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Does Mathematical Possibility Imply Existence?

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dc.abstract.enIn the article I discuss the use of modal notions in philosophy of mathematics, in particular the (seemingly) uncontroversial “maximum principle”, according to which the mathematical universe is very rich – it contains “implementations” of all coherent mathematical notions. In particular, I discuss the more general problem of ontological reductions, and argue, that completeness theorems are not the appropriate formal paraphrase of this intuition. I also discuss Gödel’s, and Quine’s versions of mathematical realism in this context. Finally, I argue, that this issue is important both for the realism-antirealism debate in philosophy of mathematics, and for the problem of mathematical explanation.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorWójtowicz, Krzysztof
dc.date.accessioned2024-01-28T20:17:50Z
dc.date.available2024-01-28T20:17:50Z
dc.date.issued2020
dc.description.financeNie dotyczy
dc.identifier.doi10.1515/9783110669411-010
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/152230
dc.identifier.weblinkhttp://dx.doi.org/10.1515/9783110669411-010
dc.languageeng
dc.pbn.affiliationphilosophy
dc.publisher.ministerialDe Gruyter
dc.relation.bookContemporary Polish ontology
dc.relation.pages161-180
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titleDoes Mathematical Possibility Imply Existence?
dc.typeMonographChapter
dspace.entity.typePublication