La logique parfois engendre des monstres. Depuis un demi-siècle on a vu surgir une foule de fonctions bizarres qui semblent s’efforcer de ressembler … - Henri Poincaré

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.

The axioms of geometry, therefore, are neither synthetic a priori judgments nor experimental facts.
They are conventions; our choice among all possible conventions is guided by experimental facts; but it remains free and is limited only by the necessity of avoiding all contradiction. . . .
In other words, the axioms of geometry (I do not speak of those of arithmetic) are merely disguised definitions.
Then what are we to think of that question: Is the Euclidean geometry true?
It has no meaning.
As well ask whether the metric system is true and the old measures false.

La sociologie est la science qui possède le plus de méthodes et le moins de résultats.