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    If every concept has a cardinal number and concepts can b... — Carmelics
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    Challenges→Hume's Principle does not require that the domain of numbers be as large as the domain of concepts

    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.

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    Key Terms

    Natural numbers(mathematics)
    The counting numbers: 1, 2, 3, 4, and so on (sometimes including 0, depending on context).
    asymmetry(Modal logic frame semantics)
    A frame property expressible in hybrid logic by the formula c→□¬◇c, meaning if world x accesses world y, then y does not access x.
    cardinal number(There are infinitely many cardinals but no set that collects them all.)
    A number used to measure the size (cardinality) of sets.
    concept(Empiricist tradition)
    A mental representation formed from copies of sensory representations, assembled in accordance with general-purpose learning rules.
    number domain(mathematics and logic)

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    The complete set or collection of all the numbers you're talking about—like all whole numbers, or all real numbers.
    number-concepts(philosophy of mathematics)
    Ideas or categories that are specifically about numbers themselves—like the concept of 'what makes something a number' or 'the property of being a number'.

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    Hume's Principle does not require that the domain of numbers be as large as the ...

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