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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Turing's thesis is not susceptible to mathematical proof

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Church's theorem and Gödel's incompleteness results demonstrate that formal unprovability claims are themselves susceptible to rigorous mathematical proof.
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    • 2.If the boundaries of mechanical computability can be precisely formalized, then whether a thesis accurately characterizes those boundaries becomes a mathematical question.
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    • 3.Wilfried Sieg's work on 'mechanical procedures' shows that Turing's own structural analysis of computation admits formalization sufficient for proof-theoretic treatment.
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    Reason for 2 of 2
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    • 1.Turing's own unprovability assertion is itself a metamathematical claim, and metamathematical claims can be given mathematical proofs, as Gödel demonstrated in 1931.
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    • 2.The inference from 'Turing did not attempt a mathematical proof' to 'no mathematical proof is possible' commits an argument from ignorance that undermines the claim's scope.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Turing did not consider argument I to be a mathematical demonstration of his thesis
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    • 2.Turing did not consider argument II to be a mathematical demonstration of his thesis
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    • 3.Turing asserted that all arguments which can be given for the thesis share this non-demonstrative character
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