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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Dictionary of Science Quotations > Scientist Names Index P > Henri Poincaré Quotes > Truth

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Henri Poincaré
(29 Apr 1854 - 17 Jul 1912)

French mathematician, physicist and astronomer , who is often described as the last generalist in mathematics.


Henri Poincaré Quotes on Truth (9 quotes)

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Les faits scientifiques, et à fortiori, les lois sont l’œuvre artificielle du savant ; la science ne peut donc rien nous apprendre de la vérité, elle ne peut nous servir que de règle d’action.
The facts of science and, à fortiori, its laws are the artificial work of the scientist; science therefore can teach us nothing of the truth; it can only serve us as rule of action.
— Henri Poincaré
In La Valeur de la Science (1904), 214, translated by George Bruce Halsted, in The Value of Science (1907), 112.
Science quotes on:  |  Action (342)  |  Artificial (38)  |  Fact (1257)  |  Facts (553)  |  Law (913)  |  Nothing (1000)  |  Rule (307)  |  Scientist (881)  |  Teach (299)  |  Teaching (190)  |  Truth (1109)  |  Work (1402)

By natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
— Henri Poincaré
Science and Hypothesis (1902), in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method(1946), trans. by George Bruce Halsted, 91.
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Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have ‘proved’ that it involves no contradiction either in its terms or with the truths previously admitted.
— Henri Poincaré
…...
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Experience is the sole source of truth: it alone can teach us something new; it alone can give us certainty.
— Henri Poincaré
In La Science et l’Hypothèse (1901, 1908), 167, as translated in Henri Poincaré and William John Greenstreet (trans.), Science and Hypothesis (1902, 1905), 140. From the original French, “L'expérience est la source unique de la vérité: elle seule peut nous apprendre quelque chose de nouveau; elle seule peut nous donner la certitude. Voilà deux points que nul ne peut contester.”
Science quotes on:  |  Certainty (180)  |  Experience (494)  |  New (1273)  |  Source (101)  |  Teach (299)  |  Truth (1109)

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 (1902), trans. W. J. G. and preface by J. Larmor (1905), 140.
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If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it.
— Henri Poincaré
Henri Poincaré and George Bruce Halsted (trans.), The Value of Science (1907), 12.
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Sometimes truth frightens us. And in fact we know that it is sometimes deceptive, that it is a phantom never showing itself for a moment except to ceaselessly flee, that it must be pursued further and ever further without ever being attained. … Yet truth should not be feared, for it alone is beautiful.
— Henri Poincaré
As translated by George Bruce Halsted, in 'The Value of Science', Popular Science Monthly (Sep 1906), 69 193.
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While speaking, M. Bertrand is always in motion; now he seems in combat with some outside enemy, now he outlines with a gesture of the hand the figures he studies. Plainly he sees and he is eager to paint, this is why he calls gesture to his aid. With M. Hermite, it is just the opposite; his eyes seem to shun contact with the world; it is not without, it is within he seeks the vision of truth.
— Henri Poincaré
From La Valeur de la Science (1904), 14, as translated by George Bruce Halsted (trans.), in The Value of Science (1907), 16. From the French, “Tout en parlant, M. Bertrand est toujours en action; tantôt il semble aux prises avec quelque ennemi extérieur, tantôt il dessine d'un geste de la main les figures qu’il étudie. Évidemment, il voit et il cherche à peindre, c’est pour cela qu’il appelle le geste à son secours. Pour M. Hermite, c’est tout le contraire; ses yeux semblent fuir le contact du monde; ce n’est pas au dehors, c’est au dedans qu’il cherche la vision de la vérité.”
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Without this language [mathematics] most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world, which is the only true objective reality. …
This harmony … is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.
— Henri Poincaré
From La Valeur de la Science, as translated by George Bruce Halsted, in 'The Value of Science', Popular Science Monthly (Sep 1906), 69 195-196.
Science quotes on:  |  Analogy (76)  |  Attach (57)  |  Attain (126)  |  Beauty (313)  |  Better (493)  |  Difficult (263)  |  Enable (122)  |  Forever (111)  |  Harmony (105)  |  Ignorant (91)  |  Internal (69)  |  Intimate (21)  |  Know (1538)  |  Language (308)  |  Little (717)  |  Mathematics (1395)  |  Mathematics As A Language (20)  |  Most (1728)  |  Objective (96)  |  Price (57)  |  Progress (492)  |  Reality (274)  |  Remain (355)  |  Slow (108)  |  Sole (50)  |  Source (101)  |  Thing (1914)  |  True (239)  |  Truth (1109)  |  Understand (648)  |  Understood (155)  |  Universal (198)  |  Unknown (195)  |  Will (2350)  |  World (1850)


See also:
  • 29 Apr - short biography, births, deaths and events on date of Poincaré's birth.
  • The Value of Science: Essential Writings of Henri Poincaré, by Henri Poincaré. - book suggestion.

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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