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    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Each branch of knowledge must be reducible to geometry to count as knowledge in the strong sense

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Arithmetic and algebra possess their own foundational rigor independent of geometric construction, as Viète and later Descartes demonstrated.
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    • 2.Reducing arithmetic to geometry would subordinate the more general to the less general, inverting the proper order of abstraction.
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    • 3.Leibniz's universal characteristic and Frege's logicism show that geometry is itself reducible to more fundamental logical principles, not vice versa.
      ?

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    Reason for 2 of 2
    ?
    • 1.Aristotle's Posterior Analytics establishes that each science has its own proper principles irreducible to those of a neighboring science.
      ?

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    • 2.The geometer who borrows from arithmetic commits a category error; importing geometry into all domains repeats this error systematically.
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    • 3.Kepler's own harmonic laws required number-theoretic and musical ratios that resist pure geometric derivation, undermining his own reductionist program.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Constructability in the classical geometric sense is the criterion for legitimate knowledge
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    • 2.Only what can be grounded in geometric principles meets the standard of rigorous knowledge
      ?

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    Strongest counterpoint
    Explore the most compelling reason on the other side.