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    A coherent semantics of Russell's formalized language can... — Carmelics
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    A coherent semantics of Russell's formalized language cannot be provided on the basis that values of propositional functions are sentences.

    Philosophy of LanguageTruth & Knowledge
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Frege's distinction between sense and reference requires that sentences refer to truth-values, not to other sentences, making sentential self-reference semantically degenerate.
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    • 2.Russell's ramified type theory demands that propositional functions and their values occupy distinct ontological levels, prohibiting sentences from serving dual roles as both values and substituends.
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    • 3.If sentences name sentences, the resulting self-referential structure generates the very semantic paradoxes Russell's theory of types was constructed to eliminate.
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    Reason for 2 of 2
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    • 1.Tarski's hierarchy of metalanguages establishes that a coherent semantics requires object-language expressions to be named by distinct metalanguage terms, never by co-level expressions.
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    • 2.Treating sentences as names of sentences collapses the use-mention distinction that Quine identifies as foundational to any rigorous formal semantics.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If values of propositional functions are sentences, then sentences must also be substituted for propositional variables.
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    • 2.If sentences are substituted for propositional variables, it would be necessary to take sentences as names of sentences.
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    • 3.Taking sentences as names of sentences is semantically incoherent.
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    Related

    Frege's distinction between sense and reference requires that sentences refer to...If sentences are substituted for propositional variables, it would be necessary ...If sentences name sentences, the resulting self-referential structure generates ...If values of propositional functions are sentences, then sentences must also be ...
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    Russell's ramified type theory demands that propositional functions and their va...Taking sentences as names of sentences is semantically incoherent.Tarski's hierarchy of metalanguages establishes that a coherent semantics requir...Treating sentences as names of sentences collapses the use-mention distinction t...

    Similar

    The conception of sentences as meaning representations is consistent w...81%If values of propositional functions are sentences, then sentences mus...80%If sentences denote truth values, sentences cannot denote propositions...79%The passages in Russell (1908) and Whitehead and Russell (1910–13) tha...79%

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    Many passages in [(Russell 1908)] and [(Whitehead and Russell 1910–13)] may be understood as saying or as having the consequence that the values of propositional functions are sentences. But a coherent semantics of Russell’s formalized language can hardly be provided on this basis (notice in particular, that, since sentences are also substituted for propositional variables, it would be necessary to take sentences as names of sentences.) And since the passages in question seem to involve confusio
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    claim
    Perspectives
    3 (2 for, 1 against)
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