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    Bolzano's replacement procedure presupposes that ideas ha... — Carmelics
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    Challenges→The simultaneous replacement of multiple ideas in a proposition yields a uniquely determined variant proposition

    Bolzano's replacement procedure presupposes that ideas have determinate, stable identity conditions that survive transplantation into new propositional contexts, a presupposition Quinean ontological relativity defeats.

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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.
    Ontology(Carnap argues this enterprise is based on a mistake)
    The philosophical discipline that tries to answer hard questions about what there really is.
    Quinean ontological relativity(as the philosophical idea that defeats Bolzano's assumption)
    A theory by philosopher Willard Quine arguing that the meaning and identity of concepts are not fixed but instead depend on the larger system of beliefs and language they're used in—so you can't just move an idea to a new context and expect it to mean the same thing.
    identity conditions(Metaphysics of mental states)

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    The criteria that determine what makes an entity the same entity across time or contexts, i.e., what individuates it.
    presupposition(Used to distinguish conditions required for an obligation from the grounds of the obligation)
    A necessary condition for something (such as an obligation) that is not itself part of the ground of that thing
    propositional contexts(as the different places where ideas are transplanted)
    Different sentences or logical statements in which an idea or concept appears and is used.
    replacement procedure(as Bolzano's technique for analyzing propositions)
    A method of swapping out one idea or concept for another in a sentence or argument while assuming the overall meaning stays the same.
    transplantation(as what Bolzano assumes ideas can survive)
    Moving an idea from one sentence or logical context into another one.

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    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    The simultaneous replacement of multiple ideas in a proposition yields a uniquel...

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