Have you ever thought about what grounds the laws of logic and mathematics? We know that they work, but why?
The Christian apologist has a quick answer: because of God. They exist and are sustained by God. The Transcendental Argument (TAG) challenges the atheist to resolve this any other way. What besides God could possibly explain the existence of something fundamental like logic? (To see the Christian case for this argument, read the selection from my Cross Examined in an earlier post.)
This argument is of particular interest to me because I was introduced to it in a radio interview—not the best place for careful study and contemplation. (But more on that later.)
1. TAG is just a deist argument
First notice that TAG is a deist argument. If it convinced you, you’d be a deist, not a Christian. The apologist would be obliged to use different arguments to show that the deity was the Christian god, not some other god.
2. We don’t get physics from Christianity
Next, notice that we’ve never gotten physics from Christianity before. Why go to Christianity now to find the fundamental basis for physics? Yes, the Bible tells us how everything got started, but science gives the evidence to make clear that the Bible is wrong.
Nothing useful has ever come from resolving a science question by concluding that God did it. No honest seeker of the truth says, “I don’t know what causes this thing … so therefore I do know! It must’ve been God.”
3. Avoiding logical puzzles invalidates TAG
Many apologists dodge the “Can God make a rock so heavy he can’t lift it?” puzzle by saying that God can’t do anything illogical (here and here)—he can’t make an impossibly heavy rock, a square circle, a married bachelor, and so on. The question is ill-formed.
But by dodging this pitfall, they land in another as God’s actions become constrained by an external logic. If God is bound by logic, logic isn’t arbitrary. God can’t change it. He acts logically because he must, just like the rest of us.
This creates a Euthyphro-like dilemma: either God is bound by an external logic (and God answers to a fixed logic that he can’t change) or he’s not (and logic becomes arbitrary—it is what it is simply because God said so, and he could change it if he wanted to).
The apologist will try to propose a third option (again, as with Euthyphro): logic is simply a consequence of God’s nature. It’s neither external nor arbitrary. But this simply rephrases the problem. Is this nature changeable? Then logic is arbitrary. Is it fixed? Then God is again bound by logic.
Can God be the origin of logic if he’s bound by it?
4. Could God create logic and mathematics? Or is he bound by them?
Let’s think about God creating arithmetic for a moment. “Creation” seems to mean more than simply “bring into existence.” Were God’s hands tied in creating arithmetic, or did he have some creative control? For example, 2 + 2 = 4 in our universe. Could God have made 2 + 2 = 9? If so, prove it. And if not, God was obliged to make arithmetic the way it is and unable to create any other kind. Here again, he answered to an external reality.
5. Consequences of a godless universe
But let’s assume the apologist’s argument and see what happens. God created logic, and logic is the way it is because God made it so. If God’s role here is important, a godless universe must be dramatically different. A godless universe could then have no logic or different logical rules.
In our universe, X can’t be the same thing as not-X (the Law of Identity). Something can’t simultaneously be a rock and not-a-rock. The apologist’s argument tells us that logic is up for grabs. In a godless universe, something might be a rock and not-a-rock. But this is an incredible claim that needs justification. TAG gives none.
Continue with part 2.

Can God make a rock so heavy
that hitting His head with it
would explain the change in personality He underwent
between the Old Testament and the New Testament?
— commenter GubbaBumpkin

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