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    Sort logic is an alternative way of looking at mathematic... — Carmelics
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    Sort logic is an alternative way of looking at mathematics where definition rather than construction is the focus

    Philosophy of LanguageTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.In sort logic, any class of structures closed under isomorphism is definable under certain constraints
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    • 2.Sort logic allows quantification over new sorts, enabling characterization of truth in structures
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    • 3.Unlike set theory, sort logic centers definition over construction
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Hilbert's formalist program demonstrates that mathematical definition is itself a constructive act, collapsing the definition/construction distinction.
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    • 2.Sort logic's typed quantification over new sorts presupposes a prior construction of those sort domains, making construction logically anterior to definition.
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    Reason against 2 of 2
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    • 1.Benacerraf's identification problem shows that definitional equivalence across structures underdetermines mathematical ontology, undermining definition as a foundational focus.
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    • 2.If any class closed under isomorphism is definable in sort logic, then sort logic inherits the same structural abstraction that set-theoretic construction already provides, making the contrast with set theory superficial.
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    Topics

    Philosophy of LanguageTruth & Knowledge

    Connections

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    Modality & Possibility1 linked

    Related

    Benacerraf's identification problem shows that definitional equivalence across s...Hilbert's formalist program demonstrates that mathematical definition is itself ...If any class closed under isomorphism is definable in sort logic, then sort logi...In sort logic, any class of structures closed under isomorphism is definable und...
    +3 moreShow less
    Sort logic allows quantification over new sorts, enabling characterization of tr...Sort logic's typed quantification over new sorts presupposes a prior constructio...Unlike set theory, sort logic centers definition over construction

    Similar

    For Hegel, logic is not simply a science of the form of our thoughts b...83%Epistemic logic is a suitable formal framework for representing episte...83%Hoare logic is a true logic of programs, not merely a proof method83%Under a proof-theoretic interpretation, a logic is understood as the s...83%

    Source

    AI-extracted1/3 agreementValid
    SEP: logic-many-sorted
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    Interpretability is a good criterion for fixing a comparison between theories \(T\) and \(T^{\prime }\), for it is characterized either in terms of “uniform definability of models” or of “the existence of an interpretation map which preserves logical form and provability” (Mceldowney 2020: 15). It is also helpful for proving consistency, as \(T^{\prime }\) is proved to be consistent when interpreted in a consistent \(T\). However, interpretability between theories of a many-sorted signature does
    Extraction notes

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

    Details

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