Xerxes D. Arsiwalla, Hatem Elshatlawy, Dean Rickles (2023), arXiv preprint (physics.hist-ph); later a chapter in Quantum Gravity and Computation (Routledge, 2025), DOI 10.4324/9781003546139-10 — ARXIV-2311.03973
Key takeaways
- The authors propose that Wheeler’s “pregeometry” is best modelled as “structureless structure” — the syntactic types and compositional rules of a formal language such as homotopy type theory — adopting a constructivist coherentism in which space and geometry are built from relations rather than a material substrate.
Seeded from the abstract and a skim, before the reading in NOTE-182. What follows is what the work says about itself.
The paper asks how to formalise the “structure of structures” that the foundations of physics would need, and sketches a metaphysics of pregeometric structure on which notions of quantum geometry could rest. It revisits Wheeler’s pregeometry, Leibniz’s monadology and modern topos-theoretic approaches, and argues that formal language — particularly homotopy type theory — supplies the building blocks. On this constructivist view, spaces and algebras are type-theoretic constructions, which could let distinct geometries be classified in one framework and address how spatiality arises in computational models such as the Wolfram model.
Standing in the record
Filed from the 2026-09-26 sweep of the papers-feed tracker for philosophy: 0 seconds of active reading over 0 sessions. It was filed Deferred, unread. NOTE-182 is the close reading of 2026-09-26, and it placed the work: Rejected — not worth a reader’s time as an argument for its thesis. The step from the regress problem to formal languages is asserted, not argued, and its one physics claim (that “widespread consensus” holds spacetime to be fundamentally discrete, p. 5) is overstated. A reader wanting pregeometry is better served by the sources it cites: Meschini, Lehto & Piilonen’s “Geometry, pregeometry and beyond” ([63]) for the history, and Döring & Isham’s topos programme ([36–40]) for a worked formal-language approach.
When seeded, before the reading in NOTE-182, the entry gave a priority for a deeper reading: low — never opened (t = 0), speculative and short; the skim captures the proposal.
What the seeding asked a deeper reading to check (NOTE-182 is that reading):
- A programmatic statement of a relational, constructivist metaphysics of spacetime; pairs with Carroll’s Hilbert-space fundamentalism (LIT-123) as another “space is not fundamental” route.
- The paper calls itself largely a synthesis; check whether any concrete construction of spatial structure from type theory is given or only promised.
- Affiliations include Wolfram Research; read the Wolfram-model claims with that context in mind.
Access when seeded: Title resolved from the arXiv id (abs page v1 7 Nov 2023) and the full v1 PDF (20 pp.) read directly; the later Routledge chapter found via Crossref (title adds a serial comma), not read.