There is a forthcoming paper that argues that God is a necessary precondition for the Laws of Logic. The argument, from the paper's conclusion is:
The laws of logic are necessary truths about truths; they are necessarily true propositions. Propositions are real entities, but cannot be physical entities; they are essentially thoughts. So the laws of logic are necessarily true thoughts. Since they are true in every possible world, they must exist in every possible world. 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. A necessarily existent person must be spiritual in nature, because no physical entity exists necessarily. Thus, if there are laws of logic, there must also be a necessarily existent, personal, spiritual being.
I've drafted a note responding to the argument and would be grateful for any feedback.
Anderson and Welty seek to establish that “(t)he laws of logic imply the existence of God”. There is, however, an equivocation in a key step in the argument. Any univocal re-statement of the argument fails.
The step in question is given in the summary of their argument in the conclusion to the paper:
“Since [the laws of logic] are true in every possible world, they must exist in every possible world.”
Now, how are we to take the two sub-clauses, “true in every possible world” and “exist in every possible world” as being logically connected?
If and only if («)
If a law of logic exists in a possible world if and only if it is true in that possible world then the step is, obviously true. However, given Anderson and Welty’s characterisation of the laws of logic as necessarily true; their conclusion, that they entail the existence of God, is contradictory.
“The laws of logic entail the existence of God” entails that if there were no God then the laws of logic would not exist. Given, though, that the laws of logic are necessarily true and that they exist if and only if they are true then the laws of logic necessarily exist. If the laws of logic necessarily exist then they would exist whether God existed or not.
So we must abandon the idea that a law of logic “exists” in a possible world if and only if it holds true in that particular world. Perhaps it is meant that if, (but not “only if”), a law of logic holds true in a world then it exists in a world? This does not remove the contradiction. The laws of logic are necessarily true, they hold in every possible world whether or not God exists in that possible world. As their holding true entails their existence the laws of logic exist in every possible world whether or not God exists in that possible world.
Only if (¬)
Anderson and Welty’s conclusion, that the laws of logic imply the existence of God, is not contradicted if we assume that “only if” is meant: the laws of logic are true in every possible world only if they exist in every possible world. Indeed, on this reading, Anderson and Welty’s conclusion would be supported. Given Anderson and Welty’s characterisation of what it means for a law of logic to “exist”, were God not to exist in a possible world the laws of logic would not exist in that possible world. If the non-existence of the laws of logic in a possible world entailed that they failed to hold in that world then an agreement that, say, the law of non-contradiction does hold entails the existence of God. Whilst this may seem like an improvement, the “only if” reading either contradicts other vital premises in the argument or renders the step itself contradictory. The step claims that the laws of logic hold true in every possible world. Why is that? If it is because they exist in every possible world (maybe because God exists in every possible world) then the laws of logic are not necessarily true; their truth is dependent upon their existence and were they do not exist they are not true. The first premise in Anderson and Welty’s, summarised, argument is that the laws of logic are necessarily true: the argument contradicts itself. So let us assume that the fact that the laws of logic hold true in every possible world is because they are necessarily true. This contradicts the assertion that they are true “only if” they exist: the step, itself, is contradictory.
Other logical connectives and conclusion
Other logical connectives are not only more of a stretch in interpretation but fail destroy the step as any link in chain of reasoning. “And” turns the step into two simple assertions. “Or”, excluding combinations of “or” and “not” that are equivalent to connectives discussed already, simply asserts the truth of one of the sub-clauses.
There may be other logical connectives that haven’t been considered or have not, even, been thought of yet. No logic is liable to correct the argument, though, as the two sub-phrases of the step simply talk about different things.
Anderson and Welty must establish that laws of logic are capable of being contingent in order to argue that they are contingent upon God. Thus the laws of logic are characterised as thoughts. Thoughts require a mind and, thus, are contingent on minds. “Exist” in the second sub-phrase refers to being thought of by a mind. Anderson and Welty also need to establish the laws of logic as necessarily true in order to argue that the mind thinking the laws of logic must be necessarily true.
However being true and being thought are wholly independent properties of propositions. The one is dependent on a mind, the other dependent on the world outside that mind. No logical connectives will bridge the gap. Differing logical connectives may save the argument from saying something contradictory, but at the expense of saying anything at all.
The assertion that God is a necessary precondition for the laws of logic is either necessarily false, or meaningless.
 Anderson, J. N., & Welty, G. (Forthcoming). The Lord of Non-Contradiction: An Argument for God from Logic. Philosophia Christi .
 It may be objected that God is, Himself, necessary and thus there is no possible world where He does not exist. The objection, however, is not only question begging but proves the counter argument. God is necessary for the laws of logic if and only if for all possible worlds were God does not exist there are no laws of logic. The universal statement, “all possible worlds x”, can be recast existentially as “there does not exist a possible world without x”. God, therefore, is necessary for the laws of logic if and only if there exists a possible world were God does not exist and neither do the laws of logic. If God is necessary there is no world were God does not exist and, thus, no world were God does not exist and neither do the laws of logic.