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    Axioms are necessary truths but not based on synthetic a ... — Carmelics
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    Home/Modality & Possibility
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    Axioms are necessary truths but not based on synthetic a priori judgments.

    Modality & Possibility
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Frege demonstrated that logical and mathematical axioms are analytic, grounded in logical laws alone, without requiring Kantian intuition or sensibility.
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    • 2.If axioms derive their necessity from purely logical relations between concepts, then synthetic a priori machinery is explanatorily redundant for their justification.
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    • 3.Redundant explanatory apparatus should be rejected per Occam's razor, making the Kantian synthetic framework an unnecessary complication for axiomatic necessity.
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    Reason for 2 of 2
    ?
    • 1.Husserl's eidetic intuition grounds necessary truths in the essential structures of phenomena themselves, bypassing Kant's subjective mental forms entirely.
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    • 2.Axioms can be understood as expressions of mind-independent eidetic necessities that are discovered, not constructed, through phenomenological reflection.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Kant's synthetic judgments presuppose a kind of 'mental machinery' to account for their formation
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    • 2.Synthetic judgments involve numerous assumptions such as the a priori forms of sensibility, intuition, and Denkformen
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    • 3.These a priori forms are mere constructions
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    Topics

    Modality & PossibilityTruth & Knowledge

    Connections

    2 topics

    Consciousness & Mind1 linkedSkepticism1 linked

    Related

    Axioms can be understood as expressions of mind-independent eidetic necessities ...Frege demonstrated that logical and mathematical axioms are analytic, grounded i...Husserl's eidetic intuition grounds necessary truths in the essential structures...If axioms derive their necessity from purely logical relations between concepts,...
    +4 moreShow less
    Kant's synthetic judgments presuppose a kind of 'mental machinery' to account fo...Redundant explanatory apparatus should be rejected per Occam's razor, making the...Synthetic judgments involve numerous assumptions such as the a priori forms of s...

    Similar

    If some necessary truths are only knowable a posteriori, then necessar...85%Axioms are not synthetic a priori judgments84%Newton's three Laws of Motion are synthetic a priori truths82%A proposition that is a priori cannot be a necessary a posteriori trut...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: stumpf
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    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

    These a priori forms are mere constructions
    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit