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Reflection and potentialism

Sam Roberts

Dissertation, Birkbeck College, University of London (2016)

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A Taxonomy for Set-Theoretic Potentialism.Davide Sutto - 2024 - Philosophia Mathematica:1-28.details 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. (...) Download Export citation Bookmark
(1 other version)Iterative Conceptions of Set.Neil Barton - 2024 - Cambridge University Press.details Many philosophers are aware of the paradoxes of set theory (e.g. Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages. This Element will examine possibilities for articulating this solution. In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best. Along the way, the author hopes to make (...) Download Export citation Bookmark 1 citation
What makes a `good' modal theory of sets?Neil Barton - manuscriptdetails I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...) Download Export citation Bookmark
Pluralities as Nothing Over and Above.Sam Roberts - 2022 - Journal of Philosophy 119 (8):405-424.details This paper develops an account of pluralities based on the following simple claim: some things are nothing over and above the individual things they comprise. For some, this may seem like a mysterious statement, perhaps even meaningless; for others, like a truism, trivial and inferentially inert. I show that neither reaction is correct: the claim is both tractable and has important consequences for a number of debates in philosophy. Download Export citation Bookmark 9 citations
Can All Things Be Counted?Chris Scambler - 2021 - Journal of Philosophical Logic 50 (5):1079-1106.details In this paper, I present and motivate a modal set theory consistent with the idea that there is only one size of infinity. Download Export citation Bookmark 6 citations

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