 (2) The inductivism that Lakatos recommends to Popper looks remarkably like the inductivism that he condemned in Russell. (“I do not see any way out of a dogmatic assertion that we know the inductive principle, or some equivalent; the only alternative is to throw over almost everything that is regarded as knowledge by science and common sense.” Russell 1944: 683, quoted disdainfully by Lakatos at Regress: 18.) But if inductivism is permissible (or even de rigueur) in the Philosophy of Science, perhaps it is permissible (or even de rigueur) in the Philosophy of Mathematics! In which case, the Renaissance of Empiricism in the Philosophy of Mathematics may count as a genuine renaissance after all, since the logical or set-theoretic axioms may (as Russell supposed) be confirmed (and hence rationally believed) because of their mathematical consequences. If epistemic support can flow upwards from evidence to theory (where the evidence consists of a sequence of novel and successful predictions), perhaps it can flow upwards from consequences to axioms.