 Why does Lakatos condemn the “empiricism” that he also commends? Because Russell, like most of his supporters, succumbs to the “inductivist” illusion that the axioms can be confirmed by the truth of their consequences. In Lakatos’s opinion this is simply a mistake. Truth can trickle down from the axioms to their consequences and falsity can flow upwards from the consequences to the axioms (or at least to the axiom set). But neither truth nor probability nor justified belief can flow up from the consequences to the axioms from which they follow. Here Lakatos out-Poppers Popper, portraying not just science but even mathematics as a collection of unsupported conjectures that can be refuted but not confirmed, anything else being condemned as to “inductivism”. However the inductivism that Lakatos scornfully rejects in Renaissance is just the kind of inductivism that he would be recommending to Popper just a few years later.