Overview of Principia Logico-Metaphysica

Edward Zalta (Stanford University)

I present an overview of the body of (formal) metaphysical theorems derived from (formal) metaphysical axioms of object theory (OT).  In particular, I plan to review the "List of the Most Important Theorems” on PDF pages 10-14 (= numbered pages xvi—xx) of the unpublished monograph https://mally.stanford.edu/principia.pdf .  The theorems demonstrate the many applications of OT for the analysis of (1) the mathematical objects and relations of  2nd-order Peano Arithmetic, (2) truth-values, (3) situations, (4) possible and impossible worlds, (5) possibilities (á la Humberstone, van Benthem, Holliday, etc.), (6) the Routley star operation, (7) Leitgeb’s HYPE logic, (8) world-indexed relations, (9) Fregean extensions, and (10) Leibniz’s calculus of concepts and modal metaphysics. The objects in (1) — (10)  are defined and the principles that govern them can be derived. And once analytic truths of the form “In theory T, φ”, for arbitrary mathematical theories T, are added, the objects and relations of T can be precisely identified and the truth conditions for the theorems of T can be given an exact formulation — mathematics is thereby shown to be about abstract objects and abstract relations. 

Link: https://us06web.zoom.us/j/87649813438