Here, I want to concentrate on the view that logic presupposes theism, using as my example Sye Ten Bruggencate's defense of this claim, which you can see in the unintentionally humorous “interview” with Eric Hovind titled Episode 2 – Logic.
According to Bruggencate, logic is one of the “fundamental assumptions of the unbeliever.” After all, one cannot conclude that atheism is correct or that religious belief is incorrect without making use of it. The problem, according to Bruggencate, is that atheists cannot justify their use of logic. To do so, they need to use logic itself, and so end up arguing in a circle. His solution is to maintain that God grounds logic and reveals it to us so that we can know that it is justified. As Eric Hovind puts it, “logic is only consistent with the God of the Bible.” (Why the God of the Bible, as opposed to the God of the Koran, or the Flying Spaghetti Monster for that matter, isn't explained.)
One obvious problem with this entire approach concerns how presuppositionalists themselves arrive at it. What is their starting point, their “fundamental assumption,” as Bruggencate might put it? Bruggencate would of course answer that it is God. But clearly that isn't the case. Like everyone else, presuppositionalists make use of logic right from the start. They argue, in other words, as for example when they conclude that the nonbeliever cannot account for logic's validity without circular reasoning, or that God is the only possible foundation for logic because he is eternal and immutable. This isn't to say that their arguments are good ones, of course. They aren't. When Bruggencate points out that the laws of logic are universal, immaterial, and unchanging, and that these same three attributes apply to God as well, he is making a very weak argument by analogy. And his reasoning is even worse when he argues that the atheist cannot account for unchanging logical laws in a universe that is constantly changing. In fact, these arguments are so bad they're laughable. But they are arguments nonetheless, and as such, they presuppose logic. This shows that in order to arrive at the conclusion that God is the source of logic, presuppositionalists must already accept logic.
Now, my point here isn't that the presuppositionalists make a mistake in starting with logic. The mistake they make (besides misusing logic in their flawed arguments) is to suppose that that's not what they're doing – to suppose instead that they are beginning with God. The irony here is that the one thing that one must be a presuppositionalist about, in a matter of speaking, is precisely logic. This is because any claim whatsoever implicitly uses the laws of logic. One cannot say “logic is valid,” or “x is true,” or anything else coherent without presupposing the law of identity, for to say that x is anything is to say something about the thing whose identity is x. Bruggencate may think that he begins with God – that he only accepts logic because God has told him he should – but in order to even think such a thought, he had to use logic.
The laws of logic are necessarily true because what they describe applies to every possible scenario. This is why they are implicit in every statement. And because the laws of logic are necessarily true, logic cannot be contingent upon anything, including God. In Episode 2, Bruggencate says – and this is one of the few instances where he is correct – that logic cannot be man-made, as some atheists claim. If it were, then it might have been different. “Could the universe,” he asks, “have both existed and not existed at the same time and in the same way?” But once again there is a bit of irony here, because in his view there would be no logic without God – and that means that a godless universe could both exist and not exist at the same time. By making logic contingent on God, Bruggencate is no better than those who make it contingent on humans.
One final example of the kind of confusion one gets into by denying the necessity of logic can be seen in how Bruggencate ends up justifying the law of non-contradiction. Logical contradictions, he says, are not allowed “because logical contradictions amount to lying, and God tells us not to lie.” This is such an amazing statement that I can only quote his interviewer and say, “Wow!” According to Bruggencate, the law of non-contradiction is valid for moral reasons! I guess it's just not very nice for the universe to both exist and not exist at the same time: it offends God.