Medieval Obligationes as Logical Games of Consistency Maintenance

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]  E. Olsson,et al.  Disputation and Change of Belief: Burley's Theory of Obligationes as a Theory of Belief Revision , 2001 .

[2]  Mirko Yrjönsuuri.  The compossibility of impossibilities and ars obligatoria , 1998 .

[3]  Mikko Yrjönsuuri.  Medieval Formal Logic , 2001 .

[4]  J. Hintikka,et al.  Game-Theoretical Semantics , 1997 .

[5]  Fabienne Pironet.  The Relations between Insolubles and Obligations in Medieval Disputations , 2001 .

[6]  M. Yrjönsuuri.  Duties, Rules and Interpretations in Obligational Disputations , 2001 .

[7]  Hajo Keffer.  De Obligationibus : Rekonstruktion einer spätmittelalterlichen Disputationstheorie , 2001 .

[8]  Jaakko Hintikka,et al.  Game-Theoretical Semantics , 1997, Handbook of Logic and Language.

[9]  Vincent Spade Paul.  Three theories of obligationes:burley, kilvington and swyneshed on counterfactual reasoning , 1982 .

[10]  Romuald Green.  An introduction to the logical treatise "De obligationibus" - with critical texts of William of Sherwood (?) and Walter Burley , 1963 .

[11]  Christopher J. Martin.  Obligations and Liars , 1993 .

[12]  Eleonore Stump,et al.  From the beginning to the early fourteenth century , 1982 .

[13]  L. M. De Rijk,et al.  Some Thirteenth Century Tracts on The Game of Obligation , 1974 .

[14]  Eleonore Stump,et al.  Walter burley and the obligationes attributed to william of sherwood , 1983 .

[15]  Eleonore Stump,et al.  Obligations: Developments in the fourteenth century , 1982 .

[16]  The Cambridge Translations of Medieval Philosophical Texts: Frontmatter , 2000 .

[17]  E. J. Ashworth.  Inconsistency and Paradox in Medieval Disputations: A Development of Some Hints in Ockham , 2015 .