Abstract Both refutationist and verificationist philosophies and practices are becoming increasingly evident in phylogenetic inference. Refutation and verification are fundamentally different epistemologies, and it seems unlikely that they can continue to coexist as the basis for inferring species history. The refutationist nature of cladistics is explored in terms of Popperian testability, in order to understand better the alternatives and to predict the outcome of the expected revolution. Testability concerns the logical relationship between a hypothesis ( h, such as a cladogram), evidence ( e, such as synapomorphy), and background knowledge ( b). Of particular importance is the direct relationship between the logical improbability of hand its potential to be tested, because for eto corroborate h, eshould be improbable given balone. Simplicity and boldness, amount of empirical content, and logical improbability all refer to the potential to be tested. That hmust be testable by severe tests is the same as saying that those tests have greater probability of failing, given only b. Descent with modification is sufficient as background knowledge ( b) in phylogenetic inference, and such a minimal assumption explains the generality of cladistics. Also of interest to the refutationist position is total evidence. In terms of testability, a statement describing the results of multiple tests is less probable than a statement describing only some of the tests, the multiple test result being more improbable, and accordingly more severe, than its component tests. All other cladistic principles and practices considered in this review are also understandable in terms of Popperian testability, refutation and corroboration. These include minimizing ad hoc hypotheses of homoplasy and minimizing explanatory power, and choosing tentatively among cladograms according to their degree of corroboration (support). Differential character weighting is determined to be unacceptable in terms of testability. Also, testability does not provide a basis for assessing the accuracy of hypotheses, but then that is of no consequence to cladists, because they are not preoccupied with knowing the absolute truth, unlike verificationists.