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According to his own narrative, and totally unaware of Saint Augustine of Hippo’s as well as Nicholas of Cusa’s (aka Nicolaus Cusanus’) notion of learned ignorance (Latin: docta ignorantia), the Baron Münchhausen pulled himself (and his horse) out of a mire by his own hair [88, Chap. 4]. (This story is not contained in Raspe’s earlier collections [427].) In the following we shall be concerned with the question exactly why it is entirely hopeless to pursue the strategy suggested by the Baron Münchhausen; and why one should be concerned about this. More generally, is it (im)plausible to attempt to reach out into some external domain with purely intrinsic means; that is, by operational (from the point of view of intrinsic, embedded observers) capacities and means which cannot include any “extrinsic handle,” or Archimedean point?

Most likely everyone pursuing that kind of strategy – with the sole exception of the Baron Münchhausen – has drowned. But maybe something general can be learned from this flawed attempt of self-empowerment? And Münchhausen’s vain attempt to lift himself entirely (and not only parts of himself, such as his hair) indicates that some internal means – tactics which rely entirely on operations referring to, and movements within himself, with rare exceptionsFootnote 1 – are useless.

Epistemic issues resembling this metaphor have been called Münchhausen trilemma : as Albert has pointed out that, “if one wants a justification for everything, then one must also require a justification for those findings and premises which one has used to derive and justify the respective reasoning – or the relevant statements.” Footnote 2

With regards to the trilemma there seem to be only three alternatives or attempts of resolutions: either (i) an infinite regress in which each proof requires a further proof, ad infinitum; or (ii) circularity in which theory and proof support each other; very much like the ouroboros symbol, serpent or dragon eating its own tail; or (iii) a termination of justification at an arbitrary point of settlement by the introduction of axioms.

When compared with the original goal of omni-justification of everything all three alternatives appear not very satisfactory. This is well in line with ancient scepticism, and Albert’s three “resolutions” of the Münchhausen trilemma can be related to the tropes or Five Modes enumerated by Sextus Empiricus, in his Outlines of Pyrrhonism. These are in turn attributed to Diogenes Laertius and ultimately to Agrippa. These tropes are [548] (i) dissent and disagreement of conflicting arguments, such that conflict cannot be decided; as well as uncertainty about arguments; (ii) infinite regress; (iii) mean and relation dependence, relativity of arguments; (iv) assumption about the truth of axioms without providing argument; as well as (v) circularity - The truth asserted involves a vicious circle.

If one pursues the axiomatic approach – by holding to some (at least preliminary) theory of everything, then what can and what cannot be expressed and formally proven is (means) relatives to the assumptions and axioms and derivation rules made. Once a formal framework is fixed, this framework constitutes a universe of expressions. If such a framework is “strong” or “sophisticated enough” it includes self-expressibility by its capacity to encode the terms occurring within it, and by substituting and applying these terms into functions which themselves are encodable. While there is nothing wrong with self-expressibility – actually it has been argued in Chap. 2 that physics is bound to reflexivity – some conceivable expressions are paradoxical, and need to be excluded for “security reasons;” in particular, to avoid contradictions. This results in provable limits to self-expressibility; limits which are even quantifiable [125, 131].

This is very different from revelations about numbers, such as Srinivasa Ramanujan’s inspirations. In such cases, no bounds to expressibility can be given. Indeed, expressibility by intuition may be unlimited. It cannot be ruled out that some agents, such as human minds, have a more direct access to truth than, say, an automated proof system.

But trusting such claims is very problematic. The claims are not correct with respect to any axioms and derivation rules which one might have agreed upon as being valid, and therefore cannot be checked and found (in-)correct relative to the latter.

Of course, one might say, that ultimately there has to be trust involved. Because also in the traditional, axiomatic ways, the axioms and derivation rules have to be trusted. (Ramsey theory might be an exception.)