Studia Neoaristotelica

Volume 10, Issue 2, 2013

A Journal of Analytic Scholasticism

Why Peter van Inwagen Does Not Help in Showing the Logical Possibility of the Trinity

I conceive the Trinity doctrine as the proposition that there are three persons each of whom is God but just one being (substance) which is God. In two papers by Peter van Inwagen I distinguish three potential candidates for a reason that the Trinity doctrine is logically possible. First, a particular conjunction entailing the Trinity doctrine is formally consistent in relative identity logic. Second, the conjunction is formally consistent in the standard logic. Third, the conjunction shares a form in relative identity logic with another logically possible conjunction. I explain how all these three reasons fail because of the distinction between logical possibility and formal consistency. In contrast to previous critiques, I dispense with epistemological and metaphysical assumptions about absolute and relative identity. Instead, I employ modal distinctions endorsed even by the inspirer of van Inwagen’s relative identity of the Trinity — the pioneering analytic scholastic Peter Geach.