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 text that presents obligations logic in a well-developed form. Furthermore, medieval authors seem to have taken Burley’s rules as standard, while alternative formulations mainly appear as suggestions for a major revision. For the most part, these suggestions were rejected in the discussion. The only important revision that was accepted seems to have been John Duns Scotus’ suggestion that the respondent need not deny the present when he has a false positum to defend. That is, the necessity of the present need not be respected in obligational disputations.
Burley’s rules tell the respondent to keep the set of his answers consistent, but otherwise to follow the truth of the matter. That is, anything that follows from the positum together with previous answers must be granted, and anything that is repugnant with them, must be denied. Any other proposition must be deemed irrelevant and answered in accordance with truth-value. After the
Henrik Lagerlund (ed.), Encyclopedia of Medieval Philosophy, DOI 10.1007/978-1-4020-9729-4, © Springer Science+Business Media B. V., 2011
Answer, the irrelevant proposition becomes relevant and can be used in inferences within the game.
Burley’s rules have the odd consequence that the respondent can be forced to grant practically any proposition, if the selection and the order of propositions are chosen for such an end. Similarly, the correct answer to a particular proposition may depend on the order of presentation. These features are explicitly recognized by Burley and others, and no medieval author calls them problems. However, interesting revisions were put forward in the second quarter of the fourteenth century by Richard Kilvington in his Sophismata (written soon after 1321) and Roger Swyneshed in a separate treatise (written 1330-1335). Neither of these revised sets of rules allows the order to have such an effect on the answers, though Swyneshed does provide a technique for achieving such effects if they are specifically aimed at.
The idea behind Kilvington’s revision is straightforward, but logically unsatisfactory. He claims that propositions should be evaluated in respect to what their truth-values would be if the actually false positum were true. In other words, Kilvington seems to think that obligations logic should be understood as being based on counterfactual reasoning. Unfortunately, he is unable to spell out specific rules that would be unambiguous in the way Burley’s rules are. Kilvington’s revision seems to have received little attention among medieval authors.
Swyneshed’s suggestion is based on keeping irrelevant propositions as irrelevant, not allowing them to be taken into inferences. That is, the respondent should grant what follows from the positum alone and deny anything that is repugnant with it alone. Swyneshed makes it clear that the whole set of answers need not be consistent if it also includes irrelevant propositions. Much attention was paid on his recognition that a conjunction can be denied when both parts have been granted (one as following from the positum and the other as irrelevant and true).
In the later period, the core of Burley’s rules seems to have gained general acceptance. For example, Ralph Strode (later fourteenth century) and Paul of Venice (see Logica magna, written 1397-1398) follow this basic structure. In the later period, some further development can be found in discussions on disputational obligations concerning the meanings of the words uttered in the disputation.
In the modern research, much time has been spent in making obligations logic understandable to modern logicians. It seems impossible to give any clear counterpart for obligations among the fields of modern logic. Theories of counterfactuals and belief revisions systems have been pointed out, but they both proceed from a semantic perspective while the sets of granted sentences in obligational disputations typically lack any meaningful interpretation.
It seems clear, however, that one logically very interesting phenomenon, which is familiar to modern logicians, is especially carefully studied in obligations logic. When an increasing number of propositions are evaluated in a dynamic setting, their consistency can either be maintained or lost. Obligations logic studies this phenomenon and thus results in an increased understanding of what is at issue in determining consistency.
From the history of modal concepts, obligations thus address a crucial issue. In late medieval developments, it became increasingly important to consider possibility as related to logical consistency. But while earlier medieval logicians often defined logical notions like consistency by leaning on some kind of real possibilities, obligations provided a framework where consistency was attended to with conscious disregard to any kinds of real possibilities. That is, consistency was understood to obtain at the sentential level in abstraction from the possible interpretations of the sentences.
See also: > Insolubles > John Duns Scotus > Paul of Venice > Richard Kilvington > Walter Burley
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