A recent paper by James Anderson and Greg Welty (link) on “An Argument for God from Logic” has been made available. It does not purport to be “incontrovertible proof” for the existence of God, though it claims to be deductively valid and superficially sound.
Some of the points made in the article which whose importance could likely be overlooked are very good: “language-independence,” for instance, is something I’ve been meaning to talk about for a while, and I hope to do so in the near future. At the same time, there were a few things I think, highly qualified as I am to make such recommendations, require clarification:
1. The title of the article is a bit of a misnomer. What I mean is that certain polytheists or non-Christian monotheists could use the arguments: "Strictly speaking, the argument shows that there must be at least one necessarily existent person; it doesn't show that there must be one and only one necessarily existent person."
The purpose of the authors’ transcendental argument is certainly more conservative than Van Til’s attempt to defend Christianity in particular (cf. here), and I would say that even if such a restriction in purpose is not due to recognition of epistemic limitations, it is at least a step in the right direction. I abandoned attempting to defend Christianity with a TAG when I realized that the step from theism – even theism with restrictions to rule out several options – to Christianity is inferential, but I’m more than willing to learn an apagogic argument.
2. The authors referred to a possible world as "a way the world could have been." But if, as some like me tend to think, this is the only possible world God could have effected due to who He is, then the authors' assumption of multiple possible worlds throughout their article is problematic. Perhaps this objection can be largely avoided if they were to switch "imaginable worlds" for "possible worlds" at the appropriate places. I would say an "imaginable world" is just a [fictional] world proceeding from our imaginations. Whatever we imagine, the laws of logic must apply to them, for our imaginings are a subset of our thoughts bound by the laws of logic.
3. They state that "There is no possible world in which... the Law of Non-Contradiction is not true." However, if the law of non-contradiction is mental, this statement begs the question: has there existed or could there have existed a world without minds and, if so, would not such a world demonstrate that the laws of logic are ontologically unnecessary?
Let me unpack this a bit: the authors argue that minds are a metaphysical precondition for the laws of logic. I agree. If the laws of logic exist necessarily, then “God” (i.e. and eternal mind) exists necessarily. I agree with that too. But I had trouble understanding how the authors claimed to know the laws of logic exist necessarily. Such only seems to be the case if minds exist necessarily; but from what I could gather, that is the purported conclusion of their argument – rather than their premise for it – according to which “God’s” existence is thereby posited. This would be circular reasoning, i.e. not a deductively valid argument.
I discussed this with a friend, and he replied that the laws of logic must be invariant in order to avoid a self-defeating position. But I didn’t find a reason given in the paper as why the existence of the laws of logic needs to be necessary in order for their invariance to hold when a contingent mind thinks. It is true that when minds think, they must think according to the laws of logic. But if all minds cease to think (exist), the metaphysical precondition is not met and the laws of logic cease to exist. This doesn’t mean that if such were to occur, true would become false, contradictories could be true, etc.; it would mean that since there would be no minds, there wouldn’t be thinking – there wouldn’t be laws of logic.
So while it’s true that “we cannot imagine the possibility of the Law of Non-Contradiction being false,” if the “we” isn’t a metaphysical necessity, neither are the laws of logic. No one would be thinking propositionally. No one would be thinking the laws of logic. Perhaps a good summary of this line of reasoning would be that a “necessary truth” is a truth without which no one could think, but it’s not a truth which must be thought. If this is possible, then this article’s argument for God’s existence fails.
I think, therefore, the argument of this paper requires a classical apologetic explaining the [pre]conditions under which a world can obtain to rule out these types of counterarguments.