obligationes the study of inferentially inescapable, yet logically odd arguments, used by late medieval logicians in analyzing inferential reasoning. In Topics VIII.3 Aristotle describes a respondent’s task in a philosophical argument as providing answers so that, if they must defend the impossible, the impossibility lies in the nature of the position, and not in its logical defense. In Prior Analytics I.13 Aristotle argues that nothing impossible follows from the possible. Burley, whose logic exemplifies early fourteenth-century obligationes literature, described the resulting logical exercise as a contest between interlocutor and respondent. The interlocutor must force the respondent into maintaining contradictory statements in defending a position, and the respondent must avoid this while avoiding maintaining the impossible, which can be either a position logically incompatible with the position defended or something impossible in itself. Especially interesting to Scholastic logicians were the paradoxes of disputation inherent in such disputes. Assuming that a respondent has successfully defended his position, the interlocutor may be able to propose a commonplace position that the respondent can neither accept nor reject, given the truth of the first, successfully defended position. Roger Swineshead introduced a controversial innovation to obligationes reasoning, later rejected by Paul of Venice. In the traditional style of obligation, a premise was relevant to the argument only if it followed from or was inconsistent with either (a) the proposition defended or (b) all the premises consequent to the former and prior to the premise in question. By admitting any premise that was either consequent to or inconsistent with the proposition defended alone, without regard to intermediate premises, Swineshead eliminated concern with the order of sentences proposed by the interlocutor, making the respondent’s task harder. See also ARISTOTLE , BURLEY, KILVINGTON, OXFORD CALCULATORS , PAUL OF VENIC. S.E.L.