Here’s a thoughtful email query I received with the title “Friendly Question about God and Logic”:
Recently, I have been reading about God and abstract objects and came across your article in Phil-Christi with Greg Welty regarding God and logic. I thoroughly enjoyed it and found it both persuasive and useful. In doing further reading on your website I came across a follow up article where you argue that atheism presupposes theism (and so does every other ism) and your argument gets close to an objection to the claim that logic depends on God that I have long wondered about. In the article, in reference to Atheism you argue the following:
(1) God does not exist. [assumption for reductio]
(2) It is true that God does not exist. [from (1)]
(3) There is at least one truth (namely, the truth that there is no God). [from (2)]
(4) If there are truths, they are divine thoughts.
(5) There is at least one divine thought. [from (3) and (4)]
(6) If there are divine thoughts, then God exists.
(7) Therefore, God exists. [from (5) and (6)]
Consider the following reconstruction:
(1*) God does not exist. [assumption for reductio]
(2*) It is true that God does not exist. [from (1*)]
(3*) There is at least one truth (namely, the truth that there is no God). [from (2*)]
(4*) Therefore, truth does not depend on God. [from (1*) and (3*)]
Let me make explicit why I think (1*-4*):
(5*) The laws of logic are divine thoughts.
(6*) According to the aseity-sovereignty doctrine if God did not exist then nothing would exist.
(7*) If God did not exist there would be no divine thoughts.
(8*) Therefore, there would be no laws of logic.
But if (5*-8*) hold, the proposition either God exists or He does not, would be a truthful description of that state of affairs and be an instance of the LEM. Likewise, the proposition God exists, would be false, not true. Not both true and false, thus an instance of the LNC.
Or another way of stating it would be:
If God did not exist then nothing would exist. But it seems that even if God did not exist there would be at least one thing that would exist, the state of affairs, nothing exists. Doesn’t that imply/entail that there is at least one truth about that state of affairs, the truth nothing exists? If that is the case don’t we have laws of logic?
I assume my objection is misguided in some way. If you have time to address this question and clarify my error I would appreciate it.
I think there are a few problems with the way the objection has been posed. For example, surely it’s incoherent to claim that if nothing were to exist, at least one thing would exist: the state of affairs, nothing exists. (What we have here, in effect, is a reductio ad absurdum of the claim that possibly nothing exists. A more rigorous argument, courtesy of the Maverick Philosopher, can be found here.) Moreover, I wouldn’t consider the proposition either God exists or He does not to be a description of a state of affairs, but rather a necessary logical truth.
Quibbles aside, however, the thrust of the objection is clear enough. I would restate it this way:
(1) If God did not exist, there would be at least one truth: the truth that God does not exist.
(2) If there are truths, there are instances of the laws of logic.
(3) If there are instances of the laws of logic, there are laws of logic.
(4) Therefore, if God did not exist, there would be laws of logic. [from (1), (2), and (3)]
(5) Therefore, the laws of logic can exist independently of God. [from (4)]
(6) Therefore, the laws of logic are not divine thoughts. [from (5)]
Assuming that this is a fair restatement of the objection, where does it go wrong? I think the inferences from (4) to (5) and from (5) to (6) are valid. I suppose premises (2) and (3) could be challenged, but I’m happy to grant them for the sake of argument. The real problem lies with (1) insofar as it begs the question against my position. Greg Welty and I gave a lengthy argument for the claim that propositions are divine thoughts. If our argument is sound then the following is true:
(1′) If God did not exist, there would be no truths.
Clearly (1) and (1′) cannot both be true; if (1) is true then (1′) is false. Hence any objection that relies on (1) actually assumes what it needs to prove, namely, that our argument is unsound.
I suppose one might reply that (1) is self-evidently true, or at least follows from a self-evident truth. Consider this generalization:
(*) If X did not exist, there would be at least one truth: the truth that X does not exist.
Isn’t this a self-evident principle? At first glance, one might think so. But then (1) follows trivially as an instance of (*).
However, this is too hasty, because the following is also an instance of (*):
(7) If truths did not exist, there would be at least one truth: the truth that truths do not exist.
Surely (7) is incoherent and therefore necessarily false. (This suggests, of course, an argument for the necessary existence of truths.) At any rate, we have good reason to think that (*) cannot be wielded in support of (1).
The fact is that (1) isn’t a trivial or obvious truth at all. It’s a counterpossible conditional (assuming that God exists necessarily if God exists at all) and there’s serious philosophical debate over how to interpret and evaluate such claims. (Compare the following claim: If 3 were equal to 2, 9 would be an even number. Is that claim true or false? Hard to say!) At a minimum, whether or not you think (1) is true will depend, in part, on what you already believe about the relationship between God and propositions (and likewise for the relationship between God and logic).
All this to say, it seems to me that objections like the one expressed above beg the question against the argument for God from logic, since they rely on counterpossible conditionals which tacitly presuppose that propositions are metaphysically independent of God.