The limits of reasoning.

Dr. Helmut Jurgensen Department of Computer Science University of Western Ontario

DEPARTMENT SEMINAR DATE: Friday, October 28, 2005 TIME: 3:30pm PLACE: Thorvaldson 105 *** Everyone is welcome ***

Abstract

One of Godel's independence theorems states, roughly, that every sufficiently rich mathematical theory allows for independent (true, but unprovable) statements.  Later Chaitin proposed that independence can be interpreted in information-theoretic terms: there is not enough information in the axioms to prove all true statements; or: proofs cannot generate new information.

What do these statements really mean?  Are they just dealing with mathematical artefacts as Godel's proof and subsequent ones seem to suggest?  Do they impose any relevant limit on what can be achieved by reasoning - or can we safely ignore them for all practical purposes?

I shall attempt to provide answers to these questions and to outline the limits of reasoning.  In particular, I shall sketch the ideas of a proof showing that Chaitin's information theoretic intuition was indeed correct.

About the speaker

Professor Helmut Jurgensen is a professor in the Department of Computer Science at the University of Western Ontario and Universitat Potsdam.  His research interests include: formal language theory, codes, information transmission systems, circuit testing and computer-mediated information access for the blind.

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