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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that There is a fundamental tension between treating logical knowledge as a priori and the computational intractability of deciding logical validity.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Knowledge of logical validities is a paradigm case of a priori knowledge.
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    • 2.If logical knowledge is a priori, normal epistemic agents should be credited with knowledge of the logically valid sentences of systems such as propositional and first-order logic that underlie everyday reasoning.
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    • 3.Deciding whether a formula is a validity of even the weakest familiar logical systems is computationally intractable.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Kant's notion of a priori knowledge requires independence from experience, not computational accessibility or feasibility for finite minds.
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    • 2.Frege and early logicists grounded logical truth in objective conceptual relations, not in agents' capacity to verify those truths algorithmically.
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    • 3.If a priori status required computational tractability, mathematical truths like Fermat's Last Theorem would lose their a priori character before proof, which is absurd.
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    Reason against 2 of 2
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    • 1.Chalmers' epistemic two-dimensionalism distinguishes ideal rational reflection from cognitively bounded reflection, making a priori truth an idealized notion.
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    • 2.Cognitive limitations of finite agents, as Harman argues in 'Change in View', are constraints on belief revision, not on the modal status of the truths themselves.
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    • 3.Therefore, computational intractability reveals a gap between idealized logical omniscience and real epistemic agents, confirming rather than dissolving the tension the claim identifies.
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