Do God's beliefs cause their objects?

Consider this Thomistic-style doctrine:

1. God’s believing that a contingent entity x exists is the cause of x’s existing.

Let B be God’s believing that I exist. Then, either

2. B exists in all possible worlds

or

3. B exists in all and only the worlds where I exist.

(Formally, there are other options, but they have no plausibility. For instance, it would be crazy to think B exists in some but not all the worlds where I exist, or in some but not all the worlds where I don’t exist.)

Let’s consider (3) first. This, after all, seems the more obvious option. God’s beliefs are necessarily correct, so in worlds where I don’t exist, God doesn’t believe that I exist, and hence B doesn’t exist. Then, B is a contingent being that causes my existing. Now apply the Thomistic principle to this contingent being B. It exists, so God believing that B exists is the cause of B’s existing. Let B₂ be God’s believing that B exists. Since B₂ causes B, B₂ must be distinct from B, as causation cannot be circular. Furthermore, if (3) is the right option in respect of B and me, then an analogue for B₂ and B should hold: B₂ will exist in all and only the worlds where B exists. The argument repeats to generate an infinite regress of divine believings: B_n is God’s believing that B_n − 1 exists and B_n causes B_n − 1. This regress appears vicious.

So, initial appearances aside, (3) is not the way to go.

Let’s consider (2) next. Then B exists in some possible world w₁ where I don’t exist. Now, at w₁, God doesn’t believe that I exist, since necessarily God’s beliefs are correct. This seems to be in contradiction to the claim that B exists at w₁. But it is only in contradiction if it is true at w₁ that B is God’s believing that I exist. But perhaps it’s not! Perhaps (a) the believing B exists at the actual world and at w₁ but with different content, or (b) B exists at w₁ but isn’t a believing at w₁.

Let’s think some more about (2). Let w₂ be a world where only God exists (I am assuming divine simplicity; without divine simplicity, it might be that in any world where God exists, something else exists—viz., a proper part of God). Then by (2), B exists at w₂. But only God exists at w₂. So, God is identical to B at w₂. But identity is necessary. Thus, God is actually identical to B. Moreover, what goes for B surely goes for all of God’s believings. Thus, all of God’s believings are identical with God.

It is no longer very mysterious that God’s believing that I exist is the cause of my existence. For God’s believing that I exist is identical with God, and of course God is the cause of my existence.

The difficulty, however, is with the radical content variation. The numerically same mental act B is actually a believing that I exist, while at w₂ it is a believing that I don’t exist. Furthermore, if truthmaking involves entailment, we can no longer say that B truthmakes that God believes that I exist. For B can exist without God’s believing that I exist.

All this pushes back against (1). But now recall that I only called (1) a “Thomistic-style” doctrine, not a doctrine of St. Thomas. The main apparent source for the doctrine is Summa Theologica I.14.8. But notice some differences between what Aquinas says and (1).

The first is insignificant with respect to my arguments: Thomas talks of knowledge rather than belief. But (1) with knowing in place of believing is just as problematic. Obviously, it can’t be a necessary truth that God knows that I exist, since it’s not a necessary truth that I exist.

The second difference is this. In the Summa, Aquinas doesn’t seem to actually say that God’s knowledge that x exists is the cause of x’s existence. He just says that God’s knowledge is the cause of x’s existence. Perhaps, then, it is God’s knowledge in general, especially including knowledge such necessary truths as that x would have such-and-such nature, that is the cause of x’s existence. If so, then God’s knowledge would be a non-determining cause of things—for it could cause x but does not have it (and, indeed, in those worlds where x does not exist, it does not cause x). This fits well with what Aquinas says in Article 13, Reply 1: “So likewise things known by God are contingent on account of their proximate causes, while the knowledge of God, which is the first cause, is necessary.”

Maybe. I don’t know.

First Order Logic and an ontological argument

[I also posted this on prosblogion.]

I want to give this argument in part to provoke a bit of discussion of the role of FOL in philosophy. I don't think the argument carries great weight, in large part because of Objection 2 (see the end).

1. (Premise) The inferences allowed by classical First Order Logic (FOL) combined with a modal logic that includes Necessitation are valid.
2. (Premise) If every being is contingent, then possibly nothing exists. (A material conditional)
3. Necessarily something exists. (By 1)
4. So, there is a necessary being. (By 2 and 3)

The proof of (3) is as follows. Classical logic allows (Ex)(x=x) to be inferred from (x)(x=x). Since (x)(x=x) is a theorem, so is (Ex)(x=x), and hence by the rule of Necessitation, we have: Necessarily (Ex)(x=x). And thus (3) follows. And of course Necessitation is a part of standard modal systems like M, S4 and S5.

I think (2) is intuitively plausible. Here is one way to try to argue for it:
5. (Premise for reductio) Premise (2) is false.
6. (Premise) The non-existence of non-unicorns does not necessitate the existence of unicorns.
7. Every being is contingent and it is necessary that at least one thing exists. (By 5)
8. Necessarily, if no non-unicorns exist, then at least one thing exists. (By 7)
9. Necessarily, if no non-unicorns exist, then at least one unicorn exists. (By 8) 
Since (9) contradicts (6), our reductio argument for premise (2) is complete.

(I am grateful to Josh Rasmussen for simplifying my original argument.)

Now, the weak point in the argument, I think, is premise 1, and specifically the assumption of classical FOL which allows the derivation of (Ex)F(x) from (x)F(x). In a free logic, this wouldn't happen.

But it is still an interesting fact, and a real cost to contingentism (the view that all beings are contingent), that it requires one to abandon classical logic or modify Necessitation. After all, there is some non-negligible prior probability that classical logic and Necessitation license only valid inferences.

Moreover, there is the question of why one should go for a free logic? If one's reason for going for a free logic is precisely that FOL licenses the derivation of (Ex)F(x) from (x)F(x), then one runs the danger of begging the question against the anti-contingentist, in that the derivation is valid (in the sense that necessarily if the premise is true, so is the conclusion) if there is a necessary being.

Objection 1: There is likewise a cost to the non-contingentist who is prevented from adopting those logics on which it is provable that possibly nothing exists.

Response: The non-contingentist who accepts such a logic can still make the move of distinguishing metaphysical and narrowly logical necessity. She can then say that the logic gives an account of narrowly logical necessity. Therefore, all that is shown in such a logic is that it is narrowly logically possible that nothing exists, but not that it is metaphysically possible that nothing exists. On the other hand, it is much harder for the contingentist to make the analogous move of saying that (3) is true in the case of "narrowly logical necessity". For it is widely accepted that if there is a distinction between metaphysical and narrowly logical necessity, the narrowly logical necessity is stronger of the two. Thus, if one accepts (3) with "narrowly logical necessity", one accepts (3) with metaphysical necessity, too.

Objection 2: There are other good reasons to accept free logic, besides the fact that FOL licenses the derivation of (Ex)F(x) from (x)F(x). Specifically, FOL+Necessitation implies that:
10. Necessarily (Ex)(x=a)
is true for every name a.

Response: This objection almost convinces me and is one of the main reasons why I think that while my argument lowers the probability of contingentism, it is not very powerful.

I do think there are two speculative responses to the objection, which is why I think my argument still has some weight.

i. The truth of (10) for every "name" a shows that FOL's "names" do not correspond in function to names in natural languages. In particular, they show that when translating natural language sentences into FOL, one can only employ FOL's "names" for necessary beings. This shows a significant limitation of FOL--namely, that FOL has no way of translating sentences like "Socrates is mortal." However, the fact that a logic has no way of translating a sentence does not mean that the logic's inferences are invalid. There is probably no standard formal logic that can translate all sentences of natural language.

ii. Another move in defense of FOL+Necessitation is that we should see the inclusion of non-dummy names in a language L as embodying existential assumptions about the referents of these names. Consequently, when we give the Tarskian semantics for a modal logic built on top of FOL, the recursive clauses for "Necessarily s" and "Possibly s" in a language L under an interpretation J should respectively read:
- Necessarily: If e(L,J), then s.
- Possibly: e(L,J) and s.
Here, e(J,L) is the conjunction of all metalanguage claims of the form "a* exists" where "a*" is a metalanguage name for the entity that the L-name "a" refers to under J, if L contains any names, and is any tautology otherwise. Then my initial argument needs to be run in a language with no names.