Oxford Calculators
With Richard Swineshead’s Book of Calculations taken as its characteristic product, the “Oxford Calculators” were a group of thinkers at Oxford University in the mid-fourteenth century, most but not all of whom were associated with Merton College, for whi
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tract Medieval obligations logic dealt with logical duties, primarily that of granting what follow from what has already been laid down. Technically these duties were put into the context of so-called obligational disputations, where the opponent puts forward propositions, which the respondent grants, denies, or doubts. For the most part, the answers do not follow truth, but some specific obligation given at the beginning of the disputation and the technical obligation rules. The main flourishing of obligations logic can be dated to the first half of the fourteenth century with authors like Walter Burley, Richard Kilvington, and Roger Swyneshed, who all presented somewhat different sets of rules for these disputations. It seems that medieval authors aimed generally at rules that take heed of two general dialectical duties: to follow truth and to remain coherent in one’s answers. The latter becomes clearly visible when exceptions to the former are allowed through issuing some special duty at the beginning of the disputation. Obligations logic, thus, can be characterized as studying what it means to be consistent and how one can remain coherent. This way, the area also contributed to the development of such modal notions as logical possibility and necessity.
Obligations Logic Obligations logic is one of the branches of medieval logic that have no modern counterpart. In obligational disputations as they were known in the late Middle Ages, the opponent puts forward propositions that the respondent must evaluate. Standard answers include granting, denying, and doubting the proposition put forward. The title word ‘‘obligations’’ derives from the special setting that the respondent is at the beginning of the disputation given
a special duty that he must follow during the disputation. In the mature form of the technique, this duty was that of holding a false sentence, called the positum, as something that has to be granted. It is unclear how the historical origin of these disputations should be construed. In a wide sense, the setting derives from the dialectical encounters described by Aristotle in book VIII of the Topics, but obligations did not develop as straightforward commentaries of this book. Rather, the beginnings in the early thirteenth century seem to be connected to logical paradoxes like the so-called insolubles. The most important treatises on obligations date from the first half of the fourteenth century. According to the rules formulated in Boethius de Dacia’s questions on Aristotle’s Topics (written between 1270 and 1276), the respondent should grant to the opponent anything except a proposition that is repugnant with what has been laid down as a positum. The gist of the game, as Boethius presents it, derives from the opponent laying progressively down a set of sentences as many posita, while the respondent must check that the set remains consistent. Modern scholars have considered Walter Burley’s treatise on obligations (written 1302) to be the most important one because it is a lengthy carefully argued te
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