In this paper I present a new approach to the so called ars obligatoria of the thirteenth and early fourteenth century. In standard medieval disputations an opponent attacks a thesis defended by the respondent. Some thirteenth-century authors distinguish two duties that the respondent has. First, he must grant whatever seems to be true. Second, he must grant whatever follows from what he has already granted. When the first duty is overridden by the specific duty to defend a false thesis (which (...) is the main requirement of ars obligatoria), the second duty becomes the logical duty of keeping the set of one's answers consistent. A natural result of this model is the development of a concept of possibility based on the syntactic concept of formally correct inference, and not on any semantic considerations. (shrink)

The current trend in knowledge revision in the Dynamic Epistemic Logic tradition focuses on the addition of new knowledge, rather than the possibility of losing knowledge. Yet there are natural situations, such as an agent who does not want another agent to know that she knows a certain piece of information, where there is a need to be able to model the retraction of a proposition from a knowledge base. One situation where this is systematically required is the variant of (...) the medieval theory of obligationes known as dubitatio, where one of the agents in the dialogue is obliged to hold the initial proposition, the dubitatum, as doubtful, regardless of what other propositions she may concede or deny during the disputation. In this paper, we use dubitatio as a motivation for studying deceitful agents, and we discuss various ways that an agent can move from a model where f is known to one where f is not known. (shrink)

Formal dialogue systems model rule-based interaction between agents and as such have multiple applications in multi-agent systems and AI more generally. Their conceptual roots are in formal theories of natural argumentation, of which Hamblin’s formal systems of argumentation in Hamblin (Fallacies. Methuen, London, 1970, Theoria 37:130–135, 1971) are some of the earliest examples. Hamblin cites the medieval theory of obligationes as inspiration for his development of formal argumentation. In an obligatio, two agents, the Opponent and the Respondent, engage in an (...) alternating-move dialogue, where the Respondent’s actions are governed by certain rules, and the goal of the dialogue is establishing the consistency of a proposition. We implement obligationes in the formal dialogue system framework of Prakken (Knowl Eng Rev 21(2):163–188, 2006) using Dynamic Epistemic Logic (van Ditmarsch et al. in Dynamic epistemic logic, Synthese Library Series. Springer, Berlin, 2007). The result is a new type of inter-agent dialogue, for consistency-checking, and analyzing obligationes in this way also sheds light on interpretational and historical questions concerning their use and purpose in medieval academia. (shrink)

An obligation, in the sense in which it was of interest to medieval logicians from about the early thirteenth century to the end of the scholastic period, is, according to Paul of Venice, a relation limiting one to take some statement affirmatively or negatively. This relation is based on the actions of two individuals: one obligates the other by first putting forward a sentence which the respondent agrees to affirm or deny for a limited time. The sentence the respondent agrees (...) to affirm is called the positum; that which he agrees to deny, the depositum; and his act of agreeing, the admissio. After this relation is established between the opponent and respondent, the opponent proceeds by putting forward a series of sentences to which the respondent replies by granting, denying, or doubting — all in accordance with certain rules the two individuals have previously accepted as governing their exchange. If the respondent at any time grants what is inconsistent with the sentence he agreed to uphold, or responds in a way that violates the accepted rules, the exchange comes to an end. The respondent has failed in his obligation. (shrink)

I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes a contradictory set (...) of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)

_ Source: _Volume 56, Issue 3-4, pp 340 - 366 The history of thinking about consequences in the Middle Ages divides into three periods. During the first of these, from the eleventh to the middle of the twelfth century, and the second, from then until the beginning of the fourteenth century, the notion of natural consequence played a crucial role in logic, metaphysics, and theology. The first part of this paper traces the development of the theory of natural consequence in (...) Abaelard’s work as the conditional of a connexive logic with an equivalent connexive disjunction and the crisis precipitated by the discovery of inconsistency in this system. The second part considers the accounts of natural consequence given in the thirteenth century as a special case of the standard modal definition of consequence, one for which the principle _ex impossibili quidlibet_ does not hold, in logics in which disjunction is understood extensionally. (shrink)

1. This paper addresses the development of mutual relations between two sets of ideas in scholastic logic. First, consider the following statements: (1) It is impossible to encounter a chimera.(2)...

Impossible antecedents entered the scene of medieval logic around the 1120s and soon started to dominate this scene, becoming one of the most debated issues from the second half of the twelfth century onwards. This article focuses on theories of counterpossibles from this period and aims to offer an overview of the different responses offered by twelfth-century logicians on whether everything, something, or nothing follows from an impossible statement. Rather than trying to historically reconstruct the positions of the different authors (...) – an operation that may be premature given the insufficient notions we still have of the authorship and dating of sources – I aim to provide a provisional map of the main arguments that were advanced in favour of or against the ex impossibili quodlibet principle. The article also aims to show that the strategies developed by twelfth-century logical schools in their approach to counterpossibles survive in logical discussions of the same topic during the thirteenth and the early fourteenth century, especially in the syncategoremata and sophistaria traditions. (shrink)

The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ other than what they are, (...) there’d be no apparent contradiction. But the meaning is what it is, and changing the meaning of our terms to avoid the apparent contradiction of Christ is an apparent flight from reality. What, in the end, is the explanation of the apparent contradiction of Christ? Theologians and philosophers have long advanced many consistency-seeking answers, all of which increase the metaphysical or semantical complexity of the otherwise strikingly simple but radical core of Christianity’s GodMan. In this paper, I put the simplest explanation on the theological table: namely, Christ appears to be contradictory because Christ is contradictory. This explanation may sound complicated to the many who are steeped in the mainstream account of logic according to which logic precludes the possibility of true contradictions. But the mainstream account of logic can and should be rejected. Ridding theology of the dogma of mainstream logic illuminates the simple though striking explanation of the apparent contradiction of Christ — namely, that Christ is a contradictory being. Just as the simplest explanation to the apparent roundness of the earth has earned due acceptance, so too should the simplest explanation of the apparent contradiction of Christ. (shrink)