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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that The correlation that Basic Law V sets up between concepts and extensions must be one-to-one.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Russell's Paradox shows Basic Law V is inconsistent: the concept 'is not a member of itself' yields a contradictory extension.
      ?

      Think about whether this reason is strong or weak

    • 2.An inconsistent principle cannot establish any well-defined correlation, let alone a one-to-one mapping.
      ?

      Think about whether this reason is strong or weak

    • 3.Therefore, Vb cannot ground a genuine injective function between concepts and extensions in any coherent domain.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Cantor's theorem proves no function from a set S to its powerset P(S) can be surjective, since |P(S)| > |S|.
      ?

      Think about whether this reason is strong or weak

    • 2.If concepts over a domain outnumber objects (extensions are objects for Frege), no injective map from concepts to extensions is globally possible.
      ?

      Think about whether this reason is strong or weak

    • 3.Basic Law V's presupposed one-to-one correlation thus violates a provable cardinality constraint, independently of Russell's Paradox.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Basic Law V (Vb) implies that if concepts F and G differ, then the extensions of F and G differ.
      ?

      Think about whether this reason is strong or weak

    • 2.A one-to-one correlation is one in which distinct inputs are mapped to distinct outputs.
      ?

      Think about whether this reason is strong or weak

    • 3.Vb correlates distinct concepts with distinct extensions.
      ?

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