Elements de la géométrie de l'infini (1727) as quoted by Amir R. Alexander, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (2002) citing Michael S. Mahoney, "Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late Seventeenth Century" in Reappraisals of the Scientific Revolution, ed. David C. Lindberg, Robert S. Westman (1990)
“However, in all honesty, I must say that one must essentially forget that all proofs are transcribed in this formal language. In order to think productively, one must use all the intuitive and informal methods of reasoning at one's disposal. At the very end one must check that no errors have been committed; but in practice set theory is treated as any other branch of mathematics. The reason that we can do this is that we will never speak about proofs but only about models.”
p. 1078 of "The discovery of forcing." http://www.logic.univie.ac.at/~ykhomski/ST2013/The%20Discovery%20of%20Forcing.pdf Rocky Mountain Journal of Mathematics 32, no. 4 (2002): 1071–1100.
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Paul Cohen 5
American mathematician 1934–2007Related quotes
1910s, Nobel lecture (1910)
Context: Moreover, and above all, let us remember that words count only when they give expression to deeds, or are to be translated into them. The leaders of the Red Terror prattled of peace while they steeped their hands in the blood of the innocent; and many a tyrant has called it peace when he has scourged honest protest into silence. Our words must be judged by our deeds; and in striving for a lofty ideal we must use practical methods; and if we cannot attain all at one leap, we must advance towards it step by step, reasonably content so long as we do actually make some progress in the right direction.
Source: Guide for the Perplexed (c. 1190), Part III, Ch.21
Context: He fully knows His unchangeable essence, and has thus a knowledge of all that results from any of His acts. If we were to try to understand in what manner this is done, it would be the same as if we tried to be the same as God, and to make our knowledge identical with His knowledge. Those who seek the truth, and admit what is true, must believe that nothing is hidden from God; that everything is revealed to His knowledge, which is identical with His essence; that this kind of knowledge cannot be comprehended by us; for if we knew its method, we would possess that intellect by which such knowledge could be acquired.... Note this well, for I think that this is an excellent idea, and leads to correct views; no error will be found in it; no dialectical argument; it does not lead to any absurd conclusion, nor to ascribing any defect to God. These sublime and profound themes admit of no proof whatever... In all questions that cannot be demonstrated, we must adopt the method which we have adopted in this question about God's Omniscience. Note it.
Source: The Emergence Of Probability, 1975, Chapter 15, Inductive Logic, p. 139.
Set theory and the continuum hypothesis, pp. 19–20 https://books.google.com/books?id=Z4NCAwAAQBAJ&pg=PA19
Set Theory and the Continuum Hypothesis (1966)
Preface (page XXIII)
The Great War for Civilization (2005)
1970's, Every Man an Artist: Talks at Documenta 5', 1972