### Graduate Student Seminar, 4:30pm March 15, 2004; HH127

#### Speaker:

Pantelis Eleftheriou
#### Title:

"I am lying"
#### Abstract:

The basic ingredients of the proof of Godel's
Incompleteness Theorem are self-reference and coding. We will spot places
where the first appears throughout logic, beginning our route with
Cantor's 'naive' set theory, his diagonal arguments and considerations of
the infinite. Russell's paradox comes next, throwing doubts in Cantor's
naiveness, and making imperative the need for a formal treatment of set
theory. When the 'axiomatic set theory' was being proposed by Zermelo,
Hilbert had already suggested his program of formalizing, if not all of
mathematics, an as large part of it as possible, in some axiomatic
theory, and then establishing its consistency by means of the theory
itself. Godel's Incompleteness Theorem marks the end of Hilbert's dream.
In order to sketch the proof of this theorem, we introduce notions from
basic logic, among others that of a computable function, which is related
with the coding part of the proof of Godel's theorem. Time permitting, we
conclude with a recent approach that treats all self-referential
'paradoxes' in a uniform way.

This talk will not be very
historically sensitive. With destination Godel's theorem, and
self-reference our guide, we will trip through basic logic.

To volunteer to give a talk, or for any other questions regarding this schedule, contact Wesley Calvert