The best reaction to a paradox is to invent a genuinely new and deep idea.
Both [Quine and Feyerabend] want to revise a version of positivism. Quine started with the Vienna Circle, and Feyerabend with the Copenhagen school of quantum mechanics. Both the Circle and the school have been called children of Ernst Mach; if so, the philosophies of Feyerabend and Quine must be his grandchildren.
Philip Kitcher thinks that mathematics is surprisingly like empirical science. Few mathematicians would agree; philosophers too, from Socrates on, have held the opposite opinion.
The word ‘revolution’ first brings to mind violent upheavals in the state, but ideas of revolution in science, and of political revolution, are almost coeval. The word once meant only a revolving, a circular return to an origin, as when we speak of revolutions per minute or the revolution of the planets about the sun.