Agrippa’s Trilemma aka Münchausen’s Trilemma

Whenever a proposition is asserted to be true, we can ask “how do we know this proposition is true?”

Agrippa’s Trilemma is one of the most ancient philosophical problems.  If one is challenged on the truth of a given assertion, one may attempt to demonstrate or prove one’s assertion to be true.  But any demonstration or proof which is given will make use of premises of which it may again be asked “Are they true?”  This generates a problem of proving one’s proofs or demonstrating one’s demonstrations, and results in the following trilemma, called Agrippa’s Trilemma:

1. There is an infinite regress in which every demonstration requires a demonstration of its own, with the result that this never comes to an end, and so no demonstration is ever accomplished, nothing is demonstrated, and one merely arbitrarily stops at some point; or
2. A circular demonstration is given in which something is ‘demonstrated’ to be true on the basis of its own truth or the assumption that it is true; or
3. Demonstration comes to an end in one or more undemonstrated and indemonstrable axioms or first principles, the truth of which, because it is undemonstrated and indemonstrable, remains unknown, thus undermining the warrant of any demonstration made on the basis of such axioms or first principles.

Agrippa’s Trilemma is also sometimes called Münchausen’s Trilemma, after the legendary Baron Münchausen, who was able to free himself and his horse from a swamp in which they had become mired, by the expedient of pulling himself and his horse up and out by lifting himself by his own hair:

This technique, often called “bootstrapping” in English (from the idea of lifting oneself up by pulling on one’s own bootlaces), seems most akin to number 2 of Agrippa’s Trilemma, the circular demonstration, insofar as Baron Münchausen is both the lifter and the one being lifted at the same time.

The essential problem is that an infinite regress seems to undermine the possibility of any demonstration, a circular demonstration seems fallacious by its very nature, and any appeal to axioms or ἀρχαί (first principles) can be interpreted as arbitrary, because the legitimacy of the appeal cannot be demonstrated.

Is Agrippa’s Trilemma inescapable?

As with so many cases in philosophy, this is one of those limits of λόγος or discursive reason that thinking will run up against if pressed far enough. The best answer to it seems to be the kind of refutation that Aristotle calls retortion, which means “to turn something back on itself.” In this case, the poser of the Agrippa’s Trilemma seems to be assuming that demonstration or discursive proof is the standard of all truth-warrant, or even that “it is the case that we are caught in Agrippa’s Trilemma.”  But how does he know this to be true?

It seems entirely reasonable not to accept Agrippa’s Trilemma until it is demonstrated that it is a correct representation of our epistemological situation.  But how exactly does the proponent of the Agrippa’s Trilemma propose to demonstrate its validity as a representation of our epistemological situation without himself falling prey to it?

Either he can, or he cannot.

If he can, then Agrippa’s Trilemma is defeated by whatever means the proponent of Agrippa’s Trilemma uses to demonstrate it, which did not fall prey to it. But this cannot happen, since the Trilemma purports to show that all demonstration is impossible; thus a demonstration of the validity of the Trilemma would defeat itself (insofar is it would necessarily require a fourth method of demonstration, thus defeating the trilemma).

On the other hand, if the proponent of Agrippa’s Trilemma cannot demonstrate that it is a correct account of our epistemological situation, then we are justified in simply refusing to accept it, as something undemonstrated.  And so again, the Trilemma is defeated.

The classical answer, besides the argument to retortion showing that the Trilemma is self-defeating, is to hold that it reduces truth-warrant to demonstration, whereas there are other ways in which truth is warranted besides demonstration. As Aristotle puts it, “it is a sign of lack of education not to know of what one ought to seek a demonstration and what not”:

The classical answer, to which I adhere, is that in addition to λόγος or discursive reason, human beings also have the cognitive power of νοῦς or νόησις (Latin: intellectus) which is a kind of direct mental “seeing” of certain basic truths, which are self-evident.  “Self-evident” means something which to understand it and to understand that it is true are one and the same.  Note that self-evident does not mean “obvious.”  A thing might be difficult to understand and so not obvious immediately or to everyone, but still be such that, once understood, it is seen to be necessarily true (e.g. that the sum of the angles of a Euclidean triangle is equal to two right angles is self-evident, but not obvious).

Despite our possession of νοῦς, human cognition is nevertheless essentially discursive. The human νοῦς, according to Socrates, Plato, and Aristotle, is essentially connected to or entangled in λόγος or discursivity (and so to language and linear, temporal thinking-through or διάνοια), such that the human νοῦς ought to be regarded as much inferior to that of God.  Aristotle in de Anima calls the human νοῦς, “the so-called νοῦς,” as if it were almost not worthy of the name.  It is also worth noting that the Christian philosophical tradition holds that the human νοῦς is not merely finite or limited as compared to that of God, but has also been darkened or impaired or damaged by the Fall of Man; although it has not been erased or obliterated entirely.  Saint Paul’s expression at 1st Corinthians 13:12 is usually taken as a characterization of the human noetic condition

For now we see through a glass, darkly, but then face to face. Now I know in part; but then shall I know, even as also I am known.

“We see through a glass, darkly” seems not only a beautiful expression, but a true one. Human cognition is neither perfect nor blind. We are creatures that both by nature and our fallen state are “in-between” perfect knowledge and complete ignorance.

As Pascal says of humanity, “We know too much to be skeptics, and we know too little to be dogmatists.”

It seems, as always, all roads of merely human wisdom lead back to Socrates, whose human wisdom was the wisdom to know what he did not know, and the resultant endless search for the wisdom he did not have called philosophy.