The Applicability of Mathematics in Science: Indispensability and Ontology (New Directions in the Philosophy of Science)

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. Series Editor's Preface Acknowledgements Introduction: The Question PART I: NATURALISM, INDISPENSABILITY AND POSIT REALISM Naturalism: Science as the Measure of All Things Holism Posit Realism PART II: THE VANTAGE POINT: MATHEMATICS IN SCIENCE Standard and Non-Standard Applications Mathematics and Scientific Discovery Wigner's Puzzle Revisited PART III: EXPLANATION AND MATHEMATICAL REALISM Inference to the Best Mathematical Explanation Explanation, Holism, and Ontological Commitment: The Objection from Scientific Practice Concluding remarks Notes Bibliography This examination of a series of philosophical issues arising from the applicability of mathematics to science consists of scientifically-informed philosophical analysis and argument. One distinctive feature of this project is that it proposes to look at issues in philosophy of mathematics within the larger context of philosophy of science.