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Vol. 7(3), 2007
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Section Logic
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"Cogito ergo sum non machina!"
About Gödel's first incompleteness theorem and turing machines
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Ricardo Pereira
Tassinari
Philosophy Department
State
University of São Paulo - UNESP
Marília, SP - Brazil
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Itala M. Loffredo
D'Ottaviano
Group
for Applied and Theoretical Logic
Centre for Logic, Epistemology and the History of Science - CLE
Philosophy Department - IFCH
State University of Campinas - Unicamp - Brazil
itala@cle.unicamp.br
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| Date Posted: July, 30th 2007
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ABSTRACT: The
aim of this paper is to argue about the impossibility of constructing
a complete formal theory or a complete Turing machines' algorithm that
represent the human capacity of recognizing mathematical truths. More specifically,
based on a direct argument from Gödel's First Incompleteness Theorem,
we discuss the impossibility of constructing a complete formal theory or
a complete Turing machines' algorithm to the human capacity of recognition
of first-order arithmetical truths and so of mathematical truths in general.
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