Representing Buridan’s Divided Modal Propositions in First-Order Logic

Formalizing categorical propositions of traditional logic in the language of quantifiers and propositional functions is no straightforward matter, especially when modalities get involved. Starting with the formulas for non-modal categoricals, we consider various ways of modalizing the formulas and semantic criteria of their evaluation that can be derived from Buridan. In addition to the logical relations included in the octagon of divided modal propositions, three interrelated aspects are taken into account—existential import, sensitivity to ampliation of terms in modal contexts, and quantification over possibilia. We end by suggesting a representation of Buridan’s divided modal propositions that relies on the use of actualist quantification over variable domains. The formulas adequately capture the truth conditions given by Buridan, and they preserve all relations of the octagon, as well as permissible conversions in modal S5.