Earlier this year I received the following thoughtful question from DG (as I will refer to him) about the argument for God from logic, which I quote in full:
In his essay [in Beyond the Control of God?] Professor Welty points out that in TCR [Theistic Conceptual Realism] “objectivity is secured by there being just one omniscient and necessarily existent person whose thoughts are uniquely identified as AOs.” But how do we get to this one from within the confines of a TCR approach alone? And in “The Lord of Non-Contradiction” you and Professor Welty state: “If the laws of logic are necessarily existent thoughts, they can only be the thoughts of a necessarily existent mind.” Here we go from plural thoughts to a singular mind as we do in the conclusion: “But if there are necessarily existent thoughts, there must be a necessarily existent mind; and if there is a necessarily existent mind, there must be a necessarily existent person.” But why not minds or persons? In note 31, you partially address my concern: “It might be objected that the necessary existence of certain thoughts entails only that, necessarily, some minds exist. Presumably the objector envisages a scenario in which every possible world contains one or more contingent minds, and those minds necessarily produce certain thoughts (among which are the laws of logic). Since those thoughts are produced in every possible world, they enjoy necessary existence.” You then show how this option fails and I agree. But what excludes many necessary beings each of which sustain some necessary truths? This is certainly ontologically extravagant and, as Adams notes in his book on Leibniz (p. 181), perhaps we can simply appeal to Ockham’s Razor to deduce one mind. But he adds, and I agree, that “a more rigorous argument would be desirable”.
At first I thought we could, as Quentin Smith suggests in his essay “The Conceptualist Argument for God’s Existence”, claim that the actual world is an infinite conjunction of all true propositions and that such a proposition, following conceptualism, could only be an accusative of one omniscient mind. But to claim there is such an infinite conjunctive proposition that needs a mind to account for it, given the view that propositions are mental effects, seems to assume there is an infinite mind who is thinking the infinite conjunction. Thus the addition of the actual world in the argument appears to beg the question.
I also considered Leibniz’s argument that without one divine mind we can’t account for how necessary truths “can be combined, any one to any one, because any two propositions can be connected to prove a new one”. But here we also seem to presuppose one mind sustaining the infinite conjunction of necessary truths that we discover in our finite combinations. Pruss, in his discussion of Leibniz’s approach, brings in a possible worlds option by pointing out that “the idea of a possible world will contain the ideas of all other possible worlds since at that world it will be true that they are possible” (Actuality, Possibility, and Worlds, 207). But wouldn’t we need one omniscient mind intending the world ensemble that is supposed to help us infer there is one omniscient mind thinking the ensemble?
I suppose we could appeal to a premise that states it is impossible for there to be a necessarily existing mind different from God. But this doesn’t seem persuasive to me at the moment.
As I understand it, the objection can be boiled down to this. Even granting that we’ve shown that necessary truths (such the laws of logic) presuppose a necessarily existent mind, it doesn’t follow that these truths are grounded in only one such mind. As DG puts it:
But what excludes many necessary beings each of which sustain some necessary truths?
An obvious first move would be to appeal to the principle of parsimony. We should not multiply entities beyond necessity. If necessary truths need to be grounded in a necessarily existent mind, then one such mind will suffice. There’s no explanatory need for further minds. But I also agree that “a more rigorous argument would be desirable,” so what follows is a preliminary sketch of one.
Assume for the sake of argument that (as Welty and I argue) that propositions are necessarily existent thoughts, that every thought must exist in a mind, and that there are two necessarily existent minds, M1 and M2. (The following argument can be generalized for any n > 1.) Take some proposition p (e.g., the proposition that 2+2=4). One of the following must be the case:
- p exists in M1 and not in M2.
- p exists in M2 and not in M1.
- p exists in both M1 and M2.
Consider case 3 first. In that case, either (a) we really have two propositions (M1’s thought and M2’s thought) or (b) we have one proposition that is a thought of both M1 and M2 (i.e., M1 and M2 have a numerically identical thought). Neither of these options looks defensible. The first option is ruled out ex hypothesi (for any proposition p, there is only one such proposition; that’s why we speak of the proposition that 2+2=4). The second option is ruled out by the fact that thoughts are indexed to particular minds (just as actions are indexed to particular agents). For any thought, we can ask the question: Whose thought is it? It has to be someone’s thought, but if it’s someone’s, it can’t also be someone else’s thought.
It’s important here not to confuse types and tokens. If you and I have the “same thought” — for example, that the sky is blue — it doesn’t follow that your thought is numerically identical to my thought. Properly speaking, we have distinct thought-tokens, but the same thought-type. Specifically, our thoughts have the same propositional content; they express or affirm one and the same proposition. But that singular proposition (the sky is blue) must be distinct from our thoughts, because, as we’ve argued, propositions exist necessarily, while human thoughts exist only contingently. What we’re considering here, in response to the objection above, is the special case where propositions are thought-tokens: thoughts that exist in a necessarily existent mind.
So case 3 above doesn’t make any sense. Against cases 1 and 2 (which are mirror-images of each other) I would raise two objections.
Objection 1: There appears to be no explanation why p belongs to M1 rather than M2. Why would, say, the proposition that 2+2=4 exist in one necessarily existent mind rather than the other? It seems wholly arbitrary. One could admit that it’s just a brute fact, but then it seems we’ve conceded an explanatory vacuum which counts against the multiple-minds scenario (over against the single-mind scenario, which requires no such explanation).
Objection 2: If p belongs to M1 rather than M2, then M1 has direct access to p in a way that M2 does not, and M2 is ontologically dependent on M1. M2’s knowledge of p depends on M1’s existence and thoughts. Thus M2 cannot be an absolute being. Moreover, if there are also some propositions that belong to M2 rather than M1, then M1 cannot be an absolute being either (since M1 would be dependent on M2). At this point we could run a modest version of the ontological argument (one that doesn’t seek to prove the existence of God, only to prove that God must be an absolute, self-existent being) to rule out the possibility of M1-M2 mutual dependency. The only way out of the dilemma would be to say that all propositions belong to either M1 or M2. But in that case we’ve basically abandoned the multiple-minds scenario for the single-mind scenario, according to which all necessary truths exist in one necessarily existent mind.
In sum, I think there are several good reasons to maintain that if necessary truths exist in a necessarily existent mind, there can be only one such mind.