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    Home/Original/inverse
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    Inverse View

    It is not the case that The theory of computing occupies common ground among competing mathematical philosophies (Formalism, Platonism, Intuitionism)

    ?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.Platonists hold that Turing machines and recursive functions are discovered abstract objects, while formalists treat them as meaningless symbol systems.
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    • 2.This ontological disagreement about what computation *is* persists even when practitioners converge on the same formal results.
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    • 3.Shared extensional output does not constitute 'common ground' when the intensional philosophical commitments remain irreconcilably distinct.
      ?

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    Reason for 2 of 2
    ?
    • 1.Intuitionists like Brouwer reject classical logic's law of excluded middle, which underlies key computability proofs (e.g., halting problem via reductio).
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    • 2.Agreement on finite computational procedures does not entail agreement on the logical foundations that justify or delimit those procedures.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Computing theory is finitistic and constructivist in nature
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    • 2.Formalist, Platonic, and intuitionistic views of mathematics each overlap on finitistic, constructivist ground
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    • 3.Adherents of any of these mathematical philosophies can agree on what effective computation is
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