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    Church's Thesis is an empirical conjecture about physical... — Carmelics
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    Challenges→The notion of a computable set generalizes effective decidability: a relation R is computable just in case there is an algorithm for deciding whether R holds of any tuple of natural numbers that always returns an answer after a finite (though potentially unbounded) number of steps

    Church's Thesis is an empirical conjecture about physical computation, not a logical necessity, as Copeland and Proudfoot argue, leaving the definition stipulative rather than revelatory.

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    Reasons For

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    • 1.Church's Thesis emerged from observing multiple independent computational models converging, suggesting empirical discovery rather than logical deduction.
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    • 2.Physical systems exhibit computational limits (quantum constraints, thermodynamics) that aren't logically necessary, suggesting Church's Thesis depends on physical facts.
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    • 3.If Church's Thesis were logically necessary, hypercomputation would be conceptually incoherent, yet it's intelligible even if physically impossible.
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    Reasons Against

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    • 1.Church's Thesis concerns mathematical functions, not physical processes, making it a conceptual claim about computability, not an empirical claim about nature.
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    • 2.The convergence of Turing machines, lambda calculus, and recursion on identical function classes reflects mathematical necessity, not contingent physical facts.
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    • 3.Declaring it merely stipulative undermines its explanatory power—it would explain why no counterexample exists without revealing why.
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    Key Terms

    Church's Thesis(Also called the Church-Turing Thesis; surveyed in Section 1.6 of the source text.)
    The claim that the class REC coincides with the class of effectively computable functions.
    Copeland and Proudfoot(as used in philosophy of mind and computation)
    Contemporary philosophers and logicians who have argued that the laws of physics might allow for forms of computation more powerful than what a standard Turing machine can do.
    Empirical conjecture(as used in philosophy of science)
    An educated guess based on observations and experiments in the real world, rather than something proven by pure reason.
    Physical computation(as used in philosophy of mind and computer science)
    The actual process of computation happening in real computers and devices in the physical world, as opposed to pure mathematical theory.
    Revelatory(as an alternative view of what measurement does)
    The idea that measurement simply reveals or uncovers something that was already there before you measured it, like finding out a coin was heads all along.
    Stipulative(as used in philosophy of logic and metaphysics)
    Something that's just defined or assumed to be true by someone's choice, rather than being proven or justified by evidence and reasoning.
    logical necessity(Distinguishing types of necessity)
    A property of statements that are true in all possible logical contexts, such as tautologies

    Connections

    2 topics

    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    Church's Thesis concerns mathematical functions, not physical processes, making ...Church's Thesis emerged from observing multiple independent computational models...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Declaring it merely stipulative undermines its explanatory power—it would explai...
    If Church's Thesis were logically necessary, hypercomputation would be conceptua...
    +3 moreShow less
    Physical systems exhibit computational limits (quantum constraints, thermodynami...The convergence of Turing machines, lambda calculus, and recursion on identical ...The notion of a computable set generalizes effective decidability: a relation R ...