A series of theories T ₁, T ₂, T ₃,… constituting a scientific research program, is "theoretically" and "empirically progressive" and therefore to be appraised as truly 'scientific" and "rational", and to be preferred methodologically, if "each subsequent theory… [has] at least as much content as the unrefuted content of its predecessor" and "leads us to the discovery of some new fact" ¹ Such is Imre Lakatos's linear theory of scientific growth. My contention is that a partial ordering of a kind represented in Figure 1 and generalized to n dimensions serves better both the purpose of explicating the historical case studies adduced by Lakatos in support of his view and the purpose of arriving at a normative structure for the appraisal of progress in scientific research. I shall conclude then that it is necessary to add to Lakatos's methodological principles an additional one: the principle of lattice-growth.