Concept
Infinitism is the view that knowledge may be justified by an infinite chain of reasons. It belongs to epistemology, the branch of philosophy that considers the possibility, nature, and means of knowledge. Since Gettier, "knowledge" is no longer widely accepted as meaning "justified true belief" only. However, some epistemologists still consider knowledge to have a justification condition. Traditional theories of justification (foundationalism and coherentism) and indeed some philosophers consider an infinite regress not to be a valid justification. In their view, if A is justified by B, B by C, and so forth, then either The chain must end with a link that requires no independent justification (a foundation), The chain must come around in a circle in some finite number of steps (the belief may be justified by its coherence), or Our beliefs must not be justified after all (as is posited by philosophical skeptics). Infinitism, the view, for example, of Peter D. Klein, challenges this consensus, referring back to work of Paul Moser (1984) and John Post (1987). In this view, the evidential ancestry of a justified belief must be infinite and non-repeating, which follows from the conjunction of two principles that Klein sees as having straightforward intuitive appeal: "The Principle of Avoiding Circularity" and "The Principle of Avoiding Arbitrariness." The Principle of Avoiding Circularity (PAC) is stated as follows: "For all x, if a person, S, has a justification for x, then for all y, if y is in the evidential ancestry of x for S, then x is not in the evidential ancestry of y for S." PAC says that the proposition to be justified cannot be a member of its own evidential ancestry, which is violated by coherence theories of justification. The Principle of Avoiding Arbitrariness (PAA) is stated as follows: "For all x, if a person, S, has a justification for x, then there is some reason, r1, available to S for x; and there is some reason, r2, available to S for r1; etc.