Why we can’t, ultimately, prove anything

Agrippa’s trilemma, named after one of the ancient Skeptics, clearly shows the limits of human knowledge

Gustave Doré's portrait of Baron Münchhausen, Wikimedia

Back in 1968, the German philosopher Hans Albert proposed an argument aimed at showing that certain knowledge is, ultimately, impossible.

The idea was that whenever someone wants to prove a proposition—of any kind—we can always ask for proof of how the proof itself works. It turns out that there are only three possibilities:

A circular argument: the proof is based on a proposition or set of propositions that is, in turn, ultimately based on the first proof;

A regressive argument: the proof is based on another proof, which is based on another proof, and so on ad infinitum;

A dogmatic argument: the proof is based on an axiom or assumption which is simply taken for granted for the purpose of the discussion.

Albert called this Münchausen’s trilemma, after a fictional character—the Baron Münchausen—created by the German writer Rudolf Erich Raspe and protagonist of his book, Baron Münchausen’s Narrative of his Marvelous Travels and Campaigns in Russia, published in 1785.

At one point in the book the Baron finds himself stuck in a mire together with his horse. He manages to pull himself out of the dire predicament by pulling his own hair up and using it as leverage (today we would talk of pulling oneself up by one’s own bootstraps). This, of course, is physically impossible, just like it is logically impossible to escape the trilemma named after the Baron.

Turns out, though, that the trilemma is far older than Albert realized. It goes back to Agrippa the Skeptic, who lived during the first century. The commentator Sextus Empiricus (late 2nd / early 3rd century) tells us in his Outlines of Pyrrhonism that Agrippa proposed five (not three) “modes” or tropes of skeptical argumentation (boldface mine):

“According to the mode deriving from dispute, we find that undecidable dissension about the matter proposed has come about both in ordinary life and among philosophers. Because of this we are not able to choose or to rule out anything, and we end up with suspension of judgement. In the mode deriving from infinite regress, we say that what is brought forward as a source of conviction for the matter proposed itself needs another such source, which itself needs another, and so ad infinitum, so that we have no point from which to begin to establish anything, and suspension of judgement follows. In the mode deriving from relativity, as we said above, the existing object appears to be such-and-such relative to the subject judging and to the things observed together with it, but we suspend judgement on what it is like in its nature. We have the mode from hypothesis when the Dogmatists, being thrown back ad infinitum, begin from something which they do not establish but claim to assume simply and without proof in virtue of a concession. The reciprocal mode occurs when what ought to be confirmatory of the object under investigation needs to be made convincing by the object under investigation [i.e., circularity]; then, being unable to take either in order to establish the other, we suspend judgement about both.” (Outlines of Pyrrhonism)

The upshot, in classic Pyrrhonist fashion, is that in all those cases the reasonable thing to do is to suspend judgment. To recap, then, the five modes are:

Dissent, when people disagree on whether something is true or not;

Infinite regress, same as in Münchausen’s trilemma;

Relativity, when different observers perceive what is allegedly the same object differently;

Dogmatic hypothesis, same as in Münchausen’s trilemma;

Circularity, same as in Münchausen’s trilemma.

Two of Agrippa’s five modes, however, “dissent” and “relativity” are really a summary of the earlier ten modes of Aenesidemus (first century BCE). You can check those for yourself and see how that works. The remaining three Agrippan modes, then, are identical with those put forth by Albert, so Münchausen’s trilemma is really Agrippa’s (modified) trilemma.

Now, why should we care about any of this? Because there is no known way to escape the trilemma. People have tried, really hard, for a long time. Finally, philosopher of science Karl Popper concluded that we simply have to accept that there is no solution to the problem and give up the notion of certain knowledge. So freed, we can keep working on probable knowledge by way of what he famously called conjectures and refutations, mixing in the most useful way the three possibilities: circularity, regress, and assumptions.

(In so doing, incidentally, Popper moved from Pyrrhonian Skepticism, which settles on suspension of judgment, to Cicero-style Academic Skepticism, which proposes probability as the criterion for tentative assent to any given proposition.)

By the way, Albert himself showed that the trilemma is not limited to empirical matters (i.e., science as well as everyday life), but it also applies to logic and mathematics. It concerns, in other words, both inductive and deductive reasoning.

The obvious question at this point might be: does Agrippa’s trilemma lend credence to epistemic relativism? Nope. We don’t need to slide into a “your opinion, my opinion” relativistic attitude because the trilemma is a statement about the human ability to prove things (i.e., it concerns epistemology) not about the existence or not of truth itself (i.e., ontology). Truths may be (likely are) out there, and yet we may be incapable of proving them.

But wait a minute! Does the trilemma apply even to itself? Yes, it does! The notion that certainty is impossible is not, itself, certain, for the very same reasons why the trilemma applies to ordinary cases outside of itself. However, so far nobody has found a way to refute it, therefore the reasonable thing to do is to tentatively regard it as correct, unless and until proven otherwise. Wanna give it a try?