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'. However, many epistemologists still consider knowledge to have a justification condition. Traditional theories of justification (foundationalism and coherentism) and indeed many 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 (a) the chain must end with a link that requires no independent justification (a foundation), or (b) the chain must come around in a circle in some finite number of steps (the belief may be justified by its coherence) or (c) our beliefs must not be justified after all (as skeptics believe).
Infinitism, the view for example of Peter D. Klein, challenges this minimal consensus, referring back to work of Paul Moser (1984) and John Post (1987). In this view, justifications have an essentially infinite, non-repeating structure.