Friday, November 14, 2014

Paperback of Mathematics and Scientific Representation is out!

Thanks to some good work at Oxford, the paperback edition of my 2012 book is now available. (It is listed on Amazon at least, and should be on the OUP USA website soon.) As much as I wanted to, I resisted the urge to make corrections and improvements.

Monday, November 3, 2014

My PSA 2014 talk (title, abstract and change in time)

This week is the 2014 edition of the Philosophy of Science Association conference. A great program has been assembled here.

Due to an oversight on my part, a conflict developed, and I had to request that the program chair move the time for my talk. The talk will now be presented on Friday Nov. 7th in the 4-6pm session on Explanation. I am grateful to the program chair for accommodating this last minute request.

Title: Newton, Laplace and Salmon on Explaining the Tides
Abstract: Salmon cites Newton's explanation of the tides in support of a causal account of scientific explanation. In this paper I reconsider the details of how Newton and his successors actually succeeded in explaining several key features of the tides. It turns out that these explanations depend on elements that are not easily interpreted in causal terms. I use the explanations offered after Newton to indicate two different ways that non-causal factors can be significant for scientific explanation. In Newton's equilibrium explanation, only a few special features of the tides can be explained. A later explanation deploys a kind of harmonic analysis to provide an informative classification of the tides at different locations. I consider the options for making sense of these explanations.

Monday, October 27, 2014

Two new papers on abstract (mathematical) explanation

There has not been much activity here lately, but I wanted to link to two new papers of mine that tackle the vexing issue of mathematical explanation in math and in science. I try to isolate a kind of "abstract" explanation using two cases, and explore their significance.

The Unsolvability of the Quintic: A Case Study in Abstract Mathematical Explanation
Philosophers' Imprint, forthcoming.
Abstract: This paper identifies one way that a mathematical proof can be more explanatory than another proof. This is by invoking a more abstract kind of entity than the topic of the theorem. These abstract mathematical explanations are identified via an investigation of a canonical instance of modern mathematics: the Galois theory proof that there is no general solution in radicals for fifth-degree polynomial equations. I claim that abstract explanations are best seen as describing a special sort of dependence relation between distinct mathematical domains. This case study highlights the importance of the conceptual, as opposed to computational, turn of much of modern mathematics, as recently emphasized by Tappenden and Avigad. The approach adopted here is contrasted with alternative proposals by Steiner and Kitcher.

Abstract Explanations in Science
British Journal for the Philosophy of Science, forthcoming.
A previous version of this paper is online here.
Abstract: This paper focuses on a case that expert practitioners count as an explanation: a mathematical account of Plateau's laws for soap films. I argue that this example falls into a class of explanations that I call abstract explanations. Abstract explanations involve an appeal to a more abstract entity than the state of affairs being explained. I show that the abstract entity need not be causally relevant to the explanandum for its features to be explanatorily relevant. However, it remains unclear how to unify abstract and causal explanations as instances of a single sort of thing. I conclude by examining the implications of the claim that explanations require objective dependence relations. If this claim is accepted, then there are several kinds of objective dependence relations.

It remains to be seen if this "ontic" approach is the best way to go, but I believe it is a promising avenue to explore.