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Why is the universe of sets not a set?

Zeynep Soysal

Synthese 197 (2):575-597 (2017)

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(1 other version)Mathematical Pluralism and Indispensability.Silvia Jonas - 2023 - Erkenntnis 1:1-25.details Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most (...) Download Export citation Bookmark 1 citation
Level Theory, Part 2: Axiomatizing the Bare Idea of a Potential Hierarchy.Tim Button - 2021 - Bulletin of Symbolic Logic 27 (4):461-484.details Potentialists think that the concept of set is importantly modal. Using tensed language as an heuristic, the following bar-bones story introduces the idea of a potential hierarchy of sets: 'Always: for any sets that existed, there is a set whose members are exactly those sets; there are no other sets.' Surprisingly, this story already guarantees well-foundedness and persistence. Moreover, if we assume that time is linear, the ensuing modal set theory is almost definitionally equivalent with non-modal set theories; specifically, with (...) Download Export citation Bookmark 1 citation
Is strict finitism arbitrary?Nuno Maia - forthcoming - Philosophical Quarterly.details Strict finitism posits a largest natural number. The view is usually thought to be objectionably arbitrary. After all, there seems to be no apparent reason as to why the natural numbers should ‘stop’ at a specific point and not a bit later on the natural line. Drawing on how arguments from arbitrariness are employed in mereology, I propose several ways of understanding this objection against strict finitism. No matter how it is understood, I argue that it is always found wanting. Download Export citation Bookmark

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