Indeed, I wasn't trying to establish foundations for thinking based on the existence of God at all. I'm familiar with that line of argument, but it doesn't convince me, and I certainly wouldn't expect it to convince an atheist.

I'm also unclear as to why you think I would be trying to use it in this argument, given that the question we were discussing was almost exactly the inverse: our question hasn't been "given that God exists, how can we rationally establish foundations for thinking?", but "given what we count as rational foundations for thinking, is it reasonable for Liz to believe that God exists?" I was arguing that the justification I have for believing that God exists is of the same kind as the justification that is available for other foundational philosophical beliefs, such as "other minds exist" and "external objects exist"; so if people can be justified in believing those things, then I am justified in believing that God exists. Given what you say about induction, maybe you'd be content to concede that no-one has justification for those beliefs; if that's the case, then I think we've hit on a more fundamental philosophical difference between us than belief in God, and I'd probably be content to agree to disagree on it for the time being.