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A Metaphysical Foundation for Mathematical Philosophy

Krzysztof, Wójtowicz and Bartłomiej, Skowron (2022) A Metaphysical Foundation for Mathematical Philosophy. [Preprint]

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Abstract

Although 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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Krzysztof, Wójtowiczkwojtowi@uw.edu.pl0000-0002-1187-8762
Bartłomiej, Skowronbartlomiej.skowron@gmail.com0000-0002-6544-7706
Additional Information: Accepted for publication in Synthese.
Keywords: mathematical philosophy, mathematical explanations in science, phenomenology, platonism, ideas, ideal qualities
Subjects: Specific Sciences > Mathematics > Ontology
General Issues > Scientific Metaphysics
General Issues > Explanation
General Issues > Philosophers of Science
General Issues > Realism/Anti-realism
Depositing User: Dr. Bartłomiej Skowron
Date Deposited: 16 Jun 2022 15:03
Last Modified: 16 Jun 2022 15:03
Item ID: 20749
Subjects: Specific Sciences > Mathematics > Ontology
General Issues > Scientific Metaphysics
General Issues > Explanation
General Issues > Philosophers of Science
General Issues > Realism/Anti-realism
Date: 14 June 2022
URI: http://philsci-archive.pitt.edu/id/eprint/20749

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