The American public is therefore much better prepared than has been thought for investigating the origin of the notion of space. - Henri Poincaré

Formal logic is nothing but the study of the properties common to all classifications; it teaches us that two soldiers who are members of the same regiment belong by this very fact to the same brigade, and consequently to the same division; and the whole theory of the syllogism is reduced to this.

Mathematicians study not objects, but relations between objects; the replacement of these objects by others is therefore indifferent to them, provided the relations do not change. The matter is for them unimportant, the form alone interests them.
Without recalling this, it would scarcely be comprehensible that Dedekind should designate by the name incommensurable number a mere symbol, that is to say, something very different from the ordinary idea of quantity, which should be measurable and almost tangible.

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.