Mathematics as a Science of Patterns

Mathematics as a Science of Patterns

Mathematics as a Science of Patterns

Mathematics as a Science of Patterns

Synopsis

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematicalknowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defence of realism about the metaphysics of mathematics--the view that mathematics is about things that reallyexist. Resnik's distinctive philosophy of mathematics is here presented in an accessible and systematic form: it will be of value not only to specialists in this area, but to philosophers, mathematicians, and logicians interested in the relationship between these three disciplines, or in truth, realism,and epistemology.

Excerpt

In this book I bring together ideas that I have been developing separately in articles written over the past fifteen years. The book's title expresses my commitment to mathematical realism, empiricism, and structuralism. For in calling mathematics a science I indicate that it has a factual subject-matter and stands epistemically with the other sciences, and in calling it a science of patterns I express my commitment to mathematical structuralism. Contemporary readers in the philosophy of mathematics are likely to know of (if not know) my structuralism and the paper from which the title of this book derives. The same is less likely to hold of my views on realism and the epistemology of mathematics, since much of it appears in conference papers that have not been published, at least not as of this writing. I hope that this book will not only make these newer ideas more readily accessible but also present them and my earlier ideas in a systematic context.

My debt to the writings of W. V. Quine will be apparent to any reader who knows his work. My combination of holism and postulationalism develops the details of Quinean suggestions for an epistemology of mathematics, and his work on ontological relativity has shaped my structuralism.

I am also indebted to a host of individuals for conversations, correspondence and other help. I have acknowledged the help of many of them in previous publications that serve as a basis for this one. I thank them again, but will confine myself to listing only those who have assisted me with this particular manuscript. These are Andrea Bagagiolo, Mark Balaguer, Pieranna Garavaso, Marcus Giaquinto, Eric Heintzberger, Colin McLarty, Geoffrey Sayre-McCord, Adrian Moore, Bijan Parsia, my son David Resnik, Stewart Shapiro, Keith Simmons, and two anonymous referees for Oxford University Press. I am especially grateful to Mark Balaguer and Eric Heintzberger for lengthy commentaries on the previous draft of the book. Angela Blackburn and Peter Momtchiloff in their capacity as philosophy editors of Oxford University Press have encouraged me from the inception of this work, and I thank them both. I also thank Angela

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