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The Incomputable Alan Turing

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by S. Barry Cooper
Citations:1 - 1 self
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BibTeX

@MISC{Cooper_theincomputable,
    author = {S. Barry Cooper},
    title = {The Incomputable Alan Turing},
    year = {}
}

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Abstract

The last century saw dramatic challenges to the Laplacian predictability which had underpinned scientific research for around 300 years. Basic to this was Alan Turing’s 1936 discovery (along with Alonzo Church) of the existence of unsolvable problems. This paper focuses on incomputability as a powerful theme in Turing’s work and personal life, and examines its role in his evolving concept of machine intelligence. It also traces some of the ways in which important new developments are anticipated by Turing’s ideas in logic.

Citations

914 On computable numbers, with an application to the ”Entscheidungsproblem - Turing - 1936
283 Classical Recursion Theory - Odifreddi - 1999
106 Recursively enumerable sets of positive integers and their decision problems - Post - 1944
103 Shadows of the Mind: A Search for the Missing Science of Consciousness - Penrose - 1996
97 Systems of Logic Based on Ordinals - Turing - 1939
64 A Mathematical Incompleteness in Peano Arithmetic, in Handbook for Mathematical Logic - Paris, Harrington - 1977
54 The Psychology of Invention - Hadamard - 1949
51 Quantum Algorithm for Hilbert’s Tenth Problem - Kieu - 2003
48 Transfinite recursive progressions of axiomatic theories - Feferman - 1962
29 Reflecting on Incompleteness - Feferman
28 Computability theory - Cooper - 2003
27 The universal computer: the road from Leibniz to Turing - Davis - 2000
26 Absolutely unsolvable problems and relatively undecidable propositions: account of an anticipation - Post - 1965
25 The myth of hypercomputation - Davis - 2004
25 Computabilityand recursion - Soare - 1996
23 The nature of the physical world - Eddington - 1928
21 Alan Turing’s forgotten ideas in computer science - Copeland, Proudfoot - 1999
20 Classical recursion theory, Vol - Odifreddi - 1999
19 Logical Dilemmas. The Life and Work of Kurt Gödel - Dawson - 1997
18 Intelligent machinery”. National Physical Laboratory Report - Turing - 1948
18 Computing machinery and intelligence, Mind 59, 433–460, (reprinted - Turing - 1950
17 Church’s thesis: A kind of reducibility axiom for constructive mathematics - Kreisel - 1970
17 Reflections on Kurt Gödel - Wang - 1988
16 Clockwork or Turing U/universe? – remarks on causal determinism and computability - Cooper - 1999
15 Narrow versus wide mechanism: Including a re-examination of Turing’s views on the mind-machine issue - Copeland - 2000
15 The chemical basis of morphogenesis, Phil - Turing - 1952
14 Incomputability in nature - Cooper, Odifreddi - 2003
11 Turing’s O-machines - Copeland - 1998
11 Out of My Later Years - Einstein - 1956
10 Turing: The Enigma. Vintage - Alan - 1992
10 Creative sets - Myhill - 1955
9 The confluence of ideas in 1936 - Gandy - 1988
9 Degrees of recursive unsolvability: preliminary report - Post - 1948
6 Off to infinity in finite time - Saari, Xia - 1995
5 Collected Works: Mathematical Logic - Turing - 2001
4 On Alan Turing’s anticipation of connectionism - Copeland, Proudfoot - 1996
4 Turing in the land of O(z - Feferman - 1988
4 Solvable and Unsolvable Problems - Turing - 1954
3 Alan Turing and the mathematical objection - Piccinini - 2003
2 Inexhaustibility - A Non-Exhaustive Treatment. Association for Symbolic Logic/ A K - Franzen - 2004
2 Incompleteness, mechanism, and optimism - Shapiro - 1998
1 FOM message of Mon - Friedman - 1999
1 Turing 2004: A celebration of his life and achievements 15 Incomputable Alan Turing - Gandy, eds
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