David Wallace (2021), Philosophical Perspectives 36(1), 345–378 (2022) — DOI-10.1111/phpe.12172
Key takeaways
- Once physical theories are read “math-first”, with content given by mathematical structure plus representation rather than by sentences, scientific realism already is structural realism. The ESR/OSR choice then becomes a choice between language-first and math-first metaphysics, and on either view objects, properties and relations are derivative except, at most, at the fundamental level.
Seeded from the abstract and a skim, before the reading in NOTE-142. What follows is what the work says about itself.
Wallace answers the charge that structural realism never clearly states an alternative to object/property/relation metaphysics done in predicate logic. He proposes a math-first view of theories, close to the semantic view, on which a theory’s content is its mathematical structure and its representational relations to systems. Adopting this view is already a form of structural realism. The ESR/OSR choice becomes a choice between language-first and math-first metaphysics. He then examines the status of objects in fundamental and non-fundamental physics on both versions.
Standing in the record
Filed from the 2026-09-26 sweep of the papers-feed tracker for philosophy: 210 seconds of active reading over 1 session. It was filed Deferred, unread. NOTE-142 is the close reading of 2026-09-26, and it placed the work: Active — worth reading as the sharpest statement of what structural realism could mean once theories are taken math-first. It gives precise definitions of math-first ESR/OSR and of real patterns, its diagnosis of why priority-thesis OSR drifted is useful, and it is candid about the undeveloped notion of mathematical equivalence it relies on.
When seeded, before the reading in NOTE-142, the entry gave a priority for a deeper reading: high — load-bearing for the whole structural-realism cluster, and it provides the math-first frame the rest of the batch can be read against. Not yet opened by the owner (t=0), but the skim shows it is central.
What the seeding asked a deeper reading to check (NOTE-142 is that reading):
- Probably the sharpest statement of what SR claims, and a direct challenge to the relation-priority readings in Floridi (LIT-152), Morganti (LIT-173) and Chakravartty (LIT-196).
- Its coarse-grained equivalence meshes with De Haro & Butterfield (LIT-199) on duality. Check whether the two accounts of theoretical equivalence agree.
- Check whether math-first metaphysics avoids smuggling predication back in when it states the representation relation.
Access when seeded: The Wiley page returned a Cloudflare challenge. Crossref gives online 2022-12-14 and the December 2022 issue. I read the preprint (45 pp., dated December 22, 2021) from PhilSci-Archive 20048 (datestamp 2021-12-27, used as first appearance) by text extraction. Volume, issue and pages are from Crossref. Keywords are my own.