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    Carmelics

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    Inverse View

    It is not the case that Hume's Principle does not require that the domain of numbers be as large as the domain of concepts

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Hume's Principle, via Frege's Theorem, actually derives the full Dedekind-infinite sequence of natural numbers, making the number domain as large as any infinite concept-extension.
      ?

      Think about whether this reason is strong or weak

    • 2.If every concept has a cardinal number and concepts can be defined over the natural numbers themselves, the number domain must be at least as large as the domain of number-concepts, collapsing the proposed asymmetry.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.George Boolos argued that Hume's Principle carries unacceptable ontological commitments by generating an object for every concept, including concepts with infinite extensions, yielding a domain of numbers co-extensive with the concept hierarchy.
      ?

      Think about whether this reason is strong or weak

    • 2.The many-to-one mapping cited in support only holds for finite, co-equinumerous concepts, but Hume's Principle is unrestricted and applies to all concepts, including those individuating each distinct cardinal, forcing a domain at least as large as the full concept domain.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Hume's Principle only requires that the correlation between concepts and numbers be many-to-one, not one-to-one
      ?

      Think about whether this reason is strong or weak

    • 2.Hume's Principle often correlates distinct concepts with the same number (e.g., 'author of Principia Mathematica' and 'positive integer between 1 and 4' are both correlated with the number 2)
      ?

      Think about whether this reason is strong or weak

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