During the 13th century, several logicians in the Latin medieval tradition showed a special interest in the nature of impossibility, and in the different kinds or ‘degrees’ of impossibility that could be distinguished. This discussion resulted in an analysis of the modal concept with a finesse of grain unprecedented in earlier modal accounts. Of
the several divisions of the term ‘impossible’ that were offered, one became particularly relevant in connection with the debate on ars obligatoria and positio impossibilis: the distinction between ‘intelligible’ and ‘unintelligible’ impossibilities. In this article, I consider some 13th-century tracts on obligations that provide an account of the relation betweenimpossibility and intelligibility and discuss the inferential principles that are permissible
when we reason from an impossible – but intelligible – premise. I also explore the way in which the 13th-century reflection on this topic survives, in a revised form, in some early 14th-century accounts of positio, namely, those of William of Ockham, Roger Swineshead and Thomas Bradwardine
