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    A formula can be invalid in a given system yet true in al... — Carmelics
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    Challenges→The full necessitism principle (Box-N) is invalid in KQML

    A formula can be invalid in a given system yet true in all genuine metaphysical possibilities if that system underrepresents modal reality.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Formal systems are finite constructs; metaphysical reality may contain infinite or non-classical modal structures inaccessible to any single system.
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    • 2.A formula's invalidity in a system reflects only that system's proof rules, not metaphysical truth. Systems can be incomplete without being false.
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    • 3.Counterexamples exist: classical logic rejects certain valid intuitionistic theorems. This suggests systems genuinely underrepresent some modal truths.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Without clear criteria for 'genuine metaphysical possibility,' the claim becomes unfalsifiable and immunizes any failed formula from criticism.
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    • 2.If a formula is true in all genuine possibilities, some formal system should capture it. Invoking hidden modal reality risks multiplying entities beyond necessity.
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    • 3.The claim conflates epistemic limitation (we can't prove it) with ontic gap (reality differs from systems). These require separate justification.
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    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    A formula's invalidity in a system reflects only that system's proof rules, not ...Counterexamples exist: classical logic rejects certain valid intuitionistic theo...Formal systems are finite constructs; metaphysical reality may contain infinite ...If a formula is true in all genuine possibilities, some formal system should cap...
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    The claim conflates epistemic limitation (we can't prove it) with ontic gap (rea...The full necessitism principle (Box-N) is invalid in KQMLWithout clear criteria for 'genuine metaphysical possibility,' the claim becomes...

    Details

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    claim
    Perspectives
    2 (1 for, 1 against)
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    1 edit