I just sent in a question to William Lane Craig via the Reasonablefaith.org Q&A form, and I wanted to repost it here in case anyone else (Christians, that is) wanted to take a crack at it. Except, for some reason, after I copy & pasted it earlier today, it didn't save so I'll just have to paraphrase what I sent in. It was inspired by a post by Massimo Pigliucci over at Rationally Speaking, and it has to do with the law of non-contradiction. I thought it was interesting because the law of non-contradiction was brought up in a recent comment thread discussion on logic.
Christian apologetics is essentially the use of logical arguments to deduce the existence of God and make inferences about his nature. This would seem to imply that God himself is subject to, or perhaps embodies, the laws of logic, which is why we could use such laws to make inferences about God in the first place (i.e., if God is exempt from the laws of logic, we'd have no grounds for using those laws to make inferences about him). Logic as part of the nature of God is even used to resolve conundrums about God's nature, such as dismissing the old "Can God microwave a burrito so hot he couldn't eat it?" paradoxes as logically absurd questions.
Which brings us to the law of non-contradiction, or ¬ (P ∧ ¬P), which means that something cannot both be and not be something else. But a central tenet of Christian theology is that God is both three persons and one god -- the Father, the Son, and the Holy Spirit. If the Christian simply attempts to avoid the conundrum by suggesting that the law of non-contradiction need not apply, then they're not being consistent in how they apply the laws of logic; this would show that the Christian is simply cherry-picking the rules of logic arbitrarily – applying them when they seem convenient, but discarding them when a theological conundrum arises.
So the question is, how can the law of non-contradiction be reconciled with the Trinity?