Davide Sutto

• Sutto, Davide (2025). The Plural Iterative Conception of Set. Journal for the Philosophy of Mathematics (JPM). 2, s. 161–193. doi: 10.36253/jpm-3549. Fulltekst i vitenarkiv Vis sammendrag

  Georg Cantor informally distinguished between “consistent” and “inconsistent” multiplicities as those many things that, respectively, can and cannot be thought of as one, i.e., as a set. To clarify this distinction, the recent debate filtered the logic of plurals through two main approaches to the process of set-formation: limitation of size (Burgess) or set-theoretic potentialism (Linnebo). In this paper I propose a third route through the development of a plural iterative conception of set. Inspired by Tim Button’s Level Theory, I define and axiomatize the notion of a plural level, which explains Cantor’s multiplicities either as level-bound (consistent) or level unbound (inconsistent) pluralities. While this framework is clearly in contrast with the limitation of size view, it also revives a plausible actualist framework prematurely dismissed by the advocates of potentialism.

• Sutto, Davide (2024). A Taxonomy for Set-Theoretic Potentialism. Philosophia Mathematica. ISSN 0031-8019. doi: 10.1093/philmat/nkae016. Fulltekst i vitenarkiv Vis sammendrag

  Set-theoretic potentialism is one of the most lively trends in the philosophy of mathematics. Modal accounts of sets have been developed in two different ways. The first, initiated by Charles Parsons, focuses on sets as objects. The second, dating back to Hilary Putnam and Geoffrey Hellman, investigates set-theoretic structures. The paper identifies two strands of open issues, technical and conceptual, to clarify these two different, yet often conflated, views and categorize the potentialist approaches that have emerged in the contemporary debate. The final outcome is a taxonomy that should help researchers navigate the rich landscape of modal set theories.

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• Sutto, Davide (2024). Potentialist set theory: New paths and open questions. Bulletin of Symbolic Logic. ISSN 1079-8986. 30(1), s. 133–133. doi: 10.1017/bsl.2024.15. Fulltekst i vitenarkiv

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