A Counterfactual Approach to Explanation in Mathematics. Issue 1 (2nd December 2019)

• Record Type: Journal Article
• Authors: Baron, Sam; Colyvan, Mark; Ripley, David
• Is Part Of: Philosophia Mathematica. Volume 28:Issue 1(2020)
• Page Start: 1
• Page End: 34
• Publication Date: 2019-12-02
• Subjects: Mathematics -- Philosophy -- Periodicals; Wiskunde; Filosofische aspecten; Mathematics -- Philosophy; Periodicals; 510.105
• DOI: 10.1093/philmat/nkz023
• Languages: English
• ISSNs: 0031-8019

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.