The Logical Geometry of John Buridan's Modal Octagon

In order to elucidate his logical analysis of modal quantified propositions (e.g. 'all men are necessarily mortal'), the 14th century philosopher John Buridan constructed a modal octagon of oppositions. In the present paper we study this modal octagon from the perspective of contemporary logical geometry. We argue that the modal octagon contains precisely six squares of opposition as subdiagrams, and classify these squares based on their logical properties. On a more abstract level, we show that Buridan's modal octagon precisely captures the interaction between two classical squares of opposition, viz. one for the quantifiers and one for the modalities. Finally, we argue that several aspects of our contemporary formal analyses were already hinted at by Buridan himself