I had to philosophize. Otherwise, I could not live in this world.
I must achieve internal consistency.
Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.
Experience by itself is not science.
All perception is a gamble.
To every object there correspond an ideally closed system of truths that are true of it and, on the other hand, an ideal system of possible cognitive processes by virtue of which the object and the truths about it would be given to any cognitive subject.