Is a necessarily necessary God possible?
Date:
Colloquium presented at The Cave Wall, a student-run philosophy club at Stellenbosch University, covering the modal ontological argument. Given the diverse interdisciplinary audience, I do not assume familiarity with formal logic.
Abstract
In Prologion III, Anselm presents a famous ontological argument for the existence of God. The argument assumes possibility of the existence of a being whose very existence is necessary, and from this possibility alone concludes the existence of such a being. On first reading, this argument may appear abstract and unconvincing - in particular, one may doubt whether the conclusion indeed follows from the premiss. Worse still, it is equally difficult to convincingly rebut this argument without first making very precise several hidden assumptions about the modalities of “necessity” and “possibility” upon which the argument depends.
In this talk, I introduce one framework in which such alethic modal reasoning may be formalised, namely the S5 modal logic. I then formally prove Anselm’s argument in S5, and discuss the implications for the forcefulness of the argument. The main reference for this talk is Philosophical and Mathematical Logic by De Swart (2018).
Mathematics $\cap$ philosophy $\cap$ computer science
While I do find Anselm’s ontological argument interesting, my real motivation for this talk was to spread awareness of the many beautiful philosophical applications of modal logics.
In the late 1950s, legendary philosopher Saul Kripke, together with (equally legendary) mathematician André Joyal, discovered an elegant formal semantics for non-classical logics, finally allowing such logics to be studied model-theoretically1.
Modal logics are surprisingly versatile in their expressiveness, and so find applications in a wide range of disciplines; thus, even if one cares little for philosophy, it may still be worth learning a little about them. The most interesting modal logics (some of which are mentioned in the slides) include the following (though the list is far from exhaustive):
| Logic | Reasons about | Example field of application |
|---|---|---|
| alethic logic | necessity & possibility | philosophy of religion (see talk) |
| deontic logic | moral obligation | ethical philosophy |
| epistemic logic | agents’ knowledge | distributed systems |
| doxastic logic | agents’ beliefs | game theory |
| temporal logic | time evolution of propositions | model checking |
| provability logic | provability of statements | mathematical logic |
| dynamic logic | states & actions of programs | formal verification |
| computation tree logic | branching time evolution | model checking |
These logics each have different axioms, but all employ modal operators, and have semantics given in terms of Kripke frames.
This is a rich theory, but too technical to be explored in an introductory talk such as this. See this book chapter by Goranko & Otto for a good survey. ↩