ABSTRACT
The mathematical experience on which L.E.J. Brouwer had laid so much emphasis was essentially private and incommunicable. M. Dummett, by contrast, took as his starting point the essential publicity and communicability of mathematical ideas, and related this to the Ludwig Wittgensteinian tenet that the meaning of a mathematical expression must ultimately be a matter of how it is used in mathematics, just as the power of a chess piece is a matter of how it is used in chess. Wittgenstein believed that the correct use of terms such as 'infinity' was to characterize the form of finite things and, relatedly, to generalize about the endless possibilities that finite things afford. Many of Wittgenstein's conclusions were reminiscent of those of his great predecessors. Wittgenstein felt very strongly that it was not his business, as a philosopher, to interfere with mathematical practice.
