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    Each branch of knowledge must be reducible to geometry to... — Carmelics
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    Each branch of knowledge must be reducible to geometry to count as knowledge in the strong sense

    Philosophy of LanguageTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 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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    Reasons Against

    2 perspectives
    Reason against 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 against 2 of 2
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    • 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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    Topics

    Philosophy of LanguageTruth & 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

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    Modality & Possibility1 linked

    Related

    Aristotle's Posterior Analytics establishes that each science has its own proper...Arithmetic and algebra possess their own foundational rigor independent of geome...Constructability in the classical geometric sense is the criterion for legitimat...Kepler's own harmonic laws required number-theoretic and musical ratios that res...
    +4 moreShow less
    Leibniz's universal characteristic and Frege's logicism show that geometry is it...Only what can be grounded in geometric principles meets the standard of rigorous...

    Similar

    Sensitive knowledge of corresponding objects can never achieve the sam...82%Constructability in the classical geometric sense is the criterion for...80%Euclidean geometry provides one kind of knowledge (a priori).79%If knowledge is an achievement, then knowledge should behave like othe...77%

    Source

    AI-extracted1/3 agreementValid
    SEP: kepler
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    While in philosophical questions related to mathematics, Proclus and Plato were Kepler’s most important inspirational sources, he did not always see Plato and Aristotle as completely opposed, for the latter—in Kepler’s interpretation—also accepted “a certain existence of the mathematical entities” (KGW 14, let. N° 226, p. 265; see Peters, p. 130). To a great extent Kepler understood his mathematical investigations of HM as a continuation of Euclid’s Elements, especially of the analysis of irrati
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    Details

    Reducing arithmetic to geometry would subordinate the more general to the less g...
    The geometer who borrows from arithmetic commits a category error; importing geo...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit