Abstract

This paper deals with two different problems in which infinity plays a central role. I first respond to a claim that infinity renders counting knowledge-level beliefs an infeasible approach to measuring and comparing how much we know. There are two methods of comparing sizes of infinite sets, using the one-to-one correspondence principle or the subset principle, and I argue that we should use the subset principle for measuring knowledge. I then turn to the normalizability and coarse tuning objections to fine-tuning arguments for the existence of God or a multiverse. These objections center on the difficulty of talking about the epistemic probability of a physical constant falling within a finite life-permitting range when the possible range of that constant is infinite. Applying the lessons learned regarding infinity and the measurement of knowledge, I hope to blunt much of the force of these objections to fine-tuning arguments.