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Informationen zum Autor Henri Poincaré was born in Nancy, France, in 1854. He joined the University of Paris in 1881 and lectured and wrote extensively on mathematics, experimental physics, and astronomy. His books have been translated into dozens of languages. In 1908, he was elected to membership in the Academie Française, the highest honor that can be accorded a French writer. He died in 1912. Stephen Jay Gould is the Alexander Agassiz professor of zoology and professor of geology at Harvard and the Vincent Astor visiting professor of biology at New York University. Recent books include Full House , Dinosaur in a Haystack , and Questioning the Millennium . He lives in Cambridge, Massachusetts, and New York City. Klappentext More than any other writer of the twentieth century! Henri Poincaré brought the elegant! but often complicated! ideas about science and mathematics to the general reader. A genius who throughout his life solved complex mathematical calculations in his head! and a writer gifted with an inimitable style! Poincaré rose to the challenge of interpreting the philosophy of science to scientists and nonscientists alike. His lucid and welcoming prose made him the Carl Sagan of his time. This volume collects his three most important books: Science and Hypothesis (1903); The Value of Science (1905); and Science and Method (1908). CHAPTER I On the Nature of Mathematical Reasoning I The very possibility of mathematical science seems an insoluble contradiction. If this science is only deductive in appearance, from whence is derived that perfect rigour which is challenged by none? If, on the contrary, all the propositions which it enunciates may be derived in order by the rules of formal logic, how is it that mathematics is not reduced to a gigantic tautology? The syllogism can teach us nothing essentially new, and if everything must spring from the principle of identity, then everything should be capable of being reduced to that principle. Are we then to admit that the enunciations of all the theorems with which so many volumes are filled are only indirect ways of saying that A is A? No doubt we may refer back to axioms which are at the source of all these reasonings. If it is felt that they cannot be reduced to the principle of contradiction, if we decline to see in them any more than experimental facts which have no part or lot in mathematical necessity, there is still one resource left to us: we may class them among à priori synthetic views. But this is no solution of the difficulty—it is merely giving it a name; and even if the nature of the synthetic views had no longer for us any mystery, the contradiction would not have disappeared; it would have only been shirked. Syllogistic reasoning remains incapable of adding anything to the data that are given it; the data are reduced to axioms, and that is all we should find in the conclusions. No theorem can be new unless a new axiom intervenes in its demonstration; reasoning can only give us immediately evident truths borrowed from direct intuition; it would only be an intermediary parasite. Should we not therefore have reason for asking if the syllogistic apparatus serves only to disguise what we have borrowed? The contradiction will strike us the more if we open any book on mathematics; on every page the author announces his intention of generalising some proposition already known. Does the mathematical method proceed from the particular to the general, and, if so, how can it be called deductive? Finally, if the science of number were merely analytical, or could be analytically derived from a few synthetic intuitions, it seems that a sufficiently powerful mind could with a single glance perceive all its truths; nay, one might even hope that some day a language would be invented simple enough for these truths to be made evident to any person of ordi...
