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    Bolzano's principle G presupposes a unique decomposition ... — Carmelics
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    Challenges→Every inference uniquely determines a corresponding argument

    Bolzano's principle G presupposes a unique decomposition of mental content into propositions, but Frege's context principle shows propositional identity is use-relative, not intrinsic.

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    Key Terms

    Bolzano
    Bolzano refers to Bernhard Bolzano (1781–1848), an Austrian mathematician and philosopher who made important discoveries about how functions behave and how infinity works in mathematics. Though his work wasn't widely recognized during his lifetime, he's now considered a pioneer who helped lay the groundwork for modern calculus and logic. His most famous contribution is the Bolzano-Weierstrass theorem, a fundamental principle in mathematics that helps us understand continuous functions and infinite sequences.
    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.
    Intrinsic(describing the kind of continuities that ground identity)
    Something that belongs to or is part of something by its very nature, rather than coming from outside or being relational.
    Propositional identity(as what the statement claims is being undermined)

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    Whether two different statements or sentences should be counted as expressing the exact same idea or meaning.
    context principle(Frege's methodological principle invoked to reframe how numbers can be epistemically accessible)
    Words have meaning only in the context of a proposition, not in isolation
    mental content(Davidsonian account)
    The content of propositional mental states such as belief, determined through causal relations between speakers and objects in the world and through the rational integration of speakers' behaviour.
    principle G(as a technical proposal about the structure of thought)
    A specific rule or law that Bolzano proposed about how mental content (the ideas in our minds) should be structured or divided up.
    propositions(Answer to the question of what metaphysical category propositions belong to)
    Entities belonging to a sui generis metaphysical category of their own kind, not reducible to other categories
    use-relative(as a way of describing how meaning works according to Frege)
    Something that depends on how it's actually used in practice, rather than being fixed or unchanging on its own.

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    1 linked claim · 2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked
    Every inference uniquely determines a corresponding argument

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    Every inference uniquely determines a corresponding argument

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