This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then (...) the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework. (shrink)

Aquinas’ famous comments in his early Scriptum on the Sentences (In I Sent., d. 38, q. 1, a. 3) regarding the intellect’s apprehension of essence and esse have traditionally been interpreted as grounding Aquinas’ doctrine on the judgment of esse. For Aquinas, it appears, what the intellect apprehends in a simple concept is essence. Since esse, for him, is not an essence, it cannot, on the received view, be the object of conceptualization. Therefore, esse is grasped by the intellect only (...) in judgment. The claim that no genuine concept of esse is possible, however, is inconsistent with Aquinas’ theory of signification. A term’s signification is constituted, at least in part, in its “signing relation” with some “concept” in the mind. If, as on the traditional reading, there is no concept of esse, the term ‘esse’ is left without signification. To respond that the term ‘esse’ signs, not a concept, but the judgment in which esse is apprehended is in direct conflict with Aquinas’ claim elsewhere that no term, including ‘ens’ and ‘esse’, signifies a judgment. I propose an alternative interpretation to In I Sent., d. 38, q. 1, a. 3, one that allows for the possibility of a conceptual apprehension of esse. The alternative reading explains Aquinas’ remarks there in light of the theoretical context of the discussion, in particular the theory of propositions and their objects. I show how and why Aquinas develops a distinctive theory of the object of the proposition, that it is concerned with “the esse of a thing” as a complex. Although this complex includes the simple act of being, as for the traditional position (contrary to its major critics), it cannot be reduced to anything simple. Despite the Sentences’ affirmation of a real distinction between a thing’s esse and essence, to which correspond two different operations of the intellect, it does not follow that the human intellect cannot conceive esse, just as it conceives essences, in a simple conception. (shrink)