Synthese (2):1-20 (2019)
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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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Keywords | Mathematical explanation Scientific explanation Mathematical practice Proof |
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DOI | 10.1007/s11229-019-02114-y |
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References found in this work BETA
Studies in the Logic of Explanation.Carl Gustav Hempel & Paul Oppenheim - 1948 - Philosophy of Science 15 (2):135-175.
Explanatory Unification and the Causal Structure of the World.Philip Kitcher - 1989 - In Philip Kitcher & Wesley Salmon (eds.), Scientific Explanation. Minneapolis: University of Minnesota Press. pp. 410-505.
Studies in the Logic of Explanation.Carl G. Hempel & Paul Oppenheim - 1948 - Journal of Symbolic Logic 14 (2):133-133.
4 Decades of Scientific Explanation.Wesley C. Salmon - 1989 - Minnesota Studies in the Philosophy of Science 13:3-219.
View all 18 references / Add more references
Citations of this work BETA
Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
Motivated Proofs: What They Are, Why They Matter and How to Write Them.Rebecca Lea Morris - 2020 - Review of Symbolic Logic 13 (1):23-46.
Philosophy of Mathematical Practice: A Primer for Mathematics Educators.Yacin Hamami & Rebecca Morris - forthcoming - ZDM Mathematics Education.
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2019-02-01
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42 ( #271,707 of 2,518,075 )
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5 ( #137,869 of 2,518,075 )
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