One way of mapping part of the domain of epistemology is to represent various theories as responses to the following argument: (I) A belief (strictly, a token state of belief) is justified only if a justified belief is a reason for it. (Premiss.) (II) There are justified beliefs. (Premiss.) (III) The proper ancestral of the reason-relation is irreflexive. (Premiss.) (IV) There is an infinite sequence (strictly, a sequence with infinite range) of justified beliefs each of which is a reason for its predecessor, if any. (From (I) to (III).) (V) There is no such sequence. (Premiss.) (VI) There both is and is not such a sequence. (From (IV) and (V).) (VII) Not-(I) / not-(II) / not-(III) / not-(V). (Reductio.