# Modality and the ontological argument

Previously, I outlined what I find to be a compelling ontological argument from Alexander Pruss. In the post, we dispelled the idea that there is a single ontological argument and distinguished between a number of families on such arguments. The one we focussed on is a so-called Gödelian ontological argument, named after the famous mathematician Kurt Gödel. Gödelian ontological arguments construct an axiomatic system and use this to prove, as a theorem in the system, that something like God exists; and this is exactly what we did. If you’ll recall, we proved the following theorem:

Theorem 2 There exists a necessary, essentially omniscient, omnipotent, omnibenevolent being.

In fact, we noted that using the same methods we used to prove theorem 2 we could prove that there exists a necessary being who possesses all strongly positive properties. Now, in the proof of this theorem, we made use of a system of modal logic called S5. The goal of this post is to discuss this system, and consider some alternative (and weaker) systems that could be used to arrive at the same result.

# A Gödelian ontological argument

I’ve never really had a nice relationship with the ontological argument from Anselm. When I first heard of it, it seemed strange that existence would be greater than non-existence, so I pushed it aside. About 2 years later, I realised that existence could maybe be bootstrapped from other properties, like power. But by then I had come to realise the distinction between epistemology and ontology, and struggled to believe that this argument wasn’t confusing the two at some point. That’s where I’m at at the moment: existence-in-mind just doesn’t seem comparable to existence-in-reality in the way that’s needed for the argument to work. Maybe I’m wrong, but that’s where I’m at[1].

Many people talk about Anselm’s ontological argument as the ontological argument. But, like many theistic arguments (and arguments in general, I suppose), to call it the ontological argument is a bit misleading. There are a number of ontological arguments out there, and Anselm’s one is but one of them. Descartes had another ontological argument which Leibniz worked on a bit, and in the 20th century we’ve had modal ontological arguments coming from Norman Malcolm, Charles Hartshorne, and Alvin Plantinga. Another “class” of ontological arguments are the so-called “Gödelian” ontological arguments. Kurt Gödel, the famous mathematician of Gödel’s Incompleteness Theorems, developed his argument using the primitive idea of a “positive property”. The arguments that follow this approach, like Gödel’s before them, are developed as formal axiomatic system with a theorem at the end that says that there is a God-like being who exists. Jordan Sobel showed, in 1987, that Gödel’s axioms also imply that every true proposition is necessarily true. This argument from Sobel is called the “modal collapse argument”, and it shows that Gödel’s argument is unsound. However, since then, there have been a number of Gödelian ontological arguments which have been formulated so as not to fall prey to the modal collapse argument. These have come from Curtis Anderson, Allen Hazen, Robert Koons, and Petr Hajek, to name four. And, then there’s the recent “Modal Perfection Argument” from Robert Maydole.

Of prime importance to this blog post is yet another Gödelian ontological argument formulated by Alexander Pruss[2]. While I’m not convinced by Anselm’s, Descartes, and many of the other ontological arguments, this one does certainly seem plausible to me. I’ll sketch it briefly in this post.

# World-types have explanations but not grounds?

On the one hand I personally like the idea of middle-knowledge for understanding the relationship between God’s providence and our libertarian-free choices[1]. On the other hand, I’m what William Lane Craig once called[2] a latter-day Leibnizian, who wants “everything to be brought into submission to the Principle of Sufficient Reason, including facts concerning human free choices.” Of course, in that context he was concerned with the grounding objection to the Molinist’s counterfactuals of creaturely freedom (CCFs). It seems to me, however, that the CCFs can be explained, even if they can’t be grounded. Let me explain.

A “subjunctive counterfactual conditional” (or just “counterfactual” for short) is something of the form “Were it/had it been the case that C, then it would be the case that A”. There are different types of counterfactuals: sometimes they describe entailments, and sometimes they don’t. An example of the former case would be some sort of grounding: were it the case the I know 2+2=4, then it would be the case that it is known that 2+2=4. Here the antecedent (I know that 2+2=4) entails the consequent (it is known that 2+2=4), that is in every possible world in which the antecedent it true, so is the consequent.

But there are cases where the counterfactual we’re talking about is not describing an entailment. For example, “If Nixon had pressed the button, there would have been a nuclear catastrophe”[3] In this case, it’s possible that Nixon presses the button and it malfunctions, thus not leading to a nuclear catastrophe. In these cases can we analyse the counterfactual in terms of possible worlds? For those who think we can, they usually analyse the counterfactual by moving to a similar possible world (for a given account of similarity) where the antecedent occurs and seeing what happens to find the consequent. For example, on this account, when we say “If Nixon had pressed the button, there would have been a nuclear catastrophe”, what we mean is that in all the closest possible worlds in which Nixon presses the button, there is a nuclear catastrophe. Of course, this makes what would be the case is dependent upon what is actually the case. That is, the truth of such counterfactuals, on this second analysis, depends on what happens in the actual world, since we need an actual world to judge similarity to before we can pick the similar worlds to check.

The Molinist cannot accept this second analysis when it comes to the CCFs, because she believes that such counterfactuals are true prior to which world is actual. She has two options: (1) introduce a third class of counterfactuals for the CCFs and accept the second analysis above for the non-entailment, non-CCF ones, but deny it for CCFs, or (2) deny the second analysis and any analysis of non-entailment counterfactuals that makes the truth of such counterfactuals depend on which possible world is actual.

I myself am inclined to go with the second option there, since I find it strange that “would” statements should depend on what actually happens, but what I say from here on will relate to both options. If CCFs are not dependent upon the actual world, how is that they can be explained? I claim that even though they are contingent themselves, they can be explained with necessary facts[4]. Before I get there, though, I thought I’d make a quick comment about semantics.

### World-types

As you may know, a possible world is a maximal description of how reality could’ve been. You can think of it as a massive conjunction of propositions C, such that for any proposition P, either P or not-P is a conjunct of C. Of course, there’s slightly more to it than that, since we also need that the conjunction is metaphysically possible (ie. that the conjuncts are compossible), but we need not worry about these details here.

By “world-type” I mean a maximal conjunction of CCFs (or, more generally, counterfactuals). Since counterfactuals are themselves propositions, it follows that every possible world contains a world-type, in fact many possible worlds can contain the same world-type. So the Molinist position says that the actual world-type is contingent and not chosen by God. This puzzling situation is what makes the Molinist position so subject to the grounding objection.

### Explaining CCFs

Now I fully admit that CCFs might not have grounds. This doesn’t bother me too much, however, because I think they can still be explained[5]. We’ve seen before, that explanations can be non-entailing, so what I seek now is an explanation of the contingent CCFs in terms of necessary facts. Think about a typical CCF: “If Adam were in circumstance A, then he would freely choose to eat the fruit from the tree”. Why is this true? Well, if Adam were in circumstance A, then he would be tempted to eat the fruit of the tree. Or, in terms we’ve used before, if Adam were in circumstance C, he’d be impressed by reason R to eat the fruit. This is necessarily true, since in every possible world in which Adam finds himself in the given circumstance, the same pressures will apply to him (since they’re included in the circumstance). But as we’ve seen in the past, merely being impressed by a reason doesn’t entail that a free agent will chose according to it, so the CCF is still contingent (given something like libertarian free will)[6].

### Notes

1. One day, when I get to writing the rest of my blog posts on God’s providence this statement will be further expounded.
2. William Lane Craig in “Ducking Friendly Fire: Davison on the Grounding Objection
3. Taken from a paper by Boris Kment called “Counterfactuals and Explanation”
4. “Fact” here means “true proposition”.
5. And I don’t think that all facts need truthmakers in the sense that is required by grounding objectors, but that’s a different issue altogether.
6. This isn’t an original idea: I got this account of explanation from Joshua Rasmussen in the comments here.