Critical Notice of Mark Wilson's Wandering Significance

I have posted a long critical notice of Mark Wilson's amazing book Wandering Significance: An Essay on Conceptual Behavior. It will eventually appear in Philosophia Mathematica. My impression is that even though the book came out in 2006 and is now available in paperback, it has not really had the impact it should in debates about models and idealization. I think this is partly because the book addresses broad questions about concepts that don't often arise in philosophy of science or philosophy of mathematics. But if you start to read the book, it becomes immediately clear how important examples from science and mathematics are to Wilson's views of conceptual evaluation. So, I hope my review will help philosophers of science and mathematics see the importance of the book and the challenges it raises.

Wilson on the Missing Physics

In “Determinism and the Mystery of the Missing Physics” (BJPS Advance Access) Mark Wilson uses the debate about determinism and classical physics to make the more general point about “the unstable gappiness that represents the natural price that classical mechanics must pay to achieve the extraordinary success it achieves on the macroscopic level” (3). Wilson focuses mostly on Norton’s “dome” example and Norton’s conclusion that it shows that classical mechanics is not deterministic. The main objection to this conclusion is that Norton relies on one particular fragment of classical mechanics, and only finds a counterexample to determinism by mistreating what are really “descriptive holes” (10). By contrast, Wilson argues that there are different fragments to classical mechanics: (MP) mass point particle mechanics, (PC) the physics of rigid bodies with perfect constraints (analytic mechanics) and (CM) continuum mechanics. Norton's example naturally lies in (PC). Each fragment has its own descriptive holes which become manifest when we seek to understand the motivation for this or that mathematical technique or assumption at the basis of a treatment of a given system. Typically, a hole in one fragment can be fixed by moving to another fragment, but then that fragment itself has its own holes that prevent a comprehensive treatment. As a result, Wilson concludes that there is no single way the world has to be for “classical mechanics” to be true, and, in particular, there is no answer to the question of whether or not classical mechanics is deterministic.

I think Wilson has noticed something very important about the tendencies of philosophers of science: philosophical positions are typically phrased in terms of how things are quite generally or universally, but our scientific theories, when examined, are often not up to the task of answering such general questions. It seems to me that Wilson opts to resolve this situation by rejecting the philosophical positions as poorly motivated. But another route would be to try to recast the philosophical positions in more specific terms. For example, if, as Wilson argues, descriptive holes are more or less inevitable in these sorts of cases, then a suitably qualified kind of indeterminism cashed out in terms of the existence of these holes can be vindicated. Other debates, like the debate about scientific realism, seem to me to be in need of similar reform, rather than outright rejection.

PSA Symposium: Applied Mathematics and the Philosophy of Science

As the final version of the PSA program is finally online, it is about time for me to promote the symposium that I will be in. Here are the details:

Applied Mathematics and the Philosophy of Science
PSA 2008 Symposium
Parallel Session 6: Saturday, November 8, 9-11:45 am
Room CCA (Conference Center A)
Chair: Paul Teller

Proposed schedule:
9:00-9:30 Christopher Pincock, “The Value of Mathematics for Scientific Confirmation”
9:30-10:00 Stathis Psillos, “What If There Are No Mathematical Entities? Lessons for Scientific Realism”
10:00-10:20 discussion
10:20-10:25 break
10:25-10:55 Mark Wilson, “Leibniz’ ‘Possibilities’ and Our Own”
10:55-11:25 Robert Batterman, “Essential Models and Explanatory Mathematics”
11:25-11:45 discussion

Abstract: This symposium will explore the relevance of philosophical reflection on the details of applied mathematics for current debates in the philosophy of science along four dimensions: (i) scientific representation, (ii) confirmation of scientific theories, (iii) idealization and scientific explanation, (iv) scientific realism. In all four cases the participants aim to show that a clear focus on the contribution that mathematics makes to science sheds new light on traditional positions in the philosophy of science. In some cases the viability of a philosophical view is called into question, while in others a standard thesis receives new support. The symposium is motivated by the realization that the philosophy of mathematics has changed considerably in the last twenty years and the hope that philosophers of science can benefit from this transformation.

For those of you who can't be there, here is a link to a rough draft of my paper. Constructive comments appreciated! Update (April 11, 2009): I have removed this old draft and hope to repost a final version sometime this spring.