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    Without a consistent principle licensing distinct extensi... — Carmelics
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    Challenges→There must be at least as many extensions as there are concepts.

    Without a consistent principle licensing distinct extensions for distinct concepts, P2 lacks the logical foundation required to derive the cardinality claim.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Cardinality claims require bijective mappings between sets, which presuppose a principled basis for individuating elements.
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    • 2.Without explicit criteria distinguishing concept-instances, P2 risks equivocation between distinct and identical extensions.
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    • 3.Mathematical rigor demands that derivations justify each step; P2's cardinality inference appears to skip this justification.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Extensions may be distinctly individuated by their *intensional definitions* alone, independent of additional licensing principles.
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    • 2.The claim conflates epistemic justification with logical foundation—P2 may derive the cardinality claim validly but lack proof.
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    • 3.Context-dependent identity criteria are common in logic; P2 might rely on implicit, contextually-sufficient individuation criteria.
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    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Cardinality claims require bijective mappings between sets, which presuppose a p...Context-dependent identity criteria are common in logic; P2 might rely on implic...Extensions may be distinctly individuated by their *intensional definitions* alo...Mathematical rigor demands that derivations justify each step; P2's cardinality ...
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    The claim conflates epistemic justification with logical foundation—P2 may deriv...There must be at least as many extensions as there are concepts.Without explicit criteria distinguishing concept-instances, P2 risks equivocatio...

    Details

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