Everyone is sure of this [that errors are normally distributed], Mr. Lippman told me one day, since the experimentalists believe that it is a mathema… - Henri Poincaré

We have selected the most convenient space, but experience has guided our choice; as this choice has been unconscious, we think it has been imposed upon us […] In this progressive education whose outcome has been the construction of space, it is very difcult to determine what is the terms of use, part of the individual, what the part of the race. How far could one of us, transported from birth to an entirely diferent world, where were dominant, for instance, bodies moving in conformity to the laws of motion of non-Euclidean solids, renounce the ancestral space to build a space completely new?

[H]ave we really the right to speak of the cause of a phenomenon?

The syllogism cannot teach us anything essentially new. It must be conceded that mathematical reasoning has of itself a sort of creative virtue, and consequently differs from the syllogism.