Minds and Machines 13 (1):23-48 (2003)

Authors
Gualtiero Piccinini
University of Missouri, St. Louis
Abstract
This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical
objection” to his view that machines can think. Logico-mathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it
should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human
mathematicians presumably do.
Keywords Artificial Intelligence  Church-Turing Thesis  Computability  Incompleteness  Ordinal Logics  Undecidability  Turing  effective procedure  mathematical objection  Undecidability
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Reprint years 2004
DOI 10.1023/A:1021348629167
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References found in this work BETA

Computing Machinery and Intelligence.Alan M. Turing - 1950 - Mind 59 (October):433-60.
On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.

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Citations of this work BETA

Computing Mechanisms.Gualtiero Piccinini - 2007 - Philosophy of Science 74 (4):501-526.
Functionalism, Computationalism, and Mental Contents.Gualtiero Piccinini - 2004 - Canadian Journal of Philosophy 34 (3):375-410.
The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.

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