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    The additivity constraint on inductive support does not a... — Carmelics
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    The additivity constraint on inductive support does not apply when C acts like a logical contradiction.

    Modality & PossibilityTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.A logical contradiction supports all sentences to the maximum possible degree.
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    • 2.In deductive logic, a logical contradiction logically entails every sentence.
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    • 3.If C supports all sentences maximally, the normal summation rule for mutually exclusive propositions breaks down.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Probabilistic inductive logic (Carnap, Keynes) treats contradictions as receiving probability zero, not as maximally supporting all sentences.
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    • 2.If P(C) = 0, then P(H|C) is undefined rather than maximal, undermining the claim that contradictions confer universal maximum support.
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    • 3.An undefined conditional probability cannot serve as a limiting case that exempts contradictions from additivity — it removes them from the probability space entirely.
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    Reason against 2 of 2
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    • 1.Paraconsistent logics (Priest, da Costa) deny that contradictions entail everything, blocking the explosion principle that underlies P2 of the supporting argument.
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    • 2.If contradictions do not logically entail all sentences in a paraconsistent framework, there is no principled reason to assign them universal maximal inductive support.
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    • 3.Exempting contradictions from additivity is thus an artifact of classical logic's ex contradictione quodlibet, not a general feature of inductive support relations.
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    Modality & PossibilityTruth & Knowledge

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    Philosophy of Language2 linked

    Related

    A logical contradiction supports all sentences to the maximum possible degree.An undefined conditional probability cannot serve as a limiting case that exempt...Exempting contradictions from additivity is thus an artifact of classical logic'...If C supports all sentences maximally, the normal summation rule for mutually ex...
    +5 moreShow less
    If P(C) = 0, then P(H|C) is undefined rather than maximal, undermining the claim...If contradictions do not logically entail all sentences in a paraconsistent fram...In deductive logic, a logical contradiction logically entails every sentence.Paraconsistent logics (Priest, da Costa) deny that contradictions entail everyth...Probabilistic inductive logic (Carnap, Keynes) treats contradictions as receivin...

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    Source

    AI-extracted1/3 agreementValid
    SEP: logic-inductive
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    Axiom 4 says that inductive support adds up in a plausible way. When C logically entails the incompatibility of A and B, i.e., when no possible state of affairs can make both A and B true together, the degrees of support that C provides to each of them individually must sum to the support it provides to their disjunction. The only exception is in those cases where C acts like a logical contradiction and supports all sentences to the maximum possible degree (in deductive logic a logical contradi
    Extraction notes

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

    Details

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