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    Carmelics

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    Made withinDC&Austin
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    Inverse View

    It is not the case that Axioms are necessary truths but not based on synthetic a priori judgments.

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    Reasons For

    1 perspective
    Reason for
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    • 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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    Reasons Against

    2 perspectives
    Reason against 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 against 2 of 2
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    • 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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