Henri Poincaré: Quotes about science
Henri Poincaré was French mathematician, physicist, engineer, and philosopher of science. Explore interesting quotes on science.
Source: Science and Hypothesis (1901), Ch. I. (1905) Tr. George Bruce Halstead
Context: But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by induction? We see successively that a theorem is true of the number 1, of the number 2, of the number 3 and so on; the law is evident, we say, and it has the same warranty as every physical law based on observations, whose number is very great but limited. But there is an essential difference. Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us. Mathematical induction, that is, demonstration by recurrence, on the contrary, imposes itself necessarily, because it is only the affirmation of a property of the mind itself.<!--pp.13-14
“The very possibility of the science of mathematics seems an insoluble contradiction.”
Source: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Context: 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.<!--pp.5-6
Source: Science and Hypothesis (1901), Ch. IX: Hypotheses in Physics, Tr. George Bruce Halsted (1913)
Context: 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.
“It is only through science and art that civilization is of value.”
Some have wondered at the formula: science for its own sake; an yet it is as good as life for its own sake, if life is only misery; and even as happiness for its own sake, if we do not believe that all pleasures are of the same quality...
Every act should have an aim. We must suffer, we must work, we must pay for our place at the game, but this is for seeing's sake; or at the very least that others may one day see.
Source: The Value of Science (1905), Ch. 11: Science and Reality
Source: Science and Hypothesis (1901), Ch. I. (1905) Tr. George Bruce Halstead
Context: This procedure is the demonstration by recurrence. We first establish a theorem for n = 1; then we show that if it is true of n - 1, it is true of n, and thence conclude that it is true for all the whole numbers... Here then we have the mathematical reasoning par excellence, and we must examine it more closely.
... The essential characteristic of reasoning by recurrence is that it contains, condensed, so to speak, in a single formula, an infinity of syllogisms.
... to arrive at the smallest theorem [we] can not dispense with the aid of reasoning by recurrence, for this is an instrument which enables us to pass from the finite to the infinite.
This instrument is always useful, for, allowing us to overleap at a bound as many stages as we wish, it spares us verifications, long, irksome and monotonous, which would quickly become impracticable. But it becomes indispensable as soon as we aim at the general theorem...
In this domain of arithmetic,.. the mathematical infinite already plays a preponderant rôle, and without it there would be no science, because there would be nothing general.<!--pp.10-12
Source: The Value of Science (1905), Ch. 11: Science and Reality
“Sociology is the science which has the most methods and the least results.”
La sociologie est la science qui possède le plus de méthodes et le moins de résultats.
Part I. Ch. 1 : The Selection of Facts, p. 19
Science and Method (1908)
Science and Hypothesis (1901)
Source: Science and Hypothesis (1901), Ch. IV: Space and Geometry, Conclusions (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Il ne faut pas comparer la marche de la science aux transformations d’une ville, où les édifices vieillis sont impitoyablement jetés à bas pour faire place aux constructions nouvelles, mais à l’évolution continue des types zoologiques qui se développent sans cesse et finissent par devenir méconnaissables aux regards vulgaires, mais où un œil exercé retrouve toujours les traces du travail antérieur des siècles passés. Il ne faut donc pas croire que les théories démodées ont été stériles et vaines.
Introduction, p. 14
The Value of Science (1905)
Source: Science and Hypothesis (1901), Ch. I. (1905) Tr. George Bruce Halstead
Author's Essay Prefatory to the Translation: "The Choice of Facts," p.4
The Value of Science (1905)