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…

210 thoughts on “Munchausen’s trilemma and the impossibility of certain truth

  1. Daniel Kaufman

    DM: Unless you really think that these candidates for foundational beliefs are incorrigibile, indubitable, necessary, or somehow otherwise enjoy a special (transcendent) epistemic status — meaning, not just locally, within a language game — then you are some variety of what Wittgenstein describes in On Certainty. You allow that certain things must stand fast — and thus have special epistemic status — within certain language games, but nothing more than that.

    Liked by 1 person

  2. Robin Herbert

    Yes Dan, but as I said I am talking about the version being presented here, where everything, including confirmation by direct experience is only a provisional working assumption that may be abandoned.

    If someone says that one set of beliefs is objectively better than another set of beliefs on the basis of confirmability by direct experience, then tautologically, they are saying that confirmability by direct experience is an objective measure of the merits of a belief system.

    If anyone claims to be using no foundational axioms then they could not say this.


  3. Robin Herbert

    Presumably there is no fact of the matter of any language game being objectively bettee than another so in the language game adopted at the Westboro Baptist church, everything they say is true and everything they do is rational.


  4. Robin Herbert

    Hi Coel,

    That does not follow. The fact that something might pass the Westboro Church’s criteria for judging the truth does not make it “true”.

    But aren’t you saying that the criteria for truth are not foundational, that they are a product of the “web”?

    If so then their statements are true by the criteria produced by their web in exactly the same way that your statements are true by the criteria produced by your web.

    You can’t say that one set of criteria is objectively better than another.


  5. synred

    So there is no objective way of saying that the folk of the Westboro Baptist Church are more or less rational than the folk at the Center for Inquiry, or Carl Sagan or Jerry Coyne.

    My mother had some dementia as she got very old. However, she was still rational in the sense that if you looked at what she thought was going on her responses to it made sense.

    So in the context of there delusions, Westboro may reason rationally. People are a mixed bag.


  6. Daniel Kaufman

    Robin: My remarks regarding Westboro are on the Quinean view that I thought you were talking about and who never quite sheds his Empiricism in his “Web” days. (i.e. prior to Epistemology Naturalized.)


  7. Coel

    Hi Robin,

    If so then their statements are true by the criteria produced by their web …

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

    … in exactly the same way that your statements are true by the criteria produced by your web.

    But “true by the criteria produced by your web” is not the same as “true”, since we accept that all science and all knowledge is provisional and fallible.

    You can’t say that one set of criteria is objectively better than another.

    What do you mean by “objectively” here? If you want some criteria that is entirely independent of human brains and human thought processes, then, yes, I agree that there is no such thing. We can produce good arguments for why our web is better than theirs but such arguments are indeed dependent on human thought processes and so are not “objective” and not infallible.

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  8. Robin Herbert

    Hi synred,

    But on the “no foundational axioms, everything a provisional working assumption, truth criteria are the product of the Quinean web” view, the Westboro folk have no delusuons. Everything they believe is true in just the same sense as you or I or Coel considers something true.

    On this view there is no objective fact of the matter of whether it is they or we who are deluded.

    Moreover, if “science” refers to any method for getting at the truth and if the criteria for truth are what emerges from any given method of getting at the truth, then the statements of the Westboro folk are scientific facts in just the same as any scientific fact.


  9. Disagreeable Me (@Disagreeable_I)

    Hi Coel, Robin,

    You can’t say that one set of criteria is objectively better than another.
    What do you mean by “objectively” here?

    Well, I guess it depends if you buy into the idea that there is a real objective world that is out there, which for some reason is controversial in philosophy.

    But if you buy into that, then one can indeed say (by which I mean claim) that one’s own web of beliefs is a better match to the real world than that of someone else. One can also claim that one set of criteria is better than another set of criteria in the sense that it is more reliable at producing webs of belief that correspond to the real world.

    One can try to justify these claims with argument, but one can’t really prove it absolutely — only to within a reasonable doubt.


  10. Robin Herbert

    Now what I suggest is that to be a foundationalist is not to arbitrarily adopt a set of axioms and never question them.

    Rather it is to think that there are foundations with respect to what is and what is not true and that the human race have been slowly, imperfectly discovering and uncovering them and that it us not that they are not to be questioned, rather that some of them are no longer reasonably questionable.


  11. Robin Herbert

    Hi synred

    “So those of us w/o expertise should just not listen to you as we are unable to understand you anyway?”

    As far as I am aware ej is not an expert in philosophy either, correct me if I am wrong.

    But if not then he is in the same boat. If you don’t have the expertise to say the Hegel passage is nonsense, he doesn’t have the expertise to say it makes sense.


  12. SocraticGadfly

    I do see where I think Robin is coming from.

    If one rests one’s truth theories on a “web of belief,” in turn, they rest on either:
    1. A quasi-axiomatic definition that the web is, ipso facto, “valid” in the logical argumentation sense, or
    2. A quasi-justified true belief sense that empirical warrants Dan cites do in fact hold up.

    So, in a sense, one can argue indeed that Quinian types are some sort of foundationalists.


  13. synred

    Moreover, if “science” refers to any method for getting at the truth and if the criteria for truth are what emerges from any given method of getting at the truth, then the statements of the Westboro folk are scientific facts in just the same as any scientific fact

    –>Sounds very ‘post-modern’ to me, i.e., Bull Shit.
    –>For one thing religion in general claims absolute truth that no evidence can disprove and science does not. They can reason from their ‘beliefs’ (though some like the trinity are incoherent), but if reason leads them to an inconsistence they will abandon reason.

    Liked by 1 person

  14. ejwinner

    “So those of us w/o expertise should just not listen to you as we are unable to understand you anyway?”
    Well, plenty of people do that, there’s actually no shame in it. Philosophy is not a popular literary pursuit. Occasionally in the past it has appeared that way, and there have been philosophers able to write as public intellectuals in influential ways. But fact remains that philosophy requires reading, patience, an open mind, and a desire to come to grips with difficult arguments and lines of thought. Even philosophers struggle with this latter demand, which is why there are strong tensions between thinkers of differing, even opposing, traditions.

    I was reacting to your “Huh?” remark on Hegel, after all. Reading Hegel with understanding takes practice; the same is true of many difficult philosophic texts, including those in the Analytic tradition.

    “We shrug and move on …” This misses the point; the question is not whether we stop various practices and wait for an answer, and nobody expects that. The question is about developing an explanation of how and why our practices work. That’s in the nature of philosophy, and why it is not a science. Because such explanations are contingent upon what our practices reveal about the world and about ourselves. But they form necessary strands in Quines’ ‘web of belief’ that sustains our sense that we can trust our practices and what they reveal.


  15. Robin Herbert

    If one of these webs can be considered better than another, even if not known infallibly or certainly, then it cannot be by criteria that are products of that web, because their web is better than yours by criteria that are products of their web.

    The very possibility of one being better than the other implies that you think there is a foundational criterion, even if you don’t claim to know it infallibly.

    Liked by 1 person

  16. ejwinner

    My doctoral dissertation was on the influence of Hegel on contemporary literary theory. Apparently it was good enough that I was asked to teach an undergraduate course on this following graduation.


  17. Coel

    Hi Robin,

    The very possibility of one being better than the other implies that you think there is a foundational criterion, even if you don’t claim to know it infallibly.

    I’d phrase it that the possibility of one being better than the other implies that there is a truth of the matter, a truth that is independent of our thoughts about it. That does not have to be a foundational criterion, but can instead be a conclusion.


  18. synred

    ej: Hegel does not appear to define his jargon. How can I even tell f an effort to master it would pay off?\

    Wittgenstein in PI I can understand sentence by sentence, but have trouble assembling the trees into a forest [a]. To the limited extent I kind of get the gist, it comes from Dan’s interview with Broad.
    There are doubtless people that ‘explain’ Hegel, but dollars to donuts they are inconsistent with each other…

    I tried to read Edith Stein (a book I picked up at Dachau where she was murdered by the Nazi), but couldn’t get anywhere with that either and it was at least clear in parts.

    [a]My high school English teacher would give him a D.


  19. ejwinner

    yes, Hegel is extremely difficult to understand; one really has to devote some time reading him to get into his groove. Inconsistencies between his differing interpreters arise partly because it’s easy to get locked into one side of his notorious dialectic; but there are political concerns as well. Hegel was enormously influential in the 19th century, and remains influential in Continental philosophy; so a dominant interpretation will itself have influence on that tradition.

    The best, clearest introduction I can think of is Peter Singer’s “A Very Short Introduction” (yes, that Peter Singer).


  20. Daniel Kaufman

    Again, Quine’s web of belief is quasi-Foundationalist. The entire network — the web, taken as a whole — is confronted by experience at its periphery. The so-called “observation statements.” It is this periphery that connects the entire web to the world, and without it — with a pure coherence theory — you have real problems with truth. Because things that are entirely fictions can be internally coherent.

    Quine uses the web to explain the appearance of certainty — things like logic and mathematics are very near the center and thus, require changes across the entire web to disconfirm. Thus, they appear to be certain, but as Quine explicitly says, sufficient disruption at the periphery, among the observation statements, can cause enough changes in the interior to disconfirm even the truths of logic and mathematics.

    So, 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 and also, therefore, beliefs in the interior of their belief system.

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  21. Massimo Post author


    I’m sure you are right about Quine, but I never got that impression. Even observational statements can be doubted, so they are in no way foundational, they don’t anchor the web, and I’m not sure how privileged they are (though it is indeed the case that some threads of the web are thicker than others, so to speak). So I always thought of a web of belief as a good metaphor for coherentism, not foundationalism, and that’s the way a number of my colleagues teach it in intro epistemology. (But maybe I should go and have a word with them!)


  22. Daniel Kaufman

    Ready Jonathan Dancy’s Introduction to Contemporary Epistemology — one of the best Intro Epistemology texts on the market. It very clearly characterizes Quine as not fully coherentist. And if you read Two Dogmas of Empiricism, Quine is quite explicit about the epistemic status of observation statements being different from those in the interior, as the following from Two Dogmas hows:

    “The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. Re-evaluation of some statements entails re-evaluation of others, because of their logical interconnections — the logical laws being in turn simply certain further statements of the system, certain further elements of the field. Having re-evaluated one statement we must re-evaluate some others, whether they be statements logically connected with the first or whether they be the statements of logical connections themselves. But the total field is so undetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to re-evaluate in the light of any single contrary experience. No particular experiences are linked with any particular statements in the interior of the field”

    Observation statements, then, are the ultimate — though fallible –epistemic tribunal.

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