Système d'Équivalences

Merleau-Ponty's phrase from L'Œil et l'esprit (1961) for the structural relation that holds between a painting and the world it brings to expression. The painting is "a system of equivalences" — its forms, colors, lines, and depths are not copies of worldly forms, colors, lines, and depths but equivalents of them in a different medium. The equivalence runs through the conditions of phenomenal givenness (what Taddio 2025 calls phenomenal-invariants): the painting and the world satisfy the same underlying organizational rules — figure-ground, principles of unification, amodal completion, transparency conditions, depth cues — and through this shared satisfaction the painting becomes "an analogue or likeness only according to the body" (E&M).

The phrase recurs at the §4 close as the "system of equivalences" through which the painter "discovers... the means by which... visible things become things, by which Being becomes Being." It is one of MP's most condensed formulations of what painting does: it is "a concept-less presentation of universal Being."

Key Points

Not similarity, not denotation: a painting is not a copy that resembles its object (Gombrich, Hopkins) and not a symbolic token that denotes its object (Goodman). It is an equivalent — an instance of the same set of phenomenal conditions the object instantiates, expressed in a different medium.
The equivalence is operative, not figurative: MP's "system" runs through the painter's manipulation of the canvas's forms, colors, depths, and edges in configurations that satisfy the same invariants the depicted scene satisfies. Equivalence is built; it is not a relation between pre-existing terms.
Multiplied across painters and works: "Since Cézanne, pictorial art has aimed to reveal new worlds, new virtualities of Being through the multiplication of systems of equivalence" (E&M §5; cited Taddio §8). Each painter establishes a new system; the multiplication of systems is the multiplication of accesses to Being.
"Concept-less presentation of universal Being": the system of equivalences operates without conceptual mediation. The painter does not think about the conditions of appearance; the painter enacts them on the canvas. The result is an unmediated presentation of Being that no concept can fully capture.
Cardinal site for phenomenal-invariants: in Taddio 2025 the system of equivalences is the operative structure linking world and image. The phenomenal invariants are the content of the equivalences; the system is the form in which the invariants are shared.

Details

MP's Use in Eye and Mind

The phrase appears with structural weight in §2 and §4 of Eye and Mind. In §2, MP introduces it via the "internal equivalent" (équivalent interne) the painter brings forth from the body's encounter with the visible: "Quality, light, color, depth, which are there before us, are there only because they awaken an echo in our body and because the body welcomes them. Things have an internal equivalent in me; they arouse in me a carnal formula of their presence... Why shouldn't these correspondences in turn give rise to some external visible shape in which anyone else would recognize those motifs which support his own inspection of the world?" (E&M §2).

In §4, MP generalizes: "A Cartesian can believe that the existing world is not visible, that the only light is that of the mind, and that all vision takes place in God. A painter cannot grant that our openness to the world is illusory or indirect, that what we see is not the world itself, or that the mind has to do only with its thoughts or with another mind. He accepts, with all its difficulties, the myth of the windows of the soul; it must be that what has no place is subjected to a body — even more, what has no place must be initiated by the body to all the others and to nature. We must take literally what vision teaches us: namely, that through it we come in contact with the sun and the stars, that we are everywhere all at once, and that even our power to imagine ourselves elsewhere... borrows from vision and employs means we owe to it" (E&M §4).

The painter's discoveries are then characterized: depth as "the experience of the reversibility of dimensions," color as "the place where our brain and the universe meet," line as the genesis of forms, movement as paradoxical arrest. Each of these is a "system of equivalences" — a way the painter brings to expression a phenomenal-invariant register that the depicted world also instantiates.

The §4 Close: "System of Equivalences" as Universal-Being Formulation

The cardinal passage Taddio cites: "Since Cézanne, pictorial art has aimed to reveal new worlds, new virtualities of Being through the multiplication of systems of equivalence" (E&M, p. 182). Two clauses do the work:

"new worlds, new virtualities of Being" — each painter does not merely access a single Being but multiplies virtualities of Being; each painting opens a region of the visible that was not previously opened.
"multiplication of systems of equivalence" — the means of this opening is the multiplication of systems. Cézanne's system, Klee's system, Matisse's system, Rodin's system are not competing accounts of the same Being but parallel openings of different virtualities. Each is a system; the multiplication is the practice of painting since Cézanne.

The "concept-less presentation of universal Being" formulation (E&M, p. 182) emphasizes that the systems operate prior to conceptual articulation. The painter does not concept-translate; the painter assembles a phenomenal-invariant configuration that is an access to Being.

Taddio's HUB-level Deployment

In Taddio 2025, "système d'équivalences" recurs 6+ times across §§ 1, 2, 7, 8 — well above the source-level threshold for HUB weight. Taddio's deployment makes the term the central explanatory device for the world-painting parallelism:

§1: "Painters disclose 'things' that are the expression of a système d'équivalences secretly linked to that dimension of Being Merleau-Ponty describes as 'raw' or 'wild': worlds belonging to the same (phenomenal) 'fabric' – to use the author's metaphor – from which the entire sphere of the experienceable is woven."
§2 close: "thereby establishing a système d'équivalences between different worlds."
§7: "Pictorial art is a 'system of equivalences' internal to appearance; it is the phenomenon itself, together with the rules of its manifestation, that we share with the world."
§7 (texture-gradient): "the 'spectacle' unveiled by Magritte implicitly employs the 'texture gradient' as a system of equivalence."
§7 (definitional): "By 'system of equivalences', we mean that within the condition of the phenomenon's appearance, both the appearance of the world and its representation are inscribed."
§8 closing (citing MP §4 close): "systems of equivalences... a concept-less presentation of universal Being."

Taddio's contribution is not a new MP-citation but a new operational use: the system of equivalences is what the phenomenal invariants make possible. World and painting both inscribe themselves "within the condition of the phenomenon's appearance," and that mutual inscription is the system of equivalences.

The Painter's "Internal Equivalent" (Équivalent Interne)

MP introduces équivalent interne in E&M §2 as the body-side correlate of the system of equivalences. Things "arouse in me a carnal formula of their presence." The painter's task is to bring forth, from this carnal formula, an external visible shape that other bodies can recognize as awakening the same formula in them. The équivalent interne is what flows from the body's reception of the world; the système d'équivalences is what the painter constructs on the canvas to externalize the internal equivalent.

The pair équivalent interne / système d'équivalences gives the operation a body-and-canvas form: the painter's body is the medium of internalization; the canvas is the medium of externalization; the system is what links them. This is why MP says the painting is "an analogue or likeness only according to the body" — the equivalence runs through the body, not through geometric correspondence.

Multiplication Across Painters and Periods

The phrase "multiplication of systems of equivalence" insists that the practice is plural and historical. Cézanne opens one system; Klee opens another; Matisse, Rodin, Giacometti each open theirs. The systems are not synonymous and do not converge on a single account. The wiki's two-historicities page captures the same insight at the level of art history: each painter's advent is a new opening, not a contribution to a cumulative project. The system-of-equivalences register is the operative form of advent in painting.

This connects to Malraux's metamorphosis: each work, recovered into a new context (the museum-without-walls), enters into new systems of equivalence with works it never knew. The system is not stable across history; works are continuously re-sited within new constellations. Système d'équivalences is therefore both a synchronic structure (this painting and this scene share invariants) and a diachronic one (this painting enters new equivalence-systems as it survives into new contexts).

Connection to Coherent Deformation

MP's coherent deformation (a phrase he takes from Malraux) is closely related. A coherent deformation is the universal index of expressive operation — style as the systematic-but-non-rule-governed alteration through which an artist's vision becomes recognizable. The system of equivalences is what such deformation produces: a coherent deformation transforms the conditions of phenomenal appearance into a configuration that is equivalent (in the system-of-equivalences sense) to the world it expresses. Style is the operation; system of equivalences is the operative result.

What the Concept Does

Système d'équivalences does four pieces of argumentative work in MP's late aesthetics. First, it displaces resemblance and denotation as the operative categories of pictorial reference. Painting is neither copy (resemblance) nor symbolic token (denotation) but an instance of the same set of phenomenal conditions the depicted scene instantiates, expressed in a different medium. The concept shifts the question from "what does the painting refer to?" to "what does the painting share with the world it expresses?" — and the answer is the conditions of phenomenal appearance themselves.

Second, it operationalizes painting as ontological inquiry. If paintings are equivalents of the world's phenomenal organization, then painting is not commentary on Being but an enactment of it: the painter, working through the body, assembles configurations that are accesses to Being rather than representations of it. The §4 close formulation — "concept-less presentation of universal Being" (E&M, p. 182) — names what the system of equivalences actually does as a philosophical operation.

Third, it makes the synchronic-structural register of MP's three-tier expressive architectonic explicit. As the live-promoted-to-supported claim (claims#coherent-deformation-universal-operative-form) establishes, coherent-deformation is the operative-form register, stiftung is the diachronic-mechanism register, and système d'équivalences is the synchronic-structure register. The concept's distinctive job is naming what style is as a structure — "style is the system of equivalences that he makes for himself for the work which manifests the world he sees" (IL raw 820).

Fourth, it enables the multiplication thesis — the claim that painting since Cézanne is the multiplication of systems, not the convergence on a single account. Each painter opens a different system of equivalences; the systems are not synonymous; their plurality is the practice of painting itself. This is the operative form of advent in painting.

What It Rejects

The concept pushes against three rival pictures of how painting refers to its object.

The primary refusal is of resemblance theories (Gombrich, Hopkins, Wollheim, the broader tradition that takes pictorial reference as similarity). Resemblance theories presume a pre-existing shared content (visual form) that painting and world both possess; the painting refers because it possesses what the world also possesses. MP's system rejects this: the equivalence is built, not given. It is established through the painter's body-work; the canvas's marks acquire their equivalence through the system the painter constructs, not through a shared visual property.

The second refusal is of denotation theories (paradigmatically Goodman's reading of pictures as symbolic tokens). Denotation makes the painting a sign that points to its referent through conventional or syntactic relations. The system of equivalences refuses the linguistic-semiotic frame: the painting is not a token but a configuration that enacts what the world enacts. The relation is operational, not semiotic.

The third, more diffuse refusal is of the Cartesian assumption that pictorial vision could be illusion or indirect access ("a Cartesian can believe... that what we see is not the world itself," E&M §4). The painter cannot grant this; painting requires that the body's reception of the world is genuine. The system of equivalences names what makes this anti-Cartesian commitment philosophically operative — the painter does not represent a world she might or might not be in contact with; she works on the conditions of contact themselves.

Finally, the concept resists the temptation to read the multiplication of systems as mere stylistic variation or as competing accounts of one Being. It is neither: each system opens a new virtuality of Being (E&M §5; cited Taddio §8), and the multiplication is constitutive, not symptomatic.

Stakes

If système d'équivalences is accepted as MP intends, three things change for the late aesthetic ontology.

First, painting becomes a privileged philosophical operation rather than a domain to which philosophy applies. The "concept-less presentation of universal Being" formulation makes painting do work that propositional philosophy cannot: assemble a phenomenal-invariant configuration that is an access to Being. MP's fundamental-thought-in-art thesis depends on this: only if paintings are equivalents (and not copies or symbols) can painting be fundamental thought, not derivative thought. (Confidence: medium — this is interpretive synthesis going beyond what E&M states explicitly, but it follows from the §4 reading and is operationalized in Taddio 2025.)

Second, the cross-source claim that coherent deformation is the universal operative form across painting AND literature (claims#coherent-deformation-universal-operative-form, supported) gains its synchronic anchor here. The three-element cluster (operative-form / diachronic-mechanism / synchronic-structure) cannot operate without système d'équivalences as the synchronic structural register; the supported claim's payoff includes a re-positioning of this concept page as load-bearing for MP's late expressive architectonic across multiple domains.

Third, the bridge to phenomenal-invariants (Taddio's contribution) makes the system of equivalences philosophically contestable in a way it would not be without empirical-phenomenological grounding. If invariants are the content of the equivalences, then the concept is hostage to a body of psychological-phenomenological evidence about figure-ground, amodal completion, transparency conditions, and depth cues — the system of equivalences is no longer a metaphor but a structurally constrained claim about what world and painting share.

Problem-Space

The concept addresses a problem that pre-dates MP: how can a painting give its world rather than merely refer to it? The problem appears in different vocabularies across the philosophical tradition — as the "iconicity" question in semiotics, as the "presentational" vs "representational" distinction in aesthetics, as the "showing vs saying" distinction in Wittgenstein, as the question of what makes a picture of its subject. MP's système d'équivalences is one philosophical answer: a painting gives its world by enacting the same phenomenal-invariant conditions the world enacts, expressed in a different medium.

The problem reframes inheritance. Where resemblance and denotation theories take the pictorial relation as a transmission of content (through similarity or through convention), MP takes it as a parallel enactment of the conditions under which content arises. This shifts the philosophical site of the problem from semantics (what does the picture mean?) to ontology (what does the picture do in the visible?). The concept does not dissolve the problem but reformulates it: the question "how does a painting refer?" becomes "what configuration of phenomenal conditions does the painting establish, and how does it parallel the configuration the depicted world establishes?"

Recurrence in the wiki: the same problem appears under different vocabularies in fundamental-thought-in-art (painting as ontological inquiry, not commentary), two-historicities (painting as advent, not cumulative knowledge), lateral-universal (non-subsumptive convergence between distinct items), and coherent-deformation (style as systematic-but-non-rule-governed alteration). When the same difficulty recurs across three or more concepts under different vocabularies, the problem-space is at threshold for promotion to a dedicated problem-space-tagged page.

Connections

is the operative form of fundamental-thought-in-art — painting as ontological inquiry happens via the construction of systems of equivalences.
is operationalized by phenomenal-invariants — the invariants are the content of the equivalences; the system is the form in which they are shared.
is the result of coherent-deformation — style as systematic deformation produces system-of-equivalences configurations.
is the synchronic side of two-historicities's advent register — each painter's advent opens a new system of equivalences.
contrasts with resemblance theories (Gombrich, Hopkins, Wollheim) — the painting is equivalent, not similar.
contrasts with denotation theories (Goodman) — the painting is equivalent, not a symbol.
is the carnal form of chiasm / reversibility — the system of equivalences is the chiasmic structure made operative in painting; world and painting cross through the body of the painter.
parallels lateral-universal — both name a non-subsumptive relation between distinct items (cultures, paintings, traditions) where convergence runs through oblique passage rather than through inclusion under a higher category.
is enacted by depth-profondeur — pictorial depth functions as a system of equivalences with worldly depth (Taddio §7).
enables the painter's "magical theory of vision" (MP, E&M §4) — the painter discovers without proving, by working through equivalences rather than by reasoning to conclusions.

Open Questions

Scope and limits: does "system of equivalences" extend to non-figurative painting, abstract art, conceptual art? MP's primary cases are figurative (Cézanne, Klee, Rodin, Matisse, Giacometti); Taddio's are also figurative (Magritte's surrealism is still figurative in the relevant sense). The applicability to genuinely non-representational art (Pollock, Rothko, Mondrian late) is unclear.
Multiplication and incompatibility: if each painter opens a different system, are the systems mutually translatable? MP suggests they are not (no cumulative progress); but if they are not, does "system of equivalences" name a single concept or a family of concepts that share only a name?
Relation to MP's "wild Being": the §1 Taddio-citation links system of equivalences "secretly" to "raw" or "wild" Being. What is the precise relation between the multiplication of systems and the unity of wild Being? Does each system partially express wild Being, or do the systems collectively constitute wild Being's expressive field?
Body-side vs. canvas-side: the équivalent interne is body-side; the système d'équivalences is canvas-side. The relation between them passes through MP's "lending the body to the world" formulation. But what is the operational mechanism by which an internal equivalent becomes an external system? MP's answer is "by the body lending itself"; this is suggestive but not detailed.

Synthetic Claims

The synthetic interpretive layer (wiki/claims.md) articulates one supported claim for which this page is a Wiki home. Supported claims may be cited as stable synthetic claims without provisional framing per CLAUDE.md §Claims Register Format.

supported claim, see claims#coherent-deformation-universal-operative-form — coherent deformation is MP's universal operative form across painting AND literature, not painterly-specific; the three-element cluster (coherent deformation + Stiftung + système d'équivalences) operates without chiasm at multiple sites in Indirect Language (1952) and The Possibility of Philosophy (1959–61). Promoted to supported 2026-05-04 under R8 user pre-authorization. The three-element cluster framing repositions the present page's système d'équivalences as the synchronic-structure register of MP's three-tier expressive architectonic, with stiftung as the diachronic-mechanism register and coherent-deformation as the operative-form register. The cardinal IL passage (raw 820): "style is the system of equivalences that he makes for himself for the work which manifests the world he sees. It is the universal index of the 'coherent deformation'" — the synchronic structure (style = système d'équivalences) is the universal index of the operative form (coherent deformation).

Sources

merleau-ponty-1961-eye-and-mind — primary text. §2 (équivalent interne, "carnal formula of their presence"); §4 (system of equivalences as multiplication of virtualities of Being, "concept-less presentation of universal Being," p. 182). Already noted on the source page; this concept page consolidates the cross-section weight.
taddio-2025-art-and-psychology — HUB-level secondary deployment. §§ 1, 2, 7, 8 with 6+ attestations; §7 supplies the operational definition ("within the condition of the phenomenon's appearance, both the appearance of the world and its representation are inscribed"). Taddio's contribution is the bridge to phenomenal-invariants as the explicit content of the equivalences.