A Counterfactual Approach to Explanation in Mathematics

Samuel Baron; Mark Colyvan; David Ripley

doi:10.1093/philmat/nkz023

A Counterfactual Approach to Explanation in Mathematics

Samuel Baron, Mark Colyvan, David Ripley

School of Humanities

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Abstract

Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

Original language	English
Pages (from-to)	1-34
Number of pages	34
Journal	Philosophia Mathematica: philosophy of mathematics, its learning, and its application
Volume	28
Issue number	1
DOIs	https://doi.org/10.1093/philmat/nkz023
Publication status	Published - 1 Feb 2020

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10.1093/philmat/nkz023

Baron et al 2019 A Counterfactual Approach to Explanation in Mathematics
This is a pre-copyedited, author-produced version of an article accepted for publication in Philosophia Mathematica following peer review. The version of record Sam Baron, Mark Colyvan, David Ripley, A Counterfactual Approach to Explanation in Mathematics, Philosophia Mathematica, nkz023 is available online at: https://doi.org/10.1093/philmat/nkz023
Accepted author manuscript, 349 KBLicence: Unspecified

A World Without Time: Timelessness in Physics and Metaphysics
Baron, S. (Investigator 01)
ARC Australian Research Council
1/01/18 → 3/06/21
Project: Research

Cite this

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A Counterfactual Approach to Explanation in Mathematics

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A World Without Time: Timelessness in Physics and Metaphysics

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