Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
–Bertrand Russell, Recent Work on the Principles of Mathematics, published in International Monthly, Vol. 4 (1901), courtesy of Wikiquote
To modern educated people, it seems obvious that matters of fact are to be ascertained by observation, not by consulting ancient authorities. But this is an entirely modern conception, which hardly existed before the seventeenth century. Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives’ mouths. He said also that children would be healthier if conceived when the wind is in the north. One gathers that the two Mrs. Aristotles both had to run out and look at the weathercock every evening before going to bed. He states that a man bitten by a mad dog will not go mad, but any other animal will (Hiss. Am., 704a); that the bite of the shrewmouse is dangerous to horses, especially if the mouse is pregnant (ibid., 604b); that elephants suffering from insomnia can be cured by rubbing their shoulders with salt, olive oil, and warm water (ibid., 605a); and so on and so on. Nevertheless, classical dons, who have never observed any animal except the cat and the dog, continue to praise Aristotle for his fidelity to observation.
—Bertrand Russell, The Impact of Science on Society (1951), p. 7
Aristotle, as a philosopher, is in many ways very different from all his predecessors. He is the first to write like a professor: his treatises are systematic, his discussions are divided into heads, he is a professional teacher, not an inspired prophet. His work is critical, careful, pedestrian, without any trace of Bacchic enthusiasm. The Orphic elements in Plato are watered down in Aristotle, and mixed with a strong dose of common sense; where he is Platonic, one feels that his natural temperament has been overpowered by the teaching to which he has been subjected. He is not passionate, or in any profound sense religious. The errors of his predecessors were the glorious errors of youth attempting the impossible; his errors are those of age which cannot free itself of habitual prejudices. He is best in detail and in criticism; he fails in large construction, for lack of fundamental clarity and Titanic fire.
I actually like Aristotle all right, and I think his virtue ethics are still relevant. However, I think many of his ideas, especially as filtered through Scholasticism had a bad effect on Western Christianity and society at large. There are still some that want to defend his philosophy, or the Thomism that comes from it, even in places where modern science has shown it to be manifestly wrong, and I’ve been in on a couple such discussions of late. Thus, while I’m not intending to dismiss his importance or influence, or trying to argue that he was always wrong, I think it’s good to post some critical quotes.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty —a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
Art that means anything in the life of a community must bear some relation to current interpretations of the mystery of the universe. Our rigid separation of the humanities and the sciences has temporarily left our art stranded or stammering and incoherent. Both art and science ought to be blended in our early education of our children’s emotions and powers of observation, and that harmony carried forward in later education. (emphasis as given at Wikiquote)
Courtesy of Wikiquotes.
I know I’ve already done the Quote of the Week, but I ran across this and it’s too good not to post.