Abstract: In his paper `The philosophical basis of intuitionistic logic' (1975), Michael Dummett discusses two arguments in favour of adopting intuitionistic rather than classical logic in number theory, one meaning-theoretical and the other ontological. He moreover argues that the former argument is preferable to the latter. Characteristic of Dummett's paper is the willful neglect of Brouwer's own writings on intuitionism. I argue that, from a Brouwerian point of view, Dummett's reservations about the ontological argument can be mitigated, and that Dummett's meaning-theoretical argument depends on the philosophy of mind as much as Brouwer's writings do.