Paul Gorbow

Research Interests

Logic in Computer science, Mathematics, and Philosophy: set theory; axiomatic theories of truth, belief, and knowledge; potential infinity; non-standardness phenomena in the foundations of mathematics; intentional attitudes (aka propositional attitudes) of agents (human, AI).

Current research

My ongoing research project "Potential infinity in the foundations of mathematics", at Stockholm University and the University of Oslo, provides a positive philosophical explanation for non-standardness phenomena in the foundations of mathematics, by applying ideas from potential infinity.

Background

My doctoral dissertation at the University of Gothenburg (supervised by Ali Enayat) provides a category theoretical theory for the set theory NF and results on embeddings and automorphisms of non-standard models of ZF. As a postdoc at the University of Gothenburg, I developed (with Graham Leigh) an untyped theory of truth in the multiverse of sets that extends ZF.

Publications

How Diverse Can Coincident Things Be?
The Journal of Philosophy, accepted for publication, but has not yet been assigned to an issue.
This article combines techniques from mathematical logic and philosophy to develop a rigorous framework for studying the metaphysical notions of coincidence and essence.
A Genuinely Untyped Solution to the Knower Paradoxes
arXiv:2304.10285 [math.LO], 2023.
This preprint shows an unexpected connection between revision semantics and a technique based on Löb’s theorem, using it to solve a paradox on knowledge from the 1960s.
Preprint
The Copernican Multiverse of Sets
Co-authored with G. E. Leigh. The Review of Symbolic Logic, Vol. 15, No. 4, 2022, pp. 1033–1069.
This article develops a conception of the multiverse of sets, guided by an innovative Copernican principle.
Published Version | Preprint
Rank-Initial Embeddings of Non-Standard Models of Set Theory
Archive for Mathematical Logic, Vol. 59, 2020, pp. 517–563.
This article proves original results on non-standard models of set theory, showcasing advanced techniques in mathematical logic.
Published Version | Preprint
The Reflective Multiverse of Set Theory
Co-authored with G. E. Leigh. Proceedings of Circularity in Syntax and Semantics, 2019.
A peer-reviewed conference contribution outlining the results of “The Copernican Multiverse of Sets.”
Algebraic New Foundations
The Journal of Symbolic Logic, Vol. 84, No. 2, 2019, pp. 798–832.
This article contributes a foundational category theoretic account of the set theory NF (analogous to topos theory for ZF), and establishes mathematical results bridging stratified set theory and category theory.
Published Version | Preprint
Self-Similarity in the Foundations
Ph.D. Thesis, University of Gothenburg, Acta Philosophica Gothoburgensia, Vol. 32, 2018.
This thesis studies self-similarity in the foundations of mathematics from the perspective of category theory and set theory.
Published Version | Preprint
Feferman's Forays into the Foundations of Category Theory
Co-authored with A. Enayat and Z. McKenzie. In Feferman on Foundations, Springer, 2018, pp. 315–346.
This article contributes original results to a festschrift honoring Feferman, focusing on the foundations of category theory.
Published Version | Preprint
Essens, att Sammanfalla och Karaktärisering
Filosofisk tidskrift, Vol. 38, No. 3, 2017, pp. 43–57.
This paper shows that Yablo's theory of contingent identity collapses under mild assumptions, using mathematical techniques.
Published Version