Canonical lacan 210 occurrences

Matheme

ELI5

A matheme is like a very precise shorthand symbol (such as $ or $◇a) that Lacan invents so that the most important psychoanalytic ideas can be written down and passed on exactly, without getting distorted by the shifting meanings of ordinary words.

Definition

The matheme (from Greek mathema, knowledge transmissible) is Lacan's term for the set of algebraic, logical, and topological notations he develops to formalize the central structures of psychoanalytic theory. Paradigmatic mathemes include: the barred subject ($), the fantasy formula ($◇a), the drive formula ($◇D), the four discourses (S1→S2 / $/a), the formulas of sexuation (∀x.Φx / ∃x.¬Φx, etc.), the Name-of-the-Father and barred Other S(Ø), and the lozenge (◇) as a relational operator. Their defining characteristic, stated most directly in Seminar XX, is integral transmissibility: "Mathematical formalization is our goal, our ideal. Why? Because it alone is matheme, in other words, it alone is capable of being integrally transmitted." A matheme does not require the receiver to understand it in order to be passed on; it can be "buried in the sand, dug up again millennia later" and read as a signifier addressing another signifier (Fink, The Lacanian Subject, 164).

The matheme's function is simultaneously epistemological and structural. Epistemologically, it escapes the imaginary register of meaning: by replacing words with letters, the algebraic notation tracks an identity (of, say, objet a) "like a golden thread" across the entire body of Lacanian theory, regardless of the different imaginary faces the object assumes (Seminar XIII, p. 59). Structurally, each matheme encodes a topology of relations — between barred subject, Other, and remainder — that cannot be fully said but can be written. S(Ø) is Lacan's canonical example: "The word cannot express S(Ø) for example" (Seminar XVIII, p. 81). The matheme therefore marks the limit where formalization touches the Real rather than representing it: Zupančič reformulates this as "a matheme is not simply a formalization of some reality; rather — it is the formalization of the impasse of formalization" (What is Sex?, p. 78).

Evolution

In the early-to-mid 1950s, Lacan's project was to demonstrate that the unconscious is structured like a language; formalization at this stage was borrowed from Saussurean and post-Saussurean structuralism. The formula S/S' → S/s for metaphor (Seminar V) or the graph of desire's notation are early instances. The term "matheme" as such does not yet appear, but Lacan already argues, in "The Freudian Thing" and "Psychoanalysis and Its Teaching," that an algebraic formula can simultaneously communicate psychoanalytic content and demonstrate how it is formed — "just as a physicist might use the language of physics, an algebraic formula, both to communicate the content of his teaching and to illustrate the way in which it is formulated" (Hook et al., Reading Lacan's Écrits). The ground for the matheme is being laid.

In Seminars X–XVI (roughly 1962–1969, the "object-a period"), Lacan formalizes the key structural nodes: the fantasy formula $◇a (Seminar XI, 224), the drive $◇D (Seminar X, 74), and the algebraic letter a as a "thread… to enable us to recognize the identity of the object behind the various incidences in which it appears" (Seminar X, 95). He defends the lozenge as an "algorithm" whose artifice is necessary precisely because "there is no topology that does not have to be supported by some artifice" (Seminar XI, 224). The matheme is also connected to the Cartesian moment: "we will be able to begin playing with the small algebraic letters that transform geometry into analysis, that the door is open to set theory" (Seminar XI, 51), locating the historical condition of mathematical formalization in Descartes' handing of truth to the Other.

In Seminars XVII–XX (1969–1973, the "discourses / encore" period), the explicit term "matheme" crystallizes. Lacan defines it in Seminar XIX as "the pivotal point of any teaching… the only teaching is mathematical, the rest is a joke" (Seminar XIX, p. 21). In Seminar XX he states the canonical definition: "Mathematical formalization is our goal, our ideal. Why? Because it alone is matheme, in other words, it alone is capable of being integrally transmitted" (Seminar XX, Fink trans., p. 128). Simultaneously, Lacan introduces the four discourses as a formal apparatus generated by quarter-turn rotation of four mathemic positions (S1, S2, $, a) and deploys the golden-number proportion (o/1−o = 1/o = 1+o) as a matheme for objet a's incommensurability (Seminars XIV–XVII). The formulas of sexuation—∀x.Φx, ∃x.¬Φx, ¬∀x.Φx, ¬∃x.¬Φx—are introduced in Seminar XIX (1971–1972) as the culminating formalizations of sexual difference.

In the Borromean period (Seminars XXII–XXIII, from 1974), Lacan qualifies the matheme's ambition: "Naturally, the ideal of the matheme is that everything corresponds. This indeed is why the matheme adds to the Real" (Seminar XXIII, 150). Topology (knots, rings) now supplements the algebraic matheme, and Žižek's later reading notes that "starting in 1976, Lacan puts an end to the reign of the matheme, namely, the pursuit of an analysis purged of meaning through mathematical-style formalizations bearing upon a senseless Real" (Hegel in a Wired Brain, p. 68). The "final Lacan" shifts toward identification with the sinthome, which Žižek distinguishes from the matheme: unlike the sinthome (which is saturated with jouissance), "mathemes do not imply any libidinal investment, they are neutral, desubjectivized" (Less Than Nothing). Commentators such as Fink, Zupančič, and Copjec continue to deploy the mathemes as rigorous analytical tools while acknowledging this terminal tension.

Key formulations

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and KnowledgeJacques Lacan · 1972 (p.128)

Mathematical formalization is our goal, our ideal. Why? Because it alone is matheme, in other words, it alone is capable of being integrally transmitted. Mathematical formalization consists of what is written, but it only subsists if I employ, in presenting it, the language (langue) I make use of.

The canonical definition of the matheme: integral transmissibility as the criterion distinguishing mathematical formalization from all other discourse, immediately qualified by the paradox that even this formalization requires living language to ex-sist.

Seminar XIX · …or WorseJacques Lacan · 1971 (p.21)

namely at Sainte-Anne, when I posed the question of what one could call a matheme, positing already that it is the pivotal point of any teaching. In other words that the only teaching is mathematical, the rest is a joke.

The earliest explicit introduction of the term 'matheme' as the necessary vehicle of genuine transmission, distinguished from speech and positioned as the condition of any real teaching.

Seminar X · AnxietyJacques Lacan · 1962 (p.95)

We designate this object with a letter. This algebraic notation has its function. It's like a thread designed to enable us to recognize the identity of the object behind the various incidences in which it appears to us.

States the epistemological rationale for the matheme: the algebraic letter secures identity across varied imaginary manifestations, escaping the metaphorical instability of ordinary words.

What Is Sex?Alenka Zupančič · 2017 (p.78)

A matheme is not simply a formalization of some reality; rather—and as Lacan himself puts it—it is the formalization of the impasse of formalization.

Zupančič's decisive reformulation: the matheme does not represent a structure but inscribes the point at which formalization itself encounters its limit — touching the Real at the site of speech's inherent contradiction.

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and KnowledgeJacques Lacan · 1972 (p.120)

the said language brings with it considerable inertia, which is seen by comparing its functioning to signs that are called mathematical - 'mathemes' solely because they are integrally transmitted. We haven't the slightest idea what they mean, but they are transmitted.

Lacan distinguishes mathemes from natural language not by superior meaning but by the paradox of transmission without comprehension — the opposite of ordinary communication, grounding the matheme's clinical and pedagogical function.

Cited examples

Little Hans's phobia — algebraic formulae for successive transformations of the phobic structure (e.g., Λ.Λ_p^P(T/M+φ+α)Mm+Π; p(M)(M')(α/φ)Π) (case_study)

Cited by Seminar IV · The Object RelationJacques Lacan · 1956 (p.378). Lacan formalizes the successive stages of Hans's phobic resolution as a sequence of algebraic mathemes, showing that clinical progress can be rigorously represented as a series of symbolic transformations. The final formula p(M)(M')~(α/φ)Π marks the terminal state, demonstrating that the matheme serves both descriptive and structural-explanatory functions.

Chomsky's 'Colourless green ideas sleep furiously' — used by Lacan to introduce formalization (formalisation) as the proper level for analyzing syntactic structure (literature)

Cited by Seminar XII · Crucial Problems for Psychoanalysis (alt. translation)Jacques Lacan · 1964 (page unknown). Lacan opens Seminar XII by using Chomsky's famous nonsense sentence to pose what counts as 'talking,' situating structuralist syntax at the precise level he calls 'formalisation' — the reduction of signifying chain linkages to transmissible rules. This anticipates the matheme as the site where linguistic relations become transmissible formal structures.

Antigone and Sygne de Coüfontaine — distinguished via the mathemes Φ (imaginary phallus) and φ (symbolic phallus) (literature)

Cited by Ethics of the Real: Kant and LacanAlenka Zupančič · 2000 (p.271). Zupančič uses the Lacanian mathemes (Φ, φ) to formalize the ethical contrast between the two heroines: Antigone incarnates the phallic signifier of desire (Φ), while Sygne's drive-logic produces the real residue of castration (φ). The mathemes allow the structural difference to be stated with precision unavailable to narrative description.

Newton's law of gravitation (F = g Mm'/d²) — invoked as a proto-matheme whose formal written character constitutes the real Copernican revolution (history)

Cited by Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and KnowledgeJacques Lacan · 1972 (p.101). Lacan argues that what changed with Newton was not the displacement of an astronomical centre but the appearance of a written formula — a proto-matheme — whose formal structure, not its imaginary representation, constituted the revolution. This illustrates the function of the written as distinct from speech, and grounds the matheme's privilege over metaphor.

Schreber's psychosis — formalized through the I-schema (P₀→Φ₀), explicitly contrasted with later mathemes (discourses, Borromean rings) (case_study)

Cited by Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache'Derek Hook, Calum Neill & Stijn Vanheule (eds.) · 2019 (p.198). The commentary explicitly downgrades the I-schema relative to Lacan's later mathemes (discourses, Borromean knot), noting that unlike true mathemes the I-schema only formalizes intuitions and cannot be straightforwardly applied to other cases — demonstrating a hierarchy of formalizing power within Lacan's corpus.

Tensions

Within the corpus

Whether the matheme achieves genuine integral transmissibility or is itself dependent on ordinary language (lalangue) in a way that undermines its ideal.

Lacan (Seminar XX, Fink trans.): Mathematical formalization 'alone is capable of being integrally transmitted' — the matheme is the ideal of a transmission that bypasses imaginary understanding. — cite: jacques-lacan-seminar-20-bruce-fink, p. 128
Lacan (Seminar XX, immediately following the same passage): 'No formalization of language is transmissible without the use of language itself. It is in the very act of speaking that I make this formalization… ex-sist.' The ideal is always already compromised by the tongue that must present it. — cite: jacques-lacan-seminar-20-cormac-gallagher, p. 240

This is not an external critique but an internal self-qualification Lacan builds into the very seminar where he most forcefully states the matheme's ideal, making the tension constitutive of the concept itself.

Whether the matheme is neutrally desubjectivized (no jouissance) or whether it 'adds to the Real' and functions as a means of approaching the Real through its impasse.

Žižek (Less Than Nothing): 'mathemes do not imply any libidinal investment, they are neutral, desubjectivized' — the matheme is the polar opposite of the sinthome precisely because it carries no jouissance-dimension. — cite: slavoj-zizek-less-than-nothing-hegel-and-the-shadow-of-dialectical-materialism-v, no page
Lacan (Seminar XXIII): 'Naturally, the ideal of the matheme is that everything corresponds. This indeed is why the matheme adds to the Real' — suggesting the matheme is not a neutral inscription but an instrument that produces a new fragment of the Real. — cite: jacques-lacan-seminar-23-cormac-gallagher, p. 150

The tension turns on whether formalization's neutrality is an achievement (Žižek: desubjectivized scientific statement) or a generative limit (Lacan: each formalisation produces a new Real).

Whether the matheme can capture the Real of psychosis, or whether later mathemes supersede earlier schematic formalizations that only capture intuitions.

Hook et al. (Reading Lacan's Écrits, on the I-schema): 'Contrary to a number of his later mathemes, like his theory of discourse, or the borromean rings, Lacan does not believe that the I-schema catches the real of psychosis' — it is explicitly downgraded to an 'intuitive image.' — cite: derek-hook-calum-neill-stijn-vanheule-reading-lacan-s-ecrits-from-the-freudian-t, p. 198
Lacan (Seminar XVII): 'The form of letters in which we inscribe this symbolic chain is of little importance provided it is distinct — this is enough for something to be manifested about constant relations' — any sufficiently distinct letter-notation captures structural relations, suggesting no hierarchy. — cite: jacques-lacan-seminar-17, p. 8

The tension concerns whether mathemes form an ordered progression in formalizing power (later > earlier) or whether any distinct algebraic inscription already achieves what is required.

Across frameworks

vs Frankfurt School

Lacanian: The matheme is a mode of formalization that brackets meaning and imaginary comprehension in favour of structural transmissibility. Its value lies precisely in its independence from lived experience, ideological content, and hermeneutic context. The Real can only be touched at the impasse of formalization, not through critical reflection on social totality.

Frankfurt School: The Frankfurt School (especially Adorno) treats mathematical formalization as a form of instrumental reason that systematically liquidates qualitative particularity and subjective experience. For Adorno, the 'identity logic' of formalization reproduces the reifying tendencies of commodity exchange and is itself an ideological form that demands immanent critique rather than deployment as a neutral epistemic tool.

Fault line: Where Lacan valorises the matheme's evacuation of meaning as the condition for reaching the Real, Frankfurt critical theory identifies this same evacuation as the ideological operation of identity-thinking that must be negated.

vs Object Oriented Ontology

Lacanian: Lacanian mathemes formalize structural relations (between barred subject, Other, and objet a) rather than representing objects with their own intrinsic qualities. The Real is not a withdrawn substance but the impasse of the symbolic-structural order itself; objects are effects of discourse, not independent entities.

Object Oriented Ontology: Object-Oriented Ontology (Harman, Bryant) argues that objects withdraw from all relations and cannot be fully captured by any relational or structural account. For OOO, Lacanian formalization is still correlationist insofar as the Real is defined in relation to the symbolic and the subject, rather than as an autonomous object-realm that would exceed both.

Fault line: Lacan's Real is constitutively relational (it is the impasse of the symbolic), while OOO's real is constitutively a-relational (objects withdraw from all access, including symbolic access); the matheme formalizes a relational structure, which for OOO already misses the object's depth.

vs Cbt

Lacanian: The matheme formalizes structures (fantasy, drive, discourse) that are constitutively non-transparent to the subject and resistant to cognitive intervention. The barred subject ($) is not a cognitive agent who can be equipped with better schemas; it is an effect of the signifying order whose division cannot be remediated by corrective information.

Cbt: Cognitive Behavioural Therapy (Beck, Ellis) assumes that psychological distress arises from identifiable, modifiable cognitive schemas and automatic thoughts. Therapeutic change occurs through systematic identification, challenge, and replacement of maladaptive beliefs — a process that presupposes a reflexive subject capable of self-monitoring and rational self-correction.

Fault line: CBT's therapeutic subject is precisely the kind of self-transparent, cognitively accessible agent that the Lacanian barred subject by definition cannot be; the matheme inscribes a structural split that CBT's interventional logic depends on denying.

All occurrences

Where it appears in the corpus (198)

#01

Ethics of the Real: Kant and Lacan · Alenka Zupančič · p.183

Ethics and Tragedy in Psychoanalysis > Some preliminary remarks

Theoretical move: Zupančič argues that Lacan's engagement with tragedy is not a poetization but a first attempt at formalization—myth and tragedy function as instantiations of formal structures analogous to mathemes—and traces a triadic movement (Oedipus→Hamlet→Sygne de Coüfontaine) in which the relationship between knowledge, desire, and guilt is progressively transformed, culminating in a radical destitution of the subject that exceeds classical symbolic debt.

Thus we can say that the myth has exactly the same function as the matheme. Myth and tragedy, as Lacan understands them, are not to be looked at in terms of narratives ... for Lacan treats myth and tragedy themselves as instantiations of formal structures.
#02

Ethics of the Real: Kant and Lacan · Alenka Zupančič · p.271

Sygne, or the Enj oyment of the Remainder > From pure desire to the drive > Notes

Theoretical move: Zupančič distinguishes two modes of "realizing desire" - Antigone's sublimation through which she becomes the phallic signifier of desire (the Φ), and Sygne de Coufontaine's drive-logic that short-circuits the infinite/finite opposition by sacrificing even the absolute condition itself, rendering the finite not-whole and making visible the Real of desire (the real residue of castration) rather than the Symbolic/Imaginary phallus.

If we translate this into Lacanian mathemes, we could say that at the end of the play, Antigone starts to incarnate the Φ, the signifier of desire
#03

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

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

Theoretical move: Lacan's "return to Freud" is argued to be a return to the structures of language operative in the unconscious, which grounds a critique of medicalized, dogmatic analytic training and calls for a perpetually self-renewing pedagogy open to the structuralized human sciences and mathematics — with the Real (as the impossible-yet-condition-of-possibility) underwriting both the necessity and the limits of analytic practice.

the unconscious-structured-like-a-language can and should be reflected and mapped by the mathematical-style formalizations of (post-)Saussurian structuralism
#04

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

[Psychoanalysis and its Teaching](#ch05.xhtml_tocbook-part-004) > The talk given was couched in the following terms

Theoretical move: The passage argues that Lacan's abstract simultaneously enacts and reflects on his mode of teaching psychoanalysis, sketching key theses (split subject, linguistic unconscious, the analyst as Other) while critically noting the social cost of psychoanalysis's fashionable acceptance—which distorts the analyst into a figure of omniscient authority rather than a rigorous clinical and theoretical position.

just as a physicist might use the language of physics, an algebraic formula, both to communicate the content of his teaching and to illustrate the way in which it is formulated
#05

Reading Lacan's Écrits: From 'The Freudian Thing' to 'Remarks on Daniel Lagache' · Derek Hook, Calum Neill & Stijn Vanheule (eds.) · p.198

[On a Question Prior to Any Possible Treatment of Psychosis](#ch05.xhtml_tocbook-part-007) > IV. Schreber’s way

Theoretical move: The I-schema formalizes Schreber's psychotic structure as the product of foreclosure of the Name-of-the-Father (P₀→Φ₀), while demonstrating that his delusion constitutes an efficient stabilizing solution rather than mere deterioration; madness is re-theorized as the extreme limit-case of human freedom in the face of constitutive lack.

Contrary to a number of his later mathemes, like his theory of discourse, or the borromean rings, Lacan does not believe that the I-schema catches the real of psychosis.
#06

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***S*** > **sexual difference**

Theoretical move: Sexual difference cannot be grounded in anatomy or biology but is constituted by a fundamental dissymmetry in the signifier: the phallus is the only sexual signifier with no feminine equivalent, so sexual positions (masculine/feminine) are symbolic constructions determined by one's relation to the phallus and formalised through the formulae of sexuation, with the result that no fully 'finished' sexual identity is achievable and the sexual relationship is structurally impossible.

In the seminar of 1970–1 Lacan tries to formalise his theory of sexual difference by means of formulae derived from symbolic logic.
#07

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***L*** > **lack**

Theoretical move: Lacan's concept of 'lack' undergoes three successive theoretical articulations across his teaching: from lack of being (tied to desire and paralleling Sartre), to lack of object (distinguished into three forms, with castration as central), to lack of a signifier in the Other (constitutive of the subject), showing how the concept evolves while remaining fundamentally anchored to desire.

Lacan introduces the symbol… to designate 'the signifier of a lack in the Other'. No matter how many signifiers one adds to the signifying chain… This 'missing signifier' (written -1 in Lacanian algebra) is constitutive of the subject.
#08

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***D*** > **drive**

Theoretical move: The passage establishes Lacan's reworking of Freudian drive theory: by distinguishing drive from instinct, articulating the drive's circuit through three grammatical voices, insisting on the irreducible partiality of drives, and identifying every drive as a death drive, Lacan reframes the drive as a symbolic-cultural construct whose circular aim — not goal — constitutes the only path beyond the pleasure principle.

Lacan proposes the formula [...] as the MATHEME for the drive. This formula is to be read: the barred subject in relation to demand, the fading of the subject before the insistence of a demand that persists without any conscious intention to sustain it.
#09

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***O*** > ***objet (petit) a***

Theoretical move: This passage traces the full conceptual evolution of objet petit a across Lacan's work, showing how it migrates from a purely imaginary little other (schema L, 1955) through the object of desire/fantasy (1957) to the real cause of desire, surplus-jouissance, and finally semblance of being at the centre of the Borromean knot—demonstrating that the concept accumulates rather than replaces its earlier determinations.

Lacan insisted that it should remain untranslated, 'thus acquiring, as it were, the status of an algebraic sign'.
#10

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***J***

Theoretical move: The passage traces the conceptual development of jouissance in Lacan's work from a simple Hegelian notion of enjoyment to a complex articulation of the paradoxical "painful pleasure" beyond the pleasure principle, culminating in the distinction between phallic jouissance and the Other (feminine) jouissance, while anchoring the concept in the prohibition inherent to the symbolic order, castration, and the death drive.

In order to differentiate between these two forms of jouissance, Lacan introduces different algebraic symbols for each; Jö designates phallic jouissance, whereas JA designates the jouissance of the Other.
#11

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***E*** > **ego-ideal**

Theoretical move: Lacan systematically differentiates three Freudian 'formations of the ego'—ego-ideal, ideal ego, and superego—by assigning them to distinct registers (symbolic vs. imaginary vs. unconscious) and developmental moments, thereby grounding their algebraic notation I(A) and i(a) in a structural topology of identification.

The ideal ego is written i(a) in Lacanian algebra, and the ego ideal is written I(A).
#12

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***M*** > **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.

'mathematical formalisation is our goal, our ideal' (S20, 108).
#13

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***A*** > **algebra**

Theoretical move: Lacan's algebraic formalisation of psychoanalysis is theoretically motivated by three interlinked aims: scientific legitimacy, integral transmission of psychoanalytic knowledge, and the prevention of imaginary (intuitive) understanding in favour of symbolic manipulation — the mathemes and associated symbols thus function as epistemic and pedagogical devices, not mere notation.

The algebraic symbols used by Lacan, which appear principally in the MATHEMES, SCHEMA L and the GRAPH OF DESIRE, are listed below
#14

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***F*** > **fantasy**

Theoretical move: Fantasy is not opposed to reality but is a discursively constituted, structurally fixed defence against castration and the lack in the Other; its mathemic formalisation ($ ◇ a) places it within a signifying structure that the analysand must ultimately traverse in the course of treatment.

The neurotic fantasy, which Lacan formalises in the matheme… The matheme is to be read: the barred subject in relation to the object.
#15

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***S*** > **Subject**

Theoretical move: The passage traces the theoretical genealogy of Lacan's concept of the 'subject', arguing that it is irreducibly distinct from the ego, constituted through language and the symbolic order, essentially split, and identified with the Cartesian cogito reread as the subject of the unconscious rather than self-conscious agency.

In 1957 Lacan strikes through this symbol to produce the symbol the 'barred subject'
#16

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***L*** > **letter**

Theoretical move: The passage establishes Lacan's concept of the Letter as the material, indivisible, and localised substrate of the Symbolic order that is itself Real (hence meaningless), persists through repetition, and positions the analyst as a reader of formal properties rather than meanings — against Saussure's privileging of the acoustic signifier.

Writing is also connected with the idea of formalisation and the mathemes; Lacan thus speaks of his algebraic symbols as 'letters'
#17

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***A*** > ***aphanisis***

Theoretical move: Lacan radically redefines Jones's concept of aphanisis: rather than the disappearance of sexual desire (Jones), aphanisis designates the fading/disappearance of the subject itself, instituting the fundamental division of the subject and the dialectic of desire, while paradoxically the neurotic actively aims at making desire disappear.

The term is used by Lacan when describing the MATHEMES of the drive and of fantasy: the subject 'fades' or 'disappears' in the face of demand and in the face of the object, as is shown by the fact that the subject is barred in these mathemes.
#18

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***S*** > **Signification**

Theoretical move: Lacan's concept of 'signification' undergoes a trajectory from a vague association with meaningfulness to a precise, imaginary-order process in which the play of signifiers produces the illusion of the signified through metonymy and metaphor, with the bar in the Saussurean algorithm marking not a bond but a rupture—a theoretical move that radically inverts Saussure's stable sign relation.

Signification is designated by the symbol s in Lacanian algebra (as in the notation s(A) which labels one of the main nodes in the graph of desire).
#19

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***D*** > **discourse**

Theoretical move: The passage systematically presents Lacan's theory of the Four Discourses as four possible social bonds founded in language, each defined by rotating four algebraic symbols (S1, S2, $, a) through four structural positions, with the discourse of the master as the generative base from which the others derive—and with the discourse of the analyst positioned as the structural inverse of mastery, making psychoanalysis inherently subversive.

Lacan represents each of the four discourses by an algorithm: each algorithm contains the following four algebraic symbols: S1 = the master signifier, S2 = knowledge, $ = the subject, a = surplus enjoyment.
#20

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***S*** > **Science**

Theoretical move: The passage traces Lacan's evolving and ambivalent relationship to science, arguing that his model of psychoanalysis oscillates between claiming scientific status (via mathematical formalisation, the isolation of objet petit a as its object) and disavowing it (as a "delusion" awaiting science), while insisting throughout that psychoanalysis operates the "subject of science" and must align with structural linguistics rather than natural sciences.

the tension between the scientific formalism of the MATHEME and the semantic profusion of lalangue constitutes one of the most interesting features of Lacan's later work
#21

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***S*** > **sexual relationship**

Theoretical move: The passage systematically unpacks Lacan's formula 'there is no sexual relationship' as condensing six distinct theoretical points about sexual difference: the mediating role of language, the asymmetry of the symbolic order (one signifier, the phallus), the impossibility of harmony between the sexes, the partiality of the drive's object, the woman's reduction to the mother function, and the opposition of sex to meaning/relation in the real.

the object a occupies the place of the missing partner, which produces the matheme of fantasy
#22

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***M*** > **matheme**

Theoretical move: The matheme is defined as a formal algebraic index of psychoanalytic concepts designed to resist univocal (imaginary) interpretation and enable integral transmission of theory precisely because its meaning remains opaque — it is to be used, not understood.

The mathemes are not transcendent signifiers; they are the indices of an absolute signification
#23

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***M*** > **metonymy**

Theoretical move: Lacan's concept of metonymy, derived from Jakobson, defines the diachronic, combinatorial relation between signifiers along the signifying chain as the structural condition for signification and the very logic of desire; the formula for metonymy shows that the bar between signifier and signified is maintained (no new signified produced), and metonymy is identified with displacement and posited as the condition of possibility for metaphor.

Lacan provides a formula for metonymy (E, 164; Figure 10)
#24

An Introductory Dictionary of Lacanian Psychoanalysis · Dylan Evans

***S*** > **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.

Each point in a schema is designated by one of the symbols of Lacanian ALGEBRA, while the vectors show the structural relations between these symbols.
#25

Seminar X · Anxiety · Jacques Lacan · p.33

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

Theoretical move: Lacan marks a decisive 'leap' beyond Hegel on the function of desire: whereas Hegel's desire is desire of/for another *consciousness* (leading necessarily to the struggle to the death), Lacanian desire is desire of the Other qua *unconscious lack*, mediated by the fantasy as image-support — a distinction formalised through four formulae and the division-remainder algebra that produces the barred subject and objet a as co-residues on the side of the Other.

First Formula d(a): d(A) < a … Second Formula d(a) < i(a): d(/A)
#26

Seminar X · Anxiety · Jacques Lacan

BookX Anxiety > *PASSAGE* **A** *L'ACTE* **AND ACTING-OUT**

Theoretical move: The passage establishes that objet petit a is doubly relational: it is isolated by the big Other and constituted as a remainder in the subject's relation to the Other, grounding the mathemic table of division that structures subject, Other, and a together.

This is why I have reproduced this table, which is homologous with the apparatus of division.
#27

Seminar X · Anxiety · Jacques Lacan · p.95

BookX Anxiety > *NOT WITHOUT HAVING IT*

Theoretical move: The passage advances the thesis that anxiety is "not without an object" — specifically objet petit a — and that this object's status is established through the logic of "not without having it," linking castration anxiety to the phallus's sociological function, the cut as operator of detachment, and the phenomenological transformation of the bodily object into a detachable, exchangeable thing.

We designate this object with a letter. This algebraic notation has its function. It's like a thread designed to enable us to recognize the identity of the object behind the various incidences in which it appears to us.
#28

Seminar X · Anxiety · Jacques Lacan · p.74

BookX Anxiety > **v** > Schema of the effaced trace

Theoretical move: The passage argues that anxiety arises when the constitutive void that preserves desire is filled in by a false response to demand, and that the drive (distinct from instinct) is structured by the cut between barred subject and demand, with partial objects (breast, scybalum) marking the place of this void rather than stages of relational maturation.

I've taught you to write the drive ($ 0 D), to be read - barred S, cut of capital D, demand... the fantasy ($ 0 a)
#29

Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.51

OF THE SUBJECT OF CERTAINTY > THE UNCONSCIOUS AND REPETITION

Theoretical move: Lacan marks the dissymmetry between Freud and Descartes: whereas Descartes grounds certainty in a cogito that then requires an Other (God) to guarantee truth, Freud grounds certainty in the unconscious itself, making the subject "at home" in that field—a move that displaces the guarantee of truth from a transcendent Other onto the structure of the unconscious.

we will be able to begin playing with the small algebraic letters that transform geometry into analysis, that the door is open to set theory
#30

Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.263

FROM INTERPRETATION TO THE TRANSFERENCE > THE FIELD OF THE OTHER

Theoretical move: The passage argues that paternity is fundamentally transbiological—a symbolic, not natural, function—and uses the matheme of metaphor to formalize this, while cautioning against reducing the bar between signifier and signified to a simple mathematical fraction, since it also carries an irreducible "effect of meaning."

if we wish to formalize it... deserves to be handled with more prudence than is in fact the case—relying, in a way, on the formalism of fraction
#31

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.

the small losange that I used as algorithm in my graph precisely because it is necessary in integrating some of the finished products of this dialectic.
#32

Seminar XI · The Four Fundamental Concepts of Psychoanalysis (alt. translation) · Jacques Lacan · p.178

THE DECONSTRUCTION OF THE DRIVE > THE DECONSTRUCTION OF THE DRIVE

Theoretical move: Lacan reframes Freud's concept of drive (Trieb) as a fundamental fiction rather than a myth or model, arguing that the Grundbegriffe of psychoanalysis must trace their way in the real to be scientifically valid, and begins a deconstruction of the drive's four terms by examining their disjointedness, starting with thrust as tendency to discharge.

This term, I should say in passing, is much more preferable than that of model, which has been all too much abused. In any case, model is never a Grundbegriff, for, in a certain field, several models may function correlatively.
#33

Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.51

OF THE SUBJECT OF CERTAINTY > THE UNCONSCIOUS AND REPETITION

Theoretical move: Lacan establishes a structural dissymmetry between Freud and Descartes: whereas Descartes's cogito grounds certainty in the subject only to hand truth over to a non-deceptive Other (God), Freud grounds certainty directly in the unconscious as a field where the subject is 'at home,' bypassing the need to guarantee truth through an external Other — a move whose algebraic and set-theoretic consequences reshape the coordinates of truth itself.

we will be able to begin playing with the small algebraic letters that transform geometry into analysis, that the door is open to set theory
#34

Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.91

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

Theoretical move: Through the Zhuangzi butterfly dream, Lacan argues that the gaze is not a function of conscious self-identity but of a pre-subjective showing that marks the subject's essence; it is in the dream-state (as butterfly) that the subject touches the root of identity via the gaze, not in waking consciousness, and this structure grounds the gaze as objet petit a within the scopic field.

the objet a of the Lacanian algebra
#35

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).

the small losange that I used as algorithm in my graph precisely because it is necessary in integrating some of the finished products of this dialectic.
#36

Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.263

FROM INTERPRETATION TO THE TRANSFERENCE > THE FIELD OF THE OTHER

Theoretical move: Lacan argues that paternity is fundamentally transbiological—exceeding biology and grounded in the symbolic order—and uses the matheme of metaphor to formalize the relation between signifier and signified, warning against a purely mathematical reading of the bar as fraction while insisting on the irreducible 'effect of meaning' that the bar also carries.

if we wish to formalize it, as the author I referred to just now tried to do, deserves to be handled with more prudence than is in fact the case
#37

Seminar XI · The Four Fundamental Concepts of Psychoanalysis · Jacques Lacan · p.267

FROM INTERPRETATION TO THE TRANSFERENCE > THE FIELD OF THE OTHER

Theoretical move: The primary signifier functions not as openness to all meanings but as their abolition, grounding the subject's freedom through infinite value (denominator = zero); the mediation between this infinity of the subject and the finiteness of desire requires a formalization via Kant's concept of negative quantities.

it will be important... to show how the experience of analysis forces us to seek a kind of formalization such that the mediation of this infinity of the subject with the finiteness of desire may occur only through the intervention of... negative quantities.
#38

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

**Seminar 1: Wednesday 2 December 1964**

Theoretical move: Lacan opens Seminar XII by using Chomsky's famous nonsense sentence to introduce the problem of the signifying chain: the question of what counts as "talking" is precisely what motivates the formalization of syntactic structure, staging the distinction between combinatory rules governing signifiers and semantic/referential meaning.

Syntax, in a structuralist perspective, is to be situated at a precise level that we will call formalisation
#39

Seminar XII · Crucial Problems for Psychoanalysis (alt. translation) · Jacques Lacan · p.334

**Seminar 22: Wednesday 9 June 1965.** > **Seminar 24: Wednesday 23 June 1965**

Theoretical move: The passage argues that American psychoanalysis has undergone a pathological inversion by becoming an 'o-object' (objet petit a) of conspicuous display and ideological suture — masking the class struggle under the 'pursuit of happiness' and the promise of adaptation — while true psychoanalysis is defined by assuming the irreparable, i.e. the lack of being, and the properly oriented desire of the analyst.

it is not easy either to diffuse precisely one or other thing that I can only designate by the letters of an algebra
#40

Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.143

**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.

it is certain that it is not for being situated, as it is, at the level of an element, that it is in effect easy...mathematics, throughout its whole history, and always in a more striking, more submerging way...manifests something which interests us to the highest degree
#41

Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan · p.334

**Seminar 22: Wednesday 9 June 1965.** > **Seminar 24: Wednesday 23 June 1965**

Theoretical move: Lacan (via a presenter's reading of Zinberg) diagnoses the "ethical illness" of American psychoanalysis as its transformation into an objet petit a — an object of ostentatious display and adaptation ideology — whose inversion of the analytic aim (assumption of irreparable lack) replaces the desire of the analyst with the pursuit of happiness as social suture; Lacan then defends his own teaching as what preserves a "breathable" theoretical atmosphere against these impasses.

it is not easy either to diffuse precisely one or other thing that I can only designate by the letters of an algebra. This is the point, this is the efficacity of the work
#42

Seminar XII · Crucial Problems for Psychoanalysis · Jacques Lacan

**Seminar 1: Wednesday 2 December 1964**

Theoretical move: Lacan opens Seminar XII by using Chomsky's famous nonsense sentence to pose the foundational question of what counts as speech/talking, situating the structuralist analysis of syntax—formalisation of signifying chain linkages—as the entry point for interrogating whether any signifier can be immediately contiguous to any other signifier.

Syntax, in a structuralist perspective, is to be situated at a precise level that we will call formalisation on the one hand
#43

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.

this is what I posited from the beginning when I got myself involved in speaking about psychoanalysis, namely, the function of language and the field of the word.
#44

Seminar XIII · The Object of Psychoanalysis (alt. translation) · Jacques Lacan · p.59

**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.

one of the useful things about the use of this algebra which means that I pinpoint this object by the letter (o), one of the functions of this use of algebraic notation is that it allows us to follow its thread, like a golden thread
#45

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.

another just as topological a shape which will crosscheck with the paradigm, the exemplification that I gave you of this scopic structure at the level of Las Meninas.
#46

Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.59

**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.

one of the useful things about the use of this algebra which means that I pinpoint this object by the letter (o)... one of the functions of this use of algebraic notation is that it allows us to follow its thread, like a golden thread.
#47

Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.271

**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).

With nothing except this 'gniaka' here you have what is called an Abelian group. This in order to indicate to you the path along which we will be led to order our reflections next year
#48

Seminar XIII · The Object of Psychoanalysis · Jacques Lacan · p.184

**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.

the S with which I designate the subject for you. Yes. Exactly for the same reason that when Monsieur Hogarth tries to designate what is involved in the structure of the beautiful, it is also exactly and specifically to this S that he refers.
#49

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.93

the smallest whole number which is not written on this board > **Seminar 9: Wednesday 25 January 1967**

Theoretical move: The passage argues that the barred Other — S(Ø) — must be understood not as the simple non-existence of the Other but as the Other being *marked* (by castration), and that this marking is the logically prior condition for the subject's alienation, the constitution of desire via the objet petit a, and the very possibility of a logic of the phantasy; it further insists that the scopic drive's proper object (the gaze) is to be sought in what the voyeur wants to see, not in the look of an arriving Other, correcting a philosophical deviation that would locate hell in the Other rather than in the subject.

If it is an algorithm of the mathematical type that I make use of to support this capital S brackets O barred, it is no doubt clearly to affirm that there is another deeper sense to be discovered.
#50

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.132

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.

o over capital O = capital O over (o plus capital O), equals what? This other value that I produced here and which has a name, which is called nothing other than minus phi
#51

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.

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.
#52

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.57

the smallest whole number which is not written on this board > KLEIN GROUP

Theoretical move: Lacan mobilises Boolean/set-theoretic negation (De Morgan's laws) to construct four logical transformations of the Cartesian cogito, arguing that the negated inverse — "either I am not thinking or I am not" — is the proper logical frame for grasping the subject of the unconscious, thereby announcing the programme of the logic of fantasy.

Starting from the written formulation of the new logic, a certain number of things were stated… if you want to deny a and b, I put in a bar, and, by convention, this constitutes negation
#53

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.83

the smallest whole number which is not written on this board > **Seminar 8: Wednesday 18 January 1967**

Theoretical move: Lacan argues that alienation is the pivotal operation through which the Freudian unconscious must be understood: by situating the Other as the locus of the word (and hence as barred, S(O)), he reframes the cogito's subject as inherently split and repressing, displacing both Cartesian self-transparency and object-relational nostalgia for primitive unity in favour of a logical articulation of the subject's constitutive dependence on the symbolic order.

that is why I write S signifier of capital O barred as constituting one of the nodal points of this network … There is no insufficiency, no reduction to some careless gesture or other, in the fact of affirming that the writing: S (O) plays here, for our thinking, an essential pivotal role.
#54

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.138

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.

We have posited that the relation o/1 is the same as the relation of 1/1+o.
#55

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.274

the smallest whole number which is not written on this board > **Seminar 24: Wednesday 21 June 1967**

Theoretical move: Lacan argues that desire structurally emerges from the gap between demand and need within language, that unconscious desire is constituted as "desire-not" (désirpas) through a broken link in the discourse of the Other, and that fantasy functions not as content within the unconscious discourse but as an axiom — a "truth-meaning" — that anchors the transformation-rules of neurotic desire.

coupling in it the small o to the S barred … the formula I gave a long time ago
#56

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.156

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.

if I put forward a certain number of little equations concerning this o, this 1+o, this 1-o which is equal to o² and everything that follows … this very pretty function which is called the golden number.
#57

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan

the smallest whole number which is not written on this board > S *W* S

Theoretical move: Lacan introduces signifier B as the signifier of sterility—that which marks the failure of the signifier's self-relation to generate meaning—and situates it within the Universe of discourse via the 'little diamond' (lozenge), anticipating the full elaboration of the subject's relation to the Other throughout Seminar XIV.

I make use for the moment... of my little diamond in order to say that B forms part of A... by decomposing this little sign in all the binary fashions in which it can be done.
#58

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.146

the smallest whole number which is not written on this board > **Seminar 14: Wednesday 8 March 1967**

Theoretical move: Lacan pivots from methodological self-reflection on the subject's implication in psychoanalytic field-theory to the conceptual forging of "the psychoanalytic act," arguing that analytic theory systematically effaces the cut-structure of the sexual act, and that neither libertarian ideology nor the genital-stage ideal resolves the structural deficit (castration, guilt) inscribed in sexuality; this sets up the question of whether hatred, not tenderness, can co-constitute the sexual act.

we have been lead to bring into play one of the most exemplary mainsprings of mathematical thinking … the ternarity that was provided for me by the proportion of the golden number
#59

Seminar XIV · The Logic of Phantasy (alt. translation) · Jacques Lacan · p.18

the smallest whole number which is not written on this board > B ◊ A

Theoretical move: Lacan deploys Russell's paradox not to stop at its logical contradiction but to show that the axiom "the signifier cannot signify itself" — operating at the level of the Universe of discourse rather than set-theoretic specification — sidesteps the paradox and opens onto the logic of fantasy as more fundamental than formal logic.

$$(B \diamond A / S W S)$$
#60

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.83

the smallest whole number which is not written on this board > **Seminar 8: Wednesday 18 January 1967**

Theoretical move: Lacan re-articulates alienation as the pivotal operation that redefines the unconscious subject in relation to the Other-as-locus-of-the-word, arguing that the Freudian step is only graspable by tracing the consequences of the Cartesian cogito and by replacing the mythological "primitive unity" reading of psychoanalysis with the rigorous formula S(Ⓞ): the Other has no existence except as the site where assertions are posited as veracious, making the barred Other the nodal point of the dialectic of desire.

that is why I write S signifier of capital O barred as constituting one of the nodal points of this network
#61

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.69

the smallest whole number which is not written on this board > **Seminar 7: Wednesday 11 January 1967**

Theoretical move: Lacan argues that the Cartesian cogito substitutes a pure affirmation of the being of the I for the traditional philosophical question of the relation of thinking to being, and that the Freudian discovery (unconscious and Id) must be understood entirely within—not as a return beyond—this modern refusal of the question of Being; de Morgan's logical transformation of negation/union/intersection is used to re-articulate the cogito in terms of the alienating forced choice between "I do not think" and "I am not," which in turn opens the question of the being of the I outside discourse and the status of the stating subject in the empty set.

it is not simply the being (l'etant) or what is, but that through which being manifests itself in it … this final term - 'the being through which, .., it is being'
#62

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.2

**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.

we will begin from the writing of it that I already constructed, namely, from the formula: S barred diamond small o ($ ◇ o).
#63

Seminar XIV · The Logic of Phantasy · Jacques Lacan

the smallest whole number which is not written on this board > S *W* S

Theoretical move: Lacan introduces the signifier B as a formalization of sterility — the signifier's constitutive inability to generate meaning in relation to itself — and situates it within the Universe of discourse via the diamond operator (◇), thereby grounding the logic of the signifier in a structural incapacity rather than a generative positivity.

That is why I make use for the moment - because after all it does not seem to me to be inappropriate - of my little diamond in order to say that B forms part of A
#64

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.18

the smallest whole number which is not written on this board > B ◊ A

Theoretical move: Lacan deploys Russell's paradox not to endorse set-theoretic logic but to mark its limit: by grounding his own inquiry in the Universe of discourse and the axiom that the signifier cannot signify itself, he argues that the contradiction Russell identifies is a product of *saying* rather than *writing*, and that the logic of fantasy is more fundamental than any formalised logic derived from set theory.

$$(B \diamond A / S W S)$$ $$(y \in B)$$ $(y \in A / y \in y)$
#65

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.243

the smallest whole number which is not written on this board > **Seminar 22: Wednesday June 7 1967**

Theoretical move: The passage argues that the sexual act is constitutively structured by the disjunction between body and jouissance, with the subject emerging precisely at that gap; the woman's body functions as a metaphor for masculine jouissance, while the phallus (distinct from the penis) marks the withdrawal of jouissance into exchange value — yet feminine jouissance remains radically unresolved and adrift, beyond any structural accounting.

| (my) body | body | |--------------|------------------| | ? | my jouissance |
#66

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.29

the smallest whole number which is not written on this board > **Seminar 3: Wednesday 30 November 1966.**

Theoretical move: Lacan retrospectively grounds his early machine-model of the signifier (from the "Purloined Letter" seminar) in Boolean logic via Miller's presentation, arguing that the formal structure of the signifier's functioning is radically prior to and independent of consciousness, and that this priority is what any properly psychoanalytic logic must demonstrate.

It showed you something in the confrontation with the first of these sets, in the mathematical-logic sense of the term … from this set itself, we are allowed to construct this logical precedence, this necessity which radically distinguishes the status of meaning and its origin in the signifier
#67

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.189

the smallest whole number which is not written on this board > **Seminar 17: Wednesday 19 April 1967**

Theoretical move: Lacan deploys the golden ratio formula (1 + o = 1/o) as a matheme for the Objet petit a's incommensurability to sex, arguing that the iterative algebraic unfolding of this relation enacts both metonymy (the sliding chain) and metaphor (the substitution of the One for the enigma of sex), while grounding the operation of measurement in the unary stroke as the condition for the Other's locus.

What does it mean to write - since we need this *One* and because we will be content with it to measure the little **o**-object - the following: *One plus o equals One over small o*?
#68

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.156

the smallest whole number which is not written on this board > **Seminar 14: Wednesday 8 March 1967**

Theoretical move: Lacan uses the golden ratio (mean and extreme ratio) as a structural matheme to differentiate the sexual act from sublimation: whereas in the sexual act the lack is obscured (the remainder o² is not noticed), sublimation begins from lack and iteratively reproduces it, with the repetitive reduction of successive powers of o converging on the original lack—thereby grounding sublimation's structure in repetition and linking objet petit a to fantasy as the subject's relation to sexual satisfaction.

if I put forward a certain number of little equations concerning this o, this 1+o, this 1-o which is equal to o² and everything that follows… there is nothing more amusing than this very pretty function which is called the golden number
#69

Seminar XIV · The Logic of Phantasy · Jacques Lacan · p.93

the smallest whole number which is not written on this board > **Seminar 9: Wednesday 25 January 1967**

Theoretical move: The passage advances the logic of the phantasy by linking alienation (the forced choice between "I do not think" and "I am not") to castration as the primordial marking of the Other: the barred Other (S(Ⓞ)) does not mean the Other is absent but that it is marked—by lack, by castration—which grounds desire through the objet petit a as cause, and against which all sexuality and philosophy defensively operate.

If it is an algorithm of the mathematical type that I make use of to support this capital S brackets O barred, it is no doubt clearly to affirm that there is another deeper sense to be discovered.
#70

Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.84

**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.

I do not see why 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
#71

Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.46

**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.

These exchanges are well designed to evoke the separation, the distance that exists between three levels of mathesis, of learned understanding.
#72

Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.105

**THE SEMINAR OF JACQUES LACAN** > **Seminar 9: Wednesday 7 February 1968**

Theoretical move: By deploying Aristotelian syllogistic logic—specifically the middle term—Lacan argues that the Objet petit a functions as the true middle term connecting the psychoanalysand-as-subject to the psychoanalyst-as-predicate, such that the psychoanalyst is defined not as a pre-given identity but as a production of the psychoanalysing task, sustained by the analyst's identification with the o-object in itself.

only sees in it relations which are properly those that I designate when I handle this algebra: the $, the o, indeed the O and the i(o).
#73

Seminar XV · The Psychoanalytic Act (alt. translation) · Jacques Lacan · p.163

**THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > **Seminar 13: Wednesday 13 March 1968** > **Seminar 15: Wednesday 27 March 1968**

Theoretical move: Lacan defends the asymmetry of "the unconscious is structured like a language" against its inversion, grounding the formula in a logic of consequence that ties signifying articulation to the analysable field, while distinguishing the Subject Supposed to Know from the teaching position of the analyst.

Mathematics are diverted into obscurantism because, probably, the rigour in the handling of the signifier becomes the alibi of the absence of rigour in the use of the signifier.
#74

Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.141

**THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > **Seminar 13: Wednesday 13 March 1968**

Theoretical move: Lacan uses Frege's Begriffsschrift to formalize the logical function of "all" (the universal affirmative) and then pivots to argue that the lost object (objet petit a) occupies the structural position of Frege's "argument," grounding the subject's illusion of totality—while exposing the Rankian myth of primal fusion with the mother as a symptomatic misrecognition of this originary loss.

the way in which, in his Begriffschrift, Frege would write it, would be in a form which posits, in the horizontal lines, the simply propositional content... By the bar he puts on the left, he marks what is called the implication, the presence of the judgement.
#75

Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.84

**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
#76

Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.46

**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.

These exchanges are well designed to evoke the separation, the distance that exists between three levels of mathesis, of learned understanding.
#77

Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.122

**THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968**

Theoretical move: Lacan argues that modern logic is defined by its function of dissolving the problem of the Subject Supposed to Know, and that psychoanalysis can leverage logical quantification precisely because logic operates in a field where that subject is reduced to nothing — enabling analytical progress where institutional qualification has failed.

these literal figures thanks to which we can progress in these problems, by figuring in them in literal terms, in terms of logical algebra
#78

Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.105

**THE SEMINAR OF JACQUES LACAN** > **Seminar 9: Wednesday 7 February 1968**

Theoretical move: Lacan uses Aristotelian syllogistic logic—specifically the middle term—to argue that the Objet petit a functions as the logical middle term connecting the psychoanalysand (as vanishing subject) to the psychoanalyst (as product/predicate), while also theorizing that the analyst's position is constituted by an 'in itself' identification with the o-object, distinguished from narcissistic human relations by the exclusion of the 'I like you' (tu me plais).

only sees in it relations which are properly those that I designate when I handle this algebra: the $, the o, indeed the O and the i(o).
#79

Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.154

**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: The psychoanalytic act constitutes the subject as divided ($) through the transference-function of objet petit a, and this structural division is analogous to the tragic schize between spectator/chorus and hero; furthermore, the logical function of the universal quantifier ("all") is grounded not in totality but in the cause effected by objet petit a, making undecidability an intrinsic feature of any subject-indexed logic.

I led you to the cross-roads of this properly logical effect that modern logic has so well defined under the term of the function of quantifiers
#80

Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.129

**THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > **Seminar 11: Wednesday 28 February 1968** > **Seminar 12: Wednesday 6 March 1968**

Theoretical move: Lacan uses a linguistic analysis of French and English negation ('pas tout' / 'anything') to motivate a transition from Aristotelian syllogistic (subalternation from universal to particular) to the logic of quantifiers, arguing that the latter—by expressing the universal affirmative through double negation ('there is no man who is not wise')—better captures the structural relationship between universal and particular that psychoanalytic theory of the subject requires.

the letters A and E which designate them among Aristotle's posterity, and the letters I and O are the particulars
#81

Seminar XV · The Psychoanalytic Act · Jacques Lacan · p.140

**THE SEMINAR OF JACQUES LACAN** > **Seminar 10: Wednesday 21 February 1968** > **Seminar 13: Wednesday 13 March 1968**

Theoretical move: Lacan argues that psychoanalysis is defined not by a criterion external to it but by the psychoanalyst as instrument, and that the psychoanalytic act brings the subject to an awareness of its constitutive, irreducible division as a language-effect — a division that definitively refutes the Hegelian project of exhaustive self-knowledge (gnothi seauton / pour-soi) and is exemplified in the contrasting logical structures of hysteria and obsession.

whose formula is the following: $ (S V S°). That for every subject in so far as it is of its nature divided, here exactly, in the same way as we can formulate that every man is wise (mVw), we have the disjunctive choice, between the no man and the to be wise.
#82

Seminar XVI · From an Other to the other · Jacques Lacan · p.188

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.

Buy the last little book that has appeared, or rather buy The axiomatic theory of sets by M Krivine. You will see there exactly Freud's schémas
#83

Seminar XVI · From an Other to the other · Jacques Lacan · p.192

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.

our formulae, in so far as they establish this first relationship linked in a way to the most simple function of number... o/1-o = 1/o = 1+o
#84

Seminar XVI · From an Other to the other · Jacques Lacan · p.120

**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.

it is enough for us to write I/o in which the proportion is inscribed. Namely, that the relationship of this 1, determining for the effect of loss, is equal and should be... to something in which there is connected by an additive 'and' this 1 and the written sign of this loss, I/o = l+o.
#85

Seminar XVI · From an Other to the other · Jacques Lacan · p.91

**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 whole structure...is what constructs this writing...there is nothing in this formalisation that is not posited as interpretation. To the...equivocation of common discourse there is opposed here the function of isomorphism
#86

Seminar XVI · From an Other to the other · Jacques Lacan · p.63

**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.

{(S1), (S1 S2)} ... the second element of this set {S1, S2}, an ordered pair is a set which has two elements
#87

Seminar XVI · From an Other to the other · Jacques Lacan · p.23

**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 would prefer what gives rise to the detaching in discourse of what must be called by its name, logic... always conditioned by nothing other than by a reduction of material
#88

Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.228

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.

This first tentative use of mathematics... a surer articulation of what is involved in the effect of discourse... by the simple operation of a fformalised truth, a science is constructed
#89

Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.130

Seminar 8: Wednesday 11 March 1970

Theoretical move: Lacan argues that surplus-jouissance (plus-de-jouir) is the structural analogue of Marxian surplus value within the Discourse of the Master, and that the Discourse of the Analyst uniquely situates knowledge in the place of truth — a position occupied by myth and governed by the law of half-saying — thereby reframing the Oedipus complex as myth rather than clinical universal.

$$\frac{\mathbf{S}_1 \longrightarrow \mathbf{S}_2}{\mathbf{S}_0}$$
#90

Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.21

**ANALYTICON**

Theoretical move: Lacan distinguishes the four discourses (Master, Hysteric, University, Analyst) and argues that psychoanalytic knowledge cannot be transmitted like ordinary university knowledge, because the being of the psychoanalyst—what is produced when a psychoanalysand commits to becoming an analyst—is the real question, a point left open in his seminar on the psychoanalytic act.

This is a sequence, an algebraic sequence S₂/S₁ → 0
#91

Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.8

**THE SEMINAR OF JACQUES LACAN BOOK XVII** > **Seminar 1: Wednesday 26 November 1969**

Theoretical move: Lacan opens Seminar XVII by introducing the Four Discourses as a formal apparatus derived from a quarter-turn operation on the algebraic chain (S1, S2, $, a), and articulates the foundational claim that 'knowledge is the enjoyment of the Other', linking repetition, the lost object, and the death drive to the structural limits of the subject within discourse.

The form of letters in which we inscribe this symbolic chain is of little importance provided it is distinct - this is enough for something to be manifested about constant relations.
#92

Seminar XVII · The Other Side of Psychoanalysis · Jacques Lacan · p.220

X: *[On revolutionaries and the proletariat]* > Seminar 13: Wednesday 20 May 1970

Theoretical move: Lacan argues that psychoanalytic discourse reveals a single foundational affect—the subject's capture as object in discourse—and that this, rather than dialectical ontology, is the proper frame for rereading the Cartesian cogito, the Master Signifier, castration, and the impossibility of the sexual relation, all grounded in the unary trait as language's inaugural effect.

what I may have to say about it, what takes shape in speech, is related only to what is written on the blackboard.
#93

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.

the S of the signifier, the signifier bearer of the function of O barred, O̸...The word cannot express S(O) for example.
#94

Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.113

**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.

Vx.F(x), the universal affirmative, 3x.F(x) here particular affirmative. Vx.F(x), I want to express that this is a negative... You have to put a bar of negation above the F(x) and not at all as is usually done above both.
#95

Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.84

*Lacan writes on the board: "L 'achose"*

Theoretical move: Lacan argues that writing is not the representation of speech but rather the material support that makes scientific and psychoanalytic formalization possible, and uses this to sharpen the claim that the sexual relationship cannot be written except through the phallus — while insisting that the unconscious is structured like a language *within which* its writing appears, distinguishing the Letter from the Signifier.

there is what is involved in the desire of man, written as Φ(o)... the desire of the woman is written Φ(φ)
#96

Seminar XVIII · On a Discourse That Might Not Be a Semblance · Jacques Lacan · p.148

**Seminar 8: Wednesday 19 May 1971**

Theoretical move: Lacan uses the failure of symbolic logic to ground itself reflexively as a demonstration that the sexual relationship cannot be written, then traces the passage from Aristotelian syllogistic to quantifier logic to show how the letter—by replacing terms with holes—is the condition for any logical articulation, ultimately linking this to the function of the master signifier and the structure of discourse.

the fruit of the operation of complete inscription, the one that was allowed, suggested, by the progress of mathematics, it is because mathematics managed through algebra to be entirely written, that the idea of making use of the letter for something other than for making holes came.
#97

Seminar XIX · …or Worse · Jacques Lacan · p.161

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.

it is at this that the proof described as contradiction culminates at... So then it is under this it is not true that - it is a matter of giving the status of the negative bar which is the one that I use at a point of my schema
#98

Seminar XIX · …or Worse · Jacques Lacan · p.117

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.

I mean mathematically acceptable, in a way that can be taught, because this is what is meant by the matheme
#99

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.

If one listened to Peirce, the theory of fixed points ought to be stated as follows - I am going to write it - ∃x . {∃x . $<∃}
#100

Seminar XIX · …or Worse · Jacques Lacan · p.27

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.

I will try right away to question what is meant by the letters that I will have written...I put down these letters as what I will subsequently turn around.
#101

Seminar XIX · …or Worse · Jacques Lacan · p.21

Seminar 2: Wednesday 15 December 1971

Theoretical move: Lacan uses the impossibility of writing the sexual relationship as the anchor for a theory of the Real, the Matheme, and the function of language, arguing that what cannot be written (the sexual non-rapport) is precisely what drives both logic/mathematics and the floundering of metaphysics (exemplified by Aristotle's confusion of the One and Being), while positioning the matheme as the only genuine mode of transmission.

namely at Sainte-Anne, when I posed the question of what one could call a matheme, positing already that it is the pivotal point of any teaching. In other words that the only teaching is mathematical, the rest is a joke.
#102

Seminar XIX · …or Worse · Jacques Lacan · p.43

Seminar 2: Wednesday 15 December 1971

Theoretical move: Lacan introduces the formulas of sexuation by deploying predicate logic's quantifiers (the universal, the particular, the existential, and their negations) to give castration a non-anecdotal, strictly logical articulation: the masculine side is defined by the universal phallic function grounded by the exception ('at least one' who is not subject to it), while the feminine side is defined by the 'not-all' — a contingent rather than particular negation — showing that the sexual relation is irreducibly non-complementary.

I put forward the essential feature of the *not all,* Vx., as being that from which there can be articulated a fundamental statement... this V* .$<, it does not matter what the proposition is here, the function takes on a true value for every x of the domain.
#103

Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.49

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.

If I was able with the passage of time, to succeed in building up with my S, my \$, my Si, my S2 and the o-object, the réson d'être
#104

Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.100

The Psychoanalyst's Knowledge > **4 1 \* May 1972**

Theoretical move: The passage advances the claim that the analytic discourse operates by reproducing neurosis through a model that isolates the master signifier, and that psychoanalysis differs from ideology only insofar as it maps out, rather than veils, the jouissance organised by the signifier's positional effects in a discourse.

This mathematical reference so called because it is of the order where the matheme reigns, namely, what produces a knowledge which even if it is only produced, is linked to the norms of surplus enjoying.
#105

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 defines a discourse, what opposes it to speech, I say, because this is what the *mathème* is, I say that this is what determines for a speaking approach, what determines the real
#106

Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.22

The Psychoanalyst's Knowledge

Theoretical move: Lacan argues that mathematical incomprehension is not a flight from truth but an over-sensitivity to it, and uses this to pivot toward the claim that there is no sexual relationship for speaking beings — because sexual enjoyment (jouissance) can only be approached through lalangue and castration, never directly articulated, requiring the mathème as its proper formalization.

indeed the introduction of a number raised higher and higher, more and more elaborated of what we must at this level call the mathème. And to know that assuredly the aforesaid mathèmes do not involve in any way a retrograde genealogy
#107

Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.116

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.

I have enough to show where my questioning is brought to bear.
#108

Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.28

The Psychoanalyst's Knowledge

Theoretical move: Lacan argues that what specifies the human animal is its anomalous, 'limping and amputated' relationship to enjoyment—a structural disjunction between copulation and jouissance—and that this very disjunction, rather than any biological reduction, is what grounds the possibility of mathemes and science, with lalangue as the medium through which this deficit-conditioned appearance leads to knowledge.

something that I call Mangue, obviously this has a relationship with something real, but from the fact that this can lead us to mathèmes that allow us to build up science, that then, that is really the question.
#109

Seminar XIX bis · The Knowledge of the Psychoanalyst · Jacques Lacan · p.132

The Knowledge of the Psychoanalyst > **1 Jane 1972**

Theoretical move: Lacan deploys set theory and the logic of the 'yad'l'un' (there is One) to ground the four formulas of sexuation, arguing that existence is constituted through a "saying not" (the exception that founds the universal), and that psychoanalysis is the only discourse in which blackguardism (corruption of desire) necessarily produces stupidity—making the mathème the privileged vehicle for approaching knowledge about truth.

I found nothing better than what I call the mathème to approach something regarding knowledge about truth, because it is there in short that one succeeds in giving it a functional bearing.
#110

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.103

**VII** > A love letter *(une lettre d'amour)* > **Knowledge and truth**

Theoretical move: Lacan argues that truth can only be "half-told" (mi-dire) because jouissance constitutes a structural limit on avowal, and that the phallic function is not necessary but merely contingent—it has "stopped not being written" through analytic experience without entering the register of the necessary or the impossible—thereby re-situating knowledge, truth, and the real within the schema of analytic discourse and the three registers.

That is why I do not believe that it was in vain that I eventually came up with the inscriptions (l'écriture) a, the $ of the signifier, A, and Φ. Their very writing constitutes a medium (support) that goes beyond speech, without going beyond language's actual effects.
#111

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.22

On Feminine Sexuality The Limits of Love and Knowledge > COMPLEMENT

Theoretical move: Lacan reframes his seminar's opening address on love as actually being about 'stupidity' (la bêtise), and argues that analytic discourse, uniquely among discourses, does not flee stupidity but rather approaches and produces it—grounding this in the non-existence of the sexual relationship as the indisputable truth that conditions the discourse.

which I formulated to you as a with S2 below it… The lower right-hand corner is where the product of a discourse appears.
#112

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.120

**IX**

Theoretical move: Lacan argues that jouissance is the substance of thought and that its irreducible gap from language—marked by the cry "that's not it"—demonstrates that structure and jouissance are co-constitutive, grounding the non-existence of the sexual relationship; Christianity and Aristotle serve as foils to show how philosophical and theological traditions have covered over this gap with the fantasy of knowledge and soul.

the said language brings with it considerable inertia, which is seen by comparing its functioning to signs that are called mathematical - 'mathemes' solely because they are integrally transmitted.
#113

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan

**107x** > Rings of string

Theoretical move: The passage establishes a structural articulation between writing, jouissance, and the Real: what is written encodes the conditions of jouissance, the Other must be barred (S(Ø)) because it is founded on the One-missing, and mathematization alone can reach a Real that is not fantasy — identified ultimately as the mystery of the speaking body and the unconscious.

That is what S(\$) means. It is in that respect that we arrive at the point of raising the question how to make the One into something that holds up, that is, that is counted without being.
#114

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.38

**II** > **The function of the written1**

Theoretical move: Lacan argues that the written (l'écrit) is not of the same register as the signifier, and uses this distinction to ground the specific function of analytic discourse: letters (a, A, $) name loci and functions rather than merely signify, while the unconscious is what is *read* beyond speech — a move that simultaneously critiques ontology (the master's discourse) for its illegitimate hypostatization of the copula "to be."

I put forward the use of a certain number of letters. First of all, a… Then A… I used the letter $… If these three letters are different, it is because they do not have the same function.
#115

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.128

**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.

Mathematical formalization is our goal, our ideal. Why? Because it alone is matheme, in other words, it alone is capable of being integrally transmitted.
#116

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.83

**II** > God and Woman's jouissance

Theoretical move: Lacan theorizes a feminine jouissance that is "beyond the phallus" — experienced but unknowable even to women themselves — and uses mystical testimony (St. Teresa, Hadewijch) as its privileged witness, then links this Other jouissance to the God-face of the big Other and the paternal/castration function, arguing these do not resolve into either one God or two.

This is, perhaps, a reference to what Lacan says elsewhere... and Lacan's second matheme for women: ∃x̄Φx.
#117

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.146

**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.

There will be a simple ring with an inner eight wound around it, the same inner eight with which I symbolize the subject - allowing us hence to recognize in the simple ring... the sign of object a
#118

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.

What is at stake for us, as you have realized, is to obtain a model of mathematical formalization. Formalization is nothing other than the substitution of what is called a letter for any number of ones.
#119

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.80

**II** > God and Woman's jouissance

Theoretical move: Lacan advances the sexuation formulas by arguing that woman's structural not-wholeness with respect to the phallic function entails a supplementary jouissance irreducible to phallic jouissance, while simultaneously grounding 'being' not in ontology but in the jouissance of the body marked by signifierness—thereby opposing his project to both philosophical idealism and vulgar materialism.

when I try to integrate my four formulas, 3xx and the rest, into Aristotle's work.
#120

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.

I came to the writing of this little o, of this capital S read as signifier, of O qua barred - 0 - and of capital ^. Their very writing constitutes the support that goes beyond the word
#121

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.101

Semina r **5:** Wednesday **16 January 1973**

Theoretical move: Lacan uses the "Copernican revolution" as a foil to argue that genuine subversion lies not in changing a centre but in substituting a new formal principle ('things fall', expressed as Newton's law of gravity written down) — an argument that privileges the function of the written over imaginary, sphere-centred thinking, while reframing the phallus, the Other, love, and the sign as the year's key compass-points.

F = g Mm'/d² ... It is here, it is in this effect of the written, that there consists what is unwarrantedly attributed to Copernicus
#122

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.

namely, gives us the model of what is involved starting from this mathematical formalisation, the one that substitutes for the function of any number whatsoever what is called a letter.
#123

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.240

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.

Mathematical formalisation which is our goal, our ideal, why? Because it alone is matheme, namely, capable of being transmitted integrally.
#124

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.

This use made by mathematics, this use made of the letter, as being singularly what, on the one hand reveals in discourse what not by chance is called grammar… it is because beyond language this effect… which is assuredly the ideal of mathematics.
#125

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.230

J.Lacan-... of this? > **Seminar 11 : Wednesday 8 May 1973**

Theoretical move: Lacan argues that jouissance (enjoyment) constitutes the substance of thinking and is irreducibly linked to the inertia of language, such that the sexual relationship remains inexistent and unthinkable — a gap named the Other — and all cultural, religious, and philosophical formations (including Christianity's baroque obscenity and Aristotle's active intellect) are so many failed attempts to make enjoyment adequate to the sexual relationship, with castration as the only price of any apparent satisfaction.

language comprises a considerable inertia, which can be seen in comparing its functioning to those signs called mathematical, mathemes, solely from the fact that they are integrally transmitted.
#126

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.203

**Seminar 10: Wednesday 10 April 1973 ..**

Theoretical move: The passage articulates the structural asymmetry between the masculine (phallic) universal—grounded in the paternal exception (∃x.¬Φx)—and the feminine not-all (∄x.¬Φx), arguing that both the father function and the "virgin function" constitute existence in an eccentric, decoupled position with respect to the phallic function Φ, such that their radical incommensurability is what grounds the inexistence of the sexual relationship.

this ∃x.¬Φx — this is what permits the universal ∀x.Φx to hold up... ∄x.¬Φx... ∄x.Φx
#127

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and Knowledge · Jacques Lacan · p.80

**Seminar 4: Wednesday 9 January 1973**

Theoretical move: Lacan argues that writing (the letter) belongs to a fundamentally different register than the signifier, and uses this distinction to theorize the specific function of writing within analytic discourse—particularly how mathemes (S(O), objet a, Φ) operate as letters that mark lack and loss within the locus of the Other, rather than as signifiers in the linguistic sense.

I articulated in writing, in the letter, something that adds a dimension to this locus of O… S(O). By this, I articulated in writing, in the letter, something that adds a dimension to this locus of O, and very precisely by showing that, as locus, it does not hold up.
#128

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.

the accessibility constituted by this sphere and the cross presents it as an example of a missed mathesis, missed inexplicably by a hairs breath
#129

Seminar XXII · R.S.I. · Jacques Lacan · p.2

**Introduction**

Theoretical move: In this opening session, Lacan frames the symptom as belonging to the Real, introduces the question of analytic identity and set-formation (can analysts "make a set"?), and links imbecility in the analytic discourse to the ethics of each discourse — previewing the year's central thesis that non-dupes err by refusing to play the game of a discourse's structure.

what is written on the board with little signs, the o, the S1, the S2, the $ of the subject
#130

Seminar XXII · R.S.I. · Jacques Lacan · p.126

**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.'

to mark that R to designate the relation, or to be put between x and y, is to enter here and now into the operation of writing
#131

Seminar XXIII · The Sinthome · Jacques Lacan · p.155

Seminar 9: Wednesday 16 March 1976

Theoretical move: Lacan uses Joyce's *Finnegans Wake* and the sinthome to distinguish the unanalysable from what analysis can address, then pivots to the Phallus as a "phunction of phonation" substitutive for man, contrasting it with S(Ⓞ) — the signifier of the non-existence of the Other of the Other — which Lacan identifies with "The woman" as the only candidate for an Other of the Other, thereby articulating the impossibility of the sexual relation through the bar that no Other can cross.

what I wrote underneath, here, S(0); S of 0 barred is something quite different... I apologise for not having anything other than the bar to make use of.
#132

Seminar XXIII · The Sinthome · Jacques Lacan · p.150

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.

Naturally, the ideal of the matheme is that everything corresponds. This indeed is why the matheme adds to the Real.
#133

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.

is not what you were doing with your knot and your mathemes, deciphering, with as consequence the dissipating of its signification?
#134

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, what is typical of systematisation, is the number: it is numbers and arithmetic...there is something in the chains which behaves like summation, like addition.
#135

Seminar IV · The Object Relation · Jacques Lacan · p.395

XVIII CIRCUITS > 'ME DONNERA SANS FEMME UNE PROGÉNITURE'

Theoretical move: The phobic object (the horse in little Hans's case) functions as a metaphorical substitute signifier for the missing paternal function, transforming free-floating anxiety into a localized, manageable fear that anchors the subject's symbolic order; Lacan traces the dialectical transformation of the phobia through a series of algebraic formulas, showing how the analysis works by allowing the signifier to evolve through its own structural laws rather than by direct suasive intervention.

All of this is taken up in a logicification, Λ. Λ_p^P (T / M+φ+α) M ~ m + Π
#136

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.

$$p(M)(M') \sim \left(\frac{\alpha}{\varphi}\right) \Pi$$ This is the formula that, in contrast to the previous one, marks the point of arrival of little Hans's transformation.
#137

Seminar IV · The Object Relation · Jacques Lacan · p.372

XVIII CIRCUITS > AN ESSAY IN RUBBER¬ SHEET LOGIC

Theoretical move: Lacan formalises the paternal metaphor through the Hugo poem on Boaz and Ruth, showing that the father's function is constitutively metaphorical (substitution + castration complex), and applies this formula to the case of Little Hans to explain how the horse-phobia acts as a substitute metaphorical mediator when the paternal metaphor is absent, while also distinguishing phobic and fetishistic objects as "milestones" of desire in the real that are nonetheless only accessible through signifying formalisation.

we can thus inscribe a crescent C or a sickle its constitutive castration complex plus something that is precisely the signification, s… (P/x) M ~ s + s
#138

Seminar IV · The Object Relation · Jacques Lacan · p.398

XVIII CIRCUITS > 'ME DONNERA SANS FEMME UNE PROGÉNITURE'

Theoretical move: By tracing Little Hans's movement through signifying permutations toward an imaginary resolution, Lacan argues that Hans's phobia dissolves not through genuine traversal of the castration complex but through a narcissistic-imaginary fixation, leaving the subject alienated from himself—he has not "forgotten" but "forgotten himself."

This is precisely what happens at the moment of the bathtub fantasy, which may for example be written out roughly as follows... $$\left(\frac{1}{M+\phi+\alpha}\right)\Pi\sim M\ (-m)$$
#139

Seminar V · Formations of the Unconscious · Jacques Lacan · p.34

THE FREUDIAN STRUCTURES OF WIT > **THE** *FAT-MILLIONAIRE*

Theoretical move: The passage argues that metaphor and condensation operate not through injection of meaning but through signifier-to-signifier relations (homonymy, equivocation), and that this same mechanism — whereby the original signifier gets "repressed" once meaning is established — underlies all formations of the unconscious, unifying wit, slips, and forgetting under a single economy of the signifier.

$$\frac{S}{S'} \to \frac{S}{s}$$
#140

Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.336

OPHELIA, THE OBJECT

Theoretical move: Lacan maps three successive stages of Hamlet's relation to the object (Ophelia) — estrangement, rejection/externalization, and mourning/reconquest — arguing that Ophelia functions structurally as the phallus that the subject externalizes and rejects, and that the fantasy formula ($◇a) tilts toward ($◇φ) in a movement that illuminates das Unheimliche and the modern hero's constitutive displacement onto the other's time.

a transformation of the formula [($0a) into] ($0cp) in the guise of rejection [rejet]
#141

Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.122

INTRODUCING THE OBJECT OF DESIRE

Theoretical move: The passage traces the movement from the animal's excremental territoriality through language's complication of the subject/object relation (use→exchange value), to the dialectic of desire: identification with the father fails to resolve desire's impasse, so the most general "solution" offered to the barred subject is narcissism, which structures fantasy by transferring the subject's anxiety onto object a, yielding the formula of the ego-ideal as i(a)/$ ◇ a/I.

$$\frac{i(a)}{\$} \quad \lozenge \quad \frac{a}{\mathsf{I}}$$ Formula of the ego-ideal
#142

Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.381

THE FUNDAMENTAL FANTASY

Theoretical move: Lacan argues that the fundamental fantasy ($ ◇ a) provides desire's minimal supporting structure by articulating, synchronically rather than diachronically, how the subject must pay the price of castration—giving up a real element (objet a) to serve as a signifier—precisely because the subject cannot designate itself within the Other's discourse (the unconscious). This move directly opposes ego-psychology's conflation of object-maturation with drive-maturation, exposing it as a confusion between the object of knowledge and the object of desire.

The symbolic formula (\$0a) gives form to what I call the fundamental fantasy.
#143

Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.341

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.

when I write the formula (\$0a) for you, it is not in order to try to provide the usual form... It is not an articulation that could be characterized as a mere formalism.
#144

Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.280

THE DESIRE TRAP

Theoretical move: The passage identifies a pivotal structural moment in Hamlet's trajectory: his sudden identification with his desire in its totality occurs precisely when the barred subject ($) enters into a specific relation with objet petit a — triggered by the scene at Ophelia's grave — resolving the long-flagging, "unfinishable" desire that had paralyzed him throughout.

It is insofar as $ is there in a certain relationship with little a that he suddenly identifies with something that for the very first time makes him find his desire in its totality.
#145

Seminar VI · Desire and Its Interpretation · Jacques Lacan · p.226

THE LAUGHTER OF THE IMMORTAL GODS

Theoretical move: Lacan argues that the phallus functions as a signifier—not a privileged object (contra Klein)—and that the subject's relation to it is structured by the dialectic of being versus having: men "are not without having it" (castration enables possession of objects), while women "are without having it," making the sexual positions asymmetrical and irreducible to each other.

In my notation, (\$0a), something presents itself as being a barred subject - namely, a desiring subject [or: subject of desire, sujet du desir]
#146

Seminar VIII · Transference · Jacques Lacan · p.350

**M EDICAL H A R M O N Y** > **CAPITAL I A N D LITTLE** *a* > **SLIPPAGE IN THE M EA N IN G OF THE IDEAL**

Theoretical move: Lacan repositions psychoanalytic action as a necessary response to the unconscious/repressed, critiques Ego Psychology as a mass-formation obstacle to analytic efficacy, and begins dismantling the conflation of ideal ego and ego-ideal by grounding both in narcissism as rethought through the mirror stage — thereby clearing space for a renewed account of analytic action and the structure of fantasy.

This is why my little notation for the structure of fantasy, (S O a), is algebraic and why it can only be written with chalk on the blackboard. It is essential that we not forget this unsayable place.
#147

Seminar VIII · Transference · Jacques Lacan · p.264

**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** > **REAL PRESENCE**

Theoretical move: Lacan distinguishes Φ (the phallus as symbolic/unconscious function operative for all speaking subjects) from φ (the imaginary phallic unit of measurement that organises the obsessive's erotic object-equivalences), arguing that in obsessive neurosis the phallic function is not repressed but emerges consciously and avowedly at the level of symptom, which is precisely what must be explained against both Bouvet's theory of imaginary introjection and a naïve psychologism.

Last time, I put up on the board the following formula for the obsessive's fantasy: A ◇ φ(a, a', a'', a''', …)
#148

Seminar VIII · Transference · Jacques Lacan · p.284

**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.

the great thing about formulas is that you can take them literally - in other words, as stupidly as possible - and that they must lead you somewhere. This is the operational facet of formulas
#149

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 you carry out the operations in question: 1+1=2, 1+2=12 etc... you have therefore the values which, if you carry them forward, will take more or less this form here until they come to converge on a perfectly constant value
#150

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.

this little quadrilateral should be read: the subject qua marked by the signifier is properly in the phantasy, the cut of o … $ ◊ o
#151

Seminar IX · Identification · Jacques Lacan · p.294

*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.

appeared to me to coincide perfectly with the formula: [image of fantasy matheme] as I formulate it for you as given, as the most simple formulisation that we are allowed to reach in contact with the different forms of clinical work
#152

Seminar IX · Identification · Jacques Lacan · p.92

*Seminar 9*: *Wednesday 24 January 1962*

Theoretical move: Lacan demonstrates that the breast as signifier is not a mammary object but a stand-in for the phallus, and uses the Fort-Da alternation (o / -o) to show that subjectivity and identification are constituted not by presence or absence alone but by their conjunction—the cut—which requires the imaginary unit √-1 as the formal root of desire's structure.

This product of o by - o, which formally gives a minus o squared: - o², we will get closer to why negation is irreducible
#153

The Triumph of Religion · Jacques Lacan · p.85

It is not my point of view. I didn r mention religion.

Theoretical move: Lacan distinguishes two registers of the real: the symptomatic real (how the real impinges on living/speaking beings) and the scientific real (accessible through mathematical formulas but producing only 'gadgets'), while grounding the irreducibility of sexual non-relation as the engine of symptomatic proliferation — with wordplay (foi/foire/forum) serving not as decoration but as the very key to psychoanalytic method.

The real to which we gain access with little formulas, the true real, is something else altogether. Up until now, all we have gotten from it are gadgets.
#154

Negative Psychoanalysis for the Living Dead: Philosophical Pessimism and the Death Drive · Julie Reshe · p.42

The Living Dead: Destructive Plasticity > ŽiŽek's Response

Theoretical move: Žižek rehabilitates psychoanalysis against Malabou's critique by arguing that the death drive is not an opposing force to the pleasure principle but its transcendental, constitutive gap, and that the Lacanian barred subject is already a post-traumatic, 'living dead' form — a zero-level subjectivity shaped by destructive plasticity — which a properly read Hegelian dialectics (via 'absolute recoil') can accommodate without reducing negativity to teleological sublation.

Lacan's matheme for the subject is $—the barred subject.
#155

Critique of Pure Reason · Immanuel Kant

THE CRITIQUE OF PURE REASON > CHAPTER III. The Ideal of Pure Reason. > SECTION I. The Discipline of Pure Reason in the Sphere of Dogmatism.

Theoretical move: Kant argues that philosophy, unlike mathematics, cannot proceed axiomatically or demonstratively because philosophical cognition operates through discursive concepts alone and not through the construction of concepts in intuition; consequently, dogmatical methods—including any attempt to import mathematical evidence into pure reason—are illegitimate and must be replaced by a critical, systematic method that grounds principles indirectly through their relation to possible experience.

A direct synthetical proposition, based on conceptions, is a dogma; a proposition of the same kind, based on the construction of conceptions, is a mathema.
#156

A Voice and Nothing More · Mladen Dolar · p.159

A month later: > Lalangue

Theoretical move: The passage argues that *lalangue* names the irreducible surplus of phonic materiality over meaning in language, and that this surplus—rather than being aestheticized as poetic effect—is the very site where unconscious desire is constituted retroactively; interpretation's aim is therefore not to supply meaning but to reduce signifiers to their non-sense, revealing desire as the fold of language itself rather than its hidden content.

he introduces two concepts whose correlation he never explains, lalangue and mathème, but both are based on that in the signifier which does not contribute to making sense
#157

A Voice and Nothing More · Mladen Dolar · p.214

Chapter 6 Freud's Voices

Theoretical move: This passage is a footnotes/endnotes section for Chapters 6 and 7, but it contains substantive theoretical moves: linking Dream-Work to Wish-Fulfillment, articulating the Drive's mythological status, connecting the fundamental fantasy to the drive, and theorizing the Voice and Objet petit a as the eternally lacking object that circumvents oral satisfaction, while also noting the structural role of the Matheme against phonological structuralism.

a very different kind of epistemology follows from the matheme as the detritus, as it were, of the phonological operation. It links the epistemology underlying psychoanalysis to that of Galilean science.
#158

A Voice and Nothing More · Mladen Dolar · p.148

A month later:

Theoretical move: The passage argues that fantasy is structurally generated by the temporal gap between hearing a voice and understanding it (après-coup), functioning as a provisional quilting point in place of understanding; crucially, true understanding never dissolves fantasy but only prolongs it, so analytic progress requires traversal of fantasy rather than understanding—with the matheme and formulas of sexuation standing as the non-fantasmatic, purely literal counterpart to the traumatic voice.

it is a matter of construction, and ultimately of matheme, letters which are precisely meaningless, which are regulated by an automatism of their own, and are, in their literality, the vehicles of the transmission of knowledge. They introduce into knowledge what eludes understanding
#159

A Voice and Nothing More · Mladen Dolar · p.165

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.

This silence is neither the imaginary overwhelming nor the symbolic pulsation... It is correlative to the advent of the letter of matheme, which is equally deprived of sense.
#160

Read My Desire: Lacan Against the Historicists · Joan Copjec · p.120

Orthopsycbism > Guilty versus Useful Pleasures > Fantasy and Fetish

Theoretical move: The passage argues that perversion (specifically fetishism) inverts the structure of fantasy: where the neurotic subject constitutes itself in relation to the object a as an externalized image of loss, the pervert positions himself as the object a in its real form, becoming the instrument of the Other's enjoyment rather than a desiring subject—and Clerambault's fetishistic photographs thereby expose, rather than obscure, the utilitarian fantasy's dependence on the supposition of an obscene Other jouissance.

Starting from the formula for fantasy: 51 0 a, that is, the split subject (51) in some form of relation (0) to an object (a), we can easily derive the formula for perversion: a 0 51.
#161

Read My Desire: Lacan Against the Historicists · Joan Copjec · p.231

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.

No phenomena are exempt from the rules of reason that alone make them objects of our experience. Or, there is no phenomenon that is not an object of possible experience (or not subject to the rule of regress): 3x 4)x. [...] Not all phenomena are a possible object of experience: Vx ct>x.
#162

Freud as Philosopher: Metapsychology After Lacan · Richard Boothby · p.262

Chapter 5 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 and by developing a series of terse symbolic expressions, his so-called mathemes, such as the formula for the phantasy, $ ◇ a.
#163

The Chattering Mind: A Conceptual History of Everyday Talk · Samuel McCormick · p.93

Fuzzy Math > **P**⊋**{{***n*+**1},{Ø}}** > *Tælle Tale*

Theoretical move: The passage argues that the "fuzzy math" of modern public life—formalized as P⊋{{n+1},{Ø}}—is structurally recursive rather than extensive, such that chatter (Snaksomhed) and common sense (Forstandighed) are not merely linked but are the paralogistic double of a self-referential counting operation that can never complete its own count; the matheme for this public is thus simultaneously a theory of modern loquacity.

P⊋{{n+1},{Ø}} is more than a precise mathematical definition of Kierkegaard's 'gallery-public.' It also provides an accurate and long-overdue account of the sorites reasoning on which members of this negative community rely, effectively serving as the matheme for their chattering common sense.
#164

The Odd One In: On Comedy · Alenka Zupančič · p.123

part iii

Theoretical move: Zupančič pushes Bergson's formula of comedy (the mechanical encrusted on the living) toward a more radical claim: the mechanical element is not one of two pre-given poles but names the very *relationship* between any two poles, and comic imitation reveals that automatism/repetition is where singularity, not its absence, resides — thereby inverting the corrective-social reading of laughter.

He (convincingly) proposed this couple as the real core or the 'matheme' of all the others.
#165

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 terms and their page references without advancing any theoretical argument.

matheme [here](#scholium_41_language_lalangue.xhtml_IDX-1363)
#166

Sex and the Failed Absolute · Slavoj Žižek

**Sex and the Failed Absolute** > [Index](#contents.xhtml_end2)

Theoretical move: This is a non-substantive passage consisting of index entries (P–S) from Žižek's *Sex and the Failed Absolute*, listing topics and their page locations with no argumentative content.

of matheme [here]
#167

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.

Although matheme and lalangue may appear opposites (signifiers reduced to formulaic letters versus the wealth of homophonies and other 'pathological' disturbances), their relationship is again that convoluted 'coincidence of the opposites' that characterizes the Möbius strip.
#168

The Sublime Object of Ideology · Slavoj Žižek

INTRODUCTION

Theoretical move: Žižek argues that Althusser's theory of ideological interpellation fails to account for the traumatic, senseless residue that is the very condition of ideological submission; drawing on Pascal, Kafka, Lacan's reading of the burning-child dream, and the Zhuang Zi paradox, he establishes that ideology functions not as illusion masking reality but as a fantasy-construction that *constitutes* reality, sustained by an irreducible surplus of jouissance ('jouis-sense') that escapes symbolic internalization.

the subject ($) is trapped by the Other through a paradoxical object-cause of desire in the midst of it (a)... $ ◊ a - the Lacanian formula of fantasy.
#169

The Sublime Object of Ideology · Slavoj Žižek

INTRODUCTION

Theoretical move: The passage advances a theory of the Graph of Desire's operation by showing that the point de capiton retroactively fixes meaning through the Master Signifier, and that this quilting operation grounds both ideology (as transferential illusion) and subjectivity (as the difference between imaginary identification with the ideal ego and symbolic identification with the ego-ideal/gaze of the Other).

the subject marked by the matheme $ (the divided, split subject, and at the same time the effaced signifier, the lack of signifier, the void, an empty space in the signifier's network)
#170

Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.248

Russell Sbriglia

Theoretical move: The passage argues that the Lacanian *objet petit a* as an extimate object—simultaneously inside and outside the subject—reveals that subjectivity is constitutively split and hystericized, and that this logic of sublimation (where "thing-power" is itself the product of the subject's anamorphic distortion) undermines new materialist "flat ontology" by showing that there is no vibrant matter (*a*) without the subject, just as there is no subject without *a*.

as Žižek more axiomatically renders Lacan's aforementioned formula for the subject's barring vis-à-vis the objet petit a ($ ◊ a), but so too is there no a without I
#171

Subject Lessons: Hegel, Lacan, and the Future of Materialism · Russell Sbriglia & Slavoj Žižek (eds.) · p.20

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.

a failure represented by Lacan via the matheme $, the graphic representation of the subject's 'barring.'
#172

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.176

Psychoanalysis and Science > **"Recreational Mathematics"**

Theoretical move: This appendix exposition demonstrates how Lacan's coin-toss formalism in the Écrits constructs a symbolic matrix in which a second-order Greek-letter overlay introduces syntactic constraints on succession, showing that the 'third position' is already partially determined by the first — a structural demonstration of how the symbolic order generates necessity from apparent contingency.

This accounts for the emblematically laconic formula that appears in Écrits (1966, p. 49) and that I have reproduced in table Al.5
#173

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.18

**THE LACANIAN SUBJECT** > Pour Heloise

Theoretical move: This passage is a preface/road map for the book, outlining its scope, methodology, and interpretive stance—it is non-substantive theoretical content, serving primarily as an editorial and navigational frame rather than advancing a theoretical argument.

The major symbols (known as 'mathemes') discussed in these pages. Lacan's mathemes condense and embody a considerable quantity of conceptualization
#174

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.153

THE PHALLUS: ONE OF W~ S PARTNERS > **The Hysteric's Discourse**

Theoretical move: The passage argues that the Hysteric's Discourse is structurally homologous with the discourse of science because both are driven by the Real (object a as truth) and by the imperative to expose the incompleteness of knowledge rather than systematize it — thus Lacan's eventual identification of the two discourses is grounded in their shared orientation toward the impossible and the unfillable hole in any knowledge-set.

$$\frac{\$}{a} \to \frac{S_1}{S_2}$$
#175

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.79

**The Lacanian Subject** > *Object* a: *The Other's Desire*

Theoretical move: Through the operation of separation, the Other's inscrutable desire constitutes object a as the remainder of a hypothetical mother-child unity, and it is only by cleaving to this remainder in fantasy that the split subject sustains an illusion of wholeness and procures a sense of being beyond mere symbolic existence.

he formalizes it with the matheme $ ◇ a, which is to be read: the divided subject in relation to object a.
#176

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.78

**The Lacanian Subject** > Signifier Mother's Desire

Theoretical move: The paternal metaphor's substitution of S2 for the mOther's desire retroactively produces S1, constitutes the desiring subject through separation, and simultaneously precipitates all four algebraic elements (S1, S2, $, and objet petit a) as a single logical event in Lacan's metapsychology.

all of the crucial elements of his algebra—S1, S2, $1, and a—arising simultaneously here.
#177

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.133

THE PHALLUS: ONE OF W~ S PARTNERS

Theoretical move: The passage argues that S(A)—the signifier of the lack in the Other—functions as Woman's second "partner" in the sexuation table, and that its meaning has shifted in Lacan's work from a symbolic designator of the Other's desire to a real-register signifier of a primordial loss; this asymmetry grounds two distinct paths beyond neurosis (desire/masculine vs. sublimation/feminine) and implies that feminine subjectivity is constituted through an encounter with jouissance rather than through subjection to a master signifier.

Consider now the symbols, or mathemes, as Lacan calls them, located under the formulas of sexuation.
#178

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.164

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.

The term 'matheme' is modeled on phoneme, semanteme, and mytheme, the smallest units of speech, meaning, and myth, respectively, and the symbols Lacan invents are quasi-mathematical in nature, providing formula-like expressions.
#179

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.194

*Glossary of Lacanian Symbols* \_\_\_\_\_\_\_ \_

Theoretical move: This passage is a glossary of Lacanian mathemes and symbols (barred S, object a, S1, S2, the Other, barred A, S(/A), phallus, phallic function, logical quantifiers, lozenge, fantasy formula, drive formula), followed by non-substantive acknowledgements pages.

S 0 a- Matherne or formula for fantasy, usually the "fundamental fantasy."
#180

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.49

The Creative Function of the Word: The Symbolic and the Real > **Incompleteness of the Symbolic Order: The (W)hole in the Other**

Theoretical move: The symbolic order (the Other as the set of all signifiers) is structurally incomplete and untotalizable: any attempt to name or close the set generates a new signifier that remains outside it, mirroring Gödel's incompleteness theorem, and these logical aporias mark the intrusion of the Real into the Symbolic.

Lacan can be seen as undertaking the first steps of axiomatization with his introduction of the mathemes S1, S2, ~.a, S(A), etc.
#181

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.165

Psychoanalysis and Science > **The Status of Psychoanalysis**

Theoretical move: Psychoanalysis is positioned as a distinct, independent discourse that shares formal features with scientific discourse (both being "IRS discourses") without being reducible to science; rather, psychoanalysis illuminates the structural conditions of scientific discourse itself, while pursuing its own forms of rigor through mathemization and clinical differentiation.

Lacanian version, seeks its own proper forms of scientificity-formalization ('mathernization'), generic procedures, rigorous clinical differentiations
#182

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.151

THE PHALLUS: ONE OF W~ S PARTNERS > **The** Four Discourses

Theoretical move: The Four Discourses are introduced as structural matrices governing different social bonds, with the Master's Discourse functioning as the primary or originary discourse from which the other three are generated by quarter-turn rotations; each discourse's positions (agent, truth, other, product/loss) assign different roles to the same four mathemes (S1, S2, $, a), making discourse a structural — not psychological — category.

Whichever matheme Lacan places in one of these four positions, it takes on the role ascribed to that position.
#183

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.97

**The Lacanian Subject** > *The Subject as Breach*

Theoretical move: The subject is theorized not as a sedimentation of meanings but as the act of forging links between signifiers (Bahnung/frayage); the analytic aim is to "dialectize" isolated master signifiers, which simultaneously precipitates subjectivity, produces metaphorization, and initiates separation—a process Lacan presents as surpassing Freud's "rock of castration."

the subject is not simply the sedimentation of meanings (under the bar in the following matheme), S1/s → S2
#184

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.191

Psychoanalysis and Science > Parenthetical Structures

Theoretical move: By mapping the asymmetry of the L Chain onto the subject/Other split and identifying the parenthesis as the operator that introduces heterogeneity into the unary-trait repetition, Fink argues that the letter imposes a "parenthetical structure" on the subject — structurally enacting alienation and separation — and that object (a) is what gets bracketed in this process.

object (a) is bracketed in a multitude of mathemes and graphs
#185

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.141

THE PHALLUS: ONE OF W~ S PARTNERS > *The Truth of Psychoanalysis*

Theoretical move: Lacan distinguishes between mathematical truth (le vrai), which is axiomatic and meaning-free, and the singular truth of psychoanalysis — that there is no sexual relationship — the analytic task being to bring the subject into encounter with this latter truth.

there is no such thing as a truth which is not 'mathematicized,' that is, written, that is, which is not based, qua Truth, solely upon axioms
#186

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.160

Psychoanalysis and Science > Su~uring **the Subject**

Theoretical move: Science "sutures" the subject by excluding it and reducing Truth to propositional value, whereas psychoanalysis is distinguished precisely by taking into account the cause, the split subject, and the subject's libidinal relation to jouissance—making science, as currently constituted, incapable of encompassing psychoanalysis.

the formalization of psychoanalysis into mathemes and rigorously defined clinical structures—so characteristic of Lacan's work at that stage—does not suffice to make psychoanalysis into a science
#187

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.235

**Index**

Theoretical move: This is an index passage (pages 235-236) from Bruce Fink's "The Lacanian Subject," listing key concepts and page references. It is non-substantive as a theoretical argument but serves as a navigational guide to the book's conceptual architecture.

Mathemes, xvii, 30, 59, 105, 113, 140, 144, 173-74. See also specific forms
#188

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.218

*Glossary of Lacanian Symbols* \_\_\_\_\_\_\_ \_ > **Chapter 9**

Theoretical move: This passage consists of scholarly endnotes for chapters on the Four Discourses, Psychoanalysis and Science, and an Afterword — it is largely bibliographic and referential, but contains several load-bearing theoretical asides: that the specific ordering of mathemes in the Four Discourses is constitutive (not merely combinatorial), that object (a) is the remainder left over after science's symbolization of the real, and that there is always a limit to formalization.

Note that other discourses than the four discussed here could be generated by changing the order of the four mathemes used here.
#189

The Lacanian Subject: Between Language and Jouissance · Bruce Fink · p.125

There's No Such Thing as a Sexual Relationship > **"There's no Such Thing** as a **Sexual Relationship"**

Theoretical move: Lacan's formula "there's no such thing as a sexual relationship" is grounded in the claim that masculinity and femininity are defined separately and differently with respect to the symbolic order—not in relation to each other—such that each sex has a distinct mode of alienation by language and a distinct form of jouissance, making any direct complementary relation between them structurally impossible.

I will attempt first to briefly explain the main outlines of his theory, only then proceeding to a discussion of the mathemes which pose a serious obstacle to certain readers at the outset.
#190

The Lacanian Subject: Between Language and Jouissance · Bruce Fink

Psychoanalysis and Science > **Probability and Possibility**

Theoretical move: By working through Lacan's second-order combinatory matrix, Fink demonstrates that the symbolic apparatus generates a distinction between probability and possibility ex nihilo: certain combinations are structurally impossible regardless of empirical probability, and the matrix's real theoretical yield is the syntactic law—the grammar—it produces, which parallels the structure of language.

One of the conclusions that can be drawn from Lacan's second-order matrix is that... certain of the letters defined, namely β and δ, can never turn up more than 50 percent of the time.
#191

The Odd One In: On Comedy (alt. ed.) · Alenka Zupančič · p.123

part iii

Theoretical move: Žižančič argues that Bergson's formula of the comic (the mechanical encrusted on the living) is both too broad and philosophically pre-loaded with an aprioristic dualism; the truly radical move is to locate the "mechanical" not as one of two independent poles but as the very *relationship* between any two poles, and further, that comic imitation reveals automatism as the site of singularity rather than its absence.

He (convincingly) proposed this couple as the real core or the 'matheme' of all the others.
#192

The Parallax View · Slavoj Žižek · p.40

The Birth of (Hegelian) Concrete Universality out of the Spirit of (Kantian) Antinomies > The Master-Signifier and Its Vicissitudes

Theoretical move: The passage argues that the Master-Signifier operates as a reflexive "quilting point" that transforms disorder into order without adding positive content, and that objet petit a functions as the "transcendental scheme" of fantasy mediating between the formal symbolic structure and the positivity of objects in reality — thereby explaining how ideology schematizes desire and hegemonizes the void left by the primordially repressed binary signifier.

The passage to truth is therefore the passage from language... to letter, to 'mathemes' which run diagonally across a multitude of worlds.
#193

The Shortest Shadow: Nietzsche's Philosophy of the Two · Alenka Zupančič · p.119

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.

analytic discourse is the Lacanian matheme for the discursivity of the event as that which appears as the reverse side of any discourse or discursivity.
#194

Žižek Responds! · Todd McGowan & Dominik Finkelde (eds.) · p.322

Žižek Responds! > [Rethinking Lacan’s Unthinkable “Thing”](#contents.xhtml_ch14)<a href="#14_harpos_grin_rethinking_lacans_unthinkable_thing.xhtml_en14-1" id="14_harpos_grin_rethinking_lacans_unthinkable_thing.xhtml_nr14-1">1</a>

Theoretical move: The passage argues that *objet a* and *das Ding* form a two-fold ontic-ontological dynamic: the *objet a* functions as the obstinate objective clue (the ontic "odd feature") that opens onto the abyssal void of *das Ding* (the ontological Real), thereby reversing Žižek's own formulation; and that *das Ding*, linked to the mother's inscrutable desire and mediated by the Name of the Father / signifier, is ultimately "extimate" — the Thing in the Other mirrors an unthinkable excess within the subject itself.

We might even read this dynamic into Lacan's matheme of the fantasy: $ <> a.
#195

What Is Sex? · Alenka Zupančič · p.38

… and Even Stranger out There > The Anti-Sexus

Theoretical move: Zupančič uses Platonov's fictional Anti-Sexus device to demonstrate that enjoyment and the Other are irreducibly co-implicated (each is "in" the other), making the non-relation not an absence of relation but a constitutive bias or curvature of discursive space—and thereby refuting both the revolutionary fantasy of liberating humanity from sexuality and the liberal-democratic ideology of neutral pluralism.

here we come to the very 'matheme' of the Anti-Sexus device, which I propose to formulate as follows: 'to make oneself masturbated,' 'se faire masturber'
#196

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, and all this (including the clinical practice of la passe) is based upon the idea of an integral transmission, a transmission without any rest.
#197

What Is Sex? · Alenka Zupančič · p.78

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.

A matheme is not simply a formalization of some reality; rather—and as Lacan himself puts it—it is the formalization of the impasse of formalization.
#198

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.

the taste for 'sophistry' (plays on words, equivocation, neologisms…) and formal rigorism (formulas, mathemes, topology)