Why is the Münchhausen trilemma unsolved? Couldn't anybody find some reasons for proving/disproving it? Or are there other reasons for it being called "unsolved"? the trilemma

If we ask of any knowledge: "How do I know that it's true?", we may provide proof; yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen trilemma is that we have only three options when providing proof in this situation: The circular argument, in which theory and proof support each other (i.e. we repeat ourselves at some point) The regressive argument, in which each proof requires a further proof, ad infinitum (i.e. we just keep giving proofs, presumably forever) The axiomatic argument, which rests on accepted precepts (i.e. we reach some bedrock assumption or certainty) The first two methods of reasoning are fundamentally weak, and because the Greek skeptics advocated deep questioning of all accepted values they refused to accept proofs of the third sort. The trilemma, then, is the decision among the three equally unsatisfying options. In contemporary epistemology, advocates of coherentism are supposed to be accepting the "circular" horn of the trilemma; foundationalists are relying on the axiomatic argument. Views that accept the infinite regress are branded infinitism.

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    Where have you found people calling it "unsolved" specifically? What attempts to deal with it have you seen? It would be helpful if we knew what you've already researched.
    – commando
    Commented Jun 21, 2013 at 14:01
  • 2
    It'd be nice to have a pithy summary of what exactly the trilemma is within the body of the question.
    – Uticensis
    Commented Jun 24, 2013 at 6:35
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    Is it a trilemma or simply a description of the facts? It seems to be the latter.
    – user20253
    Commented Oct 3, 2018 at 9:27
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    First of all, how do you prove it is unsolved?
    – RaGa__M
    Commented Jun 17, 2019 at 11:30
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    I would argue Hofstadter's model of strange loops is the only way to comprehensively address Munchausen's trilemma. In this view, we can picture each of the trilemmas tines as like a different part of the weaving process, to form a useful versatile structure, that is constantly being modified philosophy.stackexchange.com/questions/70266/… 'Why?' is our song; our answers are our shifting shimmering, plumage.
    – CriglCragl
    Commented Apr 19, 2021 at 11:54

15 Answers 15


Couldn't anybody find some reasons for proving/disproving it?

I think it is "dissolved" and not "unsolved".

Radical skepticism with regard to the possibility of ultimate philosophical grounding is based on an abstractive fallacy. It is somewhat misleading coherence to present the radical skeptic position in terms of an argument, because in presenting an argument one is usually committed to the truth of its premises and conclusion, whereas radical skeptics would suspend judgment with respect to them. Problems remain regarding the coherence of anyone who accepts the soundness of an argument whose conclusion is that we are not justified in believing anything. The so called Münchhausen trilemma can be overcome by recognizing that some presuppositions are necessary for the very possibility of intersubjectively valid criticism and argumentation. The “principle of fallibilism” which holds that any claim can, in principle, be doubted is only meaningful within an framework where some pragmatic rules and norms are not open to question. The Wittgenstein’s words are about throwing the ladder after using it to climb.

Whereas language is a medium for the communication of thought which exist independently of language, language is a vehicle of thought. What our words mean - hence what thoughts we have - is a function of what sentences we hold true. To entertain all the thoughts we currently have, while universally doubting their truth, is not straightforward. Anything may be dubitable, but not everything at once.

Ideas from Karl-Otto Apel, Wittgenstein.

  • Thanks . If you are sure that it is not unsolved . please delete it from en.wikipedia.org/wiki/List_of_unsolved_problems_in_philosophy
    – user21087
    Commented Jun 22, 2013 at 9:46
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    I find your answer very hard to understand and doubt that those who upvoted it have understood it fully. I take your answer to be a pointer to radical skepticism, which avoids the trilemma by stating that there is no justified knowledge. But what has this to do with language, frameworks, brains in vats, coherence and wittgenstein?
    – Lukas
    Commented Jun 24, 2013 at 15:35
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    @Lukas If you do not understand, it is perhaps because the ideas are very brief. People on this site do not like very long answers. The central idea is: There are problems regarding the coherence of anyone who accepts the soundness of an argument whose conclusion is that we are not justified in believing anything. The trilemma can be overcome by recognizing that some presuppositions are necessary for the very possibility of intersubjectively valid criticism and argumentation. The true skeptic is skeptical of his skepticism. The skeptic kicks the ladder after using it to climb. Commented Jun 24, 2013 at 16:34
  • Is that then again fundamentalism? Accepting 'necessary presuppositions' sound very much like it. Would be ok with me, but I'm not sure whether that is what you are saying :P
    – Lukas
    Commented Jun 24, 2013 at 16:49
  • @Lukas I'm not sure what is your doubt. The skeptic wants to prove that no proof is reliable. He is a snake eating its own tail. Commented Jun 24, 2013 at 17:24


According to the trilemma, every 'truth' is based on the circular argument, the regressive argument or the axiomatic argument. In all cases, the 'truth' can be denied.

No-one has found a way to give a truth based on another argument yet, so the trilemma is unsolved.

It isn't possible to say "the trilemma can't be solved": if that were true, it would be a truth that isn't based on one of the three arguments, which would solve the trilemma.


The Münchhausen Trilemma is unsolved, because noone successfully solved it yet. There are, for all three options: Coherentism, Infinitism and Fundamentalism, philosophers who hold one of the views, but each faces lots of difficulties.

  • How do you prove it is unsolved?
    – RaGa__M
    Commented Jun 17, 2019 at 11:33
  • @Explorer_N To prove it is unsolved would presuppose it is true and one can actually prove anything. But if it were true, we could never prove the trilemma itself, because in essence it says "you cannot prove anything satisfactory", so one could only prove it wrong, but never satisfactory prove it true. And if you can not even prove it true, how could you prove it unsolved ?
    – Falco
    Commented Jul 18, 2019 at 15:58
  • None of the solutions proposed stand up to scrutiny, hence it is unsolved.
    – Dcleve
    Commented Mar 15, 2020 at 17:49

This problem was solved by Karl Popper, who had an improved variant of this trilemma that he called Fries's trilemma, see "Logic of Scientific Discovery" escpecially Section 29. The solution is to accept the idea that proof is impossible and to drop proof as a standard. Rather, knowledge is created by conjecture and criticism. Criticisms are themselves conjectures about what might be wrong with your current ideas. All of your ideas and all criticisms should be left open to criticism. This standard is not problematic, unlike the requirement to prove ideas, which can't be met. For more details of Popper's rejection of the standard of proving ideas see "Realism and the Aim of Science", Chapter I.

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    Popper's "solution" is to accept tentative working hypotheses as our best approximation to "truth". But the rationale to use his empirical pragmatic "solution" itself needs at least pragmatic justification, and such a justification is circular (it relies upon empirical pragmatism as its "good enough" truth standard, IE it assumes its conclusion)! When Popper's "solution" itself fails the Trilemma, it is not actually a "solution", but instead just a proposed reconciliation to living with the Trilemma as unsolvable.
    – Dcleve
    Commented Mar 15, 2020 at 17:53
  • @Dcleve I believe Popper's idea is this seeming trilemma is a false problem once we change our past rigid conceptions about the descriptive mathematical precision requirement of any JTB knowledge. The justification part cannot be idealized as logical positivism's verification principle, it should be altered to falsification principle to form a logical negativism POV. All we can do is to identify the wrong knowledge, and there's no positive affirmative knowledge which can be described in either form of the purported "trilemma". It's a childish wishful thinking... Commented Apr 18, 2021 at 20:57
  • @DoubleKnot -- It is not a "false trilemma". See philosophy.stackexchange.com/questions/64638/… the trilemma remains fully operant after rejecting mathematical precision. and JTB. Falsification faces fewer logic problems than verification, but it also runs into an inability to JUSTIFY it as a criteria! And falsification actually does not work as an absolute criteria -- NOTHING can actually be falsified, as evidence ALWAYS underdetermines theory. Falsification and justification are only pragmatic approximations.
    – Dcleve
    Commented Apr 19, 2021 at 5:05
  • @Dcleve Thx for ur quick feedback. I religiously believe there're no really trilemma or dilemma in this ontic world, all these are due to our own limitations especially after the linguistic turn philosophers tend to define truth through usually self-referenced (formal) languages... I hold a kind a epistemic fictionalism, we can only say likeness never exactness, justified verification really means this epistemic knowledge more like ontology. Falsification can quickly make certain fictional "knowledge" more like fairy tale... It's not like a firm foundational building, more like a ship... Commented Apr 19, 2021 at 5:49
  • @DoubleKnot. The "linguistic turn" to philosophy is, I believe, one of the major errors of modern philosophy. Philosophy is about puzzling out the crucial subjects we don't understand yet. Focusing on the language we use while doing that is at best a massive distraction from the point. At worst, it prevents completion of useful philosophy, because the insistence on clear and well-defined terms would PREVENT understanding of the need to innovate in concepts and metrics to understand these subjects. But getting back to our subject, neither linguicism nor fictionalism solve the trilemma.
    – Dcleve
    Commented Apr 19, 2021 at 7:36

I recently tried to use the trilemma to better understand the limitations of full semantics of second order logic. I have now the opinion that the simplicity of the trilemma is treacherous, and it is not really clear what it says exactly.

I will now try to explain how the axiomatic argument caused me some confusion, and why I think that the regressive argument is treacherous, unclear and needs further elaboration.

The axiomatic argument is unclear about the situation where additional means for knowledge are postulated as axiomatic arguments. In my case I wondered about transfinite induction, but I think the problem is easier explained by one of Shakespeare's characters: The ghost of his death father appears to Hamlet and tells him that the new king is a murderer. Now even if Hamlet, by an act of faith, accepts that listening to the ghost is a way to acquire new certain knowledge, the knowledge itself will not be entirely based on the axiomatic argument, because also the fact that the ghost claimed it is important. However, Hamlet is only willing to believe the ghost, because he has other indications that the claims of the ghost may be true. So Hamlet also accepts the knowledge itself by an act of faith, and hence this example (and also my own example) is unable to disprove the axiomatic argument.

The real weakness of the trilemma is the regressive argument. Every argument that can ever be muttered is finite. But this implies that the intuitive interpretation of "ad infinitum" or "infinite regress" to mean a series of proofs that goes on forever cannot be the correct interpretation. A more reasonable interpretation is that of an unfinished argument. But it should be an unfinished argument where we have the option to hear further parts, but we don't know whether the argument will lead to an axiomatic foundation, or a circular argument, or stay a regressive argument. Another issue is that an actual argument is not a linearly ordered series of propositions, but a tree of propositions (or a directed graph, if we want to take circular arguments seriously). Some of the propositions in this tree might be proved by a circular argument, some by an axiomatic argument, and for some we can't decide yet how or whether they will be proved.

The regressive argument fails to distinguish different possible (valid and invalid) means of proof, because it doesn't investigate the consequences of "we can't decide yet where they will lead". If we can decide that an argument will never lead anywhere (for example because the propositions become less plausible instead of more plausible as the argument goes on), then it should no longer count as a regressive argument. Or at least it should be distinguished from a "proper" regressive argument. There might be more different cases hidden behind the regressive argument, but what has been said is already enough to clarify why I feel that the regressive argument needs further elaboration.

  • Very interesting considerations! +1
    – Joseph Weissman
    Commented Jun 22, 2013 at 15:47
  • Picture a small children asking "Why?" and whatever answer you give the reaction will be "Yeah, but why?". You'll either have to answer from authority "Because I say so" (axiomatic). Trick them by looping or you'll end up compiling answer after answer proof after proof only to be further interrogated why that actually works. So you essentially proof your method of proofing and then proof that method and that method and so on.
    – haxor789
    Commented Dec 14, 2022 at 12:34

"Because the Greek skeptics advocated deep questioning of all accepted values they refused to accept proofs of the third sort. The trilemma, then, is the decision among the three equally unsatisfying options." Here's my only critique, he qualifies that the third argument is "equally unsatisfying" by citing what the Greeks skeptics advocating deep questioning of all accepted values were. Prove that the Greeks are the authority on what constitutes an accepted value. Am I wrong, or does this sound like the Greek skeptics ideas are valuable because they are Greek skeptics? I understand this is merely the three possible positions, but it's the way the last one is lumped into the others that seems flawed in its reasoning.

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    I think it's fair to criticise claims to knowledge that are based on unsupported assumptions. If I claim to derive knowledge from my unsupported assumption of the existence of a flying spaghetti monster, I doubt you would accept those claims as well-founded. At very least we'd need a way of deciding what unfounded assumptions we can legitimately make without undermining our claim to knowledge - and where would that way come from?
    – digitig
    Commented May 9, 2014 at 18:21

The trilemma--as expressed above--contains its own solution, but then contradicts it. When it says that a proof may terminate by coming to an assumption or a certainty, nothing further needs to be said, since the whole point of the inquiry is to find out whether certain knowledge (i.e. "a certainty") is possible.

And since there are many examples of propositions which are known with certainty, it is irrelevant to say--as the trilemma does--that certain Greeks rejected "proofs of the third sort", for they are indeed proofs, and those Greeks are, with no justification, tossing the possibility of knowledge out the window.

One may say that the trilemma is unsolvable only because it has been defined to be so, by the covert inclusion of an unfounded Skeptical assertion that knowledge is impossible. Hence, the trilemma itself contains a circular argument and is therefore invalid.

  • An unsupported assumption is NOT a certainty! Providing demonstration that a certainty is necessarily certain, means THAT certainty at least satisfies the Trilemma. But then one has to justify the standards one used to argue and defend the supposed certainty, and then defend the standards for those secondary justifications too. Ultimately, you are back to unjustified claims.
    – Dcleve
    Commented Mar 15, 2020 at 17:58
  • In the end, argumentation is a social activity--one person's certainty could be another's unfounded assumption. I conclude from this that all arguments, if they are to exist at all, MUST begin with shared beliefs about the world, the rules of inference, and standards of proof relevant to the type of truth being sought. Without those, there is no possibility of discussion. This is true even when persuading one's self.
    – Mr. Lynch
    Commented Dec 23, 2021 at 21:01

It is a self refuting claim. If you use that type of argumentation to state that nobody can know for sure. How can you know for sure the validity of the claim itself "that nobody can know for sure"?

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    – J D
    Commented Mar 15, 2020 at 19:15
  • The trilemma necessitates a trifold nature to knowledge: All is an assumed point of view as the variable itself, All is a linear continuum as the progression of one variable to another where each variable is intrinsically empty in and of itself, all is a cycling of variables as self referential. The trilemma necessitates each variable as void, but this void is self negated through double negatipn resulting in the circularity of the variable.
    – Eodnhoj7
    Commented Apr 17, 2020 at 18:07

The trilemma has a fundamental premise, namely that all justifications are deductive in nature. This is problematic since the trilemma and its purported conclusion (the impossibility of proving any truth) is not itself deductively derived from any other statements. Albert himself claimed that the trilemma affected inductive, causal, transcendental and potentially other forms of justification too, but his reasoning, (which I don't have handy right now) is weak IMO. At least it's clear that the trilemma itself is neither inductively or causally derived either. (And most probably not transcendentally either.)

Transcendental pragmatics as developed by Karl-Otto Apel has focused on reflexive arguments to circumvent the trilemma, but this does not really answer the question why the trilemma itself is even considered as an argument. For this one needs to reflect on purely conceptual justifications. Following such conceptual reasoning the trilemma can be understood as saying "if we rule out self-founding (reflexive, conceptual or otherwise) statements only the three options remain" which, if taken as such a limited statement, is fairly plausible.

The main point I'm trying to make is that the form of justification the trilemma talks about (deduction) is necessarily different from the form of justification (or founding) that must be used to justify the trilemma itself (a conceptual one).

  • Well, this should have been the accepted answer, but that's not how philosophy works on the internet. Commented Mar 29, 2021 at 14:35
  • When new knowledge is created the stipulated relations between concepts of this new knowledge are encoded symbolically using language. There is such a thing as new knowledge the trilemma takes it as a premise that there is not.
    – polcott
    Commented Mar 29, 2021 at 15:10
  • Regarding ur fisr "The trilemma has a fundamental premise, namely that all justifications are deductive in nature." I don't think principle of sufficient reason requires deductive reasoning at all, in fact most reasoning in science are inductive. So this trilemma most concerns with inductions in practically every aspect except math... Commented Apr 18, 2021 at 20:49
  • How is it not inductively derived? It's essentially the "problem of induction" in that induction doesn't provide true knowledge but just a working hypothesis based on existing data that can still be false. Nothing else is that trilemma that argues based on existing data that any attempt at finding a universal truth so far has only produced those by means of axioms, infinite regress or circular reasoning. Which is in itself axiomatic. If it were truly true and not just accepted as truth, it would be a contradiction to itself as it would be a 4th option.
    – haxor789
    Commented Dec 14, 2022 at 12:51

I don't think the trilemma is unsolved: the third horn can produce valid arguments.

The way that this happens is this: an argument which begins from shared perceptions of facts, uses mutually agreed rules of inference in a mutually agreeable way, produces conclusions agreeable to the participants, at least to the level provided by the rules of inference (as in, for example, statistical arguments).

There will be those who object to this on the basis of it involving unproven aspects, or that it is messy or not "rigorous". I answer that we cannot escape the fact that argumentation is a social activity--an argument only matters if someone listens to it and judges it. Because of this, other social aspect present themselves: subjectivity, misused terms, and emotional button-pushing, to name only a few. For example, one person's certainty could be another's unfounded assumption. But usually, the differences aren't that stark, and the give-and-take produces a shrinking gap if people are genuinely committed to following the facts wherever they lead. In a real-life interactive argument, these can be pursued until no more dubitable ideas remain. (Or not, when one or more unresolvable stumbling blocks is found.)

Because argumentation is a social activity, what matters is not whether it constitutes "proof" under some arbitrary system of symbols and manipulation rules, but whether it persuades those who subject it to intelligent scrutiny at a level proportionate to the matter at hand.

Highly recommended: math proofs are social constructs:


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    +1 For demonstrating the validity in the application of rhetorical theory to logical discussion. I tend to believe that "philosophers" think their logos is somehow disembodied and in some sense absolutely true divorced from historical context and personal bias.
    – J D
    Commented Dec 23, 2021 at 23:07
  • Interestingly, this is your second answer to this question and only your second response on the form in 6 years. :D Care to comment on that fascinating fact?
    – J D
    Commented Dec 23, 2021 at 23:09
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    @J D - Thanks for explaining the upvote. It was that factor (the rhetorical/linguistic aspect) that was missing, before, and constituted something sufficiently different that I thought a new answer was called for. I rarely come to this forum--I only visit after I have left a comment on the software engineering forum and have some time to kill :D I looked at my old answer, started editing, then realized I wanted to start over. I'm toying with the idea of deleting the old answer.
    – Mr. Lynch
    Commented Dec 25, 2021 at 20:56
  • But this "truth" could still turn out to be "false" so how do we know it's a "truth" to begin with or does this modify the concept of what "truth" actually means?
    – haxor789
    Commented Dec 14, 2022 at 13:09

The dogmatic argument, which rests on accepted precepts which are merely asserted rather than defended. Münchhausen trilemma is overcome by this reasoning:

Stipulating relations between finite strings is the only way that arbitrary finite strings acquire any semantic meaning thus is not merely dogmatic. Language only acquires meaning on the basis of stipulating relations between otherwise arbitrary finite strings.

Although "a rose by any other name would smell as sweet" if we fail to assign any name to {a rose} then we cannot even refer to it.

The relationship between "dog" and "animal" is stipulated to be [is a type of]. The only way to prove that a dog is an animal is through other stipulated relationships.

The foundation of analytical knowledge is based on stipulated relations between otherwise arbitrary finite strings.

  • Which is just a different word for "axiom" a truth that is true because it is defined as true. Also you could find meaning in randomness on your own. Like humans are great at pattern matching and you can read poetry for example and find profound meaning in absolute nonsense.
    – haxor789
    Commented Dec 14, 2022 at 13:02
  • @haxor789 Of the entire body of analytic knowledge expressions of formal or natural language are only true if (a) they are stipulated to be true or (b) derived by applying truth preserving operations to (a) or the output of (b). [copyright 2018 polcott] This defeats the Münchhausen trilemma.
    – polcott
    Commented Dec 14, 2022 at 17:38
  • Which would make "(a)" an axiom: en.wikipedia.org/wiki/Axiom or be based on an axiom which is one of the trilemma options.
    – haxor789
    Commented Dec 14, 2022 at 18:27
  • @haxor789 The dogmatic argument, which rests on accepted precepts which are merely asserted rather than defended That cats are not dogs is not merely asserted and not supported, it is true by definition.
    – polcott
    Commented Dec 14, 2022 at 18:53

The trilemma is unsolved as it is inherent within the laws of identity and inseperable from them.

  1. "P" is an assumed variable as a point of view of the observer.

  2. (P=P) leads to an infinite regress as ((((P=P)=(Q=Q))=(R=R))=(S=S))=....

  3. (P=P) has the same premise as the conclusion thus is circular.


The problem here is ignorance. We don’t know the proofs of some proofs at some point. Also in some cases the axiomatic response is correct. For example, there is no point in proving the equivalence of two identical things, as in them being fundamentally the same entity.

A perfect example of the former case is the proofs of the various theories upon the origin of the universe.


The Münchhausen Trilemma is self-defeating by its own principle. It's an irrational stance to take, for if all proofs are left to those three options, then it follows that so is the proof of the Münchhausen Trilemma itself. Hence, it is self-defeating and thus irrational to accept. It fails to pass its own litmus test, as it were.

  • It's more of an inductive observation than a "truth". So more like a law of nature. Once you can prove an exception it automatically seizes to be a rule, but as long as you can't it seems quite reasonable to accept it based on the fact that it worked quite well so far.
    – haxor789
    Commented Dec 14, 2022 at 13:11

In epistemology, the Münchhausen trilemma is a thought experiment used to demonstrate the impossibility of proving any truth, even in the fields of logic and mathematics.

If we accept (as the Wikipedia article states) that the Münchhausen trilemma applies to analytic sentences, then sentences that are self-evidently true escape the Münchhausen trilemma.

Self-evidence In epistemology (theory of knowledge), a self-evident proposition is a proposition that is known to be true by understanding its meaning without proof...

"This sentence is comprised of words." is proved to be true entirely on the basis of the meaning of the terms: {sentence}, {comprised}, and {words} combined together to form the compositional meaning of the whole sentence.

  • It is the copula, ie. the logical operator linking these two classes, which is asserted without further justification here. It does not make a difference whether you say "A cat is an animal" or "The {cat} and {animal} classes really do have the specified inheritance relation on the basis of their defined sets of properties". Both are essentially saying the same thing and both are dogmatically stating something. "Reaĺly" is not some kind of magical justification, it is the standard guise of dogmatism.
    – Philip Klöcking
    Commented Apr 19, 2021 at 7:51
  • @PhilipKlöcking linking semantic means to the phonetic of symbolic representation in language is purely arbitrary. We could possibly encode {three is a number} as "I have a box of chocolates." The whole idea of numbers themselves and arithmetic relations between numbers is not arbitrary or dogmatic. It is a body of abstract conceptual knowledge that was created and it is true on the basis of its interconnected set of semantic meanings. It is neither circular, regressive nor dogmatic that {dogs bark}. Its encoding in English is purely arbitrary the underlying semantic meaning is not arbitrary.
    – polcott
    Commented Apr 19, 2021 at 14:41
  • What you describe would mean that you have to assume a) that there exists such a thing as a non-arbitrary system of semantic meanings, b) that this strictly corresponds to matters of fact in the world, c) that we can and do know that b) is true, and d) that we can develop a system of symbolic representation which strictly corresponds to and correctly mirrors a) and b), of which we, in turn, e) can and do know that it does so. That is an awful lot of justification which is missing there IMHO. And Occam does not like this additional layer of existence much, either.
    – Philip Klöcking
    Commented Apr 19, 2021 at 15:37
  • @PhilipKlöcking When a dog is actually barking such that the physical sensations of the dog barking are being experienced right now you could encode this in language as "an office building was just painted red" and the immutable fact of these physical sensations remains immutable (even if you are a brain in a bottle connected to a computer simulation).
    – polcott
    Commented Apr 19, 2021 at 15:46
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    I do not question that language tokens have meaning. I question that your theory does not need further justification, ie. I state that this answer does not provide what it pretends to do. You will have to justify further. You even pretend that it is not problematic that semantic meanings in the sense you imply can involve qualia (sensation of a dog barking) and abstract objects (classes like "animals"). Your post is textbook dogmatism.
    – Philip Klöcking
    Commented Apr 19, 2021 at 16:22

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