Krzysztof, Wójtowicz and Bartłomiej, Skowron (2022) A Metaphysical Foundation for Mathematical Philosophy. [Preprint]
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Text (A Metaphysical Foundation for Mathematical Philosophy. Accepted for publication in Synthese.)
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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 | |||||||||
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| 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 |
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| 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 |
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| Date: | 14 June 2022 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/20749 |
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