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    If propositions are individuated by sense-equivalence rat... — Carmelics
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    Challenges→Simple Type Theory (STT) gives rise to Russell's Appendix B paradox when supplemented with the principle that propositions differing by a constituent are distinct propositions and a correlation of propositions with classes they mention.

    If propositions are individuated by sense-equivalence rather than syntactic structure, the correlation W cannot be well-defined, since 'mentioning' a class is not a purely extensional relation.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Sense-equivalent propositions can differ in cognitive significance despite identical truth conditions, making syntactic individuation necessary.
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    • 2.The relation 'mentions' depends on intentional content, not just extensional properties, so it cannot be purely formal or truth-functional.
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    • 3.If W correlates propositions to classes based on sense rather than reference, mentioning the same class via different senses creates ambiguity.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Extensionality can be preserved by defining 'mentioning' at the level of reference rather than sense, bypassing the alleged problem entirely.
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    • 2.Well-definedness requires only that the mapping be consistent, not that the underlying relation be 'purely' extensional in all respects.
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    • 3.Many successful formal systems use sense-based individuation while maintaining well-defined correlations through canonical representation choices.
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    Key Terms

    Syntactic structure(what agents use as a proxy in this statement)
    The grammar and arrangement of symbols or components in a statement—like how words are organized in a sentence to create meaning.
    correlation W(in formal logic or philosophy of language)
    A specific mapping or matching between two sets of things (the exact meaning depends on context, but here it's likely a formal relationship being discussed).
    extensional relation(in logic and philosophy of language)
    A relationship based purely on what things actually exist or what concrete objects are involved, rather than on meaning or how we describe them.
    individuated(Chodorow's account of boys' psychological development)
    Feeling oneself to be separate or distinct from others, as a result of identifying with an absent parent
    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
    sense-equivalence(in philosophy of language)
    Two statements having the same meaning or conveying the same idea, even if they use different words (like 'bachelor' and 'unmarried man').
    well-defined(in mathematics and logic)
    Clear and precise enough that there's no confusion about what something means or how it works.

    Connections

    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Extensionality can be preserved by defining 'mentioning' at the level of referen...If W correlates propositions to classes based on sense rather than reference, me...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Many successful formal systems use sense-based individuation while maintaining w...
    Sense-equivalent propositions can differ in cognitive significance despite ident...
    +3 moreShow less
    Simple Type Theory (STT) gives rise to Russell's Appendix B paradox when supplem...The relation 'mentions' depends on intentional content, not just extensional pro...Well-definedness requires only that the mapping be consistent, not that the unde...