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    The propositional variables 'p' and 'q' have sentential s... — Carmelics
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    Home/Philosophy of Language
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    The propositional variables 'p' and 'q' have sentential status and can legitimately fill argument-slots of truth-functions

    Philosophy of LanguageTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The variables 'p' and 'q' stand for items that already contain a verb
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    • 2.The variables 'p' and 'q' express a truth-bearer
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Propositional variables in truth-functional contexts are schematic placeholders, not genuine singular terms denoting truth-bearers.
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    • 2.Frege's distinction between concept-script variables and object-denoting names shows that sentential position does not confer propositional content on a variable.
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    • 3.A variable that 'contains a verb' in its substitution instances does not itself possess verbal or sentential status any more than 'x' becomes a number by ranging over numbers.
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    Reason against 2 of 2
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    • 1.Quine argued in 'Philosophy of Logic' that quantifying into sentential position requires propositional entities as values, but no such entities can be individuated without paradox.
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    • 2.If 'p' and 'q' have genuine sentential status sufficient to fill argument-slots, substitutional quantification must be available, yet substitutional quantification collapses truth-functional logic into mere syntactic manipulation without genuine semantic content.
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    Topics

    Philosophy of LanguageTruth & Knowledge

    Related

    A variable that 'contains a verb' in its substitution instances does not itself ...Frege's distinction between concept-script variables and object-denoting names s...If 'p' and 'q' have genuine sentential status sufficient to fill argument-slots,...Propositional variables in truth-functional contexts are schematic placeholders,...
    +3 moreShow less
    Quine argued in 'Philosophy of Logic' that quantifying into sentential position ...The variables 'p' and 'q' express a truth-bearerThe variables 'p' and 'q' stand for items that already contain a verb

    Similar

    Free-standing instances of the variables 'p' and 'q' cannot fill the a...86%The variables 'p' and 'q' express a truth-bearer85%If values of propositional functions are sentences, then sentences mus...79%The variables 'p' and 'q' stand for items that already contain a verb77%

    Source

    AI-extracted1/3 agreementValid
    SEP: ramsey
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    Ramsey (1929c, [OT] 9) anticipated a possible reaction to his use of propositional variables and to the translation of (4.1)–(4.3) as (4.1*)–(4.3*). The objection is the following: (4.1*)–(4.3*) cannot be English* counterparts of English sentences because they are not well-formed. Free-standing instances, the objection goes, of the variables ‘p’ and ‘q’ cannot fill the argument-slots of truth-functions, such as conjunction and material implication, which need complete sentences as arguments. F
    Extraction notes

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

    Details

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