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    Home/Original/inverse
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    Inverse View

    It is not the case that Degrees of entailment can be construed in terms of entailment probabilities between logical forms of premise and hypothesis sentences.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Logical entailment is a truth-preserving relationship that holds necessarily, not probabilistically, between propositions (Frege, Tarski).
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    • 2.Assigning probabilities to entailment relations conflates epistemic uncertainty about logical form with the semantic relation of entailment itself.
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    • 3.A probabilistic 'degree' of entailment is therefore a category error: it measures parser confidence, not a property of the entailment relation.
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    Reason for 2 of 2
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    • 1.Natural language sentences routinely underdetermine their logical form in ways no finite enumeration of candidate forms can exhaust (Davidson, Quine on indeterminacy).
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    • 2.If the space of possible logical forms is open-ended, computing a probability distribution over them lacks a well-defined sample space.
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    • 3.Clarke's vector-algebraic framework therefore cannot yield genuine entailment probabilities, only heuristic similarity scores mislabeled as such.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Each sentence may have multiple possible logical forms.
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    • 2.Clarke's vector-algebraic framework allows statistical relationships between these logical forms.
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    • 3.Entailment probability can be computed by relating each possible logical form of a premise sentence to each possible logical form of a hypothesis sentence.
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