 Aristotle’s description of scientific procedure in the Posterior Analytics is couched in disputational language, and in Boethius’ own age disputations were a very important part of university teaching and, indeed, of philosophical research, some of them being genuine debates with several participants, others fictive ones in the form of quaestiones with the teacher presenting both the arguments pro and con and the solution. In Boethius’ trademark formulation of the autonomy of each science, the expression “grant or deny” (concedere vel negare) belongs in the context of a disputation where a questioner puts forward propositions of the form “Is S P ?” and a respondent typically answers “I grant it” or “I deny it”. Boethius seems to have conceived of scientific activity as fundamentally similar to participating in a disputation, and keeping within the limits of a particular science as being similar to obeying the rules of a particular type of disputation. Hardly by chance, he describes an unusual variant of the disputational exercise called ars obligatoria. In his version, an opponent puts forward a number of propositions to a respondent, who must grant them all, irrespective of their truth-value, rejecting only such as are incompatible with something he has already granted. After some time, the disputation passes to a second stage, in which the opponent puts forward further propositions, but this time the respondent is allowed and obliged to grant only such as follow from what he had granted in stage 1. The opponent’s job is to try to force him to contradict himself (Quaest. Top., 329–30; cf. Yrjönsuuri 1994, 31–35). This exercise imitates the gathering of a tentative set of axioms of a science, followed by a test of the set’s consistency.