chapter  14
36 Pages

Mathematical Knowledge

Empiricists deny the possiblity of a priori knowledge absolutely, and seek to accommodate it in other ways. Professor Kitcher gives a causal account of a docile schoolgirl who believes that what her teachers tell her is warrantedly true.2 As an explanation of how some people acquire mathematical abilities, it has much truth; the multiplication tables often are learned by rote. But we are seeking

a justification, not a psychological explanation-even in the bestrun schools some naughty boys ask why six sixes are thirty six, and are not prepared to accept the teacher’s say-so as an adequate reason for believing it to be true. A hard-line empiricist may refer vaguely to the experience of previous generations, and encourage us to accept mathematics as the hard-won wisdom of the many and the wise, but once we have felt the force of Plato’s Meno argument, we shall seek a more compelling account of cogency.