Department of Philosophy (University of Helsinki)
Research Seminar
Spring 2008
Meetings at the seminar room of the Department of Philosophy
(Siltavuorenpenger 20 A, sh 222) on Thursdays 4-6 pm. unless stated
otherwise.
The seminar is open to everyone interested.
19. 5. Mathieu Marion: "Wittgenstein on Mathematical Explanation and the Length of Proofs"
Mathieu Marion
(Canada Research Chair in the Philosophy of Logic and Mathematics
Université du Québec à Montréal)
"Wittgenstein on Mathematical Explanation and the Length of Proofs"
Abstract
In the writings of Dummett, Kripke and Wright, Wittgenstein's remarks on the
surveyability of proofs in his Remarks on the Foundations of Mathematics
were construed as providing an argument supporting, in tandem with the
rule-following argument in Philosophical Investigations, a radical
anti-realist programme in the foundations of mathematics, close to strict
finitism. Work within the currently trendy paradigm in Wittgenstein
scholarship, i.e., the "New Wittgenstein", has shown the limits of attempts
at understanding Wittgenstein's remarks within an anti-realist framework,
but it has had many deleterious consequences, one of them being that there
has been no new attempt at re-reading and explaining the true content of
Wittgenstein's remarks on the surveyability of proofs. In this paper, I
propose to read them as, inter alia, an argument against some uses of logic
in the foundations of mathematics, that are based on a dubious view about
mathematical explanation. Wittgenstein aimed at Russell and Principia
Mathematica, but it is only part of a venerable tradition that includes
Bolzano, and, as it turns out from discussions reported in Wittgensteins
Lectures on the Foundations of Mathematics, Turing. In contrast,
Wittgenstein seems to have rediscovered against this view a simple argument
first stated by Aristotle in his Posterior Analytics (Book I, section 13).
After showing how this reading sheds light on Wittgenstein's remarks, I
shall conclude by showing that, in virtue of this reading, these remarks
contain an argument that can be applied against the original anti-realist
proof-theoretical programme of Prawitz and Dummett. This is not a
"knock-down" argument as such, but should, as I shall claim, force the
anti-realist to pay attention to an hitherto neglected aspect of proofs,
their length.
22. 5. Tero Tulenheimo (Helsinki): TBA
29.5.2008 Prof. Douglas Anderson (Southern Illinois University Carbondale): TBA
See the seminar web page for further information and changes:
http://www.helsinki.fi/filosofia/tutkijaseminaari.htm