infinite in the "the number of beliefs I hold is growing without bound" sense, but htat's not the relevant sense here. Growth over time doesn't cut it for this - in order to have an infinite regress of beliefs, you'd have to have all infinity of them at the same time. The set of all your beliefs would have to have cardinality , AFAICT (oddly enough, I've never seen a mathematical analysis of this, but I can't see why it wouldn't be like this.)