I am now in another hole, though I have to say, it is no better than the old one. Living with human beings is hard! - Ludwig Wittgenstein

Brouwer is right when he says that the properties of his Pendelzahl [pendulum number] are incompatible with the law of the excluded middle. But, saying this doesn’t reveal a peculiarity of propositions about infinite aggregates. Rather, it is based on the fact that logic presupposes that it cannot be a priori — i.e. logically — impossible to tell whether a proposition is true or false. For, if the question of the truth or falsity of a proposition is a priori undecidable, the consequence is that the proposition loses its sense, and the consequence of this is precisely that the propositions of logic lose their validity for it.

This book is written for such men as are in sympathy with its spirit. This spirit is different from the one which informs the vast stream of European and American civilization in which all of us stand. The spirit expresses itself in an onwards movement, building ever larger and more complicated structures; the other in striving after clarity and perspicuity in no matter what structure. The first tries to grasp the world by way of its periphery — in its variety; the second at its center — in its essence. And so the first adds one construction to another, moving on and up, as it were, from one stage to the next, while the other remains where it is and what it tries to grasp is always the same.

A man will be imprisoned in a room with a door that's unlocked and opens inwards; as long as it does not occur to him to pull rather than push it.