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    Philosophical accounts of cardinality grounded in Fregean... — Carmelics
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    Challenges→Two infinite well-ordered sets with the same ordinal number have the same cardinal number.

    Philosophical accounts of cardinality grounded in Fregean abstraction principles, such as Hume's Principle, treat cardinal number as conceptually prior to and independent of ordinal structure, severing the entailment the argument assumes.

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    Key Terms

    Conceptually prior(as used in epistemology)
    Something that is logically or mentally more basic or fundamental—you need to understand it before you can understand something else.
    Fregean abstraction principles(as used in philosophy of mathematics)
    A method named after philosopher Gottlob Frege for defining mathematical objects (like numbers) by focusing on what makes things equivalent rather than what they actually are.
    Hume's Principle(Philosophy of mathematics, neo-logicism)
    A principle codifying the condition under which two concepts are equinumerous, namely when the number of objects falling under each concept is identical
    cardinal number(There are infinitely many cardinals but no set that collects them all.)
    A number used to measure the size (cardinality) of sets.

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    cardinality(Central to comparing infinite sets and establishing that no universal set exists.)
    A measure of the size of a set, indicating the number of elements it contains.
    entailment(Conceptualist framework)
    Understood in terms of truth at a world
    ordinal structure(set theory)
    The way numbers are organized in a sequence based on their order and size; it's about how mathematical objects line up relative to each other.

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    Proof of definition segments1 linkedModality & Possibility1 linked

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    Two infinite well-ordered sets with the same ordinal number have the same cardin...

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