Medieval Obligationes as Logical Games of Consistency Maintenance

C. DUTILH NOVAESMEDIEVAL OBLIGATIONES AS LOGICAL GAMES OF

CONSISTENCY MAINTENANCEABSTRACT. 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.1. INTRODUCTIONAlthough the medieval form of dialectical disputation known as obligationes has attracted the attention of medievalists as well as of philosophers

of logic over roughly the last forty years, much of it still remains mysterious. Here I shall defend the idea that, if obligationes are viewed as logical

games of consistency maintenance, much of this mystery can be dissolved.Over the last few years, historical work has greatly contributed to the

establishment of reliable manuscripts of various De Obligationibus treatises and to the understanding of the intricacies of the theories upheld in

these treatises. Within a more theoretical approach, intriguing suggestions

have been made as to how these theories should be interpreted from a

modern perspective, although no satisfying definitive solution seems to

have been found. In this paper, I will focus on a text that is perhaps the

best-known medieval text on obligationes, namely Walter Burleys treatise,

and will present a new interpretation on how to make sense of the rules

of this regimented form of dialectical disputation from the viewpoint of

modern logic.1 I suggest that obligationes be viewed as logical games in

the sense of Hintikkas game-theoretical semantics (cf. Hintikka and SanduSynthese (2005) 145: 371395 Springer 2005372 C. DUTILH NOVAES1997), Lorenzens dialogue logic (Lorenzen 1961), and, more...