 W. V. Quine famously rejected the positivist’s doctrine of truth in virtue of meaning and the quasi-logicist conception of mathematics as a body of analytic truths (and, partly as a result, also rejected his mentor Carnap’s internal/external distinction). Quine, in conjunction with Nelson Goodman, produced instead what amounts to a formalist manifesto. His formalist phase does not seem to have lasted very long: he later settled on a form of mathematical platonism, downplaying, if not largely ignoring, his relatively youthful flirtation with ‘nominalism’. But while it lasted he and Goodman greatly advanced the discussion of formalism by tackling head-on the questions which other formalists shirked or ignored.