A Counterfactual Approach to Explanation in Mathematics

Philosophia Mathematica 28 (1):1-34 (2020)
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Abstract

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.

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Author Profiles

Sam Baron
Australian Catholic University
Mark Colyvan
University of Sydney
David Ripley
Monash University

References found in this work

Counterfactuals.David Lewis - 1973 - Cambridge, MA, USA: Blackwell.
New Work for a Theory of Universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
Causality: Models, Reasoning and Inference.Judea Pearl - 2000 - Cambridge University Press.

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