Münchhausen trilemma

Inepistemology, the Münchhausen trilemma is athought experiment used to demonstrate the impossibility ofproving any truth, even in the fields of logic and mathematics. If it is asked how any knowledge is known to be true, proof may be provided. Yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen trilemma is that there are only three options when providing proof in this situation:

• Thecircular argument, in which theory and proof support each other
• Theregressive argument, in which each proof requires a further proof, ad infinitum
• Theaxiomatic argument, which rests on accepted precepts

The trilemma, then, is the decision among the three equally unsatisfying options.

The name Münchhausen-Trilemma was coined by the German philosopherHans Albert in 1968 in reference to a trilemma of "dogmatism versusinfinite regress versuspsychologism" used byKarl Popper.It is a reference to the problem of "bootstrapping", based on the story ofBaron Munchausen (in German, "Münchhausen") pulling himself and the horse on which he was sitting out of a mire by his own hair.

It is also known as Agrippa's trilemma after a similar argument bySextus Empiricus, which was attributed toAgrippa the Skeptic byDiogenes Laërtius. Sextus' argument, however, consists of five (not three) "modes". Popper in his original 1935 publication mentions neither Sextus nor Agrippa, but attributes his trilemma toJakob Fries.

In contemporaryepistemology, advocates ofcoherentism are supposed to accept the "circular" horn of the trilemma;foundationalists rely on the axiomatic argument. The view that accepts infinite regress is calledinfinitism. Advocates offallibilism, though, point out that while it is indeed correct that a theory cannot be proven universally true, it can be proven false (test method) or it can be deemed unnecessary (Occam's razor). Thus, conjectural theories can be held as long as they have not beenrefuted.

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Contents

Agrippa and the Greek skeptics [ edit ]

The followingtropes for Greek skepticism are given bySextus Empiricus, in his Outlines of Pyrrhonism . According to Sextus, they are attributed only "to the more recent skeptics" and byDiogenes Laërtius attributed to Agrippa.The tropes are:

• Dissent  – undecidable dissension, resulting in an inability to choose or exclude anything
• Progress ad infinitum  – all proof requires some further proof, and so on to infinity
• Relation  – the object is considered only in terms of how it appears to the subject and in its relations to other things
• Assumption  – a premise is simply assumed without proof
• Circularity  – the truth asserted involves a vicious circle (seeregress argument, known inscholasticism as "diallelus")

[165] 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. [166] 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. [167] 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. [168] 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. [169] 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.

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 skepticism.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 toVictor 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."

Fries' trilemma [ edit ]

Jakob Friedrich Fries formulated a similar trilemma in which statements can be accepted either:

• dogmatically
• supported by infinite regress
• based on perceptual experience (psychologism)

The first two possibilities are rejected by Fries as unsatisfactory, requiring his adoption the third option.Karl Popper argued that a way to avoid the trilemma was to use an intermediate approach incorporating some dogmatism, some infinite regress, and some perceptual experience.

Albert's formulation [ edit ]

The argument proposed byHans Albert runs as follows: All of the only three 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, only the hopeless situation of infinite regression
• A circular argument can be used to justify, 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:

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 withrelativism. One example of an alternative is thefallibilism of Karl Popper and Hans Albert, accepting thatcertainty is impossible, but that it is best to get as close as possible to truth, while remembering our uncertainty.

In Albert's view, the impossibility to prove any certain truth is not in itself a certain truth. After all, one needs to assume some basic rules of logical inference 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 and later articles.

See also [ edit ]

• Theory of justification
• Anti-foundationalism
• Critical rationalism
• Duhem–Quine thesis
• Gödel's incompleteness theorems
• Pyrrhonism
• Tarski's undefinability theorem
• What the Tortoise Said to Achilles

References [ edit ]

1. Dogmatismus – unendlicher Regreß – Psychologismus Albert, Traktat über kritische Vernunft , 1968, p. 11, cited after Westermann, Argumentationen und Begründungen in der Ethik und Rechtslehre , 1977, p. 15.
2. Robert Nola, "Conceptual and Non-Conceptual Content", in : Karl Popper: A Centenary Assessment vol 2, 2006, p. 15
3. Diogenes Laërtius, ix.
4. Sextus Empiricus, Pyrrhōneioi hypotypōseis i., from Annas, J., Outlines of Scepticism Cambridge University Press . (2000).
5. Brochard, V., The Greek Skeptics .
6. J. F. Fries, Neue oder anthropologische Kritik der Vernunft (1828 to 1831).
7. Karl Popper, "The Logic of Scientific Discovery", p. 87
8. Albert, H., Traktat über kritische Vernunft , p. 15 (Tübingen: J.C.B. Mohr, 1991).

Further reading [ edit ]

• Hans Albert, Treatise on Critical Reason , Princeton University Press , 1985, chap. I, sect. 2.
• For Hans Albert's scientific articles see List of Publications in Hans Albert at opensociety.de

External links [ edit ]

• Epistemic regress atPhilPapers