Symbolic Systems Forum - Solomon Feferman, Philosophy and Mathematics Departments

Solomon Feferman, Philosophy and Mathematics Departments, "Godel vs. Turing on Minds and Machines"

ABSTRACT:

Godel's incompleteness theorem (1931) is the most famous result of all

time in mathematical logic. Its significance has been seen as stretching

far beyond the fields of logic and mathematics to the very nature of the

human mind and its potentialities, but such claims are very controversial.

The theorem itself tells us that for any consistent mathematical axiom

system S there are simple arithmetical statements which are true but

unprovable in S. One view of the significance of this result is that

there are essential limits to human knowledge, since mind is the product

of the brain, and all of the brain?s activities (including proving

theorems in axiomatic systems) may be modeled in computational terms.

But

other philosophers and mathematicians have advanced an opposite view:

Godel's theorem shows that mind surpasses anything that can be modeled in

terms of computing machines, and is thus potentially unlimited. In this

talk I will present and critique Godel's own unusual formulation of the

issues involved.

BIO:

Solomon Feferman is Professor of Mathematics and Philosophy, Emeritus, at

Stanford University. He is the author of numerous articles on logic

and the foundations of mathematics, and of _In the Light of Logic_

(Oxford University Press 1998), editor-in-chief of the _Collected Works

of Kurt Godel_ (Vols. I-V, Oxford University Press, 1986-2003), and

co-author with Anita B. Feferman of _Truth and Consequences: The life

and logic of Alfred Tarski_ (Cambridge University Press, forthcoming).

Feferman is the recipient of the Rolf Schock Prize for Logic and

Philosophy for 2003.