(from a paper I wrote)
To understand
epistemic regress, we must first understand the fundamental definition of
knowledge. Knowledge is defined as
justified true belief. In other words, for someone to have knowledge that-p, one must first believe p, p must be true, and one must be justified in believing that-p. Consider a paranoid person who believes that the
CIA has his house bugged because he saw a UFO when he was younger. The CIA may actually have his house bugged because they think he's selling secrets to the Russians. He believes that his house is bugged, and it is in fact bugged, but does he know it? No, because his
belief is not justified. He did not reach his conclusion via a logical train of thoughts. It is the question, "when is a belief justified?" that gives rise to the epistemic regress problem.
When seeking justification for a belief, we naturally use other beliefs as supporting evidence. For example, I justify my belief that I am going to make an A on this paper with my beliefs that I am a good writer and that I understand the material. The problem of epistemic regress arises when we notice that I have introduced two more beliefs to my argument. For my original belief to obtain justification from the second two, they must also be justified. I then introduce more beliefs as evidence for these. This begins an
infinite sequence of justifying each belief with subsequent beliefs which also need justification.