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The Münchhausen-Trilemma, also called Agrippa's Trilemma (after the eponymous Greek Skeptic), is a philosophical term coined to stress the purported impossibility to prove any certain truth even in the fields of logic and mathematics. It is the name of an argument in the theory of knowledge going back to the German philosopher Hans Albert, and, more traditionally, to the skeptic Agrippa.
The term is ironically named after Baron Münchhausen, who allegedly pulled himself out of a swamp by his own hair.
These tropes are given by Sextus Empiricus, in his Outlines of Pyrrhonism. According to Sextus, they are attributed only "to the more recent skeptics" and it is by Diogenes Laertius that we attribute them to Agrippa. The tropes are:
Dissent - The uncertainty of the rules of common life, and of the opinions of philosophers.
Progress ad infinitum - All proof requires some further proof, and so on to infinity.
Relation - All things are changed as their relations become changed, or, as we look upon them from different points of view.
Assumption - The truth asserted is merely an hypothesis.
Circularity - The truth asserted involves a vicious circle (see regress argument, known in scholasticism as diallelus)
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 judgement. 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 judgement 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 judgement 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 judgement about both.
With reference to these five tropes, the first and third are a short summary of the ten original grounds of doubt which were the basis of the earlier scepticism. The three additional ones show a progress in the sceptical system, and a transition from the common objections derived from the fallibility of sense and opinion, to more abstract and metaphysical grounds of doubt.
According to Victor Brochard "the five tropes can be regarded as the most radical and most precise formulation of skepticism that has ever been given. In a sense, they are still irresistible today." 
 Albert's formulation
This argument runs as follows: All of the only three ("tri"-lemma) possible attempts to get a certain justification must fail:
All justifications in pursuit of certain knowledge have also to justify the means of their justification and doing so they have to justify anew the means of their justification. Therefore there can be no end. We are faced with the hopeless situation of 'infinite regression'.
One can justify with a circular argument, but this sacrifices its validity.
One can stop at self-evidence or common sense or fundamental principles or speaking 'ex cathedra' or at any other evidence, but in doing so the intention to install certain justification is abandoned.
An English translation of a quote from the original German text by Albert is as follows:
Here, one has a mere choice between:
an infinite regression, which appears because of the necessity to go ever further back, but isn’t practically feasible and doesn’t, therefore, provide a certain foundation;
a logical circle in the deduction, which is caused by the fact that one, in the need to found, falls back on statements which had already appeared before as requiring a foundation, and which circle does not lead to any certain foundation either; and finally:
a break of searching at a certain point, which indeed appears principally feasible, but would mean a random suspension of the principle of sufficient reason.
--Albert, H., Traktat über kritische Vernunft, p. 15 (Tübingen: J.C.B. Mohr, 1991).)
Albert stressed repeatedly that there is no limitation of the Münchhausen-Trilemma to deductive conclusions. The verdict concerns also inductive, causal, transcendental, and all otherwise structured justifications. They all will be in vain.
Therefore certain justification is impossible to attain. Once having given up the classical idea of certain knowledge one can stop the process of justification where one wants to stop, presupposed one is ready to start critical thinking at this point always anew if necessary.
This trilemma rounds off the classical problem of justification in the theory of knowledge.
The failure of proving exactly any truth as expressed by the Münchhausen-Trilemma does not have to lead to dismissal of objectivity, as with relativism. One example of an alternative is the fallibilism of Karl Popper and Hans Albert, accepting that certainty is impossible, but that it's best to get as close as we can, while remembering our uncertainty.
In Albert's view the impossibility to prove any certain truth is not in itself a certain truth. After all, you need to assume some basic rules of logical inference in order to derive his result, and in doing so must either abandon the pursuit of "certain" justification, as above, or attempt to justify these rules, etc. He suggests that it has to be taken as true as long as nobody has come forward with a truth which is scrupulously justified as a certain truth. Several philosophers defied Albert's challenge; his responses to such criticisms can be found in his long addendum to his Treatise on Critical Reason (see below) and later articles (see publication list).
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