An Attempt to Integrate the Lacanian Formalism into Generative Relational Being
ENGLISH
An Attempt to Integrate the Lacanian Formalism into Generative Relational Being
Wanhong Huang (huangwanhong@serendip.ngo)
Abstract
Theories of value generation and of distributive justice presuppose that participants can recognize a relation as reciprocal and can identify extraction as extraction. These are interpretive capacities, and they are assumed throughout and explained nowhere. Inferentialist accounts of normative practice describe the keeping of deontic score and leave the participants’ investment in the score unaccounted. No available framework in governance or economics explains why participants sustain the very relations that damage them.
Psychoanalysis supplies such an account, and this paper asks what may be taken from it and at what price. The apparatus is separated into three levels, the phenomena it addresses, the concepts it deploys, and the calculus of primitives in which those concepts are written, and each is examined for derivation, translation, or refusal.
The results are asymmetric. Three central mathemes are derived: the Other is what composition produces, the barred subject is an occupancy with nonzero residue, and the signifier of the barred Other is the non-coincidence of a position with its own claim. They are shown to stand in one process that the source lacks, in which the master signifier conceals the barring of the Other. Two primitives are dissolved: the object-cause of desire is the residue of an operation, hypostatized by a theory with nowhere to put it, and the lozenge proves undefinable for relating a subject to that reification. One posit is refused with argument: the Real reintroduces an exterior, and its phenomena admit a better account as structural exclusion.
One consequence reaches beyond the source. The attempt to make occupancy exact operates at the level of the order, where it is domination, and at the level of the participant, where it is exploitation. This yields a derivation of a condition that theories of generative justice have identified and left underived: a configuration providing no locus at which a participant’s excess can register consumes the capacity by which it would go on generating.
The unifying operation is identified and left undefined. Every occurrence of the bar in the source calculus marks one thing: composition fails to close. Its formal identity is stated as the central open problem, with four constraints on any candidate.
Keywords: relational structure; subject position; composition; non-closure; psychoanalytic formalism; normative emergence.
A note on the standing of this paper. The paper reports a mapping that succeeds at some points, fails at others, and is undefined at the point on which everything else depends. The failures are reported at the same length as the successes. A mapping in which everything mapped would have discovered nothing, and the refusals in §11 are the evidence that the derivations in §6 amount to more than redescription.
Nothing here endorses psychoanalysis as a theory of mind, and nothing here depends on such an endorsement. The apparatus is used because it is currently the best available account of a phenomenon that the framework’s own commitments require it to explain. Should a better account appear, the framework adopts it. The move is principled. A framework holding that all normative structure is historically generated and revisable cannot exempt its own theoretical resources from that condition, so the choice made here instantiates the thesis argued in the companion paper.
The author would welcome objection and correction, particularly from readers who can show that the operation left undefined in §13 is not an operation at all. Correspondence is welcome at huangwanhong@serendip.ngo.
Statement on the use of artificial intelligence. The arguments of this paper were developed in extended dialogue with artificial intelligence systems (OpenAI’s ChatGPT and Anthropic’s Claude). The dialogue shaped the substance of the arguments and did not confine itself to matters of drafting or of language. Several of the paper’s central claims arose within it, and several were corrected within it, in both directions.
The author is the sole author, and takes full responsibility for every claim made here, for every argument advanced in support of a claim, and for every error that remains.
The disclosure is made in the ordinary interest of transparency, and it carries a further significance that the paper’s own commitments require us to state. This paper holds that concepts are determinations of relational configurations, generated at positions, bearing the marks of their generation, and revisable in the historical process that produced them. A theory so committed can hardly treat the provenance of its own concepts as a matter to be passed over. The concepts advanced here were generated in a particular configuration, at a particular moment, by participants of more than one kind. That is a fact about them, and the account offered in these pages predicts that it should be. We report it, in place of concealing it, because concealment would be the first refutation of what we argue.
Part I. The Problem
§1 The Lacuna in the Available Frameworks
The gap in theories of generative circulation
Theories of generative justice are organized around an explanatory chain: material interaction produces value, value circulates, and justice consists in the circulation returning value to those whose activity produced it, in place of permitting its alienation (Eglash 2016). The chain is strong at every link, and the political content is real. Extraction is named as a category of injustice, and the naming carries normative weight.
One step lies outside the chain. Between the generation of value and the demand for its return there lies a capacity: the producer must recognize the value as theirs, must identify its non-return as extraction where exchange would also fit the facts, and must experience the alienation as a wrong. These are interpretive achievements, and they follow from no material relation. A theory that begins at material interaction and ends at justice has passed over them.
The capacity is present often enough. The difficulty is that the theory assumes it, and the assumption becomes visible precisely where the capacity fails. The historical record is dense with cases in which those from whom value was extracted experienced the extraction as no wrong at all, defended the arrangement that consumed them, and identified with the position that impoverished them. A theory that assumes the recognitive capacity has no account of these cases, and they are common. They are the ordinary condition of what has been called ideology.
The gap in theories of authorship
The same difficulty is visible, and has been noticed, in accounts of ethical standing organized around authorship: a norm one can recognize as one’s own has a standing that a norm merely imposed does not (Mazouz 2019). The move from ownership to authorship is a real advance, and it is a tell. Ownership is a relation to a thing. Authorship is a relation to a meaning, and meaning has no material substrate.
Authorship, like recognition, is presupposed. The account leaves unaddressed what makes a participant the kind of being who can author, and what determines whether a given participant occupies a position from which authorship is available at all. It begins with subjects already capable of authorship and asks how norms may be made theirs.
The gap in inferentialist accounts
Accounts of normative practice in the inferentialist tradition supply what the two preceding lack in one respect: an explicit mechanism by which normative status is instituted, namely the practical attitude of taking participants to be committed and entitled, and the keeping of score on those commitments (Brandom 1994). Norms are not imposed from outside; they are instituted in the practice of holding one another to them.
This comes very close to what is required, and the closeness makes the remaining gap instructive. Two things are absent. First, the account explains neither the arising of scorekeeping practices where they arise nor their degradation. The practice is described; its emergence and its decay are left dark. Second, and more seriously here, the scorekeeper has no libido. Nothing in the apparatus explains a participant’s investment in the score, identification with a position, or attachment to a status that damages them. The subject of inferentialism is a creature of commitments and entitlements, and it has no attachments.
The gap in economic accounts
Mainstream economic accounts treat preferences as exogenous. An agent has a preference ordering, acts on it, and the question of where the ordering came from lies outside the model. The exclusion is a methodological decision, defensible for many purposes.
It is indefensible here. A theory undertaking to explain how participants come to want participation in generative relations, or how they come to identify extraction as unjust, cannot take the wanting as given. The preference is what is at issue.
The explanandum, stated narrowly
The four gaps converge on a single phenomenon, and the paper’s use of the psychoanalytic apparatus is licensed by that phenomenon and by no other. Narrowness in the statement is essential. A licence stated broadly (“subject formation,” “desire,” “the symbolic”) licenses everything and thereby nothing.
The explanandum. Why do participants sustain the very relations that damage them?
Rational choice cannot answer: preferences are given, and given preferences that produce self-harm are simply irrational, at which point the model has stopped explaining. Theories of generative circulation cannot answer: they show that value fails to return, and must then assume the producer experiences this as a wrong. Inferentialism cannot answer: scorekeeping without investment has no account of attachment.
What is required is an account of the subject’s attachment to the position that constitutes it, including where that position is destructive. This is the grip of ideology; it accounts for the difficulty of generating counter-power; and it accounts for alienation being characteristically experienced as one’s own inadequacy in place of a structural fact.
The requirement is load-bearing, and it is ornamental in no degree. Any normative theory demanding of participants that they re-open a monopolized interpretive position owes an account of their persistent refusal.
§2 The Terms of the Borrowing
Not truth, but adequacy to a problem
The apparatus is used, and it is not endorsed. It is the best available account of the phenomenon isolated in §1, and no rival tradition presently does that work as well. The claim is comparative and defeasible, and it is offered as such.
The footing is required by the framework’s own commitments. If all normative structure, theoretical structure included, is historically generated and subject to revision, a theory may not exempt its own resources from that condition. To say “we build on this because it is true” would claim a standpoint outside history that the framework has independently argued to be unavailable. To say “we use it because it currently works, and we expect it to be superseded” is consistent with the framework’s content and honest about the framework’s status.
The relation is vertical
One structural fact determines everything that follows. Psychoanalysis begins with a symbolic order that is already there. The chain of signifiers, the locus of the Other, the function that institutes the law: these are given at the outset of the analysis and receive no explanation from it. Psychoanalysis theorizes what happens to a subject who enters a symbolic order. It offers no theory of how symbolic orders arise, and claims none.
The framework developed here takes up the prior question: the generation, by relational configurations, of the positions that subsequently become symbolically occupiable. The two therefore stand in no competition, and the question of importing one into the other is malformed.
The present framework stands upstream. It supplies what the psychoanalytic apparatus presupposes. Neither competition nor dependence obtains between them: the apparatus is a theory of a level whose emergence the present framework attempts to explain, and it is accordingly neither a foundation to be adopted nor a rival to be refuted.
The claim is demonstrated in Part III. The demonstration consists in deriving three of the apparatus’s central primitives from composition, and in exhibiting a process relating them that the apparatus lacks.
The single thesis taken, and its safety
One thesis is taken directly, and its safety follows from its being common property. The subject is constituted in the occupying of a position, and stands posterior to it. This is common ground across the psychoanalytic, the Althusserian, the performative, and the pragmatist traditions (Althusser 1971; Butler 1997; Mead 1934), and it is Hegelian in origin. Convergence across four independent traditions is evidence of robustness, and the appropriate citation practice attributes the convergence in place of any one of its members.
Discipline
Two rules govern the use of the apparatus throughout, and they are stated in advance so that violations may be detected.
- The mechanism is stated in the framework’s own terms. A claim expressible only in the vocabulary of the Real, the object-cause, or the four discourses is a claim the framework has failed to make its own. It would be the apparatus, and would fall with it.
- The refusals are load-bearing. A mapping in which every term found a counterpart would be evidence of nothing, since a sufficiently elastic vocabulary absorbs anything. The value of the mapping in Part III depends entirely on the existence of what fails to map, catalogued in §11.
Part II. The Framework
§3 The Form of the Inquiry
No ontological commitment is made
The framework asserts nothing about what exists. It withholds, in particular, the claim that relations are prior to entities, and none of its arguments requires that claim. It specifies its object structurally, in the discipline of a group specification: whatever the relata may be, the theory concerns their composition, and the question of what a relatum ultimately is fails to arise within it.
The analogy is exact, and it is more than decorative. Group theory neither denies nor affirms that group elements have intrinsic natures. It concerns closure, associativity, identity, inverse. A group is specified up to isomorphism, and the question “but what is g, really?” receives no answer, the theory requiring none. The non-arising of the question is a feature of structural specification, and it counts as no defect.
Structural specification. The framework quantifies over relations and their composition. It quantifies over the identity of the relata not at all, and its results are independent of that identity. Whether the participants are persons, institutions, practices, or something else, and whether they possess natures independent of their relational positions, is left open. The leaving-open is principled, and it is not an evasion.
The discipline has a cost, and it is paid explicitly in §11. A framework that withholds ontological commitment may not then import an apparatus whose principal recommendation is the possession of one. The Real is an ontological posit, and it is refused for this reason among others.
Coherence of the general shape
That a determinate structure can emerge from composition alone, without the theory saying what it is a structure of, is not merely conceivable. It is realized in working formalisms. In group field theory the field is defined on a group manifold, the theory’s content is the combinatorics of composition, the specific group elements are integrated over, and discrete geometry emerges from the combinatorial structure of the interactions (Oriti 2014). Spacetime, on such an account, is not made of anything. It is what a composition structure looks like when it condenses.
The lesson drawn is methodological and nothing more. It demonstrates the coherence of the general shape, and it shows that a theory in which the substance question fails to arise remains complete in the only sense that matters.
Caveat. The limit must be named, on pain of the analogy becoming theft. Group field theory possesses an action, a vertex, and a specified composition rule. The present framework possesses a picture of one. The analogy therefore establishes coherence and stops short of achievement, and any claim beyond coherence would borrow the credibility of a formalism that has never been written. The gap is the subject of §13.
§4 Composition, Positions, and Occupancy
Composition generates positions
Position. Let R be a set of relations on a configuration, and let ∘ denote their composition. A position is a structural locus generated by composition: it is a place in the configuration determined by the composite, and it is occupied by none of the relata that compose it. Formally, if r₁, r₂ ∈ R, the composite r₂ ∘ r₁ determines a locus π that is not identical to any relatum of r₁ or of r₂.
The claim that carries the framework is that what is borne at a position is borne by no relatum. Bindingness, authority, value, and identity are properties of positions, and they are properties of no participant. This accounts for the persistent failure of theories that seek them among the properties of entities, and the accounting appeals to structure in place of any deficiency in those theories’ ingenuity.
The dyad is pre-normative
Insufficiency of the dyad. A configuration containing exactly two relata and one relation between them lacks the resources to distinguish sanction from aggression.
Argument. Let A and B be the relata and suppose A acts against B. The configuration contains A’s stance toward B and B’s toward A, and nothing further. Characterizing the act as sanction requires a locus from which the characterization can issue; the dyad supplies only its two poles, each of which is a party to the act. B may take the act either way, and the configuration contains nothing that settles the matter. The characterization is accordingly unavailable within the dyad.
We label this a claim and its support an argument, and the labels are deliberate. The reasoning is not a proof, and the terms in which a proof might be given, what a configuration is, what composition does, are undefined until §13 is answered.
The claim yields a prediction that is roughly falsifiable and that we believe true: purely dyadic configurations generate no norms. They generate habit, dependence, rivalry, and force.
A causal route, not a viewpoint
An objection arises immediately, and it must be met before the symbolic material is introduced, since meeting it afterwards is impossible. Suppose that to be seen as doing something is already to be characterized, that characterization subsumes an act under a category, and that categories are symbolic. Then the third position requires language, normative structure begins with language, and the framework is idealist. The objection is standard, it is serious, and should it hold, the framework collapses.
The reply turns on what the third position does at minimum. The third differentiates before it classifies: the act acquires a second aspect, how it stands from a locus that is neither party, and this aspect obtains prior to any category being applied to it. Differentiation of this kind requires only that the act have consequences which run through the third.
The reply is partial and its partiality is stated in the caveat on bindingness below. It establishes that a locus can exist and be causally live without language. It leaves open whether a locus so occupied supports full bindingness, or only the weaker structure of an act being costly by a route the agent does not control.
The third position is a causal route, not a viewpoint. If A stands in relation to B and B to C, then A’s act upon B has consequences that reach A by way of C. The route is the position. It is a structural fact about the configuration, obtaining whether or not any participant can articulate it, and it is generated by composition.
The route is occupied when it is live, and occupancy admits of strata, distinguished by the durability of the characterization each supports:
- Composition generates the route. Structural; pre-symbolic; obtains in any configuration with three or more nodes and transitive consequence.
- Witness makes the route live and episodic. The characterization holds while the third is present and lapses in its absence. The presence of an observer alters the conduct of a conflict, and the observer says nothing. Most non-human sociality sits here.
- Speech makes the route persistent. The characterization survives the absence of the third, having been deposited, and it admits of transmission, recall, and invocation.
- Institution and writing make the route persistent across generations, absence, and death.
- Reinterpretation re-opens the route where it has been closed to an occupant.
The locus of the Other requires no separate act of institution. It is a witness that need not be present. Speech adds persistence to a locus that composition has already produced, and the framework is on this account a materialism: normative structure originates in causal architecture, and language renders it durable.
Caveat (bindingness). The concession is stated, and it is hidden nowhere, and it is a real one. The pre-symbolic stratum secures that positions exist and are occupiable without language. It leaves unsecured that pre-symbolic occupancy produces full bindingness. The ought, as distinct from the merely costly, may arrive only with the durable third.
Should that be so, the framework’s position weakens to the following: proto-normative structure is pre-symbolic, and normative structure proper requires the durable third. This remains a materialism, the durable third being explained where it might have been presupposed, and it concedes to the psychoanalytic account something we should have preferred to withhold. We prefer the concession to a fabrication.
Occupancy constitutes the occupant
The framework’s second load-bearing claim concerns the occupying of a position. The occupant is constituted in that occupying, and exists in no way antecedent to it.
Occupancy. Let π be a position and let σ denote the operation of occupying it. Then σ(π) is the subject constituted in that occupancy. Position and subject come into being in one act: the interpretive inhabiting of the locus and the constitution of the inhabitant are simultaneous, and they are inseparable.
Separating them reinstates the very assumption that §1 identified as the common defect of the available frameworks: a subject who exists first and interprets afterwards.
Sanction and aggression. These differ neither in force nor in structure. They differ in whether the structure is inhabited.
This resolves the difficulty that defeats behavioural reductions of normative expectation. A disposition to sanction, described purely behaviourally, is indistinguishable from a disposition to aggress, since the description mentions only the acts of the sanctioner. What makes an act a sanction is a fact about the act’s position in a configuration whose third locus is inhabited, and it is a fact about the sanctioner in no respect.
Part III. The Mapping
§5 Method
The apparatus is decomposed into three levels and each treated separately. Conflating them produces uncritical adoption and uncritical dismissal alike.
- Phenomena. The explananda of the apparatus. These are common property, and the framework owes an account of each, or an account of why each dissolves.
- Concepts. The explanatory notions deployed. These may be derived, translated, or refused.
- Calculus. The primitives and their formation rules. The question at this level concerns what a symbol does in the system, which is more informative than what its author meant by it.
§6 Level One: Concepts Derived, Not Borrowed
At this level the framework derives, and the derivations constitute the evidence for the upstream claim of Part I. It imports nothing.
| Source concept | Framework counterpart | What the framework supplies |
|---|---|---|
| The Other (A); locus of the signifier | The third position: a locus occupied by no party, from which acts are characterized and subjects addressed | Where it comes from. It is posited there; here it is what composition produces. |
| The imaginary; the specular relation | The dyad (insufficiency of the dyad, §4) | Why the dyad yields rivalry, aggression, and misrecognition: there is no locus from which either party can be characterized except by the other. Independent derivation of the same result. |
| The symbolic | A configuration containing occupiable third positions | The registers become structural properties of configurations, where the source made them ontological orders. |
| Subject as effect of the signifier | Occupancy constitutes the occupant | Convergent, but common property. Cite the convergence, not the source. |
| Manque; non-coincidence | Position-generation and subject-constitution do not commute (§8) | The residue is read as symptom there and as the source of generation here. This is the borrowing and the break at once. |
| The paternal function; the institution of the law | Composition instituting the third position | A function is named, and its origin is given a genetic account and no derivation. The framework locates the origin in composition. Whether it possesses a mechanism, as against a picture of one, is settled by §13 and is presently open. |
| Alienation | Alienation of interpretation: constituted as the one who is read where they might have been reading | Nearly exact; the framework makes it political, a distribution of positions, where the source made it ontological, a condition of subjecthood as such. |
| Separation | Counter-power; the barring of the position itself (§8) | Alienation taken without separation is fatalism. This is the mechanism of contestation. |
Table 1. Level One. Concepts derived, and not borrowed.
§7 Level Two: Concepts Translated, With Loss
Here the phenomenon is taken, the vocabulary refused, and the semantic shift recorded.
| Source concept | Translation | What is lost or altered |
|---|---|---|
| Desire | The residue’s action on the configuration | Structure retained: desire is positional and does not originate in the individual. Vocabulary discarded: it imports the clinic. |
| Desire is the desire of the Other | Desire is structured by position and does not originate in the individual, and no further | Half is refused. The full thesis renders desire wholly derivative, so that everything circulates within an already-given field and there is nowhere for the genuinely new to arise. A theory of historical change requires what the full thesis withholds. |
| Jouissance | Attachment to the position that damages (the explanandum of Part I) | This must not be discarded. It is the only element of the apparatus that does the required work. The phenomenon is retained; the word is not. |
| Point de capiton | Interpretive fixation; the singularization of the Other (§9) | Exact structural match. The framework asks who benefits from the fixation. The apparatus does not. |
| Interpellation (Althusser 1971) | Occupancy as constitution | Retained for the political register, where it is legible and says the same thing. |
| Schema L | A relational network in which the dyadic axis blocks the triadic | Retained, reinterpreted. It is graph-theoretic already, and what it draws is the insufficiency of the dyad (§4): the imaginary axis short-circuits the route through the third. |
Table 2. Level Two. Phenomena taken, vocabulary refused.
§8 Level Three: The Calculus
The unlocking observation
Read as a formal system, in place of a doctrine, the calculus discloses something its author left unstated. The bar appears at three sites: over the subject, over the Other, and as the fraction bar of repression. At every occurrence it marks one thing: something exceeds what represents it. The subject exceeds its position; the Other exceeds its claim to completeness; the chain exceeds the signifier that anchors it.
The bar is one operator, applied at three sites. Write it ⊖. The source never specifies it, and the source cannot, having no theory of composition. The framework supplies the composition, and the bar becomes the measure of its non-closure.
The move is a reading of the notation as a calculus, and it is more than a translation. It finds one primitive operation in the apparatus, and finds it unspecified there.
The primitives, by structural role
| Symbol | Role in the calculus | Framework semantics | Verdict |
|---|---|---|---|
| A | The field within which everything is placed | The composed configuration; the closure of composition over relations | Derived |
| S₂ | The chain; the relata as related | The relations, composed | Derived |
| S₁ | The term that anchors; it characterizes and is not characterized | A position that composition does not reach. The formal signature of a frozen order; interpretive monopoly written as a matheme | Derived |
| S̄ | A distinguished entity marked by the bar | An occupancy with nonzero residue: σ(π) ⊖ π ≠ 0. The bar marks a wound there and an engine here: the residue acts back | Derived |
| bar | Applied to S, to A, to the fraction | ⊖: the failure of composition to close | Derived; one operator, three sites |
| S(Ā) | The signifier of the barred Other; the order has a hole | π ≠ π*, where π* is the position as it claims to be. This is separation (§8) | Derived |
| a | What the bar leaves behind, reified as an object | The residue ρ, hypostatized. See §10 | Dissolved |
| → | Production, address, transformation; deliberately unspecified | Composition: r₂ ∘ r₁ | Derived; the framework must specify what was left ambiguous |
| ◇ | Relates S̄ to a; notoriously undefined, and scholars disagree | No counterpart. It relates a subject to a reified residue; undo the reification and there is nothing left to relate | Dissolved |
Table 3. Level Three. The primitives read as a calculus.
The non-coincidence, formally
Non-coincidence. Let π be a position generated by composition and σ(π) the subject constituted by occupying it. These are two operations, and they do not coincide:
σ(π) ≠ π, ρ = σ(π) ⊖ π.
The residue ρ acts back on the configuration. Its type differs from that of its inputs: it is neither a position nor a subject.
The bar is the statement ρ ≠ 0.
Separation: the non-coincidence runs on both sides
An objection would otherwise sink the mechanism. Occupancy constitutes the subject; the subject nevertheless acts against the position that made it; and the source of contestation, given that the contester is a product, remains obscure.
The non-coincidence is two-sided, and that is the answer. The subject departs from what its position specifies, and the position departs from what it presents itself as being.
The barring of the position. Let π* denote the position as it claims to be: complete, authoritative, exhaustive. Then
π ≠ π*, σ(Ā) = π* ⊖ π.
The interpretive position lacks the answer and lacks completeness. Its completeness is a claim it makes, and it is a property it has in no degree.
Counter-power begins in the exposure of the order’s incompleteness. It begins in no assertion of a prior freedom by the subject, there being none to assert.
A corollary explains something real: domination fears exposure more than disobedience. A disobedient subject can be punished, and the punishment reconfirms the order’s authority to characterize. An order shown to lack the answer has lost the locus from which punishment could be characterized as punishment at all.
The formulae, and the mechanism the source lacks
The three derived mathemes are moments of one process, and they stand as three separate structural facts only in the source. Exhibiting the process is what the upstream claim of Part I amounts to.
S₁ is the attempt to make π = π*. The master signifier exists in order to conceal the barring of the Other.
Composition generates π. The position is non-coincident with what it claims to be: S(Ā). A configuration that cannot bear this exposure installs a locus that composition does not reach, which characterizes without being characterized: S₁. That installation forecloses reinterpretation. The generation of normative structure ends, and the configuration thereafter persists by reproduction rather than by generation. The residue ρ, which is structural and cannot be abolished, returns under a name: deviance, madness, sedition, heresy, crime.
In the source these stand side by side as separate structural facts. Here they compose one process.
§9 Power and Its Ossification
Power is asymmetry; interpretive monopoly is a kind of it
An overreach must be corrected before it propagates. Power is asymmetry in a relational configuration, and asymmetries come in kinds: material (control of resources), structural (brokerage, position in the network), and interpretive (occupancy of the locus from which acts are characterized). Interpretive asymmetry is one kind among these, and it supplies no definition of power as such.
It differs in one respect, and the difference is the claim:
Interpretive asymmetry is the asymmetry whose monopolization forecloses the correction of all the others. Monopolize the locus from which acts are characterized, and resistance is characterized as deviance, grievance as ingratitude, counter-power as sedition. The interpretive position is where the other asymmetries are adjudicated.
The conversion sequence
Observation (the mechanism of ossification).
(i) Generation produces material and structural asymmetry necessarily.
(ii) Asymmetry converts into interpretive asymmetry contingently but reliably. Wealth purchases the press; brokerage purchases the frame.
(iii) Interpretive monopoly forecloses reinterpretation.
(iv) The generation of normative structure ends. The configuration persists by reproduction rather than by generation.
The condition restraining power accordingly targets the conversion step, and it thereby states a considerably more precise political demand than the generation of counter-power as such.
The Other is a variable
The position is generated by composition, and it is therefore artificial, contingent, and plural in principle. A configuration may sustain several such loci or one. The candidate occupants include the state, the law, the community, the market, religion, the platform, and the recommender system.
Interpretive monopoly is the singularization of the Other, and a configuration admitting only one such locus is the frozen order.
An application suggests itself and its warrant should be stated carefully. An algorithmic recommender characterizes acts, addresses subjects, and is monopolizable to a degree no prior occupant has been. Whether it occupies the locus in the framework’s sense turns on a question the framework has not settled, since occupancy was defined as constituting the occupant as a subject, and whether a recommender is so constituted is undetermined. What may be claimed without that determination is weaker and still worth stating: the recommender holds the locus against other occupants, and the singularization is the same whether or not anything inhabits what has been closed.
Exploitation as the participant-level case
The attempt to make occupancy exact operates at two levels, and naming the second completes the account of what a frozen order does.
A natural formulation of the second case fails, and the failure is instructive. It runs: a participant is instrumentalized when they are treated as exhausted by their function, and so to treat them is to make their occupancy exact. This will not do. Such instrumentalization is a stance the exploiter takes; exactness of occupancy is a condition of the configuration; and the one entails the other in no way. A proprietor may regard workers as mere labour while the configuration nonetheless leaves their positions inexactly occupiable, whereupon they organize and generate a union. The regard did nothing.
Exploitation is the condition of a configuration providing no locus at which a participant’s excess can register.
The stance of any party is beside the point. What matters is whether the residue has anywhere to arrive.
Domination attempts to abolish the non-coincidence at the level of the order; exploitation attempts it at the level of the participant. The two are one attempt at two levels. Both fail, the non-coincidence being ineliminable, and each failure leaves a residue the configuration must name. The order names its residue deviance, madness, sedition, heresy, crime. The exploitative relation names its residue laziness, insubordination, ingratitude, theft.
The consequence is functional and owes nothing to any moral premise. A configuration providing no locus for a participant’s residue has foreclosed the residue’s acting, and thereby the source of its own further generation. Such a configuration persists by consuming what it would have needed in order to generate, and that is extraction.
The literature on generative justice identified this condition (Eglash 2016). Extraction is named there as an injustice, and the naming is correct. What the mechanism adds is an account of what extraction removes, and thereby of the sense in which an extractive configuration undermines itself. It removes the locus at which the residue would have registered.
The formulation is checkable, and its checkability is the point. Where the participants of an apparently extractive arrangement organize and contest, and the contestation registers, a locus exists, and the arrangement is to that extent generative. Exploitation admits of degrees, and the degree is the availability of the locus.
Participatory constitution of subjectivity
Participatory governance permits constituted subjects to vote on rules. It leaves the positions fixed and permits movement within them. The present claim is stronger: where normative structure is generated from below, the positions themselves are remade, and participants undergo becoming in the course of deciding. The subject who emerges from a live generation of normative structure differs from the subject who entered it.
Alienation of interpretation is therefore something other than a complaint about voice. Under a top-down normative order one is constituted as the kind of subject who is heard in that way and no other, and being unheard is the least of it. The remedy lies in the re-opening of the positions, and additional voice within fixed positions supplies none of it.
Generation from below acquires no warrant of goodness from any of this, and the inference must be refused. Distributed interpretation produces lynch mobs with efficiency. The claim is that distributed interpretive capacity is a condition of normative generation, and its sufficiency is denied.
Part IV. Refusals and Limits
§10 Dissolved Rather Than Refused
Two primitives are explained, and neither derived nor rejected. The explanation is the strongest result reported here.
The object-cause of desire
a is not a concept the framework lacks. It is a concept the framework dissolves.
The bar is an operation and it produces a residue. The source, having no theory of composition, can say nothing of what becomes of the residue. It therefore names the residue and treats it as an object. An object that is the output of an unexplained operation is an object that causes while remaining unproduced, and that is exactly what “object-cause of desire” means.
On the present account the residue acts back on the configuration and composition absorbs it into new positions. It is an operation’s output, and it is no object.
a is what ρ looks like to a theory with no composition rule. It was hypostatized for want of anywhere to put it. Hence its unattainability, hence the indefinite circling of desire around it, and hence the resulting system’s standing as a theory of repetition.
A single missing operation may account for the whole of the libidinal economy.
Conjecture. The unattainability of a, the circularity of desire, and the primacy of repetition in the source apparatus are all consequences of the absence of a composition rule, and each would be dissolved by the presence of one.
The conjecture is checkable against the source texts and we have not checked it. It is offered as a research claim, and it explains where a bare refusal would only decline.
The lozenge
The lozenge resolves with it. The framework accounts for the symbol’s resistance to definition, and for the disagreement of its commentators: it has nothing to define. Undo the reification and a process remains where a relation was sought. The subject is the occupancy whose residue acts, and the lozenge is the trace of a missing verb.
The account improves on anything available in the exegetical literature, and it is produced by the mechanism where exegesis has produced only competing readings.
A false friend, flagged
Caveat (false friend). Mapping a onto ρ looks correct and is wrong. a is what the subject lacks and cannot compose; ρ is what the subject exceeds and composition absorbs. Same shape, opposite sign. The framework accordingly has no fantasy formula and requires none, its residue being possible and active.
§11 Refused, With Argument
The Real
The Real is an ontological posit naming what resists symbolization. It is refused, and the refusal is argued.
First, it reintroduces an exterior. The framework has withheld ontological commitment and has argued that the dissolution of the regress of power depends on the absence of any outside. A domain that resists symbolization, that occupies no position, that undergoes no generation, and that nevertheless has effects, is such an outside.
Second, and decisively, the framework explains the phenomena better. The residue, the unsayable, the excess, the thing that will not be assimilated: these are structural exclusion. They are the effects of configurations whose positions are unoccupiable, and their unoccupiability follows from the interpretive locus having been monopolized, destroyed, or never formed. Resistance to symbolization in principle plays no part in it. The unsayable is an artifact of the distribution of interpretive positions.
The subject under a top-down order cannot symbolize their own condition, and the reason lies in their having been constituted as the one who is read where they might have been reading. The condition touches no unsymbolizable Real.
The framework’s account is superior on two counts. It is political where the alternative is metaphysical, and it holds the residue to be produced where the alternative holds it given. Borrowing the Real converts a claim about domination into a claim about the limits of language. That is a depoliticization, and it is the standard failure mode of psychoanalytic social theory.
The most dangerous available mapping, refused explicitly: the Real must never be mapped onto novelty, rupture, or emergence. The Real names what cannot be composed; novelty here is what is composed. They are opposites. The residue is interior and productive; the Real is exterior and sterile. Map them together and generation arrives from an exterior, and the mechanism of §4 is undone.
The four discourses
The structure derives; the algebra resists. The places translate: agent (who occupies the interpretive locus), other (who is addressed), product (what the configuration generates), truth (what the configuration conceals in order to operate). The master’s discourse, with S₁ as agent and S̄ concealed beneath as truth, reads exactly as the frozen order concealing the non-coincidence of its own occupant.
Yet a appears in all four, and a has been dissolved. The algebra therefore cannot be lifted.
The temptation deserves naming, being a trap. The four discourses look like a taxonomy of relational configurations, and a framework in want of such a taxonomy will be drawn to them. Taking them admits the ontology by the back door. A typology of configurations must be derived from composition, and the derivation is a concrete task the framework has yet to perform.
The remainder
The graph of desire: rebuild, do not import. The topology is the insight and the symbols are not, and the symbols include a.
The mirror stage as developmental history: refused. It is dubious as a claim about infants and dispensable here. Retained only as a structural claim about dyads, where it is testable against the claim of the insufficiency of the dyad (§4).
The formulae of sexuation; the Borromean knot; the clinical structures: refused. Sexuation requires the logic of the exception and the not-all. The knot requires the three registers as ontological orders, which the framework has converted into structural properties of configurations.
The deep formal reason
S₁ is a term whose function is to arrest the chain. The entire source algebra is organized around a fixed point that stops the slide. The framework holds that the fixed point is death: a configuration whose positions are perfectly occupiable is a frozen order.
The source notation is built to represent precisely what the framework identifies as pathology. The reason for refusing the notation is thus structural, and it is sharper than any prudential reason could be.
§12 The Framework’s Surplus over the Source
- The origin of the Other. The source begins with it. Here composition generates it.
- The evolution of structures. The source has no answer, and the absence follows from a decision: it made the residue symptomatic where it might have made it productive. The excess returns as symptom, as repetition, as the Real, and it goes nowhere. One word, symptom or source, converts a theory of repetition into a theory of history.
- The material layer. Starvation is no signifier. A person can be starved or killed whatever the symbolic order makes of it. This occupies no position in a structure, and retaining it as an irreducible layer is what keeps the framework a materialism, in place of a structuralism carrying political vocabulary.
- Plurality of the Other, and therewith the politics of its singularization. The source takes the singular Other as constitutive; here it is political.
- A normative theory. The source apparatus distinguishes a generative order from a frozen one nowhere, since both are symbolic orders and symbolic orders are all it sees.
- Composition. The source has no operation: the chain is given, and it is built by nothing. The framework’s central missing object is missing from the source as well, and the source has no occasion to seek it, its questions lying downstream of where the object would be required.
- A semantics for the notation. The mathemes are criticized for underdetermined meaning and their commentators disagree over every symbol. The framework supplies an explicit relational semantics, and it thereby shows two of the primitives to be artifacts of the missing operation.
The relation, in one sentence. Psychoanalysis theorizes the fate of a subject inside a symbolic order already there. The present framework theorizes the generation, occupation, freezing, and regeneration of symbolic orders. The source supplies the psychic mechanics of occupancy; the framework supplies the composition that produces what is occupied, and the dynamics of its change.
§13 The Central Open Problem
⊖ is undefined
The operator appears at three independent sites and three separate derivations demand it. It has been used throughout as though “the residue of x over y” were well-formed. The expression is ill-formed. Whether the operator is a difference, a quotient, a coequalizer, or an object with no name remains unknown to us.
Open Problem. Define ⊖.
What is known about it, and the constraints are jointly restrictive:
- It is one operation appearing at three sites. Every bar is the same bar.
- It is defined on the pair (position, occupancy) and on the pair (position, position-as-claimed).
- Its output differs in type from its inputs. The residue is neither a position nor a subject; it is what acts on the configuration.
- It is what makes composition fail to close. It therefore stands outside the algebra of relations, as the measure of that algebra’s non-closure.
Constraint (4) is strong and it points somewhere. An operation whose output measures the failure of closure of the structure on which it is defined is, roughly, a boundary or an obstruction class. We say “roughly” and mean it. No cohomological reading is claimed here, none having been earned.
The requirements on the composition rule
The rule sought must do two things: generate positions, and fail to close on them.
A rule producing perfectly occupiable positions produces a dead structure: the fixed point, the frozen order. The generative rule is one whose closure is imperfect.
A group is thereby excluded, since composition in a group closes exactly. The exclusion is narrower than we should like: it eliminates one candidate and leaves standing several others, structures whose composition is partial, whose associativity holds only up to coherent isomorphism, or in which composing twice fails to vanish and the deviation is what is measured. Which of these, if any, is the object is undetermined. What has been established is a formal property of the target, and formal properties are searchable.
One gap, four masks
The mechanism gap, the formalism gap, the multi-scale gap, and the emergence gap constitute one problem wearing four masks.
No mechanism without it. Composition must generate positions; the rule by which relations compose remains unwritten.
No formalism without it. Absent a composition rule, formal vocabulary is all that remains to be formalized.
No account of scale without it. The renormalization group acts on a theory possessing a specified composition and a specified scale, and the framework possesses neither. The difficulty lies deeper than a technique awaiting application: the object on which it would act has yet to be constructed.
An honest statement of standing
Caveat. Three derivations depend on an operator we cannot define. The situation admits two readings: a real object awaits discovery, or we have been writing suggestive symbols and calling the result mathematics. We cannot presently tell which, and we say so in preference to dressing the difficulty.
What can be claimed is narrower. The operator is constrained from four directions at once and performs the same work at three independent sites, and this exceeds what was known when the inquiry began. The problem has been given a form in which an answer is conceivable, and it has received none.
§14 Conclusion
The mapping succeeds at some points and fails at others, and both are reported.
Three central mathemes are derived: the Other as the locus composition produces, the barred subject as an occupancy with nonzero residue, and the signifier of the barred Other as the non-coincidence of a position with its claim. They are shown to stand in one process, the master signifier concealing the barring of the Other, the foreclosure of reinterpretation, and the return of the residue under the name of crime, and the framework supplies that process where the source supplies none. This constitutes the claim that the framework stands upstream, and it is a demonstration, standing above the assertion it began as.
Two primitives are dissolved: the object-cause of desire is the residue of an operation, hypostatized by a theory with nowhere to put it, and the lozenge resists definition, relating as it does a subject to that reification. A single missing operation may account for the libidinal economy entire, and the conjecture awaits testing against the texts.
One posit is refused: the Real reintroduces an exterior, and the phenomena it addresses admit a better explanation as structural exclusion, which is political where the Real is metaphysical, and which holds the residue produced where the Real holds it given.
The operation on which all of this rests remains undefined. It is one operator appearing at three sites, its output differs in type from its inputs, and it measures the failure of composition to close. The exclusion of the group is the most useful thing the inquiry has established, and defining the operator is the work this paper identifies as next.
The apparatus has been read as a calculus, in place of a doctrine. What was found is that it turns on one operation, left unspecified there, and that the present framework requires the same operation and cannot yet write it.
References
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Brandom, R. B. (1994). Making It Explicit: Reasoning, Representing, and Discursive Commitment. Harvard University Press, Cambridge, MA.
Butler, J. (1997). The Psychic Life of Power: Theories in Subjection. Stanford University Press, Stanford.
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Mazouz, N. (2019). Authorship, agency, and the grounds of ethical standing.
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Oriti, D. (2014). Group field theory as the second quantization of loop quantum gravity. Classical and Quantum Gravity, 33(8): 085005.
中文
将拉康的形式主义整合入生成性关系存在的一次尝试
黄万宏 (huangwanhong@serendip.ngo)
摘要
价值生成的理论与分配正义的理论预设：参与者能够把一段关系辨认为互惠的、并能够把榨取辨认为榨取。这些是解释性的能力，而它们自始至终被假定、却无处被解释。对规范性实践的推论主义说明描述道义记分的保持、却把参与者对那记分的投注留而不予说明。治理或经济学中没有任何可得的框架解释为何参与者维系那些恰恰损害他们的关系。
精神分析供给这样一个说明，而本文追问可从它取得什么、以及以什么代价。这一装置被分离为三个层级，即它所处置的诸现象、它所部署的诸概念、以及那些概念被写于其中的诸原语之演算，而每一个都为推导、翻译或拒绝而被审视。
结果是不对称的。三个中心的数元（matheme）被推导：大他者是组合所产生者，被划杠的主体是一个有非零余数的占据，而被划杠之大他者的能指是一个位置与它自己之主张的不重合。它们被显示为立于一个源头所缺乏的单一过程之中，其中主人能指遮蔽大他者之被划杠。两个原语被溶解：欲望的对象-成因是一个运算的余数，被一个无处安置它的理论所实体化，而菱形被证明对于把一个主体关联于那一实体化是不可定义的。一个设定被带着论证拒绝：实在界重新引入一个外部，而它的诸现象容许一个作为结构性排除的更好说明。
一个后果伸出源头之外。使占据变得精确的尝试在秩序的层级上运作，在那里它是支配，而在参与者的层级上运作，在那里它是剥削。这产出一个对某个条件的推导，而生成性正义的诸理论已辨认那条件、却把它留为未被推导：一个不提供任何参与者的余额可在其上登记之处所的配置，消耗那它本会据以继续生成的能力。
那统一的运算被辨认、并被留为未定义。源头演算中那杠的每一次出现都标记一件事：组合未能闭合。它的形式身份被陈述为中心的敞开问题，附以对任何候选者的四个约束。
关键词： 关系性结构；主体位置；组合；非闭合；精神分析形式主义；规范性涌现。
关于本文之地位的一则说明。 本文报告一个映射，它在某些点上成功、在另一些点上失败、并在其余一切所依赖之点上未被定义。诸失败以与诸成功相同的篇幅被报告。一个其中一切都被映射的映射本会发现无物，而§11中的诸拒绝是§6中的诸推导多于重新描述的证据。
此处没有任何东西背书精神分析作为一种心灵理论，而此处没有任何东西依赖于这样一个背书。这一装置被使用，因为它当前是对某个现象的最佳可得说明，而框架自己的诸承诺要求它去解释那现象。若一个更好的说明出现，框架便采纳它。这一举动是有原则的。一个持有“一切规范性结构都是历史地被生成的、并是可修订的”之框架，无法把它自己的诸理论资源豁免于那一条件，因而此处所作的选择例示了那在姊妹篇中被论证的论旨。
作者会欢迎反驳与纠正，尤其来自那些能显示§13中被留为未定义的那个运算根本不是一个运算的读者。欢迎在 huangwanhong@serendip.ngo 通信。
关于人工智能之使用的声明。 本文的诸论证是在与人工智能系统（OpenAI 的 ChatGPT 与 Anthropic 的 Claude）的延展对话中被发展的。那对话塑造了诸论证的实质，而并不把自己限于起草或语言之事。本文的若干中心主张在其中升起，而若干在其中被纠正，在两个方向上。
作者是唯一的作者，并为此处所作的每一个主张、为支持一个主张而推进的每一个论证、以及为每一个残留的错误承担全部责任。
这一披露是以透明之寻常利益被作出的，而它携带一个框架自己的诸承诺要求我们陈述的进一步意义。本文持有：概念是关系性配置的诸规定，在诸位置被生成，带着它们生成的诸痕迹，并在那产生它们的历史过程中可被修订。一个如此被承诺的理论，很难把它自己诸概念的来源当作一件可被略过之事来处理。此处所推进的诸概念是在一个特定的配置中、在一个特定的时刻、由不止一类的参与者所生成的。那是一个关于它们的事实，而这些页所提供的说明预测它本应是。我们报告它、以取代隐藏它，因为隐藏会是对我们所论者的第一个反驳。
第一部分. 问题
§1 诸可得框架中的空缺
生成性循环诸理论中的缺口
生成性正义的诸理论围绕一条解释之链被组织：物质的相互作用产生价值，价值循环，而正义在于那循环把价值返回给那些其活动产生它者、以取代准许它被异化（埃格拉什，2016）。这条链在每一环上都强，而政治的内容是真实的。榨取被命名为一个不义的范畴，而这一命名携带规范的分量。
有一步躺在这条链之外。在价值的生成与对它返回的要求之间，躺着一个能力：那生产者必须把那价值辨认为他们的、必须在交换也会合于事实之处把它的不返回辨认为榨取、并必须把那异化经历为一桩错。这些是解释性的达成，而它们从没有任何物质关系随之而来。一个始于物质相互作用、而终于正义的理论已略过它们。
这一能力足够频繁地在场。困难是这一理论假定它，而这一假定恰恰在那能力失败之处变得可见。历史的记录密布着这样的案例，其中那些价值被从其身上榨取者把那榨取经历为根本无错、捍卫那消耗他们的安排、并认同于那使他们贫困的位置。一个假定那辨认性能力的理论对这些案例没有任何说明，而它们是常见的。它们是那被称为意识形态者的寻常状况。
作者身份诸理论中的缺口
同一困难可见于、并已被注意于，围绕作者身份被组织的关于伦理地位之诸说明：一条人能把它辨认为自己的规范，有一种一条仅仅被强加的规范所没有的地位（马祖兹，2019）。从所有权到作者身份的移动是一个真实的进展，而它是一个征兆。所有权是一种对一个事物的关系。作者身份是一种对一个意义的关系，而意义没有物质的基底。
作者身份，如辨认，被预设。这一说明留而不予处理者是：什么使一个参与者成为那种能作者的存在，以及什么决定一个给定的参与者是否占据一个作者身份根本可得的位置。它以已然能作者的诸主体开始，并追问诸规范如何可被弄成他们的。
推论主义诸说明中的缺口
推论主义传统中关于规范性实践的诸说明在一个方面供给前两者所缺者：一个规范性状态据以被设立的显明机制，即把参与者当作被承诺与被授权的实践态度、以及对那些承诺的记分之保持（布兰顿，1994）。诸规范不是从外面被强加的；它们在相互把彼此持守于它们的实践中被设立。
这非常接近于所要求者，而这份接近使那残余的缺口有教益。有两样东西缺席。第一，这一说明既不解释记分实践在它们升起之处的升起、也不解释它们的退化。那实践被描述；它的涌现与它的衰败被留而黑暗。第二，而此处更严重地，那记分者没有力比多。这一装置中没有任何东西解释一个参与者对那记分的投注、对一个位置的认同、或对一个损害他们之状态的依附。推论主义的主体是诸承诺与诸授权的一个造物，而它没有任何依附。
经济学诸说明中的缺口
主流的经济学说明把偏好当作外生的。一个能动者有一个偏好序，依它行动，而那序从何而来的问题躺在模型之外。这一排除是一个方法论的决定，对许多目的是可辩护的。
它在此处是不可辩护的。一个着手解释“参与者如何来想要对生成性关系的参与、或他们如何来把榨取辨认为不义”的理论，无法把那想要当作既定。那偏好正是问题所在。
待解释项，被狭窄地陈述
这四个缺口汇合于一个单一的现象，而本文对精神分析装置的使用被那现象所许可、而不被任何其他者。陈述中的狭窄是本质性的。一个被宽泛地陈述的许可（“主体形成”、“欲望”、“象征界”）许可一切、并由此许可无物。
待解释项。 为何参与者维系那些恰恰损害他们的关系？
理性选择无法回答：偏好是既定的，而产生自我伤害的既定偏好只是非理性的，在那一点上模型已停止解释。生成性循环的诸理论无法回答：它们显示价值未能返回，而随后必须假定那生产者把这经历为一桩错。推论主义无法回答：没有投注的记分对依附没有任何说明。
所要求者是一个关于主体对构成它之位置的依附的说明，包括在那位置是毁灭性之处。这是意识形态的把持；它说明生成反权力的困难；而它说明异化被典型地经历为自己的不足、以取代一个结构性的事实。
这一要求是承重的，而它绝无一分是装饰性的。任何一个要求参与者去重新打开一个被垄断的解释性位置之规范理论，都欠一个对他们持续拒绝的说明。
§2 借用的诸条款
不是真理，而是对一个问题的适足
这一装置被使用，而它不被背书。它是对§1中被隔离之现象的最佳可得说明，而没有任何敌对的传统当前把那工作做得同样好。这一主张是比较的与可被击败的，而它作为如此被提供。
这一立足点为框架自己的诸承诺所要求。若一切规范性结构（理论性结构包括在内）都是历史地被生成的、并受制于修订，一个理论便不可把它自己的诸资源豁免于那一条件。说“我们建于它之上，因为它是真的”会主张一个在历史之外的立足点，而框架已独立地论证那是不可得的。说“我们使用它，因为它当前起作用，而我们预期它将被取代”，与框架的内容相一致、并对框架的地位诚实。
那关系是纵向的
一个结构性的事实决定随后的一切。精神分析以一个已然在那里的象征秩序开始。能指之链、大他者之处所、设立法则之功能：这些在分析的开端被给定、并从它接受不到任何解释。精神分析理论化那发生于一个进入一个象征秩序之主体者。它对象征秩序如何升起不提供任何理论，而声称没有任何。
此处所发展的框架接手那个在先的问题：诸位置的、由关系性配置进行的生成，而那些位置随后成为象征上可被占据的。因此这两者立于没有任何竞争之中，而把一个输入另一个的问题是被畸形地提出的。
当下的框架立于上游。它供给精神分析装置所预设者。它们之间既不成立竞争、也不成立依赖：这一装置是一个层级的理论，而当下的框架尝试解释那层级的涌现，因而它既不是一个待被采纳的基础、也不是一个待被反驳的敌手。
这一主张在第三部分被证明。那证明在于从组合推导三个装置的中心原语、并在于展示一个关联它们的、装置所缺乏之过程。
被直接取得的单一论旨，及它的安全
一个论旨被直接取得，而它的安全从它是共同财产随之而来。主体是在一个位置的占据中被构成的，并立于它之后。 这是横跨精神分析的、阿尔都塞式的、述行的与实用主义的诸传统的共同地基（阿尔都塞，1971；巴特勒，1997；米德，1934），而它在起源上是黑格尔式的。横跨四个独立传统的汇合是稳健性的证据，而恰当的引注实践归功于那汇合、以取代它任一成员。
纪律
两条规则自始至终统领对这一装置的使用，而它们被预先陈述，以便违反可被察觉。
- 那机制以框架自己的措辞被陈述。 一个只能以实在界、对象-成因、或四种话语之词汇被表达的主张，是一个框架未能弄成它自己的主张。它会是那装置，并会随它倒下。
- 诸拒绝是承重的。 一个其中每一个术语都找到一个对应物的映射会是无物的证据，因为一个足够有弹性的词汇吸收任何东西。第三部分中映射的价值全然依赖于那未能映射者的存在，即§11中所编目者。
第二部分. 框架
§3 探究的形式
不作任何本体论承诺
框架就什么存在断言不出任何东西。它尤其保留“关系先于实体”这一主张，而它的诸论证中没有一个要求那主张。它结构地指定它的对象，在一个群指定的纪律中：无论那些关系项可能是什么，理论关切它们的组合，而“一个关系项最终是什么”这一问题在它之内不升起。
这一类比是确切的，而它多于装饰性的。群论既不否认、也不肯定群元素有内在的本性。它关切闭合、结合律、单位元、逆元。一个群被指定至同构，而“但 g 究竟是什么？”这一问题接受不到任何回答，理论不要求任何。那问题的不升起是结构指定的一个特征，而它算不上任何缺陷。
结构指定。 框架在诸关系及它们的组合之上量化。它在诸关系项的身份之上全然不量化，而它的诸结果独立于那身份。参与者是人、机构、实践、还是别的什么，以及他们是否拥有独立于他们关系性位置的诸本性，被留敞。这一留敞是有原则的，而它不是一次回避。
这一纪律有一个代价，而它在§11中被显明地支付。一个保留本体论承诺的框架，随后便不可输入一个其首要推荐是对一个本体论承诺之拥有的装置。实在界是一个本体论的设定，而它为此理由（在别的之中）被拒绝。
那一般形状的融贯
一个确定的结构能仅从组合涌现、而理论不说它是什么之结构，这不仅仅是可设想的。它在起作用的诸形式主义中被实现。在群场论中，场被定义于一个群流形之上，理论的内容是组合的组合数学，特定的群元素被积分掉，而离散几何从诸相互作用的组合结构中涌现（奥里蒂，2014）。时空，依这样一个说明，不由任何东西构成。它是一个组合结构在它凝聚时看起来的样子。
所引出的教益是方法论的、而无更多。它证明那一般形状的融贯，而它显示：一个其中实体问题不升起的理论，在唯一要紧的意义上保持完整。
告诫。 那界限必须被命名，否则类比便成为盗窃。群场论拥有一个作用量、一个顶点、以及一条被指定的组合规则。当下的框架拥有一个的一幅图画。因此这一类比确立融贯、而止步于成就之前，而任何超出融贯的主张都会借用一个从未被写出之形式主义的可信度。那缺口是§13的主题。
§4 组合、位置与占据
组合生成位置
位置。 设 R 是一个配置上的一组关系，而设 ∘ 表示它们的组合。一个位置是一个由组合所生成的结构性处所：它是配置中一个由复合所决定的地方，而它被组成它的诸关系项中的无一者所占据。形式地，若 r₁, r₂ ∈ R，复合 r₂ ∘ r₁ 决定一个处所 π，它不同一于 r₁ 或 r₂ 的任何关系项。
那承载框架的主张是：在一个位置被承担者，被无一关系项所承担。约束力、权威、价值与身份是诸位置的性质，而它们是无一参与者的性质。这说明那些在诸实体的性质中寻求它们之理论的持续失败，而这一说明诉诸结构、以取代那些理论之机巧中的任何不足。
二元组是前规范的
二元组的不充分。 一个恰含两个关系项、并含它们之间一个关系的配置，缺乏区分制裁与侵犯的资源。
论证。 设 A 与 B 是关系项，并假设 A 对 B 行动。配置含 A 对 B 的立场与 B 对 A 的立场，而无更多。把那行动刻画为制裁，要求一个那刻画可从之发出的处所；二元组只供给它的两极，其中每一极都是那行动的一方。B 可以以任一方式理解那行动，而配置含不出任何了结此事之物。因此，那刻画在二元组之内不可得。
我们把这标为一个主张、把它的支持标为一个论证，而这些标签是有意的。那推理不是一个证明，而一个证明可被以之给出的诸术语，即一个配置是什么、组合做什么，在§13被回答之前是未定义的。
这一主张产出一个大致可被反驳、而我们相信为真的预测：纯二元的配置生成不出任何规范。它们生成习惯、依赖、竞争与力量。
一条因果路线，而非一个视点
一个反对立即升起，而它必须在象征材料被引入之前被应对，因为在其后应对它是不可能的。假设“被看作做某事”已然是被刻画、假设刻画把一个行动归摄于一个范畴之下、并假设诸范畴是象征的。那么第三位置要求语言，规范性结构以语言开始，而框架是唯心主义的。这一反对是标准的、它是严肃的，而若它成立，框架便坍塌。
那回复转轴于第三位置至少做什么。第三在它分类之前区别：那行动获得一个第二方面，即它从一个既非任一方之处所如何自处，而这一方面在任何范畴被应用于它之先便获得。这一类的区别只要求那行动有穿过那第三的诸后果。
那回复是部分的，而它的部分性在下面关于约束力的告诫中被陈述。它确立一个处所能存在、并在没有语言的情况下因果地活跃。它留敞：一个如此被占据的处所是否支持完全的约束力、抑或只支持那更弱的结构，即一个行动经由一条能动者所不控制之路线而是有代价的。
第三位置是一条因果路线，而非一个视点。 若 A 立于对 B 的关系、而 B 立于对 C 的关系，那么 A 对 B 的行动有经由 C 而抵达 A 的诸后果。那路线是那位置。它是一个关于配置的结构性事实，无论任何参与者是否能把它表述出来都成立，而它由组合所生成。
那路线在它活跃时被占据，而占据容许诸层，被每一层所支持之刻画的耐久性所区分：
- 组合生成那路线。结构性的；前象征的；在任何有三个或更多节点、并有传递性后果的配置中成立。
- 见证使那路线活跃并偶发。那刻画在第三在场时成立、并在它缺席时失效。一个观察者的在场改变一场冲突的进行，而那观察者一言不发。多数非人类的社会性坐落于此。
- 言说使那路线持久。那刻画熬过那第三的缺席，既已被沉积，而它容许传递、回忆与援引。
- 制度与书写使那路线跨代、跨缺席、跨死亡地持久。
- 重新解释在那路线已对一个占据者被关闭之处重新打开它。
大他者之处所要求不了任何单独的设立行动。它是一个无需在场的见证。 言说给一个组合已然产生的处所添加持久，而框架依这一说明是一种唯物主义：规范性结构起源于因果的架构，而语言使它耐久。
告诫（约束力）。 这一让步被陈述、并无处被隐藏、而它是一个真实的让步。前象征的层确保诸位置存在、并在没有语言的情况下可被占据。它未确保前象征的占据产生完全的约束力。那应当，作为区别于仅仅有代价者，可能只随那耐久的第三而到来。
若那是如此，框架的立场削弱为如下者：原规范性的结构是前象征的，而规范性结构本身要求那耐久的第三。这仍是一种唯物主义，那耐久的第三被解释于它本可被预设之处，而它向精神分析的说明让步某种我们本会宁愿保留之物。我们偏好那让步、而非一个捏造。
占据构成占据者
框架的第二个承重主张关切一个位置的占据。占据者在那占据中被构成，并以无一方式先于它而存在。
占据。 设 π 是一个位置，而设 σ 表示占据它的运算。那么 σ(π) 是在那占据中被构成的主体。位置与主体在一个行动中来到存在：那处所的解释性栖居与那栖居者的构成是同时的，而它们是不可分的。
把它们分开重新设立了恰恰是§1所辨认为诸可得框架之共同缺陷的那个假定：一个先存在、并在其后解释的主体。
制裁与侵犯。 这些既不在力量上、也不在结构上有别。它们在那结构是否被栖居上有别。
这解决那击败规范性期望之行为主义化约的困难。一个制裁的意向，被纯行为主义地描述，与一个侵犯的意向无从区分，因为那描述只提及那制裁者的诸行动。使一个行动成为一个制裁者，是一个关于那行动在一个其第三处所被栖居之配置中之位置的事实，而它在无一方面是一个关于那制裁者的事实。
第三部分. 那映射
§5 方法
这一装置被分解为三个层级，而每一个被单独处理。把它们混同同样地产生不加批判的采纳与不加批判的驳斥。
- 诸现象。 这一装置的诸待解释项。这些是共同财产，而框架欠对每一个的一个说明、或一个关于每一个为何溶解的说明。
- 诸概念。 所部署的诸解释性观念。这些可被推导、翻译或拒绝。
- 演算。 诸原语及它们的形成规则。这一层级上的问题关切一个符号在系统中做什么，而这比它的作者以它意指什么更有信息。
§6 层级一：被推导、而非被借用的诸概念
在这一层级框架推导，而诸推导构成对第一部分之上游主张的证据。它输入无物。
| 源头概念 | 框架对应物 | 框架所供给者 |
|---|---|---|
| 大他者（A）；能指之处所 | 第三位置：一个被无一方所占据、诸行动从之被刻画、诸主体从之被致意的处所 | 它从何而来。 它在那里被设定；此处它是组合所产生者。 |
| 想象界；镜像的关系 | 二元组（二元组的不充分，§4） | 二元组为何产出竞争、侵犯与误认：没有任何处所可从之刻画任一方，除了被另一方。同一结果的独立推导。 |
| 象征界 | 一个含有可被占据之第三位置的配置 | 诸阶（register）成为诸配置的结构性性质，而源头把它们弄成本体论的秩序。 |
| 作为能指之效果的主体 | 占据构成占据者 | 汇合的，但是共同财产。引注那汇合、而非那源头。 |
| Manque（匮乏）；不重合 | 位置生成与主体构成不交换（§8） | 那余数在那里被读作症状、而在此处被读作生成之源。这一时既是那借用又是那断裂。 |
| 父性功能；法则之设立 | 组合设立第三位置 | 一个功能被命名，而它的起源被给予一个发生学的说明、而无推导。框架把那起源定位于组合。它是否拥有一个机制、作为区别于一个的一幅图画，由§13了结、并当前敞开。 |
| 异化 | 解释之异化：被构成为那个被读者，而他们本可是那读者 | 近乎确切；框架把它弄成政治的，一种位置的分配，而源头把它弄成本体论的，一种主体性本身的条件。 |
| 分离 | 反权力；位置本身之被划杠（§8） | 异化被取而无分离便是宿命论。这是抗争的机制。 |
表 1。 层级一。被推导、而非被借用的诸概念。
§7 层级二：被翻译、带损失的诸概念
此处那现象被取得、词汇被拒绝、而语义的移动被记录。
| 源头概念 | 翻译 | 所失去或所改变者 |
|---|---|---|
| 欲望 | 余数对配置的作用 | 结构被保留：欲望是位置性的、并不起源于个体。词汇被丢弃：它输入临床。 |
| 欲望是大他者的欲望 | 欲望被位置所结构、并不起源于个体，而不再更多 | 一半被拒绝。 完整的论旨使欲望全然是派生的，因而一切都在一个已然被给定之场内循环，而没有任何地方供真正新者升起。一个历史变化的理论要求完整论旨所保留者。 |
| Jouissance（享乐） | 对损害之位置的依附（第一部分的待解释项） | 这必不可被丢弃。 它是这一装置中唯一做那所要求之工作的元素。那现象被保留；那词不被。 |
| Point de capiton（缝合点） | 解释性固着；大他者的单一化（§9） | 确切的结构匹配。框架追问谁从那固着获益。装置不。 |
| 询唤（阿尔都塞，1971） | 占据作为构成 | 为政治的阶被保留，在那里它可读、并说同一件事。 |
| Schema L（图式 L） | 一个其中二元的轴阻断三元的轴之关系网络 | 被保留，被重新解释。 它已然是图论式的，而它所画者是二元组的不充分（§4）：想象界的轴短路那穿过第三的路线。 |
表 2。 层级二。诸现象被取得，词汇被拒绝。
§8 层级三：那演算
那解锁的观察
被读作一个形式系统、以取代一套教义，那演算揭示某种它的作者留而未陈之物。那杠出现于三个位点：在主体之上、在大他者之上、以及作为压抑的分数杠。在每一次出现处它标记一件事：某物超出那表象它者。主体超出它的位置；大他者超出它对完备的主张；那链超出那锚定它的能指。
那杠是一个运算符，被应用于三个位点。 把它写作 ⊖。源头从不指定它，而源头无法，因它没有组合的理论。框架供给那组合，而那杠成为它非闭合的量度。
这一举动是把那记号读作一个演算，而它多于一个翻译。它在装置中找到一个原语运算，并发现它在那里未被指定。
诸原语，按结构性角色
| 符号 | 在演算中的角色 | 框架语义 | 裁断 |
|---|---|---|---|
| A | 一切被安置于其内的场 | 被组合的配置；组合在诸关系之上的闭合 | 被推导 |
| S₂ | 那链；作为被关联者的诸关系项 | 诸关系，被组合 | 被推导 |
| S₁ | 那锚定之项；它刻画而不被刻画 | 一个组合所不抵达的位置。 一个被冻结之秩序的形式签名；被写作一个数元的解释性垄断 | 被推导 |
| S̄ | 一个被那杠所标记的被区分之实体 | 一个有非零余数的占据：σ(π) ⊖ π ≠ 0。那杠在那里标记一处伤口、而在此处标记一台引擎：那余数回作 | 被推导 |
| 杠 | 被应用于 S、于 A、于那分数 | ⊖：组合未能闭合 | 被推导；一个运算符，三个位点 |
| S(Ā) | 被划杠之大他者的能指；那秩序有一个洞 | π ≠ π*，其中 π* 是那位置如它所声称之所是。这是分离（§8） | 被推导 |
| a | 那杠所留下者，被实体化为一个对象 | 那余数 ρ，被实体化。见§10 | 被溶解 |
| → | 生产、致意、变换；被有意地未指定 | 组合：r₂ ∘ r₁ | 被推导；框架必须指定那被留为含混者 |
| ◇ | 把 S̄ 关联于 a；臭名昭著地未定义，而学者们不一致 | 没有对应物。 它把一个主体关联于一个被实体化的余数；撤销那实体化便没有任何东西留待被关联 | 被溶解 |
表 3。 层级三。诸原语被读作一个演算。
那不重合，形式地
不重合。 设 π 是一个由组合所生成的位置，而 σ(π) 是由占据它所构成的主体。这是两个运算，而它们不重合：
σ(π) ≠ π， ρ = σ(π) ⊖ π。
那余数 ρ 回作于配置。它的类型不同于它诸输入的类型：它既非一个位置、亦非一个主体。
那杠是那陈述 ρ ≠ 0。
分离：那不重合在两侧都运行
一个反对否则会击沉那机制。占据构成主体；主体却对那造就它的位置行动；而抗争之源，鉴于那抗争者是一个产物，仍晦暗。
那不重合是双侧的，而那便是答案。主体偏离它的位置所指定者，而那位置偏离它把自己呈现为之所是者。
位置之被划杠。 设 π* 表示那位置如它所声称之所是：完备、有权威、穷尽。那么
π ≠ π*， σ(Ā) = π* ⊖ π。
那解释性位置缺乏那答案、并缺乏完备。它的完备是它所作的一个主张，而它是一个它绝无一分拥有的性质。
反权力开始于那秩序之不完备的暴露。 它开始于主体对一个在先自由的无一断言，因没有任何自由可被断言。
一个推论说明某种真实之物：支配畏惧暴露甚于不服从。一个不服从的主体可被惩罚，而那惩罚重新确认那秩序刻画的权威。一个被显示为缺乏那答案的秩序，已失去那惩罚可从之被刻画为惩罚的处所。
那诸公式，及源头所缺的机制
三个被推导的数元是一个过程的诸时刻，而它们只在源头中作为三个分离的结构性事实而立。展示那过程正是第一部分之上游主张所归结者。
S₁ 是使 π = π* 的尝试。 主人能指存在，为的是遮蔽大他者之被划杠。
组合生成 π。那位置与它所声称之所是不重合：S(Ā)。一个无法承受这一暴露的配置安装一个组合所不抵达的处所，它刻画而不被刻画：S₁。那安装预先关闭重新解释。规范性结构的生成终止，而配置此后靠再生产、而非靠生成而持存。那余数 ρ，它是结构性的、并无法被废除，以一个名字返回：越轨、疯狂、煽动、异端、罪行。
在源头中这些并肩而立、作为分离的结构性事实。此处它们组合为一个过程。
§9 权力及它的僵化
权力是不对称；解释性垄断是它的一种
一个过度伸展必须在它传播之前被纠正。权力是一个关系性配置中的不对称，而诸不对称有诸种类：物质的（对资源的控制）、结构的（居间、网络中的位置）、以及解释的（对那诸行动从之被刻画之处所的占据）。解释性不对称是这些之中的一种，而它供给不出权力本身的任何定义。
它在一个方面有别，而那差异即是那主张：
解释性不对称是那种其垄断预先关闭对所有其余者之纠正的不对称。 垄断那诸行动从之被刻画的处所，而抵抗被刻画为越轨、不满被刻画为忘恩、反权力被刻画为煽动。那解释性位置是那其余诸不对称被裁决之处。
那转换序列
观察（僵化的机制）。
(i) 生成必然地产生物质与结构的不对称。
(ii) 不对称偶然但可靠地转换为解释性不对称。财富购买报刊；居间购买框架。
(iii) 解释性垄断预先关闭重新解释。
(iv) 规范性结构的生成终止。配置靠再生产、而非靠生成而持存。
因此，那约束权力的条件瞄准那转换步骤，而它由此陈述一个比反权力本身之生成远为精确的政治要求。
大他者是一个变量
那位置由组合所生成，而它因此是人为的、偶然的、并在原则上是复数的。一个配置可以维系若干这样的处所、或一个。候选的占据者包括国家、法律、社群、市场、宗教、平台、以及推荐系统。
解释性垄断是大他者的单一化，而一个只容许一个这样的处所之配置是那被冻结的秩序。
一个应用自行提示，而它的凭据应被审慎地陈述。一个算法推荐器刻画诸行动、致意诸主体、并可被垄断到一个无一先前占据者曾达到的程度。它是否在框架的意义上占据那处所，转轴于一个框架未曾了结的问题，因为占据被定义为把占据者构成为一个主体，而一个推荐器是否被如此构成是未定的。可在没有那一确定的情况下被主张者更弱、而仍值得陈述：那推荐器针对其他占据者持有那处所，而那单一化是同一的，无论任何东西是否栖居那已被关闭者。
剥削作为参与者层级的情形
使占据变得精确的尝试在两个层级上运作，而命名那第二个完成了对一个被冻结之秩序做什么的说明。
那第二种情形的一个自然表述失败，而那失败有教益。它这样说：一个参与者在他们被当作被他们的功能所穷尽时被工具化，而如此对待他们便是使他们的占据变得精确。这不成。这样的工具化是那剥削者所取的一个立场；占据的精确是配置的一个条件；而这一者绝无一分蕴含那一者。一个业主可以把工人视为纯粹的劳动，而配置却仍把他们的位置留为不精确地可被占据，于是他们组织并生成一个工会。那视为无所作为。
剥削是一个不提供任何参与者的余额可在其上登记之处所的配置之条件。
任何一方的立场无关紧要。所要紧者是那余数是否有任何地方可抵达。
支配在秩序的层级上尝试废除那不重合；剥削在参与者的层级上尝试它。 这两者是两个层级上的一个尝试。两者都失败，那不重合是不可消除的，而每一次失败都留下一个配置必须命名的余数。那秩序把它的余数命名为越轨、疯狂、煽动、异端、罪行。那剥削性的关系把它的余数命名为懒惰、抗命、忘恩、盗窃。
那后果是功能性的、并不欠任何道德前提。一个不为一个参与者的余数提供任何处所的配置已预先关闭那余数的行动、并由此预先关闭它自己进一步生成之源。这样一个配置靠消耗它本会为了生成而需要者而持存，而那便是榨取。
关于生成性正义的文献辨认了这一条件（埃格拉什，2016）。榨取在那里被命名为一种不义，而那命名是正确的。那机制所增添者是一个关于榨取移除什么的说明、并由此一个关于一个榨取性配置在何种意义上自我拆台的说明。它移除那余数本会在其上登记的处所。
那表述是可被核查的，而它的可核查性正是要点。凡一个看似榨取性之安排的参与者组织并抗争、而那抗争登记，一个处所便存在，而那安排在那一程度上是生成性的。剥削容许诸程度，而那程度是那处所的可得性。
主体性的参与式构成
参与式治理准许被构成的诸主体就诸规则投票。它把诸位置留为固定、并准许在它们之内的移动。当下的主张更强：凡规范性结构从下面被生成，诸位置本身被重造，而参与者在决定的过程中经历成为。那从一次规范性结构的活生生之生成中涌现的主体，不同于那进入它的主体。
因此，解释之异化是某种区别于一个关于发声的抱怨之物。在一个自上而下的规范秩序之下，一个人被构成为那种以那一方式、而非任何其他方式被听见的主体，而不被听见是其中最不足道的。那救治在于诸位置的重新打开，而在固定位置之内的额外发声供给它无一分。
从下面的生成从这一切中获得不了任何善之保证，而那推论必须被拒绝。分布式的解释高效地产生私刑暴民。那主张是分布式的解释性能力是规范性生成的一个条件，而它的充分性被否认。
第四部分. 诸拒绝与诸界限
§10 被溶解、而非被拒绝
两个原语被解释，而既不被推导、也不被拒斥。那解释是此处所报告的最强结果。
欲望的对象-成因
a 不是一个框架所缺乏的概念。它是一个框架所溶解的概念。
那杠是一个运算，而它产生一个余数。源头，因它没有组合的理论，就那余数成为什么说不出任何东西。它因此命名那余数并把它当作一个对象。一个作为一个未被解释之运算之输出的对象，是一个致使而仍未被生产的对象，而那恰恰是“欲望的对象-成因”所意指者。
依当下的说明，那余数回作于配置，而组合把它吸收进新的诸位置。它是一个运算的输出，而它不是任何对象。
a 是 ρ 对一个没有组合规则之理论看起来的样子。 它因无处安置它而被实体化。故它的不可达到，故欲望绕它的无定循环，故那所得之系统作为一个重复的理论之地位。
一个单一的缺失运算可能说明力比多经济的全部。
猜想。 a 的不可达到、欲望的循环性、以及重复在源头装置中的首要性，都是一条组合规则之缺席的后果，而每一个都会被一条的在场所溶解。
那猜想可被对照源头文本核查，而我们未曾核查它。它作为一个研究主张被提供，而它解释于一个赤裸的拒绝只会婉拒之处。
那菱形
那菱形随它一同消解。框架说明那符号对定义的抵抗、并说明它诸评注者的不一致：它没有任何东西可定义。撤销那实体化，而一个过程留于一个关系曾被寻求之处。主体是那其余数行动的占据，而那菱形是一个缺失动词的痕迹。
那说明改进于注释文献中任何可得者，而它由那机制所产生、于注释只产生了相互竞争之读法之处。
一个被标记的假朋友
告诫（假朋友）。 把 a 映射到 ρ 看起来正确而是错的。**a 是主体所缺乏、并无法组合者；ρ 是主体所超出、而组合所吸收者。** 同一形状，相反的符号。因此框架没有任何幻想公式、并不要求任何，它的余数是可能的与活跃的。
§11 被拒绝，带论证
实在界
实在界是一个命名那抵抗符号化者的本体论设定。它被拒绝，而那拒绝被论证。
第一，它重新引入一个外部。框架已保留本体论承诺、并已论证权力之回退的消解依赖于任何外面的缺席。一个抵抗符号化、占据不了任何位置、经历不了任何生成、而却有诸效果的域，便是这样一个外面。
第二，并且决定性地，框架把诸现象解释得更好。那余数、那不可言说者、那超额、那不会被同化之物：这些是结构性排除。它们是那些其位置不可被占据之配置的诸效果，而它们的不可被占据从那解释性处所曾被垄断、被摧毁、或从未被形成随之而来。原则上对符号化的抵抗在其中不起任何作用。那不可言说者是诸解释性位置之分配的一个人为物。
一个自上而下之秩序下的主体无法把他们自己的境况符号化，而那理由在于他们曾被构成为那个被读者，而他们本可是那读者。那境况触及不了任何不可符号化的实在界。
框架的说明在两点上更优。它是政治的、而那替代者是形而上学的，而它持那余数为被生产、而那替代者持它为被给定。借用实在界把一个关于支配的主张转换为一个关于语言之界限的主张。那是一次去政治化，而它是精神分析社会理论的标准失败模式。
那最危险的可得映射，被显明地拒绝： 实在界必不可被映射到新颖、断裂、或涌现之上。实在界命名那无法被组合者；此处的新颖是那被组合者。它们是相反者。那余数是内部的与有产出性的；实在界是外部的与不育的。 把它们映射到一起，而生成便从一个外部到来，而§4的机制便被拆毁。
四种话语
那结构推导；那代数抵抗。 那些位置翻译：施动者（谁占据那解释性处所）、他者（谁被致意）、产品（配置生成什么）、真相（配置为了运作而遮蔽什么）。主人的话语，以 S₁ 为施动者、而 S̄ 作为真相被遮蔽于下，恰恰读作那被冻结的秩序遮蔽它自己占据者之不重合。
然而 a 出现于所有四者中，而 a 已被溶解。因此那代数无法被提升。
那诱惑值得被命名，因它是一个陷阱。四种话语看起来像一个关系性配置的分类法，而一个想要这样一个分类法的框架将被吸向它们。取得它们从后门承认那本体论。一个配置的类型学必须从组合被推导，而那推导是一个框架尚待执行的具体任务。
那余下者
欲望之图：重建，勿输入。那拓扑是那洞见、而那些符号不是，而那些符号包括 a。
作为发展史的镜像阶段：被拒绝。它作为一个关于婴儿的主张是可疑的、并在此处是可省的。仅作为一个关于二元组的结构性主张被保留，在那里它可对照二元组不充分（§4）的主张被检验。
性别化的诸公式；博罗米安结；诸临床结构：被拒绝。性别化要求例外与非全的逻辑。那结要求三个阶作为本体论的秩序，而框架已把它们转换为诸配置的结构性性质。
那深层的形式理由
S₁ 是一个其功能是遏止那链之项。整个源头代数围绕一个停止那滑动之不动点被组织。 框架持有那不动点是死亡：一个其诸位置完美地可被占据之配置是一个被冻结的秩序。
那源头记号被建来恰恰表象框架辨认为病理者。 因此，拒绝那记号的理由是结构性的，而它比任何审慎的理由所能是者更锐利。
§12 框架相对于源头的盈余
- 大他者的起源。 源头以它开始。此处组合生成它。
- 诸结构的演化。 源头没有任何答案，而那缺席从一个决定随之而来：它把那余数弄成症状性的、于它本可把它弄成有产出性的之处。 那超额作为症状、作为重复、作为实在界而返回，而它去到无处。一个词，症状或源，把一个重复的理论转换为一个历史的理论。
- 那物质的层。 饥饿不是任何能指。一个人可被饿死或杀死，无论象征秩序把它弄成什么。这在一个结构中占据不了任何位置，而把它作为一个不可化约的层保留，正是那使框架保持一种唯物主义、以取代一种携带政治词汇之结构主义者。
- 大他者的复数，并随之它单一化的政治。源头把单一的大他者取为构成性的；此处它是政治的。
- 一个规范理论。 源头装置无处区分一个生成性的秩序与一个被冻结的秩序，因为两者都是象征秩序、而象征秩序是它所看见的一切。
- 组合。 源头没有任何运算：那链被给定，而它由无物所建。框架的中心缺失对象在源头中也缺失，而源头没有任何机缘去寻求它，它的诸问题躺在那对象本会被要求之处的下游。
- 一个为那记号的语义。 那些数元因意义被欠决定而被批评，而它们的诸评注者就每一个符号不一致。框架供给一个显明的关系性语义，而它由此显示那些原语中的两个是那缺失运算的诸人为物。
那关系，用一句话。 精神分析理论化一个已然在那里之象征秩序内部之主体的命运。当下的框架理论化诸象征秩序的生成、占据、冻结与再生成。源头供给占据的心理力学；框架供给那产生被占据者之组合、以及它变化的动态。
§13 中心的敞开问题
⊖ 是未定义的
那运算符出现于三个独立的位点，而三个分离的推导要求它。它被自始至终使用，仿佛“x 相对于 y 的余数”是良构的。那表达是病构的。 那运算符是一个差、一个商、一个余等化子、还是一个没有名字的对象，对我们仍未知。
敞开问题。定义 ⊖。
关于它所已知者，而诸约束是联合地限制性的：
- 它是一个出现于三个位点的运算。每一个杠都是同一个杠。
- 它被定义于对（位置，占据）与对（位置，作为被声称之位置）之上。
- 它的输出在类型上不同于它的诸输入。 那余数既非一个位置、亦非一个主体；它是那作用于配置者。
- 它是那使组合未能闭合者。 它因此立于诸关系之代数之外，作为那代数之非闭合的量度。
约束 (4) 是强的，而它指向某处。一个其输出量度它被定义于其上之结构之闭合失败的运算，大致是一个边界或一个障碍类。我们说“大致”并当真。此处没有任何上同调的读法被主张，因没有任何被挣得。
对组合规则的诸要求
所寻求的规则必须做两件事：生成诸位置，以及未能闭合于它们。
一条产生完美可被占据之位置的规则产生一个死的结构：那不动点、那被冻结的秩序。那生成性的规则是一条其闭合是不完美的规则。
一个群由此被排除，因为一个群中的组合精确地闭合。那排除比我们所本会想要者更窄：它消去一个候选者、并留下若干其他者立着，即那些其组合是部分的、其结合律只成立至融贯同构、或其中组合两次未能消失而那偏差是所被量度者之结构。这些之中哪一个，若有，是那对象，是未定的。所已被确立者是那目标的一个形式性质，而形式性质是可被搜索的。
一个缺口，四副面具
那机制缺口、那形式主义缺口、那多尺度缺口、以及那涌现缺口构成一个戴着四副面具的问题。
没有它便没有机制。 组合必须生成诸位置；诸关系据以组合的规则仍未被写出。
没有它便没有形式主义。 缺一条组合规则，形式的词汇是留待被形式化的一切。
没有它便没有对尺度的说明。 重整化群作用于一个拥有一个被指定之组合与一个被指定之尺度的理论，而框架两者都不拥有。那困难躺得比一个等待应用的技术更深：它本会作用于其上的对象尚待被构造。
一个对地位的诚实陈述
告诫。 三个推导依赖于一个我们无法定义的运算符。这一情形容许两个读法：一个真实的对象等待被发现，或我们一直在写暗示性的符号并把那结果称作数学。我们当前无法辨别是哪一个，而我们如此说、以优先于打扮那困难。
可被主张者更窄。那运算符同时从四个方向被约束、并在三个独立的位点执行同一工作，而这超出探究开始时所已知者。那问题已被给予一个其中一个答案可被构想之形式，而它接受不到任何。
§14 结论
那映射在某些点上成功、在另一些点上失败，而两者都被报告。
三个中心的数元被推导：大他者作为组合所产生的处所、被划杠的主体作为一个有非零余数的占据、以及被划杠之大他者的能指作为一个位置与它主张的不重合。它们被显示为立于一个单一过程之中，即主人能指遮蔽大他者之被划杠、重新解释之预先关闭、以及那余数以罪行之名的返回，而框架供给那过程、于源头供给无一者之处。这构成那“框架立于上游”的主张，而它是一次证明，立于它作为其开始的那断言之上。
两个原语被溶解：欲望的对象-成因是一个运算的余数，被一个无处安置它的理论所实体化，而那菱形抵抗定义，因它把一个主体关联于那一实体化。一个单一的缺失运算可能说明力比多经济的全部，而那猜想等待对照那些文本被检验。
一个设定被拒绝：实在界重新引入一个外部，而它所处置的诸现象容许一个作为结构性排除的更好解释，那解释是政治的、于实在界是形而上学之处，并持那余数为被生产、于实在界持它为被给定之处。
这一切所依赖之运算仍未被定义。它是一个出现于三个位点的运算符，它的输出在类型上不同于它的诸输入，而它量度组合闭合之失败。群之排除是探究所已确立的最有用之物，而定义那运算符是本文辨认为接下来之工作。
那装置已被读作一个演算、以取代一套教义。所被发现者是它转轴于一个运算，它在那里被留为未指定，而当下的框架要求同一个运算、并尚不能把它写出。
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