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Do mathematical explanations have instrumental value?

Morris, Rebecca (2019) Do mathematical explanations have instrumental value? Synthese. ISSN 1573-0964

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Abstract

Scientific explanations are widely recognized to have instrumental value by helping scientists make predictions and control their environment. In this paper I raise, and provide a first analysis of, the question whether explanatory proofs in mathematics have analogous instrumental value. I first identify an important goal in mathematical practice: reusing resources from existing proofs to solve new problems. I then consider the more specific question: do explanatory proofs have instrumental value by promoting reuse of the resources they contain? In general, I argue that the answer to this question is "no" and demonstrate this in detail for the theory of mathematical explanation developed by Marc Lange.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Morris, Rebeccaemail@rebeccaleamorris.com0000-0002-1216-6900
Keywords: Mathematical explanation, Scientific explanation, Mathematical practice, Proof
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Depositing User: Dr Rebecca Lea Morris
Date Deposited: 02 Feb 2019 05:17
Last Modified: 02 Feb 2019 05:17
Item ID: 15700
Journal or Publication Title: Synthese
Publisher: Springer (Springer Science+Business Media B.V.)
DOI or Unique Handle: https://doi.org/10.1007/s11229-019-02114-y
Subjects: Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Date: 1 February 2019
ISSN: 1573-0964
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15700

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