Both Popper and Lakatos are strong advocates of the idea of scienti c method, although they di er in several crucial respects as to what this might be. ey also give di erent metamethodological arguments on behalf of their di ering conceptions of scienti c method. In this chapter we shall focus on their conception of method and their attempts at a metamethodological justi cation of it. Much has been written on other aspects of their views, especially on Popper’s anti-inductivism, his non-inductivist account of corroboration, his account of verisimilitude, and the like. ese will enter into our discussion only in so far as it is necessary to develop Popper’s rule-based conception of method and its justi cation. Popper’s basic stance is that of a hypotheticodeductivist, but with several distinctive variations. Arising from this is a proposal for a criterion for the demarcation of science. is is itself a central rule of method that is intended to realize certain aims, and that needs to be accompanied by several other methodological rules if it is to be e ectively applied. Taken together these rules and values constitute the principles of Popper’s theory of scienti c method, o en called critical rationalism; they govern what he calls “the game of science”, the many particular moves in theory change made by scientists in the many episodes within the history of science. ere are a number of ways to evaluate Popper’s rules for science, some of which will arise in §10.1.2. Popper himself gives two varieties of metamethodological justi cation employing his h-d stance as a metamethod; these are explored in §10.1.3.