Exactly! The more you think about it the more brilliant it gets. Like the Babel Fish argument against the existence of God in the Hitchhiker's Guide:
The argument goes something like this: "I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED"
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
The argument goes something like this: "I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing." "But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED" "Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.