The Applicability of Mathematics in Science: Indispensability and Ontology Indispensability and Ontology

Do electrons and genes exist? If inclined to answer 'yes', let's ask a harder question: do numbers exist? This book argues that the answer should be, again, affirmative. It elaborates a philosophical position according to which all, and only, entities truly indispensable to the formulation of modern scientific theories should be recognized as existent, regardless of how we might be initially tempted to categorize them - as concrete-physical or abstract-mathematical. In addition to explicating the subtleties of the positive reasons supporting this form of realism, the book clarifies and rebuts a variety of objections raised against this position.

Introduction
Mathematical Symmetries and their Predictive Role
Mathematical Idealization
The Explanatory Role of Mathematics and the 'Enhanced' Indispensability Argument
Criticisms of the Explanationist Strategy
Unreasonable Effectiveness: Mathematics, Scientific Representation and Naturalism
Unreasonable Effectiveness and Heuristics
Conclusion
References
Index