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    The simultaneous replacement of multiple ideas in a propo... — Carmelics
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    Home/Philosophy of Language
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    The simultaneous replacement of multiple ideas in a proposition yields a uniquely determined variant proposition

    Philosophy of LanguageTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 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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    Philosophy of LanguageTruth & Knowledge

    Related

    Bolzano's replacement procedure presupposes that ideas have determinate, stable ...Frege's context principle holds that words have meaning only in the context of a...Given a proposition s and two sequences of ideas i_1...i_n and j_1...j_n, each i...Quine's thesis of the indeterminacy of translation establishes that no unique pr...
    +5 moreShow less
    The i_k values are pairwise distinct, preventing ambiguity in which replacement ...The replacement sequence pairs are fixed and the substitution is performed exhau...Therefore the variant proposition is not uniquely determined by the replacement ...When ideas i_k and i_m are semantically interdependent, replacing both simultane...Without stable identity conditions for the replaced ideas, the 'same' replacemen...

    Similar

    The idea-variation method requires that at least one of the replaced i...84%Given a proposition s and two sequences of ideas i_1...i_n and j_1...j...79%The idea-variation method requires that the replacing idea belong to t...78%Performing variation on the subject idea of a proposition frequently p...78%

    Source

    AI-extracted1/3 agreementValid
    SEP: bolzano
    View source passageHide passage
    The basic insight underlying Bolzano’s method of idea-variation is quite simple (WL II, 77 ff.). Let us take as our first example \(S_1\) the proposition [Kant is a German philosopher]. (In order to simplify matters linguistically, we do not adhere to Bolzano’s formulation ‘\(A\) has \(b\)’ but will allow also formulations of the kind ‘\(A\) is (a) \(B\)’. Moreover, we will take in what follows words like ‘German’, ‘French’, ‘European’, ‘American’ etc. in the sense of ‘born in Germany’, ‘born in
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit