Quote: new theories replace the dominant, mathematical theories; e.g., arithmetic to geometry to algebra to arithmetic, probability to measure theory

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KAPPA: You will never know beyond any possibility … replace it by another dominant theory. … [footnote:] Such changes in the dominant theory imply … induced the Greeks to abandon arithmetic as the … arithmetic into geometry. They were convinced that all … by algebra; … The modern mathematical 'revolution of rigour' consisted in … [Cauchy, Weierstrass] … Russell in turn made logic the dominant theory … Another example of a remarkable Euclidean translation was …   Google-1   Google-2

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Group: philosophy of mathematics   (11 topics, 330 quotes)