Jonathan Bain (2013), Synthese 190(9), 1621–1635 (June 2013), Springer — DOI-10.1007/s11229-011-9896-6
Key takeaways
- Bain argues that the “relations without relata” objection to radical OSR depends on defining structure set-theoretically, where a relation is a subset of X × X. If a structure is instead “an object in a category”, its elements (arrows 1 → A) are “not essential”, because category-theoretic objects need not be structured sets. His examples are sheaves of Einstein algebras for GR with asymptotic boundary conditions, which may lack global sections (§3), and nCob and Hilb (§4). He concludes that ROSR “avoids the charge that it rests on an incoherent claim” (p. 1634). The paper never mentions the Yoneda lemma, representable functors or universal properties by name.
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-193 is the close reading of 2026-09-26, and it placed the work: Active — Worth reading as the short, canonical statement of the category-theoretic defence of radical OSR, which the later literature (yo3; Lal & Teh; Eva 2016) responds to. Read it with yo3. Its central inference is overstated, and its GR section contains technical errors that yo3 documents.