What do I know about God and the purpose of life? I know that this world exists. That I am placed in it like my eye in its visual field. That somethi… - Ludwig Wittgenstein

A logical picture of facts is a thought.

If a blind man were to ask me “Have you got two hands?” I should not make sure by looking. If I were to have any doubt of it, then I don’t know why I should trust my eyes. For why shouldn’t I test my eyes by looking to find out whether I see my two hands? What is to be tested by what?

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.