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… - Henri Poincaré

I shall conclude that there is in all of us an intuitive notion of the continuum of any number of dimensions whatever because we possess the capacity to construct a physical and mathematical continuum; and that this capacity exists in us before any experience, because, without it, experience properly speaking would be impossible and would be reduced to brute sensations. ... And yet this capacity could be used in different ways; it could enable us to construct a space of four just as well as a space of three dimensions.

only the relations between things. Outside of these relations there is no knowable reality.

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.