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Volume 1, Issue 3, Summer 2019

Demetra Christopoulou
Pages 99-110

Sets and Necessity

Τhis paper addresses the issue of the metaphysical status of sets and their interconnections. It discusses a foundational approach of the iterative set theoretic hierarchy comparatively to a regressive approach. Then it takes under consideration some naturalistic accounts of set theory and presents certain difficulties naturalism faces. It claims that the ontological status of sets should be dealt with in non-naturalistic terms and suggests that the issue in question could rather be placed in the context of a metaphysical discussion concerning abstract objects. So it investigates the operation ‘set of …’ as governed by necessary ontological dependence. After comparing some of the platonistic views S. Cowling (2017) has discussed, it proposes one of them as an appropriate account of sets as abstract objects with a modal status.

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