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    Carmelics

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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 'all natural numbers' is not a determinate domain, the universal claim lacks a truth-condition independently of a background theory that itself requires justification.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Mathematical domains need not be 'determinate' in a metaphysical sense; formal definitions suffice for truth-conditions within formal systems.
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    • 2.Justification regress is unavoidable everywhere; demanding independent justification of background theory sets an impossible standard for all knowledge.
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    • 3.Universal claims about natural numbers remain truth-apt relative to standard interpretations; indeterminacy at foundations doesn't undermine local truth-conditions.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The natural numbers lack intrinsic boundaries; what counts as 'all' depends on constructive or set-theoretic assumptions not self-evident.
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    • 2.Universal claims require determinate domains to have truth-values; indeterminate domains make truth-conditions relative to framework choice.
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    • 3.Background theories justifying 'natural numbers' (ZFC, intuition, etc.) are themselves philosophically contested and need independent grounding.
      ?

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