“There are many things—some true, some false— unsupportable by rational means.”
Barry Mazur,
Context: Sometimes the mathematical anti-Platonist believes that headway is made by showing Platonism to be unsupportable by rational means, and that it is an incoherent position to take when formulated in a propositional vocabulary. It is easy enough to throw together propositional sentences. But it is a good deal more difficult to capture a Platonic disposition in a propositional formulation that is a full and honest expression of some flesh-and-blood mathematician’s view of things. There is, of course, no harm in trying—and maybe its a good exercise. But even if we cleverly came up with a proposition that is up to the task of expressing Platonism formally, the mere fact that the proposition cannot be demonstrated to be true won’t necessarily make it vanish. There are many things—some true, some false— unsupportable by rational means.
