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A metaphysical foundation for mathematical philosophy

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dc.abstract.enAlthough mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern is that even if formal tools serve to clarify reasoning, they themselves contribute nothing new or relevant to philosophy. We defend mathematical philosophy against such concerns here by appealing to its metaphysical foundations. Our thesis is that mathematical philosophy can be founded on the phenomenological theory of ideas as developed by Roman Ingarden. From this platonist perspective, the “unreasonable effectiveness of mathematics in philosophy”—to adapt Wigner’s phrase—is analogous to that of mathematical explanations in science. As success-criteria for mathematical philosophy, we propose that it should be correct, responsive, illuminating, promising, relevant, and adequate.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorWójtowicz, Krzysztof
dc.contributor.authorSkowron, Bartłomiej
dc.date.accessioned2024-01-24T17:54:41Z
dc.date.available2024-01-24T17:54:41Z
dc.date.issued2022
dc.description.financeNie dotyczy
dc.description.number4
dc.description.volume200
dc.identifier.doi10.1007/S11229-022-03760-5
dc.identifier.issn0039-7857
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/101661
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s11229-022-03760-5
dc.languageeng
dc.pbn.affiliationphilosophy
dc.relation.ispartofSynthese
dc.relation.pagesArticle number: 299
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enMathematical philosophy
dc.subject.enMathematical explanations in science
dc.subject.enPhenomenology
dc.subject.enPlatonism
dc.subject.enIdeas
dc.subject.enIdeal qualities
dc.titleA metaphysical foundation for mathematical philosophy
dc.typeJournalArticle
dspace.entity.typePublication