"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 …"

— Henri Poincaré

principle of relativity1854–1912

#science

"We can not... escape the conclusion that the rule of reasoning by recurrence is irreducible to the principle of contradiction. ...Neither can this rule come to us from experience... This rule, inacces…"

— Henri Poincaré

principle of relativity1854–1912

#mind

"What we call objective reality is, in the last analysis, what is common to many thinking beings, and could be common to all; this common part, we shall see, can only be the harmony expressed by mathem…"

— Henri Poincaré

principle of relativity1854–1912

#truth

"The Sciences and the Humanities."

— Henri Poincaré

principle of relativity1854–1912

#science

"Is the position tenable, that certain phenomena, possible in Euclidean space, would be impossible in non-Euclidean space, so that experience, in establishing these phenomena, would directly contradict…"

— Henri Poincaré

principle of relativity1854–1912

#mind

"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…"

— Henri Poincaré

principle of relativity1854–1912

#philosophy

"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…"

— Henri Poincaré

principle of relativity1854–1912

#science

"What is objective must be common to many minds and consequently transmissible from one to the other, and as this transmission can only come about by... discourse... we are even forced to conclude: no …"

— Henri Poincaré

principle of relativity1854–1912

#mind