Instituted Unity: A Rule Suffices to Bind What No Space Grounds

Research note — Audit of the 31 Propositions, series note 2, Proposition P9 (Multimodal Unity). Disputatio form. This document is a research note examining a proposition of the ideamorphist corpus against the philosophical literature; it is not a source text.

Arnaud Quercy · Multimodal Institute (research project)

I. Quaestio

Do the expressive modalities share a common space? Is there one ideational interior of which sound, color, rhythm, space, and language are the surfaces — or are there only correspondences instituted between irreducibly distinct domains? The question is framed to admit two answers, and the note instructs both.

II. Current Statement

Verbatim, from Les 31 Propositions de l'Idéamorphisme (revised edition, March 2026) ^[1], without alteration:

Proposition 9 — Unité multimodale. Toutes les modalités expressives appartiennent à un seul espace idéationnel. Son, couleur, rythme, espace, langage — différentes surfaces d'un même intérieur. La translittération est possible parce que la séparation n'a jamais été fondamentale.

In English: all expressive modalities belong to a single ideational space; sound, color, rhythm, space, language are different surfaces of the same interior; passage between modalities is possible because the separation was never fundamental.

The statement makes three claims: an ontological claim (the unity is discovered, pre-existing), a topological claim (modalities are faces of one thing), and a historical-negative claim (the separation was never fundamental). The proposition sits in the ontological foundations of the corpus ^[2]: the entire codex practice — binding harmonic structure to chromatic composition, rhythm to sand, morphology to poem — presupposes that such cross-modal binding is possible, and Proposition 9 states why. If the stated ground falls, the ground of the practice must be restated. The stakes of this note are therefore maximal.

III. What the Practice Says

Written by the author before any research was launched, as the protocol requires. This section is a source, not an illustration.

The question poses itself intellectually. If A exists, and if B exists, may I institute arbitrarily that A = B — the idea carrying this equation being the equation as such?

It is like a game. I can perfectly well say that in this game, A = B, simply because those are the rules of this game. The player is the one who accepts the invitation. He is not forced to enter. He may see A or B separately, see only one rather than the other, or see B = C because he does not understand A. But my rules are that A = B.

It is like languages. Why does to be equal être? The answer is: because. And yet everyone conforms to this rule of the game. Not obliged — but if you want to play the English/French game, that is the rule. Why? Because it exists as a rule, and for no other reason.

And of course, I can also institute that A ≠ B, just as arbitrarily — assert that in this game, A and B do not belong to the same ideational space. Both rules are equally available. That availability is the proof that neither one describes.

This work will validate or invalidate the proposition and the language it uses.

IV. Videtur quod — the thesis, sourced

The thesis was instructed twice: once for the statement as written, once for the statement as displaced by Section III.

The strong thesis — a single discovered ideational space — finds no direct defender. Its most literal version exists as a reported position: the idealism of Croce and Collingwood, for which the work is mental, the intuition already expression, the material object an external representative of the true work ^{[3] [4]}. But the literature carries it only flanked by its standard refutations — the Mona Lisa would no longer exist; the theory cannot account for the difference between oil and watercolor, ice and marble — and presents it under the heading of the collapse of metaphysical aesthetics. The literature carries the strong thesis as a refuted position.

The strongest ally defends unity while dislodging it from the idea. Merleau-Ponty ^[5]: synaesthetic perception is the rule; the senses communicate by opening onto the structure of the thing; man is a perpetual sensorium commune. The separation of the senses is the product of an analytic attitude. So far, P9 seems carried. But the same pages place this unity in the body as a synergetic system, never completed, realized transversally — and maintain that the senses are distinct, each bringing a structure of being that is never exactly transposable: the senses understand each other without passing through the idea. The intellectualist reading (the object as common reason of its appearances) is explicitly rejected. The best ally grants "the separation was never fundamental" at the level of the perceiving body, and refuses "ideational space" in the same breath. Cassirer offers a unity of the symbolic function, not of a space, with no idea prior to its medium ^[6]; Langer warns that speaking of a "language" of the senses deceives ^[7].

The weakened thesis — pre-existing constraints on which equations take — has a real empirical file. Crossmodal correspondences are systematic and predictable, between polarized dimensions: pitch with elevation, size, brightness; congruent pairings measurably enhance multisensory integration ^[8]. Infants use intersensory redundancy before any learning. Something constrains what can be instituted; not all equations stand equal before execution. But the same file gives the two limits: genuinely intersensory Gestalten remain undocumented after decades of search, and the feeling of rightness produced by congruent pairings arises, in Spence's own words, despite the fact that there may be no objective truth about the matter. Dimensional constraints, no common space.

The displaced thesis — unity as instituted — has real foundations. Searle ^{[9] [10] [11]}: constitutive rules do not regulate an antecedent activity, they create its very possibility; the rules of chess did not regulate people already pushing wood around boards; the canonical form is X counts as Y in context C; such rules are almost tautological, halfway between rule and definition — neither true nor false. Institutional facts exist only within systems of constitutive rules; outside the institution, the man who "has five dollars" holds a rectangle of green-inked paper. The conventionalism of frameworks establishes the freedom to institute: after the non-Euclidean geometries, axioms become matters of convention, truth largely replaced by coherence, the pure mathematician indifferent to whether Euclid's axioms are true ^[12]; and Reichenbach adds the structure of the present case — the choice of a geometry is free only until the coordinative definitions have been formulated; after that decision, the question becomes empirical ^[13]. Free at the origin, binding thereafter. Goodman is the most exact ally ^[14]: the choice among symbol systems is free, but given a system the question becomes one of propriety under that system; systems are products of stipulation and habituation in varying proportions; and decisively — two domains can always be sorted and correlated in countless ways, but to have two sortable, correlatable realms is not yet to have a system: only when custom or express stipulation actually effects a classification of each realm and a correlation of the two do we have a system. Standard musical notation has made that selection; the pictorial sketch has not. The harmonic-chromatic codex is precisely such an express stipulation: it partitions the harmonic domain, partitions the chromatic domain, and institutes their correlation. Express stipulation, in Goodman, requires no collectivity. Finally Russell and Carnap, from an unexpected quarter: only experience teaches us to correlate the space of sight with the space of touch; the one all-embracing space is a construction ^[15]; the only intersensory validity science obtains passes through a stipulated common language — the unity is fabricated by the adoption of a language, never found among the qualities ^[16]. The instituted unity of the sensory fields, formulated by logical empiricism a century ago.

V. Sed contra — the antithesis, sourced

The antithesis was instructed in the dimension of the instituted — no longer the biological or experimental real, which attacks the old statement, but the displaced thesis itself. Two lines of attack, and an internal division.

The private language argument. Philosophical Investigations §258 ^[17]: the diarist who associates "S" with a sensation has no criterion of correctness — whatever is going to seem right to me is right, and that only means that here we can't talk about "right." §202: to think one is obeying a rule is not to obey a rule; hence it is not possible to obey a rule privately. Bouveresse hardens the requirements ^[18]: what is missing is a public expression of the rule and an established practice determining correct application; a rule must be followable several times and by several — one must be in a position to explain it and teach it to someone else; a private practice is a contradiction in adjecto. But the argument's exact target must be read: §258 concerns an inner sensation for which no definition can be formulated, with no bodily expression, checkable only against memory — a sign whose referent is inaccessible in principle. The scholarly reading confirms the restricted scope: by "practice" Wittgenstein means practice as fundamental human activity, not practice of a community; by "privately" he means by reference to one's own interpretation, not in isolation from other people. The requirement is externality — an objective regularity, a criterion independent of impression — not collectivity; there is no reason to insist that correction-practices must stem from other people, and hence no reason to reject individualistic rule-following ^[19]. The codex is the term-for-term contrary of the diary case: the rule is formulated, stipulated, documented; its application bears on public objects; the gap between prescribed and realized is verifiable by an instrument, not by the impression of the moment. The criterion of correctness that Wittgenstein declares impossible for "S" exists for A = B.

Convention as collective institution. Hume's analysis requires the common interest publicly expressed, the rule publicly known, and effective adherence by most — the rule must actually be followed in society for a convention to exist ^{[20] [21]}; conventional rules normally lose their point if not actually followed in the relevant community ^[22]. If the codex is a convention in this sense, the antithesis wins: no one convenes alone. But the collectivist front fissures from within, and precisely over chess. Millikan ^[23]: a convention is not tied by definition to any particular group; it is not necessary that any particular people follow it, nor that a large number do; the rules of chess do not tell you what to do, but what to do if you wish to play chess; you can get them wrong — but the standard then violated was set by your own intention; no public prescriptive rule will have been violated. The invitation freely accepted, the rule binding only the one who enters: the practice section, stated from within the antithesis's own camp.

The empty stipulation. A legitimate stipulation must satisfy two criteria ^[24]: Conservativeness — it must not establish new truths about the world; one cannot, by mere stipulation, establish new things about the moon — and Use — it must fix the employment of the defined term, render it executable. A stipulation can fail: if its consequences meet the false, it does not take ^[25]. Port-Royal grants the stipulative definition its charter ^[26]: arbitrary, incontestable, admissible as a first principle without further justification, provided the author makes his usage clear and holds to it. Arbitrary, incontestable, on condition of constancy — the statute of A = B, written in 1662. And Goodman closes the loop from within this file: in a notational system, the distinction between real and nominal definition still stands, as illustrated by the difference between writing a score for a work already extant and composing a new work. The codex composes; it does not transcribe. Conservativeness, in return, bounds what P9 can say: the stipulation A = B can establish no fact about the modalities — no common space, no discovered unity. It institutes a usage, nothing more. The antithesis, attacking, confirms the verdict against the old statement while leaving the displaced one intact.

Balance of the Sed contra. The antithesis holds on one point and yields on the other. It holds: a rule requires objectivity and normativity — a criterion of correctness independent of the impression of the one who follows; no decree escapes this. It yields: none of its best sources establishes that this criterion requires several persons. The Wittgensteinian requirement, read at its source, is externality and teachability-in-principle; the collectivist reading generalizes beyond the text.

VI. Respondeo

Do the modalities share a common space? In one sense no, in another yes, and here is what separates the two senses.

No, in the sense of discovery: no ideational space pre-exists in which sound and color would be surfaces of one interior. Neither perception (where unity belongs to the body, never to an idea), nor experiment (dimensional constraints, no intersensory Gestalt), nor logic (where the intersensory unity of science is fabricated by a stipulated language) supplies one. The internal proof is the symmetry argument of Section III: A ≠ B is institutable with the same legitimacy as A = B; that whose contrary remains available as the rule of another game describes nothing.

Yes, in the sense of institution: a constitutive rule suffices to bind two domains that no space grounds. The rule is arbitrary in its content, not in its status — free at the origin, it binds once posed, and it binds only the emitter: the receiver inherits an invitation, not an obligation; he may see A alone, B alone, or institute B = C, and that instituting is not a failure of the rule but the inheritance of its gesture. Unity is not the ground of the codex; it is its effect.

What the synthesis produces, contained in neither thesis nor antithesis: the criterion dividing the two families of instituted facts. A rule is constitutable by one person alone if and only if its execution is complete without others. Money is not — its only use is circulation; the acceptance of others is internal to it; a bill no one accepts is not currency lacking authority, it is not currency. The codex is — execution completes in the studio; the gap between prescribed and realized is measurable before the first gaze. The collective validates — confers authority, circulation, currency; it does not constitute. For constitution, externality suffices, and externality has three marks: a formulated rule; a criterion of correctness independent of impression; and teachability — the rule must be explicable and transmissible to a third party who could execute it in turn. The codex satisfies all three: stipulated, measured, teachable. Its teachability is not a promise but a standing fact — the formal level is documented and articulable on demand, and the measurement instrument that compares prescription to surface is itself a third-party executant of the rule, its permanent demonstration. Here the note records a recurrence: the corpus already held this criterion under another name. Explicability as condition (Proposition 19a) was framed as the condition of the ricochet; this note finds it a deeper office — it is what makes the solitary stipulation a rule at all. P9 reformulated and P19a support each other: one poses that the rule instituted by one suffices; the other supplies the criterion that makes that sufficiency non-private.

VII. Verdict

FALSE in its statement; the object it aimed at survives, reformulated. The current statement asserts a discovery ("the separation was never fundamental"): withdrawal. The reformulated proposition — instituted unity — is anticipated in its elements (constitutive rules, conventionalism of frameworks, notational stipulation) but their assembly for the case of the solitary emitter, with the criterion of complete execution, is formulated nowhere in the literature examined: it is the note's own ground.

VIII. Reformulation

No common space binds sound and color. I institute it. In this game, this chord is this color, because those are the rules of this game — and for no other reason. The rule is free at the moment I pose it; it binds me once I have posed it. It binds only me: the player enters if he wishes, sees what he sees, institutes his own equations if he wishes. The unity of the modalities is not what makes the codex possible. It is what the codex does.

IX. Debt Note

The notion of constitutive rule comes from Searle (1964, 1969, 1995); the freedom of the framework and its binding character once adopted, from the conventionalist tradition (Poincaré, Carnap, Reichenbach); the express stipulation that institutes a system of correlation between two domains, from Goodman (1968). The teachability condition as the criterion of a rule's externality comes from the Philosophical Investigations (§§202, 258) as read by Bouveresse (1976). The application to the case of the solitary emitter, and the criterion of complete execution without others, are proper to this text.

X. Falsification Condition

The institution itself is a decision — neither true nor false, it does not falsify, and this must be said. But the reformulation carries one falsifiable thesis: if the institution is free, then any equation stipulated with equal rigor must be executable with equal completeness. If certain equations systematically resist execution — if A ≠ B exhausts itself where A = B holds across four hundred canvases — then something pre-existing constrains the institution, and the thesis of a weak common space regains its rights. The corpus and the prescribed/realized instrument can judge.

XI. Remaining Objections

First, the dimensional relief: the crossmodal-correspondence file shows that some pairings take universally and others never. This note rules that a relief which constrains is not a space which grounds — the relief belongs to the material of execution, not to the foundation of the rule, and the feeling of rightness it produces arises without objective truth in the matter. But the objection remains formulable as a weak common space, and Section X states the test that would revive it. Second, the language analogy of Section III: the convention to be = être belongs, in Hume and Lewis, to the collective family — millions of executants sustain it. The analogy correctly illustrates the arbitrariness of the bond and the constraint of the convention once posed; it does not illustrate solitary constitution, and must be handled as a partial analogy in any final text.

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