“It used to be said that God could create anything except what would be contrary to the laws of logic.—The truth is that we could not say what an 'illogical' world would look like.”
~ Ludwig Wittgenstein, Tractatus Logico-Philosophicus, 3.031
And this is precisely why Christianity is utterly dependent upon revelation as opposed to reason or natural science. The core of Christianity can only be understood as 'logical' after it has been revealed as that which is real. Thus, for example, it is only after encountering Jesus as both God and man that we are able speak of a person who is both divine and human without drifting into 'illogical' or impossible expressions.
This, then, is why the suggestion that “God can create anything except what would be contrary to the laws of logic” is not a complete or genuine Christian statement. It must be dramatically modified to read as follows: “God can create anything according to God's logic.” Logic, in particular our understanding of logic, does not rule over God's actions; rather, God rules over our logic and only through revelation can we discern what is truly logical and what is not.
(As an aside: I am currently reading my way through both Barth and Wittgenstein and I have been struck by the ways in which their works challenge, compliment, and further each other. Does anybody know any good studies that compare and contrast the two?)