“Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.”

Mathematics Magazine, Vol. 23-24. (1949), p. 161
Context: Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. Then, in the alleged proof, be alert for inexplicit assumptions. Euclid's notorious oversights drove this lesson home.

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Eric Temple Bell 14
mathematician and science fiction author born in Scotland w… 1883–1960

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“These are the assumptions we must make to give the questions the polemical force they are supposed to have. Not a single one of them stands up to closer examination.”

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Context: Is it not a fact that a learned physician is better equipped to diagnose and to cure an illness than a layman or the medicine-man of a primitive society? Is it not a fact that epidemics and dangerous individual diseases have disappeared only with the beginning of modern medicine? Must we not admit that technology has made tremendous advances since the rise of modern science? And are not the moon-shots a most and undeniable proof of its excellence? These are some of the questions which are thrown at the impudent wretch who dares to criticize the special positions of the sciences. The questions reach their polemical aim only if one assumes that the results of science which no one will deny have arisen without any help from non-scientific elements, and that they cannot be improved by an admixture of such elements either. "Unscientific" procedures such as the herbal lore of witches and cunning men, the astronomy of mystics, the treatment of the ill in primitive societies are totally without merit. Science alone gives us a useful astronomy, an effective medicine, a trustworthy technology. One must also assume that science owes its success to the correct method and not merely to a lucky accident. It was not a fortunate cosmological guess that led to progress, but the correct and cosmologically neutral handling of data. These are the assumptions we must make to give the questions the polemical force they are supposed to have. Not a single one of them stands up to closer examination.

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