Contribution
Earlier objections to phenomenal structuralism appeal to intuitions about intrinsic character that structuralists reject. This paper plays “the structuralist game through and through” (abstract). It takes structural facts about colour that colour science accepts, and argues that the similarity geometry the structuralist must explain them with does not contain them. The claim is that structuralism cannot account for them, not only that it has not yet.
Key insight
A similarity space records how far apart colours are. It does not record that orange looks like red and yellow together while red looks like nothing else, nor that grey lies between black and white as a mixture while it lies between red and green as neither. Those are facts of composition, not of distance. Strip the colours and axes from CIELAB and the colourless solid “encodes only its own shape” (p. 11). If the shape does not mark the unique hues, structuralism has nothing to explain them with.
Assumptions
- Similarity structuralism is the target: “The phenomenal character of a mental quality is fully determined by its similarity relations with the other phenomenal characters in the similarity space” (p. 4). Rosenthal’s discrimination-based quality-space theory is set aside, though the arguments “could be adaptable to it” (pp. 4–5). Tsuchiya allows other relations in principle but works with similarity in practice (fn. 2).
- What structuralism implies (p. 5): a system cannot experience only red; losing one character changes others; similarity spaces “must be asymmetric”, since symmetric points are “structurally indistinguishable … they should feel the same, hence they should be the same point”; and a subject’s several similarity spaces must all differ in geometry. Characters have “neither microstructure … nor any intrinsic nature”.
- The colour composition claims (p. 7). 1.1: exactly four hues (red, green, blue, yellow) are experienced as pure, and all others as combinations of them. 1.2: exactly six colours (the four saturated unique hues, white, black) are pure. 2.1: composite hues are weighted combinations of two unique hues, and red with green, blue with yellow, are “prohibited”. 2.2: composite colours combine one or two saturated unique hues with white and/or black.
- CIELAB is a good approximation. Euclidean distance in CIELAB is imprecise for small differences, and CIEDE2000, CAM16-UCS and Oklab are better, but CIELAB is close enough to make it “improbable that structuralism will find in the other models what it does not already find in Euclidean CIELAB” (p. 12).
- Colour as the test case. The paper is silent on other modalities, but argues that if colour needs a non-structuralist account, others likely do too (pp. 2–3).
Key results
- The evidence for the composition claims (§3, pp. 7–10). Leonardo’s six simple colours; Hering’s opponent theory; hue-naming studies in which naïve subjects describe orange as red and yellow but cannot describe the region around 580 nm without “yellow”; Clark’s observation that unique colours match every colour in mixture and cannot themselves be matched by others. Some cross-cultural and infant evidence is cited against a purely linguistic origin. The opponent-process model accounts for the claims, though its neural basis for unique hues is “elusive” (p. 9).
- Against the critics of unique hues (pp. 9–10). Wright’s appeal to Bosten & Boehm 2014 (hue scaling with only non-unique hues) is said not to generalize, since that design forced reliance on similarity. Conway et al.’s Tsimane’ study is said to have had 9 of 40 participants misread the task. Arstila’s citation of Jameson is said to cite an assertion, not an argument. “On the whole, the case against unique hues is weak” (p. 10).
- The unique hues objection (§4.1, pp. 11–13). (1) Structuralism must explain character by the geometry of the similarity space. (2) Exactly four hues are experienced as distinct from all others. (3) No geometric property of the space distinguishes unique from composite hues. (4) Structuralism is wrong. On premise 3: CIELAB shows no such property; better metrics are unlikely to; and the colours missing from current models (chimerical colours, psychedelic colours, and “olo”, the saturated teal produced by stimulating M cones alone, Fong et al. 2025) would add mainly saturated teals and light blues (Figure 3), which “does not seem enough to do the job” (p. 13). Even a distinctive location would not explain why composite hues “seem to be composed of unique hues, while the converse does not hold” (p. 13).
- The opposing dimensions objection (§4.2, pp. 13–15). The black–white axis “exhibits the same gradual change from black to white, whereas the perpendicular dimensions are opposing dimensions” (p. 14): along red–cyan one goes from red to grey and then a different way from grey to cyan. Current models are asymmetric, so every axis is geometrically unique, but “only the black-white axis is so peculiar in its phenomenology, and it is not equally peculiar in its geometrical uniqueness” (p. 15). This argument does not need the composition claims, since the difference is “an immediately evident qualitative fact” (p. 15).
- Introspection (§5, pp. 15–18). Structuralism is built on introspected similarity, so it cannot dismiss introspection wholesale. Judgements that a hue contains other hues are component analyses within introspection’s operating range, like noticing citrus notes in a perfume, unlike the judgement that experience has an intrinsic character. The structuralist reply that orange “seems to contain red and yellow because it is similar to them” (p. 17) is called incomplete, since it does not explain why we describe hues as “pure” and “mixture” at all. This is offered as a third, less decisive argument.
- Conclusion (§6, p. 18). “the structure of our color experience is incompatible with structuralism”. The suggested alternative is to ask how far neuroscientific models such as opponent-process theory “might inform a metaphysics of mental qualities”.
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Exactly four hues are experienced as unmixed and all others as mixtures of two non-opponent ones; white, black and these four are the pure colours | moderate to strong as reported; the critics’ case is answered, not refuted with new data | §3; Hering, hue scaling, cross-cultural studies, as cited |
| C2 | No geometric property of the colour similarity space distinguishes the unique hues | moderate for CIELAB by inspection; asserted, not computed, for CIEDE2000, CAM16-UCS and Oklab | §4.1; Figure 1 |
| C3 | Completing the colour space with colours now missing will not supply such a property | weak: an extrapolation from where olo-like colours fall | §4.1; Figure 3 |
| C4 | The black–white axis differs in kind from the opponent axes, and no adequate geometric feature marks the difference | moderate: the phenomenology is plain; “adequate” carries the argument | §4.2 |
| C5 | Similarity structuralism cannot dismiss these facts as introspective error without undercutting its own data | moderate | §5 |
| C6 | Similarity structuralism is false for colour experience | follows if C2 and C4 hold | §4, §6 |
Concepts
- Similarity structuralism: character fully fixed by similarity relations, hence by location in, and geometry of, a similarity space.
- Similarity space: the structure of a subject’s phenomenal characters in one modality and their similarities, often a geometric solid in which distance is proportional to dissimilarity. Called a quality space by others.
- Unique hues and pure colours: the four hues, and six colours, experienced as unmixed.
- Opposing dimensions: axes through grey along which each half shows only one of its extremes.
- Natural Color System: a system expressing colours as combinations of pure colours; not a similarity space, because it is not perceptually uniform (Figure 2).
Connections
The paper takes its definition of structuralism from Clark (1993, 2000) and names Lyre 2022 (LIT-1344, NOTE-1060), Fink et al., Fleming & Shea, Malach, Lau and Tsuchiya’s group as defenders. It sets itself apart from Negro 2025 (LIT-1346, NOTE-1054) and Chalmers 1996, whose critiques rest on intuition; Negro is thanked in the acknowledgements. Its colour science runs through Hering, Hardin, Matthen and Cohen. Two internal slips: the introduction says introspection is treated in “Section 6”, which is §5, and premise 2 of §4.2 is said to draw “from structural fact 3”, where the composition claims number only two.
Bearing on the record
- CLAIM-412 (constitution by interpretive organization). The claim already records that Aldé bears on it only if its relations are similarities, and that A7 lists causal, counterfactual, temporal and evaluative ones. The reading confirms the scope: Aldé’s arguments are against similarity geometry alone, and he says Rosenthal’s discrimination view would need its own version. But it also gives the claim something to meet. The composition facts are facts about how one colour experience contains others. If interpretive organization fixes character, it must yield unique hues and the opponent structure. Aldé’s own pointer, to the opponent-process mechanism, is a causal organization, so the claim’s relational vocabulary may have the resources that a similarity space lacks. That is a reading, not something the paper says.
- TERM-073. Aldé’s “component analysis” in introspection, the judgement that a colour contains red and yellow, is an interpretation in the term’s sense, a distinction with context and consequence. Whether it constitutes the composite character or reports it is the claim’s question in miniature.
- CLAIM-136 (relata without primitive identity). By analogy only. Aldé states that a structuralist must make similarity spaces asymmetric, because two symmetric points “should feel the same, hence they should be the same point” (p. 5). That is the strict version of CLAIM-136 applied to phenomenal characters: no difference without a relational difference, and so no plurality either. The weak version, which allows two structurally indistinguishable positions to be two, is the move a phenomenal structuralist would need if colour space had a symmetry, and Aldé does not consider it. His arguments are about character, not identity, and they do not reach communicative acts.
- THEORY-095 (Inverted Earth). Aldé cites Chalmers’s “structure-preserving spectrum inversion” as the intuition-based objection he means to improve on. His unique-hue facts would also block simple inversion, since swapping unique and composite hues would be noticed. He does not draw that consequence.
- THEORY warranted. THEORY-867 states the paper’s thesis. It is a second objection to THEORY-880, with a different footing from THEORY-868’s.
- No instruction for machine-learning practice; nothing for the anthology.
Limitations
- Premise 3 of the unique hues objection is argued by inspection of CIELAB and by extrapolation. No geometric analysis of a uniform colour space is reported, though the paper says one “could” be carried out (p. 12).
- “Adequately” in the opposing dimensions objection carries the weight. The paper grants that the black–white axis is geometrically unique and argues only that its uniqueness is “unremarkable”.
- The case for unique hues answers the critics’ studies and does not add data. The paper itself notes that unique-hue loci vary widely across subjects and are not opposite in colour space (p. 9), which the structuralist could also use.
- The target is similarity structuralism. Structuralisms that use other relations (discrimination, causal or computational relations, or the internal structure Negro distinguishes) are not shown to fail.
- Colour only.
Open questions
- Run the analysis the paper calls possible: search CIEDE2000, CAM16-UCS or Oklab for any invariant (curvature, a singularity, a symmetry axis) that singles out the unique-hue loci, and check it against each observer’s unique-hue settings.
- Can a structuralism whose relations include composition or containment, not only similarity, account for the composition claims? If so, is it still structuralism in Lyre’s sense?
- Does the opponent-process mechanism’s organization fix the composition facts, as Aldé suggests? That would move the explanans from a similarity space to a causal structure.