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  1. Identity and Extensionality in Boffa Set Theory.Nuno Maia & Matteo Nizzardo - 2024 - Philosophia Mathematica 32 (1):115-123.
    Boffa non-well-founded set theory allows for several distinct sets equal to their respective singletons, the so-called ‘Quine atoms’. Rieger contends that this theory cannot be a faithful description of set-theoretic reality. He argues that, even after granting that there are non-well-founded sets, ‘the extensional nature of sets’ precludes numerically distinct Quine atoms. In this paper we uncover important similarities between Rieger’s argument and how non-rigid structures are conceived within mathematical structuralism. This opens the way for an objection against Rieger, whilst (...)
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  • A Counterfactual Analysis of Infinite Regress Arguments.İskender Taşdelen - 2014 - Acta Analytica 29 (2):195-213.
    I propose a counterfactual theory of infinite regress arguments. Most theories of infinite regress arguments present infinite regresses in terms of indicative conditionals. These theories direct us to seek conditions under which an infinite regress generates an infinite inadmissible set. Since in ordinary language infinite regresses are usually expressed by means of infinite sequences of counterfactuals, it is natural to expect that an analysis of infinite regress arguments should be based on a theory of counterfactuals. The Stalnaker–Lewis theory of counterfactuals, (...)
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  • Foundations as truths which organize mathematics.Colin Mclarty - 2013 - Review of Symbolic Logic 6 (1):76-86.
    The article looks briefly at Fefermans own foundations. Among many different senses of foundations, the one that mathematics needs in practice is a recognized body of truths adequate to organize definitions and proofs. Finding concise principles of this kind has been a huge achievement by mathematicians and logicians. We put ZFC and categorical foundations both into this context.
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  • Set theoretic naturalism.Penelope Maddy - 1996 - Journal of Symbolic Logic 61 (2):490-514.
    My aim in this paper is to propose what seems to me a distinctive approach to set theoretic methodology. By ‘methodology’ I mean the study of the actual methods used by practitioners, the study of how these methods might be justified or reformed or extended. So, for example, when the intuitionist's philosophical analysis recommends a wholesale revision of the methods of proof used in classical mathematics, this is a piece of reformist methodology. In contrast with the intuitionist, I will focus (...)
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  • Conceptions and paradoxes of sets.G. Aldo Antonelli - 1999 - Philosophia Mathematica 7 (2):136-163.
    This paper is concerned with the way different axiom systems for set theory can be justified by appeal to such intuitions as limitation of size, predicativity, stratification, etc. While none of the different conceptions historically resulting from the impetus to provide a solution to the paradoxes turns out to rest on an intuition providing an unshakeable foundation,'each supplies a picture of the set-theoretic universe that is both useful and internally well motivated. The same is true of more recently proposed axiom (...)
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  • Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (7):1-57.
    In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n (...)
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