Brouwer is right when he says that the properties of his Pendelzahl [pendulum number] are incompatible with the law of the excluded middle. But, sayi… - 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.