clarification on "mixing models"

[NOTE: This is a post on Pastor Seger's argument. For the discussion with Sye Ten Bruggencate, go here.]

This past Thursday Michael Long and I sat down to have a taped conversation (over Skype) with Sye Ten Bruggencate and Pastor Dustin Segers about the existence of God. We all had a great time, and plan to perhaps do it again at some point in the future. In the mean time, I'd like to clarify some comments I made.

Not surprisingly, they appealed to their "assumption" that God exists, and boldly asserted that God somehow "grounds" the so-called "laws of logic" (among other things). Michael and I expressed our concern, however, that they don't have a coherent idea of what it means for logic to have a "ground," and we asked them to explain how they took God to serve this purpose. (We're also rather skeptical that they have a clear notion of what they're talking about when they refer to "laws of logic," but unfortunately we didn't have much time to get to that in the podcast.) Towards the end, though, Pastor Segers told us that he took the laws of logic to be "necessarily existent thoughts" and suggested that a "ground" for the laws of logic consists of the mind or minds which contain(s) those thoughts. In particular, he said:

Laws of logic are necessary truths about truths. They are necessarily true propositions. Propositions are real entities, but they can't be physical entities. They are essentially thoughts. So laws of logic are necessarily true thoughts. Since they are true in every possible world they must exist in every possible world, but they are necessarily existent thoughts. Therefore there must be a necessarily existent mind. --1:25

[EDIT 2011 Dec 29: It turns out that this is a verbatim quote from a forthcoming paper by James Anderson and Greg Welty. For a fuller discussion of that paper, go here (on-site).]

Of course there are multiple problems with this argument, but I think it's most important for us to look at how possible worlds language operates, and consider in what ways we must be careful with its use. In the limited time available to me at the end of the podcast, I tried to point out to him that even if we take propositions to be "thoughts," they aren't guaranteed to exist as such within our possible worlds model:

Perhaps you could say that there are certain laws of thought that maybe in some sense exist as thoughts, or ideas or something. But within the model of looking at statements and truth-bearers, and possible worlds, and necessary existence and all that, within that model they aren't thoughts. They're just abstract properties of the model. So I'm suspicious that you're mixing models, there, in an inappropriate way. --1:30

I wish we could have explored this criticism during the podcast more than we did, but I will just take the present opportunity to clarify. To put it plainly, I accept that there are mathematical structures, elements of which we can label "possible worlds," and that these structures can aid in our use of modal language. A possible world, in this case, we might take to consist of the state of affairs described by some maximally-consistent set of propositions. On this interpretation, an entity E "exists" in world W just in case the set S(W) of propositions describing W includes the proposition P = "E exists." Notice, however, that this does not require S(W) to include some other proposition Q(P) = "proposition P exists." (Not only that, to maintain logical consistency we might be forced to stipulate that a possible worlds structure be non-self-referential, which is to say that no element of S(W) can refer to another element of S(W); but we shall assume for the present discussion that such self-reference is not logically incoherent.)

With this in mind, recall that Pastor Segers claims necessarily true propositions "must exist in every possible world." In terms of the possible worlds structure I've outlined, this is equivalent to the property that if for every world W in the possible worlds structure P is an element in the set S(W) describing W, then for every W we must have Q(P) be an element in S(W). However, there seems to be no reason to insist on always building this property into the models we use for our modal talk. Yet if we use a model without that property, then Pastor Segers' claim that necessary truths must exist in every possible world will be rendered false. Now, we can always abandon the use of models of the form I've outlined, and liken possible worlds to something other than states of affairs described by maximally-consistent sets of propositions. However that won't change the fact that we will still be using a model, and whenever we build something into that model, namely the necessary existence of certain propositions and/or thoughts, we can always ask, "why do so?" Pastor Segers has essentially demanded that we only use those models consistent with his view of necessary truths existing as thoughts in all possible worlds. However, it seems to me that this is only a roundabout way of assuming in advance what he is attempting to prove.

I suspect, however, that Pastor Segers hasn't thought about possible worlds in this fashion. Instead, it seems like he just conflates the possible worlds model with higher-level models we use to talk about it. So, he begins by observing within the possible worlds model that some proposition P is true. Jumping outside that model into a higher-level model, he (correctly) notices that P exists as a proposition, but then he mistakenly steps back inside the possible worlds model while still holding onto the existence of P from the higher-level model. This is clearly an intolerable move, and it's what I'm talking about when I suggest that he is "mixing models" inappropriately.

So, while I'm happy that Pastor Segers made a genuine attempt to explain what he means by having a "ground" of logic (which is more, in my experience, than most presuppositionalists would ever care to do), his account appears incoherent at worst and overly presumptuous at best. Of course, if he has a solution to this problem, naturally I would love to hear it. However I don't see any way around it, myself.