The Münchhausen Trilemma

A Random Introduction


The Münchhausen Trilemma (Rockin' the Umlaut!) is one of my favorite philosophical premises. The basic idea (one I had intuited but never really formulated) is that you can't really prove...anything. It is closely related to fallibilism, the idea that absolute certainty about knowledge is impossible (according to Wikipedia). It also can be associated with solipsism, although I would argue that the solipsist's certainty in his mind's existence runs contrary to it. Hans Albert, a German philosopher, described the pitfalls of the three means of justifying truth (hence "Trilemma," not "Dilemma"):

1. All justifications in pursuit of certain knowledge have also to justify the means of their justification and doing so they have to justify anew the means of their justification. Therefore there can be no end. We are faced with the hopeless situation of 'infinite regression.'
   
2. One can justify with a circular argument, but this sacrifices its validity.
   
3. One can stop at self-evidence or common sense or fundamental principles or speaking 'ex cathedra' or at any other evidence, but in doing so the intention to install certain justification is abandoned.

But that is Wikipedia's version. Albert's original words (translated) are:

Here, one has a mere choice between: 1. an infinite regression, which appears because of the necessity to go ever further back, but isn’t practically feasible and doesn’t, therefore, provide a certain foundation; 2. a logical circle in the deduction, which is caused by the fact that one, in the need to found, falls back on statements which had already appeared before as requiring a foundation, and which circle does not lead to any certain foundation either; and finally: 3. a break of searching at a certain point, which indeed appears principally feasible, but would mean a random suspension of the principle of sufficient reason.

Of course, this is philosophy, so not everyone will agree. In fact, almost no one will agree. In fact, a lot of philosophers seem kind of silly to me. But oops, I've almost begun a rant. Anyway, in another grand irony, Aristotle (kind of) argued against this theory thousands of years before Hans Albert's Rhineland even existed:(It's kind of long, if you don't want to read it.)

Some hold that, owing to the necessity of knowing the primary premises, there is no scientific knowledge. Others think there is, but that all truths are demonstrable. Neither doctrine is either true or a necessary deduction from the premises. The first school, assuming that there is no way of knowing other than by demonstration, maintain that an infinite regress is involved, on the ground that if behind the prior stands no primary, we could not know the posterior through the prior (wherein they are right, for one cannot traverse an infinite series): if on the other hand – they say – the series terminates and there are primary premises, yet these are unknowable because incapable of demonstration, which according to them is the only form of knowledge. And since thus one cannot know the primary premises, knowledge of the conclusions which follow from them is not pure scientific knowledge nor properly knowing at all, but rests on the mere supposition that the premises are true. The other party agree with them as regards knowing, holding that it is only possible by demonstration, but they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal. Our own doctrine is that not all knowledge is demonstrative: on the contrary, knowledge of the immediate premises is independent of demonstration. (The necessity of this is obvious; for since we must know the prior premises from which the demonstration is drawn, and since the regress must end in immediate truths, those truths must be indemonstrable.) Such, then, is our doctrine, and in addition we maintain that besides scientific knowledge there is its originative source which enables us to recognize the definitions.

To be honest, I'm not sure what Aristotle is getting at here. This is, partially, a problem of semantics; he's making a distinction between a priori and a posteriori knowledge, but since most people don't start taking Philosophy classes until college (which is, conveniently, the time they also are given free reign to engage in various non-philosophical pursuits), the difference seems to escape them.

The point is, Aristotle was wrong about a lot of things, including this one. I think. The problem with this stuff is that it hearkens (nice word) to the foundations of our reasoning, which generally have no foundation themselves. We should note that the Münchhausen Trilemma refutes itself, because it asserts that it (as a member of the set "Everything," or more formally "Potential Certain Truth") cannot be proven. In other words, since nothing can be proven, the Münchhausen Trilemma cannot be proven.

That being said, I've decided to accept it a priori, if you will. Or at least by faith. Because even though it can't be proven by its own standards, it can be proven by the (substandard) standards of logic, which it refutes.

The way I think about it is this: There are two kinds of truths, independent and dependent. As you might suspect, the dependent truths depend upon the independent truths. Nowhere is this better illustrated than in mathematics. Mathematics has axioms (also known as postulates), baseless assumptions [Note: I'm just kidding! String theory really is great! I think.] from which theorems and other goodies are derived. The validity of the dependent truths - theories, laws, etc. - cannot be ascertained without full knowledge of the validity of the independent truths, which cannot be ascertained because they are independent. Even worse, mathematicians can create complete new theoretical worlds just by changing the axioms. In Euclidean geometry, for example, only one line passing through a certain point can be parallel with another line. But what if this weren't true? By scratching that assumption, we come up with non-Euclidean geometry, which just so happens to be essential to general relativity.

This malleability of independent truth is not just true for mathematics, but for basically everything I can think of. And it's really, really funny, because certainty kind of gets thrown out the window. As François-Marie Arouet so eloquently (that's a stretch, but whatever) stated, "Doubt is not an agreeable condition, but certainty is an absurd one."

So why is this important?

The assumptions we make are generally a big deal. And avoiding them is pretty difficult. Two of my favorites are:

1. There is an external reality. This one is pretty interesting.
   
2. We are not insane (i.e., our senses and perceptions generally correlate to the external reality). This is the probably the worst assumption we have ever made. As Einstein said, "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." But this basically means that when we see oranges, for example, they are really there, and not just an illusion.

It is an interesting mental exercise to determine what exactly the fundamental truths upon which we rely (no dangling prepositions here) are. Or, even better, we can (try to) determine the fundamental truths of those who disagree with us fundamentally [Note to Democrats: I still love you! No really, why are you running away?]. Of course, as David Mahfood has pointed out, proving something and knowing something are two (very) different things. He also has noted that we can't really disprove the skeptical hypotheses, which doubt our perceptions themselves. Which is true, but if we're doubting our senses, what's the point?

Certain assumptions must be made for our lives to make any sense or have any meaning. I believe that the assumption of an external reality is kind of important (Imagine if you really believed it was all in your head. Then imagine if everyone else believed it was all in their heads.). However, we must also recognize that the nature of how we think depends upon the biological, perceptual, informational, and experiential limitations of our cognitive faculties.

Which assumptions are reliable? That's something we have to answer for ourselves. I know a lot of people will think that my beliefs are based on invalid assumptions. In fact, some people [Note: Doesn't he look like a pedophile or something in that picture?] think I'm deluded. For more on that, check out this blog and this guy, Alister McGrath.

Finally, this is important because it demonstrates what I will call the non-universality of reason. At least, human reason. Our minds are fallible and imprisoned in a Euclidean reality that our mathematicians tell us isn't true, and I think this should lead us to be weary of a completely rationalistic outlook on life. This is especially true because nature seems to demonstrate clear causal and temporal patterns. So what was the first cause? I think we should be open to the consideration of a worldview in which human reason is merely a subset of all knowledge. Put another way, we (at least now) cannot possibly know everything there is to know.

So there it is.