AAP 2026 CONFERENCE

Philosophical logicians often develop a language and a semantics to represent and study a body of philosophically interesting sentences whose truth conditions are ontologically puzzling. Examples include: possible world semantics, situation semantics, impossible world semantics, Routley star semantics, possibility semantics, etc. The philosophical action takes place in the semantics, which includes set- and model-theoretic constructions and so assumes mathematics. By contrast, in object theory (OT), the philosophical work is carried out in an axiom and proof system that assumes no mathematics. The system is couched in 2nd-order quantified modal logic (with complex terms), extended with one new primitive. Existence and identity (for both individuals and relations) are defined and three axioms for abstract objects are stated. The system then allows one to prove in the object language what others stipulate in the semantics, without assuming any mathematics. In particular, one may to define and prove the basic principles governing possible worlds (Kripke), situations (Barwise/Perry), Routley-starred situations, impossible worlds (a la Nolan), and (Humberstone) possibilities. Though there are other examples as well, these may be of special interest for this conference.