Mark Povich's "Rules to Infinity"

Mark Povich is Visiting Assistant Professor in Philosophy at University of Rochester. He has published articles in The British Journal for the Philosophy of Science, Erkenntnis, Mind, Philosophy of Science, Studies in History and Philosophy of Science Part A, Synthese, among others.

Povich applied the “Page 99 Test” to his new book, Rules to Infinity: The Normative Role of Mathematics in Scientific Explanation, and reported the following:

On page 99, I am in the middle of developing my theory of distinctively mathematical explanation. Distinctively mathematical explanations are scientific explanations of natural phenomena that differ from standardly mathematical explanations in that mathematics plays a special role in the former that it doesn't play in the latter. In distinctively mathematical explanations, mathematics itself is, in some sense, what explains natural phenomena. A central task of the book is to specify what this sense is and to develop a theory that tells us when an explanation is distinctively mathematical and when it isn't. Specifically, on page 99 I am struggling to find counterfactuals that correctly distinguish phenomena that have distinctively mathematical explanations from those that do not. I am concerned with this because I hold that counterfactuals are essential to scientific explanations generally: to explain a natural phenomenon P is to find other phenomena p1,...,pn on which P counterfactually depends. This means that if the phenomena p1,...,pn had been different, then P would have been different. I argue that the counterfactuals given on page 99 will not work to correctly distinguish phenomena that have distinctively mathematical explanations from those that do not, but on the following pages I suggest amendments that fix them.

The Page 99 Test works well, but not great, for my book. It works well because my theory of distinctively mathematical explanation is a core thesis of my book, but it does not work great because that theory is not the only core thesis of the book.

In much of the rest of the book, I am concerned with the nature of mathematical objects and of mathematical necessity. I am concerned with this because my theory of distinctively mathematical explanation appeals to mathematical objects and mathematical necessity. What are numbers? What explains why mathematical truths are necessary, i.e., why they could not have been false? My answers to these questions stem from the conventionalist tradition in philosophy. I call my version of conventionalism "normativism." According to conventionalists, the nature of mathematical objects and of mathematical necessity is explained by convention, specifically semantic conventions governing our use of mathematical terms. Although conventionalism is intuitive, it is subject to many influential objections. Answering those objections and engaging with contemporary opponents (and allies) takes up most of the rest of the book.

Visit Mark Povich's website. Rules to Infinity is an open access title: read it here.

--Marshal Zeringue