Tuesday 28 May 2013

Maydole's Modal Ontological Argument for God

This argument is very complex, involving a very long and tedious derivation in modal logic that I don't really understand myself, and so I'm not going to attempt to give it or even explain it. Suffice to say, the argument involves a controversial premise called the Barcan formula (◊∃xFx → ∃x◊Fx), or in English; if it's possible that a property be instantiated in some thing, then there exists a thing that possibly instantiates that property. When this was pointed out to me I found it quite unintuitive, but wasn't ever quite happy with the counterexamples I could come up with. But now I think I've come up with a strong counterexample that even the most stubborn theist couldn't deny.

Prior to creation, God—an essentially perfect being—was alone. Of course the property of imperfection would had to have been possibly instantiated, or else God couldn't have possibly created us; beings that sometime down the road became imperfect (if we weren't already from the start). But if this is the case, then prior to creation there was a possibility of imperfection while the only thing in existence was necessarily perfect, and thus could not possibly be imperfect. And so there's some condition (to the atheist a hypothetical, but to the theist it's very real!) under which the antecedent of the Barcan formula is true, but the conclusion is false. And, as everyone knows, that means the Barcan formula must itself be false. And, finally, since Maydole's ontological argument relies (at least from what I've seen) on the Barcan formula, the argument as a whole must be unsound.

Here is another: Because evil is possibly instantiated in us, prior to creation there must have been something that possibly instantiated evil. But God is essentially good, and thus he cannot possibly be evil. Of course only persons can be evil, and so prior to creation there must have been a person who was not God. Uncreated persons are gods, being eternal and self-sufficient, and therefore if the barcan formula holds and evil is possible, then we're left with polytheism.


  1. Of the modern modal ontological arguments, I think Plantinga's is best (though it is utterly unpersuasive). It keeps the complexity to a minimum, and avoids getting lost in the technicalities of modal logic as much as possible.

    Maydole's argument, on the other hand, is a mess. It uses long technical derivations and a high amount of abstraction, and since very few people are conversant with modal predicate logic (which is an order more complex than modal propositional logic), most people can't see what's going on, and since it's a philosopher using advanced logical machinery writing in a journal, they give him the benefit of the doubt. To really understand what's going on, one needs to understand the material in the first ten chapters of Fitting and Mendelsohn's First-Order Modal Logic.

    To begin with, there is nothing wrong with the Barcan formula in and of itself. The problem isn't that Maydole uses the Barcan formula; the problem is that he uses it along with two other decisions he makes.

    In doing predicate modal logic, one needs to decide between a Possibilist and an Actualist approach. Every possible world has a set of entities associated with it that "exist" in some sense in that world. In an Actualist approach, the entities that exist are the actual entities that really exist in that world. In a Possibilist approach, the entities represent ideas or concepts of things that could exist in that world. One then needs to use a separate Concreteness predicate to assert the concept actually exist.

    So for example, suppose that I, Rick, am a person who lived in World1, but that I was never actually born in World2. Using an actualist approach, Rick would exist in World1 and not in World2. In a possibilist approach, Rick might very well exist in both worlds, but Rick would only be Concrete in World1, not in World2. The idea is that in World2, I would be a coherent concept, but I was never actually born.

    From a mathematician's point of view, it's a matter of taste whether one uses an Actualist or a Possibilist approach. One can formally prove that any model you can do using one approach, you can do using the other. >>

    1. >> Now, the problem with Maydole's argument is that he does three things together.

      (1) He uses the Barcan formula

      (2) He uses an actualist approach

      (3) He works in S5

      Now there's nothing wrong with the Barcan formula; there's nothing doing (1) and (3). There's also nothing wrong with doing (2) and (3). But when you do (1), (2), and (3) together,there's a problem.

      When you do (1) and (3) together, mathematically you are effectively assuming that every possible world has the same set of entities existing in it. This is not a problem if you are taking a possiblist approach; then you're just assuming that the entities that conceptually might exist do not vary from world to world. In that case, which entities are actually concrete in each world can vary, as I described earlier, where Rick existed as a concept in World1 and World2, but was only instantiated (concreate) in World1.

      But when you do (1), (2), and (3) together as Maydole does, you are effectively assuming that everything that possibly exists must also necessarily exist in every possible world. This makes the proof much easier of course, because with that foundation, one need only show that God possibly exists and has any properties necessarily; then God's necessary existence will follow from the logical assumptions. Of course any entity that possibly exists will necessarily exist, including for example Pegasus. This may be why Maydole in the responses to counterarguments takes to time to argue why it's not possible Pegasus exists. It's also why Maydole has that odd passage addressing the problems that arise if there exists a possible world containing only men (in this case, either all worlds contain only men, or people who are men in one world must be women in the actual world).

      So that's one objection I have to Maydole's argument, and unfortunately it can't really be appreciated without a significant amount of study of formal modal predicate logic. There's another objection that is much more intuitive but equally definitive, in my opinion. I'll save that for another post.