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    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

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

    It is not the case that There must be at least as many extensions as there are concepts.

    ?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 that not every concept determines a well-defined extension (e.g., the concept 'is not a member of itself' yields contradiction).
      ?

      Think about whether this reason is strong or weak

    • 2.If some concepts fail to determine any extension, the mapping from concepts to extensions is not total, undermining P1.
      ?

      Think about whether this reason is strong or weak

    • 3.A non-total mapping cannot guarantee that the cardinality of extensions meets or exceeds the cardinality of concepts.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Frege's Basic Law V, which grounds the one-to-one correlation in P2, was proven inconsistent by Russell and abandoned even by Frege himself in 1902.
      ?

      Think about whether this reason is strong or weak

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

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Every concept is correlated with some extension (the correlation is total).
      ?

      Think about whether this reason is strong or weak

    • 2.The correlation between concepts and extensions is one-to-one (distinct concepts map to distinct extensions).
      ?

      Think about whether this reason is strong or weak

    • 3.In a total one-to-one mapping from concepts to extensions, the cardinality of extensions is at least as large as the cardinality of concepts.
      ?

      Think about whether this reason is strong or weak

    Next step

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    Strongest counterpoint
    Explore the most compelling reason on the other side.