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    The truth of 'necessarily A' does not require A to be tru... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    The truth of 'necessarily A' does not require A to be true in all possible worlds

    Modality & Possibility
    ?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.In ordinary speech, 'A is necessary' is used in contexts where the speaker knows there exist possible worlds where A is false
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    • 2.The claim 'I must pay my bills' is intelligible and true even though there are possible worlds where the speaker fails to pay
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Kripke's semantic framework establishes that 'necessarily A' is formally defined as A's truth across all worlds accessible from the actual world.
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    • 2.Ordinary language uses of 'necessary' conflate alethic necessity with deontic or epistemic modalities, which require distinct logical treatment.
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    • 3.Collapsing these modal distinctions, as the supporting argument does, undermines the very framework needed to give 'necessity' precise philosophical content.
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    Reason against 2 of 2
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    • 1.Lewis's modal realism entails that possible worlds are concrete, causally isolated entities, making 'necessarily A' a universal quantifier over all such worlds.
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    • 2.If 'necessarily A' permits worlds where A is false, the logical inference from 'necessarily A' to A—axiom T—becomes invalid, destabilizing standard modal logic.
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    Topics

    Modality & Possibility

    Related

    Collapsing these modal distinctions, as the supporting argument does, undermines...If 'necessarily A' permits worlds where A is false, the logical inference from '...In ordinary speech, 'A is necessary' is used in contexts where the speaker knows...Kripke's semantic framework establishes that 'necessarily A' is formally defined...
    +3 moreShow less
    Lewis's modal realism entails that possible worlds are concrete, causally isolat...Ordinary language uses of 'necessary' conflate alethic necessity with deontic or...The claim 'I must pay my bills' is intelligible and true even though there are p...

    Similar

    That which is necessarily true of a thing must also be true of that wh...84%Whatever is necessarily false is impossible84%If a statement is both necessarily false and true at some world, it is...84%For φ to be necessarily true, the proposition φ expresses must necessa...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: logic-modal
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    Even in modal logic, one may wish to restrict the range of possible worlds which are relevant in determining whether \(\Box A\) is true at a given world. For example, I might say that it is necessary for me to pay my bills, even though I know full well that there is a possible world where I fail to pay them. In ordinary speech, the claim that \(A\) is necessary does not require the truth of \(A\) in all possible worlds, but rather only in a certain class of worlds which I have in mind (for examp
    Extraction notes

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

    Details

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