The compossibility of impossibilities and ars obligatoria

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