Source
Kleiner & Ludwig (2023), “What is a Mathematical Structure of Conscious Experience?”, LIT-143, read in full in NOTE-135 in the Synthese version of record (2024, 203:89), compared against arXiv v1. Section and page numbers are the Synthese version’s.
What was actually shown
The implicit criterion and its failure (§1). The authors reconstruct the standard in use as (MDC): a structure is of conscious experience if its domains are sets of experiential aspects (D1) and its axioms hold (D2). As a sufficient condition it fails three ways, each by explicit construction:
- Incompatible structures (p. 4): any aspect set X carries both the discrete topology and {∅, A, A^⊥, X}, so (MDC) certifies both.
- Arbitrary re-definitions (pp. 4–5): if (M, d) passes, so does (M, C·d) for every C > 0, and (f(a)+f(b))·d(a,b) passes under modified axioms, which can break the triangle inequality.
- Indifference (p. 5): the first two need no input about experience beyond “some set of aspects”.
The replacement (pp. 10–12). A variation is a change e → e′ of experience with a partial map between their aspects. (MSC): S is a structure of experience iff its domains are aspects (S1) and every relation or function S_j has an S_j-aspect (S2): an aspect that, for all variations and all relata, changes exactly when the variation fails to preserve S_j. (MSC) implies (MDC), so every structure of experience also describes it.
The two cases that pass. Relative similarity to a reference colour is a strict partial order satisfying (MSC), if transitivity holds, which the authors assume and call “ultimately, an empirical question” (p. 14). The regions of visual experience form a topology satisfying (MSC), given the subsumptive unity thesis of Bayne and Chalmers, restricted to sets “experienced as unified” (§4, fn. 12), and closure properties that “seem to” hold (p. 18).
How (MSC) meets the three problems (§5). No aspect can be both an S-aspect and an S′-aspect of incompatible structures, since one variation cannot both change and not change it. A rescaled C·d has different relata, so whether it has an aspect is a question about experience, not automatic. And (MSC) cannot be applied without examining experience.
What could have come out otherwise. The constructions in §1 are proofs; they could not have failed. The positive cases could have failed had the similarity aspect or the unity aspects not tracked the relations. NOTE-135 records that the relative-similarity proof is near-definitional, since < is defined from the experienced aspect.
What this does not say
- That metric spaces cannot model experience. That argument (from the construction of ℝ, and from doubt that two qualities are experienced as “a specific number apart”) is in arXiv v1 §4 only. The published paper removes it and concludes for relative similarity and topology alone. A citation for “metric structure is not a structure of experience” is a citation of a withdrawn preprint argument.
- That incompatible structures cannot both pass. The §5 argument shows only that no single aspect serves both. Two incompatible structures could each pass through different aspects. It also assumes that a mathematical automorphism is realised as a variation of some actual experience, which is not argued (NOTE-135, C5).
- That any S-aspect can be certified. (MSC) quantifies over all variations of all experiences in E. Any real application checks a finite sample, and the paper does not say how to certify an aspect from finite data.
- That rescaled metrics are excluded. §5 shows that they no longer pass automatically, not that they fail.
- Which account of experience is right. The definition is neutral between qualia, qualities and IIT’s phenomenal distinctions (fn. 3). It presupposes that experiences have well-defined sets of aspects, so an illusionist would read the aspects as quasi-phenomenal properties (THEORY-633).
Connections
- IIT (LIT-185, LIT-445): (MSC) is the test IIT’s cause-effect structures would have to pass to count as structures of experience rather than descriptions of it, and Problem 2 cites IIT’s asymmetric distance as an arbitrarily re-axiomatised structure. The paper does not apply the test. The grid-to-space and chain-to-time results that Barrett et al. credit to IIT (THEORY-523) are the natural first cases.
- The unity premise is shared with THEORY-063 (Metzinger’s globality) and with THEORY-573 (cross-modal processing feelings), which offer a mechanism for felt unity rather than a structure.
- The analogy to claims that learned representation spaces mirror phenomenal structure (ANTH-LIT-458) is NOTE-135’s, not the paper’s.