Henri Poincaré Quotes

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.

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.

What is zero? It is the number of elements in the class nil. And what is the class nil? It is the class which contains none.
To define zero as nil and nil as none is really an abuse of the wealth of language, and so [Logicists] introduced an improvement into the definition, ... which means in English: zero is the number of the objects that satisfy a condition that is never fulfilled. But as never means in no case, I do not see that any very great progress has been made.

Why then does this judgement [mathematical induction] force itself upon us with an irresistible evidence? It is because it is only the affirmation of the power of the mind which knows itself capable of conceiving the indefinite repetition of the same act when once this act is possible. The mind has a direct intuition of this power, and experience can only give occasion for using it and thereby becoming conscious of it.

Il n'y a pas de logique et d'épistémologie indépendantes de la psychologie.