The Regress Problem

A child who keeps asking why will exhaust any adult within about six steps. The pattern is familiar enough to be a joke, and it encodes an argument that ancient sceptics used to attack the possibility of knowledge and that every modern theory of justification is still answering.

How the problem arises

Most justification looks like this. You believe the meeting is at two because the calendar says so. You believe the calendar is right because you entered it yourself. Each step cites something further back.

The regress is not a pathology that arises in odd cases. It is generated by two things that look individually harmless: that a belief is justified only if the believer has a reason for it, and that having a reason means having some further belief that supports it. Grant both and every justified belief sits at the end of a chain, and the chain can be asked about.

There are exactly four things such a chain can do. It can go on forever. It can come back on itself. It can stop somewhere. Or there is no chain because there is no justified belief.

The name comes from Agrippa, a sceptic of the first century BCE to whom Diogenes Laërtius attributes a set of five modes. Sextus Empiricus records them in the Outlines of Pyrrhonism at I 164 to 177, attributing them to the more recent sceptics rather than to Agrippa by name. Three of the five make up the trilemma as it is now stated: the mode of infinite regress, where what is offered as a source of conviction itself needs another such source without end; the mode of reciprocity, where what should confirm the matter under investigation itself needs to be made convincing by that matter; and the mode of hypothesis, where the dogmatist simply assumes a starting point without proof. The remaining two modes concern disagreement and relativity, and they do different work.

The ancient use was not to solve the problem but to establish that it has no solution, and thereby to recommend suspending judgement.

The argument stated

The conclusion is not one that anybody accepts, and the argument is valid, so a premise has to go. Which one you reject determines your theory of justification, and there are only so many places to stand. This is why the regress is worth the trouble: it does not merely raise a problem, it exhausts the options in advance.

The first premise is the weak point

Almost every developed response denies the first premise rather than one of the later ones, and denies it in the same way: by holding that some beliefs are justified without resting on other beliefs.

The move is not a trick, and the reason it is not is worth making explicit. The fifth premise says that a terminating chain fails because the last belief has no support. That is only true if the sole possible support is another belief. If something other than a belief can confer justification, then a chain can terminate in a belief that is supported without being inferred, and the third horn of the trilemma is refused rather than accepted.

What that non-doxastic support could be is the hard part. Candidates include experience itself, the self-evidence of certain simple truths, and the reliability of the process that produced the belief. Each has been developed and each has been attacked, and the intermediate tier examines them.

The three exits, named

Each horn of the trilemma has been embraced by somebody, and the three resulting positions are the subject of one of the intermediate tier's central articles. They are worth naming here so that the map is visible.

Take the third horn and deny that stopping is arbitrary. This is foundationalism: there are basic beliefs, and everything else is justified by inference from them. The burden is to say which beliefs are basic and what makes them so, without either admitting too much or leaving too little to build on.

Take the second horn and deny that circularity is vicious. This is coherentism: justification is not a chain at all but a matter of how a body of beliefs fits together, so that beliefs support one another mutually and none is foundational. The burden is to explain why a coherent set has to be a true one, since a well-constructed fiction is coherent.

Take the first horn and deny that infinite chains fail. This is infinitism, defended in its contemporary form by Peter Klein, on which the reasons available to a person are genuinely endless and non-repeating, and justification is a matter of having them available rather than of having traversed them. The burden is to explain how a finite mind has infinitely many reasons.

And the fourth option is to accept the argument, which is what the ancient sceptics did.

What the beginner tier has established

Six articles have built a vocabulary and located the disputes rather than resolved them.

Knowledge was separated from belief and from true opinion, and the difference was found to lie in what supports the belief rather than in its content. Justification was distinguished from practical reasons for believing, and from the mere availability of good reasons that a believer is not actually using. The four sources were surveyed with their failure modes, and none of them can be validated without using itself or another one. The skeptical argument was stated in the form that makes it hard, and the responses were sorted by which premise they deny. The standard analysis was assembled and then shown to be refuted by cases that exploit the gap between being justified and being right. And the regress has now shown that the theories of justification are not an open-ended list but a small set of forced choices.

The intermediate tier takes each of these in turn with the apparatus this tier withheld: the Gettier cases in detail, the three structural theories, the internalism dispute, the modal conditions, and the shift from belief to degrees of confidence.