This paper explores a currently unnoticed argument used by John Buridan to defend his analysis of modal propositions and to reject the analysis of modal propositions of necessity put forward by William of Ockham. First, I explore this argument and, by considering possible responses of Ockham to Buridan, show some of the ways in which Ockham seems to be keeping closer to Aristotle's remarks about modal propositions in Prior Analytics, 18.

There is an obvious paradox in any attempt to map the topography of Paradise, for Paradise, theologians assure us, is outside of space as well as time. Yet mapping Paradise is what Dante's poem, the Paradiso, attempts to do. For the two preceding realms of the afterlife, hell and purgatory, Dante provides numerous finely articulated descriptions of rigorously ordered regions. And again for Paradise, the variegated states of the souls making up the spiritual order of the realm are expressed very (...) precisely by a topographical scheme, one in this case based on Ptolemy's system of the heavens. The seven planetary spheres are followed by the sphere of the fixed stars and the primum mobile, the whole finally bordering on the completely nonspatial heaven of the Empyrean. But this last “sphere” alone is Paradise in the full and strict sense. As Dante has Beatrice explain in canto 4.28–48, the whole poem attempts to describe this totally nonspatial order in terms of the array of the nine physical heavens as metaphorical correlatives for the successive degrees of beatitude experienced by the souls “in” the Empyrean. Paradise in this sense—as the Empyrean—is thus utopic, if any place is: it is literally “no place” at all. (shrink)

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

This thesis addresses three challenges posed by intentionality - the ability of our mental states and language to be about something - to a logician: an apparent reference to non-existent objects, intentional indeterminacy and the failure of substitutivity of coextensive terms in an intentional context. Since intentionality plays an important role in our everyday reasoning, a proper formal account of it is highly desirable, yet it requires a departure from classical logic. One can modify classical logic and adapt the formal (...) apparatus to account for the aforementioned problems (Graham Priest’s logic for intentionality serves as an example of such an approach in this work) or one can make an even more radical shift and seek for inspiration in a different logical tradition like the terminist logic developed in the Late Middle Ages by figures like William of Ockham or John Buridan. The second path is explored here as a modest attempt to show that once we abandon the bias against the history of logic as irrelevant, we can actually get access to firm logical solutions inaccessible from a classical perspective, while still practising logic proper. (shrink)