Seven ways to defeat the Inherent-Property objection
Now we know that there is only one objection presuppositionalists have to TANG and the materialist strategy in general, and that's "Logic (or any other X) is an inherent part of God's nature, so God couldn't make contradictions (or make miracles, or make gratuitous evil moral, etc) and logic is not subjective".
Of course, one easy way to refute this is to show that Chrsitianity is founded on contradictions (everything popping out of nothing, primacy of consciousness, etc), miracles (Creation, Jesus avatar, afterlife), gratuitous evil (Flood, Hell). So right away, we can reject the idea that a hypothetical god would be inherently logical or moral. But here are seven other ways to defeat the objection and win the debate.
1. A critical problem is that it is absolutely irrelevant to the materialist argument. The Christian is not addressing the fact that logic becomes subjective if God creates it, he is only specifying the nature of that subjectivity. So instead of presenting a rebuttal, he is in fact supporting it ! Whether logic is part of God's nature or not does not change the fact that it originates from a will, not from exterior reality - which is the very definition of subjective.
2. Another critical problem is that the Christian has absolutely no grounds to discuss the specifics of God's nature. Once we accept the possibility of a Sovereign, Creator being, we cannot assume anything about its properties (any more than we can posit "anarchy" and then try to define further political properties).
Not only that, but the Christian cannot refute the possibility that this infinite god is deluding him into believing the statement "God's nature is logical". Once the Christian accepts the possibility of a Sovereign god, he can no longer refute arguments based on extreme skepticism. We can only refute the idea of a Sovereign being manipulating our minds if our worldview includes a self-contained universe.
3. It is also a complete ad hoc rationalization : nothing about the idea of a god indicates that it must be necessarily logical or rational. Indeed, since humans are capable of being both logical and illogical, it seems impossible for a more powerful being to not being able to do such a simple thing as making an illogical proposition.
4. Furthermore, even if that was the case, there would be no necessary relation between God's inherent properties and its creation, and the theologian would need to prove this relation before his objection can have any weight. More specifically, one would need to prove that powerful beings are restricted in their creations. There is no obvious correlation, it is inductively unsound, and I have never seen any such attempt.
5. It is impossible to make sense of the proposition that "logic is part of God's nature", insofar as TAG itself proposes that logic was in fact a creation of God. Logic cannot both be an intrinsic part of God's actions and created by God.
6. The objection is self-defeating. If logic existed first as a property of God, then it is a non-material principle, and divine causation is not necessary at all. All it would prove, at best, is that a non-material principle is involved, but there is a definite lack of specificity in his objection.
7. The objection presumes that it makes sense to speak of logic as a non-material entity, which seems to indicate a commitment to idealism. From our perspective, logic is a human concept derived from facts of reality. How can a human concept be an inherent part of God's nature ? This view is absolutely nonsensical.
All in all, it's a pitifully weak ad hoc rationalization to an insurmountable problem. The fact that it's all they have, is a clear indication that presuppositionalism is complete window dressing. What's hiding behind it, however, is another matter - their open hostility towards moral autonomy and science is something that deserves far more examination than their silly paper tigers.