One of the bad effects of an anti-intellectual philosophy such as that of Bergson, is that it thrives upon the errors and confusions of the intellect. Hence it is led to prefer bad thinking to good, to declare every momentary difficulty insoluble, and to regard every foolish mistake as revealing the bankruptcy of intellect and the triumph of intuition. There are in Bergson's work many allusions to mathematics and science, and to a careless reader these allusions may seem to strengthen his philosophy greatly. As regards science, especially biology and physiology, I am not competent to criticize his interpretations. But as regards mathematics, he has deliberately preferred traditional errors in interpretation to the more modern views which have prevailed among mathematicians for the last eighty years. In this matter, he has followed the example of most philosophers. In the eighteenth and the early nineteenth centuries, the infinitesimal calculus, though well developed as a method, was supported, as regards his foundations, by many fallacies and much confused thinking. Hegel and his followers seized upon these fallacies and confusions, to support them in their attempt to prove all mathematics self-contradictory. Thence the Hegelian account of these matters passed into the current thought of philosophers, where it has remained long after the mathematicians have removed all the difficulties upon which the philosophers rely. And so long as the main object of philosophers is to show that nothing can be learned by patience and detailed thinking, but that we ought rather to worship the prejudices of the ignorant under the title or 'reason' if we are Hegelians, or of 'intuition' if we are Bergsonians, so long philosophers will take care to remain ignorant of what mathematicians have done to remove the errors by which Hegel profited.
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Bertrand Russell (1946)Henri-Louis Bergson
» Henri-Louis Bergson - all quotes »
Mathematics is not a deductive science — that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork. You want to find out what the facts are, and what you do is in that respect similar to what a laboratory technician does. Possibly philosophers would look on us mathematicians the same way as we look on the technicians, if they dared.
Paul Halmos
What happened was, 2,400 years ago, the Greek Gang of Three, by whom I mean Aristotle, Plato and Socrates, started to think based on analysis, judgment and knowledge. At the same time, church people, who ran the schools and universities, wanted logic to prove the heretics wrong. As a result, design and perceptual thinking was never developed. People assumed philosophers were doing it and so they blocked anyone else from doing it. But philosophers were not. Philosophers may look out at the world from a stained-glass window, but after a while they stop looking at the world and start looking at the stained glass.
Edward de Bono
The French philosophy of the eighteenth century was in full strength. Those were the years in which Voltaire ruled European opinion, and Turgot could not but take account of his influence. Yet no one could apparently be more unlike those who were especially named as the French philosophers of the eighteenth century. He remained reverential; he was never blasphemous, never blatant; he was careful to avoid giving needless pain or arousing fruitless discussion; and, while the tendency of his whole thinking was evidently removing him from the orthodoxy of the Church, his was a broader and deeper philosophy than that which was then dominant.
Andrew Dickson White
The French philosophy of the eighteenth century was in full strength. Those were the years in which Voltaire ruled European opinion, and Turgot could not but take account of his influence. Yet no one could apparently be more unlike those who were especially named as the French philosophers of the eighteenth century. He remained reverential; he was never blasphemous, never blatant; he was careful to avoid giving needless pain or arousing fruitless discussion; and, while the tendency of his whole thinking was evidently removing him from the orthodoxy of the Church, his was a broader and deeper philosophy than that which was then dominant.
Anne Robert Jacques Turgot
...it is rare that mathematicians are intuitive, and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it. 1
Blaise Pascal
Bergson, Henri-Louis
Beria, Lavrentiy
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