Why is the Münchhausen trilemma an unsolved problem?

Question

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.

Answer 1

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.

Answer 2

http://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

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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.

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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.

Answer 6

"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.

Answer 7

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.

Answer 8

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"?

Answer 9

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).

Answer 10

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:

https://www.cs.umd.edu/~gasarch/BLOGPAPERS/social.pdf

Answer 11

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.

Answer 12

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.

Answer 13

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.

Answer 14

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.

Answer 15

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.