On Mathematical Explanations of Empirical Phenomena Indispensability, Number Theory, and Mathematical Counterfactual Dependence

This book addresses contemporary issues in the philosophy of mathematics that deal with the role of mathematics in explanations of empirical phenomena. It brings together various debates, such as on indispensability, number theory, abstraction principles, and counterpossibles, which turn out to be highly relevant for evaluating the role of the mathematics in question. The book consists of two parts and has a general introduction of the broader context in which the discussions take place. The first part focuses on the possibility of extracting an argument for mathematical realism in relation to the explanatory indispensability argument, and shows that circularity looms unless a controversial abstraction principle is assumed. It also offers an alternative non-mathematical explanation that makes use of relative interpretation. The second part focuses on the possibility of bringing out the explanatory role of mathematics counterfactually, and shows that, due to the necessary nature of mathematics, any proposal should take into account discussions on the knowledge and the structure of numbers. As a whole, this book is of great use to academic research in the field of philosophy of mathematics.

1 Introduction.- Part I: The Indispensability of Mathematics.- 2 The enhanced indispensability argument.- 3 Objections.- 4 Circularity and interpretability.- 5 Conclusion of Part I.- 6 Counterfactual explanation and mathematics.- 7 A number-theoretic counterpossible.- 8 De Re knowledge of numbers.- 9 Conclusion of Part II.- 10 Epilogue.- Bibliography.