51 quotes
To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.
Science and Hypothesis (1901)
The very possibility of the science of mathematics seems an insoluble contradiction.
Science and Hypothesis (1901)
The essential characteristic of reasoning by recurrence is that it contains, condensed, so to speak, in a single formula, an infinity of syllogisms.
Science and Hypothesis (1901)
There is no science apart from the general. It may even be said that the very object of the exact sciences is to spare us these direct verifications.
Science and Hypothesis (1901)
It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.
Science and Method (1908)
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.
Science and Hypothesis (1901)
We must, for example, use language, and our language is necessarily steeped in preconceived ideas.
Science and Hypothesis (1901)
What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
The analyst, who pursues a purely esthetic aim, helps create, just by that, a language more fit to satisfy the physicist.
The Value of Science (1905)
Without interpolation all science would be impossible.
The Value of Science (1907)
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.
Science and Hypothesis (1901)
Thought is only a flash between two long nights, but this flash is everything.
Point set topology is a disease from which the human race will soon recover.
Sociology is the science which has the most methods and the least results.
Science and Method (1908)
We do not have and cannot have any means of discovering whether or not we are carried along in a uniform motion of translation.
L’état actuel et l’avenir de la physique mathematique (1904)
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.
Science and Hypothesis (1905)
When shall we say two forces are equal?
Science and Hypothesis (1901)
Science is built of facts the way a house is built of bricks: but an accumulation of facts is no more science than a pile of bricks is a house.
We have not a direct intuition of the equality of two intervals of time.
The Value of Science (1905)
Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures.