Popper’s falsifiability criterion, cast in the form of modus tollens, or ((P > Q). ~Q) > ~P, has often been applied to phylogenetic and cladistic theories. A severe criticism of such application is here examined. Questions concerning the universality, strict or numerical, of the propositions involved are irrelevant, but it is clear nevertheless that some workers have used modus tollens in an inappropriate way. Reliance on it is incorrect if the implicational statement, P > Q, is either a definitional or stochastic conditional. But if it is framed as a causal conditional then a Popperian approach to phylogenetics remains viable, although it is doubtful that this is true also of cladistics, which eschews a causal approach.