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    Euclidean geometry possesses certainty and necessity — Carmelics
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    Euclidean geometry possesses certainty and necessity

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Euclidean geometry consists of synthetic a priori statements
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    • 2.Synthetic a priori knowledge does not rely on experience and is therefore necessary and certain
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    • 3.Knowledge that is both non-tautological and independent of experience can still be necessarily true
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.The discovery of consistent non-Euclidean geometries (Riemann, Lobachevsky) demonstrates that Euclid's parallel postulate is not logically necessary.
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    • 2.If a proposition can be coherently denied without contradiction, it cannot qualify as a priori necessary in Kant's sense.
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    • 3.Therefore, Euclidean geometry expresses contingent structural assumptions about space, not necessary truths.
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    Reason against 2 of 2
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    • 1.General relativity empirically confirmed that physical space conforms to non-Euclidean geometry in regions of significant mass-energy curvature.
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    • 2.A geometric system whose applicability to the actual world depends on empirical verification cannot claim the context-independent certainty synthetic a priori status requires.
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    • 3.Euclidean geometry is thus best understood as one formal system among many, whose truth is relative to axiom choice, not guaranteed by pure reason.
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    Related

    A geometric system whose applicability to the actual world depends on empirical ...Euclidean geometry consists of synthetic a priori statementsEuclidean geometry is thus best understood as one formal system among many, whos...General relativity empirically confirmed that physical space conforms to non-Euc...
    +5 moreShow less
    If a proposition can be coherently denied without contradiction, it cannot quali...Knowledge that is both non-tautological and independent of experience can still ...Synthetic a priori knowledge does not rely on experience and is therefore necess...The discovery of consistent non-Euclidean geometries (Riemann, Lobachevsky) demo...Therefore, Euclidean geometry expresses contingent structural assumptions about ...

    Similar

    Euclidean geometry provides one kind of knowledge (a priori).82%To know a geometric truth (e.g., that an isosceles triangle has two eq...80%Arithmetic, like geometry, is a deductive science based on a priori an...80%Sensitive knowledge of corresponding objects can never achieve the sam...79%

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    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

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit