Abstract / résumé
Name / nom: Matthew Chiasson
School / école: Mount Allison University
Length / durée: 25 min
Title / titre: Exploring Gödel's Incompleteness Theorem
Abstract / résumé: In a short paper published in 1931 under the inconspicous title "On
Formally Undecidable Propositions of Principia Mathematica and Related Systems," the
25 year-old logician Kurt Gödel shook the very foundations upon which formal
mathematics was built. Among other things, Gödel showed that any axiomatic
system that allows you to define the natural numbers is necessarily
incomplete:
it contains statements that are neither provably true nor provably false.
He
was also able to show that no consistent system can be used to prove its
own
consistency, a significant blow to Hilbert's programme and advocates of mathematical formalism. In this talk I hope to
illuminate some of the key
components of Gödel's ingenious proof and discuss some of its
philosophical
implications without getting into the more technical aspects.
Prerequisites / choses nécessaires: This should
be
more of a recreational talk, and so no prior knowledge of the subject will
be
assumed.
PDF format / format PDF: chiasson.pdf