Unificatory Understanding and Explanatory Proofs

Foundations of Science 26 (4):1105-1127 (2020)
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Abstract

One of the central aims of the philosophical analysis of mathematical explanation is to determine how one can distinguish explanatory proofs from non-explanatory proofs. In this paper, I take a closer look at the current status of the debate, and what the challenges for the philosophical analysis of explanatory proofs are. In order to provide an answer to these challenges, I suggest we start from analysing the concept understanding. More precisely, I will defend four claims: understanding is a condition for explanation, unificatory understanding is a type of explanatory understanding, unificatory understanding is valuable in mathematics, and mathematical proofs can contribute to unificatory understanding. As a result, in a context where the epistemic aim is to unify mathematical results, I argue it is fruitful to make a distinction between proofs based on their explanatory value.

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References found in this work

Explaining the brain: mechanisms and the mosaic unity of neuroscience.Carl F. Craver - 2007 - New York : Oxford University Press,: Oxford University Press, Clarendon Press.
The Scientific Image.William Demopoulos & Bas C. van Fraassen - 1982 - Philosophical Review 91 (4):603.
Studies in the logic of explanation.Carl Gustav Hempel & Paul Oppenheim - 1948 - Philosophy of Science 15 (2):135-175.

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