is structured by this foundational gap.

     in the way in which I symbolise it when I make it operate on what is called 'the projective plane', I am claiming not to construct a metaphor, but, properly speaking, to speak about *the real support* of what is involved.

362. #362

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.131

     the smallest whole number which is not written on this board > acting-out

     Theoretical move: Lacan deploys the harmonic (mean and extreme) ratio — anchored in the Phallus as signifier — to formalise the sexual act's relation to repetition, castration, and subjective lack, then uses this quadrangular proportion to position passage à l'acte, acting-out, sublimation, and repetition in structural relation to one another and to the analytic act.

     the double loop of repetition: a simple line … Let us place on it the four points (points of origin), of two other cuts that define the mean and extreme ratio.

363. #363

     Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.107

     the smallest whole number which is not written on this board > **Seminar 10: Wednesday 1 February 1967**

     Theoretical move: Lacan uses an interrupted seminar session (deferred by a strike and Jakobson's presence) to sketch the theoretical stakes of the year's work on the *Logic of the Fantasy*: the Es/Unconscious cannot be substantified as an "outlaw ego"; its proper status must be derived from the barred Other as locus of speech, while topology (Möbius strip → torus) is introduced as a demonstration that structure is real, not metaphorical—culminating in the question of what authorises a teaching addressed to analysts who do not yet exist.

     you will recognise once again the Moebius strip, the Moebius cut in two in so far as this does not divide it... to obtain this something which is perfectly closed, which has an inside and an outside and which is the fourth figure, which is here that of a torus. **The structure is something which is like that - is real.**

364. #364

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.200

     **Annex 3**

     Theoretical move: Lacan's annex summary argues that the psychoanalytic act is the pivotal moment of passage from analysand to analyst, structurally constituted by the objet petit a, and that this act—which dismisses the very subject it establishes—grounds an ethics of jouissance, exposes the fault in the subject supposed to know, and requires that there is no Other of the Other (no metalanguage) as the condition for a consistent theory of the unconscious.

     it can be deduced that he operates by not thinking... by situating his act in the ideal topology of the o-object

365. #365

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.87

     **THE SEMINAR OF JACQUES LACAN** > **Seminar** 7: **Wednesday 24 January 1968**

     Theoretical move: Lacan uses the tetrahedron of alienation (the "either/or," "I am not/I do not think," etc.) to articulate the structure of the psychoanalytic act, arguing that the analyst's unique advantage is knowing from experience what is involved in the Subject Supposed to Know, and that the telos of the analytic act is to reduce that subject to the function of the objet petit a.

     In this little tetrahedron which we have started from these last times, something all the same must be quite tangible in it: the multiplicity of translations that it [offers]

366. #366

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.47

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 4: Wednesday 6 December 1967**

     Theoretical move: Lacan uses the triad "I read / I write / I lose" to differentiate three levels of knowing and to position the psychoanalytic act as structured around failure and parapraxis, arguing that the analyst's act is irreducible to teaching (thesis) or doing (faire), and that the passage from analysand to analyst marks the critical, untheorised limit at which the act encounters its own obstacle.

     this is properly to sketch out a topology that can be expressed as follows. That by simply sketching its way out, one enters into it without even thinking.

367. #367

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.192

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > *Lecture of 19th June. 1968*

     Theoretical move: Lacan uses the "events" of May '68 as occasion to articulate the structural relation between the Other as locus of knowledge, truth as what is refused from the symbolic and returns in the real as symptom, and the subject's secondary determination by knowledge — positioning psychoanalysis as a radical modification of the subject-Other relation that goes beyond mere discovery.

     it is a quite indispensable topological function to bring out the radical and logical structure that is at stake in what I called earlier this knot or this bubble, this hollow in the world

368. #368

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.79

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 4: Wednesday 6 December 1967** > **Seminar 5: Wednesday 10 January 1968.** > **Seminar 6: Wednesday 17 January 1968**

     Theoretical move: Lacan argues that the psychoanalytic act is structurally grounded in the analyst's prior traversal of analysis, whereby the analyst's *désêtre*—his shedding of the Subject Supposed to Know—positions him as pure support for the objet petit a, and that this logic illuminates the status of every act, distinguishing the Freudian dialectic of enjoyment from both Cartesian and Hegelian suspensions of knowledge.

     it is necessary to see by a rotation, or a tipping over, to a certain number of degrees, as this figure is drawn, by 180° in order to see passing, coming back what has been realised here to the starting position

369. #369

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.159

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > **Seminar 13: Wednesday 13 March 1968** > **Seminar 14: Wednesday 20 March 1968**

     Theoretical move: Lacan argues that the not-all logic of the unconscious prevents any totalisation of psychoanalytic knowledge, and that the psychoanalyst's proper position is defined not by mastery-knowledge but by occupying the place of the objet petit a — cause of desire and object of demand — a position exemplified through the Gaze as the most occluded partial drive in clinical practice.

     there appears there this closed structure, starting from which I was able to try to isolate, to define for you amongst all the others... the function of the little o-object called the look.

370. #370

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.188

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > *Lecture of 19th June. 1968*

     Theoretical move: Lacan reflects ceremonially on the interrupted Seminar on the psychoanalytic act, arguing that the act's constitutive paradox—that the analyst must operate from a position that gives the lie to their own position—requires the concept of Verleugnung (fetishistic disavowal) rather than Verwerfung (foreclosure), while also registering the political events of May 1968 as an index of a structural gap in the universe of knowledge.

     the famous internal eight that I have been producing for some eight years... this little knot (see the scheme) that is constructed in a certain way by cutting into a certain bubble

371. #371

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.95

     **THE SEMINAR OF JACQUES LACAN** > **Seminar** 7: **Wednesday 24 January 1968**

     Theoretical move: Lacan distinguishes the act from the doing in order to locate the analyst's position as a specific structural function: psychoanalytic practice, as a doing of pure speech, approaches the act through the 'signifier in act', and the analyst must occupy this corner of the barred subject supposed to know precisely by absenting himself from the doing—a structural self-effacement that risks collapsing into a 'hypochondriacal jouissance' if theorised away as mere equidistance from all schools.

     whether one expresses things in terms of instinct, of behaviour, of genesis, of Lacanian topology. All of that, we should find ourselves equidistant from this sort of discussion.

372. #372

     Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.52

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 4: Wednesday 6 December 1967**

     Theoretical move: Lacan uses a triangular mapping of the Symbolic, Imaginary, and Real as cardinal poles to locate the Barred Subject, the unary stroke (first Identification), and the objet petit a, arguing that Truth belongs to the Other/Symbolic, Jouissance to the Real, and Knowledge to the Imaginary—positioning the analyst in the void between them. He then reads Winnicott's transitional object as an inadvertent, incomplete articulation of the objet petit a, showing how object-relations theory approaches but fails to theorize the subject commanded by that object.

     why not put the barred Subject like a projection onto the other side? This will allow there to be asked what is involved in the relation of the Subject between the Imaginary and the Real.

373. #373

     Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.159

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > **Seminar 13: Wednesday 13 March 1968** > **Seminar 14: Wednesday 20 March 1968**

     Theoretical move: Lacan argues that the "not-all" logic of quantification—applied to the proposition "not all knowledge is conscious"—does not entail the existence of a positive unconscious knowledge; instead, the analyst's proper position is determined by their identification with the objet petit a (as cause of desire and object of demand), and each register of this object (gaze, voice, breast, anal) carries an immunity to negation that grounds the psychoanalytic act.

     there appears there this closed structure, starting from which I was able to try to isolate...the function of the little o-object called the look...perspective comes into its proper structure with Dessargue. Namely, when it establishes this other definition of space called projective geometry.

374. #374

     Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.87

     **THE SEMINAR OF JACQUES LACAN** > **Seminar** 7: **Wednesday 24 January 1968**

     Theoretical move: The psychoanalytic act is structurally defined through the tetrahedron of alienation (the forced choice between "I do not think" and "I am not"), and the analyst's function is to reduce the Subject Supposed to Know to the objet petit a — a move that distinguishes genuine analytic structure from mere discourse and rehabilitates resistance as a structural necessity rather than a defect of the analysand.

     a schema of the type of the Klein group, upon which I am trying for the moment to articulate what is involved in the act... In this little tetrahedron which we have started from these last times, something all the same must be quite tangible in it: the multiplicity of translations that it [allows].

375. #375

     Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.52

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 4: Wednesday 6 December 1967**

     Theoretical move: Lacan argues that the Freudian primary process introduces jouissance as a constitutive dissatisfaction—not reducible to general psychology's satisfaction-seeking—and then maps the three registers (Symbolic, Imaginary, Real) onto a topological diagram, locating Truth at the Other/Symbolic pole, Jouissance at the Real pole, and Knowledge as an imaginary idealisation, with the barred Subject, the unary stroke (I), and objet petit a as the three projected points, using Winnicott's transitional object as a clinical illustration that points toward—but stops short of—the full concept of the objet petit a as the subject's first object of enjoyment.

     why not put the barred Subject like a projection onto the other side? This will allow there to be asked what is involved in the relation of the Subject between the Imaginary and the Real.

376. #376

     Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.47

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 4: Wednesday 6 December 1967**

     Theoretical move: Lacan distinguishes three levels of "mathesis" (I read / I write / I lose) to argue that the psychoanalytic act is constitutively structured around failure and loss, and that teaching (thesis/antithesis) is not itself an act — but the act's topology, in which failure is primary, is what analysis uniquely inaugurates and what analysts themselves resist recognising.

     this is properly to sketch out a topology that can be expressed as follows. That by simply sketching its way out, one enters into it without even thinking.

377. #377

     Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.200

     **Annex 3**

     Theoretical move: Lacan's seminar summary argues that the psychoanalytic act—the transition from analysand to analyst—is constituted by and through the objet petit a, such that it enacts a 'subjective dismissal' (destitution of the subject supposed to know) and grounds a new ethics of psychoanalysis organized around the structural negativity of the sexual relation and jouissance rather than norms or sublimation.

     by situating his act in the ideal topology of the o-object, it can be deduced that he operates by not thinking.

378. #378

     Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.89

     **THE SEMINAR OF JACQUES LACAN** > **Seminar** 7: **Wednesday 24 January 1968**

     Theoretical move: The passage argues that the psychoanalytic act is constituted by the analyst's refusal to act, which structurally opens the space for transference and the Subject Supposed to Know; simultaneously, Lacan grounds the necessity of signifying sequence for any 'consequence' to be conceivable, and maps the objet petit a as the horizon-end of every act, not just the analytic one.

     It is enough to turn the tetrahedron, to make horizontal or vertical lines of it, but for reasons of imagination, it is more convenient to represent in this way.

379. #379

     Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.192

     **THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > *Lecture of 19th June. 1968*

     Theoretical move: Lacan argues that the unconscious is structured like a language such that truth is produced at the precise point where the subject refuses to know—what is rejected from the Symbolic reappears in the Real as symptom—and that psychoanalysis contributes a radical new dimension to the subject-Other relation by showing that knowledge is only constituted through recognition by the Other, while scientific knowledge, purified of this relation, functions as a complement to (rather than identity with) the Real.

     it is a quite indispensable topological function to bring out the radical and logical structure that is at stake in what I called earlier this knot or this bubble, this hollow in the world

380. #380

     Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.95

     **THE SEMINAR OF JACQUES LACAN** > **Seminar** 7: **Wednesday 24 January 1968**

     Theoretical move: Lacan argues that the gap between 'the act' and 'the doing' is the central problem of psychoanalytic practice, distinguishing the analyst's peculiar position—a doing of pure speech in which the subject absents itself so the signifier may operate—from mere activity, and linking this to the question of the Subject Supposed to Know, the logic of quantifiers, and the impossibility of meta-language.

     whether one expresses things in terms of instinct, of behaviour, of genesis, of Lacanian topology. All of that, we should find ourselves equidistant from this sort of discussion.

381. #381

     Seminar XVI · From an Other to the other · Jacques Lacan · p.187

     Seminar 12: Wednesday 26 February 1969

     Theoretical move: Lacan argues that the Freudian unconscious apparatus — grounded in the pleasure principle, repetition, and homeostatic return to perceptual identity — is not a neurophysiological mechanism but a minimal logical structure of signifying articulation (difference and repetition), such that the dream functions as a 'wild interpretation' whose analysis reveals desire precisely at the point where the reconstituted sentence fails as a sentence, not as meaning.

     it is enough to refer to this project, to this Entwurf, to see the decisive importance in the articulation of what is involved in this trellis, lattice, of this texture

382. #382

     Seminar XVI · From an Other to the other · Jacques Lacan · p.372

     Seminar 24: Wednesday 18 June 1969

     Theoretical move: Lacan formalizes the structural necessity of the "additional one" (un-en-plus) and the empty set within the field of the Other, demonstrating through set theory that the inclusion of a first signifier into the Other necessarily generates a second term (the empty set/S(Ø)) and that subjectivity only appears at the level of S2, reorienting the field from intersubjectivity to intra-subjective structure.

     Already, by their articulation, they constitute a knowledge. This an Other here inscribed by 1 on the left of the circle, shows itself for what it is, namely, one in the Other

383. #383

     Seminar XVI · From an Other to the other · Jacques Lacan · p.303

     Seminar 18: Wednesday 30 April 1969 > Seminar 19: Wednesday 7 May 1969

     Theoretical move: Lacan argues that lack—as the precondition of anxiety's "not without an object"—only arises within a symbolic order capable of counting, and uses this logic to theorize the objet petit a as the effect of symbolic counting on the imaginary field, while simultaneously framing the modern disjunction between knowledge and power as the broader historical context in which this structural analysis gains its urgency.

     What is indicated here as effect in the field of the imaginary, is nothing other than the fact that this field of the Other is, as I might say, in the form of o. In this field, this is inscribed in a topology that, to image... presents itself as holing it.

384. #384

     Seminar XVI · From an Other to the other · Jacques Lacan · p.345

     Seminar 21: Wednesday 21 May 1969

     Theoretical move: Lacan argues that neurosis (hysteria and obsession) stages the fundamental aporia between knowledge and enjoyment, and that the neurotic's testimony—not therapeutic benefit—is what gives psychoanalysis its historical and theoretical stakes, particularly within capitalism's structuring of enjoyment.

     in the articulation that I gave of the 1 and the o... there is inscribed in a series what is connected to the simple repetition of the 1... the Fibonacci sequence... strictly defines the function of o

385. #385

     Seminar XVI · From an Other to the other · Jacques Lacan · p.286

     Seminar 18: Wednesday 30 April 1969

     Theoretical move: Lacan displaces the classical inside/outside opposition—via commodity, money, Berkeley's idealism, and Aristotle's optics—to argue that the scopic field is structured not by a synthesising subject in a darkroom but by the objet petit a as lack/stain, a third term missing from both ancient and modern accounts of vision.

     What becomes of inside and outside? And if what we are forced to redraw to find ourselves on this limit, on this middle line between the symbolic and the imaginary

386. #386

     Seminar XVI · From an Other to the other · Jacques Lacan · p.274

     Seminar 15: Wednesday 19 March 1969 > **Seminar 17: Wednesday 23 April 1969**

     Theoretical move: Lacan argues that the structure of desire—grounded in the impossibility of the sexual relation and the barrier jouissance poses to Other jouissance—is homologous to formal logical flaws (the undecidable, Gödelian incompleteness), and that psychoanalytic stagnation consists in analysts becoming hypnotized by the patient's demand rather than dissolving the neurotic knot at its structural root.

     suppose that the structure is effectively here that of the Klein bottle, that the limit is effectively this locus of turning inside out where what was the front becomes the back

387. #387

     Seminar XVI · From an Other to the other · Jacques Lacan · p.195

     Seminar 12: Wednesday 26 February 1969

     Theoretical move: Lacan uses Freud's dream of the burning child as a pivot to argue that the proper analytic question is not "what does the dream mean?" but "where is the flaw (desire) in what is said?"—and then formalizes the relationship between Knowledge and Truth via the golden-ratio proportion (o/1-o = 1/o), establishing the objet petit a as the structural hinge that articulates desire, knowledge, and truth in the unconscious.

     what will be written in terms of a cross conjunction of the type that people use in arithmetic... In so far as it constitutes this very object towards which there tends every desire in so far as it is produced at the level of articulation.

388. #388

     Seminar XVI · From an Other to the other · Jacques Lacan · p.283

     Seminar 18: Wednesday 30 April 1969

     Theoretical move: Lacan argues that the unquestioned presupposition of the Subject Supposed to Know—the assumption that knowledge is already organized somewhere—is the hidden theological core of idealism, and that psychoanalytic practice remains trapped in this idealism so long as it uncritically employs spatial metaphors (inside/outside, projection/introjection) derived from the camera-obscura model of representation.

     It is simply to remark that here, and here alone, is the support for the fact that what concerns the psyche is to be situated in an inside limited by a surface.

389. #389

     Seminar XVI · From an Other to the other · Jacques Lacan · p.87

     **Seminar 6: Wednesday 8 January 1969**

     Theoretical move: Lacan argues that the minimal requirement for renewing psychoanalytic questioning is restoring the subject's dependency on the signifier, and that this project must move beyond phonology/linguistics toward a 'logical practice' (mathematical logic) as a discipline that maps an isomorphism—possibly an identity of material—between the structure of the subject and formal discourse; he also insists on the distinction between form and formalism as a structural, not specular/imagistic, operation.

     the holed pot on which I left you last year. It is quite clear that one does not see the hole in this pot in the mirror if one looks through the aforesaid hole

390. #390

     Seminar XVI · From an Other to the other · Jacques Lacan · p.106

     **Seminar 6: Wednesday 8 January 1969** > **Seminar 7: Wednesday 15 January 1969**

     Theoretical move: Lacan argues that Jouissance is irreducible to the pleasure principle and is topologically structured as the subject's own topology; he then deploys this against Hegel's Master/Slave Dialectic (where the master renounces enjoyment from the start) and Pascal's Wager (where Surplus-jouissance, not enjoyment itself, is what is actually at stake in the bet).

     it is clear that at every stage people speak only of this - rejection, formation of the non-ego... but a function of what is called incorporation and what is expressed as introjection, as if what were at stake was a relationship of the inner to the outer and not a much more complex topology.

391. #391

     Seminar XVI · From an Other to the other · Jacques Lacan · p.26

     **Seminar 2: Wednesday 20 November 1968**

     Theoretical move: Lacan advances the argument that surplus-jouissance (surplus enjoying) is structurally homologous to Marx's surplus value: both arise from the renunciation of enjoyment within a discourse, and both only become visible once knowledge is unified and marketised under capitalist logic — establishing that the conflictual 'truth' of the capitalist system is a problem of knowledge, jouissance, and discourse, not merely of political economy.

     in its junction whose topology I tried to draw, in its junction with knowledge, because it is difficult to speak about anything whatsoever in psychoanalysis without introducing this junction.

392. #392

     Seminar XVI · From an Other to the other · Jacques Lacan · p.270

     Seminar 15: Wednesday 19 March 1969 > **Seminar 17: Wednesday 23 April 1969**

     Theoretical move: Lacan stages a confrontation between Hegel's Selbstbewusstsein and the Freudian unconscious to argue that thinking is constitutively a censorship of an originary "I do not know," and that desire (to know) is born from this nodal failure of knowledge — a topology illustrated via the Klein bottle and Möbius strip, and clinically anchored in free association and the objet petit a.

     this reference to the Klein bottle in so far as it gives us in a surface topology the possibility of a division, in which what is at the neck, namely, this little circle, where the surface is supposed to retrogress. And we will put on the one hand the truth and on the other knowledge.

393. #393

     Seminar XVI · From an Other to the other · Jacques Lacan · p.252

     Seminar 15: Wednesday 19 March 1969 > Seminar 16: Wednesday 26 March 1969

     Theoretical move: Lacan argues that the perverse drives (scoptophilic, sadomasochistic) are fundamentally asymmetrical and structured around the topology of the Objet petit a: each drive operates not as a return of its counterpart but as a supplement to the Other, aimed at producing or evacuating the jouissance of the Other rather than of the subject—a logic that makes the pervert a "defender of the faith" of the Other's jouissance.

     there is something in the voice that is more topologically specified, namely, that nowhere is the subject more interested in the other than through this o-object... the topological comparison, the one that is illustrated here by the hole in a sphere which is not one since precisely it is in this hole that it folds back on itself.

394. #394

     Seminar XVI · From an Other to the other · Jacques Lacan · p.123

     **Seminar 6: Wednesday 8 January 1969** > **Seminar 8: Wednesday 22 January 1969**

     Theoretical move: Lacan uses the mathematical proportion I/o = 1+o (the golden ratio / Fibonacci series) and Pascal's wager to argue that the Objet petit a (o) is the structural measure of loss in relation to the Other, and that surplus-jouissance (masochistic enjoyment) is the analogical position by which the subject takes on the role of the waste-product (o) in order to constitute the Other as a complete field — thus linking the formalization of desire's cause to the topology of the Other.

     We project this o onto this field considered in its function as 1. What we have just written indicates to us that what will be here will be o². The folding back of the o² gives us here an o³.

395. #395

     Seminar XVI · From an Other to the other · Jacques Lacan · p.96

     **Seminar 6: Wednesday 8 January 1969**

     Theoretical move: Lacan uses Gödel's incompleteness theorems as a structural analogy for the psychoanalytic subject: just as formalization reveals a constitutive limit (incompleteness) at the heart of the most consistent discourse, the subject is nothing but the function of the cut that separates formal from natural language—and this structural lack grounds both the desire of the mathematician and, via the Graph of Desire, the alienation of meaning and the exclusion of jouissance.

     the function of the cut that answers 'no!'...And that, on the other hand, on a different register, the one in appearance where enjoyment is waiting.

396. #396

     Seminar XVI · From an Other to the other · Jacques Lacan · p.307

     Seminar 18: Wednesday 30 April 1969 > Seminar 19: Wednesday 7 May 1969

     Theoretical move: Lacan argues that the anaclitic relation is structurally grounded in the operation of objet petit a as a masking of the Other, that perversion consists in returning o to the big Other, and that phobia reveals the true function of anxiety-objects: the substitution of a frightening signifier for the object of anxiety, marking the passage from the imaginary (narcissism) to the Symbolic field.

     this topology that is outlined, and that the advance of knowledge specifies at many other levels than that of pathological experiences

397. #397

     Seminar XVI · From an Other to the other · Jacques Lacan · p.128

     **Seminar 6: Wednesday 8 January 1969** > **Seminar 8: Wednesday 22 January 1969**

     Theoretical move: Lacan deploys the golden ratio (φ, written 'o') and the Fibonacci series to demonstrate the structural reciprocity between the divided subject and objet petit a, arguing that the 'I' of enjoyment is necessarily excluded from any totalised field of knowledge, and that the question of subjective existence must be posed impersonally — 'does it exist?' rather than 'I exist'.

     This will allow us to situate better what is involved in a certain number of human activities... I am calling that of pure logical consistency.

398. #398

     Seminar XVI · From an Other to the other · Jacques Lacan · p.64

     **Seminar 4: Wednesday 4 December 1968**

     Theoretical move: Lacan argues that the truth "speaks I" (rather than being spoken by a subject), and formalises this through the ordered pair of signifiers to show that the subject is constituted as infinite repetition within—and thus excluded from—absolute knowledge; this logical structure grounds both the analytic rule of free association and the link between the subject supposed to know, transference, and objet petit a.

     the topology suggested by such an imaging, makes of it the index of the fact that big O, if we define it as possibly including itself

399. #399

     Seminar XVI · From an Other to the other · Jacques Lacan · p.19

     **Seminar 2: Wednesday 20 November 1968**

     Theoretical move: Lacan introduces *surplus-jouissance* (Mehrlust) as the psychoanalytic homologue to Marx's surplus value (Mehrwert), and grounds this move in the claim that structure is real — not metaphorical — because it is determined by convergence toward an impossibility; discourse is what constitutes, rather than merely represents, the real, and this principle is the condition of seriousness for any practice of psychoanalysis.

     I already underlined that in this case, it was in no way a kind of metaphor... the scissors' cut in the Moebius strip makes a strip that no longer has anything to do with what it was previously.

400. #400

     Seminar XVI · From an Other to the other · Jacques Lacan · p.224

     Seminar 12: Wednesday 26 February 1969 > Seminar 13: Wednesday 5 March 1969

     Theoretical move: Lacan argues that the absence of a sexual signifier means Woman is irreducibly unknown, accessible only through representatives of representation (Vorstellungsrepräsentanz); sublimation is then theorised as the objet petit a functioning as what "tickles das Ding from the inside," linking drive topology (edge-structure, vacuole) to the production of art and courtly love.

     in the drive there intervenes what is called in topology an edge structuré, that it is the only way of explaining some of its traits... the constancy of the flux that this edge conditions

401. #401

     Seminar XVI · From an Other to the other · Jacques Lacan · p.243

     Seminar 15: Wednesday 19 March 1969 > Seminar 16: Wednesday 26 March 1969

     Theoretical move: Lacan advances the thesis that the o-object is fundamentally an extimate topological structure that functions as the locus of captured enjoyment within the field of the Other, and that the pervert's clinical function is precisely to fill the hole that this structure opens in the Other—making him, paradoxically, a "defender of the faith" rather than a contemner of the partner.

     whether we pursue it in this shape, of what produces the torus, by joining the two opposite edges… or on the contrary we have the structure of the cross cap, or that we have by combination of two different possibilities the structure described as the Klein bottle.

402. #402

     Seminar XVI · From an Other to the other · Jacques Lacan · p.176

     Seminar 10: Wednesday 5 February 1969 > **Seminar 11: Wednesday 12 February 1969**

     Theoretical move: Lacan advances the argument that the objet petit a (o) is not merely a remainder or lost object within the field of the Other, but the very cause of thinking itself — its shadow and ground — such that the supposed unity of the One (the field of discourse, the Other) is always already constituted by an arbitrary act of positing, and desire's lack is redefined through the mathematical structure of the Fibonacci series and the o-function rather than through the traditional ontological appeal to the infinite.

     it is always the same circle that is at stake. And that this circle, in so far as we ground it, but in an arbitrary, chosen fashion, it is by an act that we posit this Other as field of discourse

403. #403

     Seminar XVI · From an Other to the other · Jacques Lacan

     **Seminar 2: Wednesday 20 November 1968** > **Seminar 3: Wednesday 27 November 1968**

     Theoretical move: Lacan grounds surplus-jouissance as a structural (not merely analogical) homologue to Marxist surplus value, with jouissance itself designated as the substance of psychoanalytic discourse — the move establishes jouissance as a formal, topological concept rather than a formless background.

     It requires me to give you today some clarifications that I would call topological.

404. #404

     Seminar XVI · From an Other to the other · Jacques Lacan · p.47

     Am I making myself understood?

     Theoretical move: By mapping Russell's paradox onto the relation of the subject (S) to the big Other (O), Lacan demonstrates that the Other cannot be totalized as a closed code or complete set of discourse, and that this structural impossibility — topologically figured by the cross-cap and Klein bottle — is precisely what produces the split subject and positions the objet petit a as the hole in the Other.

     this is what - you may or may not sense the kinship - what we have drawn in one of the previous years in the topological form of the projective plane and illustrated in a materialised fashion for the eye by the cross-cap.

405. #405

     Seminar XVI · From an Other to the other · Jacques Lacan · p.293

     Seminar 18: Wednesday 30 April 1969

     Theoretical move: Lacan articulates the stain/gaze as the structuring lack in the field of vision that inserts vision into desire via the o-object, then leverages this to distinguish perversion (where objet a fills/masks the phallic lack, restoring o to the Other) from neurosis (where the signified of the barred Other reveals the conflictual articulation at the level of logic itself), with the neologism 'hommelle/famil' marking the transition between these clinical structures.

     This is of great interest in topological organisation. Because it also shows that it is at the level of the statement that the text of the neurotic symptom is articulated.

406. #406

     Seminar XVI · From an Other to the other · Jacques Lacan · p.321

     Seminar 18: Wednesday 30 April 1969 > **Seminar 20: Wednesday 14 May 1969**

     Theoretical move: The passage advances the argument that the phallus functions as the "missing signifier" of the sexual relation precisely because sexual jouissance is outside the system of the subject — there is no subject of sexual enjoyment — and this impossibility is demonstrated by the untraceable, non-coupled nature of the male/female distinction at the level of the signifier.

     only substructural considerations are involved here... it says how it holds together when it is there... a topology is constructed as defining the Other

407. #407

     Seminar XVI · From an Other to the other · Jacques Lacan · p.315

     Seminar 18: Wednesday 30 April 1969 > **Seminar 20: Wednesday 14 May 1969**

     Theoretical move: Lacan grounds the subject's structure in the logic of the signifier as self-othering: the signifier can only represent the subject for another signifier, and this irreducible alterity of the signifier to itself constitutes the big Other as necessarily incomplete (holed by objet petit a), while the subject is redefined as "what effaces its tracks," making the trace-effacement the originary operation from which the signifier and language emerge.

     the topological structure of O itself, which means that the O is not complete, is not identifiable in any case to a 1, to a whole.

408. #408

     Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.175

     Seminar 10: Wednesday 8 April 1970 > (12) OK, let's go and after that we'll leave it.

     Theoretical move: Lacan reframes the "Copernican revolution" not as a change of centre but as the discovery that knowledge can be structured without a knowing subject, paralleling Newton's "unthinkable" formula for gravity and Freud's discovery of the unconscious as a knowledge that escapes consciousness—both pointing to the impossible as the Real; simultaneously he argues that the concept of "revolution" only acquires structural dignity from Marx's discovery of surplus value as foreclosed in the capitalist discourse, and that being itself is born only from the flaw (lack) introduced by the speaking being.

     completely insouciant, we could say, of the requirements of a topology because of what it is simply unaware of

409. #409

     Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.233

     X: *[On revolutionaries and the proletariat]* > Seminar 13: Wednesday 20 May 1970

     Theoretical move: Lacan uses the Fibonacci series and its limiting proportion (the golden number) as a mathematical formalization of the structure of affect, cause, and the repetition of the unary trait, arguing that science—grounded in symbolic/combinatorial proof rather than perception—produces an "unsubstance" that dissolves the male/female forming principles, and that each subject is ultimately determined as objet petit a, the cause of desire.

     What are we going to call this locus?... you could, unless you find something better, call it the alethosphere

410. #410

     Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.181

     Seminar 10: Wednesday 8 April 1970 > (12) OK, let's go and after that we'll leave it.

     Theoretical move: Lacan argues that the structure of the unconscious is analogous to mathematical logic (Gödel-type incompleteness), where the "false" (falsus) is causally operative in the production of being through interpretation — and that Freud's unique insight into this topology was sustained by a Jewish hermeneutic tradition (the Midrash) of reading the letter literally, rather than by any natural truth.

     let us say that it is textile, made up of knots which only means the holes that are found there.

411. #411

     Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.58

     *[A porter appears]*

     Theoretical move: Lacan introduces and distinguishes the Four Discourses (Master, Hysteric, Analyst, University) by identifying the structural "dominant" place each discourse organizes around — locating the objet petit a as what occupies the dominant place in the Discourse of the Analyst — while simultaneously critiquing how University discourse systematically reverses his formula ("language is the condition of the unconscious") and thus distorts analytic discourse.

     simply try, in each of these figures of discourse, as we will call them, to require yourself simply to choose a different place, defined in function of the terms above, below, on the right, on the left. No matter how you go about it you will not succeed in getting each of these places to be

412. #412

     Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.170

     Seminar 10: Wednesday 8 April 1970

     Theoretical move: Lacan argues that structure is the effect of language already operative in reality—not a representational function of any subject—and uses this to demarcate psychoanalysis from linguistics and ethnology: neither can master the unconscious because psychoanalysis operates within a particular tongue where there is no metalanguage, the signifier represents a subject (not another signifier), and sexual non-relation is the irreducible structural remainder that myth and linguistics cannot formulate.

     Its universality is only the topology that is rediscovered, because of the fact that a discourse is displaced in it

413. #413

     Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.65

     **Seminar 4: Wednesday 17 February 1971**

     Theoretical move: Writing is theorized as the necessary condition for logic and for questioning the symbolic order, while the Phallus is recast not as a missing signifier but as an obstacle to the sexual relationship—what establishes jouissance as the condition of truth in analytic discourse.

     What is essential in the relationship, is an application, a applied onto b (a→b), and if you do not write this a and b, you do not sustain the relationship as such.

414. #414

     Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.163

     **Seminar 8: Wednesday 19 May 1971** > - We can't hear you!

     Theoretical move: The passage argues that the hysteric's desire—structurally unsatisfied because it emphasises the invariance of the unknown—functions as a formal schema for the logic of the Not-all (pas-toute), such that 'a woman' can only emerge by sliding beyond the hysteric's phallic semblance; simultaneously, Lacan grounds the unconscious-structured-like-a-language thesis in the irreducible division between jouissance and semblance, and links truth to half-saying rather than full articulation.

     That's how it is drawn, huh? In this family-friendly topology, this is how the Klein bottle is drawn.

415. #415

     Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.103

     **Seminar 6: Wednesday 17 March 1971**

     Theoretical move: Lacan uses the analysis of Poe's "The Purloined Letter" to argue that the circulation of the letter (as a structural object) produces castration effects on all subjects who handle it, and that writing—as a material, literal support—exceeds both intuition and the tetrahedric structure of the four discourses, ultimately framing the unreadable as the condition of meaning in psychoanalysis, particularly through the written myth of the Oedipus complex.

     beyond the tetrahedron, already, intuition has to be supported by the letter. [...] It is based on a tetrahedric structure

416. #416

     Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.68

     **Seminar 4: Wednesday 17 February 1971**

     Theoretical move: Lacan argues that language occupies the gap left open by the phallus in the place of the sexual relationship, substituting a law of desire/prohibition for any mathematical relation between the sexes; this move is theoretically grounded in Peirce's logical schema to establish that there is no universal of Woman (not-all), while the phallus-as-instrument is posited as the "cause" (not origin) of language, and the truth—like the unconscious—sustains contradictory positions that only become paradoxical when written.

     in accordance with a topology that I have already for long enough given a destiny not to have to recall it, ritual and myth are like the front and the back (l'endroit et l'envers), on condition that this front and this back are in continuity.

417. #417

     Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.81

     *Lacan writes on the board: "L 'achose"*

     Theoretical move: Lacan argues that 'l'achose' (the thing-as-absent) can only be approached through writing (l'écrit), not speech, because the thing's place is always marked by the absence of the o-object (castration), and topology—exemplified by the Graph of Desire—is irreducibly a written form that the spoken word cannot substitute for.

     this graph, what it represents, is what is called, in the evolved language that has been given to us little by little by the questioning of mathematics by logic, is what is called a topology. There is no topology without writing.

418. #418

     Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.100

     **Seminar 6: Wednesday 17 March 1971**

     Theoretical move: Lacan reviews his early work on "The Purloined Letter" as a foundational articulation of the phallus within discourse, arguing that it already contained the key signifier-based articulations he continues to develop — including the impossibility of the sexual relation — while pivoting toward the function of writing (the Letter) and its relationship to logical/mathematical reasoning as distinct from spatial intuition.

     This famous space which has been indeed for our logic, for a good while, since Descartes, the most bothersome thing in the world... as the dimension of the imaginary.

419. #419

     Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.110

     **Seminar 6: Wednesday 17 March 1971**

     Theoretical move: Lacan argues that sexual jouissance cannot be written (inscribed in the symbolic), and that this unwriteability is the structural condition from which both the Oedipus complex and the formulas of sexuation derive — specifically: "the woman" does not exist because the universal affirmative ("all women") is impossible, while the prohibition on jouissance (pleasure principle as "not too much enjoyment") and the maternal body supply the only available symbolic scaffolding for the sexual relationship.

     there is only one structure... and first of all the tetrahedron in which something is outlined that situates it, but is inseparable from a certain number of functions

420. #420

     Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.93

     *Lacan writes on the board: "L 'achose"*

     Theoretical move: Lacan argues that the lapsus is always fundamentally a written phenomenon (lapsus calami even when linguae), and uses this to establish that there is no metalanguage because one only ever speaks *about* language by starting from writing—culminating in the claim that his seminar on the Purloined Letter is ultimately an extended discourse on the phallus.

     How could he have done his little bar with this thing underneath and these things above, that I have sufficiently used and abused, if there were no writing?

421. #421

     Seminar XIX · …or Worse · Jacques Lacan · p.174

     J Lacan - Pierce as astronomer > Seminar 12: Wednesday 21 Jane 1972

     Theoretical move: In this closing session of Seminar XIX, Lacan condenses the year's argument: the *Yadl'un* (the One makes Being) is not ontology but the structural ground of analytic discourse, and Freud's essential contribution—overdetermination—is precisely the irreducible relation of the signifying chain to the body as the site of jouissance, a jouissance that is always "hand to hand" and never attributable to a single body.

     Obviously if it is there, in this form, in this form of tetrad, it is not a topology which is....which is without any kind of sense.

422. #422

     Seminar XIX · …or Worse · Jacques Lacan · p.133

     Seminar 9: Wednesday 10 May 1972

     Theoretical move: Lacan uses mathematical logic (Boole, Frege, Cantor) to argue that Truth can only "half-say" itself — that 0 is not the negation of 1 but the mark of a constitutive lack, such that the impossibility of reaching 2 from 0 and 1 formally mirrors the impossibility of the sexual relationship and the inaccessibility of the Real; the analyst's position as semblance of Objet petit a grounds a non-initiatory knowledge of truth that is structural, not esoteric.

     it is quite striking that from Cantor's construction there results that there is no aleph that starting from alepho cannot be held to be accessible. It is no less true that... it is only on the supposition that in these alephs, there are inaccessibles, that there can be reintroduced into what is involved in whole numbers what I will call consistency.

423. #423

     Seminar XIX · …or Worse · Jacques Lacan · p.103

     Seminar **6:** Wednesday **8** March 1972 > Seminar 7: Wednesday IS March 1972

     Theoretical move: Lacan traces the problem of the One through Parmenides, Plato, Hegel, Frege, and Aristotle to argue that the One is not univocal and cannot be deduced from logic alone—its emergence from the empty set (zero) inaugurates both the arithmetic series and the question of existence, which always rests on a foundation of inexistence; this re-reading of the Platonic Parmenides positions Plato as proto-Lacanian insofar as the Real is approached through the gap in what can be said.

     we are renewing the Platonic dialogue. This indeed is how I claim to lead you somewhere to pursue, through this bifidity of the One

424. #424

     Seminar XIX · …or Worse · Jacques Lacan · p.73

     Seminar 5: Wednesday 9 February 1972

     Theoretical move: The passage argues that the Objet petit a emerges not from any single term (demand, refusal, offer) but from their triadic knotting—a Borromean-style structure where each term only holds meaning through the others, and the "it's not that" at the heart of every demand is precisely the irreducible gap that generates the object of desire in analytic discourse.

     It is not space that is at stake. It is space in so far as we project into it our objective schémas. But that already indicates to us enough about it. Namely, that our objective schémas determine perhaps something about our notion of space

425. #425

     Seminar XIX · …or Worse · Jacques Lacan · p.137

     Seminar 9: Wednesday 10 May 1972

     Theoretical move: Lacan grounds the sexual non-relation and the logic of sexuation in the mathematical real, arguing that the One (Y a d'l'un) does not found a binary complementarity between man and woman because the not-all prevents any consistent application of the principle of contradiction to gender; simultaneously, he insists that the analyst must hold the position of the little o-object as semblance, and that the mathematical real—which resists both truth and meaning—is the proper anchor for analytic discourse.

     I began with a little graph which was designed to give you the core, or the map, for the Formations of the unconscious, to circumscribe it at a point from which it could not move

426. #426

     Seminar XIX · …or Worse · Jacques Lacan · p.160

     J Lacan - Start that again.

     Theoretical move: The passage turns on the structural homology between the logical form of double negation (as deployed in the fixed-point theorem and Lacan's own formulas), Peirce's distinction between the field of the potential (pure zero) and the field of the impossible (zero of repetition), and an empiricist prehistory of this distinction traced through Locke and Condillac — arguing that the "point that escapes" distortion in topology mirrors the logical and ontological status of the non-inscribed, which is the condition of possibility for any inscription at all.

     the theorem of fixed points, if one takes for example something like a disk... distorting a disk on its edge in a continuous manner... at least one point of the disc escapes this distortion, namely, remains fixed

427. #427

     Seminar XIX · …or Worse · Jacques Lacan · p.79

     Seminar **6:** Wednesday **8** March 1972

     Theoretical move: Lacan argues that enjoyment is always "from the Other" but never sexual (there is no sexual relation), and that the Other must be barred — emptied out — to become the locus where the sexuation formulae and knowledge are inscribed; this move connects the barred Other S(Ø) to lalangue, fantasy, repetition (Nachträglichkeit), and the necessity of writing for psychoanalysis to be possible at all.

     One of the terms of the relation must be emptied out in order to allow this relation to be written down.

428. #428

     Seminar XIX · …or Worse · Jacques Lacan · p.118

     Seminar 8: Wednesday 19 April 1972

     Theoretical move: Lacan uses the history of mathematics—from the Pythagorean irrationals through Cantor's set theory—to argue that the One cannot be grounded on sameness but only on pure difference and lack: the empty set is the constitutive "door" through which the One first emerges, and this structural priority of lack over identity is what Lacan designates as the matheme.

     Nothing is One except what comes out or which, from this sack, or which does not re-enter this sack; this is the original foundation, if we are to take it intuitively of the One.

429. #429

     Seminar XIX · …or Worse · Jacques Lacan · p.159

     accommodate yourselves.

     Theoretical move: Through Recanati's intervention on Peirce, the passage argues that the universal quantifier cannot stand alone but requires a prior inscription of inexistence (negation as function), and that the repetition of inscribed inexistence—not bare inexistence—grounds logical and mathematical structures; this move aligns Peirce's logic of the continuous with Lacan's concerns about the Not-all and the grounding of the universal.

     The same type of example could be taken up eventually in topology. If one listened to Peirce, the theory of fixed points ought to be stated as follows

430. #430

     Seminar XIX · …or Worse · Jacques Lacan · p.29

     Seminar 2: Wednesday 15 December 1971

     Theoretical move: Lacan introduces the formulas of sexuation through a quasi-mathematical notation, arguing that sexual enjoyment constitutes the obstacle to the sexual relationship, that every sexed signifier falls under the castration function (ΦΧ), and that the logic of quantifiers—specifically the 'not-all'—is the proper instrument for writing what cannot be said in classical predicate logic.

     it will only be known after having brought into operation at different levels of topological relations a certain way of changing the letters and of seeing how it is distributed.

431. #431

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.45

     The Psychoanalyst's Knowledge

     Theoretical move: Lacan uses topology (the non-orientable surface) to argue that castration is structurally ubiquitous—present at every point of the relational surface between man and woman—and then anchors this topological claim to the Four Discourses, showing that the mathemes ($, S1, S2, a) constitute the logical "walls" behind which enjoyment, surplus-enjoyment, truth, and semblance must be situated.

     it is not a surface that one can represent to oneself, but that it is something that is defined by certain co-ordinates - let us call them, if you wish, vectorial - such that in each one of the points of the surface the return is always there

432. #432

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.25

     The Psychoanalyst's Knowledge

     Theoretical move: Lacan argues that the objet petit a is not a localized object but the very tetrahedral structure of the four discourses, and that each discourse constitutively prevents its own agent from comprehending it — the analyst included — because it is castration (as a gap) that guarantees the Real from which all discourse stems.

     what I call the master signifier, and what I designate by the body of knowledge were not distributed at the four points of a tetrahedron

433. #433

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.141

     The Knowledge of the Psychoanalyst > **1 Jane 1972**

     Theoretical move: Lacan formalises the sexuation formulas by mapping the masculine side (universal castration grounded by the exceptional father who says-no) against the feminine side (not-all, grounded not by an exception but by the absence/void of any denial of the phallic function), and identifies the four logical relations between the quadrant terms as existence, contradiction, undecidable, and lack/desire/objet a, while equating the mathematical notion of the set with the barred subject and the non-numerable with feminine not-all.

     what is between the One and the Zero... It is quite provable that what is between the One and the Zero - this can be shown thanks to decimals... the method described as diagonal can always permit there to be forged a new decimal series

434. #434

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.114

     The Psychoanalyst's Knowledge > **4 1 \* May 1972**

     Theoretical move: Lacan disputes the standard set-theoretic introduction of non-numerability via induction by substituting the notion of "partition" for "parts," showing this yields 2^n − 1 rather than 2^n, and uses this to argue that the One emerging from the empty set is the ground of repetition — directly linking set-theoretic structure to the analytic concept of the One as reiteration of lack.

     in substituting for the notion of the parts that of partition, it is necessary in the same way, that we have admitted that the parts of the infinite set, must be two the power of alpha zero

435. #435

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.43

     The Psychoanalyst's Knowledge

     Theoretical move: Lacan uses a Klein bottle topology and a playful six-verse poem to demonstrate that the relation between man and woman passes through love, then substitutes the world for the sexual partner, and terminates at a wall that is not a cut but the locus of castration — the point where truth and knowledge are held apart. This topological demonstration grounds the claim that the discourse of capitalism forecloses castration, and that it is only the analytic discourse (emerging from logic, the four discourses, and language) that re-introduces castration as the hinge between truth and knowledge.

     What I have traced out for you there, on the board, this board that turns, is a way, a way like any other of representing the Klein bottle. It is a surface that has certain topological properties...It is very like a Moebius strip

436. #436

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.72

     The Psychoanalyst's Knowledge > **3"¹ March 1972**

     Theoretical move: The Borromean knot is introduced as a topological figure whose structural property — that removing any one ring dissolves the chain entirely — poses the fundamental question of the conditions of the discourse of the unconscious and of what language is, linking topology directly to grammar and the unconscious.

     Language ought to be tackled in its grammar, in which case - this is certain, it relates to a topology...

437. #437

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.81

     The Psychoanalyst's Knowledge > I ASK YOU TO REFUSE WHAT I AM OFFERING YOU.

     Theoretical move: Lacan argues that the formulas of sexuation cannot be read through standard propositional logic (negation, conjunction, disjunction) because the phallic function governs both sexes asymmetrically: the masculine side is structured by a universal ('All x') grounded in an exception ('there exists an x that negates φx'), while the feminine side is 'not-all' within the phallic function, which opens onto a dual, properly feminine jouissance irreducible to phallic jouissance—and it is precisely this asymmetry that marks the non-existence of the sexual relationship.

     this writing is only authorised, only takes its form from a very specific writing, namely, what allowed there to be introduced into logic the irruption precisely of what I was asked about earlier, namely, a mathematical topology.

438. #438

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.52

     The Psychoanalyst's Knowledge

     Theoretical move: Lacan uses the topology of the tetrahedron to ground the Four Discourses as a structural necessity derived from the properties of four points in space, then pivots to the question of the function of speech as the unique form of action that posits itself as truth—establishing the epistemological basis for the knowledge of the psychoanalyst.

     I arranged them according to what is called a topology, one of the simplest topologies, but which is nonetheless a topology, a topology in the sense that it can be put into mathematics.

439. #439

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.65

     The Psychoanalyst's Knowledge

     Theoretical move: The passage argues that the analyst's knowledge is constituted by a "scrap of knowledge" drawn from the subject's own jouissance—unconscious knowledge that is not "supposed" but emerges from slips, dreams, and the analysand's work—and locates this within the Four Discourses structure where S2 occupies the place of truth and $ occupies the place of enjoyment, distinguishing scientific (mathematical/topological) writing from the zone of discourse where meaning is always partial and borrowed from another discourse.

     this fact pushes him towards this extrapolation of thinking that topology can provide a typology for natural tongues.

440. #440

     Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.74

     The Psychoanalyst's Knowledge > I ASK YOU TO REFUSE WHAT I AM OFFERING YOU.

     Theoretical move: Lacan argues that the entry of language into the speaking being structurally voids the "second sex" (the Other as *heteros*), making sexual difference not a natural binary but a topological-linguistic problem: there is no sexual relationship because "the Other" is the very locus that language empties of being, and universals like "Man" and "Woman" are linguistic constructs required by language itself, not grounded in animal copulation.

     What I, for my part, am in the process of putting forward for you, is something that fundamentally is attached to the purely topological origin of language.

441. #441

     Seminar II · The Ego in Freud's Theory and in the Technique of Psychoanalysis · Jacques Lacan · p.20

     THE SEMINAR OF JACQUES LACAN > Psychology and metapsychology

     Theoretical move: Lacan argues that Freud's fundamental contribution is the decentring of the subject from the individual—the subject is ex-centric to the ego and to consciousness—and reads this discovery as the culmination of a moralist tradition (La Rochefoucauld, Nietzsche) that exposes the deceptive, inauthentic hedonism of the ego, thereby grounding the necessity of Freud's post-1920 metapsychological revision.

     We will confine ourselves to this topological metaphor for the moment - the subject is decentred in relation to the individual.

442. #442

     Seminar II · The Ego in Freud's Theory and in the Technique of Psychoanalysis · Jacques Lacan · p.150

     XII

     Theoretical move: Lacan argues that Freud's topographical regression is not a primary theoretical datum but a forced construction imposed by the internal paradox of his schema—the dissociation of perception and consciousness at opposite ends of the psychic apparatus—and that a more coherent schema would render the concept of regression unnecessary at this level.

     Valabrega's remark is worthwhile on its own terms... Freud presents something as having a topographical unity which is split at both ends.

443. #443

     Seminar II · The Ego in Freud's Theory and in the Technique of Psychoanalysis · Jacques Lacan · p.142

     THE FR EUDIAN SCHEMATA OF TH E P S YCHIC APP ARATUS > Censorship is not resistance

     Theoretical move: Lacan distinguishes censorship from resistance by locating censorship at the level of discourse itself — as the structural impossibility of anyone fully mastering the law of discourse — rather than at the level of the subject or ego, thereby grounding the Freudian concept in a symbolic-discursive order that precedes and exceeds individual psychology.

     the psychic locality in question is not psychic, it is quite simply the symbolic dimension, which is of another order

444. #444

     Seminar II · The Ego in Freud's Theory and in the Technique of Psychoanalysis · Jacques Lacan · p.129

     THE FR EUDIAN SCHEMATA OF TH E P S YCHIC APP ARATUS > From the Entwurf to the Traumdeutung

     Theoretical move: Lacan argues that Freud's progressive theorisation of the psychic apparatus traces a "negative dialectic" in which the same antinomies recur in transformed guises, and that this progression—from a mechanical/neurological model to a logical/symbolic one—reveals that the fundamental object of psychoanalysis is the autonomous symbolic order, not the biological organism; consciousness functions as the irreducible paradox that prevents any closed energetic model.

     In the text, he tells us that there is something it must be like. Remember what I told you last year during the lectures on transference, about the optical images which are nowhere. They are seen at a given place when one is somewhere else to see them.

445. #445

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.78

     **II** > God and Woman's jouissance

     Theoretical move: Lacan advances the argument that the non-existence of the sexual relationship is the ground from which its supplements (love, phallic jouissance, courtly love) must be theorised, and uses the distinction between reading and understanding—illustrated by commentary on *Le titre de la lettre*—to reframe the Subject Supposed to Know as the very structure of love/transference.

     the importance of the term 'excluded' in my topology - but it's of no import, since that's not what we're here to talk about.

446. #446

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.27

     **II** > To Jakobson > **What is the signifier?**

     Theoretical move: Lacan redefines the signifier topologically by insisting on the bar between signifier and meaning-effect, introduces 'signifierness' (signifiance) as the excess of the signifier over signification, and pivots from asking about 'a signifier' to the signifier 'One' (Un), arguing that the unconscious structured like a language displaces the Cartesian cogito by making the subject the one who utters stupidities rather than the one who thinks.

     the signifier…must be structured in topological terms.

447. #447

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.20

     On Feminine Sexuality The Limits of Love and Knowledge > On jouissance

     Theoretical move: The passage argues that feminine sexuality is constituted by a logical "one by one" (une par une) structure that derives from the Other rather than from bodily substance, making sexual jouissance "compact" and the feminine sexed being "not-whole"—a claim illustrated through the Don Juan myth and grounded in a topology that refuses any reference to being or substance.

     I could not summarize it with a topology that does not involve the same mainspring, the same discourse, but rather a different one, one that is so much purer

448. #448

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.18

     On Feminine Sexuality The Limits of Love and Knowledge > On jouissance

     Theoretical move: Lacan argues that sexual jouissance is structurally defined by an impasse—the impossibility of the sexual relationship—and uses topological concepts (compactness, open sets, finity) to articulate how phallic jouissance constitutes an obstacle to jouissance of the Other, while the Not-all marks the female pole's irreducible remainder. Love is revealed as narcissistic, and its object-like substance is in fact the objet petit a as remainder in desire.

     In this space of jouissance, to take something that is limited or closed constitutes a locus, and to speak of it constitutes a topology... I believe I demonstrate the strict equivalence between topology and structure.

449. #449

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.133

     **¹⁰⁷x** > Rings of string

     Theoretical move: Lacan uses the impossibility of metalanguage to pivot toward topology: because the symbolic ex-sists rather than being, and because language can only be transmitted through further language, the matheme/formalization points beyond itself to the Borromean knot as the structural figure that can 'operate' on the first knot—linking writing, jouissance, and the non-rapport of sexuation under a single topological framework.

     It took a long time for people to realize, thanks to topology, that what is enclosed in a torus has absolutely nothing to do with what is enclosed in a bubble.

450. #450

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.141

     **¹⁰⁷x** > Rings of string > Answers 119

     Theoretical move: Lacan argues that topology founded on the Borromean knot and rings of string — rather than on dimensional cuts — provides a more fundamental approach to space, ultimately identifying the "inner eight" produced by reducing the Borromean knot as the symbol of the subject, and the simple ring as object a, thus grounding the cause of desire in topological structure rather than intuitive spatial intuition.

     It is remarkable that a figure as simple as that of the Borromean knot has not served as a point of departure for - a topology.

451. #451

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.140

     **¹⁰⁷x** > Rings of string

     Theoretical move: Lacan uses the topology of Borromean knots and rings of string to ground a theory of desire, the subject, and the Other: object a is the void presupposed by demand, the subject's division is structurally equivalent to the 'bending' of a ring, and the Other is not additive to the One but is the 'One-missing' — a difference internal to the One rather than supplementary to it.

     There is no topological analogy between the two ways of knotting the rings of string I showed you. In the case of the sailor's knots, there is what might be called a topology of twisting compared to the preceding one, which is simply one of bending.

452. #452

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.53

     **II** > Love and the signifier

     Theoretical move: Lacan argues that analytic discourse breaks with the cosmological presupposition of a unified world-substance by privileging the letter and writing over lived meaning-effects; love is posited as what "makes up for" the non-existent sexual relationship, and the unconscious is clarified as structured *like* (not *by*) a language—specifically like the assemblages of set theory, which are constituted (not merely designated) by letters.

     following the thread of analytic discourse goes in the direction of nothing less than breaking up anew (rebriser), inflecting, marking with its own camber... that which produces the break (faille) or discontinuity.

453. #453

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.43

     **II** > **The function of the written¹**

     Theoretical move: There is no prediscursive reality — every reality is founded by discourse — and the non-existence of the sexual relationship is the negative foundation on which all writing (and analytic discourse specifically) rests; the bar in the Saussurean formula is the graphic index of this impossibility, marking that the written is precisely what cannot be understood, while man and woman exist only as signifiers articulated through the phallic and not-all positions respectively.

     Let us take things at the level of a writing (un écrit) that is itself the effect of a discourse, scientific discourse, namely the writing (l'écrit) S, designed to connote the place of the signifier, and s with which the signified is connoted as a place. Place as a function is created only by discourse itself.

454. #454

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.177

     **Seminar 9: Wednesday 20 March 1973**

     Theoretical move: Lacan distinguishes the true from the real by arguing that truth can only be "half-said" (because jouissance constitutes its limit), while the real is accessible only through the impasse of formalisation; the mathemes (objet a, S(Ø), $) are introduced as written supports that, unlike speech, can designate the limits where the symbolic encounters the real—culminating in the claim that the phallic function is a contingency (ceases not to be written) rather than a necessity or impossibility.

     the spider's web, a truly miraculous function to see...from the surface itself, the one which for us allows the outline of the tracing of these writings which are finally the only point where we might find graspable these limits

455. #455

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.12

     **Seminar 1: Wednesday 21 November 1972**

     Theoretical move: Lacan deploys topological concepts of compactness and open sets to demonstrate that the impossibility of the sexual relationship is what structures all discourse, and that feminine sexuality is characterized by the 'not-all'—women taken 'une par une'—rather than by phallic jouissance or universal fusion, grounding sexuation in a logical rather than anatomical requirement.

     it is a locus, and to speak about it is a topology... I believe I demonstrated the strict equivalence between topology and structure

456. #456

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.259

     (3) Naturally since I made a small mistake

     Theoretical move: Lacan uses the Borromean knot topology to ground the asymmetry between the One and the Other (woman as "less One"), arguing that mathematisation alone accesses the Real—defined as the mystery of the speaking body and the unconscious—while distinguishing the Real from both fantasy and traditional reality.

     Is it not in this possibility of difference, since moreover there is no topological analogy between the two ways of knotting these rings of string?

457. #457

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.246

     Seminar 12: Wednesday 15 Ma y 1973

     Theoretical move: Lacan advances the thesis that there is no metalanguage by distinguishing the Symbolic from being, grounding formalisation in the act of saying rather than in ontological subsistence, and then demonstrates how topology—specifically the Borromean knot and the torus—provides the only adequate 'writing' of what cannot be said about the sexual non-relation and the structure of the subject.

     It took a long time for it to be noticed thanks to topology that what is enclosed in a torus, is something that has absolutely nothing to do with what is enclosed in a bubble.

458. #458

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.103

     Semina r **5:** Wednesday **16 January 1973**

     Theoretical move: Lacan advances the claim that analytic discourse, grounded in the letter rather than in lived experience or phenomenal appearance, compels an abandonment of the ontological "world" in favour of *par-être* (being-to-one-side), and that mathematics—specifically set theory's use of the letter—provides the orientation point for reading the effects of language precisely where the sexual relationship is absent.

     to break up again, to inflect, to mark by its own incurvation, and an incurvation which could not even be maintained as being that of lines of force, which produces as such the flaw, the discontinuity, the rupture.

459. #459

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.272

     Seminar 13: Wednesday 26 Jun e 1973

     Theoretical move: The passage argues that the subject is constituted by the signifier (as hypothesis necessary to lalangue), that love is grounded in a subject-to-subject relation of unconscious knowledges, and that the sexual non-relation is modalized through the logic of necessity/contingency (ceasing/not ceasing to be written), with love as the illusory passage from contingency to necessity.

     I brought along here the piece of string to illustrate it. The piece of string in so far as it makes this ring (rond), this ring whose possible knot with another I began to examine.

460. #460

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.255

     (3) Naturally since I made a small mistake

     Theoretical move: Lacan uses the Borromean knot as a topological demonstration that the One (ring of string enclosing nothing but a hole) grounds both the structure of desire—where the objet petit a is not a being but a void supposed by demand, sustained only by metonymy—and the logic of mathematical language, where removing a single element disperses all the rest simultaneously.

     the third element in its topological relationship would not have the same relationship with the two others as the two others among themselves.

461. #461

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.15

     **Seminar 1: Wednesday 21 November 1972** > What does that mean?

     Theoretical move: Lacan argues that psychoanalytic discourse resists grounding in any substance or being, and that the impossibility of predication (the absolute 'being' that cannot be completed) is revealed precisely through the fracture of sexed being as it is constituted by jouissance—thus breaking with philosophy and grounding analysis in topology rather than ontology.

     a topology of which nevertheless we cannot say does not arise from the same source

462. #462

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.140

     Semina r **5:** Wednesday **16 January 1973** > **Seminar 7: Wednesday 20 February 1973**

     Theoretical move: Lacan advances the argument that what supplements the absent sexual relationship is not a dyadic fusion but a singular "there is something of the One" — irreducibly solitary — and that love (including transference as love) is the operative name for this supplement; the big Other, far from being abolished, must be reckoned with precisely as the site that mediates between the sexes in the absence of a sexual relationship, a point that also grounds his endorsement of courtly love as a "feint" for the missing relation.

     the terms excluded, to exclude have all their importance in our topology.

463. #463

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.88

     **Seminar 4: Wednesday 9 January 1973**

     Theoretical move: Lacan argues that ontology is a product of the accentuation of the copula "to be" within philosophical/master discourse, that there is no pre-discursive reality (all reality is grounded in discourse), and that the sexual relationship cannot be written — a claim sustained by the bar in the Saussurean algorithm and the letter as a radical effect of discourse.

     it is not simply that linguistics has distinguished them... If the bar were not there you could not see that there is something of the signifier injected into the signified.

464. #464

     Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan

     What is the signifier?

     Theoretical move: The passage argues that the signifier must be understood topologically rather than purely phonologically: it produces a meaning effect, and between signifier and signified a bar is inscribed that must be crossed over — a structure whose lineage runs from the Stoics through Augustine, not merely from Saussure, and which cannot be reduced to its phonematic support.

     the signifier as the rites of the linguistic tradition... is to be structured in topological terms.

465. #465

     Seminar XXII · R.S.I. · Jacques Lacan · p.163

     **Introduction** > **Seminar 10: Tuesday 15 April 1975**

     Theoretical move: Lacan argues that the Borromean knot provides the only adequate structural account of desire, the Symbolic, and the Name-of-the-Father: the Symbolic consists precisely in the hole it makes, the prohibition of incest is not historical but structural (identical with that hole), and the Name-of-the-Father is the Father-as-naming that knotted through that hole – a logic that admits an indefinite plurality of Names-of-the-Father, each resting on one hole that communicates consistency to all the others.

     a hole provided it is consistent, that is circumscribed, a hole is sufficient to knot together a strictly indefinite number of consistencies. And this begins with two as is manifest by this Borromean knot here

466. #466

     Seminar XXII · R.S.I. · Jacques Lacan · p.101

     **Introduction** > **Seminar 7: Tuesday 11 March 1975**

     Theoretical move: Lacan reframes the Names-of-the-Father as identical to the RSI triad (Real, Symbolic, Imaginary), argues that the phallus furnishes the consistency of the Real while enjoyment ek-sists with respect to it, and situates naming/the Borromean knot as the structural answer to the philosophical impasse between realism and nominalism about language and the Real.

     I have been led to the showing of this knot, while what I was looking for was a demonstration of a doing, the doing of analytic discourse

467. #467

     Seminar XXII · R.S.I. · Jacques Lacan · p.143

     **Introduction** > **Seminar 9: Tuesday 8 April 1975**

     Theoretical move: Lacan uses the Borromean knot's topology — particularly the distinction between ek-sistence (the track/cycle) and the hole — as the operative figure for primordial repression (Urverdrängt), arguing that the difficulty of mentally grasping the knot is itself the trace of an irreducible, foundational repression, and that the inexistence of the sexual relationship is not a failure but the very structure knotted into being.

     There is all the same an approach, an approach that is expressed in what mathematics has described as topology which envisages space differently.

468. #468

     Seminar XXII · R.S.I. · Jacques Lacan · p.80

     **Introduction** > **Seminar 5: Tuesday 11 February 1975**

     Theoretical move: Lacan argues that the Borromean knotting of the Symbolic, Imaginary, and Real requires a fourth supplementary element—the Name-of-the-Father (functioning as a fourth torus)—to hold the three registers together, while simultaneously opening the question of whether this paternal supplement is strictly indispensable or merely historically contingent in Freud and in current analytic practice.

     what is meant by the fact that there ek-sists a construction whose consistency must not be imaginary? There is only a single condition which is quite readable…for that there must be a hole. And this is what brings us to what is called the topology of the torus

469. #469

     Seminar XXII · R.S.I. · Jacques Lacan · p.94

     **Introduction** > **Seminar 6: Tuesday 18 February 1975**

     Theoretical move: Lacan reframes ek-sistence as the Real dimension of the Borromean Knot, uses this to articulate the triadic RSI structure as an "infernal trinity," and pivots to redefine the symptom—against both Hegelian repetition (via Kierkegaard) and Marxian social analysis—as the particular way each speaking being (parlêtre) enjoys their unconscious.

     nodalising of the Imaginary, the Symbolic and the Real

470. #470

     Seminar XXII · R.S.I. · Jacques Lacan · p.153

     **Introduction** > **Seminar 10: Tuesday 15 April 1975**

     Theoretical move: Lacan argues that the Borromean knot is not a model or representation but the Real itself — its topological structure (where breaking one element unknots all others) grounds the concepts of the unconscious as Real, the non-existence of the sexual relationship, and hainamoration, while the signifier is redefined as that which makes a hole, linking the Symbolic to the Real through knotting.

     A topology is what, at the start, indicates how what is not knotted two by two can nevertheless make a knot.

471. #471

     Seminar XXII · R.S.I. · Jacques Lacan · p.167

     **Introduction** > **Seminar 10: Tuesday 15 April 1975**

     Theoretical move: Lacan re-reads Freud's three identifications through the topology of the Borromean knot, arguing that the cartel's structure (three plus-one) is grounded in the Name-of-the-Father as the fourth term that knots the triskel of Symbolic, Imaginary and Real into a genuine Borromean bond, thereby locating identification, love, and desire at the topological heart of the social knot.

     in the three, one never knows which of the three is real, and that indeed is why there must be four

472. #472

     Seminar XXII · R.S.I. · Jacques Lacan · p.22

     **Introduction** > **Seminar 2: Tuesday 17 December 1974**

     Theoretical move: Lacan argues that the Borromean knot is not a model (which would be grounded in the Imaginary) but rather a writing that directly supports the Real; the three registers (R.S.I.) achieve consistency only by holding together, and jouissance ek-sists to the Real as a hole, with phallic jouissance functioning as the nodal term that analytic experience discovers as primary.

     each of its elements can have two forms, the form of the infinite straight line, and the form that I designate…by a ring of string, which proves when one studied it to be a torus.

473. #473

     Seminar XXII · R.S.I. · Jacques Lacan · p.88

     **Introduction** > **Seminar 6: Tuesday 18 February 1975**

     Theoretical move: Lacan advances the Borromean knot as the primary topological operator of his theory, arguing that its three constitutive dimensions—consistency, hole, and ek-sistence—correspond respectively to the Imaginary, Real, and Symbolic; the passage works through errors in flattening the knot to demonstrate that mathematical/geometric intuition is rooted in the cord (material consistency) and that the straight line as infinity is itself a ring, implicating the knot structure throughout.

     I noted the fact that it was no less drawable and that it remained a knot on this single condition that one of its buckles is opened out and that it is transformed into a straight line.

474. #474

     Seminar XXII · R.S.I. · Jacques Lacan · p.18

     **Introduction** > **Seminar 1: Tuesday 10 December 1974**

     Theoretical move: Lacan assigns the Borromean knot to the Imaginary register (grounded in three-dimensional space), then uses it as a topological framework to redistribute Freud's triad of Inhibition/Symptom/Anxiety across the three registers: Inhibition as arrest in the Symbolic, Anxiety as arising from the Real, and the Symptom as the effect of the Symbolic in the Real—with Jouissance locatable at the intersections of the knot.

     How does it happen that we must have this flattening out in order to be able to depict any topology whatsoever? It is very certainly a question which reaches out towards that of the defectiveness that I qualified as mental

475. #475

     Seminar XXII · R.S.I. · Jacques Lacan · p.46

     **Introduction** > **Seminar 3: Tuesday 14 January 1975**

     Theoretical move: Lacan reframes the Borromean knot topology as the minimal structure of existence (ek-sistence), arguing that Freud's Oedipus complex functions as a fourth term (psychical reality) needed to knot the Symbolic, Imaginary, and Real because Freud lacked the three-ring Borromean solution; analysis itself operates by making the Real surmount the Symbolic at two crossing points, rendering the fourth term (Oedipus complex / Name-of-the-Father) superfluous.

     existence is of its nature what eks. What turns the consistent but what creates an interval, and which in this interval has many ways of being knotted.

476. #476

     Seminar XXII · R.S.I. · Jacques Lacan · p.120

     **Introduction** > **Seminar 8: Tuesday 18 March 1975**

     Theoretical move: Lacan uses the topology of oriented Borromean knots to argue that the Symbolic, Imaginary, and Real are homogenised by 'consistency' (similarity, not sameness), and that the necessity of 'flattening-out' the knot to demonstrate its uniqueness exposes a fundamental limitation of conceptual thought in grasping the Real — a limitation that underwrites the formula 'there is no sexual relationship.'

     it is possible to depict, I am not saying to write, to depict the Borromean knots, in such a way… that they only come undone from one end

477. #477

     Seminar XXII · R.S.I. · Jacques Lacan · p.7

     **Introduction** > **Seminar 1: Tuesday 10 December 1974**

     Theoretical move: Lacan opens Seminar XXII by arguing that the Real, Symbolic, and Imaginary only acquire a "common measure" — i.e., can be said to be genuinely three — through the Borromean knot, which provides the minimal topological structure (requiring three as its minimum) that holds them together; this displaces Freud's spatial-geometrical (sack) topology in favour of a knot-based topology, and identifies the Imaginary as grounded in the body, the Symbolic in equivocation/writing, and the Real as strictly unthinkable.

     This geometry of the sack is indeed this thing that we have to deal with at the level of topology, except for the fact that, as perhaps the idea has come to you, this is drawn on a surface and that we are forced to put the sack onto it.

478. #478

     Seminar XXII · R.S.I. · Jacques Lacan · p.149

     **Introduction** > **Seminar 9: Tuesday 8 April 1975**

     Theoretical move: Lacan argues, via topological analysis of orientation, that the Borromean knot is not intrinsically orientated, but that as soon as one of its three rings is specified (coloured, or rendered non-orientatable by being treated as an infinite straight line), two distinct orientated Borromean knots necessarily emerge — a result that bears on the structural irreducibility of dextro- vs. laevo-gyratory gyres and, implicitly, on the sexuation of topological space in his clinical theory.

     there are two gyres, two orientated Borromean knots, not just one, starting from the moment when we made an infinite straight line from one of the three, in so far as the infinite straight line is defined as non-orientatable.

479. #479

     Seminar XXII · R.S.I. · Jacques Lacan · p.180

     **Introduction** > **Seminar 11: Tuesday 13 May 1975**

     Theoretical move: Lacan uses projective geometry (points at infinity, Desargues) and the topology of the Borromean knot to argue that the unknotted status of two terms is precisely the condition for their being knotted by a third, and then extends this to a fourth term—nomination—distributed across the three registers (Imaginary, Real, Symbolic), with each mode of nomination corresponding to inhibition, anxiety, or symptom respectively, and ultimately to the Name of the Father.

     By raising the question of the knot, we are going to see, I am going to depict something for you here, ah!, that I hope to get to the end of, in the form of a knot, a true one

480. #480

     Seminar XXII · R.S.I. · Jacques Lacan · p.76

     **Introduction** > **Seminar 5: Tuesday 11 February 1975**

     Theoretical move: Lacan argues that the Borromean knot provides the model for a "Real meaning effect" in analytic interpretation: by homogenising the three registers (Symbolic, Imaginary, Real) as equally consistent and showing their non-chain knotting, he repositions the analytic saying (*dire*) as what makes a knot—not mere word-use—while introducing "ek-sistence" as the Real correlate of the knotted Imaginary.

     I could of course have taken it in any way whatsoever... there is not only one way and only one single way, because there is more than one to make this knot Borromean.

481. #481

     Seminar XXII · R.S.I. · Jacques Lacan · p.177

     **Introduction** > **Seminar 11: Tuesday 13 May 1975**

     Theoretical move: Lacan uses the topology of the Borromean knot to argue that the Real, Symbolic, and Imaginary are not distinguished by their threeness alone but by the specific logical properties of the knot (necessity and sufficiency of each element), and introduces 'nomination' as a fourth element that knots an otherwise unknotted triad — advancing toward a topology of four that will structure his next year's work (4, 5, 6).

     mathematics, the one properly qualified as topology, gives us a figure in the form of the torus of something that can depict the hole. Now topology does nothing of the kind, if only because the torus has two holes

482. #482

     Seminar XXII · R.S.I. · Jacques Lacan · p.40

     **Introduction** > **Seminar 3: Tuesday 14 January 1975**

     Theoretical move: Lacan deploys the Borromean knot as a material figure of "consistency" — a real, non-linguistic holding-together that underlies the knotting of the three registers (Real, Symbolic, Imaginary) — and uses this to argue that topology, not geometry, is the proper medium for grasping what psychoanalysis works on, while also implicating number (via Peano's successor axiom) and the dimension of the spoken being (dit-mansion) in the same problematic.

     we had to be well advanced into the 20th Century for something to be outlined that could be called a theory of knots…this theory of knots is in its infancy, is extremely clumsy.

483. #483

     Seminar XXII · R.S.I. · Jacques Lacan · p.141

     **Introduction** > **Seminar 9: Tuesday 8 April 1975**

     Theoretical move: Lacan argues that the Imaginary is structurally "stuck" in the sphere-and-cross figure (a pre-topological image of the body), and that the Borromean knot represents the proper topological instrument for escaping this captivity — linking the knot's discovery to the analytic discourse as a new social bond and to the Freudian "hole" in the universe, while insisting that truth can only be half-said.

     What is the equivalence of the straight line to the circle? It is obviously to make a knot. It is a consequence, is it not, of the Borromean knot.

484. #484

     Seminar XXII · R.S.I. · Jacques Lacan · p.59

     **Introduction** > **Seminar 4: Tuesday 21 January 1975**

     Theoretical move: Lacan advances the thesis that "a woman is a symptom" for a man, grounding this in the structure of phallic jouissance, the non-existence of The woman (not-all), and the logic of belief — distinguishing believing-in (the symptom/neurosis) from believing-her (love/psychosis) — while also reformulating the paternal function as père-version and redefining the symptom as an untamed form of writing from the unconscious.

     this interval between, as I might say, two consistencies, the one that is noted here by an edge that I made the edge of a page [IV-1] and the one that is buckled here [IV-2], is buckled, being buckled implying the hole without which there is no knot.

485. #485

     Seminar XXII · R.S.I. · Jacques Lacan · p.111

     **Introduction** > **Seminar 7: Tuesday 11 March 1975**

     Theoretical move: The passage advances the thesis that the Real is defined by its ek-sistence *outside* meaning—as the impossible, the expelled, the anti-meaning—and that the Borromean knot of Real, Symbolic, and Imaginary is the structural form of the Name-of-the-Father, with feminine ek-sistence (as symptom) arising where the Symbolic circles an inviolable hole and the not-all resists phallic universality.

     Is there a discernible order here? Is the Borromean knot a whole, a conceivable whole, make no mistake, or indeed does it imply an order?

486. #486

     Seminar XXII · R.S.I. · Jacques Lacan · p.52

     **Introduction** > **Seminar 4: Tuesday 21 January 1975**

     Theoretical move: Lacan uses the Borromean knot's topological properties to argue that the three consistencies—Symbolic, Imaginary, and Real—are irreducibly linked and that this triadic structure grounds both representation and the subject's condition, while the objet petit a (small o), as cause of desire rather than its object, marks an irrational, non-conjunctive gap between the One of the signifier and the One of meaning.

     The true knot, the knot with which we busy ourselves in the theory of knots, is that which...is precisely what is not transformed by a continuous distortion into the trivial figure of the ring.

487. #487

     Seminar XXII · R.S.I. · Jacques Lacan · p.129

     **Introduction** > **Seminar 8: Tuesday 18 March 1975**

     Theoretical move: Lacan argues that the Borromean Knot—understood through the topology of the torus—displaces the insoluble question of objectivity and grounds the three consistencies (Imaginary, Symbolic, Real) as irreducible, such that their triple points generate meaning, phallic jouissance, and the Name-of-the-Father respectively; identification is then reformulated as three distinct operations corresponding to the three registers of the knot's real Other.

     It allows you to think, but it is a retrospective thought, that aesthetics, that what you sense, in other words, is not in itself, as they say, transcendental, that it is linked to what we can very well conceive of as contingency

488. #488

     Seminar XXII · R.S.I. · Jacques Lacan · p.30

     **Introduction** > **Seminar 2: Tuesday 17 December 1974**

     Theoretical move: Lacan argues that the Borromean knot structures the three registers (R.S.I.) such that phallic enjoyment, ek-sistence, and the hole are each topologically grounded: phallic enjoyment is produced through the knotting of the Symbolic ring; the Real is made by jouissance that ek-sists; and the sexual non-relationship is inscribed in language rather than filled by it, with anxiety marking the limit of enjoyment of the other body.

     this phantastical topography which the second is…the sack of the body, it is with this sack that the ego is depicted

489. #489

     Seminar XXIII · The Sinthome · Jacques Lacan · p.177

     Seminar 10: Wednesday 13 April 1976 > There you are!

     Theoretical move: Lacan advances the Borromean knot as the first genuine philosophical writing—a "logic of sacks and cords"—and uses Joyce's anomalous relationship to his own body (body-as-foreign, affect that "drains away" like a fruit skin) to theorise a specific ego-function that writing fulfils when the normal bodily imaginary fails, distinguishing this from the Freudian Unconscious as ignorance of the body.

     Topology indicates to us that in a circle, there is a hole in the middle... The infinite straight line has as a virtue having the hole all around. It is the most simple support of the hole.

490. #490

     Seminar XXIII · The Sinthome · Jacques Lacan · p.118

     Seminar 7: Wednesday 17 February 1976

     Theoretical move: The sinthome is theorized topologically as a fourth ring that repairs an error in the Borromean knot—where the Symbolic, Imaginary, and Real come undone—and is deployed to explain both Joyce's artistic practice (as compensation for paternal lack) and the clinical phenomenon of imposed words in psychosis, thereby linking the topology of knotting to the structure of symptom formation and paternal function.

     So then, what I said the last time is the following. Alluding to the fact that the symptom, what I called this year the sinthome, that the sinthome is what in the Borromean, the Borromean chain, is what allows...

491. #491

     Seminar XXIII · The Sinthome · Jacques Lacan · p.175

     Seminar 10: Wednesday 13 April 1976 > QUESTIONS

     Theoretical move: Lacan argues that the Borromean knot/chain must be written (not merely thought) to function as a support for thinking, and that this written topology transforms the very meaning of writing by granting it an autonomy irreducible to the signifier's precipitation—the latter being Derrida's domain—while the knot's own logic operates through the 'dit-mension' (dimension of the said), which structurally implies that what is said is not necessarily true.

     What is at stake in reality, is not a knot but a chain - this Borromean chain.

492. #492

     Seminar XXIII · The Sinthome · Jacques Lacan · p.26

     **Seminar 2: Wednesday 9 December 1975**

     Theoretical move: Lacan pivots the Borromean knot from a topological figure to a methodological foundation, arguing that the knot's three-fold structure (Symbolic/Imaginary/Real) captures the subject as constitutively divided by language, which operates not as an organ or message but by making a hole in the Real — thereby placing psychoanalysis in opposition to both science's objectivism and Chomsky's organicist linguistics.

     For this there is the path of our new mos geometricus, namely, of the substance that results from the efficacity, from the proper efficacity of language, and which is supported by this function of the hole.

493. #493

     Seminar XXIII · The Sinthome · Jacques Lacan · p.165

     Seminar 10: Wednesday 13 April 1976

     Theoretical move: Lacan argues that his invention of the Borromean knot as a writing of the Real constitutes a 'forcing'—a traumatic inscription of a new symbolic form—that both responds symptomatically to Freud's energetics and exposes the absence of any Other of the Other, while also identifying the Real as his own sinthome rather than a spontaneous idea.

     Is illustrated by the fact that in this flattened-out knot, I show a field as essentially distinct from the Real which is the field of meaning.

494. #494

     Seminar XXIII · The Sinthome · Jacques Lacan · p.148

     Seminar 9: Wednesday 16 March 1976

     Theoretical move: Lacan advances the Real as fundamentally unbound and orientating-without-meaning, distinguishes a more radical foreclosure than that of the Name-of-the-Father, and ties the Death Drive to the Real itself, while the matheme (and the Borromean knot as topological device) are offered as instruments for reaching "bits of Real" that resist symbolic embroidery.

     The ego is a device. It's a device about which I have cogitated in terms of a knot, of a knot that has been cogitated by a mathematician who has no other name than Milnor. He invented something, namely, the idea of chain he called that, in English, link.

495. #495

     Seminar XXIII · The Sinthome · Jacques Lacan · p.97

     **Seminar 5: Wednesday 20 January 1976** > Jacques Aubert's intervention > *Where now?*

     Theoretical move: Jacques Aubert's intervention traces Joyce's deployment of legitimacy, certitude, and the voice-effects of the signifier across his work, while Lacan closes by grounding these in the Borromean knot and its irreducible topological ambiguity (the indistinguishability of its rings without colouring), arguing that right/left orientation cannot be expressed in the Symbolic.

     If the knot, if the properly speaking Burromean knot, which is not a knot but a chain, if one can locate the duplicity of this knot... it is only with the help of this messing that we carry on with, that there are two knots.

496. #496

     Seminar XXIII · The Sinthome · Jacques Lacan · p.186

     Seminar 10: Wednesday 13 April 1976 > There you are!

     Theoretical move: Lacan uses the topology of the Borromean knot to reframe Joyce's ego as a reparatory/corrective function that compensates for the failure of the Imaginary to knot properly with the Real and the Unconscious, thereby subordinating Joyce's singularity to the structural logic of père-version (perversion-as-father-function) and arguing that all human sexuality is perverse in Freud's sense.

     I am incarnating the ego, here, the ego as a corrector of this lacking relationship… in drawing it. Here exactly is what happens

497. #497

     Seminar XXIII · The Sinthome · Jacques Lacan · p.36

     **Seminar 2: Wednesday 9 December 1975** > QUESTIONS

     Theoretical move: Lacan uses a seminar Q&A to clarify the topological function of the Borromean knot as the fourth term (symptom) that holds RSI together, argues that the Real operates as a third pole mediating between body and language rather than being reducible to either, and distinguishes the knot from a 'model' on the grounds that it resists imagination while topology itself remains insufficient to prove its four-fold Borromean realisation.

     Its mathematical approach in topology is insufficient. I, I can all the same tell you, in short, can I not, my experience during this vacation.

498. #498

     Seminar XXIII · The Sinthome · Jacques Lacan · p.20

     Seminar 1: Wednesday 18 November 1975

     Theoretical move: By introducing an infinite straight line into a "false hole," Lacan demonstrates topologically that this operation converts it into a genuine Borromean hole — the infinite line playing the structural role that allows the knot to subsist. Hegel's figure of the circle is invoked as a philosophical precursor that grasped circularity's function, though without addressing the Borromean stakes.

     simply suppose here a straight line, this will fulfil the same role, a straight line provided it is infinite.

499. #499

     Seminar XXIII · The Sinthome · Jacques Lacan · p.31

     **Seminar 2: Wednesday 9 December 1975**

     Theoretical move: Lacan argues that the Borromean knot—understood as the concrete support of any relation between things—constitutes the Real, Symbolic, and Imaginary as interdependent, and that the parlêtre's bodily status depends entirely on this knot; Joyce's art is then positioned as uniquely aimed at substantialising the fourth term (the sinthome) that completes and holds this knot.

     it is always the same folded circle that is found here, in a special position, namely bent twice… taken four times, as one might say, with itself. This effectively permits it to be seen that just as here each of these circles corner twice the buckle

500. #500

     Seminar XXIII · The Sinthome · Jacques Lacan · p.61

     **Seminar 4: Wednesday 13 January 1976** > W w e W.

     Theoretical move: Lacan uses Joyce's riddle (the fox burying his grandmother) as an exemplar of the analytic response — necessarily "stupid" relative to the poem-like symptom — and argues that meaning is produced by suturing/splicing the Imaginary to the Symbolic, while simultaneously splicing the sinthome to the parasitic Real of enjoyment; the Borromean knot is the structural model for this therapeutic operation.

     Writing may have always something to do with the way in which we write the knot. It is obvious, that a knot is usually written like that. That already gives an S.

501. #501

     Seminar XXIII · The Sinthome · Jacques Lacan · p.19

     Seminar 1: Wednesday 18 November 1975

     Theoretical move: Lacan argues that the Borromean Knot must be understood as a tetradic (four-ring) structure in which the sinthome serves as the fourth element linking the otherwise separate Symbolic, Imaginary, and Real; the Oedipus complex is recast as a symptom/sinthome, and the father's name is itself a sinthome, with Joyce's art exemplifying how artifice can work upon and through the symptom via equivocation in the signifier.

     Each of these holes must be circumscribed by something which makes them hold together, in order for us to have here something that can be described as a true hole... what we call in topology a torus.

502. #502

     Seminar XXIII · The Sinthome · Jacques Lacan · p.137

     Seminar 7: Wednesday 17 February 1976 > **Seminar 8: Wednesday 9 March 1976**

     Theoretical move: Lacan uses the Borromean chain's topological manipulability (turning inside-out, colouring, orientation) to argue that the Real is not a single ring but is constituted by the knot-relation itself, and that the circle's hole—not its closure—is what founds both set theory's not-all and the chain's supple geometry as opposed to rigid, formal demonstration.

     It is a different geometry which is founded on the chain.

503. #503

     Seminar XXIII · The Sinthome · Jacques Lacan · p.43

     **Seminar 3: Wednesday! 6 December 1975**

     Theoretical move: Lacan deploys the Borromean knot topology to distribute the three registers (Real, Symbolic, Imaginary) as structurally equivalent yet functionally differentiated supports—assigning consistency to the Imaginary, the hole to the Symbolic, and ex-sistence to the Real—and argues that a fourth term (the sinthome) is always required to prop up the subject, which the minimum Borromean chain of four demonstrates.

     this geometry which is that of knots, which I told you manifests an altogether specifically original geometry, is something that exorcises this uncanny

504. #504

     Seminar XXIII · The Sinthome · Jacques Lacan · p.57

     **Seminar 4: Wednesday 13 January 1976**

     Theoretical move: Lacan argues that the Borromean knot is the proper topological support for "first truths" about the Real, which is founded precisely by excluding meaning; and that the speaking being's (parlêtre's) only consistency is bodily/imaginary, while the knot — not the cord — is what properly ex-sists, grounding both truth and the analyst's responsibility in know-how (savoir-faire) rather than in any Other of the Other.

     In a cord, the knot is all that ex-sists in the proper sense of the term, as I write it, is all that properly speaking exists... we must all the same distinguish between consistency and knot.

505. #505

     Seminar XXIII · The Sinthome · Jacques Lacan · p.105

     **Seminar 5: Wednesday 20 January 1976** > **Seminar 6: Wednesday 10 February 1976**

     Theoretical move: Lacan uses Joyce's relationship to madness, faith, and writing as a clinical-theoretical probe to distinguish the true from the Real, locating jouissance (including masochism) in the Real rather than the true; he simultaneously advances a topological argument about the Borromean knot and the torus as the best available "physics" for measuring belief and subjective structure.

     topology is based on the fact that there is at least without counting whatever else is there- that there is at least something called the torus.

506. #506

     Seminar XXIII · The Sinthome · Jacques Lacan · p.166

     Seminar 10: Wednesday 13 April 1976 > QUESTIONS

     Theoretical move: Lacan distinguishes the sinthome from psychoanalysis proper, arguing that it is the *psychoanalyst* (not psychoanalysis) who functions as a sinthome — a "help against" in the biblical sense — and that the Real, as lawless and devoid of meaning, may itself be illuminated as sinthome; simultaneously, the Borromean knot is defended as a topology that can hold Symbolic, Imaginary, and Real together as separable rings without a common point.

     It is in the measure that I believe I am able, first, from something which is a crude topology, to support what is at stake. Namely, the very function of the Real as distinguished

507. #507

     Seminar XXIII · The Sinthome · Jacques Lacan · p.48

     **Seminar 3: Wednesday! 6 December 1975**

     Theoretical move: Lacan advances the argument that the Borromean knot of three (Imaginary, Symbolic, Real) constitutes the minimal support of the subject — and is itself the structure of paranoid psychosis — while the Sinthome emerges as a necessary fourth term that knots the three rings when they would otherwise come apart, with phallic jouissance located at the conjunction of the Symbolic and the Real, and meaning at the conjunction of the Symbolic and the Imaginary.

     there are two depending on whether it is dextrogyratory or laevogyratory. This is then a problem that I am putting to you: what is the link between these two kinds of Borromean knots and the two kinds of knots of three?

508. #508

     Seminar XXIII · The Sinthome · Jacques Lacan · p.124

     Seminar 7: Wednesday 17 February 1976

     Theoretical move: Lacan argues that the sinthome is precisely what installs sexual non-equivalence and thereby makes the sexual relationship possible: it is not despite the absence of the sexual relationship but through the sinthome (which repairs the failed Borromean knot asymmetrically) that something like a relation is structured, such that woman is the sinthome for man and man is a "devastation" for woman.

     between this and this, namely, the sinthome and the loop which is made here, as I might say, spontaneously, can be inverted from this to that, namely, let us say the red eight and the green ring, is strictly equivalent.

509. #509

     Seminar XXIII · The Sinthome · Jacques Lacan · p.108

     **Seminar 5: Wednesday 20 January 1976** > **Seminar 6: Wednesday 10 February 1976**

     Theoretical move: Lacan argues that Joyce's artistic ambition functions as a topological compensation for a de facto Verwerfung (foreclosure) by the father, and uses this to stage the broader claim that the Borromean knot articulates the entanglement of Symbolic, Imaginary, and Real — with the sinthome as the supplementary loop that prevents their dissolution, while also developing the logic of per-version (père-version) as the son-to-father relation structuring the drive.

     We must really believe that it happens like this (VI-4), namely, that there is an infinite straight line that penetrates into a torus... There is no real space. It is a purely verbal construction that has been spelled out in three dimensions.

510. #510

     Seminar XXIII · The Sinthome · Jacques Lacan · p.138

     Seminar 7: Wednesday 17 February 1976 > **Seminar 8: Wednesday 9 March 1976**

     Theoretical move: Lacan argues that the Borromean knot's essential property is the "false hole" produced when two circles conjoin, and that it is the Phallus—as the verifier of this false hole—that constitutes the Real; he then extends this topological claim to the sinthome (specifically Joyce's), lalangue, and the relation between the sexes, positioning the phallus as the sole signifier that creates every signified and thereby verifies the Real.

     the infinite straight line which, prudently, Soury and Thome do not use, the infinite straight line is an equivalent of the circle... at least as regards the chain. It is an equivalent whose point, one point of which is at infinity.

511. #511

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.53

     So then what is this lack? > **Seminar 5: Wednesday 18 January 1977**

     Theoretical move: Lacan uses the topology of the Borromean knot—approached through plaiting (tresse/quatresse), tetrahedra, and the torus—to argue that all nodal knotting is fundamentally toric, and then maps the four-element quatresse onto the registers of Real, Imaginary, Symbolic, and Symptom, concluding that the Real is specially suspended on the body and that language (the signifier as symptom) supplies for the absence of a sexual relationship.

     everything that concerns the Borromean knot is only articulated by being toric… A torus is characterised quite specifically as being one hole.

512. #512

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.92

     **Seminar 8: Wednesday 8 March 1977**

     Theoretical move: Lacan argues that the Real cannot constitute a universe on its own but only through its knotting with the Imaginary and Symbolic via the Borromean structure, and that the torus — not the simple ring — is the proper topological unit for this knotting; he further exploits the distinction between metaphor and structure to insist that topology here is structural (not merely analogical), while his anecdote about his grandson reframes the Unconscious as the intrusion of words one does not understand — language as parasitic.

     the rings of string on this particular occasion do not hold up. Something more is needed… these rings of string only held up on condition of being something that must be called by its name, a torus.

513. #513

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.45

     So then what is this lack? > **Seminar 4: Wednesday 11 January 1977**

     Theoretical move: Lacan argues that Knowledge (as unconscious signifier-effects) and Truth have no relation to one another, that the unconscious is structured as signifier-effects rather than philosophy, and that psychoanalysis is a 'scientific delusion' awaiting a science it may never produce — pivoting through the Four Discourses, the Borromean Knot, and the parlêtre to situate the irreducibility of the Real to matter.

     Language is always flattened out. And that indeed is why my twisted business of the Imaginary, the Symbolic and the Real... this indeed is what gives it its value. The value is that it is flattened out.

514. #514

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.62

     So then what is this lack? > **Seminar 6: Wednesday 8 February 1977**

     Theoretical move: Lacan introduces topological figures (flattening of the Borromean knot) to generate the Real/Imaginary distinction, then cedes the floor to Alain Didier Weill, who constructs a multi-stage circuit using the Graph of Desire and the Purloined Letter schema to theorise the *Passe* as a process by which successive inversions of knowledge between subject (Bozef) and Other (the King) propel the subject through positions of innocence, duplicity, and finally radical exposure before the Other.

     I think I have eventually found what could account for a topological montage which does not exist and which would account for the fact that the jury d'agrement perhaps does not manage to use

515. #515

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.26

     **Seminar 3: Wednesday 21 December 1976**

     Theoretical move: Lacan demonstrates that a double cut of a torus produces a double Möbius strip, and that this topological object has the key property that front and back (inside and outside) are indifferent from any fixed point of view — a structural indeterminacy he links to the possibility of the *une-bévue* (misreading/error), which can only be resolved by finding a dominant way of distinguishing the two cases.

     If in a systematic cutting up of a torus, a cutting up which has the result of producing a double Moebius strip, this cutting up is present here.

516. #516

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.106

     **Seminar 9: Wednesday 15 March 1977**

     Theoretical move: Lacan distinguishes sense (double-sens, meaning-effect rooted in the duplicity of the signifier) from meaning (a purely empty knotting of word to word), and uses torus topology to articulate the relations between Symbolic, Real, and Imaginary—arguing that anxiety is the symbolically real, the symptom is the only real thing that preserves sense, and that there is no sexual relationship except incestuous, with castration as the only truth.

     a holed torus… by holing this torus at the same time one makes a hole in another torus… the green torus is very precisely what we can call the complement of the other torus, namely, the linked torus.

517. #517

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.83

     So then what is this lack? > **Seminar 7: Wednesday 15 February 1977**

     Theoretical move: Lacan re-reads "The Purloined Letter" through the figure of Bozef (introduced by Alain Didier Weill) as an incarnation of Absolute Knowledge — knowledge that is in the Real but does not speak — to argue that the Borromean topology of RSI, the structure of the Passe, and the objectification of the unconscious all hinge on the same redoubling of knowledge ("I know that he knows that I know that he knows"), while distinguishing the silent, real truth from the lying Symbolic and the false-but-consistent Imaginary (consciousness).

     namely, not a relation between these terms which is spherical, but a relation that I could call toric.

518. #518

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.6

     **Seminar 1: Wednesday 16 November 1976**

     Theoretical move: Lacan opens Seminar XXIV by proposing 'une-bévue' as a superior translation of the Unbewusst, then pivots to argue that the end of analysis is not identification with the analyst or the unconscious but rather 'knowing how to deal with one's symptom' — and grounds this clinical proposition in a topological account of the torus (and its inside-out inversion) as the proper model for the relationship between inside and outside, Imaginary, Symbolic, and Real.

     A topology, such as you can grasp simply by opening anything at all called General Topology, a topology is always founded on a torus, even if this torus is at times a Klein bottle

519. #519

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.72

     So then what is this lack? > **Seminar 6: Wednesday 8 February 1977**

     Theoretical move: The passage theorises the Passe as the moment at which the split between knowledge and the locus of enunciation is overcome, producing a paradoxical "communion in non-being" at S(Ø) where subject and Other share the same lack, beyond fantasy and transference—this constitutes the structural condition for the emergence of a heretical, self-responsible analytic subjectivity.

     what he loses, is the dimension of topology that there is in him, namely, the dimension of the locus of enunciating, namely, the dimension of presence which in him can answer 'Present'

520. #520

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.20

     **Seminar 1: Wednesday 16 November 1976** > **Seminar 2: Wednesday 14 December 1976**

     Theoretical move: Lacan advances the thesis that the structure of man (and the living body) is toric rather than spheroidal, and uses this topology to reframe the relationship between the conscious and the unconscious as a double Möbius strip cut from a torus — displacing any notion of psychic "progress" and redefining the une-bévue (mis-hearing/blunder) as the structural condition of the signifier's exchange value.

     I am attached to considering the torus as being capable of being cut out in terms of a Moebius strip. And it is enough...for there to be cut out in it not a Moebius strip, but a double Moebius strip.

521. #521

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.30

     What is the way of distinguishing these two cases?

     Theoretical move: The passage pivots on two interlocking theoretical moves: Lacan argues for the primacy of topological structure over phenomenal shape (using the torus and Klein bottle), and Alain Didier extends this by mapping the circuit of the invocatory drive onto the logic of separation, proposing that musical jouissance operates as a sublimation that "evaporates" the lost object and thus transmutes lack into nostalgia.

     The distinction between the shape and the structure is important here. It is not for nothing that I marked here something which is a torus, is a torus even though its shape does not allow this to appear.

522. #522

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.10

     **Seminar 1: Wednesday 16 November 1976**

     Theoretical move: Lacan proposes that the three classical Freudian modes of identification (paternal, hysterical, and identification to a single/any trait) can be mapped topologically onto three distinct operations of turning the torus inside out, using cuts on the toric surface to produce what he calls the "torus-rod" — thereby grounding a typology of identification in topology rather than clinical description alone.

     It is a rod which nonetheless remains for all that a torus. I mean that as you have already seen here, what has been formed, is something that has nothing to do with the first presentation, the one that knots the two tori.

523. #523

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.58

     So then what is this lack? > **Seminar 5: Wednesday 18 January 1977**

     Theoretical move: Lacan refuses the framing of art (painting, music) as "preverbal" and instead insists it is "hyper-verbal" — saturated by the symbol and the signifier — while simultaneously distinguishing art as a form of know-how (savoir-faire) that goes beyond symbolism and carries more truth than discursive elaboration. The theoretical pivot is that the Real/Imaginary continuity invoked by the interlocutor does not bypass the Symbolic but is, in Lacan's formulation, "verbal to the power of two."

     I see in this graph, which is the representation of a cut, but where there is a possibility of an opening

524. #524

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.41

     So then what is this lack?

     Theoretical move: The passage maps a four-moment dialectical circuit of the drive (using music as its privileged illustration) in which the subject's repeated failure to encounter the objet petit a gradually confirms its radical impossibility, ultimately enabling a leap "through the fantasy" toward an ecstatic, desexualised Other jouissance that Lacan identifies with sublimation – and which constitutes the terminal point of the analytic process beyond ordinary surplus-jouissance.

     two torsions or three torsions therefore, of which I spoke to you at the start, it is therefore these which can be mapped out between the passage from the first to the second moment... I do not know whether one can really speak about torsion for the topology of what I would call the fourth moment.

525. #525

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.78

     So then what is this lack? > **Seminar 6: Wednesday 8 February 1977**

     Theoretical move: The passage argues that the Passe cannot be transmitted by a speaking subject alone (the *passant*) because the locus of enunciating from which S(Ø) is emitted cannot itself be said; only a topological writing—a graphical arrangement that articulates the subject of the enunciated and the subject of enunciating in a transmissible way—can function as the true Passer, which is why Lacan's seminars and graphs perpetually recreate the conditions of division.

     Can we at the same time speak about this locus, B4-R4, and say this locus?... if the Passer, this writing, these graphs function as Passers in that they testified from the locus of enunciating strictly articulated to enunciation

526. #526

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.22

     **Seminar 1: Wednesday 16 November 1976** > **Seminar 2: Wednesday 14 December 1976**

     Theoretical move: Lacan argues that the topological operation of turning the Symbolic torus inside-out—analogous to what psychoanalysis performs on the unconscious—produces a fundamentally different arrangement than the Borromean knot: the Symbolic comes to totally envelop the Real and Imaginary, raising a structural problem about what a completed analysis actually does to the subject's organization of the three registers.

     It is clear that it is not today or yesterday that I made use of these concatenations. Already to symbolise the circuit, the cutting of desire and demand, I made use of this, namely, of the torus.

527. #527

     Seminar XXIV · L'insu que sait de l'une-bévue s'aile à mourre · Jacques Lacan · p.69

     So then what is this lack? > **Seminar 6: Wednesday 8 February 1977**

     Theoretical move: Through a game-theoretic allegory (Bozef/king chess positions), the passage argues that the subject's total dispossession before an omniscient Other (Absolute Knowing at R3) forces the emergence of the repressed signifier S2 into the Real—constituting aphanisis/fading—and that the only exit from this petrified position is a single word ("it is you," S(Ø)) which, rather than merely keeping one's word, *sustains* speech as an act anchored in the subject's desire, making the pass (passe) the topological test of whether enunciation corresponds to enunciating.

     it is already from topology that we can see that one word can only be given at one locus and that the tongue itself shows you that it knows this topology

528. #528

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.11

     13.12.77 (CG Draft 2)

     Theoretical move: By demonstrating that reversing any one torus in a Borromean knot produces topologically distinct figures (some more complex, some equivalent), Lacan argues that the Borromean knot is asymmetrically sensitive to where and how a rupture or reversal occurs — privileging one torus relative to others produces qualitatively different relational consequences, including the possibility of dissolving the knot entirely.

     as you see, there are four of them and it is by choosing one and reversing it that one obtains the figure that you see on the left... these reversed tori envelopes the two other tori

529. #529

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.27

     **Two lines of numbers**

     Theoretical move: Lacan develops a topology of the Real grounded in writing, arguing that (1) the Real is only accessible through writing as artifice, (2) the torus—unlike the sphere—introduces a structural asymmetry and equivocation between inside/outside and hole/rod that models the living body and sexuality, and (3) the Borromean knot's necessary alternation formalizes the non-relation, with zero as hole and one as consistency providing an arithmetic analogue for chain-topology.

     There is nothing more asymmetrical than a torus. That leaps to the eyes...I recommend you to take advantage of the double thickness so that you can see that it is a torus.

530. #530

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.50

     **X**: What does systematising mean? [*Laughter]* > **Seminar 7: Wednesday 21 February 1978**

     Theoretical move: Lacan uses a topological dispute about toric knittings and mirror-inversions to assert that a mirror-image is not identical to its original figure, introducing an "essential difference" produced by a single inversion — a claim that does theoretical work on the non-coincidence of the subject with its mirror representation and on the nature of topological equivalence in his knot theory.

     by a progressive transformation we have, we have something which has the same three elements.

531. #531

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.14

     Perpendicular section 2

     Theoretical move: The passage advances a topological argument that the dissolution of the Borromean knot depends on the direction of the cut made on a reversed torus — longitudinal (concentric) cuts dissolve the knot while transversal (perpendicular) cuts do not — and extends this to a six-fold Borromean structure, positing that the results of reversal differ depending on the structural arrangement of the rings.

     The distinction between what I called the longitudinal cut and the transversal cut is essential. I think I have given you a sufficient indication of this by this cut here. The way in which the cut is made is quite decisive.

532. #532

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.90

     **X**: What does systematising mean? [*Laughter]* > **Annexe to Session VIII** > **Seminar 11: Tuesday 18 April 1978**

     Theoretical move: Lacan and collaborators work through the topological properties of the Möbius strip—its half-twists, edge-knotting, flattening into regular polygons, and relationship to the torus—as preparatory groundwork for investigating whether a Borromean knot can be constructed from a threefold knot, showing that topology functions here as the operative language for structural relations in the theory.

     This is what is realised in the torus of which we obviously only have....The complete twist is everything that one can do on the torus

533. #533

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.99

     **X**: What does systematising mean? [*Laughter]* > **Annexe to Session VIII** > **Seminar 12: Tuesday 9 May 1978**

     Theoretical move: Lacan argues that the topological operations on the torus, Möbius strip, and Borromean plait are not merely formal exercises but reveal the structural gap between the Imaginary and the Real — a gap that constitutes inhibition — and that this triadic RSI structure is intrinsic to psychoanalysis, specifically to distinguishing representation from object.

     The triple Möbius strip is not capable of lying on a torus; hence it results that, if one cuts out this as it was originally, namely, the cut, the simple cut, this does not make a threefold knot

534. #534

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.2

     **Seminar I: Wednesday 15 November 1977**

     Theoretical move: Lacan opens his final seminar by positioning psychoanalysis as an irrefutable practice of equivocation (not a science), grounding this in the non-existence of the sexual relationship, the inadequation of the Symbolic to the Real, and the analyst's function as rhetor — then transitions to topological exploration of the Borromean knot and torus as structural models for the RSI (Real-Symbolic-Imaginary) articulation.

     I mean that topology has restored what we should call weaving (*tissage*). The idea of neighbourhood is simply the idea of consistency

535. #535

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.85

     **X**: What does systematising mean? [*Laughter]* > **Annexe to Session VIII** > **Seminar 10: Tuesday 11 April 1978**

     Theoretical move: Lacan reconfigures the topological grounding of psychoanalysis by moving from a simple Möbius strip to a doubled/tripled one that flattens into a threefold knot, arguing that the absence of the sexual relationship—screened by the incest prohibition and crystallised around the Oedipus myth—requires a material geometry of thread and fabric rather than a metaphorics of thought, because the passage from signifier to signified always involves a loss that mere 'free association' cannot overcome.

     This at least is where the fact of analysis has led me... I strive to make a geometry of fabric, of thread, of stitching.

536. #536

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.16

     **Seminar 3: Wednesday 20 December 1977**

     Theoretical move: Lacan argues that both analytic speech and analytic intervention are fundamentally acts of writing/equivocation rather than saying, and develops a topological identification of fantasy with the torus within the Borromean knot structure, mapping three coupled pairs (drive–inhibition, pleasure principle–unconscious, Real–fantasy) onto a 'six-fold torus'; simultaneously, he reframes the end of analysis as recognising what one is captive of (the sinthome), and characterises science, history, and psychoanalysis itself as forms of poetry rooted in fantasy.

     How did I slip from the Borromean knot to imagining it composed of tori and, from there, to the thought of reversing each one of these tori?

537. #537

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.65

     **X**: What does systematising mean? [*Laughter]* > **Seminar 8: Wednesday 14 March 1978**

     Theoretical move: Through Soury's presentation, the passage deploys the topology of torus reversal (by holing vs. by cutting) to demonstrate that the two operations differ precisely in whether they preserve or dissociate the coupling between inside/outside and the two faces of a surface — a distinction that carries structural implications for how topological transformations can model psychoanalytic concepts such as Objet petit a.

     the reversal by holing does not touch, anyway does not change this link between the two faces with the inside/outside while the reversal by cutting dissociates this link.

538. #538

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.35

     **X**: What does systematising mean? [*Laughter]*

     Theoretical move: Soury demonstrates that the threefold Borromean chain is the generative/exemplary element of chain operations (analogous to the arithmetic 'one'), while the twofold chain is a degenerate/neutral element (analogous to zero), establishing a systematic arithmetic of topological chain structures; Lacan then intervenes to expose an unmastered conceptual gap in the categories of interlacing versus interlocking.

     systematisation depends on ways of writing (écritures) and precisely speech cannot practically take charge of anything that is systematic.

539. #539

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.76

     **X**: What does systematising mean? [*Laughter]* > **Annexe to Session VIII** > **Seminar 9: Tuesday 21 March 1978**

     Theoretical move: Lacan and Soury work through the topology of toric reversal—demonstrating that holing enables inversion of inside/outside on the torus and that the two descriptions of reversal (with or without a complementary "hand"/torus) are equivalent—advancing Lacan's broader project of grounding psychoanalytic concepts in topological rather than intuitive spatial logic.

     I am very concerned about what is involved specifically in the torus. Soury is going to pass you tori, tori on which there is something knitted. There is something that particularly worries me, which is the relationship between what can be called toricity and holing.

540. #540

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.56

     **X**: What does systematising mean? [*Laughter]* > **Seminar 8: Wednesday 14 March 1978**

     Theoretical move: Lacan and his collaborator Soury advance the thesis that the Borromean topology must be re-grounded in toric surfaces rather than simple rings, and that the distinction between holing and cutting a torus (the latter being strictly more powerful than the former) carries theoretical weight for the topological treatment of desire and demand—cutting implicitly contains holing while enabling additional reversals not available through holing alone.

     the torus is at the centre of these features, it is fabricated more or less like that and the features are on the surface. This implies that the torus itself is not Borromean.

541. #541

     Seminar XXV · The Moment to Conclude · Jacques Lacan · p.45

     **X**: What does systematising mean? [*Laughter]* > **Seminar 6: Wednesday 14 February 1978**

     Theoretical move: Lacan works through the topological construction of the threefold Borromean knot from a double-loop starting configuration, arguing that it achieves a genuine knotting only when closed circularly, and that this triadic structure directly mirrors the clinic's triad of Imaginary, Symbolic, and Real.

     I put this to the test with Soury whom I am meeting for the moment. I am meeting him because he tells me sensible things on the subject of Borromean knot.

542. #542

     Seminar III · The Psychoses · Jacques Lacan · p.156

     **X** > **On the signifier in the real and the bellowing-miracle**

     Theoretical move: By tracking the gradations between the bellowing-miracle (pure signifier without meaning) and the call for help (meaning without genuine subjecthood), Lacan argues that in psychosis the unconscious signifier is situated as externally real rather than internally repressed — pointing toward the structural difference between Verwerfung (Foreclosure) and Verdrängung (Repression) as two distinct modes of subjective localization of the signifier.

     There is a subjective topology here based entirely upon the fact, given to us by analysis, that there may be an unconscious signifier.

543. #543

     Seminar III · The Psychoses · Jacques Lacan · p.60

     **IV** > **"I've just been to the butcher's"**

     Theoretical move: Lacan uses Freud's neurosis/psychosis distinction to sharpen the concept of Verwerfung (foreclosure): whereas in neurosis a repressed element returns symbolically within the subject's psychical reality, in psychosis what has been excluded from the symbolic order entirely returns from without in the Real — a structural difference that cannot be reduced to projection. A clinical vignette (the butcher's remark) then demonstrates that the signifier can carry meaning erotically/allusively without being identical to the message received in inverted form.

     What is this three-card trick we are all prey to, this strange juggler's game between the symbolic, the imaginary, and the real? Since we don't know the juggler we can ask the question. I am putting it on this year's agenda.

544. #544

     Seminar IV · The Object Relation · Jacques Lacan · p.378

     XVIII CIRCUITS > P(M) (M')

     Theoretical move: Lacan concludes his analysis of Little Hans by arguing that Hans's resolution of the phobia follows an atypical Oedipal path—owing to the father's shortcoming—that installs an imaginary paternity and a narcissistically structured object relation, formalised topologically as p(M)(M')~(α/φ)Π, and closing with a parallel to Freud's Leonardo study to underscore the structural necessity of a fourth (animal/residual) term beyond the trinity.

     Since topology is a rubber-sheet geometry, here it's a matter of rubber-sheet logic... nothing allows us to unlink two interconnected rings, even rubber ones.

545. #545

     Seminar IV · The Object Relation · Jacques Lacan · p.9

     Jacques Lacan The Object Relation > THEORISING THE LACK OF OBJECT > <span id="page-7-0"></span>INTRODUCTION

     Theoretical move: Lacan inaugurates Seminar IV by arguing that the Object Relations school's reduction of analytic experience to a dual subject-object relation (line a-a') is theoretically inadequate: against this, he retrieves Freud's own notion of the object as a *lost* and re-found object, constitutively marked by repetition and irreducible tension, which requires the full complexity of the L-Schema (subject/Other/imaginary axis) rather than a simple dyadic rectification.

     On no account is the spatiality of these schemas to be taken in the intuitive sense of the term schema, but rather in another sense that is altogether legitimate, the topological sense. It's not a matter of localisations, but rather of relationships between loci, interposition, for example, or succession, sequence.

546. #546

     Seminar IV · The Object Relation · Jacques Lacan · p.227

     ON THE OEDIPUS COMPLEX > THE SIGNIFIER IN THE REAL

     Theoretical move: Lacan clarifies and defends the formal network constructed in his "Seminar on 'The Purloined Letter,'" arguing that the introduction of the signifier into the real generates a structural law—orthography—that irreducibly differentiates human memory from any vitalist or purely chance-based model, making the signifier the organiser of memory's structure.

     we can construct it as a parallelepiped formed of vectors… The network has to be oriented… A series that cannot be set into this network is an impossible series.

547. #547

     Seminar IV · The Object Relation · Jacques Lacan · p.305

     XVIII CIRCUITS

     Theoretical move: Lacan argues that in the Little Hans case, the phobia's meaning cannot be grasped by symbolic analogies or biographical extrapolation but only by tracing the autonomous operation of signifying laws—the "circuit system" of the horse and the railway network—as a structural (symbolic, not real) topology that maps Hans's impossible position between mother and father.

     The network forms a loop, a virtual loop because the two lines don't connect. They simply allow each of them to get to Lainz.

548. #548

     Seminar IV · The Object Relation · Jacques Lacan · p.318

     XVIII CIRCUITS > PERMUTATIONS

     Theoretical move: Lacan reads Little Hans's successive transgressive fantasies as a mythical permutation-structure — a series of attempts to articulate and exhaust every form of an impossible solution to the deadlock between the maternal and paternal circuits — and uses this to distinguish Hans's neurotic trajectory from the perverse (fetishistic) path that remained structurally available to him.

     the street-door is no small matter in the topology of what relates to little Hans

549. #549

     Seminar IV · The Object Relation · Jacques Lacan · p.243

     WHAT MYTH IS FOR

     Theoretical move: Lacan argues that childhood sexual theories have the structural character of myth — not mere intellectual superstructure but a fictive yet structurally stable relation to truth — and uses this to reframe the topography of the preoedipal triangle (mother/father/child) and to insist that perversion, like neurosis, is structured around the castration complex and the presence/absence of the phallus, being neurosis's inverse rather than its simple positive.

     It's about topography, and not some random walk, though indeed it's by taking you on an unusual walk that I hope to represent this topography for you.

550. #550

     Seminar V · Formations of the Unconscious · Jacques Lacan · p.140

     **FORECLOSURE OF THE NAME-OF -THE-FATHER**

     Theoretical move: Lacan uses Bateson's double bind as a foil to argue that the genesis of psychosis cannot be reduced to double-meaning communication but requires identifying the missing signifier — the Name-of-the-Father — as the grounding element of the law in the Other; its Verwerfung (foreclosure) is what distinguishes psychotic from neurotic structure, while the accompanying schema of the witticism illustrates how desire is essentially transformed (betrayed) by its passage through the signifying chain.

     The space of the signifier, the space of the unconscious, is effectively a typographical space, which we must try to define as being constituted along lines and little squares, and as corresponding to topological laws.

551. #551

     Seminar V · Formations of the Unconscious · Jacques Lacan · p.391

     **THE OBSESSIONAL AND HIS DESIRE**

     Theoretical move: Lacan argues that obsessional desire is structured by dependence on the Other, and that fantasy must be redefined not as a blind imaginary image but as the imaginary captured in a particular use of signifiers—a scenario ($◇a) in which the subject is implicated—thereby distinguishing the obsessional's relation to desire from the hysteric's identificatory structure.

     I ask you to represent it to yourselves first of all through an intuitive aspect, taking into account the fact that this isn't a real space, of course, but a topology in which homologies can be sketched out.

552. #552

     Seminar V · Formations of the Unconscious · Jacques Lacan · p.408

     **TRANSFERENCE AND SUGGESTION**

     Theoretical move: Lacan maps Freud's three types of identification onto his schema of need/demand/desire, distinguishing the line of suggestion (identification with the Other's insignia along the demand axis) from the line of transference (a second, properly analytic articulation beyond demand), thereby reframing the transference/suggestion opposition as a topological split within the structure of demand itself.

     The separation does not mean that they are not one single, unique line on which what the child articulates for the mother is inscribed.

553. #553

     Seminar V · Formations of the Unconscious · Jacques Lacan · p.325

     **SIGNIFIER, BAR** AND PHALLUS

     Theoretical move: Lacan distinguishes desire from demand by insisting on desire's eccentricity to satisfaction and its irreducibility to any graspable meaning produced by signification, while simultaneously grounding the signifier's distinctive status in its capacity for self-substitution within the topological space of the big Other — a structure animals lack, since they possess no law organizing signifiers into a concatenated discourse.

     what is dominant, what matters, is the place it occupies in the Other. What points in that direction... is this topological, not to say typographical, space whose law is the law of substitution.

554. #554

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.141

     DESIRE'S PHALLIC MEDIATION > But Freud adds the following:

     Theoretical move: Lacan uses Freud's three-phase schema of "A Child Is Being Beaten" and the optics of the inverted bouquet to argue that the subject constitutes itself as barred subject ($) only by passing through a fantasmatic phase of near-abolition (primary masochism), and that the phallus functions as the mediating signifier through which desire is structured in the imaginary-symbolic interplay.

     the imaginary set of fragmented bodily elements must be distributed across the puppet with which we deal in the symbolic... But these puppets are missing something: the phallus.

555. #555

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.76

     LITTLE ANNA'S DREAM

     Theoretical move: Lacan uses Little Anna's dream as a pedagogical entry point to articulate the strict distinction between the pleasure principle (primary process, hallucination) and desire, arguing that hallucination—produced by topographical regression when motor discharge is blocked—constitutes the foundational backdrop against which human reality is constructed, while the secondary process substitutes for instinct by testing hallucinatory reality against experience.

     Hallucination is produced by a process of regression that he calls 'topographical.' The different schemas Freud drew of what motivates and structures the primary process all have in common the fact that they are grounded in the trajectory of the reflex arc

556. #556

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.414

     CUT AND FANTASY

     Theoretical move: Lacan argues that the "cut" (coupure) is the fundamental structural characteristic of the symbolic order and the locus of the subject's relation to being, and that works of art—exemplified by Hamlet—do not sublimate or imitate reality but structurally instantiate this cut, thereby making accessible, via fantasy, the subject's real as an unconscious speaking subject.

     If I may use, in this regard, the topology of my graph to convey this, this dimension is not parallel to the field of reality created in reality by human symbolization, but cuts across it

557. #557

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.205

     SACRIFICING THE TABOO QUEEN

     Theoretical move: Lacan reappropriates Jones's term "aphanisis" — redirecting it from a fear of desire's disappearance rooted in developmental psychology toward a structurally prior effect of castration, arguing that it is precisely because the signifier is operative in castration that the subject can become alarmed at the potential disappearance of his desire; this allows Lacan to reframe the clinical material of Ella Sharpe's patient in terms of intersubjective topology rather than imaginary equivalences.

     The point is to see if the problem cannot be clarified by being articulated in a way that better links the interpretation with what I am trying to stress here — namely, the intersubjective topology.

558. #558

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.321

     OPHELIA, THE OBJECT

     Theoretical move: Lacan deploys the Graph of Desire to distinguish fantasy's imaginary object (a) from the signifiers of demand, arguing that Object Relations theory errs by collapsing this distinction—Ophelia serves as the dramatic instantiation of objet petit a, and Hamlet's vacillating desire is theorized as the subject's fading (aphanisis) at the intersection of demand and fantasy.

     The signifier is, on the contrary, one of the essential, initial components of a topology without which all psychoanalytic phenomena would be reduced or flattened out.

559. #559

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.342

     MOURNING AND DESIRE > What is Hamlet missing?

     Theoretical move: Lacan uses Hamlet's final duel to demonstrate that desire is structured by the formula ($◇a) — fantasy — where the object in desire functions as a substitute for the phallus the subject sacrifices to the signifier; Hamlet's inability to act from desire proper (he engages only at the level of imaginary, specular rivalry) reveals the structural gap between the object of need and the object in desire, and exposes the mirror stage as the imaginary short-circuit that occludes the real stakes of his action.

     The square root of minus one cannot in itself correspond to anything real, in the mathematical sense of the term. The same is true of the object.

560. #560

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.423

     THE FUNCTION OF THE SUBJECTIVE SLIT IN PER VERSE FANTASIES

     Theoretical move: Lacan establishes that being is co-extensive with the cut/gap in the signifying chain, and that the subject, constituted as "not one" (barred, split), appears precisely at those gaps in desire — a structural account that displaces both ego-psychological notions of genital maturity and religious/moral frameworks for desire's satisfaction, while insisting on desire as the irreducible proof of the subject's presence.

     I shall try to articulate the level at which the subject is a barred subject further on with the help of a notion that I will deliberately begin by making more ambiguous than that of the One

561. #561

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.85

     LITTLE ANNA'S DREAM

     Theoretical move: The passage develops the distinction between the subject of enunciation and the subject of the statement as the structural foundation of the Graph of Desire's two lines, arguing that repression is essentially the effacement of the subject at the level of the enunciation process, and that all speech is primordially the Other's discourse — with Foreclosure (Verwerfung) marking the pathological limit of this structure.

     I am not developing this topology in order to simply give you the answer... the topology of repression is involved in it.

562. #562

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.82

     LITTLE ANNA'S DREAM

     Theoretical move: By reading Freud's Niederschrift (inscription) through the topology of two superimposed signifying chains—illustrated via Anna Freud's dream—Lacan argues that the unconscious is structured as a topology of signifiers, where desire appears not as naked immediacy but only through its signifying articulation, and the subject is constituted differentially by the upper (desire/message) versus lower (demand/sentence) chain of the Graph of Desire.

     This introduces us to what I call the topology of repression - the clearest, the most formal as well, and the most articulated.

563. #563

     Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.200

     THE IMAGE OF THE INSIDE-OUT GLOVE > I am going to skip here a little,

     Theoretical move: Lacan uses a clinical case analysis to argue that the patient's fundamental fantasy is structured around an "inside-out glove" image — a masturbatory, non-separating envelopment of male and female elements — and that the analyst's (Sharpe's) interpretive errors stem from reducing a complex signifying fantasy to a dyadic, imaginary transference and crude screen-memory reconstruction, thereby missing the structural topology of the subject's desire.

     the fundamental image presented in the dream is that of a sort of glove or sheath turned inside out.

564. #564

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.329

     **XXIII** > **XXIV**

     Theoretical move: Lacan advances the ethical thesis that the only genuine form of guilt is "having given ground relative to one's desire," grounding this in the structural relationship between the subject, the signifier, and an irreducible "keeping of accounts" that persists across moral, religious, and political frameworks; this is illustrated through Antigone, Philoctetes, and a reading of the film *Never on Sunday*.

     Someone among you has baptized the topology that I have sketched out for you this year with the apt and somewhat humorous phrase, the zone between-two-deaths.

565. #565

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.260

     **XIV** > **XIX**

     Theoretical move: Lacan locates the ethical and aesthetic force of Antigone in the liminal zone between life and death (the 'second death'), arguing that it is precisely there that desire is both reflected and refracted to produce the effect of beauty — a zone Hegel's dialectical reading of reconciliation entirely misses, and which requires a rigorous analysis of signifiers rather than a moralising or aesthetic reduction.

     Don't forget one of the effects in which the topology I refer to may be recognized. If Hamlet stops when he is on the point of killing Claudius, it is because he is worried about that precise point I am trying to define here

566. #566

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.318

     **XXIII**

     Theoretical move: Lacan articulates the Oedipus complex's decline and superego formation by distinguishing three registers of the father (real/castrating, imaginary/privating, symbolic/dead) and the corresponding mourning work, arguing that the superego ultimately expresses hatred toward the imaginary father-God who "handled things badly," while the paternal function is always and only the Name-of-the-Father — the dead father as myth — and desire is constituted through a necessary crossing of limits.

     I showed you the reverse and derisory side of this topology, which is the topology of tragedy, in connection with poor Lear

567. #567

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.49

     **Ill**

     Theoretical move: By reading Freud's 'Project for a Scientific Psychology' closely, Lacan argues that the apparatus described there is fundamentally a topology of subjectivity, and that the principle of repetition is grounded in the constitutive gap between desire's articulation and its satisfaction — the 'refound object' is always missed, rendering specific action structurally incomplete.

     It seems obvious to me that this apparatus is a topology of subjectivity, of subjectivity insofar as it arises and is constructed on the surface of an organism.

568. #568

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.321

     **XXIII** > **XXIV**

     Theoretical move: Lacan's ethics of psychoanalysis is grounded not in the service of goods or traditional moral regulation, but in the question "Have you acted in conformity with your desire?" — a standard derived from the topology of desire that both tragedy and comedy reveal, and which Kant's categorical imperative partially anticipates but fails to complete, leaving a void that psychoanalysis identifies as the place of desire.

     the experimentum mentis that I have been proposing to you throughout the year is directly connected to something that our experience points to whenever we try to articulate it in its own topology, in its own structure

569. #569

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.295

     **XIV** > **XXI** > **SUPPLEMENTARY NOTE**

     Theoretical move: Lacan concludes his reading of Antigone by situating its ethical force at the intersection of the second death, language, synchrony/diachrony (via Lévi-Strauss), and the beauty-effect produced by the hero's proximity to Ate, then pivots to Kant's analytic of the beautiful and sublime as the necessary conceptual bridge for his ongoing topological argument.

     Involved there is a form of category analysis that is of the highest significance in any effort to connect up with the topological structuration that I am pursuing with you here.

570. #570

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.48

     **Ill**

     Theoretical move: Lacan argues that Freud's foundational texts—especially the *Entwurf*—are grounded not in psychology but in ethics, and that the opposition between the pleasure principle and the reality principle must be understood as an ethical (not merely psychological) problem, with the *Nebenmensch* (the Other as speaking subject) as the hinge through which satisfaction and reality are constituted for the subject.

     I also regretted that you didn't remind us of the topology that the system ψ, ω, presupposes.

571. #571

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.126

     **IX** > On creation *ex nihilo*

     Theoretical move: The passage advances a theory of sublimation grounded in the topological function of Das Ding: the Thing is that which "in the real suffers from the signifier," is constitutively veiled, and is represented—never directly encountered—by the created object, whose paradigmatic form is the potter's vase, a void-around-which that enacts creation ex nihilo.

     How can we define it more precisely in our topology?... a topological diagram of the way in which the question of what we call the Thing is raised.

572. #572

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.59

     **IV**

     Theoretical move: Lacan explicates Freud's *Entwurf* and Letter 52 to establish that *Das Ding* (the *Nebenmensch* as irreducible alien core) is the primordial outside around which the subject's entire economy of desire is oriented, and that the lost object — structurally unfindable — is what drives the subject's search for satisfaction; simultaneously, the signifying structure interposing between perception and consciousness is what constitutes the unconscious as such.

     what goes on between Wahrnehmung and Bewusstsein must after all have to do with the unconscious... this time not simply in the form of a function, but of an Aufbau, of a structure

573. #573

     Seminar VII · The Ethics of Psychoanalysis · Jacques Lacan · p.120

     **VIII**

     Theoretical move: Lacan advances the defining formula of sublimation — "raising an object to the dignity of the Thing" — as the key to understanding how the drive finds satisfaction beyond its aim, and he illustrates this via courtly love and a concrete fable of collecting, arguing that sublimation reveals the relationship of the drive to das Ding as distinct from any imaginary object.

     The object is elevated to the dignity of the Thing as we define it in our Freudian topology, insofar as it is not slipped into but surrounded by the network of Ziele.

574. #574

     Seminar VIII · Transference · Jacques Lacan · p.111

     **M EDICAL H A R M O N Y** > *AGATH ON*

     Theoretical move: Lacan grounds the topology of desire in the death drive and the "between-two-deaths," arguing that Freud's discovery of the unconscious is not reducible to the content of the Oedipus myth but to its structural form—"he did not know"—which inscribes the subject's desire in a signifying chain beyond consciousness, beyond adaptation, and in permanent tension with individual life.

     I am trying to ground with you the basic topology of desire, its interpretation, and - in short - its rational ethics.

575. #575

     Seminar VIII · Transference · Jacques Lacan · p.105

     **M EDICAL H A R M O N Y** > *ARISTOPHANES*

     Theoretical move: Lacan uses Aristophanes' myth of the spherical beings in the Symposium to argue that what is being satirized is not mere comedy but the philosophical figure of the *sphairos* — the self-sufficient, self-identical sphere central to ancient cosmology (Empedocles, Plato's Timaeus) — thereby revealing that Plato stages a comic deflation of his own cosmological imaginary through Aristophanes' discourse on love. This move prepares a critique of unification as the model of love (contra Freud's Eros/Thanatos opposition) and links the Imaginary register to the fascination with spherical wholeness.

     I should cut this sphere — which, as you know, served in the usual symbol for infinity ∞ — down to size, reduce it to a point, and infinitize it for you.

576. #576

     Seminar VIII · Transference · Jacques Lacan · p.206

     **M EDICAL H A R M O N Y** > **THE OBJECT OF DESIRE A N D THE DIALECTIC OF CASTRATION** > <span id="page-192-0"></span>**A CRITIQUE OF CO UNTERTRANSFERENCE**

     Theoretical move: Lacan argues that what Object Relations analysts call "countertransference" is actually an irreducible structural effect of transference itself: by virtue of the analytic situation, the analyst is necessarily positioned as the container of *agalma* (objet petit a), and this positioning—not the analyst's personal psychology—explains phenomena like projective identification, transference love, and the analyst's affective responses; the categories of desire, fantasy, and topology are required to articulate this adequately.

     It is only through this topology that we can understand such an approach. Indeed, this topology allows us to say that, even if the subject is unaware of it, by the very presupposition... of the analytic situation, little a, agalma, is already functioning in the other.

577. #577

     Seminar VIII · Transference · Jacques Lacan · p.364

     **M EDICAL H A R M O N Y** > **CAPITAL I A N D LITTLE** *a* > **IDENTIFICATION VIA** *"E IN E IN Z IG E R Z U G* **"**

     Theoretical move: Lacan uses his optical schema to argue that the emergence of the ego-ideal and ideal ego requires the intervention of the big Other (capital O) as a third term that exceeds the dyadic, radically imaginary and destructive conflict of the mirror stage, thereby grounding narcissistic development in a symbolic register that neither Hegel's dialectic nor the Jekels-Bergler introjection/projection model can adequately account for.

     It is no accident that it reintroduces a metaphor of an optical nature. It does so, not for reasons of convenience, but rather for structural reasons. If mirrors are involved, it is because, as concerns the imaginary mainspring, what is based on mirrors goes much further than the model.

578. #578

     Seminar VIII · Transference · Jacques Lacan · p.390

     **M EDICAL H A R M O N Y** > **THE RELATIONSHIP BETW EEN ANXIETY A N D DESIRE** > **"A D R EA M OF A SHADOW IS M A N "**

     Theoretical move: The passage argues that the subject's exit from narcissistic captivity depends on the structuring function of the signifier in the field of the Other: the distinction between Ideal Ego and Ego Ideal, mapped through the optical schema, shows that it is only by traversing the dream-field of wandering signifiers that the subject can glimpse the "reality of desire" beyond the shadow of narcissistic cathexis.

     it does not suffice to topologically define this awakening by saying that what wakes me up is when there is a little too much reality in my dream.

579. #579

     Seminar VIII · Transference · Jacques Lacan · p.160

     **M EDICAL H A R M O N Y** > *ÂGALMA*

     Theoretical move: Lacan defines the psychoanalytic object as *àgalma* — the partial object of desire that is incommensurable with ordinary objects of equivalence — and argues that this object, not identificatory or metaphysical constructs, is the true pivot of love, desire, and analytic practice, requiring a strict topology of subject, little other, and big Other to be properly situated.

     If we are unable to point out, in a strict topology, the function of what this partial object signifies - which is both so limited and so slippery in its figure

580. #580

     Seminar VIII · Transference · Jacques Lacan · p.218

     **M EDICAL H A R M O N Y** > **D E M A N D A N D DESIRE IN THE ORAL A N D A N A L STAGES**

     Theoretical move: Lacan argues that the oral and anal stages must be understood through the structural distinction between need, demand, and desire—where desire emerges as a gap or negation irreducible to need's satisfaction—and uses the anal stage to demolish the myth of "oblativity," revealing that anal desire is constituted by the subject's identification with the excremental object (objet a) and its symbolic evacuation, which grounds the obsessional's fundamental fantasy.

     If you have remained deaf [to this key point] for so long, it is because things are not indicated in the literature in their fundamental topology, as I am attempting to do for you here.

581. #581

     Seminar VIII · Transference · Jacques Lacan · p.300

     **M EDICAL H A R M O N Y** > **THE OEDIPAL MYTH TODAY** > **TU R E L U R E 'S ABJECTION**

     Theoretical move: Lacan reads Claudel's play as a dramatization of the Oedipus complex that goes beyond its classical form: the 'imaginary dimension' of the father is shown to be sufficient for efficacy (the father dies of fright, not from a real bullet), while two women engineer the parricide by exploiting the father's desire, revealing the father as a passive, 'duped' element in a four-player game that mirrors the structure of the analytic situation.

     Claudel's play is thus arranged in a way that is undoubtedly designed to bring out elements that will get us interested in this plot, topology, or fundamental dramatic action

582. #582

     Seminar VIII · Transference · Jacques Lacan · p.151

     **M EDICAL H A R M O N Y** > *ÂGALMA*

     Theoretical move: Through a close reading of Alcibiades' speech in Plato's *Symposium* and a verse from Euripides' *Hecuba*, Lacan argues that *âgalma* names the hidden precious object inside the other that captures desire — a specifically psychoanalytic notion whose fetishistic function displaces the dyadic dialectic of beauty with a triadic topology of the subject's relation to the symbolic.

     This topological indication is essential. What is important is what is inside.

583. #583

     Seminar VIII · Transference · Jacques Lacan · p.324

     **M EDICAL H A R M O N Y** > **PENSÉE'S DESIRE** > And a bit further on she continues:

     Theoretical move: Lacan reads Claudel's figure of Pensée as a topology of desire in which the woman, by becoming frozen into the object of love, incarnates the structure of desire itself — revealing that desire necessarily involves the four terms (two imaginary doubles a/a, the barred subject, and the big Other), and that the analyst's task is to locate those extreme points rather than succumb to therapeutic normalization.

     Such is the topology in which the long path of the tragedy culminates.

584. #584

     Seminar VIII · Transference · Jacques Lacan · p.308

     **M EDICAL H A R M O N Y** > **THE OEDIPAL MYTH TODAY** > **TU R E L U R E 'S ABJECTION**

     Theoretical move: Lacan uses Claudel's trilogy to argue that castration is constitutive of the desiring subject—not as frustration of need but as the structural elevation of the phallus to a signifying function—and locates the composition of desire across three generational stages: the mark of the signifier, the undesired object, and finally the constitution of desire proper, while critiquing ego-psychology's reduction of desire to need and the concurrent eclipse of the father function.

     this is why I strive to come up with topological schemas for you that allow us to do so... whose topology I not only try to illustrate for you in a para-spatial sense, but whose various stages I endeavor to indicate.

585. #585

     Seminar VIII · Transference · Jacques Lacan · p.85

     **M EDICAL H A R M O N Y** > *ERYXIM ACHUS*

     Theoretical move: Lacan reads Eryximachus' speech in Plato's Symposium as staging the foundational antinomy between concord-from-similarity and concord-from-dissimilarity/conflict, using it to illuminate topology's "full and empty," the pre-Socratic logic of contraries (Heraclitus), and—obliquely—the definition of psychoanalysis as "the science of the erotics of bodies." The comic register of the Symposium is foregrounded as philosophically significant, not merely ornamental.

     What I wish to underscore here are the two terms 'full' and 'empty' - whose role we shall see in topology and in intellectual positions

586. #586

     Seminar VIII · Transference · Jacques Lacan · p.79

     **M EDICAL H A R M O N Y** > *ERYXIM ACHUS*

     Theoretical move: Lacan uses Eryximachus' medical speech in the Symposium to argue that transference reformulates the Platonic search for 'a good' (ktésis) into the emergence of desire as such — and that medicine's self-conception as scientific rests on an unexamined notion of harmony (harmonia) that exposes the irreducible gap at the heart of any normative ideal of health.

     having already seriously studied the topology of what the subject must find in analysis in the place of what he is seeking

587. #587

     Seminar VIII · Transference · Jacques Lacan · p.116

     **M EDICAL H A R M O N Y** > *AGATH ON*

     Theoretical move: Lacan reads Socrates' desire as an atopia — an unclassifiable, unsituable place of pure desire for discourse — which he locates topologically in the space between-two-deaths, and uses this to frame the question of the analyst's desire as something that must be articulated beyond the vague notion of training catharsis.

     I have at length described for you the topology that gives it its meaning... we cannot find appropriate landmarks by referring to articulations of the situation for the therapist or the observer, nor in any of the phenomenological notions

588. #588

     Seminar VIII · Transference · Jacques Lacan · p.56

     **Jacques Lacan** > **THE M AINSPRING OF LOVE** > *Phaedrus*

     Theoretical move: Lacan uses a close reading of Phaedrus' speech in the Symposium to argue that the succession of eulogies traces a fundamental topology of love's impossibility, and introduces a theological framework (the gods belong to the Real) to situate Eros within the tripartite RSI schema, while the myth of Orpheus anchors the distinction between the fantasmatic object and the Other's being.

     what Plato shows...is that the contour traced out by this difficulty indicates to us the point at which lies the fundamental topology which stops us from saying anything about love that holds water.

589. #589

     Seminar VIII · Transference · Jacques Lacan · p.17

     **Jacques Lacan** > <span id="page-15-0"></span>**IN THE BEG IN N IN G WAS LOVE**

     Theoretical move: Lacan opens Seminar VIII by situating transference not within an intersubjective framework but within a constitutive disparity, tracing its origin back to love (the Breuer/Anna O. encounter), and connecting it to the prior year's ethical reflection — especially the rejection of the Sovereign Good (Plato's Schwärmerei), the function of beauty as a barrier to the death drive, and the 'between-two-deaths' — in order to establish Socrates' secret knowledge of love as the hidden key to understanding transference.

     a correct topology is required here and, consequently, a rectification of what is commonly implied by our everyday use of the theoretical notion of transference.

590. #590

     Seminar VIII · Transference · Jacques Lacan · p.361

     **M EDICAL H A R M O N Y** > **CAPITAL I A N D LITTLE** *a* > **IDENTIFICATION VIA** *"E IN E IN Z IG E R Z U G* **"**

     Theoretical move: Lacan critiques the Jekels-Bergler theory of narcissism and the ego-ideal by showing that their reliance on a "neutral energy" oscillating between Eros and Thanatos, and their attribution of object-creation to the death drive, result from a failure to distinguish the Symbolic, Imaginary, and Real registers — a failure that his optical schema (mirror A, real image *i(a)*, and flowers *a*) is designed to correct and generalize.

     The concept of an 'inside' serves a major topological function in psychoanalytic thinking... If the observer's eye is - owing to certain topological or spatial conditions

591. #591

     Seminar VIII · Transference · Jacques Lacan · p.289

     **M EDICAL H A R M O N Y** > **THE OEDIPAL MYTH TODAY** > **SY G N E'S NO**

     Theoretical move: Lacan pivots from critiquing reductive accounts of desire to introducing Claudel's trilogy as a contemporary tragedy that, like Antigone, pushes the subject to the limit of the "second death" — here uniquely demanding that the heroine sacrifice not merely life but her very being, the sacred pact constituting her identity, going *beyond* the limits Antigone reached.

     I showed you last year what tragic fate signifies; managed to get you to locate it in a topology that we called Sadean

592. #592

     Seminar IX · Identification · Jacques Lacan · p.305

     *Seminar 26: Wednesday 27 June 1962*

     Theoretical move: Lacan argues that the analytic object (objet petit a) is specifically the object of castration — distinguished from objects of privation or frustration — and demonstrates this through topological analysis of the cross-cap, showing that the object of desire only rejoins its intimacy by a centrifugal (outside-in) path, structurally irreducible to Aristotelian logic's object of privation.

     The surface of projective planes is completed, closed, finished. The object defined as our object, the object which forms the world of desire only rejoins its intimacy by a centrifugal path.

593. #593

     Seminar IX · Identification · Jacques Lacan · p.279

     *Seminar 24*: *Wednesday 13 June 1962*

     Theoretical move: Lacan uses the topology of the cross-cap/projective plane—specifically the hole structure of the Möbius strip and the double cut that yields a central piece plus a Möbius surface—to formalise the structure of fantasy ($ ◇ a), showing how the Objet petit a is situated at the point of lack in the Other and how narcissistic/specular identification serves as a lure that covers the true relationship to the object of desire.

     in order to determine properties such as the type, the number of connections, the characteristic, everything that is of interest in this topology, you ought to take into account that the Möbius strip has an edge and has only one, that it is constructed on a hole

594. #594

     Seminar IX · Identification · Jacques Lacan · p.219

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 19*: *Wednesday 9 May 1962*

     Theoretical move: Lacan uses the cross-cap as a topological surface to argue that the interior "excluded" field is not foreclosed but must be retained, thereby displacing classical set-theoretic (Eulerian circle) logic with a topological intuition that reframes the relationship between inside and outside, limit and field.

     it is a question of knowing very differently whether this surface makes a case for us which finds itself intuitively, aesthetically symbolised. Another possible import of the signifying limit of the field marked out is realisable in a way that is different and in a way immediately obtainable through the simple application of the properties of a surface

595. #595

     Seminar IX · Identification · Jacques Lacan · p.62

     *Seminar 2: Wednesday 22 November 1961* > *Seminar 7*: *Wednesday 10 January 1962* > What is the proper name?

     Theoretical move: Lacan argues that the proper name reveals the signifier "in the pure state" — not as phonemic differentiation but as the mark/sign that is read as an object, tracing writing's genesis to a primordial coalescence of sign and vocal utterance that already carries a negativity-reference; the unary trait, extracted from the object by effacement, is the hinge point at which sign becomes signifier.

     It is therefore in so far as the subject, in connection with something which is mark, which is sign, already reads before there is question of the signs of writing

596. #596

     Seminar IX · Identification · Jacques Lacan · p.240

     *Seminar 21*: *Wednesday 23 May 1962* > *Seminar 22*: *Wednesday 30 May 1962*

     Theoretical move: The cut—not the surface—is the generative operation that engenders topological surfaces and, by analogy, the subject: because the signifier is constitutively different from itself, it can only achieve consistency by closing on the real (which alone furnishes identity/sameness), and this closure-through-repetition is structurally identical to the logic of demand, thereby grounding the subject's constitution in the loop of demand around the signifier.

     these topological formulae which you have already sensed are not purely and simply this intuitive reference to which the practice of geometry has habituated you, is to consider that these surfaces are structures

597. #597

     Seminar IX · Identification · Jacques Lacan · p.211

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 19*: *Wednesday 9 May 1962*

     Theoretical move: Lacan argues that desire is not beyond language but structured through it, and that the subject's constitution as desire requires grasping both the topological dimension of the objet petit a and its role in fantasy—where the Graph of Desire's two-level structure reveals that fantasy anticipates the ideal ego in a temporal logic of the future perfect, pointing toward a 'temporal dynamics' that exceeds mere spatial topology.

     I am leading you along this path when all is said and done... it is a question of escaping from the pre-eminence of the intuition of the sphere... to those who say to me: 'Could you not really tell us things... without going through your little tori and other detours?'

598. #598

     Seminar IX · Identification · Jacques Lacan · p.276

     *Seminar 24*: *Wednesday 13 June 1962*

     Theoretical move: Lacan develops the topology of the cross-cap's singular point—the "hole-point"—arguing that it is not merely a mathematical abstraction but an irreducible, paradoxical structure whose properties (punctiform yet indivisible, a hole formed by two coupled edges) are the generative locus around which the projective plane is constructed, with analogies drawn to embryological structures (Hensen's node) to authenticate the topological claim.

     A very close discussion on the plane of the formalism of these topological constructions would only go on forever and would perhaps weary you.

599. #599

     Seminar IX · Identification · Jacques Lacan · p.293

     *Seminar 24*: *Wednesday 13 June 1962*

     Theoretical move: At the close of Seminar 9, Lacan positions the logic of desire—articulated through the fantasy matheme ($◇a) and the topology of the subject's relation to the object—as the necessary supplement to Lévi-Straussian structuralism, while simultaneously arguing that the three clinical structures (neurosis, perversion, psychosis) are each 'normal' expressions of the three constitutive terms of desire, and that misreading drive as biological agency is the foundational error of ego-psychology/American psychoanalysis.

     to make it function in the Freudian topology as topology and to see in it some biologism or other which is supposed to be radical, inaugural, co-extensive with the function of drive, is what gives here the whole breadth, the whole gap of what is called a misinterpretation

600. #600

     Seminar IX · Identification · Jacques Lacan · p.131

     *Seminar 13*: *Wednesday 14 March 1962*

     Theoretical move: Lacan advances the structural derivation of desire through three ordered moments—real privation, imaginary frustration, and their articulation in the symbolic via the Other—arguing that the torus topology formalises how the subject's uncounted circuit (−1) grounds universal affirmation, and that the neurotic impasse is constitutively the collapse of desire into demand.

     What led us to the construction of the torus at the point that we are at, is the necessity to define each one of the circuits as an irreducibly different one.

601. #601

     Seminar IX · Identification · Jacques Lacan · p.112

     *Seminar 10*: *Wednesday 21 February 1962* > *Seminar 11*: *Wednesday 28 February 1962*

     Theoretical move: Lacan pivots from the unary trait's role in constituting the subject to the logic of privation, arguing that the "minus one" (the subject's non-identity with the unary trait) is the structural condition for lack in the Real, and that this founds the connection between the signifier, narcissism of small differences, and the sexual drive's privileged function in subjectivity.

     the possibility of fatum, casus, saltus, is precisely the way in which I hope beginning from the next session to show you what other form of pure and even spatial erudition is especially involved in the function of surface.

602. #602

     Seminar IX · Identification · Jacques Lacan · p.246

     *Seminar 21*: *Wednesday 23 May 1962* > *Seminar 22*: *Wednesday 30 May 1962*

     Theoretical move: By mapping the torus topologically, Lacan formalises the structural inversion between the subject's demand/object and the Other's demand/object, deriving from this the differential structure of obsessional and hysterical neurosis, and showing that the neurotic's impasse consists in pursuing objet a through the specular image i(o) rather than acceding to it directly.

     the torus allows something which undoubtedly you can see the cross-cap for its part does not allow… the torus, through its topological structure, implies what we can call a complement, another torus which can come to concatenate with it

603. #603

     Seminar IX · Identification · Jacques Lacan · p.169

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 16*: *Wednesday 4 April 1962*

     Theoretical move: The passage advances a structural account of anxiety as the desire of the Other (not a defence against which one defends, but the source of defences), articulates the phallus as the mediating object between demand and desire, and then pivots to a topological grounding of these arguments through the introduction of the torus and a critique of Eulerian circles as an inadequate logical model—establishing topology as the rigorous foundation for Lacanian logical claims about identification and negation.

     more rigorously than ever, we are going to do topology, and it is necessary to do it because you cannot but do it at every instant

604. #604

     Seminar IX · Identification · Jacques Lacan · p.312

     *Seminar 26: Wednesday 27 June 1962*

     Theoretical move: In this closing session of the seminar, Lacan consolidates the year's teaching by articulating the structural difference between i(o) and o (the specular image and the object), grounding desire in the phantasy formula $◊a, identifying the desirer as always already implicated in the object of desire via the "Che vuoi?", and situating castration's object as the very object of analytic science—while using Blanchot's prose and the hysteric's relation to the Other's desire as literary and clinical anchors.

     to these lost envelopes where there is so well read this continuity between the inside and the outside, which is the one to which my model of this year introduced you

605. #605

     Seminar IX · Identification · Jacques Lacan · p.161

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 16*: *Wednesday 4 April 1962*

     Theoretical move: Lacan pivots from a critique of psychoanalytic congress discourse to articulate the structural relationship between anxiety, desire, jouissance, and the Other: the prohibition of jouissance (its Aufhebung) is the supporting plane on which desire is constituted, the Other is the metaphor of this prohibition, and anxiety must be understood through the desire of the Other rather than as the jouissance of a mythical self—a move that corrects both Jones's aphanisis and a Jungian-inflected misreading of the drive.

     this infinitely flat being whose necessary propulsion I demonstrate for you on this closed object which I am here calling the torus... in another different shape... it is in the very structure of these shapes to which I introduced you a little the last time, that the subject in displacing himself finds himself with his left placed on the right

606. #606

     Seminar IX · Identification · Jacques Lacan · p.208

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 18*: *Wednesday 2 May 1962* > Lacan

     Theoretical move: Lacan argues that topology—specifically the theory of knots and surface dimensions—is necessary to account for the subject's relation to desire and the constitution of the imaginary mediating function (i(o)), and that anxiety arises precisely when this imaginary mediation is lacking; topology is proposed as the proper formalism to replace naive spatial intuition derived from the specular image.

     it is not geometry, because it is not metric, it is something about which geometers have not had the slightest idea up to the present: the dimensions of space

607. #607

     Seminar IX · Identification · Jacques Lacan · p.138

     *Seminar 14*: *Wednesday 21 March 1962*

     Theoretical move: Lacan argues that the torus topology — not the sphere — is the fundamental structure of the desiring subject, because desire is constitutively knotted to the law of the Oedipus complex (the prohibition on the Other's desire), which installs an irreducible void/hole that demand and desire can never simply substitute for one another; this topological duplicity also accounts for the subject's split position as simultaneously inside and excluded from the field of the Other, grounding the impossibility of reducing desire to need.

     I am fomenting for you this topology of the torus that I believe to be very fundamental. It has the function of what one calls moreover in topology the fundamental group

608. #608

     Seminar IX · Identification · Jacques Lacan · p.80

     *Seminar 2: Wednesday 22 November 1961* > *Seminar 8*: *Wednesday 17 January 1962*

     Theoretical move: Lacan uses a visual "dial" apparatus to reframe the classical logic of universal/particular propositions, distinguishing *lexis* (the selection/extraction of the signifier) from *phasis* (existential engagement/assertion), and deploys this distinction to argue that the Name-of-the-Father functions as a universal *lexis* whose validity does not depend on any empirical instantiation—the empty sector (void) confirms rather than refutes the universal, grounding the paternal function structurally rather than existentially.

     Here is a dial in which we are going to put vertical traits (subject). The trait function is going to fulfil here that of the subject and the vertical function... Here, we have a segment of the dial where there are vertical traits, but also oblique traits, here there are no traits.

609. #609

     Seminar IX · Identification · Jacques Lacan · p.178

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 16*: *Wednesday 4 April 1962*

     Theoretical move: Lacan uses the topology of Boolean logic (union, intersection, symmetric difference) and the paradox of self-including sets to argue that the signifier cannot signify itself — it must be posed as different from itself — and that this logical structure maps onto the topology of the torus, thereby grounding the structure of desire topologically rather than through flat Eulerian representation.

     There is no need for this torus to be a regular torus nor a torus on which we could make measurements. It is a surface constituted according to certain fundamental relationships

610. #610

     Seminar IX · Identification · Jacques Lacan · p.230

     *Seminar 21*: *Wednesday 23 May 1962*

     Theoretical move: Lacan argues that classical logic's universality (the Eulerian circle, *dictum de omni et nullo*) is grounded in nullifiability, and that what logic truly circles around is not extensional inclusion but the object of desire — the "whirlwind" or hole at the centre of the concept (*Begriff*). The cut (la coupure), as a closed and nullifiable line, is the structural origin of signification, and the death drive names the condition under which life perpetually twists around a void rather than simply opposing the inanimate.

     What are we trying to get close to in our apparatus concerning surfaces, surfaces in the sense that we intend giving them here a usage which... is all the same something which is nothing other than to renew, to re-interrogate the Kantian function of the schema.

611. #611

     Seminar IX · Identification · Jacques Lacan · p.220

     *Seminar 20*: *Wednesday 16 May 1962*

     Theoretical move: Lacan argues that topology—specifically the properties of surfaces such as the torus and cross-cap—provides the structural ground for understanding the signifier, whose essence as difference and discontinuity (the cut) can only be fully theorized once the inside/outside distinction is destabilized by non-orientable surfaces; this move displaces spatial intuition in favour of a topological account of the signifying cut.

     The step that I am trying to get you to take has already begun to be traced, it is the one in which discontinuity is bound to what is the essence of the signifier, namely difference.

612. #612

     Seminar IX · Identification · Jacques Lacan · p.257

     *Seminar 21*: *Wednesday 23 May 1962* > *Seminar 23*: *Wednesday 6 June 1962*

     Theoretical move: Lacan uses the topology of the torus (and its paired-torus construction) to formalise the formula "the desire of the subject is the desire of the Other," and then pivots to the cross-cap/projective plane as the privileged topological support for the structure of fantasy, before offering contextual remarks on Heidegger and Lévi-Strauss.

     the particular structure called the cross-cap or the projective plane, in so far as I also gave you already enough pointers for this object to be, if not altogether familiar to you

613. #613

     Seminar IX · Identification · Jacques Lacan · p.135

     *Seminar 13*: *Wednesday 14 March 1962*

     Theoretical move: By mapping desire and demand onto two interlocking tori, Lacan demonstrates that the subject's inside and outside spaces are topologically identical, and that the object of desire emerges precisely from the Other's structural inability to respond to demand — the Other is "not without" power, and this negation grounds the absolute conditionality of desire.

     A topological construction is imaginable of another torus which has the property of allowing us to imagine the application of the object of desire, the internal empty circle of the first torus, onto the full circle of the second which establishes a buckle, one of these irreducible loops.

614. #614

     Seminar IX · Identification · Jacques Lacan · p.119

     *Seminar 12*: *Wednesday 7 March 1962*

     Theoretical move: Lacan introduces the torus as the privileged topological surface for modelling the subject, arguing that the subject's structure is founded not on inclusion but on exclusion via the unary trait, such that class formation (and the universal/particular dialectic) originates in a "minus one" — the subject as constitutively lacking — which generates the logic of castration, foreclosure, and ultimately the loop-topology of the torus rather than the closed interiority of the sphere.

     Because the torus is what I am going to speak to you about today... I am quite determined to transport the question elsewhere... the structure of the subject as that of a ring.

615. #615

     Seminar IX · Identification · Jacques Lacan · p.106

     *Seminar 10*: *Wednesday 21 February 1962* > *Seminar 11*: *Wednesday 28 February 1962*

     Theoretical move: Lacan uses the critique of Kantian "pure intuition" (grounded in Euclidean geometry and refuted by non-Euclidean geometry, Gödelian incompleteness, and Fregean arithmetic) as a lever to argue that the combinatory/logical function of number and reason is independent of sensible intuition, and that this has direct consequences for how psychoanalysis must situate the subject's body, drive, and fantasy beyond any spatio-temporal naturalism.

     the investigation of the trace described by a point linked to the circumference of a circle, what is called a Pascalian cycloid, will show you that a rectilinear figure... is something which is truly primordial, essential to any kind of geometrical comprehension

616. #616

     Seminar IX · Identification · Jacques Lacan · p.68

     *Seminar 2: Wednesday 22 November 1961* > *Seminar 7*: *Wednesday 10 January 1962* > I am - I think.

     Theoretical move: Lacan introduces imaginary numbers (√-1) as a formal analogy for the subject "before any nomination," arguing that replacing the unary trait (1) with the imaginary unit (i) in a continued-fraction series produces a periodic rather than convergent function — thereby modeling the subject's irreducible instability and its structural relation to the ego-ideal and the imaginary phallus, while connecting this back to the logical scansion of the three-hesitation structure of Logical Time.

     if this has an interest, it is in so far as it is operational: a formula like this in mathematics, is what is called a series... is it a convergent series?

617. #617

     Seminar IX · Identification · Jacques Lacan · p.149

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 15*: *Wednesday 28 March 1962*

     Theoretical move: Lacan uses the topology of the torus (and introduces the cross-cap) to formalise the dialectical relationship between Demand and desire in the subject, showing how the torus's privileged circle—encompassing both the generating circle (Demand) and the inner circle (metonymical desire)—allows him to locate objet petit a and the phallus as structural measures of the subject's relation to desire, while insisting that identification is strictly a dimension of the subject and not of drive or image.

     Of what use to us is the topology of this surface, of this surface called the torus, in so far as its constituting inflection which makes necessary its turns and returns is what can best suggest to us the law to which the subject is submitted in the processes of identification?

618. #618

     Seminar IX · Identification · Jacques Lacan · p.306

     *Seminar 26: Wednesday 27 June 1962*

     Theoretical move: At the close of Seminar 9, Lacan articulates the objet petit a as a topological-ontological operator: it is the object of castration that, by its enucleation from the cross-cap, transforms the imaginary sphere into a Möbius surface, thereby constituting the subject's world while marking the irreducible hole at the centre of desire and the Other's desire—a 'acosmic point' that underlies every metaphor, every symptom, and the anxiety of confronting what the Other desires of the subject.

     It is a sphere with a hole, which you organise in a certain way... each of these points is joined to the opposite point

619. #619

     Seminar IX · Identification · Jacques Lacan · p.228

     *Seminar 20*: *Wednesday 16 May 1962*

     Theoretical move: Lacan uses the topology of the Möbius strip and cross-cap to argue that desire, though non-articulatable, is nonetheless articulated — and that the operation of the cut transforms a non-orientable surface into an orientable one, modelling how the fantasy ($◊a) knots desire (as field of demand) to the object petit a through a topological torsion rather than a logical opposition.

     The quadrilateral polygon originates the torus and the cross-cap. If I never introduced the true verbalisation of this shape ◊, stamp, desire, uniting the $ to the o in the $ ◊ o

620. #620

     Seminar IX · Identification · Jacques Lacan · p.63

     *Seminar 2: Wednesday 22 November 1961* > *Seminar 7*: *Wednesday 10 January 1962* > What is the proper name?

     Theoretical move: The proper name serves as the theoretical pivot for rethinking the border between unconscious and preconscious: because the enunciating subject necessarily names itself without knowing it, the unconscious is constituted at a more radical level than preconscious discourse (which is already "in the real"), and what the unconscious seeks—perceptual-identity with a lost original signifier—is structurally unfulfillable, explaining its irreducible insistence.

     I will limit myself to a topologisation as simple as the one that he gives at the end of the Traumdeutung, namely that of the layers across which there can occur breakthroughs, thresholds, eruptions from one level into another

621. #621

     Seminar IX · Identification · Jacques Lacan · p.179

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 16*: *Wednesday 4 April 1962*

     Theoretical move: Lacan uses the topology of the torus—its two irreducible circles, their symmetric difference without intersection, and a privileged composite circle that both encircles and passes through the hole—to provide an intuitive topological model for the structural relationship between demand and desire, where the "self-difference" of the objet petit a and the void of desire are formalised through non-intersecting, non-unifiable fields.

     This in order to lead us to what? Let us make no longer a single section but two sections on the single base of the torus.

622. #622

     Seminar IX · Identification · Jacques Lacan · p.251

     *Seminar 21*: *Wednesday 23 May 1962* > *Seminar 22*: *Wednesday 30 May 1962*

     Theoretical move: Lacan argues that the obsessional's sadistic fantasy misses its true target: it aims at the specular image i(o) rather than at the object of desire o itself, because a fundamental asymmetry between the specular image and the object (which has no specular image) leads the neurotic astray—and it is this structural confusion, not narcissism per se, that accounts for neurosis and radically distinguishes it from perversion and psychosis.

     they have a nature which, as you see, is sufficiently illustrated topologically because here the asymmetry which would be the one that we would call specular

623. #623

     Seminar IX · Identification · Jacques Lacan · p.296

     *Seminar 24*: *Wednesday 13 June 1962*

     Theoretical move: Lacan argues that the proper aim of analysis is not therapeutic adaptation but the subject's entry into desire, and grounds this claim structurally by showing that the object of desire (objet petit a) is constituted not by privation or frustration but by castration, and that this castrated object uniquely "carries number with it" — a point illustrated through re-reading the Wolf Man's primal-scene fantasy.

     the logical definition of the object… is illustrated here… the little circle which I teach you to circumscribe by telling you that it is essentially constituted by the presence of this point which is here, either in its central field, or at the limit of this field

624. #624

     Seminar IX · Identification · Jacques Lacan · p.233

     *Seminar 21*: *Wednesday 23 May 1962*

     Theoretical move: Lacan uses topological surfaces—sphere, torus, Möbius strip, and cross-cap—to formalize the structural relations between cut, hole, and desire, arguing that the cross-cap is the privileged surface for representing desire-as-lack, with the phallus functioning as the structural double-point that allows the objet petit a to occupy the place of the hole.

     the existence of the function of defined topological surfaces, because it is enough that the line should be drawn on a surface defined in a certain fashion, the torus for example for it to be apparent that, while retaining its function of cut, it is not able in any way to fulfill here the same function

625. #625

     Seminar IX · Identification · Jacques Lacan · p.284

     *Seminar 24*: *Wednesday 13 June 1962*

     Theoretical move: Lacan uses the Symposium's agalma — what Alcibiades seeks at the heart of Socrates — to argue that the object of desire is ultimately the Other's desire itself (the pure eron), and that the phallus functions as the punctual, organising point that connects the barred subject ($) to the object (o) in the fundamental fantasy, while also introducing the third Freudian mode of identification as constituted through desire at the locus of the big Other.

     this schema of the figure 4 gives because here nothing other than this point guarantees for this surface cut in this way its character as a unilateral surface, but entirely guarantees it to it, making truly of $ the cut of o

626. #626

     Seminar IX · Identification · Jacques Lacan · p.299

     *Seminar 24*: *Wednesday 13 June 1962*

     Theoretical move: The passage argues that the signifier's essential non-identity to itself (a ≠ a) is the logical ground for the constitution of the object of desire at the place of the splitting of the subject, thereby differentiating psychoanalytic logic from classical formal logic and grounding reality-constitution in the furrow of desire.

     What we find, is undoubtedly here the same topological space which defines the object of desire.

627. #627

     Seminar IX · Identification · Jacques Lacan · p.141

     *Seminar 14*: *Wednesday 21 March 1962*

     Theoretical move: Lacan uses the topology of the torus and the Graph of Desire's four nodal points to articulate the structural difference between message and question, grounding desire as precisely that part of demand hidden from the Other—and showing how the neurotic (especially the obsessional) constitutes himself as a real/impossible in face of the Other's impotence to respond.

     it is enough to reverse what, it appears, the last time I did not sufficiently image in showing you this particular form of the torus in the form of a handle standing out from a plane

628. #628

     Seminar IX · Identification · Jacques Lacan · p.267

     *Seminar 21*: *Wednesday 23 May 1962* > *Seminar 23*: *Wednesday 6 June 1962*

     Theoretical move: By cutting the cross-cap with an interior-eight (double-loop signifier) around its privileged origin point, Lacan demonstrates that the surface divides into two topologically distinct parts—one that preserves the central point and is specularis­able, and a Möbius strip that is irreducibly non-specularis­able—thereby grounding the structural relationship between the barred subject ($) and objet petit a in fantasy in rigorous topological terms, with the phallus as the key to the constitution of the object of desire at the central (archèn) point.

     It is in articulating the function of this point that we will be able to find all sorts of auspicious formulae which allow us to conceive the function of the phallus at the centre of the constitution of the object of desire.

629. #629

     Seminar IX · Identification · Jacques Lacan · p.121

     *Seminar 12*: *Wednesday 7 March 1962*

     Theoretical move: Lacan deploys the topology of the torus to argue that the subject's structure is characterised by irreducible loops—unlike the sphere or plane where any loop can be collapsed to a point—and that the interplay between 'full circles' (demand) and 'empty circles' (desire/the object) on the torus structurally accounts for the constitutive 'minus one' of the unconscious, the detour through the Other, and the impossibility of a purely tautological (fully analytic) subjectivity.

     I am proposing that one should admit in a fashion which no doubt involves a concealment, something hidden which is going to have to be carried forward, rediscovered where it is, one should pose that there is a topological structure regarding which it is going to be a question of showing how it is necessarily that of the subject

630. #630

     Seminar IX · Identification · Jacques Lacan · p.186

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 16*: *Wednesday 4 April 1962*

     Theoretical move: Through sustained topological demonstration using the torus, spread-out torus, inverted eight, and cross-cap, Lacan argues that the asymmetry between the two fundamental circles (of desire and demand) cannot be grounded in the torus's own surface structure, and that this irreducible asymmetry—always escaping formalization—is precisely what makes the toric topology productive for psychoanalytic modeling of the subject's relation to the Other.

     Because it is a question of topology and not of metrical properties, the question of the greater length of one side with respect to the other has no significance.

631. #631

     Seminar IX · Identification · Jacques Lacan · p.43

     *Seminar 2: Wednesday 22 November 1961* > *Seminar 5: Wednesday 13 December 1961*

     Theoretical move: Lacan distinguishes between a productive 'crystallographic Gestalt' (structurally homologous to the signifying combinatory) and a confusing 'anthropomorphic Gestalt' (the macrocosm/microcosm analogy), then pivots to argue that the automatism of repetition is not a natural cycle of need-satisfaction but the compulsive re-emergence of a unique signifier — a letter — that a repressed cycle has become, thereby grounding repetition in the agency of the signifier rather than in biological or imaginary schemas.

     the change that is in question is defined as such in the topological combinatory which it allows us to define as the emergence of this fact, of the fact of structure

632. #632

     Seminar IX · Identification · Jacques Lacan · p.214

     *Seminar 14*: *Wednesday 21 March 1962* > *Seminar 19*: *Wednesday 9 May 1962*

     Theoretical move: The passage argues that the phallus functions as the pivot of desire's constitution by operating as a signifier that cannot signify itself — the transmutation from need to desire passes through the phallic function — and that this structure can only be adequately rendered through topology (torus, cross-cap), which provides the 'transcendental aesthetic model' for the subject's exclusion from the signifying field and the analyst's place as incarnated desire.

     this is the use of the topology of the torus — as achieving something. The bobbining movement of the repetition of demand closes somewhere even virtually, defining another loop

633. #633

     Seminar IX · Identification · Jacques Lacan · p.262

     *Seminar 21*: *Wednesday 23 May 1962* > *Seminar 23*: *Wednesday 6 June 1962*

     Theoretical move: Lacan distinguishes the psychoanalytic search for the primordial status of the object—irreducibly the object of desire—from parallel but distinct enterprises in Heidegger (utensil/Zuhandenheit) and Lévi-Strauss (bricolage), then deploys the topology of the cross-cap (projective plane) as the structural support for the fundamental fantasy, arguing that the non-eliminable singular point on this surface captures something intrinsic to the subject-object relation of desire that cannot be dissolved into three-dimensional representational conventions.

     the fundamental distinction that I too have reminded you of incessantly in order to tell you that we should not consider the ring, the torus as a solid

634. #634

     Seminar IX · Identification · Jacques Lacan · p.86

     *Seminar 9*: *Wednesday 24 January 1962*

     Theoretical move: The passage advances the argument that the subject is constituted through its relation to the signifier, where the signifier's origin lies in the subject's own effacing of a trace—a redoubled disappearance that is the mark of subjectivity itself—and that negation, the phallic object, and the obsessional's compulsion to undo are all facets of this foundational structure of the subject-as-signifier.

     I announced it to you the other day in introducing the minus 1 - that we will see that there is measured, as I might say, the vectorial angle of the subject with respect to the thread of the signifying chain.

635. #635

     The Triumph of Religion · Jacques Lacan · p.54

     II. Can Psychoanalysis Constitute the Kind of Ethics Necessitated by our Times?

     Theoretical move: Lacan critiques the ego-psychological reduction of desire to libidinal object-relations (oral/anal/genital stages), arguing instead that desire has no proper object but only the Thing as its impossible horizon, and that the commandment to love one's neighbour exposes the irreducible ambivalence (love/hatred) that makes any ethics of psychoanalysis inseparable from sublimation, the death drive, and the laws of speech that encircle das Ding.

     Have I at least succeeded in conveying to you the topological chains that situate at the heart of each of us the gaping place from which the nothing questions us about our sex and our existence?

636. #636

     The Triumph of Religion · Jacques Lacan · p.87

     VII. Not Phtlosophizing

     Theoretical move: Lacan distances his concept of the Real from both ontological metaphysics and Kantian epistemology, insisting instead that the Real is irreducibly non-whole, non-transcendent, and open to future formalization — a methodological wager that refuses premature systematization while holding open the possibility of an evolving law of the real.

     It would be an incredibly anticipatory notion to think that the real constitutes a whole.

637. #637

     Negative Psychoanalysis for the Living Dead: Philosophical Pessimism and the Death Drive · Julie Reshe · p.130

     <span id="page-126-0"></span>Human Animal, Positive Psychology, and Trauma: A Conversation Between Alenka Zupancič and Julie Reshe ̌

     Theoretical move: The passage argues that the human animal's constitutive lack is not a deviation from a complete Nature but the very proof that Nature (with a capital N, as harmonious totality) does not exist; the subject emerges as the point where nature's own inconsistency becomes 'for itself', and lack and surplus-jouissance are topologically inseparable rather than opposites.

     from the perspective of Lacanian theory, lack and surplus are part of the same topology. Surplus (positivity) is generated at the topological place of the lack

638. #638

     Critique of Pure Reason · Immanuel Kant

     THE CRITIQUE OF PURE REASON > PREFACE TO THE SECOND EDITION, 1787

     Theoretical move: Kant defines the Critique of Pure Reason as a propaedeutic — a negative, corrective science of the sources and limits of pure reason — that falls short of full transcendental philosophy but constitutes its complete architectural plan, grounded in the distinction between a priori and empirical cognition and between sense (by which objects are given) and understanding (by which they are thought).

     Transcendental philosophy is the idea of a science, for which the Critique of Pure Reason must sketch the whole plan architectonically, that is, from principles, with a full guarantee for the validity and stability of all the parts which enter into the building.

639. #639

     Critique of Pure Reason · Immanuel Kant

     THE CRITIQUE OF PURE REASON > BOOK I. > SECTION IX. Of the Empirical Use of the Regulative Principle of Reason with regard to the Cosmological Ideas.

     Theoretical move: Kant resolves the first two cosmological antinomies by converting the dialectical (constitutive) principle of reason into a regulative one: the empirical regress in the series of conditions proceeds not in infinitum (which would presuppose a given infinite totality) but in indefinitum, because the world of sense is never given as a complete whole but only through the regress itself.

     Every limited part of space presented to intuition is a whole, the parts of which are always spaces—to whatever extent subdivided. Every limited space is hence divisible to infinity.

640. #640

     Critique of Pure Reason · Immanuel Kant

     THE CRITIQUE OF PURE REASON > CHAPTER III. The Ideal of Pure Reason. > SECTION II. The Discipline of Pure Reason in Polemics.

     Theoretical move: Kant argues that dogmatism and scepticism are both insufficient stages in the development of reason, and that only the critical method—which examines reason's own powers and determines the necessary (not merely empirical) limits of cognition—can resolve the disputes raised by pure reason and establish secure grounds for a priori synthetic knowledge.

     Reason is not to be considered as an indefinitely extended plane, of the bounds of which we have only a general knowledge; it ought rather to be compared to a sphere, the radius of which may be found from the curvature of its surface

641. #641

     Critique of Pure Reason · Immanuel Kant

     THE CRITIQUE OF PURE REASON > BOOK I. > SECTION IX. Of the Empirical Use of the Regulative Principle of Reason with regard to the Cosmological Ideas.

     Theoretical move: Kant distinguishes mathematical from dynamical antinomies to argue that while mathematical cosmological ideas require homogeneous sensuous conditions (forcing both sides false), dynamical ideas admit an intelligible, non-phenomenal condition that stands outside the series, thereby allowing nature and freedom to coexist without contradiction—freedom as a transcendental idea grounding practical freedom through the distinction between phenomena and things-in-themselves.

     the dynamical series of sensuous conditions admits a heterogeneous condition, which is not a member of the series, but, as purely intelligible, lies out of and beyond it

642. #642

     Critique of Pure Reason · Immanuel Kant

     THE CRITIQUE OF PURE REASON > BOOK II. > CHAPTER III Of the Ground of the Division of all Objects into Phenomena and Noumena.

     Theoretical move: Kant argues that the pure categories of the understanding have no legitimate transcendental use beyond possible experience: without a corresponding sensuous intuition, the categories are empty forms of thought incapable of determining any object, and the concept of the noumenon must therefore be understood only in a negative, limitative sense—as a boundary-marker for sensible cognition rather than a positive domain of intelligible objects.

     our understanding attains in this way a sort of negative extension. That is to say, it is not limited by, but rather limits, sensibility, by giving the name of noumena to things, not considered as phenomena, but as things in themselves.

643. #643

     Critique of Pure Reason · Immanuel Kant

     THE CRITIQUE OF PURE REASON > BOOK I. > CHAPTER I. Of the Paralogisms of Pure Reason.

     Theoretical move: Kant argues that rational psychology collapses into a paralogism by mistaking the mere formal unity of consciousness (the "I think") for an intuition of a substantial subject, thereby illegitimately applying the category of substance to what is only a logical unity; this critique demolishes speculative proofs of the soul's immortality while clearing space for a practical (moral) grounding of belief in a future life.

     inasmuch as the formal condition of the intuition of the one is time, and of that of the other space also. But if we consider that both kinds of objects do not differ internally, but only in so far as the one appears externally to the other

644. #644

     Critique of Pure Reason · Immanuel Kant

     THE CRITIQUE OF PURE REASON > CHAPTER III. The Ideal of Pure Reason. > APPENDIX.

     Theoretical move: Kant argues that the transcendental ideas of pure reason (psychological, cosmological, theological) cannot be constitutive principles extending cognition beyond experience, but function legitimately as regulative/heuristic principles that guide the understanding toward systematic unity—their "transcendental deduction" consists precisely in demonstrating this regulative role rather than any ostensive reference to objects.

     this empirical employment stands to these ideas in an asymptotic relation alone (to use a mathematical term), that is, continually approximate, without ever being able to attain to them

645. #645

     A Voice and Nothing More · Mladen Dolar · p.176

     Silence

     Theoretical move: The passage argues that the voice occupies a structurally privileged position at the point of exception within the law: it epitomizes "validity beyond meaning" (Geltung ohne Bedeutung), functioning as the non-universal partial object that captures desire and holds the subject in thrall, thereby linking Lacan's topological account of subject/Other desire (via the torus) to Kafka's literary figures of bare life and sovereignty, and to Agamben's inclusive exclusion.

     Lacan develops his use of topology for the first time at some length. He takes the 'image' of a torus and sees the problem of the subject's desire in topological terms

646. #646

     A Voice and Nothing More · Mladen Dolar · p.69

     chapter 2 > Shofar

     Theoretical move: The passage argues that the object voice — paradigmatically embodied in the shofar — is not simply opposed to logos but is its hidden support: the paternal voice that founds the Law is structurally identical to the "other" voice it ostensibly persecutes, and both are organized around an ineradicable lack (S(A/)) that links voice, jouissance, femininity, and the impossible foundation of the Other. The voice is further theorized as the missing link between bodies and languages, connecting Lacanian object-theory to Badiou's ontology.

     its topology dislocates it in relation to presence... the voice as the object, the paradoxical creature that we are after, is also a break

647. #647

     A Voice and Nothing More · Mladen Dolar · p.80

     chapter 2 > The acousmatics of the voice

     Theoretical move: The acousmatic voice structurally resists 'disacousmatization': its source is constitutively concealed, meaning ventriloquism is not an exception but the very condition of voice as object—the voice emerges precisely in the void from which it supposedly stems, operating as both surplus-of-body and no-more-body (plus-de-corps), and thus as the operator of the impossible division between interior and exterior.

     In a curious bodily topology, it is like a bodily missile which separates itself from the body and spreads around, but on the other hand it points to a bodily interior, an intimate partition of the body

648. #648

     A Voice and Nothing More · Mladen Dolar · p.130

     The voice and the drive > The voice and the letter

     Theoretical move: The voice occupies the structural position of sovereignty (inside/outside the law simultaneously), functioning as a permanent threat of a "state of emergency" within the symbolic order; this topology extends to psychoanalysis, where the analyst's silence incarnates the object voice as a pure enunciation compelling the subject's response—making the voice the pivot of transference and of political, ethical, and linguistic subjectification alike.

     The paradoxical topology of the voice as essentially between-the-two that we have been pursuing all along can be prolonged here to the relation between phone and logos as well as zoe and bios.

649. #649

     A Voice and Nothing More · Mladen Dolar · p.116

     The voice and the drive > The voice of the superego

     Theoretical move: By drawing on Agamben's analogy between phone/logos and zoe/bios, Dolar argues that the voice occupies the topology of extimacy — it is neither simply exterior to speech nor a pre-cultural remnant, but a product of logos itself that is simultaneously included and excluded, haunting language at its core.

     the basic structure, the topology of the political, is for Agamben that of an 'inclusive exclusion' of naked life

650. #650

     A Voice and Nothing More · Mladen Dolar · p.112

     The voice and the drive > The voice of the superego

     Theoretical move: The passage argues that the voice occupies an irreducible ambiguous position between the ethical and the perverse: the ethical voice is pure enunciation without statement (demanding the subject supply the statement/act), while the superego is a "fat voice" that fills this void with positive content, guilt, and transgressive enjoyment — yet neither exhausts the voice, which always marks a void in both the subject and the Other. The chapter then opens onto the political dimension by following Aristotle's division between mere voice (phone) and speech (logos) as the foundation of the political.

     So again we find the ambiguous ontology—or, rather, topology of the status of the voice as 'between the two,' placed precisely at the curious intersection.

651. #651

     A Voice and Nothing More · Mladen Dolar · p.82

     The voice and the drive

     Theoretical move: Dolar argues that the voice, as objet petit a, occupies the paradoxical topological intersection of language and the body that belongs to neither, and that this position is what makes the voice the object of the drive rather than of desire — the drive's "aim" (the voice as by-product) is satisfied on the way to the "goal" (meaning), precisely because the voice is a non-dialectical, aphonic remainder that resists signification.

     the voice stands at a paradoxical and ambiguous topological spot, at the intersection of language and the body, but this intersection belongs to neither.

652. #652

     A Voice and Nothing More · Mladen Dolar · p.91

     The voice and the drive > His Master's Voice, His Master's Ear

     Theoretical move: The voice, as object of the drive, operates through a constitutive asymmetry of incorporation and expulsion that makes it extimate—belonging to neither interior nor exterior—and this same structural topology grounds the intimate connection between voice and conscience that has animated the ethical tradition.

     the voice presents at its clearest the mechanism of the object of the drive, its topology, its topological paradox

653. #653

     A Voice and Nothing More · Mladen Dolar · p.166

     Silence

     Theoretical move: Dolar argues that silence must be theorized across Lacan's three registers—symbolic (silence as structural differential element), imaginary (silence as supposed plenitude), and real (silence as the mute insistence of the drives)—and that the analyst's silence is not merely an absence of speech but an act that homologizes the silence of the drives, making it the operative lever of analytic practice.

     the simplest clue is offered by the topology that we have detected in different realms: their intersection is the drive, which does not simply pertain to either the signifier or the organic; it is placed at the point of their 'impossible' juncture.

654. #654

     Read My Desire: Lacan Against the Historicists · Joan Copjec · p.162

     The Unvennogender Other: Hysteria and DeDlocracy in ADlerica > The Tefton Totem

     Theoretical move: Copjec argues that the psychoanalytic subject is objectively indeterminate (not merely vaguely described), and uses the need/demand/desire triad to theorize how democracy itself hystericizes the subject by structuring its relation to an impotent (unvermögender) Other—a relation that sustains demand precisely through the Other's failure to deliver, while American pluralism forecloses the radical difference psychoanalysis defends by clinging to belief in a consistent Other of the Other.

     The grid does not rule in advance the sort of building, city, or whatever will come to occupy any particular quadrant; it was perceived to be a plan without a program... There is within the law itself something lawless—let us call it, with reference to our image of the grid, Broadway.

655. #655

     Read My Desire: Lacan Against the Historicists · Joan Copjec · p.228

     LetbalJouissance and the FemlDe Fatale > The Female Side: Mathematical Failure

     Theoretical move: By mapping Kant's first mathematical antinomy (the "not-all" structure of phenomena) onto Lacan's formulas of sexuation for the female side, the passage argues that "the woman does not exist" is a rigorously Kantian thesis about the internal limit of reason—not a historicist claim about particular, discursively constructed women—thereby distinguishing Lacanian universality from both Aristotelian particularity and Butler-style anti-universalism.

     the sexes and the antinomies should be read as positions on a Moebius strip

656. #656

     Read My Desire: Lacan Against the Historicists · Joan Copjec · p.190

     Detour through the Drive

     Theoretical move: The shift from classical detective fiction to film noir is reinterpreted not as a narrative identification of hero with criminal but as a topological transition between two orders—desire (sense, the signifier, the fort/da game as lack) and drive (being, jouissance, repetition-as-satisfaction)—which Copjec maps onto a broader historical transition from an Oedipal order of desire to a contemporary order of drive in which jouissance is socially commanded rather than privately protected.

     One of the most theoretically compelling aspects of Double Indemnity is its inscription not only of this difference but of the very topological incompatability of classical detective fiction and film noir.

657. #657

     Read My Desire: Lacan Against the Historicists · Joan Copjec

     Detour through the Drive > The Voice and the Voice-Over

     Theoretical move: The passage argues that when desire gives way to drive, the intimate core of being—jouissance—ceases to be merely supposed and becomes exposed at the surface of speech, yet without becoming phenomenal or communicable; this topological shift is then applied to film noir, where the voice-over materializes the subject's irreducible absence from the diegetic reality it narrates.

     In shifting its topological position, being does not lose its essential nature as resistance to sense.

658. #658

     Read My Desire: Lacan Against the Historicists · Joan Copjec · p.143

     Vampires, Breast-Feeding, and Anxiety > The Drying Up of the Breast

     Theoretical move: The passage argues that vampirism figures the collapse of fantasy's support of desire—the "drying up of the breast" as objet petit a—when the extimate object loses its proper distance and returns as an uncanny double endowed with surplus jouissance, threatening the subject's constitutive lack; this structure is traced across breast-feeding advocacy, vampire fiction, Hitchcock's Rebecca, and La Jetée.

     Within Manderley there is one room, one exceptional space whose primary function is to mark this emptiness; this space is Rebecca's bedroom. Both the beach house and Rebecca's bedroom have an exceptional status, but while the beach house marks a surplus, Rebecca's room marks an absence, a deficiency.

659. #659

     Beyond the Pleasure Principle and Other Writings · Sigmund Freud

     The Ego and the Id

     Theoretical move: Freud introduces the structural distinction between ego and id by arguing that the ego develops from the perceptual surface of the psychic apparatus, while the id names the unconscious remainder; this move reframes the topographical (Cs/Ucs/Pcs) model by showing that the ego itself is partly unconscious, and that word-notions are the mechanism by which inner processes gain access to consciousness.

     this is one of the difficulties that result once we make any serious attempt to envisage the workings of the psyche in spatial, topical terms

660. #660

     Beyond the Pleasure Principle and Other Writings · Sigmund Freud

     The Conscious and the Unconscious

     Theoretical move: Freud argues that the descriptive conscious/unconscious distinction must be replaced by a structural and dynamic tripartite topology (Cs/Pcs/Ucs), and then further complicated by the discovery that part of the ego itself is unconscious—rendering 'unconsciousness' a multivalent quality rather than a single definitive category, and obliging a shift from the Cs/Ucs antithesis to the structural opposition between the coherent ego and the repressed split from it.

     We now realize that the Ucs and the repressed are not conterminous; while it remains correct to say that all of the repressed is Ucs, it is not also the case that all of the Ucs is repressed.

661. #661

     The Singularity of Being: Lacan and the Immortal Within · Mari Ruti · p.140

     6. *The Dignity of the Thing*

     Theoretical move: The passage argues that sublimation—the elevation of mundane objects to the dignity of the Thing—is structurally grounded in the constitutive lack introduced by the signifier: it is precisely because the Thing resists symbolization that the subject becomes an inexhaustible creature of signification and creative capacity, with lack and the possibility of filling it arising simultaneously.

     a hollow piece of macaroni ('a hole with something around it') … render concrete a fundamental fact about human life, namely that 'the fashioning of the signifier and the introduction of a gap or a hole in the real is identical'.

662. #662

     The Singularity of Being: Lacan and the Immortal Within · Mari Ruti · p.32

     1. *The Singularity of Being* > *Repetition as Destiny* > *The Crisis of Consciousness*

     Theoretical move: The passage argues that desire functions as a defense that maintains a productive distance from jouissance (which the subject is constitutionally incapable of managing), while the drive's surplus enjoyment perpetually destabilizes the subject from within — making the drive a fundamental ontological notion that deepens the crisis of consciousness beyond what Freud's unconscious or Lacan's early linguistic theory alone could account for.

     Lacan's increasing emphasis on the real towards the end of his career was designed to foreground this much more than has been recognized by those who have focused exclusively on his early theories of language and the unconscious.

663. #663

     Read My Desire: Lacan Against the Historicists · Joan Copjec · p.176

     **Locked Room/Lonely Room: Private Space in Film Noir** > **The Locked-Room Paradox and the Group**

     Theoretical move: Copjec argues that the "locked-room paradox" in detective fiction is the structural equivalent of language's internal limit: the excess element is not a hidden surplus beneath the structure but the limit immanent to it, which is why the detective's interpretive act is constitutively desire—the quasi-transcendental principle that posits a gap irreducible to evidence—and why the sexual relation is structurally foreclosed from the genre by the absence of the final, woman-signifier.

     The excess element is, instead, located on the same surface as the structure, that is, it is manifest in the latter's very functioning.

664. #664

     Read My Desire: Lacan Against the Historicists · Joan Copjec · p.180

     **Locked Room/Lonely Room: Private Space in Film Noir** > **Detour through the Drive**

     Theoretical move: The shift from classical detective fiction to film noir is theoretically recast not as a narrative inversion of identification but as a structural choice between desire (sense, language, lack) and drive (being, jouissance), homologized through Freud's fort/da game and mapped onto a broader historical transition from an Oedipal order of desire to a contemporary order of commanded jouissance with political consequences.

     One of the most theoretically compelling aspects of Double Indemnity is its inscription not only of this difference but of the very topological incompatability of classical detective fiction and film noir.

665. #665

     Read My Desire: Lacan Against the Historicists · Joan Copjec · p.190

     **Locked Room/Lonely Room: Private Space in Film Noir** > **The Voice and the Voice-Over**

     Theoretical move: Copjec argues that the "grain of the voice" operates as a structural limit that collapses universal sense and installs the listener in a relation of transference/desire toward an unknown X; when desire gives way to drive, this private beyond is no longer hidden but exposed as a void—jouissance surfacing within the phenomenal field without becoming phenomenal—a move that explains the film noir voice-over's materialization of the narrator's irreducible absence from diegetic reality.

     In shifting its topological position, being does not lose its essential nature as resistance to sense

666. #666

     Freud as Philosopher: Metapsychology After Lacan · Richard Boothby · p.115

     <span class="chnum ordinal">Chapter 2 </span><span id="ch2.xhtml_p71" class="pagebreak" aria-label=" page 71. " role="doc-pagebreak"></span>Between the Image and the Word > The Dream's Solution

     Theoretical move: The passage argues that dream-work enacts a "short circuit" between verbal (preconscious) and imagistic (unconscious) registers of the dispositional field, and that free association as analytic method constitutes a principled resistance to the fusional, totalizing power of the dream-image—reversing condensation by dissolving the image back into its conditioning field.

     Similar analogies to a landscape continued to shape Freud's thinking throughout his career and especially his mature theory of the mind as a topography. This spatial-topographical conception can be said to be relevant in a special way to the phenomenology of dreams.

667. #667

     Freud as Philosopher: Metapsychology After Lacan · Richard Boothby · p.244

     <span class="chnum ordinal">Chapter 5 </span><span id="ch5.xhtml_p241" class="pagebreak" aria-label=" page 241. " role="doc-pagebreak"></span>Figurations of the *Objet a* > The Object-Cause of Desire

     Theoretical move: The passage argues that the *objet petit a* is the "object-cause" of desire: a primordially lost, liminal object that is simultaneously imaginary, symbolic, and real yet belongs to none, and whose retroactive ceding—not subtraction from a pre-formed subject—constitutes the desiring subject itself, such that desire paradoxically originates only in and through the loss of its object.

     By virtue of its paradoxical constitution the objet a can only be described topologically as the perpetually absent locus around which the drives revolve.

668. #668

     Freud as Philosopher: Metapsychology After Lacan · Richard Boothby · p.258

     <span class="chnum ordinal">Chapter 5 </span><span id="ch5.xhtml_p241" class="pagebreak" aria-label=" page 241. " role="doc-pagebreak"></span>Figurations of the *Objet a* > Between the Look and the Gaze

     Theoretical move: By identifying the gaze with objet petit a and locating it in a triadic, topological structure that pre-exists and constitutes the field of the visible, Boothby argues that the Lacanian gaze is not a competing look but the dispositional horizon of consciousness itself—the desire of the Other that frames all positional awareness—with distinct political and clinical consequences in mass psychology versus analytic transference.

     By identifying the gaze with objet a, Lacan describes a structure that in principle cannot be mapped in a linear fashion but can be described only by recourse to topology.

669. #669

     Freud as Philosopher: Metapsychology After Lacan · Richard Boothby

     <span id="Index.xhtml_p323" class="pagebreak" aria-label=" page 323. " role="doc-pagebreak"></span>Index

     Theoretical move: This is a back-of-book index from Boothby's "Freud as Philosopher: Metapsychology after Lacan" (2001), listing concepts and page references from S through V. It is a navigational aid and contains no substantive theoretical argument.

     Topology 258, 262

670. #670

     Freud as Philosopher: Metapsychology After Lacan · Richard Boothby · p.262

     <span class="chnum ordinal">Chapter 5 </span><span id="ch5.xhtml_p241" class="pagebreak" aria-label=" page 241. " role="doc-pagebreak"></span>Figurations of the *Objet a* > Why One and One Make Four

     Theoretical move: By mapping the *objet a* across Schema L, Schema R, the Gestalt figure/ground distinction, and the Greimasian semiotic square, Boothby argues that the *objet a* is not a positional object but an "objectality" function that emerges from the structural tension between das Ding (maternal) and the paternal Law (symbolic order), a tension whose topology is best captured by Schema R rather than Schema L.

     Lacan sought to theorize the nature and function of the objet a by relying on analogies to mathematical topology

671. #671

     The Chattering Mind: A Conceptual History of Everyday Talk · Samuel McCormick · p.220

     Ancient Figures of Speech > **Babbling** *Bathos* > **Scales of Existence**

     Theoretical move: The passage argues that authenticity and inauthenticity in Heidegger are not opposed states but modal counter-possibilities of each other, and that the key operative concept—*Modus*/modification—structures a descending/ascending scale of discourse (from babble to silence) as existential trajectories rather than fixed conditions, with implications for Lacan's parallel theorization of alienation and authentic existence.

     What is ultimately at stake in the spectrum of discourse ranging from silence to babble, *Schweigen* to *Geschwätz*, is a series of existential transitions between authentic and inauthentic ways of living.

672. #672

     The Chattering Mind: A Conceptual History of Everyday Talk · Samuel McCormick · p.253

     The Writing on the Wall > First and Final Words > **Where I Was**

     Theoretical move: By reading Lacan's spatial grammar of "where" (où) in his re-analysis of the dream of Irma's injection, the passage argues that the moi/je split is a topological-temporal event of resubjectivization: the subject's assumption of its history through speech addressed to another is the founding gesture of psychoanalytic technique.

     the crucial question in Freud's analysis and Lacan's re-analysis of this iconic dream is not when but, instead, where. Where, exactly, does the moi fall and the je rise

673. #673

     The Odd One In: On Comedy · Alenka Zupančič · p.28

     part i

     Theoretical move: Zupančič uses Hegel's account of comedy in the Phenomenology—specifically the "noumenological" movement whereby Absolute Spirit must come to know itself—to argue that what Hegel and Lacan share is a structural insight: genuine transformation requires not only a change in the subject's consciousness but a shift in the external Symbolic/Other in which the subject's unconscious is materialized, and this "short circuit" between the lack in the subject and the lack in the Other is the properly comic (and analytic) dimension of experience.

     the encounter of the two entities at a very precise (or precisely right) point of their topology

674. #674

     The Odd One In: On Comedy · Alenka Zupančič · p.65

     Physics of the Infinite against Metaphysics of the Finite

     Theoretical move: Against the contemporary "metaphysics of finitude" (which closes off the human within its limits), Zupančič argues that comedy enacts a "physics of the infinite" by demonstrating that human finitude is always already a *failed* finitude—a finitude with a structural hole—whose Lacanian name is objet petit a, and whose topology is best rendered by the Möbius strip: immanence that generates an other side without ever crossing to it.

     To articulate it, Lacan had recourse to topology and came up with the figure of the Möbius strip.

675. #675

     The Odd One In: On Comedy · Alenka Zupančič · p.226

     Wozu Phallus in dürftiger Zeit? > Concluding Remarks

     Theoretical move: Zupančič argues that comedy is essentially the "genre of the copula" — the signifying articulation of the missing link between life and the Symbolic — and that the phallus, appearing in comedy as a partial object rather than merely a signifier, materialises this constitutive contradiction; comedy's "realism" is thus the realism of the Real of desire and drive, not the reality principle.

     what the topology of the Möbius strip reveals is that the missing link that structures our reality is not a missing link between two neighbor elements, the connection between which would thus be interrupted—instead, its very missing *is* the linkage between two neighbor elements.

676. #676

     The Odd One In: On Comedy · Alenka Zupančič · p.143

     Structural Dynamics and Temporality of the Comical

     Theoretical move: Zupančič argues that tragedy and comedy are not two attitudes toward the same discrepancy but two structurally distinct standpoints *within* it: tragedy stands at the point of demand (articulating discrepancy as desire), while comedy stands at the point of satisfaction (articulating discrepancy as jouissance/surplus-satisfaction), and this standpoint-difference entails a reversal of temporality in which satisfaction precedes and overtakes demand rather than lagging behind it.

     The discrepancy at stake could also be formulated in topological instead of temporal terms: the satisfaction is produced somewhere else than where we expect it or await it.

677. #677

     Beyond the Pleasure Principle and Other Writings (alt. ed.) · Sigmund Freud

     The Ego and the Id

     Theoretical move: Freud introduces the structural distinction between ego and id by grounding consciousness in the perceptual surface system (Pcpt-Cs) and word-notions as the mechanism of preconscious linkage, while arguing that the ego, though rooted in perception, flows continuously into the unconscious id — thereby initiating the second topography that supersedes the simple Cs/Ucs binary.

     If we are aiming to represent this diagrammatically, then we need to add that the ego does not envelop the id completely… rather in the way that the germinal disk sits on the top of the egg. The ego is not sharply separated from the id, but flows on down into it

678. #678

     Reading Marx · Slavoj Žižek, Frank Ruda & Agon Hamza

     *Unexpected Reunions* > **The Phenomenal In-Itself**

     Theoretical move: The passage argues that the Kantian/OOO framework for accessing the In-itself remains trapped in a masculine (phallic) logic of exception, while a Hegelian-Lacanian "feminine" (not-all) logic reveals the In-itself not as a transcendent beyond but as the very cuts and inconsistencies within phenomena—cuts that mark the inscription of a desubstantialized, non-actant subject defined as "that which in the Real suffers from the signifier."

     it is what makes every figuration of 'external reality' inconsistent, thwarted, non-all – and these cuts are the sites of the intervention of subjectivity into reality.

679. #679

     Reading Marx · Slavoj Žižek, Frank Ruda & Agon Hamza · p.32

     *Unexpected Reunions* > **Diagram Traversed by Antagonism**

     Theoretical move: The passage argues that the identity of an object resides not in an inner core but in its "diagram" — the virtual structure of non-actualized potentials — and crucially refines this by distinguishing accidental non-actualizations from essentially impossible ones (the impossible-real), applying this logic to politics to show that capitalism's particular malfunctions are structurally necessary rather than accidental symptoms to be reformed away.

     this involves a proper conceptualization of a topological animal that can be folded and stretched into the multitude of different animal species that populate the world

680. #680

     Sex and the Failed Absolute · Slavoj Žižek · p.212

     **Sex and the Failed Absolute** > The Hegelian Repetition

     Theoretical move: By mapping Hegel's theory of repetition onto the Möbius strip, Žižek argues that repetition does not merely confirm contingency but dialectically sublates it into necessity, and that this movement only achieves its full force when it reaches "concrete universality"—where the universal appears as one of its own species, exemplified by the rabble as the repressed universal of bourgeois society—thereby marking Hegel's decisive step beyond Kantian transcendentalism.

     the minimal form of the Möbius strip … one side as the side of error and the other as the side of truth: by progressing on the side of error, we (may) find ourselves on the side of truth

681. #681

     Sex and the Failed Absolute · Slavoj Žižek · p.292

     **Sex and the Failed Absolute** > The Retarded God <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-780"></span>of <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1619"></span><span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1834"></span>Quantum <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1168"></span>Ontology > [The Two Vacuums: From Less than Nothing to Nothing](#contents.xhtml_ahd20)

     Theoretical move: Žižek argues that ontology requires a pre-ontological register of "less-than-nothing" (den) distinct from both Nothing and Something, and uses the Klein bottle topology and the Higgs field paradox to demonstrate that Void/Nothing is not the ground but itself an achievement requiring energetic expenditure — thereby establishing a materialist distinction between two vacuums (false/true) that is strictly homologous to the Lacanian distinction between the death drive's circular movement and nirvana, and between den and objet a.

     in order to account for the Klein bottle structure, for its reflexive turn-into-itself which cannot be represented in our ordinary three-dimensional space, it is not enough to add another (fourth) dimension of space; the dimension to be added is a purely negative one

682. #682

     Sex and the Failed Absolute · Slavoj Žižek · p.322

     **Sex and the Failed Absolute** > The World With(out) a <span id="scholium_34_the_world_without_a_snout.xhtml_IDX-138"></span><span id="scholium_34_the_world_without_a_snout.xhtml_IDX-2118"></span><span id="scholium_34_the_world_without_a_snout.xhtml_IDX-2519"></span>Snout

     Theoretical move: Žižek argues against Badiou's "positivism of Truth-Event" by insisting that the Death Drive—understood as radical (self-relating) negativity rather than any ontic positivity—is the primordial opening that makes an Event possible, and that sexuality (as the site of this void) cannot be reduced to the order of Being but is already a "brush with the Absolute" that love merely supplements, not elevates.

     Sloterdijk fails to locate spheres into the twisted space of a Klein bottle.

683. #683

     Sex and the Failed Absolute · Slavoj Žižek · p.9

     **Sex and the Failed Absolute** > The <span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-2453"></span>Unorientable Space of <span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-498"></span><span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-1339"></span>Dialectical Materialism

     Theoretical move: The passage advances a programmatic argument that dialectical materialism must be reconceived as a formal materialism of unorientable surfaces—without substantial matter or teleological development—and that sexuality (understood as radical negativity following Lacan) is the privileged site where the parallax gap between ontology and the transcendental is redoubled and thus our sole contact with the Absolute, with topology (Möbius strip, cross-cap, Klein bottle) providing the structural vocabulary for this redoubling.

     dialectical materialism is a theory of (twisted, curved) surfaces—for dialectical materialism, depth is an effect of convoluted surface

684. #684

     Sex and the Failed Absolute · Slavoj Žižek · p.357

     **Sex and the Failed Absolute** > The Persistence of <span id="theorem_iv_the_persistence_of_abstraction.xhtml_IDX-17"></span>Abstraction > [How to Do Words with Things](#contents.xhtml_ahd23)

     Theoretical move: The subject is not merely related to a traumatic gap or rip in reality but IS that gap—a self-reflective reversal that reframes symbolic castration as the violent ontological opening that makes language's distance from reality possible; this crack of negativity then drives a critique of assemblage theory's virtual diagram, which must be amended to include essentially non-realized possibilities that are the impossible-real of any structure.

     this involves a proper conceptualization of a topological animal that can be folded and stretched into the multitude of different animal species that populate the world

685. #685

     Sex and the Failed Absolute · Slavoj Žižek · p.281

     **Sex and the Failed Absolute** > The Retarded God <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-780"></span>of <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1619"></span><span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1834"></span>Quantum <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1168"></span>Ontology > [The Implications of Quantum Gravity](#contents.xhtml_ahd19)

     Theoretical move: The passage argues that the collapse of the wave function in quantum physics is structurally homologous to the Lacanian concept of symbolic registration by the big Other, and further proposes a three-level ontology (quantum Real, abyssal Void, macroscopic reality) modeled on the Klein bottle, where the collapse of the wave function is not an anomaly but constitutive of quantum reality itself — with the 'snout' of the Klein bottle retroactively producing the 'mollusk' of the Real.

     This brings us back to the model of the Klein bottle: insofar as its rounded surface stands for the Real… the hole in its midst indicates that something, a kind of abyssal attractor, drags down the field

686. #686

     Sex and the Failed Absolute · Slavoj Žižek · p.290

     **Sex and the Failed Absolute** > The Retarded God <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-780"></span>of <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1619"></span><span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1834"></span>Quantum <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1168"></span>Ontology > [The Implications of Quantum Gravity](#contents.xhtml_ahd19)

     Theoretical move: Žižek uses quantum physics (wave-function collapse, decoherence, virtual particles) to argue that ignorance is not merely epistemic but has a positive ontological status inscribed in reality itself, which in turn redefines the big Other/God as necessarily non-omniscient and "retarded" (always registering too late), and connects this to a Hegelian dialectic in which the indivisible One of a thing is identical with a void of Nothing at its core.

     the snout-like twist of the Klein bottle (rendered possible by the abyssal Void that renders the 'mollusk' of quantum waves unstable, incomplete) accounts for the rise of 'objective' spatio-temporal reality out of this 'mollusk.'

687. #687

     Sex and the Failed Absolute · Slavoj Žižek

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables > [<span id="theorem_iii_the_three_unorientables.xhtml_p259" class="pagebreak" title="259"></span>A Snout in Plato’s Cave](#contents.xhtml_ahd18)

     Theoretical move: By reinterpreting Plato's cave through topology (Möbius strip, Klein bottle) and the Lacanian Real, Žižek argues that the Self is a fragile surface between two outsides, that authentic emancipation requires a dialectics of master and volunteer structurally homologous to the analytic relation, and that capitalist "freedom" and emancipatory "servitude" are two inversions of the same Möbius-strip reversal of freedom/servitude.

     So let's add yet another version of Plato's cave, that of the inside of the Klein bottle.

688. #688

     Sex and the Failed Absolute · Slavoj Žižek · p.439

     **Sex and the Failed Absolute** > Language, *Lalangue*

     Theoretical move: Žižek argues that in every parallax gap (production/representation, drive/desire, lalangue/language) true materialism requires asserting the primacy of the *second* term—the gap, representation, desire, language—because the supposedly "more basic" first term only functions against the background of the lack opened by the second; and he maps four modes of relating to language (praxis, lalangue, science, and the radical cut of philosophy/poetry/mysticism), concluding that the Klein bottle, not the cross-cap or quilting point, is the appropriate topological model for subjectivization.

     a more complex model is needed which accounts for the turn-towards-itself, for the reversal of externality into the point of subjectivization, a model provided by the Klein bottle.

689. #689

     Sex and the Failed Absolute · Slavoj Žižek · p.300

     **Sex and the Failed Absolute** > The Retarded God <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-780"></span>of <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1619"></span><span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1834"></span>Quantum <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1168"></span>Ontology > [The Two Vacuums: From Less than Nothing to Nothing](#contents.xhtml_ahd20)

     Theoretical move: Žižek maps a triadic ontological structure—Nothing/Void ($), the One (objet a), and the Two (sinthome)—onto unorientable topological surfaces (Möbius strip, cross-cap, Klein bottle), arguing that at every level there is a constitutive antagonism: nothing is never fully nothing, the One is never one, the Two never forms a relation, and the barred subject ($) is the operator that transforms pre-ontological void into ontological nothingness.

     this is why the entire structure of the Klein bottle remains an unorientable surface: when we slide down onto its surface into the central abyss, we come back to our starting point on the inside

690. #690

     Sex and the Failed Absolute · Slavoj Žižek · p.274

     **Sex and the Failed Absolute** > The Retarded God <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-780"></span>of <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1619"></span><span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1834"></span>Quantum <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1168"></span>Ontology

     Theoretical move: To escape the hermeneutic circle of transcendental presuppositions, Žižek argues that material reality itself must be structured by a network homologous to symbolic space — the self-reflexive topology of the Klein bottle is not merely a feature of signification but is inherent to reality at its most basic level, as quantum physics confirms.

     the self-reflexive turn that characterizes the Klein bottle must be somehow inherent to reality itself at its most basic—therein resides the lesson of quantum physics

691. #691

     Sex and the Failed Absolute · Slavoj Žižek

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables > Notes

     Theoretical move: This is a notes/endnotes section for the chapter "The Three Unorientables," providing bibliographic references and brief theoretical asides; the substantive theoretical moves are minimal, though note 15 articulates a dialectical reversal (form/content relation) and note 38 alludes to the Klein bottle's topological obscenity.

     It is just an essay to elucidate one of the basic matrixes of dialectical thinking... when, in a public talk, I recently projected on the screen a short video clip displaying the gradual emergence of a Klein bottle out of simple strip

692. #692

     Sex and the Failed Absolute · Slavoj Žižek · p.244

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables > [Suture Redoubled](#contents.xhtml_ahd15)

     Theoretical move: Žižek argues that the Lacanian barred subject inverts the standard (cinematic) suture theory: rather than the subject being merely an illusory stand-in for an absent external cause, the externality of the generative process itself only ex-sists insofar as the subject's constitutive gesture is already present within it — suture is thus logically prior to (not derivative of) the split between subjective and objective levels it bridges.

     Lacan aims at in his persistent reference to torus and other variations of the Möbius-strip-like structures in which the relationship between inside and outside is inverted.

693. #693

     Sex and the Failed Absolute · Slavoj Žižek · p.47

     **Sex and the Failed Absolute** > The <span id="theorem_i_the_parallax_of_ontology.xhtml_IDX-1608"></span>Parallax <span id="theorem_i_the_parallax_of_ontology.xhtml_IDX-1657"></span>of Ontology > [Varieties of the Transcendental in Western Marxism](#contents.xhtml_ahd3)

     Theoretical move: Žižek surveys Western Marxist attempts to break out of the transcendental circle (Lukács, Bloch, Ilyenkov), arguing that each attempt either regresses to naive-realist ontology of levels or returns to premodern cosmology, and that such regressions symptomatize an inability to confront the radical negativity at the core of modern subjectivity.

     in contrast to our emphasis on unorientables

694. #694

     Sex and the Failed Absolute · Slavoj Žižek · p.222

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables

     Theoretical move: Žižek argues that Hegel's dialectical system is not a smooth logical machine but a chain of constitutive failures and deadlocks, where things ex-sist out of their own impossibility—a structure he maps onto the topological triad of Möbius strip / cross-cap / Klein bottle as homologous to Hegel's triad of being / essence / notion, with the Lacanian insight that the Möbius strip's apparent continuity already implies an internal cut.

     one can continuously deform the Möbius strip into cross-cap, and two cross-caps glued together at their boundaries form a Klein bottle

695. #695

     Sex and the Failed Absolute · Slavoj Žižek · p.233

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables > [The “Inner Eight”](#contents.xhtml_ahd14)

     Theoretical move: The Möbius-strip topology of the "inner eight" (self-reflecting hierarchical inversion) is deployed to argue that true materialist dialectics requires acknowledging that the Universal is *already* barred/voided from within—not sublated into the Idea—and that fantasy, repression, and the Form/content split all operate according to this same logic of a loop immanent to hierarchy.

     the two surfaces or levels not only intersect but, at this point of intersection, they turn around and replicate themselves, forming what is usually referred to as the 'inner eight.'

696. #696

     Sex and the Failed Absolute · Slavoj Žižek · p.299

     **Sex and the Failed Absolute** > The Retarded God <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-780"></span>of <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1619"></span><span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1834"></span>Quantum <span id="corollary_3_the_retarded_god_of_quantum_ontology.xhtml_IDX-1168"></span>Ontology > [The Two Vacuums: From Less than Nothing to Nothing](#contents.xhtml_ahd20)

     Theoretical move: Žižek deploys Lacan's formal logic of 1+a and 2+a to argue that neither the One nor the Two are primordial: the originary level is a "less than zero" (the quantum distinction between two vacuums), whose internal tension generates the entire series One→supplement→Two→excess, identifying the operator of this transformation with the barred subject ($) as the inverted counterpart of objet a.

     we were simply referring to the two stages of the whole series which is: +, M+, MF+

697. #697

     Sex and the Failed Absolute · Slavoj Žižek · p.269

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables > [<span id="theorem_iii_the_three_unorientables.xhtml_p259" class="pagebreak" title="259"></span>A Snout in Plato’s Cave](#contents.xhtml_ahd18)

     Theoretical move: The passage argues that ideology functions by retroactively constructing its own past (its "fossils"), and that the closed ideological universe conceals its constitutive blind spot—the withdrawal of the subject's objectal correlate (objet petit a)—which is the structural condition for the appearance of reality; this is articulated topologically through the distinction between the Möbius strip and the Klein bottle, the latter alone capturing the emergence of the subject as pure difference.

     We can see clearly here the difference between the Möbius strip and the Klein bottle: in the Möbius strip, we pass from one to the other side of the strip… while in the Klein bottle, we pass from the hole in the midst of a circular body to the substance of this body itself

698. #698

     Sex and the Failed Absolute · Slavoj Žižek · p.200

     **Sex and the Failed Absolute** > Marx, <span id="scholium_22_marx_brecht_and_sexual_contracts.xhtml_IDX-211"></span>Brecht, and Sexual Contracts

     Theoretical move: The Möbius strip topology of political logic reveals that the incel/hierarchy position flips into a demand for egalitarian redistribution at its extreme, just as the logic of egalitarian human rights flips into its opposite at the point of sexuality; simultaneously, Marx's analysis of the 'free' labor contract is extended to the sexual contract to show that formal consent/freedom conceals structural coercion, and that surplus-jouissance is the sexual homologue of surplus-value, making contractual sex inherently asymmetric and ideologically limited.

     A supreme political example of the reversal that characterizes Möbius strip comes from a new marginal movement… we should… oppose the logic of universal human rights and the logic of social hierarchy as the two sides of a Möbius strip

699. #699

     Sex and the Failed Absolute · Slavoj Žižek · p.229

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables > [Möbius Strip, or, the Convolutions of Concrete Universality](#contents.xhtml_ahd13)

     Theoretical move: The Möbius strip serves as the topological model for dialectical "coincidence of opposites," showing how a line brought to its extreme intersects with its opposite — a structure that governs politics (Fascism), sexuation (universality/exception), the psychoanalytic relation of contingency to symbolization, and the Signifier/Signified relation in language, with the quilting point as the element of contingent Real that concludes the symbolic process by throwing it back to its origin.

     This is how the Möbius strip provides a model for what Hegel calls 'negation of negation.'

700. #700

     Sex and the Failed Absolute · Slavoj Žižek · p.243

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables > [Suture Redoubled](#contents.xhtml_ahd15)

     Theoretical move: By redoubling the Möbius strip into the cross-cap, Žižek argues that suture must be understood in two asymmetric versions — (1) an internal lack covered by a symptomal element that holds the place of excluded production, and (2) an external reality that requires a subjective supplement (objet petit a) to cohere — and that only the second version institutes subjectivity proper, inscribed into the order of things rather than reducible to ideological misrecognition.

     The two versions of suture should not be opposed as right and wrong, they are both true, in accordance with the cross-cap structure.

701. #701

     Sex and the Failed Absolute · Slavoj Žižek · p.15

     **Sex and the Failed Absolute** > The <span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-2453"></span>Unorientable Space of <span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-498"></span><span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-1339"></span>Dialectical Materialism > Notes

     Theoretical move: This endnotes passage is non-substantive bibliographic and clarificatory content, but note 5 makes a theoretically load-bearing move: it argues that the topological triad of Möbius strip, cross-cap, and Klein bottle does not map one-to-one onto examples (quilting point, class struggle) but rather that each example instantiates all three figures differently, so the triad illuminates distinct aspects of a single phenomenon.

     the numerous examples we use (from ontology, psychoanalytic theory, and politics) to illustrate the triad of Möbius strip, cross-cap, and Klein bottle do not fit perfectly just one of the terms of this triad.

702. #702

     Sex and the Failed Absolute · Slavoj Žižek · p.388

     **Sex and the Failed Absolute** > Ibi <span id="corollary_4_ibi_rhodus_ibi_saltus.xhtml_IDX-952"></span>Rhodus Ibi Saltus!

     Theoretical move: The passage argues that the triple anniversary of Marxist milestones in 2017 (Marx's Capital, the October Revolution, the Shanghai Commune) reveals an unresolved problem in Communist emancipatory politics, and proposes that Protestantism — rather than this Marxist lineage — may supply the coordinates for an ethics adequate to an 'unorientable space' and to the subject's constitutive entrapment (Plato's cave).

     an ethics that fits the unorientable space, an ethics for a subject caught into Plato's cave.

703. #703

     Sex and the Failed Absolute · Slavoj Žižek · p.148

     **Sex and the Failed Absolute** > Sex as Our Brush with the Absolute > [Plants, Animals, Humans, Posthumans](#contents.xhtml_ahd10)

     Theoretical move: Žižek argues that "Absolute Knowing" names a redoubled not-knowing in which ontological incompleteness is displaced into reality itself, and that this logic—exemplified by the Lacanian "subject of the unconscious" structured as a Kierkegaardian apostle—entails rejecting the human/animal exception as the origin of sexual deadlock: the rupture of sexuality is pre-human, constitutive of nature as such, with humanity merely the site where this constitutive gap "appears as such."

     And this brings us back to the starting point of this book: unorientables.

704. #704

     Sex and the Failed Absolute · Slavoj Žižek · p.13

     **Sex and the Failed Absolute** > The <span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-2453"></span>Unorientable Space of <span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-498"></span><span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-1339"></span>Dialectical Materialism

     Theoretical move: The passage maps the book's structural architecture (theorem/corollary/scholia) as a self-enacting ontological form, and closes by defending the "thwarted identity" of the Real—the irreducible gap between transcendental space and reality—against both new realist critics and the ideological "fine art of non-thinking" that converts the symbolic into image and forecloses genuine thought.

     they constrain the unorientable surface into the horizon of 'orientable' progress.

705. #705

     Sex and the Failed Absolute · Slavoj Žižek · p.225

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables

     Theoretical move: The passage argues that the logic of reflection, mapped onto topological surfaces (Möbius strip, cross-cap, Klein bottle), culminates in a 'pure difference' that precedes and constitutes its terms rather than distinguishing pre-existing entities — sexual difference and class struggle are paradigmatic cases. From this, Žižek proposes extending Lacan's point de capiton into a triad (quilting point, quilting line, quilting tube) corresponding to the three unorientable surfaces, and defends topology against the 'Hegelian' figural/conceptual hierarchy by arguing that self-referential twists ARE conceptual thinking.

     what, at the 'lower' level of the figural model (say, the reversal that characterizes the Möbius strip), cannot but appear a paradox, an exception, is, at the 'higher' level of conceptual thinking the very basic feature of the process

706. #706

     Sex and the Failed Absolute · Slavoj Žižek · p.131

     **Sex and the Failed Absolute** > Sex as Our Brush with the Absolute > [Sexual Parallax and Knowledge](#contents.xhtml_ahd8)

     Theoretical move: Sexuality is constitutively grounded in a structural impossibility ('il n'y a pas de rapport sexuel') rather than in repressed instinct: fantasy fills the gap opened by this impossibility, infantile sexuality is not a pre-normative productive base but the very site where the impossibility first registers, and copulation itself has two sides—the Master-Signifier of orgasmic culmination and S(Ⱥ), the signifier of the barred Other as irreducible antagonism.

     The act of copulation is thus a little bit like the Castle from Kafka's novel of the same name: viewed from up close, it is a heap of old dirty cottages, so one has to withdraw to a proper distance to see it in its fascinating presence.

707. #707

     Sex and the Failed Absolute · Slavoj Žižek

     **Sex and the Failed Absolute** > The World With(out) a <span id="scholium_34_the_world_without_a_snout.xhtml_IDX-138"></span><span id="scholium_34_the_world_without_a_snout.xhtml_IDX-2118"></span><span id="scholium_34_the_world_without_a_snout.xhtml_IDX-2519"></span>Snout > Notes

     Theoretical move: This endnotes passage is largely bibliographic, but note 7 makes a substantive theoretical move: it distinguishes the Klein bottle's twisted structure from classical structuralist-materialist ideology critique by arguing that the "machinery" behind the ideological spectacle is symbolic/virtual rather than material, so demystification cannot dissolve the effect.

     we also have to draw a clear distinction between this twisted structure of the Klein bottle and the old structuralist-materialist topic

708. #708

     Sex and the Failed Absolute · Slavoj Žižek

     **Sex and the Failed Absolute** > [Index](#contents.xhtml_end2)

     Theoretical move: This is a non-substantive index passage from Žižek's *Sex and the Failed Absolute*, listing alphabetical entries (I–L) with page cross-references; it carries no independent theoretical argument.

     Klein bottle [here](#introduction…), [here](#theorem_iii_the_three_unorientables…) cross-cap and [here](#theorem_iii_the_three_unorientables.xhtml_IDX-1117)

709. #709

     Sex and the Failed Absolute · Slavoj Žižek · p.430

     **Sex and the Failed Absolute** > Language, *Lalangue*

     Theoretical move: By mapping the Lacanian triad of language/*lalangue*/matheme onto the RSI (Real/Symbolic/Imaginary) structure and arguing through the topological figures of the Möbius strip and cross-cap, Žižek resists any materialist-genetic primacy of *lalangue* over language, insisting instead that the cut introducing differential symbolic order is originary and irreducible to bodily or pre-symbolic ground.

     the couple offers a perfect example of the redoubled Möbius strip that gives us the cross-cap … their relationship is again that convoluted 'coincidence of the opposites' that characterizes the Möbius strip

710. #710

     Sex and the Failed Absolute · Slavoj Žižek · p.264

     **Sex and the Failed Absolute** > The Three <span id="theorem_iii_the_three_unorientables.xhtml_IDX-862"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-1095"></span><span id="theorem_iii_the_three_unorientables.xhtml_IDX-2455"></span>Unorientables > [<span id="theorem_iii_the_three_unorientables.xhtml_p259" class="pagebreak" title="259"></span>A Snout in Plato’s Cave](#contents.xhtml_ahd18)

     Theoretical move: The Klein bottle's topology—specifically its "snout" as the subject's inscription in reality—is used to argue that the subject is not merely a fiction generated by objective neuronal processes (contra Metzinger) but the very convolution through which the Real observes itself; the Splitting of the Subject ($) and Objet petit a are shown to be two aspects of the same topological feature seen from inside and outside respectively.

     what Metzinger ignores is the additional convolution, the 'snout' which gives birth to the very observer … therein resides the lesson of the Klein bottle

711. #711

     Sex and the Failed Absolute · Slavoj Žižek · p.344

     **Sex and the Failed Absolute** > The Persistence of <span id="theorem_iv_the_persistence_of_abstraction.xhtml_IDX-17"></span>Abstraction > [Madness, Sex, War](#contents.xhtml_ahd22)

     Theoretical move: Žižek argues that "abstract negativity" (madness, sexuality, war) is not an accidental excess to be sublated but a constitutive, immanent remainder that persists at the heart of every ethical and ontological edifice; the Möbius-strip topology of this persistence means that the barbaric core sustaining civilization cannot be simply overcome by expanding rational order, and Hegel's own failure to follow through on this insight (in sexuality and in his conservative politics) reveals the limit of any synthesis from Substance to Subject.

     This is why a Möbius-strip reversal complicates today's urgent task of civilizing (the relationship between) civilizations themselves

712. #712

     Sex and the Failed Absolute · Slavoj Žižek · p.61

     **Sex and the Failed Absolute** > The <span id="theorem_i_the_parallax_of_ontology.xhtml_IDX-1608"></span>Parallax <span id="theorem_i_the_parallax_of_ontology.xhtml_IDX-1657"></span>of Ontology > [<span id="theorem_i_the_parallax_of_ontology.xhtml_p57" class="pagebreak" title="57"></span>The Margin of Radical Uncertainty](#contents.xhtml_ahd4)

     Theoretical move: The passage argues that radical materialism requires rejecting both "objective reality" and consistent subjectivity, identifying the Real not with nature-in-itself but with the crack/gap in every ontological edifice—a deficiency shared by transcendental reason and reality itself—which Freud/Lacan name 'sexuality,' and whose trans-ontological elaboration requires a concept of 'less than nothing' formalized through the Klein bottle as the minimal definition of the Absolute.

     In more concrete topological terms, only such an agency can account for the reflexive 'snout' of the Klein bottle by means of which reality can relate to itself.

713. #713

     Sex and the Failed Absolute · Slavoj Žižek · p.2

     **Sex and the Failed Absolute** > The <span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-2453"></span>Unorientable Space of <span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-498"></span><span id="introduction_the_unorientable_space_of_dialectical_mater.xhtml_IDX-1339"></span>Dialectical Materialism

     Theoretical move: Žižek proposes "dialectical materialism of a failed ontology" (DM2) against Stalinist DM1, arguing that the theoretical space of dialectical materialism is topologically "unorientable" — structured like a Möbius strip or cross-cap — because antagonism is not the struggle of external opposites but the constitutive self-contradiction of an entity with itself, a minimal reflexivity (gap, mediation, failure) that cuts through every immediate unity, including sexuality.

     In mathematics, the convoluted structure implied by such reflexivity is called unorientable: an unorientable surface is a surface (the Möbius strip and its derivations, the cross-cap and Klein bottle) on which there exists a closed path such that the directrix is reversed when moved around this path.

714. #714

     Sex and the Failed Absolute · Slavoj Žižek · p.329

     **Sex and the Failed Absolute** > The World With(out) a <span id="scholium_34_the_world_without_a_snout.xhtml_IDX-138"></span><span id="scholium_34_the_world_without_a_snout.xhtml_IDX-2118"></span><span id="scholium_34_the_world_without_a_snout.xhtml_IDX-2519"></span>Snout

     Theoretical move: The passage argues that the Lacanian Real harbours a constitutive self-blockage that generates appearing from within, against Badiou's presupposition of appearing as given and his masculine-exceptional logic of Truth-Event; the Death Drive and the feminine Not-all formula are mobilised to articulate this as the properly Lacanian (and Hegelian) alternative to Badiou's ontology.

     A kind of push, which is essentially topological, makes it that the multiple is not satisfied by being what it is since, as appearing, it is there that it has to be what it is.

715. #715

     Sex and the Failed Absolute · Slavoj Žižek · p.18

     **Sex and the Failed Absolute** > The <span id="theorem_i_the_parallax_of_ontology.xhtml_IDX-1608"></span>Parallax <span id="theorem_i_the_parallax_of_ontology.xhtml_IDX-1657"></span>of Ontology > [<span id="theorem_i_the_parallax_of_ontology.xhtml_p18" class="pagebreak" title="18"></span>Modalities of the Absolute](#contents.xhtml_ahd1)

     Theoretical move: Žižek argues that Absolute Knowing is not a revelation of hidden content but a "redoubling of the gap"—the gap separating subject from the Thing is transposed into the Thing itself—and defends this move against Pippin's critique by insisting that unity (the One) is a retroactive effect of division rather than its presupposition, a structure he calls "absolute recoil," which he then differentiates from Meillassoux's speculative-materialist ontologization of contingency.

     just a purely topological transposition of the gap that separates me from the Thing into the Thing itself … in the figure of the Klein bottle, this redoubling is located in the 'snout' through which the bottle reflexively turns back into itself

716. #716

     Sex and the Failed Absolute · Slavoj Žižek · p.139

     **Sex and the Failed Absolute** > Sex as Our Brush with the Absolute > [The Sexed Subject](#contents.xhtml_ahd9)

     Theoretical move: The passage argues that subjectivity is constitutively sexed by mapping the Kantian mathematical/dynamic antinomy onto Hegel's logic of Being/Essence, and then showing that each domain, when carried to its limit (via differential calculus as the paradigm case), self-sublates into a void that constitutes a distinct sexed subject: "feminine" subjectivity emerges from the self-sublation of the mathematical/Being domain, while "masculine" subjectivity emerges from the dynamic/Essence domain.

     when we calculate the slope of the straight line that is tangential to the curve at a given point, we effectively calculate the slope (spatial direction) of a given point of the curve, the spatial direction of something whose spatial length is reduced to the infinitely small, to zero.

717. #717

     Sex and the Failed Absolute · Slavoj Žižek · p.154

     **Sex and the Failed Absolute** > Sex as Our Brush with the Absolute > [Plants, Animals, Humans, Posthumans](#contents.xhtml_ahd10)

     Theoretical move: The passage argues that human sexuality is not a "civilized" displacement of natural animal sexuality but rather the point where the dislocation/impossibility immanent in all sexed reproduction becomes registered as such—via the Unconscious and surplus-jouissance—so that culture retroactively denaturalizes nature itself, while the transition from animal to human mirrors the Hegelian move from In-itself to For-itself applied to not-knowing.

     Two are never Two but the One and its void which is filled in by an inconsistent multiplicity. 'Two' (in the sense of a complementary couple of opposites) is a dream of sexual relationship.

718. #718

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.164

     Alenka Zupancˇ icˇ

     Theoretical move: Zupančič argues that while Deleuze and Lacan share a tripartite topology grounded in an originary negativity (crack/hole/Real) around which the drives congregate, Deleuze ultimately "liquefies" this topological rift into a pure dynamic movement of Difference, thereby obliterating the Lacanian Real as a third term irreducible to both the signifying chain and surplus-enjoyment.

     This shift from topological to dynamic tropes is indeed crucial for Deleuze: the topological noncoincidence of being and appearing, their rift, is 'liquefied' into Being as a pure movement of Difference.

719. #719

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.225

     Becoming and the Challenge of Ontological Incompleteness: Virginia Woolf *avec* Lacan *contra* Deleuze

     Theoretical move: The passage argues that Woolf's novels stage a Hegelo-Lacanian ontology in which subjectivity is constituted by irreducible negativity and the interruptive structure of memory, contra Deleuze's notion of Becoming as anti-memory; Clarissa's "flowers of darkness" and Septimus's dissolution together demonstrate that the evacuation of subjective lack (the Deleuzean line of flight) leads not to liberation but to the dead end of pure drive, stripping the subject of the productive reflexivity that iterability and temporal disparity make possible.

     a vertical ontology in which she can hesitate on the threshold of the empty room at the heart of life

720. #720

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.22

     Russell Sbriglia and Slavoj Žižek

     Theoretical move: The subject is not a substance but a nonsubstantial, purely relational entity—the very wound/cut in the Real it attempts to heal—and any materialism or realism that posits a "democracy of objects" without accounting for this void at the core of subjectivity already relies on an unexamined transcendental constitution of reality; only a dialectical materialism that takes the subject as nothing but its own relationality and division can avoid this obfuscation.

     the subject is not just split like every other object between its phenomenal qualities (actualizations) and its inaccessible, virtual In-itself; the subject is divided between its appearance and the void at the core of its being

721. #721

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.276

     Index > **INDEX**

     Theoretical move: This is a book index (pages 276–277) listing terms and proper names with page references; it contains no substantive theoretical argument of its own.

     topology, 153, 156–57, 200–206, 208n31. See also Möbius typology

722. #722

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.229

     Becoming and the Challenge of Ontological Incompleteness: Virginia Woolf *avec* Lacan *contra* Deleuze

     Theoretical move: Against Deleuze's affirmative ontology of Becoming as positive flux without lack, the passage argues—through a Hegelo-Lacanian reading of Woolf's *Mrs Dalloway*—that subjectivity is constituted by an irreducible structural lack, and that this very lack (figured as absence, the void, *das Ding*, *objet a*) is what generates multiplicity, desire, and the intensity of lived experience rather than cancelling them.

     Note the chiasmic structure of this revelation, in which absence (death) is bookended by the discourse markers of thought ('thought Clarissa,' 'she thought'), again intimating the metaphysical structure of subjectivity as the edge(s) of absence.

723. #723

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.213

     The Search for a Möbius Topology and Extimate Causality

     Theoretical move: The passage argues that Object-Oriented Ontology (OOO) unwittingly presupposes the very Lacanian framework it tries to circumvent: the "object-in-itself" it posits is nothing other than the Real of the cut (objet petit a), which functions simultaneously as object-cause and void of desire, thereby demonstrating that a dialectical materialist account of objet a—with its Möbius topology and extimate causality—supersedes OOO's subject-less ontology.

     Both object and subject in the Lacanian framework have the same Möbius topology—both are self-inconsistent and both are coextensive with the cut.

724. #724

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.209

     The Search for a Möbius Topology and Extimate Causality

     Theoretical move: By theorizing "extimate causality" through Lacanian non-orientable topology (Möbius), the passage argues that both subject and objet a emerge from the same formal negation—a cut that is simultaneously internal and external—thereby dissolving the OOO impasse between relational dissolution and objectal isolation, and showing that self-inconsistency (non-self-coincidence) is the ontological condition of identity itself.

     When Jacques Lacan needed to devise a new kind of object and a new kind of causation to account for subjectivization, he drew from these non-orientable objects.

725. #725

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.19

     Russell Sbriglia and Slavoj Žižek

     Theoretical move: Against new materialisms and realist ontologies, the passage argues for a Lacano-Hegelian dialectical materialism in which the subject—understood as the void of absolute negativity and identified with the Lacanian objet petit a—is not one object among others but constitutes the very hole in reality, such that "the hole in reality is the subject," and material reality is properly characterized as "non-all" rather than a fully constituted whole.

     the objet petit a is a strange object which is not only lacking, never fully here… an 'impossible' object… whose status is that of an anamorphosis, a distorted projection.

726. #726

     Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.215

     The Search for a Möbius Topology and Extimate Causality > Notes

     Theoretical move: This passage is a notes/bibliography section for a chapter on Möbius topology and extimate causality; it is non-substantive in itself, but several footnotes perform brief theoretical moves—notably connecting extimacy to the empty set, non-orientable topology, and the critique of Object-Oriented Ontology.

     anteriority does not remain extrinsic to substance, but is incorporated within it, suggesting a topological asymmetry between container and contained

727. #727

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.64

     <span id="page-53-0"></span>**The Lacanian Subject** > **Lacan's Split Subject**

     Theoretical move: The Lacanian subject is nothing but the split itself — a radical separation between ego (false being) and unconscious (the Other's discourse) produced by alienation in language; this split, which exceeds purely linguistic/structural explanation, serves as the foundational diagnostic divide between neurosis and psychosis.

     The splitting of the I into ego (false self) and unconscious brings into being a surface, in a sense, with two sides: one that is exposed and one that is hidden.

728. #728

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.184

     <span id="page-156-0"></span>Psychoanalysis and Science > **Network Mappings** > <span id="page-182-0"></span>TABLE Al.S

     Theoretical move: This passage is a technical appendix table presenting the combinatory network mappings used to construct Lacan's graph of desire, showing how numeric triplets recoded as binary (odds/evens) yield eight points that, when linked, produce the Network Lacan deploys — a structure Miller identifies as closely related to the graph of desire in the Écrits.

     while there are a whole variety of ways of drawing this sort of "Network," Lacan's is one of the most elegant.

729. #729

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.162

     <span id="page-156-0"></span>Psychoanalysis and Science > **The Three Registers and Differently "Polarized" Discourses**

     Theoretical move: Lacan's late discourse theory in Seminar XXI reorganizes discourses not by agent/position (as in the four discourses) but by the sequential *order* in which the three registers (RSI/IRS/etc.) are traversed, and this allows Fink to argue that psychoanalysis—as an IRS discourse that "imagines the real of the symbolic"—is a praxis unifying theory and clinical practice, sharing this orientation with mathematics and potentially the best of science.

     Lacan adopts the term 'right polarization' *(dextrogyre)* for clockwise directions and 'left polarization' for counterclockwise directions *(levogyre),* terms used to describe the 'orientation' of knots

730. #730

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.224

     <span id="page-191-0"></span>*Glossary of Lacanian Symbols* \_\_\_\_\_\_\_ \_ > **Appendix 2 Stalking the** Cause

     Theoretical move: The passage argues that the subject's being is entirely dependent on the marks (letters/quotes) that constitute it—the subject has no being other than as mark or as being-set-off—connecting the typographical device of quotation marks to Lacan's claim that the subject is never more than supposed, and that its being is bound to the registers of speech and writing.

     the object here is contained within the subject, at least within one of his or her folds or linings

731. #731

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.164

     <span id="page-156-0"></span>Psychoanalysis and Science > **Formalization and the Transmissibility of Psychoanalysis**

     Theoretical move: Lacan's mathemes are theorized as a non-quantitative, qualitative mode of formalization whose value lies not in guaranteeing perfect communication but in the transmissibility of the written trace itself across time and interpreters; the "pass" is offered as an allied institutional mechanism for establishing a scientificity peculiar to psychoanalysis.

     Like the figures discussed at the end of chapter 8, whose dimensions can be varied indefinitely without ever changing their fundamental topological properties, the relations written or ciphered using Lacan's algebra are qualitative, structural relations.

732. #732

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.103

     <span id="page-101-0"></span>Object (a): Cause of Desire

     Theoretical move: Fink establishes Objet petit a as Lacan's most significant and polyvalent contribution to psychoanalysis, cataloguing its many avatars and situating it across the registers of the imaginary, symbolic, and real as a prerequisite for systematic exposition in the chapter ahead.

     many of his elaborations involve algebraic, topological, and logical formulations that would require extensive commentary

733. #733

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.143

     THE PHALLUS: ONE OF W~ S PARTNERS > <span id="page-141-0"></span>**A New Metaphor for Sexual Difference**

     Theoretical move: Lacan's account of sexual difference introduces a genuinely new topological metaphor—grounded in the cross-cap and set-theoretic distinctions between open and closed sets—that replaces the classical Western model of concentric spheres and recasts masculine/feminine structure as closed/open sets respectively; this is further characterised as a "Gödelian structuralism" that systematically points to incompleteness and undecidability within any formal system.

     it involves a new topology: it breaks with the age-old Western conception of the world as a series of concentric circles or spheres, and instead takes as its model such paradoxical topological surfaces as the Mobius band, the Klein bottle, and the cross-cap.

734. #734

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.181

     <span id="page-156-0"></span>Psychoanalysis and Science > **Network Mappings**

     Theoretical move: The passage performs a detailed technical reconstruction of Lacan's 1-3 Network and its transformation into the α, β, γ, δ Network, showing how successive recodings of binary combinatories (same/different, odd/even, symmetrical/asymmetrical) generate higher-order graphs, and identifying that mirror-image structures in these networks instantiate the logic of the mirror stage.

     Lacan seems to have been led to the final form of this complex network by first putting the eight possible 1/0 triplets on the corners of a cube (or parallelepiped).

735. #735

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.188

     <span id="page-156-0"></span>Psychoanalysis and Science > <span id="page-183-0"></span>Stalking the Cause

     Theoretical move: By retranscribing Schema L as Chain L using a parenthetical/binary formalism, Fink shows how object a emerges as a structural remainder—the *caput mortuum* of the signifying chain—thereby demonstiting that object a's causal function with respect to desire is inscribed in the very topology of the symbolic chain rather than being a supplementary concept added from outside.

     the 10 and 01 pairs in the right- and left-hand 'lining' concern the privileged status—which Lacan claims to have more adequately explained in his later topological investigations—of a and a' themselves.

736. #736

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.205

     <span id="page-191-0"></span>*Glossary of Lacanian Symbols* \_\_\_\_\_\_\_ \_ > The Subject and the Other's Desire

     Theoretical move: This footnote apparatus elaborates key theoretical moves from the main text: the neurotic's fantasy structure as ($◇D) rather than ($◇a) - conflating the Other's demand with the Other's desire - and the topology of the subject/Other relation, while clarifying that separation involves replacing demand with objet a in the neurotic's fantasy.

     If we think of the Other as a simple strip (of paper, for example) whose two ends are attached directly, we can think of the subject as the Other with a twist (figure 5.9).

737. #737

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.212

     <span id="page-191-0"></span>*Glossary of Lacanian Symbols* \_\_\_\_\_\_\_ \_ > There's No Such Thing as a Sexual Relationship

     Theoretical move: This endnote apparatus consolidates and defends Fink's interpretive positions on Lacan's formulas of sexuation, the non-existence of the sexual relationship, the structure of the signifier, and the Other jouissance—correcting common misreadings while flagging key conceptual distinctions (existence vs. ex-sistence, the bar of negation, the role of the phallus, S1/S2, and object a).

     Consider also the functioning of certain puzzles made up of little squares with letters, numbers, or images on them, with one square missing, allowing the player to reposition all of the others

738. #738

     The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.233

     <span id="page-231-0"></span>**Index**

     Theoretical move: This is the index of Bruce Fink's *The Lacanian Subject*, listing key concepts, proper names, and page references — a non-substantive navigational apparatus with no original theoretical argumentation.

     Cross-cap, 123 … Borromean knot, 123

739. #739

     The Odd One In: On Comedy (alt. ed.) · Alenka Zupančič · p.66

     Physics of the Infinite against Metaphysics of the Finite

     Theoretical move: Against the contemporary "metaphysics of finitude" that makes finitude a Master-Signifier closing off the infinite, Zupančič argues that comedy enacts a "physics of the infinite" grounded in the Lacanian insight that human finitude is always-already a *failed finitude* — a finitude with a constitutive hole — whose materiality is objet petit a, and whose topology is best captured by the Möbius strip as the figure of immanent transcendence.

     The paradox embodied by the topology of the Möbius strip thus consists in there being only one surface (in this sense we are dealing with immanence), yet at every point there is also the other side.

740. #740

     The Odd One In: On Comedy (alt. ed.) · Alenka Zupančič · p.28

     part i

     Theoretical move: Zupančič uses Hegel's treatment of comedy in the *Phenomenology* as a lens to argue that genuine subjective change requires not merely the subject's self-knowledge but a corresponding shift in the external Symbolic (the "Other"), and that this double movement—where lack in the subject must coincide with lack in the Other—is shared by both Hegel and Lacan, with transference as its analytic condition.

     what is needed is the encounter of the two entities at a very precise (or precisely right) point of their topology.

741. #741

     The Odd One In: On Comedy (alt. ed.) · Alenka Zupančič · p.226

     Wozu Phallus in dürftiger Zeit? > Concluding Remarks

     Theoretical move: Comedy is theorized as the genre of the copula—the site where the missing link between life and the signifier is made to appear—and the phallus is identified as the privileged signifier of this copula, one that appears in comedy not as signifier but as partial object, materializing the contradictions of the Symbolic. The 'realism' of comedy is then relocated from the reality principle to the Real of desire/drive as an irreducible incongruence within human existence.

     what the topology of the Möbius strip reveals is that the missing link that structures our reality is not a missing link between two neighbor elements, the connection between which would thus be interrupted—instead, its very missing is the linkage between two neighbor elements

742. #742

     The Odd One In: On Comedy (alt. ed.) · Alenka Zupančič · p.143

     Structural Dynamics and Temporality of the Comical

     Theoretical move: Zupančič argues that tragedy and comedy are not different attitudes toward the same configuration of discrepancy but rather two standpoints *within* it: tragedy stands at the point of demand (articulating discrepancy as desire's constitutive non-satisfaction), while comedy stands at the point of satisfaction (articulating discrepancy as jouissance/surplus-satisfaction), and this difference in standpoint entails a reversal of temporal sequence in which satisfaction precedes and overtakes demand rather than trailing after it.

     The discrepancy at stake could also be formulated in topological instead of temporal terms: the satisfaction is produced somewhere else than where we expect it or await it.

743. #743

     The Parallax View · Slavoj Žižek · p.216

     Copernicus, Darwin, Freud . . . and Many Others > A Cognitivist Hegel?

     Theoretical move: The passage argues that the Lacanian objet petit a is formally homologous to the neural "attractor" — an insubstantial quasi-object generated by the very process that reacts to it — and that the subject/object distinction is purely topological (two sides of a Möbius strip), not ontological, thereby grounding a cognitivist-Hegelian account of self-consciousness as self-relating.

     it is crucial to bear in mind that this difference is purely topological: 'subject' and 'object' are not two entities which interact at the same level

744. #744

     The Parallax View · Slavoj Žižek · p.85

     The Birth of (Hegelian) Concrete Universality out of the Spirit of (Kantian) Antinomies > Kierkegaard as a Hegelian > Die Versagung

     Theoretical move: Žižek uses Lacan's reading of Claudel's *The Hostage* and James's *The Portrait of a Lady* to argue that the feminine "No" (Versagung) is not a signifying negation grounded in the paternal "No," but a bodily, excremental gesture of pure loss that enacts separation from the Symbolic—prefiguring the sinthome—and that this "No as such" (form without content) is the hidden materialist core linking Kierkegaard's infinite resignation to Hegelian speculative identity.

     The two 'No's are thus like the same X on the two opposed sides of a Moebius strip: if the paternal 'No' is the pure form, an empty place without content, Sygne's 'No' is an excessive element that lacks its 'proper' place.

745. #745

     The Real Gaze: Film Theory After Lacan · Todd McGowan · p.193

     **The Overlapping Worlds of Andrei Tarkovsky**

     Theoretical move: The passage argues that Tarkovsky's "cinema of intersection" achieves its distinctive effect by dramatically separating the worlds of desire and fantasy only to reveal their fundamental identity—that the objet petit a remains constant across both registers—thereby exposing the traumatic proximity of the gaze and dissolving the illusion of difference that sustains ordinary desiring subjectivity. This move is theorized as simultaneously Hegelian (identity-in-difference) and Lacanian (the drive's monotony beneath desire's metonymy).

     This emphasis on the constancy of the object locates Tarkovsky within the cinema of intersection and within Hegelian ontology.

746. #746

     The Shortest Shadow: Nietzsche's Philosophy of the Two · Alenka Zupančič · p.101

     <span id="page-33-0"></span>part i

     Theoretical move: Zupančič identifies two distinct Nietzschean conceptions of truth: one that identifies truth with the Real (as inaccessible, dangerous force requiring dynamical 'dilution'), and another grounded in perspectivity (a structural/topological disjunction where truth is internal to its situation) — arguing that conflating or choosing between them misreads both the passion for the Real at work in each and the specific way nuance functions in each configuration.

     The other line of conceptualization of truth (and of the Real) to be detected in Nietzsche's work implies a rather different configuration. Here, the disjunction of being and truth is not dynamical, but structural or topological.

747. #747

     The Shortest Shadow: Nietzsche's Philosophy of the Two · Alenka Zupančič · p.23

     The Shortest Shadow

     Theoretical move: Zupančič argues that the Nietzschean event has the structure of a "time loop" in which the subject who declares the event is constituted retroactively by it—the event is immanent to its own declaration—and that this constitutive splitting ("One became Two") is not a synthesis or mystical transformation but the minimal, topological difference (the "edge") that names the nonrelationship between two incommensurable terms, a logic Zupančič explicitly aligns with Lacan's formula of the sexual non-rapport.

     This specific redoubling (as the co-positing of a two in the topology of the minimal difference), which is the very name of the event.

748. #748

     The Shortest Shadow: Nietzsche's Philosophy of the Two · Alenka Zupančič · p.17

     The Shortest Shadow

     Theoretical move: The passage argues that the Nietzschean "declaration" is not caught in a lack of the Real but constitutes a specific duality in which declaration and event are co-immanent—the Real is not external to speech but structurally redoubled within it—and that this logic of the "Two" (rather than multiplicity) governs both Nietzsche's theory of the event and the temporal structure of truth and subjectivity.

     It is perhaps best articulated in the topology of the edge as the thing whose sole substantiality consists in its simultaneously separating and linking two surfaces.

749. #749

     The Shortest Shadow: Nietzsche's Philosophy of the Two · Alenka Zupančič · p.158

     <span id="page-33-0"></span>part i

     Theoretical move: By reading the Zeno paradox of Achilles and the tortoise through Lacan's sexuation, Zupančič argues that masculine and feminine positions represent two structurally different relations to the Other and to Nothingness—metonymic pursuit versus immanent internal split—and then extends this to Nietzsche's "beyond good and evil," showing that Nothingness is not a transcendent void beyond the good/evil pair but its inner organizing structure, thereby redefining nihilism as capture between good and evil rather than their surpassing.

     the fact that, for Nietzsche, good and evil do not simply form a complementary couple, but are topologically dislocated and positioned in relation to a third term

750. #750

     The Shortest Shadow: Nietzsche's Philosophy of the Two · Alenka Zupančič · p.175

     <span id="page-33-0"></span>part i

     Theoretical move: The passage argues that the comic paradigm—unlike the tragic/sublime—constitutes the proper structural analogue of love: both work through a "parallel montage" of two semblances whose non-coincidence produces the Real as a gap-become-object, rather than incorporating the Real as an inaccessible Thing circled by sublime friction. Love's miracle is preserving transcendence within accessibility, not sublimating the banal into the inaccessible.

     It is as though one were to spread the extreme edge of a body, the skin, so that it becomes the scene for the encounter of two things that it usually separates, the exterior and the interior of the body.

751. #751

     The Shortest Shadow: Nietzsche's Philosophy of the Two · Alenka Zupančič · p.121

     <span id="page-33-0"></span>part i

     Theoretical move: Zupančič argues that truth-as-perspective (in Nietzsche) and analytic discourse (in Lacan) share a structurally homologous status: both are constituted not by a new stable position but by the irreducible gap or decentering produced in the *shift* between perspectives/discourses, figured as a "Two" of pure disjunction rather than either the One or the multiple.

     the two theatrical realities…are not exactly in a relationship of concentric circles: of the narrower and the broader, or the interior and the exterior, circle.

752. #752

     Theory Keywords · Various · p.8

     **Conscious**

     Theoretical move: The passage theorizes consciousness not as a privileged site of psychical truth but as a topographic layer embedded within a multi-system censorship apparatus (Freud), and then as a structural barrier to the Real and an ideological modality of mastery (McGowan) — arguing that submission to the unconscious logic of film/dream is the condition of possibility for an encounter with the gaze.

     now in addition it seems to take account of psychical topography as well, and to indicate in respect of any given mental act within what system or between what systems it takes place

753. #753

     Theory Keywords · Various · p.89

     **Transference** > **Unconscious**

     Theoretical move: The passage advances a multi-pronged account of the Lacanian unconscious: it is structured like a language (via the metaphor/metonymy–condensation/displacement homology), it is spatial and relational (between subject and Other), it operates independently of meaning/signification, and its logic can be extended to critique ideological systems like capitalism where surface avowals conceal the real engine (loss/sacrifice) driving the system.

     the spatialization of the unconscious becomes important for Lacan...if the same idea can be in two places at once.

754. #754

     Žižek Responds! · Todd McGowan & Dominik Finkelde (eds.)

     Žižek Responds! > [Response to Bou Ali](#contents.xhtml_ch9a)

     Theoretical move: Žižek argues that sublimation, repression, and jouissance are structurally inseparable—desublimation is always already repressive, primordial repression constitutes rather than suppresses its content, and castration and the death drive are two faces of the same parallax structure rather than opposing forces—thereby refuting any emancipatory vision premised on overcoming repression or positing a new Master Signifier as sufficient.

     one and the same entity inscribed onto the two surfaces of a Möbius strip.

755. #755

     Žižek Responds! · Todd McGowan & Dominik Finkelde (eds.)

     Žižek Responds! > [Introduction](#contents.xhtml_ch01) > Universally Antagonistic

     Theoretical move: Žižek's political project is grounded in a reconceptualization of universality as constitutive antagonism rather than totalizing wholeness: particulars, identities, and social structures emerge from and are sustained by a universal antagonism that can never be resolved, making emancipation consist not in overcoming antagonism but in insisting on it—a position figured topologically through the Möbius strip and the objet a as the excremental singular point that embodies the universal.

     The topology of the Moebius strip, which Lacan highlights, shows how a dialectical contradiction works.

756. #756

     Žižek Responds! · Todd McGowan & Dominik Finkelde (eds.) · p.53

     Žižek Responds! > [Response to Johnston](#contents.xhtml_ch1a)

     Theoretical move: Žižek defends the "doughnut" (Möbius-band) model of dialectical structure against Johnston's "layer-cake" model, arguing that the process of rational mediation must return to a contingent piece of the Real (le peu du réel) and that a primordial parallax gap—not a pure flux—is inscribed at the very bottom of ontology, rendering reductionism and simple gradualism both inadequate.

     my model is that of a doughnut, a twisted space that resembles the structure of the Moebius band

757. #757

     Žižek Responds! · Todd McGowan & Dominik Finkelde (eds.) · p.216

     Žižek Responds! > [On Žižek’s Theory of the Subject](#contents.xhtml_ch9)

     Theoretical move: Bou Ali reconstructs Žižek's theory of the subject as a non-ontological point of negativity that is extimate to symbolic structure, correlative to the objet a as object-cause of desire, and grounded in the retroactive (Nachträglichkeit) constitution of the Real as cause—arguing further that this account of subjectivity is inseparable from Lacanian sexuation, read against both Hegelian dialectics and Kantian antinomies.

     Žižek proposes to do this by reading Hegel through Lacan … through a topological account that can represent the extimate status of the subject to structure.

758. #758

     What Is Sex? · Alenka Zupančič · p.114

     Object-Disoriented Ontology > <span id="page-102-0"></span>Death Drive I: Freud

     Theoretical move: Zupančič argues that the death drive involves two distinct splits—the genesis of surplus satisfaction from organic need, and a constitutive negativity (inbuilt lack of being) around which the drive circulates—and that satisfaction/enjoyment is not the goal but the *means* of the drive, whose true aim is the repetition of negativity; this reframes the death drive not as a return to the inanimate but as the opening of alternative paths to death beyond those immanent in the organism.

     sexuality proper involves a further step in which the 'minus,' the negativity involved in sexuation and sexual reproduction, gets a positive existence in partial objects as involved in the topology of the drive.

759. #759

     What Is Sex? · Alenka Zupančič · p.73

     Contradictions that Matter > Hm…

     Theoretical move: Zupančič argues that the apparent opposition between equivocity (Cassin) and formalization/univocity (Badiou) in Lacan is false: equivocity is not the opposite of formalization but its very condition, since the "right word" in analytic interpretation functions like a formula by targeting the singular impasse/contradiction that the symptom "solves," rather than by conveying a determinate meaning.

     we are in the domain of formalization, formulas, mathemes, knots, and other topological models

760. #760

     What Is Sex? · Alenka Zupančič · p.80

     Contradictions that Matter > Hm…

     Theoretical move: Zupančič argues that Lacanian formalization is not a truth *about* the Real but the formalization of the impasse of formalization itself—the point where speech "holds onto" the Real through its own impossibility—and that the proper psychoanalytic position is not passive acceptance of contradiction but active engagement with it, taking one's place within it as the condition of emancipation.

     Lacan, in his last seminars, almost stopped talking—instead he would make some of his famous knots… Lacan relied on topology as a means of destroying language.

761. #761

     What Is Sex? · Alenka Zupančič · p.124

     Object-Disoriented Ontology > Death Drive II: Lacan and Deleuze

     Theoretical move: Zupančič argues that Lacan and Deleuze share a common theoretical move: rejecting the pleasure principle as primary and affirming the primacy of the death drive, which they reconceptualise not as a tendency toward destruction but as the transcendental/ontological condition of repetition itself—a faceless negativity or "crack" that is irreducible to either life or death, and which constitutes rather than follows from the surplus excess and repression it generates.

     the crack conversely pursues its course, spreads out its web, changes direction and is actualized in each body in relation to the instincts which open a way for it…The two orders are tightly joined together, like a ring within a larger ring, but they are never confused.

762. #762

     What Is Sex? · Alenka Zupančič · p.102

     Object-Disoriented Ontology > Human, Animal

     Theoretical move: Zupančič argues that jouissance/the drive is neither simply animal instinct nor the marker of human exception, but rather the point at which nature's own inherent impossibility gets articulated as such — making the human being not an exception to the animal but the 'question mark' to the very consistency of the Animal, and by extension the point at which the incomplete ontological constitution of reality becomes visible.

     The topology of the drive can in fact be understood in two ways. It could be understood as positing that with humans the deviation from organic need (piloting the Animal) is original…Yet there is also another possible reading.

763. #763

     What Is Sex? · Alenka Zupančič · p.58

     Contradictions that Matter > Sexual Division, a Problem in Ontology

     Theoretical move: Zupančič argues, via a close reading of Freud and Lacan, that sexual difference does not arise from the existence of two sexes but from the non-existence of the "second sex"—a constitutive ontological deficit—and traces Lacan's shift from locating "pure loss" on the side of the body (early work) to locating it within the signifying order itself (late work), showing that surplus-enjoyment emerges at the place of a missing signifier ("with-without"), which is also the origin of sexual division.

     This topological addition (in respect to Freud) is what makes the Freudian observations quite compatible with Lacan's late work.

764. #764

     What Is Sex? · Alenka Zupančič · p.38

     <span id="page-29-0"></span>… and Even Stranger out There > The Anti-Sexus

     Theoretical move: The passage argues that the antagonism between signifier and enjoyment, and between the Other and jouissance, arises not from heterogeneous origins but from their co-origination in the same locus; the Other and enjoyment are 'extimately' related such that any attempt to purify one of the other rediscovers what was expelled at the very heart of the purified term, producing a structural twist rather than a symmetrical relation.

     this is what twists what may look like a symmetry (or relation) in a way that resembles some of Escher's drawings of impossible objects

765. #765

     What Is Sex? · Alenka Zupančič · p.71

     Contradictions that Matter > Sexual Division, a Problem in Ontology

     Theoretical move: Sexual difference is not merely one example of signifying differentiation but rather the ontological presupposition of the signifier's functioning: the constitutive gap and surplus-enjoyment that prevents the signifying field from being a closed, consistent structure are the very ground on which sexuation is configured, making the subject of the unconscious irreducibly sexed.

     Minus one/plus enjoyment—this is the necessarily distorted structural topology where the subject of the unconscious dwells.

766. #766

     What Is Sex? · Alenka Zupančič · p.127

     Object-Disoriented Ontology > Death Drive II: Lacan and Deleuze

     Theoretical move: Zupančič argues that Lacan and Deleuze converge in treating the death drive as a foundational "crack" around which drives congregate, but diverge crucially: where Deleuze collapses the tripartite topology (original negativity / surplus-enjoyment / signifiers) into a single dynamic movement of pure Difference, Lacan preserves the Real as an irreducible third term whose effect is the subject itself — making subjectivation the very index of an irreducible Real rather than an obstacle to realism.

     This shift from topological to dynamic tropes is indeed crucial for Deleuze: the topological non-coincidence of being and appearing, their rift, is 'liquefied' into Being as a pure movement of Difference.

767. #767

     What Is Sex? · Alenka Zupančič · p.72

     Contradictions that Matter > Sexual Division, a Problem in Ontology > Je te m'athème … moi non plus

     Theoretical move: The Badiou-Cassin polemic over sophistry is mobilized as a philosophical performance of the Lacanian claim that there is no sexual relation: their respective stances (truth-oriented philosophy vs. language-immersed sophistry) are themselves staged as an enactment of the masculine/feminine divide in Lacan's formulas of sexuation.

     formal rigorism (formulas, mathemes, topology)