Federico Holik, Juan Pablo Jorge, Décio Krause, Olimpia Lombardi (2021), Synthese 200(5), article 401 (2022) — DOI-10.1007/s11229-022-03884-8
Key takeaways
- If quantum systems are bundles of property-instances with no principle of individuality, then standard logic and set theory, which are built on individual constants and variables, cannot describe them. Quasi-set theory can, with bundles formed by a choice over qsets of indistinguishable property-instances.
Seeded from the abstract and a skim, before the reading in NOTE-127. What follows is what the work says about itself.
Earlier work by the authors (Lombardi, da Costa and others) proposed an ontology of properties for quantum mechanics, in which quantum systems are bundles of properties that lack any principle of individuality. This paper argues that quasi-set theory, built to handle collections of items that are not individuals, is a suitable meta-language for that ontology and its structure.
Standing in the record
Filed from the 2026-09-26 sweep of the papers-feed tracker for philosophy: 65 seconds of active reading over 2 sessions. It was filed Deferred, unread. NOTE-127 is the close reading of 2026-09-26, and it placed the work: Active — worth reading as a short, clear bridge between the modal-Hamiltonian “ontology of properties” (Lombardi et al.) and quasi-set theory (French & Krause 2006). The new formal content is about two pages (§6). Most of §5 restates Q’s axioms, and the printed proofs contain errors. It is a useful statement of the position, not a result.
When seeded, before the reading in NOTE-127, the entry gave a priority for a deeper reading: medium — a distinctive formal contribution (t=65s, 2 sessions). The skim captures the construction, but the technical §§5–6 were only skimmed.
What the seeding asked a deeper reading to check (NOTE-127 is that reading):
- A worked formal answer to the complaint, which Wallace (LIT-151) also addresses, that structuralist and non-individual ontologies cannot be stated in standard logic. Compare quasi-set theory with Wallace’s math-first route.
- Relevant to identity and individuality (the Identity of Indiscernibles). Compare with Leitgeb & Ladyman (LIT-154) on criteria of identity in structuralist ontology.
- Check whether using the Axiom of Choice to form bundles quietly reintroduces a selection, and so a form of individuation.
Access when seeded: The Springer page and the PhilArchive copy (HOLQTA-3) were blocked by bot challenges. I read the authors’ preprint “Quasi-set theory for a quantum ontology of properties” (dated September 24, 2021; 26 pp.) from PhilSci-Archive 19725, deposited 2021-10-24, which I used as first appearance. The journal version (online 2022-09-21 per Crossref) was retitled and may differ. Keywords are the PhilSci record’s. Volume and article number are from Crossref.