Science and Hypothesis Quotes

“Le savant doit ordonner ; on fait la science avec des faits comme une maison avec des pierres ; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison.

The Scientist must set in order. Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.”
― Henri Poincare, Science and Hypothesis

“Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty.”
― Henri Poincaré, Science and Hypothesis

“The essential characteristic of reasoning by recurrence is that it contains, condensed so to speak, in a single formula, an infinite number of syllogisms.”
― Henri Poincaré, Science and Hypothesis

“The notion of infinity had long since been introduced into mathematics, but this infinity was what philosophers call a becoming. Mathematical infinity was only a quantity susceptible of growing beyond all limit; it was a variable quantity of which it could not be said that it had passed, but only that it would pass, all limits.”
― Henri Poincaré, Science and Hypothesis

“The very possibility of mathematical science seems an insoluble contradiction. If this science is deductive in appearance only, from where does it get its perfect rigor that no one dares to doubt? If, on the contrary, all the propositions it sets forth can be derived from one another by the rules of formal logic, why is mathematics not reducible to an immense tautology? Syllogism can teach us nothing that is essentially new and, if everything originated in the principle of identity, it should also be possible to reduce everything to it. Are we then to concede that the statements of all those theorems filling so many volumes are merely roundabout ways of saying that A is A?”
― Henri Poincaré, Science and Hypothesis

“The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A! ...Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive? ...If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.”
― Henri Poincaré, Science and Hypothesis

“Are the laws of acceleration and composition of forces nothing but arbitrary conventions? Conventions, yes; arbitrary, no; they would seem arbitrary if we forgot the experiences which guided the founders of science to their adoption and which are, although imperfect, sufficient to justify them. Sometimes it is useful to turn our attention to the experimental origin of these conventions.”
― Henri Poincaré, Science and Hypothesis

“The logical correctness of the arguments that lead from axioms to theorems is not the only thing we have to attend to. Do the rules of perfect logic constitute the whole of mathematics? As well say that the art of the chess-player reduces itself to the rules for the movement of the pieces. A selection must be made out of all the constructions that can be combined with the materials furnished by logic. The true geometrician makes this selection judiciously, because he is guided by a sure instinct, or by some vague consciousness of I know not what profounder and more hidden geometry, which alone gives a value to the constructed edifice.”
― Henri Poincaré, Science and Hypothesis

“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?”
― Henri Poincaré, Science and Hypothesis

“When we say force is the cause of motion, we are talking metaphysics; and this definition, if we had to be content with it, would be absolutely fruitless, would lead to absolutely nothing.”
― Henri Poincaré, Science and Hypothesis

“Douter de tout ou tout croire, ce sont deux solutions également commodes, qui l’une et l’autre nous dispensent de réfléchir.”
― Henri Poincaré, La Science et l'Hypothèse