TY - JOUR

T1 - A Counterfactual Approach to Explanation in Mathematics

AU - Baron, Samuel

AU - Colyvan, Mark

AU - Ripley, David

PY - 2019/12/2

Y1 - 2019/12/2

N2 - 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.

AB - 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.

U2 - 10.1093/philmat/nkz023

DO - 10.1093/philmat/nkz023

M3 - Article

JO - Philosophia Mathematica: philosophy of mathematics, its learning, and its application

JF - Philosophia Mathematica: philosophy of mathematics, its learning, and its application

SN - 0031-8019

ER -