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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The simultaneous replacement of multiple ideas in a proposition yields a uniquely determined variant proposition

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Frege's context principle holds that words have meaning only in the context of a proposition, so replacing multiple ideas simultaneously may alter the semantic context each replacement operates within.
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    • 2.When ideas i_k and i_m are semantically interdependent, replacing both simultaneously produces a proposition whose meaning cannot be derived from either substitution considered in isolation.
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    • 3.Therefore the variant proposition is not uniquely determined by the replacement sequence alone, but depends on holistic semantic relations Bolzano's substitution procedure leaves unspecified.
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    Reason for 2 of 2
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    • 1.Quine's thesis of the indeterminacy of translation establishes that no unique proposition is determined by a mapping between expression-sequences without a prior translation manual fixing reference.
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    • 2.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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    • 3.Without stable identity conditions for the replaced ideas, the 'same' replacement sequence applied to the 'same' proposition can yield extensionally divergent variant propositions.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Given a proposition s and two sequences of ideas i_1...i_n and j_1...j_n, each idea i_k is replaced uniformly (wherever it occurs) by the corresponding j_k
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    • 2.The replacement sequence pairs are fixed and the substitution is performed exhaustively and uniformly
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    • 3.The i_k values are pairwise distinct, preventing ambiguity in which replacement applies
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