E-LOGOS - University of Economics, Prague
Faculty of Economics, University of Economics, Prague

Godel on the mathematician’s mind and Turing Machine (2014)

Author: I. Hipólito

Affiliation: Faculty for Science and Technologies, New University of Lisbon, Portugal.

Article type: Standard scientific article

Section: Philosophy of Science

Language: language

Abstract (english):

Godel’s incompleteness theorems are categorically among the most philosophically important logico-mathematical discoveries ever made not only to Mathematics an logics, but also to Philosophy. Godel’s incompleteness theorems can be applied to demonstrate that the human mind overtakes any mechanism or formal system. Anti-mechanism theses from the incompleteness theorems were presented in Godel’s Proof by Nagel and Newman (1958). Subsequently, J. R. Lucas (1961) claimed that Godel’s incompleteness theorem “proves that mechanism is false, that is, that minds cannot be explained as machines”. Furthermore, given any machine which is consistent and capable of doing simple arithmetic, there is a formula it is incapable of producing as being true ...but which we can see to be true” (1961). Moreover, “if the proof of the falsity of mechanism is valid, it is of the greatest consequence for the whole of philosophy” (1961). More recently, a similar claim has been made by Roger Penrose (1990, 1994) and by Crispin Wright (1994, 1995) in an intuitionist perspective. Generally speaking, all of these support that Godel’s theorems imply, without qualifications, that the human mind infinitely surpasses the power of any finite machine. In the light of these thesis, I would like to consider Godel’s own perspective on an anti-mechanical thesis. Would Godel support a thesis that the mathematician mind could be a Turing Machine? What did Godel think that his theorem implied about the mathematician mind? I will start this discussion with a short review on Lucas and Penrose’s arguments, and subsequently I will explore Godel’s own considerations on the disjunction between mathematicians’ mind and Turing machines.

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