Munchausen’s trilemma and the impossibility of certain truth

Munchausen'S bootstrapOne day the Baron Munchausen found himself stuck in a mire together with his horse. The situation was dire, but he managed to save himself (and his horse!) by pulling his hair up until he was lifted out of the mud.

Obviously, Munchausen’s feat is impossible, as it violates the law of gravity. So it is fitting that it gives the name to the most compelling demonstration of the impossibility of another impossibility that human beings have been after for quite some time: certain knowledge.

One of the earliest demonstrations that certainty isn’t something that human beings can reasonably aspire to was given by the ancient skeptics. Julia Annas (who, incidentally, will be one of the speakers of the forthcoming STOICON event in New York City, on 15 October) presents the argument as articulated by Sextus Empiricus (in her translation of Outlines of Scepticism):

“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 judgment. 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 judgment 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 judgment 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; then, being unable to take either in order to establish the other, we suspend judgment about both.”

The modern version of the argument relies on three alternative paths to certain knowledge, all judged to be dead ends (hence Munchausen’s tri-lemma, also known as Agrippa’s trilemma, from the Greek skeptic to whom Diogenes Laertius attributes the original formulation). If someone states something to be certainly true, we are well within our rights to ask him how does he know that. To which there can be only three classes of answers:

1. A circular argument, where at some point the theory and the alleged proof support each other, however indirectly.

2. An argument from regression, in which the proof relies on a more basic proof, which in turn relies on an even more basic one, and so on, in an infinite regress.

3. An axiomatic argument, where the proof stems from a (hopefully) small number of axioms or assumptions which, however, are not themselves subjected to proof.

It is self-evident why none of the above options are good enough, if one’s objective is to arrive at certainty. And I should immediately add that these are the only three modes available not just in the case of deductive logic (which means most of mathematics), but also in the case of inductive inference (which means the rest of math and all of scientific as well as common knowledge — see Hume’s problem of induction).

There are, of course, different ways of biting the bullet, and they correspond to some of the major schools of epistemology. Say you find the first option (circularity) as the most palatable — or the least distasteful — one. Then you are a coherentist about knowledge, arguing for something like Quine’s web of belief approach. If you’d rather go for infinite regression you are, quite appropriately, an infinitist (which, as far as I know, is not a popular position among epistemologists). But if your taste agrees more with the idea of unproven axioms, then you are a foundationalist, someone who thinks of knowledge as built, metaphorically, like an edifice, on foundations (which, however, cannot be further questioned).

If none of the above does it for you, then you can go more radical. One way to do so is to be a fallibilist, that is someone who accepts that human knowledge cannot achieve certainty, but that we can still discard notions because they have been shown to be false (see Popper’s falsifiability criterion).

Karl Popper, who wrote about Munchausen’s trilemma in his The Logic of Scientific Discovery (a book that I’m re-appreciating the more I am sent to it by way of other readings) opted for a mixed approach: he thought that a judicious combination of dogmatism (i.e., assuming certain axioms), regress, and perceptual experience is the best we can do, even though it falls short of the chimera of certainty.

It has to be noted that Munchausen’s trilemma does not imply that we cannot make objective statements about the world, nor that we are condemned to hopeless epistemic relativism. The first danger is avoided once we realize that — given certain assumptions about whatever problem we are focusing on — we can say things that are objectively true. Just think, for instance, of the game of chess. Its rules (i.e., axioms) are entirely arbitrary, invented by human beings out of whole cloth. But once accepted, chess problems do admit of objectively true solutions (as well as of a large number of objectively false ones). This ought to clearly show that arbitrariness is not equivalent to lack of objectivity.

The second danger, relativism, is pre-empted by the fact that some solutions to whatever problem do work (whatever the criterion for “working” is) better than others. It is true that engineers have to make certain assumptions about the laws of nature, as well as accept the properties of the materials they use as raw facts. But it is equally true that bridges built in a certain way stay up and function properly, while bridges built in other ways have a nasty tendency to collapse.

So, it looks like the quest for certainty, which has plagued both philosophy and science since the time of Plato, is doomed to failure. But are we certain of this? If so, then doesn’t that certainty itself undermine our very contention that there can be no certainty to begin with? Nice try, but no, because we do not actually have a proof that there can be no certainty. Munchausen’s trilemma is a reasonable conclusion arrived at by logical reasoning. But logic itself has to make certain assumptions in order to work, so there…

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Categories: Epistemology, Logic

210 replies

  1. So what happens when the premises of the base of a ‘web’ are incoherent. Presumably Westboro ‘believes’ in the doctrine of the trinity.

    Now in Catholic teaching the trinity is a mystery, i.e.,. something you as a mere mortal cannot understand, but has it is doctrine must believe!

    Now w/o judging it’s truth, how can I believe something I don’t understand?

    How can I say “God is three persons in one God’ is true or false or paraconsistent, if I can’t in principle know what it means?

    At best I could assert that whatever the sentence means it is true!

    The priest in Graham Green’s ‘Power and Glory” [a] struggles mightily with the trinity. I figure it is something like a Zen koan, intended to induce an endorphin high, so you feel one with whatever …

    [a] https://en.wikipedia.org/wiki/The_Power_and_the_Glory

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  2. Hi Massimo,

    So I always thought of a web of belief as a good metaphor for coherentism, not foundationalism, …

    I largely agree with Dan’s explanation, though I would not call it foundationalist because the periphery of the web is not so much connected to “observation statements” so much as raw sense data — effectively a stream of photon-arrival events, translated into electrical impulses along nerves.

    Any “observation statement” in the English language or any other human language is going to be an interpretation of that sense data that must involve a large swathe of the web, rather than being a directly verified statement.

    So yes, there is a distinction between human-language statements that are nearer the sense-data periphery and those that are further from it, but there are no human-language statements that could be regarded as foundational. What does matter, then, is the coherence of the statements with the raw sense data, though since the sense data is an external input, perhaps the better term for that is correspondence.

    On Dan’s point:

    Westboro Baptists might be able to claim their belief system “equal” on a truly coherentist epistemology, but definitely could not, on a Quinean one. Because many of their observation statements are going to suffer massive discomfirmation …

    Though theologians are generally sufficiently wiley not to hold any beliefs about observational statements that are vulnerable to being disconfirmed. All the action tends to take place in non-observable places such as heaven and hell, precisely to get round this problem.

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  3. Coel: The problem is that sense data — i.e. uninterpreted content — is pretty widely agreed to be a hopeless notion. And Quine’s anti-verificationism — of which the web of belief is a part — is one of the works that led to that widely held conclusion.

    I don’t think it matters much to what we are talking about here, though.

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  4. Re: Westboro Baptists, Coel, I wasn’t thinking of their theological beliefs so much as their toxic social beliefs, most of which would be straightforwardly disconfirmed in observation.

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  5. Hi all (late as usual), what I got out of my philosophy courses (back in the late 80’s) is that Quine’s “web” was some hybrid between coherence and foundational accounts. As such I basically agree with Dan’s take on this.

    I personally differ from Quine by making that foundational aspect very clear (which really Quine didn’t, though it can be inferred as Dan has shown). I openly admit there are axioms (unproven) underlying the system. I never saw any reason to apologize for that, or think it was a weakness… given Massimo’s OP I think that view is validated.

    Unproven axiom does not mean wrong.

    It is the most robust epistemic account I have come across.

    …………………

    Hi Synred,

    “How can I say “God is three persons in one God’ is true or false or paraconsistent, if I can’t in principle know what it means?”

    Did you ever watch Bill Maher’s “Religulous”? I was also confused by that concept until Maher, in an overtly anti-religious documentary, brought it up to some actor that plays Jesus as a full time gig.

    Jesus/actor analogized it to water. Water has three different phases (solid, liquid, gas) and we don’t have problems understanding that. What’s the problem?

    Despite being an atheist, I was like…yeah ok that makes sense. It suggests that the form of God is environment/context dependent. Even Bill was stopped short and said that was a good answer.

    Though yeah, that doesn’t answer many other problems.

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  6. Strictly, in the interests of humor, the Lucky Luciano episode of NYPD Blue, sequence beginning at 25:43 continuing through 36:45, although the whole episode is a riot.

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  7. Jesus/actor analogized it to water. Water has three different phases (solid, liquid, gas) and we don’t have problems understanding that. What’s the problem?

    As I was taught it is a mystery that humans cannot in principle understand! Maybe that’s not the protestant doctrine…

    And it’s not a good analogy anyway. God is a ‘person’, not substance. Three person in one God, not three forms of God stuff. That Hindu!

    You’re working on the Koan?. Are you getting high?

    The priest in ‘The Power and the Glory’ goes through a bunch of such metaphors and then feels guilty when he remembers that very doctrine is that he can’t understand it.

    I loved religious!

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  8. Hi synred

    “So what happens when the premises of the base of a ‘web’ are incoherent. Presumably Westboro ‘believes’ in the doctrine of the trinity.”

    No problem if the need for coherence is only a working assumption.

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  9. Hj dbholmes

    “Unproven axiom does not mean wrong.”

    Of course nor. In fact as I understand the term, “unproven axiom” is a tautology.

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  10. DrHolmes:

    As I was taught it is a mystery that humans cannot in principle understand! Maybe that’s not the protestant doctrine…
    And ‘phase’ is not a good analogy anyway. God is a ‘person’, not substance. Three persons in one God, not three forms of God stuff. That’s kind of Hindu!
    You’re working on the Koan?. Are you getting high?
    The priest in ‘The Power and the Glory’ goes through a bunch of such metaphors and then feels guilty when he remembers that very doctrine is that he can’t understand it.

    I loved religious! I couldn’t find he the Trinity scene on YouTube.

    -Traruh

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  11. In this shockingly bold manner, Gödel stormed the fortress of Principia Mathematica and brought it tumbling down in ruins. He also showed that his method applied to any system whatsoever that tried to accomplish the goals of Principia Mathematica. In effect, then, Gödel destroyed the hopes of those who believed that mathematical thinking is capturable by the rigidity of axiomatic systems, and he thereby forced mathematicians, logicians, and philosophers to explore the mysterious newly found chasm irrevocably separating provability from truth.

    Nagel, Ernest; James R. Newman; Douglas R. Hofstadter. Godel’s Proof (Kindle Locations 105-109). NYU Press. Kindle Edition.

    ==>So what are the consequences of Gödel’s theorem.? You can prove theorems from axioms but there are truths about the system specified by the axioms that can’t be proved.

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  12. Just another trivial example of an objective fact about a convention.

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  13. The Quinean web seems to me to have issues with both the original and new problems of induction. Per my first comment here, the whole set of alternatives is cocked up. You make your choice, drink your poison, and then try to be like Hume going to sleep happy.

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  14. ALL of my beliefs are “incorrigible,” so to speak. Not quite as incorrigible as my bad puns, but that’s another story.

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  15. encourageble ? Give us a really bad pun…

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  16. A cheap and easy one: “I got my literary skills at Pun State.”

    Liked by 1 person

  17. Al Gore Rhythm — a contradiction in terms…

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  18. Hi Dan,

    “Westboro Baptists might be able to claim their belief system “equal” on a truly coherentist epistemology, but definitely could not, on a Quinean one. Because many of their observation statements are going to suffer massive discomfirmation ”

    But I am not sure why that is relevant. If a good belief system need be coherent and not disconfirmed by evidence then the Westboro crowd don’t have a good belief system. I am not aware that anyone here doubts that, certainly not me.

    But, as you know, I am referring to the version of the Quinean web suggested hear where the requirement to be coherent and not disconfirmed by the evidence are merely provisional working assumptions.

    In that case their beliefs can be incoherent and massively disconfirmed by evidence, but that would be no reason that it wasn’t a good belief system.

    Are their any other ways, apart from those, why the belief system of the Westboro Baotists could be considered any worse than any other?

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  19. “Al Gore Rhythm — a contradiction in terms”

    Yes, but unfortunately there is no halting Al Gore Rhythm.

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  20. What do you mean by ‘good belief system’? I take it this is some technical definition as Westboro’s beliefs are not ‘good’ in any sense I can think of…not ethical, accurate, or consistent…effective at raising money?

    “All good, all powerful, all wise and needs MONEY”

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  21. “What do you mean by ‘good belief system’?”

    That is just the question I asked, if nothing is foundational and everything is provisional then what is there to distinguish the belief system of the Westboro folks from the belief system of the Center for Inquiry folks?

    As far as I can see this would make it purely subjective. Clearly the Westboro Baptists beliefs work for them.

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  22. Hi Coel

    But “true by the criteria produced by their web” is not the same as “true”.

    The idea that the criterion for ‘truth’ waa a product of the Quinean web came from what you said :

    Thus an account of “truth” as being correspondence is then a product of the Quinean-web interations, just like everything else.

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  23. ‘>Clearly the Westboro Baptists beliefs work for them.

    I don’t know about ‘them’. It works for their leadership whether he wants money or just to be the alpha in a small pond. Basically, they are being scammed. No coherent system of belief is need; ‘word salad’ and fear mongering will work just fine.

    So I looked up Quine (on Stanford). The word ‘web’ only occurs once, so I still do not understand what it’s all about, but if allows for Westboro ‘beliefs’ to on a par with science or even Thomas Aquinas, it is absurd.

    I don’t think this can be what Quine was trying to say.

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  24. DR: Reductio ab absurdum?

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  25. Hi synred

    I was addressing the version being suggested here, rather than Quine’s original.

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  26. Again, I thought that I had made it clear a number of times that I was addressing the version of the “Quinean web” suggested here, where nothing is foundational and everything provisional, ie:

    a. The need for coherence/consistency is a provisional working assumption

    b. The need for it to be confirmed by evidence or not disconfirmed by the evidence is a provisional working assumption

    c. The account of “truth” used is itself a product of the web.

    Those are the claims I am referring to specifically and nothing else. I am saying that, given a, b, c above the Westboro Baptists’ there could be no meaningful distinction between the belief system of the Westboro Baptists and, say the Center for Inquiry.

    Does anyone specifically disagree with that?

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  27. Mucked up the penultimate paragraph, which should say:

    “Those are the claims I am referring to specifically and nothing else. I am saying that, given a, b, c above there could be no meaningful distinction between the belief system of the Westboro Baptists and, say the Center for Inquiry.”

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  28. It interests me to hear that Quine was considered somewhat foundationalist by at least some experts in the field. In order for me to get a sense of the founding which he theorized, I suppose that I’d need to read a good bit more than I’m willing to (especially since even Massimo was surprised by this).

    I consider myself a “coherentist,” and in the sense that I’m an extreme naturalist. Another way of putting it is that I believe in perfect causality — or something which implies that all of reality coheres. This is also why I’m a determinist for example, (though merely in an ultimate sense). Calling reality a “web” actually seems a bit understated to me by comparison, not that I can think of a stronger analogy.

    I consider myself a “foundationalist” as well, and in the sense that I have a single founding truth about reality which guides my beliefs. Fortunately this can be stated quite simply. It’s that… I think. While some may metaphorically “yawn” at this assertion, I consider it quite instructive. This teaches me a humility which seems quite warranted. Thus I don’t claim to “know” about reality (beyond the premise of course), but rather I have associated “beliefs.”

    (To this I may be asked, “But don’t you ‘know’ that 1 + 1 = 2 ?” Well yes, but this is merely an example of language, or a manifestation of my thought. I can’t actually “know” that 1 + 1 = 2 exists in reality itself beyond my thought. The same can be said of all such statements. I doubt that “words” exist beyond me, or if others exist, then beyond us.)

    From here perhaps my two principals of epistemology become predictable.

    P1: There are no true definitions.

    P2: The only process by which anything conscious, consciously figures anything out, is that it takes what it thinks it knows (evidence) and uses this to test what it’s not so sure about (theory).

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  29. Hi Eric,

    I am with Lichtenberg who said that “I think” was assuming too much and that the best we can do is “there is some thinking”.

    Maybe we could hedge our bets further and say “there appears to be some thinking (whatever thinking is)”.

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  30. Hi Robin,

    The idea that the criterion for ‘truth’ waa a product of the Quinean web came from what you said :

    Yes, our ideas about what “truth” is and about how to attain truth are indeed a product of the Quinean web. But that doesn’t alter the point that there is a big difference between what we believe to be the case and what is the case. Thus, the fact that a Westboro belief might pass their criterion for them to believe it true does not actually make it true.

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