Skepticism & the Regress
Every justification needs a justification. The regress was never solved — only managed, three ways.
Ask someone why they believe something and you get a reason. Ask why they believe the reason and you get another one. Keep going and there are only three places the conversation can end, and the ancient skeptics noticed that none of them is comfortable.
This is the strongest argument in ancient philosophy in a specific sense: no one has refuted it. What has happened instead is that everyone has chosen which of the three uncomfortable endings to accept, and the choice is still live.
The trilemma
It comes down to us through Sextus Empiricus as part of a set of modes attributed to Agrippa, and it is short enough to state completely.
An infinite regress cannot be traversed, so nothing at the end of it ever gets justified. A circle assumes what it was meant to establish, however wide you draw it. And a stopping point is by definition a claim asserted without further support — which is exactly what was being asked for.
Notice that this applies to the trilemma itself, and to any argument for or against it. That is not a flaw the skeptics missed; it is the reason they drew the conclusion they did.
What the skeptics did with it
Pyrrhonian skepticism is not the claim that nothing can be known — that would be a piece of knowledge, and Sextus is careful to distinguish his position from the Academic skeptics who came closer to asserting it. The Pyrrhonist reports rather than asserts. Finding that for every argument there is an opposing argument of equal weight, he arrives at epoché: suspension of judgment. Not denial. A refusal to assent either way.
Then comes the part that is easy to miss and is the whole point of the exercise. Sextus says the skeptics took up philosophy hoping to resolve the contradictions and attain peace of mind; they failed to resolve them, arrived at suspension instead — and tranquility followed unexpectedly, "as a shadow follows a body." Not because they stopped caring, but because the disturbance had been coming from the effort to determine how things really are, and the effort had ended.
And they kept living. The standard objection — that a consistent skeptic would starve, since they could not judge food to be edible — is answered directly: the skeptic follows appearances. Honey appears sweet, and they will eat it; what they suspend judgment on is whether it is sweet in its nature. Custom, bodily need, appearance and craft are enough to act on. The suspension is about hidden natures, not about lunch.
"Your argument that nothing can be justified is itself unjustified." Sextus saw it coming and answered with an image: skeptical arguments are like purgative drugs, which expel the disease and then themselves. The arguments are not doctrines to be defended; they are instruments used to reach suspension and discarded there. Whether this fully works is still debated — but it is not the obvious blunder the objection assumes.
Three managements, all with costs
Modern epistemology is essentially the study of which branch to take and how to survive it.
Foundationalism takes the stopping point and tries to make it respectable: some beliefs are basic and do not require support from other beliefs — the deliverances of the senses, perhaps, or self-evident truths. Descartes' project is the most famous attempt. The cost is that the foundations always turn out to be either too small to build on or not as self-supporting as advertised, and the question "why are those basic?" is uncomfortably close to the arbitrary stop the skeptic complained about.
Coherentism takes the circle and argues that it is not vicious if it is wide enough: beliefs are justified by their fit with the whole system rather than by a linear chain. The cost is that a large consistent system can be entirely detached from reality — a well-built delusion coheres beautifully — so coherence alone does not obviously track truth.
Infinitism takes the regress and bites down: chains of reasons are infinite, and justification is a matter of having reasons available rather than having traversed them all. It is the least popular option and the most consistent one.
A fourth approach declines the question. Wittgenstein, in the notes published as On Certainty, observed that some propositions function as the hinges on which enquiry turns rather than as claims within it. Doubting that the world existed before your birth, or that this is a hand, does not raise a hard question — it removes the framework that makes questions possible. That is not a proof that the hinges are true; it is a claim about what doubting is for. Whether that dissolves the problem or renames it depends on who you ask.
The practical residue
None of this recommends doubting your evidence. What it recommends is knowing where you stopped.
Any chain of justification you rely on — an argument, a system's assurances, a measurement — terminates somewhere, and the terminus is almost never examined, because by the time a practice is running smoothly the stopping points have been forgotten. A monitoring system's numbers rest on an agent's correctness, which rests on the clock, which rests on the assumption that the thing being measured is the thing you care about. Each is a hinge, and hinges are invisible until they fail.
The skeptical exercise is simply to walk the chain deliberately and notice where the asking stopped. Sextus would say you cannot get behind the last one. That is probably right, and it is not an argument for despair — it is an argument for knowing which of your foundations were chosen rather than discovered, so that when something inexplicable happens you have a list of the places to look that nobody has looked at in years.
Justification can end in a regress, a circle, or an unsupported stop, and there is no fourth option. Every theory of knowledge is a choice among the three, each with a known cost. The useful residue is not doubt but bookkeeping: know where your chain stopped, because that is where the failures nobody predicted will come from.