Having visual impressions is, of course, necessary for seeing things, but it is not sufficient. What must be added is not anything sensible. And it is precisely this that unlocks the outer world for us; for without this non-sensible something, each of us would remain locked up in his inner world.
Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.
Arithmetic has began to totter.
What are numbers? What is the nature of arithmetical truth?