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Pearls of Computation: Alvaro Garcia-Perez

  • 8.4.2016, 12:15 - 13:00

 

DATE: Friday, 8 April 2016
TIME AND PLACE: 12:15 in room V1.02

TITLE: On Hopefully Intelligible Contributions to Seminar Series and Related Events (aka. This Talk on Kurt Gödel is not a Pearl of Computation)
SPEAKER: Alvaro Garcia-Perez (Reykjavik University)

ABSTRACT: In his 1931 paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" Kurt Gödel introduced his Incompleteness Theorem, which has had deep implications in Logic, Mathematics, Computer Science, and in the theory of the mind and Artificial Intelligence. Rather than focusing on Kurt Gödel, this talk presents Gödel's Theorem in a hopefully accessible way by revising some popularising sources on it. The theorem says that in every deductive system that is stronger enough as to represent natural number arithmetic, there exist sentences of the kind "this sentence is false", which cannot be proven nor disproven within the system itself. Self-reference is a primordial mechanism in the proof. Gödel's Theorem reveals an intrinsic limitation of formal deductive systems and of provable mathematical truth. Incompleteness is not due to a defective system (actually, due to self-reference, incompleteness is due to the *strength* of the system) nor to any psycho- or physio-logical limitation of human thought. Gödel's Theorem has the same flavour than well-know paradoxes like the Liar's Paradox and Russell Paradox, and resembles other self-defeating arguments like the ones based on variations of Cantor's diagonal argument.

This talk is a part of the Pearls of Computation Lecture Series given by the School of Computer Science at Reykjavik University, which profiles the life and work of outstanding computer scientists that have shaped their respective fields of study. See http://www.icetcs.ru.is/poco.html for further details on this public seminar series.