21-26 April 2010
Helsinki, Finland
FOUR LECTURES BY JOHN AND ALEXIS BURGESS IN HELSINKI APRIL 21, 22, 23, 26. For exact times and locations see http://www.math.helsinki.fi/logic/opetus/burgess4.html 1. JOHN BURGESS, APRIL 21: MATHEMATICAL PRACTICE, PHILOSOPHY OF MATHEMATICS, AND STRUCTURALISM ABSTRACT: One textbook may introduce the real numbers in Cantor's way, and another in Dedekind's, and the mathematical community as a whole will be completely indifferent to the choice between the two. This sort of fact about mathematical practice, famously called to the attention of philosophers by Paul Benacerraf, has motivated the development of a distinctively "structuralist" philosophy of mathematics. I will argue that structuralism is a mistake, a generalization in the wrong direction, resulting from philosophers' preoccupation with ontology. 2. ALEXIS BURGESS, APRIL 22: TRUTH IN FICTIONALISM ABSTRACT: Fictionalism about any arbitrary subject matter seems to require realism about other subject matters. Even if there is a coherent fictionalism about fictional characters, for example, it's hard to make sense of fictionalism about fictions themselves. Hence the modal fictionalist's concern that prefixes like 'According to the tall-tale of extreme modal realism...' may turn out to be ineluctably modal. Fictionalism about truth would therefore seem to be a non-starter---not because fictions are intuitively false, but because the notion of truth seems to be implicated in the semantics of fictionalization prefixes. Yet something like the revolutionary fictionalist stance toward alethic discourse would be a sensible reaction to the inconsistency theory of truth (which Matti Eklund and others have argued convincingly is an attractive response to the semantic paradoxes). The purpose of this paper, then, is just to make the world safe for alethic fictionalism, by showing that the most promising versions of fictionalism in general provide for a coherent fictionalism about truth in particular. 3. ALEXIS BURGESS, APRIL 23: AN ALETHIC THEORY OF REFERENCE Inferentialists are divided over deflationism aboutrepresentational notions like truth and reference. Inferential- or conceptual-role semantics provides a more "substantive" theory of reference than the sort of anaphoric account on offer in Brandom. This opposition obscures an alternative in the theory of reference available to deflationists and inflationists alike (provided we abandon the correspondence theory of truth constitutive of referentialism). The alternative emerges upon recognition of the fact that the theory of reference involves two separable projects, usually run together: to specify the referent of an arbitrary term, and to explain what it takes for a term to refer in the first place. In the general spirit of conceptual-role semantics, I develop an explanation of referential success that essentially involves the notion of truth (coupled with a familiar, deflationary specification of referents). Very roughly, the idea is just that an expression refers iff it can be used to state a truth. The most troubling objection to this style of view arguably has to do with the phenomena of referential indeterminacy. Dealing with this objection leads to a speculative resolution of the problem of the many, and a diagnosis of the urge to posit vagueness in the world. 4. JOHN BURGESS, APRIL 26: DEFINITIONS vs MODELS vs AXIOMS IN THE THEORY OF TRUTH ABSTRACT: Attempts since Tarski to characterize a consistent and mathematically respectable notion of truth in the face of the well-known paradoxes have faced a choice of how to proceed: by propounding an explicit definition, by describing a model or class of models, or by advancing a list of axioms. I will describe some recent successes (and failures) in the axiomatic tradition, and their relation to work of Kripke, Feferman, and Friedman.