This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations. One of the central aims of science is to provide explanations of natural phenomena. What role does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science?
Rules to Infinity defends the thesis that mathematics contributes to the explanatory power of science by expressing conceptual rules that allow for the transformation of empirical descriptions. It claims that
mathematics should not be thought of as describing, in any substantive sense, an abstract realm of eternal mathematical objects, as traditional Platonists have thought. This view, which Mark Povich calls "mathematical normativism," is updated with contemporary philosophical tools, which are used to form the argument that normativism is compatible with mainstream semantic theory. This allows the normativist to accept that there are mathematical truths, while resisting the
Platonistic idea that there exist abstract mathematical objects that explain such truths. There is a distinction between scientific explanations that are in some sense distinctively mathematical--those
that explain natural phenomena in some uniquely mathematical way--and those that are only standardly mathematical, and Povich defends a particular account of this distinction. Rules to Infinity compares normativism to other prominent views in the philosophy of mathematics, such as neo-Fregeanism, fictionalism, conventionalism, and structuralism, and offers an entry point into debates at the forefront of philosophy of science and mathematics as it defends its novel
positions.
Industry Reviews
"An excellent book for anyone who wants to think seriously about how mathematical explanations work in science, and especially for those who think this may have important consequences for a Platonic view of mathematics." -- Alan Sidelle, Professor of Philosophy, University of Wisconsin-Madison
"Rules to Infinity is one of the most creative and insightful books written on the relationship between mathematics and scientific explanation in several decades. At a time when many philosophical discussions on these issues travel well-worn paths, Mark Povich's work charts a new and exciting course." -- Kareem Khalifa, Professor of Philosophy, University of California, Los Angeles
"The kind of philosophy I like best involves connecting seemingly disparate ideas to solve a stubborn philosophical problem in an unexpected way. That is exactly what Mark Povich achieves. This is a wonderful contribution to the debate!" -- Agustín Rayo, Professor of Philosophy, Massachusetts Institute of Technology
"This book is essential reading for those working on scientific explanation, scientific representation and the metaphysical interpretation of pure mathematics." -- Christopher Pincock, The Ohio State University
"Mark Povich's ontic conception of scientific explanation, combined with his deflationary conception of mathematics, has many attractive features, but also faces significant challenges. Povich offers vigorous arguments in defense of this combination, as well as incisive comparisons to rival accounts." -- Marc Lange, University of North Carolina at Chapel Hill
"If you thought scientific explanations are made true by the facts, you might wonder what makes mathematical assertions true. Mark Povich provides a subtly defended and illuminating approach to these and related questions, bringing together topics that are often treated as orthogonal. The result is an important, timely, and most impressive book." -- John Heil, Washington University in St. Louis
"It is not written for students or mathematicians, but for post-graduate philosophers of a very specific bent-those interested in such questions as to whether mathematics is a body of knowledge reflecting an abstract Platonic point of view, a more basic, empirically-generated kind of knowledge, or numerous views in between these two extremes." -- J. W. Dauben, Choice
