I recently came across the Münchhausen trilemma, which I think helps to explain my question. Basically, according to the trilemma, we have three options for explaining the ultimate justification of our knowledge: coherentism, foundationalism, and infinitism.

My question concerns how we can rationally choose any of the three views. If someone were to accept one of the views, how would they justify their acceptance of that view. Well, they would need to offer an argument. Here's the problem though: To offer an argument, it seems that one must already assume a view of justification, which is of course circular.

To make my point more clear, here is an example: Suppose that Bob were to accept coherentism. Bob then proceeds to offer an argument in support of coherentism. However, for Bob to even be able to make an argument, he must assume that he is justified in accepting certain logical principles as true. The question can then be asked how Bob knows he is justified in accepting those logical principles as true. The answer Bob gives must already assume one of the views listed above, which is of course circular, because that's what's being argued about - which view to accept. For example, if Bob answers the previous question raised by stating that the laws of logic are self-evident or intuitive, he seems to be assuming a form of foundationalism. If Bob proceeds to offer circular arguments in favor of the laws of logic, then it seems he holds to some form of coherentism. And a similar point can be made concerning infintism.

So my question boils down to this: Given the options we have for accounting for the ultimate justification of our knowledge, how is it possible to rationally decide which option to accept, given the seeming difficulties I raised above?

  • 2
    Here is a recent question related to the Trilemma, and two good answers. philosophy.stackexchange.com/questions/64638/… I think your question is far better phrased.
    – Dcleve
    Commented Jul 28, 2019 at 5:15
  • « Presuppositionalism is a school of Christian apologetics that believes the Christian faith is the only basis for rational thought» (from wikipedia ) where would you class presuppositionalism along the 3 alternatives you give? Note that currently fashionable p-ists like Sye Bruggencate have a flat-earther-like notoriety for being asinine. This doesn't necessarily carry over to the more respectable founders like van Til and Haddon Clarke.
    – Rushi
    Commented Aug 19, 2019 at 8:23
  • More generally presuppositionalism need not be christian. What the Bible is to the Christian p-ist, the Koran would be to the Muslim the Torah to the Jew the Vedas to the Hindu etc.
    – Rushi
    Commented Aug 19, 2019 at 8:25
  • philosophy.stackexchange.com/questions/7325/…
    – alanf
    Commented Aug 19, 2019 at 9:01

9 Answers 9


You are correct, the Munchausen Trilemma shows that that none of our beliefs are justified knowledge, per the standards of reasoning.

As you note, the most subversive aspect of the Trilemma is that reasoning itself is no longer justifiable.

A brief excursion: Math, and in particular arithmetic and Euclidean geometry, were considered undeniable -- necessary. Yet now we know that math has multitudes of possible forms, and whether any of them apply to our world or not -- is a contingent, not a necessary fact. The refutation of necessity in mathematics followed the discover that the central example Kant used for necessity -- Euclidean Geometry, was not necessary at all: https://jhaponline.org/jhap/article/view/3438 And if the math that applies to our world is a contingent fact -- potentially arbitrary from a plenitude of options, then logic, which includes the set theory branch of math, is at risk of contingent arbitrariness too.

The historical view of logic is that it is: the “laws of thought,” “the rules of right reasoning,” or “the principles of valid argumentation.” https://www.britannica.com/topic/philosophy-of-logic These definitions give logic its traditional exalted status. However, logic has another less exalted reference, and that is as a Darwinian accident. We humans seem to have an inborn basic reasoning skill: https://www.scientificamerican.com/article/babies-think-logically-before-they-can-talk/ http://citeseerx.ist.psu.edu/viewdoc/download?doi= This basic reasoning is mostly effective, but has some major shortcomings: https://www.edge.org/conversation/daniel_kahneman-the-marvels-and-the-flaws-of-intuitive-thinking-edge-master-class-2011 When we use our inborn basic reasoning to critique itself, then correct the discovered shortcomings, we basically end up with formal Aristotelian logic.

But if one looks at logic as a just a set of propositions and postulated operation laws, then in principle one could postulate an almost infinite number of variant logics. This is a hypothesis that people have explored, and they HAVE come up with multitudes of self-consistent logic types, which would produce different truth outcomes from each other if applied to a problem: https://en.wikipedia.org/wiki/Non-classical_logic. Therefore Aritotelian logic has no special place or precedence, and any choice of a logic NEEDS justification. Yet per the Trilemma, no justification is possible.

If no beliefs are justified by our current form of rationality/reasoning, then philosophy and knowledge must both become non-rationalist. The response to this has varied between Europe and the US. In Europe, it has been an embrace of radical relativity -- IE postmodernism.

In the US it has typically lead to pragmatism, where one can justify beliefs based on the pragmatic criteria of their utility/effectiveness.

Elaborating on the consequences of the pragmatic re-evaluation of reasoning and rationalism: This involves accepting that truth is not an absolute -- but only "approximately true", and that reasoning is not itself justified, or always valid, hence logic problems such as circularity, or unjustified assumptions, are not fatal problems for an assertion or justification.

If one accepts this, then flawed justifications are not automatically rejectable, such as the Thomist "5 Proofs" of God. Showing they are not actually "Proofs" does not refute Thomism as a POV. One needs to evaluate its pragmatic effectiveness/value in explaining the world, and the revival of Thomism in recent years shows it is pragmatically useful.

Another application of this principle -- while Descartes' Foundationalism is actually questionable on several fronts (there have been challenges on selfhood, much more widely accepted challenges on God, and in particular challenges to the trustworthiness of our reasoning) he still assembled a pretty good foundational case, and much modern thinking is still indebted to him due to the usefulness of his argument.

The coherentist response to Munchausen's Trilemma may be logically circular, but the argument that we HAVE to be circular to build a worldview at all, is a highly useful and powerful one anyway.

Similarly, the entire basis of the validity of the scientific/empirical method to attain knowledge is an effectiveness argument -- IE it uses empirical justifications to validate empiricism -- in fairly explicit circularity. Yet science is demonstrably useful, hence the logically invalid justification is -- pragmatically still valid.

  • Well, the typical standard for "knowledge" is the consensus of experts. Which means that "it is popular to do so", if the popularity actually involves the consensus view of the relevant expert community, actually does "make it a fact".
    – Dcleve
    Commented Aug 20, 2019 at 15:06
  • My discussion does not presuppose Platonism or Formalism. The discovery that Euclidean Geometry was not intrinsically or logically preferable to any other geometry, and that our world is actually non-Euclidean, has a profound impact in how math, and it s nature is perceived. The subsequent discoveries that all sorts of other very odd and non-intuitive math speculations sometimes correspond with actual parts of our world just reinforced this point. Math is INFINITE. This is true, independent of Platonism vs. Formalism.
    – Dcleve
    Commented Aug 20, 2019 at 21:21
  • In empiricism, how do you propose to establish what is true, other than by expert consensus? How do you propose that one establish how to do logic, math, history, etc?
    – Dcleve
    Commented Aug 20, 2019 at 21:24
  • @jobermark The potential infinitude or math, and the intrinsic uncertainty of whether any specific concept within that infinite space couples into physics or not, are the discoveries I am citing. These are not the "position of formalism", I myself am a Platonist. I accept the reality of abstract objects. It is not Platonism which is refuted by these discoveries, but the claim of necessity. Necessity assertions involve constrained math options -- the infinitude of math, and inapplicability of most of it to the world, is what refutes necessity claims
    – Dcleve
    Commented Aug 21, 2019 at 21:19
  • All observations are theory laden, and subject to error. How do you propose to establish truth other than by voting?
    – Dcleve
    Commented Aug 21, 2019 at 21:21

Antifoundationalism is the other option. We can shift to observations of how humans actually practice reason, like Popper and Kuhn. And to pragmatism, or other non-rational criteria for analysing what we do, like Nietzsche and Foucault. These are typically unsatisfying in failing to account for the substantial power of pursuing mathematical and logical consistency.

For me the most satisfying reconciliation, is in Hofstadter's strange loops, which as described here has a longer and more honourable pedigree than generally recognised. As you may know the characteristic of strange loops is tangled hierarchies between different layers or orders, which can be thought of as combining the core types of knowledge foundation & more, eg circular reasoning to justify an axiom, which both are really justified by the useful structure generated in that process.

Formal equivalence is a key way in which different mathematical tools are identified as belonging to or being attachable to the same reasoning structure. This happened with matrix mechanics, the Schroedinger formulation, and the Dirac formulation, of quantum mechanics: where they are all equivalent but facilitate different operations, and so observations of dynamics. Tools like symmetry and Noether's theorem, don't as I see it get their power from being foundational but from bridging domains, in this case by identifying the geometrical consequences of conservation laws, we can jump out of the domains of GR & of QFT to look for bridges between those domains. There continue to be powerful and intriguing parallels between structures identified in pure mathematics and our reality, like the indications that octonions (the generalisation of imaginary numbers to 8 components, beloved of string theorists) and the E8 symmetry structure may be able to account for the specific ranges of particles we have.

The parallel I would draw to formal equivalence, is translatability between languages. It has to begin with some Rosetta stone equivalent, a sharing of modes of life and the language games that back up two languages do as to be accessible by a single mind. We see the issue with this in our inability to communicate with dolphins, even though frequency analysis suggests they use logic and grammar at least equivalent to a 3 year old human - and given variance among individuals and groups it's really inevitable there are some who are more sophisticated. Alex, a famous and really exceptional parrot raised by humans has shown the most sophisticated maths ability of any animal in the world, but no other parrot has reached that, and we have little to no idea what such exceptional individuals are doing in the wild (and may never, as they are wiped out by the pet trade). So, an overlap is established between languages, an equivalence by sharing modes of life, and then crucially each logical structure can be explored in terms of the other, with eg. the creation of loan words, the borrowing of new systems of numerals, and expansion of shared cognitive space. I would argue this is a classic example of developing a tangled hierarchy founded in modules of modes of life, rather than development toward a universal 'foundational' or transcendent language, because that would imply a single foundational or transcendent mode of life, and that is always changing diversifying, and reconnecting.

Following this, of particular interest is that strange loops may be able to account for autopoeisis, and provide a materialist account of consciousness in tangled supervenience, generated from our eusocial modes of life. Our cognitive capacities seem to have begun with creche-rearing and mirror neurons, and been further triggered at the paleolithic-neolithic boundary by the need to develop trading networks to survive climactic change when the human ancestor population bottlenecked. These steps can account for the development not just of language but cognitive structure in shared modes of life; dealing with the private language objection to the universality of maths & logic. They are then seen as tools for bridging and translating abstractions of modes of life, and for exploring between them using terms from other modes.

  • 2
    Interwoven sets of loops are still loops. You have still chosen circularity as a basis, even if your circles need to be of a given sort and pasted together to create larger structures. If your basis for axiomatics is via what circular structures the sets of axioms are bound together, you still need another source for the sets of axioms you bind together, if you want this to be a real departure from mere circularity. At some point intuition or usefulness has to be a real criterion, over and above strange looping.
    – user9166
    Commented Aug 19, 2019 at 22:56
  • "At some point intuition or usefulness has to be a real criterion" Absolutely. But I'm pointing to the difference from something seemingly purely aesthetic or about usefulness. How do explain the utility (distinct from usefulness) of mathematics, as 'just' language? It has to be appeal to the whole structure. Things like elegance and symmetry in maths & science go beyond usefulness, and indeed, reasoning. We step outside the Godelian system, adding to the hierarchy by intuition, but then systemising. Like, just start knitting where you are, latter find the pattern
    – CriglCragl
    Commented Aug 27, 2019 at 22:46

The Muenchausen Trilemma has been formulated by Hans Albert in Treatise on Critical Reason (1985) (Original German: Traktat über kritische Vernunft (1968)).

Albert uses the Muenchausen Trilemma to show that the search for final justification leads to at least one alternative of the trilemma:

• Circular argumentation

• infinite regress

• dogmatism.

Apperently, none of the three alternatives is satisying. Hence the conclusion is:

Dismiss the search for final justification.

• Accept that all general statements are hypothetical. Change your view point. Check whether you can falsify a proposed hypothesis. If yes, then make a better hypothesis.

Albert is an adherent of critical rationalism. He supports the principle of falsification as stated by Karl Popper.


You may believe that I don't know whatever I say I know, but then your belief is only a belief whereas what I know is actual knowledge.

That I can't justify that I know what I know doesn't make my knowledge disappear in a puff of logic.

Do you not know that reality exists? I hope you do. Yet, how do we justify that we do? Me, I don't know, and I certainly don't think anyone does.

Asking me to justify that I know what I know is like asking me to walk the shortest route between where I am and where I am. Sorry, no, the shortest route is that I don't need to walk at all.

How do you explain that there is something rather than nothing? I don't think anyone can explain that but whether we can explain it is irrelevant to the existence of reality. That there is something doesn't depend on our ability to explain why.

There is no solution to the Münchhausen trilemma.

However, the trilemma is only effective against the claims to knowledge we make about things we don't actually know, such as for example whether there is a material world as we think of it, or whether the tree I am looking at really exists as I naively think it does. The absence of proper justification shows it isn't knowledge but rational belief.

Yet, we don't need to know whether there really is a material world as we naively think there is. We only ever believe there is one and this is good enough. What matters is that we should exchange on what is best to believe and that our beliefs should help us survive and prosper. So far so good.

And then if most people can't resist calling our rational beliefs "knowledge", then let them justify their claims to knowledge.

There is no difficulty justifying one's rational beliefs, at least on principle. And if our beliefs turn out to be false, we just adopt different beliefs. This is the way science works. We started with simple theories and we just adopted new theories to accommodate discoveries that falsified our initial theories.

We have a long experience now of scientific theories being falsified and replaced by what we see as better theories. We also all have first hand experience of having our personal beliefs being falsified again and again. But we are never short on new beliefs to replace them and in any case we don't know how to know the world. We just keep going regardless just because we can.

Nobody can justify that science is knowledge but there is no difficulty articulating a good justification that science is our best belief. And if that is not even true, then we may have to change our belief at some point in the future. Meanwhile, we will keep relying on science.

The solution to the Münchhausen trilemma is simple. We just have to admit that we don't know what we don't know. And I think we can all live with the fact that we still won't be able to justify that we know what we do know.

While we don't seem to know the material world as we think of it, we do know quite a few things. Broadly, what we know are our qualia. Whenever I look--or rather believe that I am looking--at the blue sky, what I cannot deny is the blueness I subjectively experience. The suggestion that I don't know this blueness at the moment that I experience it is merely nonsensical. What I don't know, is whether there is really a sky as I think of it and that this sky is really of the same blue as the blueness I experience.

Obviously, I cannot prove to anyone else I know the blueness I experience, but I also don't need to. In fact, I don't even need to justify it to myself. All I need is to fail to be able to deny this blueness.

And I also don't need to believe, let alone know, that other people experience the same blueness. As a matter of fact, I don't think they do. All we need is that we should be able to communicate effectively and cooperate, i.e. agree on whatever actions we need to carry out.

Different computers using different operation systems and different standard of internal data coding can communicate with each other. We can communicate to some surprising extent with dogs and cats and most animals. And we act on the basis of this communication. And, although it is often protracted and laborious, we seem to be able to communicate and cooperate with each other.

Indeed, it is arguable that human beings are the most successful species in that respect, with now some degree of communication and cooperation and understanding extending over a big chunk of the 7 billion people living today on Earth. No only that, but we can still read, and understand, and therefore communicate, if only one-way, with many long-dead people like Aristotle and many others.

The Münchhausen trilemma is a necessary argument because it successfully falsify our many claims to knowledge and claims to knowledge are often made in support of bad ideologies. However, it would be a mistake to interpret the dilemma as proving we don't know anything. I certainly know pain whenever I am in pain and I have no good reason to believe that other people don't.

Our individual ability to know what we know is also the basis of our cooperation as a community of rational beings. The Münchhausen trilemma is a salutary reminder that humanity exists as the cooperation of individual human beings, which itself relies on the human individuals' capacity to cooperate.

  • Qualia (e.g. your final example of pain) are not strictly logical. The Trilemma is about strictly logical arguments. The trilemma does not intend to prove we know nothing, it proves that nothing can be known on a strictly logical basis. We need experience to back up axioms or to shrink the cycles of a circular argument or the divergences in an infinite regress. But we cannot directly share experience, so there is always uncertainty.
    – user9166
    Commented Aug 19, 2019 at 23:05

First, note that the Trilemma purports to show no truth is possible by an exhaustive argument. To claim no truth is possible is a radical claim that seems to clash with our intuition. Next, let's address an interpretation of your question. I think your question is best rephrased as following:

What is our justification for our justification, or how do we choose among axiomatic, infinite regress, or circular reasoning with symbolic reasoning to show our justification is right in producing truth and knowledge rationally, and how do we deal with the assertion of the Trilemma that it "demonstrate[s] the impossibility of proving any truth, even in the fields of logic and mathematics."

First, let's recognize that your question is highly metaphysical in nature, because the question regarding justification is dependent on your choices of epistemologies and ontologies to arrive at an answer. From Borchert's Encyclopedia entry on "truth", for instance, truth can be understood differently among correspondence, coherence, pragmatic, identity and deflationary theories of truth. Your statement "The question can then be asked how Bob knows he is justified in accepting those logical principles as true" calls for you decide what you consider "truth" before your question can be answered. Quine, considered an influential philosopher of the 20th century developed a disquotational theory of truth which asserted that truth-bearers, for example an assertion that alleges something is true, is essentially equivalent to the assertion itself and that truth is rather extraneous.

Since you haven't given your theory of truth, let's adopt one to see what happens rationally. In Wittgenstein's version of correspondence theory of truth (logical atomism), there must be a match between the truth-bearer (the abstraction purporting to assert a truth, be it a phrase or claim) and the atomic, objective fact (a real context of which the agent is aware). If your version of truth is coherent or correspondent, then as the article on the Trilemma suggests, you accept circular rationality which is still one of three unacceptable and exclusive choices. Another theory of truth might land you on one of the other horns depending on the theory of truth!

So, the question you ask is displaced by another, which is how do we select our theory of truth purely rationally, and the answer to that question seems to be from a scientific perspective that we don't at all. "[S]tudies have shown emotions to aid in decision-making processes." Decisions Can Be Complicated In fact, cognitive science has teased apart the brain into two systems (System I, fast and stereotypical and System II, slow and rational) which has lead to the death of Homo economicus, an assault on the Enlightenment's view of man's purported rational human nature. In fact, a Nobel prize was awarded to Daniel Kahneman for his work along with Tversky on how irrational decision making really is. (See Thinking, Fast and Slow, or Stephen Pinker's The Blank Slate for contemporary perspectives of the psychological origins of choice and what science says about human nature). Don't think for a second that the philosopher's mind is beyond the certainty of the scientific method.

This interplay between science and philosophy may be ultimately where to find the answer to your question, and consider why. The rational arguments and conclusions surrounding the chicken and egg (a rational, philosophical question) come in many shapes and sizes, but ultimately if one accepts evolution (an empirical matter), then clearly the egg comes first. Empiricism is more often the source of answers with certainty than pure rationality, because empiricism, or truths from intersubjective reality affect our values and choices in ways that mere speculation cannot. Perhaps the over-arching value in the Trilemma is not that one need not reject all notion of truth as the Trilemma claims to accomplish, but rather it demonstrates the metaphysics that our truths rest on are not selected rationally at all, but are subject to our biased, metaphysical presuppositions about truth. In fact, whether or not anyone agrees with this response will be a function of their metaphysical presuppositions.

Use Occam's razor here: what is more likely, that the rationalist argument of the Münchhausen trilemma, a self-professed Gedankspiel, actually demonstrates truth doesn't exist, despite it's prominence in Western philosophy's metaphysical developments of ontology for 2,000 years, that it's a mere illusion and there is no abstraction with pragmatic function called "truth", or that three horns failing to provide certainty is a clue that when we wield modality alongside truth, that ultimately what is true is a function of our physical being and our personal values and bias?


It seems obvious that we never would, and no one really suggested that we should. Your question misunderstands what is going on here.

I have three problems with this question: Why ignore the original motivation? Why should one choose a single option? and Why accept this level of logic as the only standard for understanding?

The trilemma is actually only three out of a set of five. They are isolated from Sextus Empiricus' list of reasons to suspend judgement: the Five Modes of Dispute, Regress, Relativity, Hypothesis and Reciprocity. These are reasons not to doubt, but to suspend judgement.

Suspension of judgement is not refusal to believe, it is a reason to compare your options as they arrive, without becoming attached to any one of them. It is a reason to never choose a single reason to believe anything that you do believe, but to accept it provisionally, as a compromise between multiple perspectives and subject it to constant testing. So the question ignores the context of the argument -- problem 1.

The Trilemma suggests that Reciprocity = Circularity, Regress = Regress, and Hypothesis = Axioms, are the only three of these that matter. But that requires a very rigid form of logic, which has ruled out vagueness and emotional resonance up front. You don't have to do that. You can admit the other two modes as terms by which to judge your use of the three purer modes.

We do not, whatever mathematicians may tell you, choose axioms at random. We choose them because they have some kind of beauty, or because they provide a productive way of looking at a situation.

The former of these two reasons is a part of the standard of Disputation. Arguments of certain sorts feel good. They just do. And we will trust that. We just will. Because when push comes to shove we are evolved animals. Why fight that?

The latter reason is a part of the standard of Relativity -- the math works as the explanation of the needed result. Neither is more basic, and they support one-other's importance. The math has truth relative to our finances and the building of our houses. That truth need be no deeper.

But each of these is also useless alone, they are just appeals to our animal nature or to our current circumstance. It is only by connecting these kinds of things into an axiomatic and deductive structure that we really make headway. We therefore make the best progress combining the modes, and not selecting one - problem 2

And we need these two 'squishier' modes. We know better than to think that even mathematics can proceed from a single first principle. We need sets of axioms, and we need experience or intuition to choose or discard those. That is how we get from religion to science. We plan to be able to destroy our own bases and reinterpret our situation. Throwing those things out puts us totally at sea about everything in our lives, not just our beliefs. Do you trust your landlord? If so, not on the basis of any of the three 'pure' modes. You do it on the basis of intuition and experience, even if you weave those into a larger framework like understanding his best self-interest as a common motivation. So for reasonable belief, you really need non-logical content -- problem 3.

As a whole, in context and all together, this way of looking at the world (skepticism) works. It suggests something like a simplified Kuhnian view of scientific advancement. We accept our data and try to unify and concentrate it, until we don't, and then we try again. As we fail, we do not believe nothing, we accept what we have.

  1. That is where the failure occurs, as for each of those schools you have to assume them as axioms, continually define them, and observe circularity within and or between them (and they are circular).

  2. The trillema observes a basic form of platonism where the assumption represents a point of observation, the continuum linearism, and circularity of axioms...the circle.

  3. This necessitates dually Neitzchian perspectivism as well, as the nature of assumption (as perseptive) is grounded in platonic forms. Heideggers observation of time being grounded in a point (assumption) progressing (line) to another point (assumption) with the reverse of this progress observed a connection (cycle of assumptions) also observe time as being a priori in a kantian sense due to its grounding in platonic forms.

  4. This also further necessitates Parmedian wholism (where each aspect of the trillema represents one fundamental form as the monad ⊙) and dually Democitus' atomism as the observation of many assumptions as many "points of view" equivalent to atoms within a jungian zietgiest (which represents a whole point of view in itself).

  5. Then you have Wittgenstiens language games and private language which deals with the problem of symbols following this trillema...or peirces triadic logic which necessitates symbols following this say projective divergence of one symbol to another.

  6. The progressive recursion of axioms observes a linearism, as well as the inversion of one axiom to many...thus necessitating taoism as order (repetition and symmetry) and chaos (isomorphism as inversion of one assumption into a fragmented stated) This can be observed within the Neitzchian apollo and dionysus metaphor.

  7. So you have alot of options, not limited to any of the above nor the arguments applied. Best just to assumed all the philosophers as all the philosophers grounded their arguments in assumptions thus can be viewed as variations of the trillema.

Best to look at the common elements of the trillema as a representation of the monad (point, line and circle) as platonic forms where form is the purest assumption we can make with all assumptions existing through form.

Hope this helps, I may have to clarify some points or expand upon them.


Analytic–synthetic distinction
Analytic propositions are true or not true solely by virtue of their meaning:
thus we can know that "dogs are animals" entirely on the basis of the meaning of the words.

The Münchhausen trilemma is a key counter-argument against foundationism.
In epistemology, the Münchhausen trilemma, also commonly known as the Agrippan trilemma, is a thought experiment intended to demonstrate the theoretical impossibility of proving any truth, even in the fields of logic and mathematics, without appealing to accepted assumptions.

Analytic truth An “analytic” sentence, ... has historically been characterized as one whose truth depends upon the meanings of its constituent terms (and how they’re combined) alone.

We don't merely assume that a "dog" is an "animal" and not an "office building", this is completely proven entirely on the basis of the meaning of the words: {"dog", "animal", "office building"}.

Meaning Postulates Rudolf Carnap 1952 -------> ∀(x) (Bachelor(x) → ¬Married(x))
The above shows how one element of semantic meaning of the otherwise totally meaningless terms of: "Bachelor" and "Married" is specified by their relation to each other. To prove that Bachelor(x) is ¬Married(x) we simply refer to this established axiom.

This natural language axiom is not any mere assumption. It defines the process by which language acquires semantic meaning. Without such a process as this all expressions of language could be nothing more the meaningless gibberish.


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.

The foundation of analytical knowledge:
[I] Semantic meanings exist.
[II] Semantic meanings are encoded using language.

this forms a valid counter-example to the Münchhausen trilemma of the impossibility of proving any truth.

Every rebuttal to the claim that [semantic meanings using language exist] is self refuting because it is example of [semantic meanings using language] thus proving that [semantic meanings using language exist] is true.

This makes the assertion [semantic meanings using language exist] comparable to René Descartes [I think therefore I am], every rebuttal proves that the assertion is true.

  • 1
    Stating foundations is not the same as proving something. An axiomatic system can be engineered to only produce true propositions, yet it is still axiomatic, ie. it contains propositions which are, by definition, not proven but assumed. Given it is sufficiently expressive, not even every expression generated from these axioms can be proven.
    – Philip Klöcking
    Commented Apr 22, 2021 at 12:33
  • @PhilipKlöcking There is such a thing as self-evidently true propositions such that the meaning of their words proves the truth of their assertion. The assertion that words exist and convey meanings is proved by these words conveying their meanings.
    – polcott
    Commented Apr 22, 2021 at 13:29

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