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    Frege's applicability constraint holds that any adequate ... — Carmelics
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    Supports→Carnap's formalist position has not adequately answered the problem of applicability of mathematics

    Frege's applicability constraint holds that any adequate philosophy of mathematics must explain why arithmetic applies to empirical objects without treating numbers as mere uninterpreted symbols.

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    Key Terms

    Applicability constraint(as a demand that philosophy of mathematics must meet)
    A rule or requirement stating that a philosophical theory must be able to explain how and why something works in real life, not just in theory.
    Arithmetic
    Arithmetic is the branch of mathematics dealing with basic number operations—addition, subtraction, multiplication, and division. It's the foundation of math that you use in everyday life, like calculating change at a store, splitting a bill, or figuring out measurements. Essentially, it's the practical math skill everyone learns early in school to work with numbers in simple, straightforward ways.
    Frege(as a major historical figure in philosophy)
    Gottlob Frege (1848-1925) was a German logician and philosopher who founded modern logic and did groundbreaking work on how language relates to meaning and existence.
    Philosophy of mathematics(the field Wittgenstein is working in)
    The area of philosophy that asks fundamental questions about math itself: What are numbers? Do they exist in the world, or only in our minds? Are mathematical truths discovered or invented?

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    Uninterpreted symbols(as what numbers must NOT be treated as)
    Mathematical signs or marks (like '2' or '+') that are just meaningless squiggles without any real-world meaning or connection to actual things.
    empirical objects(metaphysics/epistemology)
    Things that actually exist in the world and can be experienced through our senses—like a chair or a tree, as opposed to abstract concepts.

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    Carnap's formalist position has not adequately answered the problem of applicabi...

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