Do mathematical explanations have instrumental value?

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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Rebecca Morris
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References found in this work

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 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.
Mathematical explanation.Mark Steiner - 1978 - Philosophical Studies 34 (2):135 - 151.

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