23 November 2020
(please contact the organisers to receive the link)
1.45pm Spencer Johnston (University of Cambridge), “Connexive Logic in Brito, Buridan, and Pseudo-Scotus”
2:45pm Hanoch Ben-Yami (Central European University) “Quarc & Buridan’s Modal Logic”
3.45 short break
4pm Cecilia Trifogli (Oxford University) “Final Causality in Buridan”
5pm Magali Roques (Centre National de la Recherche Scientifique, SPHERE Paris) “Meaning and Reference in Medieval Logic”
Spencer C. Johnston “Connexive Logic in Brito, Buridan, and Pseudo-Scotus”
The aim of this talk is to look at how three 14th century Parisian Arts masters, Rudulphus Brito, Pseudo-Scotus, and John Buridan, understood inferences like 'No proposition follows from its own negation' based on their discussions of these rules in Questions texts on the Prior
Analytics. Such inferences, which in contemporary logic has been discussed under the heading of 'connexive' logic, form the basis of an interesting and somewhat unusual family of non-classical logics. In the eyes of some medieval authors, Aristotle in Prior Analytics II seems to endorse some of these 'connexive' rules. We will argue that these three authors offer two ways to interpret connexive principles so as to allow them to be situated within the general framework of logical consequences that they were using. One interpretation views connexive inferences as limited only to a particular class of demonstrative arguments, with the interesting suggestion that, at least for Brito (and likely Buridan), the logic of demonstration is connexive. The other interpretation requires that the antecedent needs to be (at least) formally possible.
Hanoch Ben-Yami “The Quantified Argument Calculus & Buridan’s Modal Logic”
The Quantified Argument Calculus, or Quarc, is a powerful formal logic system, recently developed by Ben-Yami (RSL 2014) and others. Quarc is closer to Natural Language than is the Predicate Calculus (PC) in its syntax and the logical relations it validates, and it incorporates some features of Natural Language which PC does not. Quarc has been applied in several works to the study of Aristotle’s logic, primarily in (Raab, HPL 2018). Raab notes that the reconstruction Quarc offers of Aristotle’s assertoric logic is ‘much closer to Aristotle's original text than other such reconstructions brought forward up to now’. This suggests that Quarc’s application to the study of medieval logic might be fruitful. This talk is a first venture in this direction, primarily intended as explorative and suggestive. I focus on Buridan’s modal octagon. I first formalise the propositions of the octagon in Quarc. All logical relations Buridan claims to hold are valid in Quarc, and I shall prove some of them. A more thorough analysis of Buridan’s system by means of Quarc might not only show that the system is consistent but may also facilitate an investigation into its other logical properties and comparison with contemporary modal logic.
Cecilia Trifogli “John Buridan on Final Causality”
Departing from the dominant medieval interpretation of Aristotle’s concept of the final cause, Buridan does not try to defend the idea that the end to which an action or change is directed is properly speaking a cause of that action. While Aristotle uses the example of the health for the sake of which I take a walk as a paradigmatic case of a final cause, Buridan argues that health cannot be a cause of my walking. More generally, Buridan undermines some major assumptions at work in the Aristotelian account of finality in nature. He does not, however, reject final causality altogether. He defends Aristotle's view that there are four kinds of cause (material, formal, efficient, and final) and in particular maintains that the final cause is distinct from and irreducible to the efficient cause. He then offers an alternative positive account of the final cause. In my talk I will briefly present both the pars destruens and the pars construens of Buridan's view. I will point out that while the pars destruens is relatively straightforward, the significance of the pars construens is harder to grasp.
Main primary sources: John Buridan, Questions on Aristotle's Physics, Book II, q. 7 and q. 13 (ed. M. Streijger & P. J.J.M. Bakker, Brill 2015).
Magali Roques “Meaning and Reference in Medieval Logic”
This paper is a clarificatory attempt concerning the use of the term "reference" when speaking of medieval logic (and especially supposition theory). I want to propose the idea that research on medieval supposition theory and medieval counterparts to the modern theory of reference would benefit from a distinction - that is never or rarely made, although it is so important in modern semantics - between reference and rigid reference. By coming back to the root of the illusion that made us think that we don't need such a distinction in order to understand what medieval semantics is about, I will tentatively argue that Peter Geach had no good argument in favor of his claim that Aquinas had something like a good theory of reference and that Ockham had something like a bad theory of reference. On the contrary, I will argue that I don't see how Aquinas can be attributed with a theory of reference at all, since he doesn't seem to have, properly speaking, a theory of reference for singular terms, and that Ockham was probably the first medieval logician to have something like at least a sketch (and a good sketch indeed) of a theory of rigid reference, based on the idea that a term refers to something in the proper sense of the term if it picks out the same individual in every possible world in which the individual exists.