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    Geometric knowledge is grounded in the pure intuition of ... — Carmelics
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    Home/Modality & Possibility
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    Geometric knowledge is grounded in the pure intuition of space rather than in empirical observation or logical analysis alone

    Modality & PossibilityTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.To know a geometric truth (e.g., that an isosceles triangle has two equal base angles), the mathematician must produce a particular spatial construction that makes the truth demonstrable
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    • 2.Such constructions appeal to spatial intuition, not mere conceptual analysis or sensory experience
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Frege and Russell demonstrated that all geometric truths can be derived from purely logical axioms without invoking spatial representation.
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    • 2.If geometric knowledge were grounded in spatial intuition, non-Euclidean geometries would be inconceivable, yet mathematicians reason rigorously about them.
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    • 3.The logical derivability of geometric theorems from formal axioms is sufficient to explain geometric knowledge without positing a faculty of pure intuition.
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    Reason against 2 of 2
    ?
    • 1.Hilbert's formalist program showed that geometric axioms are uninterpreted strings manipulated by syntactic rules, requiring no intuitive spatial content.
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    • 2.Kant's pure intuition was tied specifically to Euclidean space, but the empirical discovery that physical space is non-Euclidean severs intuition from geometric truth.
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    • 3.If spatial intuition once licensed false beliefs about physical geometry, it cannot serve as the reliable epistemic ground Kant claimed it to be.
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    Topics

    Modality & PossibilityTruth & 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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    Perception2 linked

    Related

    Frege and Russell demonstrated that all geometric truths can be derived from pur...Hilbert's formalist program showed that geometric axioms are uninterpreted strin...If geometric knowledge were grounded in spatial intuition, non-Euclidean geometr...If spatial intuition once licensed false beliefs about physical geometry, it can...
    +4 moreShow less
    Kant's pure intuition was tied specifically to Euclidean space, but the empirica...Such constructions appeal to spatial intuition, not mere conceptual analysis or ...

    Similar

    The representation of space is an intuition, not a concept.83%The categories and principles of pure understanding yield knowledge on...82%Mathematics is embedded in theoretical physics and broader scientific ...81%Space is a genuine epistemic condition of our cognition, so empirical ...80%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemology-geometry
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    In Kant’s Critique of Pure Reason (1781/1787) (see the entry Kant’s views on space and time) the situation is more complicated or sophisticated. Kant introduced the notion of a priori knowledge in contrast to a posteriori, and synthetic knowledge in contrast to analytical knowledge to allow for the existence of knowledge that did not rely on experience (and was thus a priori) but was not tautological in character (and therefore synthetic and not analytic). The contentious class of synthetic a
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    Details

    The logical derivability of geometric theorems from formal axioms is sufficient ...
    To know a geometric truth (e.g., that an isosceles triangle has two equal base a...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit