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    The theory of computing occupies common ground among comp... — Carmelics
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    The theory of computing occupies common ground among competing mathematical philosophies (Formalism, Platonism, Intuitionism)

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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 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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    Related

    Adherents of any of these mathematical philosophies can agree on what effective ...Agreement on finite computational procedures does not entail agreement on the lo...Computing theory is finitistic and constructivist in natureFormalist, Platonic, and intuitionistic views of mathematics each overlap on fin...
    +4 moreShow less
    Intuitionists like Brouwer reject classical logic's law of excluded middle, whic...Platonists hold that Turing machines and recursive functions are discovered abst...Shared extensional output does not constitute 'common ground' when the intension...This ontological disagreement about what computation *is* persists even when pra...

    Similar

    Adherents of any of these mathematical philosophies can agree on what ...81%The theory of Turing machines is the most general theory of computatio...80%The theory of Turing machines is based on a very limited set of assump...79%Once the concepts of data set and algorithm are accepted as fundamenta...77%

    Source

    AI-extracted1/3 agreementValid
    SEP: information
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    If we look at the foundations of information and computation there are two notions that are crucial: the concept of a data set and the concept of an algorithm. Once we accept these notions as fundamental the rest of the theory data and computation unfolds quite naturally. One can “plug in” one’s favorite epistemological or metaphysical stance here, but this does not really affect foundational issues in the philosophy of computation and information. One might sustain a Formalist, Platonic or intu
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit