Indispensability and Explanation

Abstract

The question as to whether there are mathematical explanations of physical phenomena has recently received a great deal of attention in the literature. The answer is potentially relevant for the ontology of mathematics; if affirmative, it would support a new version of the indispensability argument for mathematical realism. In this article, I first review critically a few examples of such explanations and advance a general analysis of the desiderata to be satisfied by them. Second, in an attempt to strengthen the realist position, I propose a new type of example, drawing on probabilistic considerations. 1 Introduction 2 Mathematical Explanations 2.1 ‘Simplicity’ 3 An Average Story: The Banana Game 3.1 Some clarifications 3.2 Hopes and troubles for the nominalist 3.3 New hopes? 3.4 New troubles 4 Conclusion

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