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Abstract: This article compares Belyiʼs Istoriia stanovleniia samosoznaiushchei dushi (ISSD) – his personalized scheme for the evolving self-consciousness of culture – with Bakhtinʼs concept of the “event”. It criticizes the contemporary neurological negation of notions such as “mind”, “consciousness” and “soul”, and explores the concept of self-consciousness in Belyiʼs poem ‘Samosoznanie’. It argues that, by implying knowledge of the world and the self, Belyiʼs understanding of “(samo-)soznanie” aims at a certain verbal and semantic completeness, or even integrity, which is considered an analogue of Bakhtinʼs term “so-bytie”, meaning the “being-together” of Self and Other in the event. Bakhtinʼs concept rejects the romantic philosophical idea of an all-embracing autonomous subject from the viewpoint of philosophical pragmatism in an avant-garde world. Belyiʼs axiological model of an evolving self-consciousness of culture in the Self repudiates Cartesian philosophy as “culturosophy” together with its positivist model of the world (which implies a Self separated from the world). In this way, the modes of thinking observed in Belyi and Bakhtin are complementary to each other. [Copyright &y& Elsevier]

Can the so-called first incompleteness theorem refer to itself? Many or maybe even all the paradoxes in mathematics are connected with some kind of self-reference. Gödel built his proof on the ground of self-reference: a statement which claims its unprovability. So, he demonstrated that undecidable propositions exist in any enough rich axiomatics (i.e. such one which contains Peano arithmetic in some sense). What about the decidability of the very first incompleteness theorem? We can display that it fulfills its conditions. That's why it can be applied to itself, proving that it is an undecidable statement. It seems to be a too strange kind of proposition: its validity implies its undecidability. If the validity of a statement implies its untruth, then it is either untruth (reductio ad absurdum) or an antinomy (if also its negation implies its validity). A theory that contains a contradiction implies any statement. Appearing of a proposition, whose validity implies its undecidability, is due to the statement that claims its unprovability. Obviously, it is a proposition of self-referential type. By Gödel's words, it is correlative with Richard's or liar paradox, or even with any other semantic or mathematical one. What is the cost, if a proposition of that special kind is used in a proof? In our opinion, the price is analogous to «applying» of a contradictory in a theory: any statement turns out to be undecidable. If the first incompleteness theorem is an undecidable theorem, then it is impossible to prove that the very completeness of Peano arithmetic is also an undecidable statement (the second incompleteness theorem). Hilbert's program for an arithmetical self-foundation of mathematics is partly rehabilitated: only partly, because it is not decidable and true, but undecidable; that's why both it and its negation may be accepted as true, however not simultaneously true. The first incompleteness theorem gains the statute of axiom of a very special, semi-philosophical kind: it divides mathematics as whole into two parts: either Gödel mathematics or Hilbert mathematics. Hilbert's program of self-foundation of mathematic is valid only as to the latter. [ABSTRACT FROM AUTHOR]