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    Hume's Principle, which grounds the Precedes relation via... — Carmelics
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    Challenges→If Precedes(n,a) and n is a natural number, then a is a natural number

    Hume's Principle, which grounds the Precedes relation via equinumerosity, is a material abstraction principle, not a logical truth, as George Boolos argued in 'Is Hume's Principle Analytic?'.

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    Key Terms

    George Boolos(as the philosopher who challenged Hume's Principle's status)
    An American philosopher and logician (1940–1996) who wrote influential papers about mathematical logic, philosophy of mathematics, and what counts as truly logical versus empirical truths.
    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
    Material abstraction principle(as the classification of what Hume's Principle is)
    A rule about how we form general ideas by drawing from real, physical facts about the world—rather than being true just from pure logic alone.
    Precedes relation(as what Hume's Principle supposedly explains)
    A logical relationship where one thing comes before or is ordered earlier than another thing.

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    analytic(Used to establish that males exist if bachelors exist)
    A sentence or truth that holds in virtue of meaning alone, such that the predicate is contained in the subject concept.
    equinumerosity(as used in set theory)
    The property of two groups having the same size or number of items, even if the items themselves are different.
    logical truth(Bolzano's formal definition, inapplicable to purely logical propositions)
    A proposition is logically true if all of its i^s-variants (substitutions of extra-logical ideas) are true

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    Proof of definition segments1 linkedTruth & Knowledge1 linked

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    If Precedes(n,a) and n is a natural number, then a is a natural number

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