Lange, Marc (2021) Inference to the Best Explanation as Supporting the Expansion of Mathematicians' Ontological Commitments. [Preprint]
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Abstract
This paper argues that in mathematical practice, conjectures are sometimes confirmed by “Inference to the Best Explanation” (IBE) as applied to some mathematical evidence. IBE operates in mathematics in the same way as IBE in science. When applied to empirical evidence, IBE sometimes helps to justify the expansion of scientists’ ontological commitments. Analogously, when applied to mathematical evidence, IBE sometimes helps to justify the expansion of mathematicians’ ontological commitments. IBE supplements other forms of non-deductive reasoning in mathematics, avoiding obstacles sometimes faced by enumerative induction or hypothetico-deductive reasoning. Mathematical platonists can appeal to mathematicians’ use of IBE even though it cannot supply a non-circular argument for platonism. This paper offers an inductive account of why mathematical IBE tends to lead to mathematical truths, thereby addressing part of the Benacerraf/Field challenge to our knowledge of abstract mathematical entities.
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| Item Type: | Preprint | ||||||
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| Keywords: | mathematics, platonism, Field, Benacerraf, explanation, inference to the best explanation | ||||||
| Subjects: | Specific Sciences > Mathematics > Ontology General Issues > Confirmation/Induction General Issues > Explanation Specific Sciences > Mathematics General Issues > Realism/Anti-realism |
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| Depositing User: | Prof. Marc Lange | ||||||
| Date Deposited: | 12 Mar 2022 18:56 | ||||||
| Last Modified: | 12 Mar 2022 18:56 | ||||||
| Item ID: | 20340 | ||||||
| Subjects: | Specific Sciences > Mathematics > Ontology General Issues > Confirmation/Induction General Issues > Explanation Specific Sciences > Mathematics General Issues > Realism/Anti-realism |
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| Date: | 2021 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/20340 |
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