The Foundations of Science Quotes

“To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“The geometric language is after all only a language. Space is only a word that we have believed a thing.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“The readings we shall be able to make on our instruments at any instant will depend only on the readings we could have made on these same instruments at the initial instant.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“Correlative movement' therefore constitutes the sole connection between two phenomena which otherwise we never should have dreamt of likening.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“In general, the totality A will have nothing in common with the totality A´, nor the totality B with the totality B´. The transition from the totality A to the totality B and that from the totality A´ to the totality B´ are therefore two changes which in themselves have in general nothing in common. And yet we regard these two changes both as displacements and, furthermore, we consider them as the same displacement. How can that be? It is simply because they can both be corrected by the same correlative movement of our body.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“When a body changes its place and its shape, we can no longer, by appropriate movements, bring back our sense-organs into the same relative situation with regard to this body; consequently we can no longer reestablish the primitive totality of impressions.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“It follows from this that sight and touch could not have given us the notion of space without the aid of the 'muscular sense.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“None of our sensations, isolated, could have conducted us to the idea of space; we are led to it only in studying the laws, according to which these sensations succeed each other.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“What I do see is that the sensations which correspond to movements in the same direction are connected in my mind by a mere association of ideas. It is to this association that what we call 'the sense of direction' is reducible. This feeling therefore can not be found in a single sensation”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“Each muscle gives rise to a special sensation capable of augmenting or of diminishing, so that the totality of our muscular sensations will depend upon as many variables as we have muscles. From this point of view, motor space would have as many dimensions as we have muscles.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“only reach him after having traversed reflecting media of complicated form. The two indications which serve us in judging distances would cease to be connected by a constant relation. A being who should achieve in such a world the education of his senses would no doubt attribute four dimensions to complete visual space.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“if the contrary takes place, if these two muscular sensations vary independently of one another, we shall have to take account of one more independent variable, and 'complete visual space' will appear to us as a physical continuum of four dimensions.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“in every limited frame the point occupying the center of the frame will never appear as equivalent to a point near one of the borders.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“In other words, the axioms of geometry (I do not speak of those of arithmetic) are merely disguised definitions.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“The axioms of geometry therefore are neither synthetic a priori judgments nor experimental facts.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“the sum of the angles of a triangle is equal to two right angles; but this is because the triangles we deal with are too little; the difference, according to Lobachevski, is proportional to the surface of the triangle; will it not perhaps become sensible when we shall operate on larger triangles or when our measurements shall become more precise? The Euclidean geometry would thus be only a provisional geometry.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“Since several geometries are possible, is it certain ours is the true one?”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“It may happen that the motion of a rigid figure is such that all the points of a line belonging to this figure remain motionless while all the points situated outside of this line move. Such a line will be called a straight line.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“in a word, their geometry will be the spherical geometry.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“Every conclusion supposes premises; these premises themselves either are self-evident and need no demonstration, or can be established only by relying upon other propositions, and since we can not go back thus to infinity, every deductive science, and in particular geometry, must rest on a certain number of undemonstrable axioms.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“The mind uses its creative faculty only when experience requires it.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“In recapitulation, the mind has the faculty of creating symbols, and it is thus that it has constructed the mathematical continuum, which is only a particular system of symbols. Its power is limited only by the necessity of avoiding all contradiction; but the mind only makes use of this faculty if experience furnishes it a stimulus thereto.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“Despite the employment of the most highly perfected methods, the raw results of our experience will always present the characteristics of the physical continuum with the contradiction which is inherent in it.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“only the relations between things. Outside of these relations there is no knowable reality.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method

“The American public is therefore much better prepared than has been thought for investigating the origin of the notion of space.”
― Henri Poincaré, The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method