Computability in Europe 2006
Logical Approaches to Computational Barriers

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Regular Talk:
Gödel, Turing, the Undecidability Results and the Nature of Human Mind

Speaker: Riccardo Bruni
Presentation: RB_CIE06_talk.pdf
Slot: Sat, 17:00-17:20, Faraday E (col. 4)


In this paper Turing and Gödel's standpoints toward the implications
the undecidability results are addressed. In the case of Turing, we
show how his account on the issue was deeply connected to his project
of actually building a computing machine showing an intelligent
behaviour. Furthermore, we argue that his claim that the argument based
on the halting problem offers no objection to that very project, is
strenghtened by a general view on mathematical resoning and
intelligence which has an anti-mechanistic flavour. As to Gödel's
position, we reformulate, by enhancing its modal
character,  an argument that is contained in an unublished
paper belonging to the early 1950's which ends in an open conclusion on
minds and machines. We finally present Gödel's interpretation of the
solution of the famous P=NP problem contained in a letter to von
Neumann as a further contribuition in this direction of working out the
philosophical significance of certain mathematical achievements. 

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