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    Statements about 'all propositions' are meaningless. — Carmelics
    Statements
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    Perspectives
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    Home/Philosophy of Language
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    Statements about 'all propositions' are meaningless.

    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.The paradoxes to be avoided all result from a kind of vicious circle.
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    • 2.Vicious circles arise from supposing that a collection may contain members which can only be defined by means of the collection as a whole.
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    • 3.A statement like 'all propositions are either true or false' could only be legitimate if 'all propositions' referred to some already definite collection.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Gödel demonstrated that semantic totalities can be coherently quantified over without generating paradox, as in his completeness theorem.
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    • 2.Russell's vicious circle principle proves too strong: it eliminates not only paradoxes but also legitimate classical mathematics requiring impredicative definitions.
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    • 3.If impredicative definitions are permissible in arithmetic (as Ramsey and Gödel argued), quantification over all propositions need not be self-undermining.
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    Reason against 2 of 2
    ?
    • 1.Tarski's hierarchy of metalanguages shows that 'all propositions' can be rendered meaningful by stratifying truth-talk across object and meta-levels.
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    • 2.On Tarskian grounds, a statement about all object-level propositions is itself a metalinguistic claim, avoiding self-reference without declaring such statements meaningless.
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    Philosophy of LanguageTruth & Knowledge

    Related

    'All propositions' cannot refer to a definite collection if new propositions are...A statement like 'all propositions are either true or false' could only be legit...Gödel demonstrated that semantic totalities can be coherently quantified over wi...If impredicative definitions are permissible in arithmetic (as Ramsey and Gödel ...
    +5 moreShow less
    On Tarskian grounds, a statement about all object-level propositions is itself a...Russell's vicious circle principle proves too strong: it eliminates not only par...Tarski's hierarchy of metalanguages shows that 'all propositions' can be rendere...The paradoxes to be avoided all result from a kind of vicious circle.Vicious circles arise from supposing that a collection may contain members which...

    Similar

    Conceptualism about propositions is ruled out82%'All propositions' cannot refer to a definite collection if new propos...82%There are no propositions.81%Sentences apparently expressing truths about propositions are false, b...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: russell-paradox
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    An analysis of the paradoxes to be avoided shows that they all result from a kind of vicious circle. The vicious circles in question arise from supposing that a collection of objects may contain members which can only be defined by means of the collection as a whole. Thus, for example, the collection of propositions will be supposed to contain a proposition stating that “all propositions are either true or false.” It would seem, however, that such a statement could not be legitimate unless “all
    Extraction notes

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

    Details

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