PHIL 455W/814: The Applicability Of Mathematics

Spring Semester 2013 | Evening | Burnaby

INSTRUCTOR: P. Hanson, WMC 5658 (hanson@sfu.ca)

COURSE DESCRIPTION

A paper by Mark Steiner that we will read opens by defending the claim that “…to an unprecedented degree, the history of Western philosophy is the history of attempts to understand why mathematics is applicable to Nature, despite apparently good reasons to believe that it should not be.” This course will examine recent philosophical work on the role of mathematics in the discovery, description, prediction, and explanation of empirical phenomena. Often, attempts to articulate such roles start from prior metaphysical positions (e.g., platonism or nominalism) and epistemological positions (e.g., a priorism or empiricism) about mathematics per se (“pure math”), and then try to explain, or explain away, the would-be “miracle of applied mathematics” – the apparent indispensability of mathematics to the enterprise of empirical science. Recently, though, there have been attempts to go in the other direction, to start by examining the apparent contributions of mathematics to the empirical sciences, and then use that as a constraint on the development of an adequate metaphysics and epistemology of mathematics. Either way, it seems that a philosophical account of mathematics is incomplete if it lacks an account of mathematics’ empirical applicability. And some of the more obvious moves that one might want to make with respect to the latter seem to be in tension with more general philosophical considerations about the nature of mathematics. There are, of course, long recognized tensions between the apparent ontological commitments of mathematical theory and the development of a naturalistic epistemology for rational mathematical belief, spawning, e.g., structuralist (Resnik) and fictionalist (Field) accounts. Taking mathematicians themselves as authoritative about the ontological commitments of their theories and about their methods of theory construction has led Maddy to recently propose a kind of deep-seated indeterminacy about the nature of the ontological commitments of mathematics, an indeterminacy between what she calls ‘thin realism’ and ‘arealism’. Nothing in the mathematician’s methods helps us choose between these. Balanguer has gone so far as to argue forcefully that that there are no decisive arguments for or against a robust platonic realism about mathematics. These, then, are representative of core issues to be explored in this course, and that will help to frame our further explorations of the problem of applicability.

REQUIRED TEXTS

• The readings are nearly all available on the web through SFU library. They include papers, or chapters, by Quine, Benacerraf, Michael Resnik, Hartry Field, James Brown, Mark Steiner, Jodi Azzouni, Mark Colyvan, Mark Balaguer, Penelope Maddy, Mark Wilson, Ulrich Meyer, Robert Holland, Kit Fine, and Robert Batterman. (About half of them have “applied” or one of its cognates in the title.)
  

COURSE REQUIREMENTS

For 455W:

• 2 shorter written assignments - 25% apiece, one of which will be rewritten based on feedback both about its content and its form
• a term paper -  50%

 For 854:

• one shorter written assignment - 25%
• one class presentation -  25%
• a term paper -  50%
  

Note: For Phil 455W, one or both of Phil 203 and 201 would be an asset, as would some formal logic, e.g. 110. The usual prerequisites for taking a 400 level course apply (two 300-level PHIL courses), or permission of the instructor.