God's word

Discussions about the inerrancy of the Bible often stray into the swamp of quibbling over details. I've gone there, too. But recently I got into some interesting discussions with inerrancy advocates by trying to understand their core assumptions. So I asked, "How do we know that the Bible is God's inerrant word?" A common answer was "Because the God says so." So then I asked, "How do we know that God even exists to speak to us?" The answer was: "Because the Bible says so." So God validates the Bible and the Bible validates God. I must admit, it doesn't seem very productive to argue with circular logic like that, but it's not very persuasive if you're outside the circle. I'm curious if anyone has a non-circular argument for the Bible's inerrancy?