Infinitism is an often ignored alternative to foundationalism.
Although the position may seem incredible, infinitists think that it is supported by two simple principles about justification: it can’t go in a circle, and it can’t stop in an arbitrary place.
Infinitists insist that there is no non-arbitrary place to stop the process of justification. Although stopping somewhere is inevitable given our finite lifespans, in principle the chain of justifications could be drawn out ad infinitum. For infinitists, the longer one spins out the yarn of justifications, the more justified one becomes.
Opponents often hold that infinitism is simply incredible, or even unintelligible. Isn’t an infinite regress of justification akin to no justification at all? Isn’t it like saying that our justification comes from nowhere?
If you agree with this criticism, perhaps you want to switch to coherentism instead. Or perhaps you maintain that there’s nothing wrong with an infinite regress of justification, even if we find it hard to understand.