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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that If the domain contains only finitely many objects, substitutional invariance can be satisfied by arguments whose validity depends on contingent cardinality facts, not logical form.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.Logical validity should be form-dependent, not cardinality-dependent; an argument valid in one domain shouldn't become invalid elsewhere.
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    • 2.If validity requires knowing domain size, logical truths become metaphysically hostage to contingent existence facts, conflating logic with metaphysics.
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    • 3.Standard substitutional invariance principle demands arguments remain valid across all domain interpretations, not just those of particular cardinalities.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Substitutional semantics treats validity as preserving truth under all uniform substitutions, making cardinality constraints legitimate validity conditions.
      ?

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    • 2.Finite domains can make arguments like 'Everything is F or not-F' valid purely because exhaustion over finitely many objects is guaranteed.
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    • 3.Logical form alone cannot determine validity in finite domains; contingent facts about how many objects exist become semantically relevant.
      ?

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