15 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)
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)
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)
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)
If, then, a phenomenon admits of a complete mechanical explanation, it will admit of an infinity of others, that will render an account equally well of all the particulars revealed by experiment.
Science and Hypothesis (1901)
For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.
Science and Hypothesis (1901)
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.
Science and Hypothesis (1901)
Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.
Science and Hypothesis (1901)
... treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention, and what is hypothesis.
Science and Hypothesis (1901)
It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, for example, use language, and our language is necessarily steeped in preconceived ideas.
Science and Hypothesis (1901)