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    Carmelics

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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Kant's thesis that the origins of the necessity of our knowledge of axioms lie in intuition is mistaken.

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    Reasons For

    1 perspective
    Reason for
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    • 1.If the necessity of axioms is grounded in intuition, then knowledge of mathematics becomes dependent upon experience
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    • 2.Intuition understood in the Kantian sense is inductive
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    • 3.Inductive intuition only leads to concepts and never to propositions
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Frege demonstrated in Grundlagen that arithmetic truths follow from purely logical definitions without appeal to any form of intuition.
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    • 2.If logical derivation alone suffices to ground the necessity of axioms, then Kantian intuition is explanatorily redundant for mathematical necessity.
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    • 3.A grounding condition that is explanatorily redundant cannot be the correct account of the necessity it purports to explain.
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    Reason against 2 of 2
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    • 1.Husserl's eidetic intuition in Logical Investigations distinguishes categorial intuition of essences from Kant's sensible intuition of particulars.
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    • 2.Kantian pure intuition of space and time is tied to the conditions of sensible experience, not to the eidetic structure of mathematical objects themselves.
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    • 3.If mathematical necessity derives from the eidetic structure of ideal objects rather than sensible conditions, Kant's account misidentifies the source of that necessity.
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