In pursuit of a mind untroubled by bothersome knowledge, Pyrrhonian skeptics, such as Sextus Empiricus, employed various arguments designed to bring about suspension of judgment. One such argument is to be found in the second of the Five Modes of late Pyrrhonism. Sextus presents this argument in the fifteenth chapter of his Outlines of Pyrrhonism.
The mode based upon regress ad infinitum is that whereby we assert that the thing adduced as a proof of the matter proposed needs a further proof, and this again another, and so on ad infinitum, so that the consequence is suspension [of judgment], as we posses no starting point for our argument.
The argument could be rendered thus:
1. For any given belief, a proof is required for that belief to be justified (assumed).
2. However, for every proof given, yet another proof is required for that proof to be justified; leading to vicious infinite regress of proofs.
3. An infinite regress of proofs provides no basis for justification since it is impossible to determine if every belief in the series is justified.
4. Therefore, it is impossible to justify any given belief and so one should suspend judgment.
Sextus goes on to anticipate and reject two possible solutions to the problem of an infinite regress: these are expressed in the fourth and fifth modes, in which the former is concerned with circular reasoning and the latter is concerned with hypotheses (assumptions of knowledge).
As to the initial argument, it does appear to be valid given the skeptic’s criteria of justification. Furthermore, the third premise seems to be quite self-evident. It does not seem possible to provide individual justifications for an infinite series of beliefs; at least, not in a finite measure of time (which would unfortunately describe the lifespan of all known human beings). A criticism of the argument must therefore focus upon the first two premises, both of which are based upon a certain assumption of justification.
Adopting circular reasoning would be one way of rejecting the second premise. As stated above, Sextus anticipates this objection in the fourth mode:
The Mode of circular reasoning is the form used when the proof itself which ought to establish the matter of inquiry requires confirmation derived from that matter; in this case, being unable to assume either in order to establish the other, we suspend judgment on both.
To illustrate the point very simply:
1. Sextus Empiricus’ arguments for skepticism are irrefutable (how do you know that?).
2. Because he is the most persuasive skeptic in history (how do you know that?)
3. Because his arguments for skepticism are irrefutable.
While this example is quite simple, it does demonstrate that circular reasoning is patently absurd. One can prove anything by begging the question. Likewise, one can justify any claim to knowledge if they are allowed to engage in a vicious circle of justifications.
Assuming a belief (hypothesis) to be true would be another way of avoiding an infinite regress. Sextus deals with this in the fifth Mode:
We have the Mode based on hypothesis when the Dogmatists, being forced to recede ad infinitum, take as their starting-point something which they do not establish by argument but claim to assume as granted simply and without demonstration.
Under this scheme, an infinite regress can be avoided by digging one’s epistemological heels into a belief that requires no justification. Sextus assumes that this position is invalid since the hypothesizer provides no argument or demonstration for the belief to which he holds. This seems to be a valid objection to a whole assortment of unjustified beliefs. Take, for example, the belief that I am Napoleon Bonaparte. Using the logic of the hypothesizer, could I not simply assert this belief firmly and with no justification? One can see why Sextus considers this position to be untenable.
What about other beliefs though? There are certainly beliefs that seem to be more reasonable that the one given above. Take, for example, the belief that I am presently sitting before my computer typing this post. Must this belief be ‘proven’ somehow before it can count as knowledge? Sextus would say ‘yes’, but there are many who would disagree with him. This leads us to examine the epistemological assumption that underlies the first premise of the infinite regress argument.
Sextus merely assumes that every belief requires some form of proof before it can be justified and count as knowledge. Deductive certainty, however, is an incredibly high standard of justification. Given his assumption, one can see how it would be impossible to know almost anything. But do we have to grant his assumption? Do we have to explain how we have knowledge of some specific thing for that knowledge to be justified? If so, would it not be reasonable to ask the skeptic how he knows that we do not have knowledge of a specific item?
It is at this point that the skeptic would probably launch into various arguments attacking the reliability of the senses; such as “How do you know that you are not dreaming?” or “How do you know that you are not insane or a brain in a vat?” However, the hypothesizer may respond that just because something is logically possible, this does not mean that it is reasonable to believe it. It is logically possible that a teddy bear is orbiting Mars or that the moon is actually made of green cheese, but this does not mean that I am required to believe these things to be so, or that it would be reasonable to do so. Likewise, it may be logically possible that I am merely dreaming that I am typing this post or that I am insane, but the skeptic must provide me with good reasons to believe these things. And I think that this is something that Sextus, for all his mighty modes, fails to provide.
Therefore, the infinite regress argument of the skeptic is as only as powerful as its underlying assumption. If deductive certainty is the required justification for knowledge, then we indeed know very little. However, if certainty is not required, then the second Mode is unpersuasive. It all depends upon who shoulders the burden of proof.