“You can find aspects of vagueness in most words of English or any other language. Out loud or in our heads, we reason mostly in vague terms. Such reasoning can easily generate sorites-like paradoxes. Can you become poor by losing one cent? Can you become tall by growing one millimetre? At first, the paradoxes seem to be trivial verbal tricks. But the more rigorously philosophers have studied them, the deeper and harder they have turned out to be. They raise doubts about the most basic logical principles.”