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

What we call geometry is nothing but the study of formal properties of a certain continuous group; so that we may say, space is a group. The notion of this continuous group exists in our mind prior to all experience; but the assertion is no less true of the notion of many other continuous groups; for example, that which corresponds to the geometry of Lobatchevski.

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.

Hilbert justifies vicious circles by defining a ’proof’ only by postulates, thus turning it into a new dead mathematical element. But should not an existence proof or the absence of possible contradictions be given for this new symbol? And is this not just moving the difficulty?
(...)
From our point of view Hilbert’s ‘replâtrage’ is superfluous.