Logic and Modalities in the Late Middle Ages. The Tradition of the Oxford Calculators

The essays collected in this issue aim to explore several topics connected to the logical theories of the Oxford Calculators and the impact that they had on later developments in logic. They present new evidence and new interpretations on three main subjects that are central to the production of the Calculators, namely: (i) their theory of modalities and understanding of the nature of (im)possibility; (ii) their views on insolubles and semantic paradoxes; and finally (iii) their approach to epistemic sophisms and to the logic of knowing, doubting, and believing. In my contribution, I investigate the relation between the modal notion of impossibility and the epistemic concepts of intelligibility or imaginability. This relation, which was already advanced in several 13th-century works devoted to the analysis of impossible positio, survives in a revised form in some early 14th-century accounts of positio, such as those put forward by Walter Burley, William of Ockham, and by the two ‘Calculators’ Roger Swineshead and Thomas Bradwardine. The second essay, by Barbara Bartocci and Stephen Read, includes a new critical edition and an English translation of an anonymous Epitome of John Dumbleton’s solution to insolubilia. This Epitome, preserved in a single manuscript from the Biblioteca Antoniana in Padua, includes both a survey of different types of insolubles, and a presentation of Dumbleton’s cassationist solution – a solution which the anonymous author professedly adopts. However, the author of the Epitome does not uncritically follow Dumbleton’s solution, but rather revises it quite substantially, as Bartocci and Read show. The third essay, by Miroslav Hanke, takes its move from the approach to epistemic sophisms taken by William Heytesbury and by other Calculators in the first half of the 14th century, and then passes to examine the impact that these views had on 16th-century logical developments connected to the circle of John Mair in Paris, an impact that was probably mediated by authors like Paul of Venice and Cajetan of Thiene.