Johannes Kleiner, Tim Ludwig (2023), arXiv preprint; published in Synthese (online 2024-03-05) — ARXIV-2301.11812
Key takeaways
- Saying that a mathematical structure “describes” experience is not enough, since it admits incompatible, arbitrarily redefined and consciousness-indifferent structures. A structure S is of conscious experience only if experience has an “S-aspect” — one that a variation of experience changes exactly when the variation fails to preserve S. On this test relative similarity and topology (via phenomenal unity) qualify and metric spaces do not.
Seeded from the abstract and a skim, before the reading in NOTE-135. What follows is what the work says about itself.
Consciousness science has several promising ways of representing experience with mathematical spaces and structures (quality spaces, qualia spaces, phenomenal spaces), but no explicit definition of what a “mathematical structure of conscious experience” is. Kleiner and Ludwig propose one. It connects abstract mathematical entities with the concrete facts of experience, complements existing quality-space approaches, gives a general method for finding and studying experiential structures, and may unify approaches across fields. They hope it will ground a common formal language for studying consciousness.
Standing in the record
Filed from the 2026-09-26 sweep of the papers-feed tracker for philosophy: 30 seconds of active reading over 1 session. It was filed Deferred, unread. NOTE-135 is the close reading of 2026-09-26, and it placed the work: Active — worth reading as the most explicit criterion for when a formal model is of experience rather than a convenient description of it. Its two positive results are conditional: transitivity of relative similarity is assumed, and the topology result assumes the subsumptive unity thesis. Cite the Synthese version, which has dropped v1’s argument against metric structure.
When seeded, before the reading in NOTE-135, the entry gave a priority for a deeper reading: medium — t=30 s. The definition is compact and the skim captures it, but the metric and topology results (§§4–5) need a fuller reading before any note relies on them.
What the seeding asked a deeper reading to check (NOTE-135 is that reading):
- It gives a principled criterion for when a formal model is of experience rather than a convenient description. That matters for IIT’s Φ-structures (LIT-185) and for any claim that an ML representation space mirrors phenomenal structure.
- The rejection of metric structure is striking and bears on psychophysical quality-space work that assumes metrics. A deeper reading should check the second reason for rejecting metrics, which this skim did not reach.
- Compare the Synthese version with arXiv v1 before citing section numbers.
Access when seeded: arXiv abstract page (v1 submitted Thu 26 Jan 2023; only v1 is listed) and the full v1 PDF (24 pp.). Read the abstract, introduction, §1 “The Status Quo” including Problems 1–3, the opening of §2, the opening of §4, the start of §6 and §7 Conclusion. The Synthese version (DOI and online date 5 Mar 2024 from a Crossref bibliographic search) was not read, and differences from v1 are unverified. The paper lists no keywords; the keywords above are its own terms.