David Corfield (2015), Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59, 55–61 (2017) — DOI-10.1016/j.shpsb.2015.07.004
Key takeaways
- Mathematical duality, which philosophers have neglected since Nagel (1939), is best understood category-theoretically as structural reversal organised around adjunction. Philosophers of physics should adopt category theory, because physicists’ “dualities” often fall short of duality proper and predicate logic is ill-suited to the sameness questions they raise.
Seeded from the abstract and a skim, before the reading in NOTE-141. What follows is what the work says about itself.
Nagel in 1939 described how projective duality freed mathematicians from thinking they had to describe intuitive elements, but philosophers have largely ignored duality since, even as it spread through twentieth-century mathematics. Corfield argues that a reassessment is overdue. Category theory has much to say about duality, through arrow reversal, dualising objects and adjunctions, alongside changes in how mathematics understands identity and structure. Physicists’ use of “duality” does not always match mathematicians’, but the mathematical analysis is still useful, and category theory is an important language for philosophy of physics.
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-141 is the close reading of 2026-09-26, and it placed the work: Active — worth reading, briefly, as the mathematician-philosopher’s counterweight to the physics-first accounts of duality this record holds: it is the clearest statement that what physicists call a duality is often what a mathematician calls an equivalence, and it is only seven pages. Its positive programme (HoTT for philosophy of physics) is announced, not carried out.
When seeded, before the reading in NOTE-141, the entry gave a priority for a deeper reading: low — a short paper the skim covers well (t=30s), and more about mathematics than about the ontology questions driving the batch.
What the seeding asked a deeper reading to check (NOTE-141 is that reading):
- A mathematician-philosopher’s counterweight to the physics-first accounts of duality in LIT-199 and LIT-113. It is sharp on when “duality” is mere equivalence.
- Its claim that predicate logic is the wrong tool echoes Wallace’s math-first structural realism (LIT-151) and the quasi-set motivation in LIT-107.
- A deeper reading should check the §2 survey and whether Corfield’s structural-reversal criterion excludes gauge–gravity duality.
Access when seeded: ScienceDirect was unreachable (bot-check page, and 403 via WebFetch). I read the author-hosted copy of the published article (7 pp., journal layout with article history) from ncatlab.org/davidcorfield/files/duality.pdf by text extraction. The article history gives “Available online 20 August 2015” (received 11 Dec 2014, accepted 23 Jul 2015). Volume, pages and the August 2017 issue date are confirmed by Crossref and the Kent Academic Repository record (kar.kent.ac.uk/60387). The batch had no author; the author is taken from the article itself. Keywords are the article’s.