Source
Isaac (2025), Philosophy and the Mind Sciences 6, LIT-1361, read in full in NOTE-1163 from the publisher’s open-access PDF. §2.2 (“Perceptual constancies: Group-theoretic structure”) with footnotes 3–8 and Figure 1, and §3 with the Cassirer quotation and Figure 3. The argument for objectivity is Cassirer’s, “The concept of group and the theory of perception” (1944), quoted at length, and is not reconstructed beyond what Isaac quotes.
What was actually shown
Nothing was tested in the paper. It argues in two steps.
The transformations are internal. Constancy is “something about its phenomenal character” that “remains ‘constant’ across gross transformations in the signal incident at the retina”: colour, size, shape and timbre. One could model it as an artefact of physical transformations, rotation groups or the projective group acting on planar projections, with no structure in experience (Gibson, Noë). Isaac argues that this is wrong, for two reasons.
- Experience of shape is not flat. Converging tracks and a carpet that turns trapezoidal down a hallway are contracted in depth, and perceived angles measured with an adjustable compass “do not match those of a linear projection” (Erkelens 2015; Wagner et al. 2018, cited). So the invariant cannot be that of planar projections. It “must instead be invariant over some internal analog to such transformations”.
- The transformations occur with no physical analogue. Two static images at suitable intervals are seen as one object rotating or translating (Shepard 1984), and same–different judgements take time linear in the angle between the two orientations (Shepard and Cooper 1982).
The projective invariants the paper uses as the physical alternative are correct as stated. Under random projective maps, the line cross-ratio (EG × FH)/(FG × EH) of footnote 7 and Niall and Macnamara’s planar cross-ratio [area(EFC) × area(GHC)]/[area(FGC) × area(EHC)] of footnote 3 were invariant to a relative error below 10⁻¹¹ in 2,000 trials each, checked here. For the planar ratio this follows because each triangle’s area is multiplied by the same determinant over the product of its vertices’ homogeneous weights, and every vertex appears equally often above and below the line.
The invariants make experience objective. Colour experience has two levels at once: the shadowed and sunlit parts of a wall differ in “apparent, subjective” colour, and the wall is seen as uniformly coloured. Instructions can move subjects between the two (Radonjić and Brainard 2016), and the painter’s attitude reaches the first. Cassirer: wherever there is “an opposition and separation between an ‘ego’ and the ‘world’”, perception “is a process of objectification, the characteristic nature and tendency of which finds expression in the formation of invariants. It is within this process that the distinction between ‘reality’ and ‘appearance’ emerges.” Isaac concludes that the group-theoretic structure of perception “ensures phenomenal experience constitutes a genuine representation of an objective world”, and the abstract that it “induces a distinction between subject and object”.
What could have failed: the first half could be refuted, modality by modality, by showing that a constancy is fully explained by an invariant of the stimulus, with no internal transformation. For shape in depth the cited angle measurements count against that. Nothing in the paper could show the second half false.
What this does not say
- Not that constancy is a group. The paper calls the link between invariance and group theory “conceptual”, not empirical, and its own cases are not groups: constancy is “at best approximate”, Krantz’s structures for metamers are groupoids (footnote 5), and in the illumination toy model the inverse of adding a light is defined by filtering the white baseline, so it is an inverse only from that baseline. “Group-theoretic” means invariance under transformation.
- Not a test of objectivity. No criterion separates a process that extracts invariants, which a camera pipeline with white balance or any object recognizer also does, from one for which there is a subject–object distinction. The co-presence of the two levels is offered for introspective verification (footnote 6).
- Not about whether a state is conscious. Like the rest of the paper, it concerns the character of experience.
- Not a claim about mechanism. Isaac takes “no position” on whether perception involves multiple stages of representation (footnote 6). The internal transformations are functional analogues, not identified processes.
- Not that illusions are errors, or that they are not, in general. The checker-shadow case is read as veridical recovery of reflectance; the paper says “many”, not all, illusions are mislabelled.
Connections
- QUESTION-254 and CLAIM-412. The record filed the paper for this layer, as a candidate for what a perspective adds to an interpretation. It offers a structural mark of perspective, a varying level and an invariant level present together, and no criterion that would keep a perspective-free invariant extractor out. So it narrows the question and does not answer it. CLAIM-411’s gap, why any such organization is conscious, is outside it.
- THEORY-880. Lyre’s similarity structuralism places an experience by its position in a quality space. This account adds a layer above the geometry that Lyre lacks, and denies that geometry alone generates meaning. THEORY-867’s finding that colour-space geometry does not mark the unique hues does not touch it.
- QUESTION-255. The two levels are a case of one experience holding two incompatible-seeming descriptions of the same surface (different and the same colour), which is not a gluing failure: one global state holds both, indexed by level. The reading is the record’s.