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  • Is Non-Euclidean Geometry Favorable to Apriorism?

    Philosophy & Thought

    Is Non-Euclidean Geometry Favorable to Apriorism?

    Non-Euclidean geometry is generally thought to be a “fatal blow” to Kantian transcendental theory. In an earlier article, I expressed doubt about this overly simplistic idea. But recently, as I happened to mull over the question again, an even bolder thought popped into my head — the discovery of non-Euclidean geometry is actually favorable to transcendental theory! It should be noted that Kant’s transcendental theory is neither empiricism nor rationalism. Kant is not saying that if one first finds a few axioms in human a priori intuition, then one can deduce the true state of the objective world. Kant is answering this question: since human experience of this world is…

    philosophyKantspacePoincaré
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  • [Fr.] Poincaré: “Last Thoughts”

    History of Science & Scholarship

    [Fr.] Poincaré: “Last Thoughts”

    [French] Poincaré: “The Last Reflections,” translated by Li Xingmin, proofread by Fan Dainian, Commercial Press, December 1996 Poincaré was such a great, even legendary, figure! Poincaré is widely regarded as the “last all-around mathematical genius,” comparable to Gauss; in fact, it would not be at all excessive to remove even the word “mathematical.” “Poincaré’s achievements in the four main branches of mathematics—arithmetic, algebra, geometry, and analysis—were all pioneering; in particular, he made outstanding contributions to branches such as function theory, algebraic geometry, number theory, the mathematics of strings, differential equations, and algebraic topology.” (p. ii) “In astronomy, Poincaré’s main work fell into three areas: the equilibrium shapes of rotating fluids;…

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