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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Kant's thesis that the origins of the necessity of our kn... — Carmelics
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    Perspectives
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    Home/Skepticism
    HistoryEditSee Inverse

    Kant's thesis that the origins of the necessity of our knowledge of axioms lie in intuition is mistaken.

    Skepticism
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 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 for 2 of 2
    ?
    • 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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    Reasons Against

    1 perspective
    Reason against
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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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    Topics

    SkepticismTruth & Knowledge

    Key Terms

    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

    Connections

    2 topics

    Modality & Possibility2 linkedPhilosophy of Language1 linked

    Related

    A grounding condition that is explanatorily redundant cannot be the correct acco...Frege demonstrated in Grundlagen that arithmetic truths follow from purely logic...Husserl's eidetic intuition in Logical Investigations distinguishes categorial i...If logical derivation alone suffices to ground the necessity of axioms, then Kan...
    +5 moreShow less
    If mathematical necessity derives from the eidetic structure of ideal objects ra...If the necessity of axioms is grounded in intuition, then knowledge of mathemati...

    Similar

    If the necessity of axioms is grounded in intuition, then knowledge of...84%Searle's Chinese Room argument relies on untutored intuitions rather t...80%Scientific axioms are not derived from a total understanding of the Fi...80%Skeptical arguments against intuitions aim to show that intuitions do ...80%

    Source

    AI-extracted1/3 agreementValid
    SEP: stumpf
    View source passageHide passage
    In the critical part of his work, Stumpf raises the problem of the origins of the laws and principles of logic and mathematics as follows: if these principles are inductive in nature, as Mill believes them to be, then they do not constitute necessary truths; if, on the contrary, they are necessary truths, then the question arises as to whether they are synthetic a priori judgments as Kant claims or analytic a priori propositions as Stumpf claims. Against Mill, Stumpf argues that the axioms are n
    Extraction notes

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

    Details

    Inductive intuition only leads to concepts and never to propositions
    Intuition understood in the Kantian sense is inductive
    Kantian pure intuition of space and time is tied to the conditions of sensible e...
    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit