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Münchhausen trilemma : ウィキペディア英語版
Münchhausen trilemma

The Münchhausen trilemma is a term used in epistemology to stress the impossibility to prove any truth even in the fields of logic and mathematics.
The name ''Münchhausen-Trilemma'' was coined by the German philosopher Hans Albert in 1968 in reference to a ''Trilemma'' of "dogmatism vs. infinite regress vs. psychologism" used by Karl Popper;〔
''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.
〕 it is a reference to the problem of "bootstrapping", after the story of Baron 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 by Sextus Empiricus, which was attributed to Agrippa the Skeptic by Diogenes Laertius; Sextus' argument, however, consists of five (not three) "modes". Popper in his original 1935 publication mentions neither Sextus nor Agrippa, but attributes his trilemma to Jakob Fries.〔Robert Nola, "Conceptual and Non-Conceptual Content", in : ^Karl Popper: A Centenary Assessment'' vol 2, 2006, p. 158.〕
==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. The view that accepts the infinite regress is called infinitism. Advocates of fallibilism, 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 been refuted.

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