Infinitism, developed by Peter Klein, accepts the infinite regress of reasons rather than terminating it. For infinitism, a belief is justified if there is an infinite, non-repeating chain of reasons available to the believer — even if the believer has not consciously articulated them. The regress is virtuous rather than vicious because what matters is not that the chain is traversed psychologically but that reasons are available at each step. Infinitism is meant to explain how justification can be augmented by further reasons: each new reason one considers makes a belief more justified, indefinitely.
From your study of the regress problem, you know the central puzzle: any justified belief seems to require a justifying reason, which is itself a belief that requires justification, which requires another reason, and so on. The regress appears vicious: it threatens to go on forever, leaving no belief genuinely justified. Foundationalism terminates the regress with basic beliefs that are self-justifying or non-inferentially justified. Coherentism abandons the linear structure entirely, treating justification as a property of a whole web of mutually supporting beliefs. Infinitism, associated with philosopher Peter Klein, takes the most counterintuitive path: it accepts the regress.
The core move is to distinguish between traversing an infinite chain and having one available. Klein argues that the regress, far from being vicious, is actually virtuous — it represents the genuine structure of justification. What makes a belief justified is not that some chain of reasons terminates, but that for every step in the chain, there is a further reason available to the believer. "Available" is doing important work here: a reason is available if the believer could provide it when challenged, not if they have consciously articulated it already. You do not need to have mentally reviewed an infinite number of reasons in order to have them available; the structure of what you know and could reason about provides that availability.
This explains one of infinitism's most attractive features: it offers a natural account of why justification comes in degrees. If you have considered one reason for your belief, it is somewhat justified. If you have thought through that reason and found a further reason supporting it, your justification deepens. Each additional step in the chain you have consciously traversed adds to the justification — and crucially, there is always more to be gained by going further. On foundationalist accounts, once you reach the basic level, justification is exhausted; you cannot justify a basic belief further. For infinitists, this seems like an arbitrary stopping point. Every belief, no matter how seemingly basic, can receive additional support from further considerations, and that possibility is what keeps justification open-ended and improvable.
The most common objection is the finite minds problem: human beings are finite, so we cannot consciously process an infinite chain of reasons. Klein's reply is that what matters is availability, not actual mental traversal. A parallel: a dictionary can contain a finite number of entries while the language it represents is productively infinite. The fact that no speaker has produced every possible grammatical sentence does not mean those sentences are not available in the language. Similarly, the fact that no thinker has consciously reviewed an infinite chain of reasons does not mean those reasons are unavailable to them given their cognitive dispositions and background knowledge. Infinitism thus reframes justification as a practice of inquiry that can always be extended — not a state to be achieved and then secured.
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