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    Probability functions that assign probability 1 to contin... — Carmelics
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    Probability functions that assign probability 1 to contingent claims should be considered mere abbreviations for proper, logically explicit, non-enthymematic, inductive support relations.

    Truth & Knowledge
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    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.Probabilistic logicians commonly assign probability 1 to provisionally accepted contingent claims to avoid repeatedly writing them as premises.
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    • 2.When P(B|C) = 1, then P(A|B·C) = P(A|C), making the convention computationally convenient.
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    • 3.This convenience does not reflect genuine logical or evidential status of the contingent claim.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.De Finetti's representation theorem shows probability-1 assignments encode genuine epistemic commitments, not mere notational shortcuts.
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    • 2.If a probability-1 assignment were merely abbreviational, updating via conditionalization on its negation would be coherent, but it produces undefined results.
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    • 3.Undefinability under conditionalization reveals a substantive logical role, not an eliminable convenience.
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    Reason against 2 of 2
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    • 1.Levi's epistemology treats probability-1 assignments as expressions of full belief within a corpus, carrying genuine inferential weight.
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    • 2.Treating full beliefs as abbreviations collapses the distinction between settled and unsettled epistemic states, which Levi argues is indispensable to rational inquiry.
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    Topics

    Philosophy of LanguageTruth & Knowledge

    Key Terms

    Abbreviations (in logic)(in philosophical notation)
    Shorthand ways of writing something that really mean something longer and more complicated underneath.
    Contingent claims(in logic)
    Statements that could be either true or false—they're not necessarily true or false just by definition, but depend on how the world actually is.
    Inductive support relations(in epistemology and logic)
    Connections between pieces of evidence and conclusions, where the evidence makes the conclusion more likely to be true (but doesn't prove it for certain).
    Non-enthymematic(in logic and argumentation)
    Stating all the steps and assumptions explicitly, rather than leaving some parts unsaid or assumed.
    Probability functions(describes what the inductive logic uses to measure likelihood)
    Mathematical tools that calculate how likely something is to be true, assigning numbers between 0 (impossible) and 1 (certain) to different outcomes.

    Connections

    2 topics

    Causation1 linkedSkepticism1 linked

    Related

    De Finetti's representation theorem shows probability-1 assignments encode genui...If a probability-1 assignment were merely abbreviational, updating via condition...

    Source

    AI-extracted1/3 agreementValid
    SEP: logic-inductive
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    Nevertheless, it is common practice for probabilistic logicians to sweep provisionally accepted contingent claims under the rug by assigning them probability 1 (regardless of the fact that no explicit evidence for them is provided). This practice saves the trouble of repeatedly writing a given contingent sentence B as a premise, since \(P_{\gamma}[A \pmid B\cdot C]\) will equal \(P_{\gamma}[A \pmid C]\) whenever \(P_{\gamma}[B \pmid C] = 1\). Although this convention is useful, such probability
    Extraction notes

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

    Details

    Levi's epistemology treats probability-1 assignments as expressions of full beli...
    Probabilistic logicians commonly assign probability 1 to provisionally accepted ...
    +4 moreShow less
    This convenience does not reflect genuine logical or evidential status of the co...Treating full beliefs as abbreviations collapses the distinction between settled...Undefinability under conditionalization reveals a substantive logical role, not ...When P(B|C) = 1, then P(A|B·C) = P(A|C), making the convention computationally c...

    Similar

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    Type
    claim
    Perspectives
    3 (1 for, 2 against)
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