The Münchhausen-Trilemma, also called Agrippa's
Trilemma (after the eponymous Greek Sceptic), is a philosophical
term coined to stress the impossibility to prove any certain
truth even in the fields of logic and mathematics. It is the name of a
logical proof in the theory of knowledge going back to the German
philosopher Hans Albert, and, more traditionally, to the sceptic
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 sceptics" 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
- 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
With reference to these five tropes, that 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 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."
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
- 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 at all. 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. Until now he
refuted them all in his long addendum to his Treatise on Critical
Reason (see below) and later articles.
- Hans Albert, Treatise on Critical Reason, Princeton
University Press, 1985, chap. I, sect. 2.