Vincent Lam, Christian Wüthrich (2015), The British Journal for the Philosophy of Science 66(3), 605–634 (2015) — DOI-10.1093/bjps/axt053
Key takeaways
- Lam and Wüthrich argue that category theory gives radical OSR no support. Identifying objects with identity arrows is relabelling (§3). Generalized elements X → A exist in every category, so elements are not eliminated (§4). Categories without products also lose set-style relations, “throwing out the relations with the relata” (§4). Morphisms relate C-objects, not the elements that stand for physical relata, and they “only distinguish isomorphism classes of structures” (§5). Bain’s GR and TQFT cases eliminate at most spacetime points, not relata tout court (§§6–7). They conclude that category theory “offers little if any comfort to ROSR” (abstract) and favour “balanced” OSR. The Yoneda lemma is not named, although §§4–5 state two of its consequences.
Standing in the record
Filed at the owner’s request on 2026-09-26, for an account of the Yoneda lemma, connected where the literature allows to ontic structural realism. It was filed Deferred, unread. NOTE-194 is the close reading of 2026-09-26, and it placed the work: Active — Worth reading as the most careful direct refutation of Bain (yo2). Its main points (generalized elements, morphisms relate C-objects, determination only up to isomorphism, sections are not maximal ideals) are correct and are exactly what the Yoneda reading needs. It has a few category-theoretic slips of its own: Hilb said to lack products, a mis-definition of topos, and the claim that non-commutative algebras have no maximal ideals.