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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The justification for classifying specific problems as undecidable can be no stronger than the confidence placed in Church's Thesis.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Church's Thesis is not a mere empirical conjecture but is supported by the mutual reducibility of all known models of computation, constituting a form of mathematical convergence evidence distinct from physical induction.
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      Think about whether this reason is strong or weak

    • 2.Gödel, Turing, and Church independently arrived at extensionally equivalent formalizations, and this invariance across disparate formalisms gives the thesis a quasi-definitional status rather than a contingent one.
      ?

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    • 3.A claim whose negation would require positing an effective procedure that resists all known formal characterization bears a burden of proof that skeptical invocation of 'it's just a thesis' does not discharge.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
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    • 1.Kreisel's analysis shows undecidability results like the halting problem can be established relative only to the formal system itself, without invoking Church's Thesis as a bridge principle to informal effectivity.
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      Think about whether this reason is strong or weak

    • 2.The diagonal argument in Turing's halting problem proof yields a contradiction within the formal model alone, so the mathematical result stands independently of any claim about informal computation.
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      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
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    • 1.Undecidability proofs proceed by showing that the characteristic function of a problem is not recursive.
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      Think about whether this reason is strong or weak

    • 2.The inference from 'not recursive' to 'not effectively decidable' depends entirely on Church's Thesis.
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    • 3.Church's Thesis is an empirically supported thesis, not a proven mathematical theorem.
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    Strongest counterpoint
    Explore the most compelling reason on the other side.