Can the so-ca\led first incompleteness theorem refer to itself? Many or maybe even all the paradoxes in mathematics are connected with some kind of self-reference. Gбdel built his proof on the ground of self-reference: а statement which claims its unprovabllity. So, he demonstrated that undecidaЬle propositions exist in any enough rich axiomatics (i.e. such one which contains Peano arithmetic in some sense). What about the decidabllity of the very first incompleteness theorem? We can display that it fulfills its conditions. That's (...) why it can Ье applied to itself, proving that it is an undecidaЬle statement. It seems to Ье а too strange kind of proposition: its validity implies its undecidabllity. If the validity of а statement implies its untruth, then it is either untruth (reductio ad absurdum) or an antinomy (if also its negation implies its validity). А theory that contains а contradiction implies any statement. Appearing of а proposition, whose validity implies its undecidabllity, is due to the statement that claims its unprovability. Obviously, it is а proposition of self-referential type. Ву Gбdel'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 а proposition of that special kind is used in а proof? ln our opinion, the price is analogous to «applying» of а contradictory in а theory: any statement turns out to Ье undecidaЬ!e. Ifthe first incompleteness theorem is an undecidaЬ!e theorem, then it is impossiЬle to prove that the very completeness of Peano arithmetic is also an tmdecidaЬle statement (the second incompleteness theorem). Hilbert's program for ап arithmetical self-foundation of matheшatics is partly rehabllitated: only partly, because it is not decidaЬ!e and true, but undecidaЬle; that's wby both it and its negation шау Ье accepted as true, however not siшultaneously true. The first incompleteness theoreш gains the statute of axiom of а very special, semi-philosophical kind: it divides mathematics as whole into two parts: either Godel шathematics or Нilbert matheшatics. Нilbert's program of self-foundation ofmatheшatic is valid only as to the latter. (shrink)

От гледна точка на литературно философски анализ се обсъжда особения наратив на предание, в който са написани редица от произведенията на класика на българската литература, Йордан Радичков. Разказаните истории са сякаш от "памтивека". подобно на народни приказки и легенди с неизвестен автор и видоизменяни при всеки устен преразказ. чрез какъвто са единствено предавани.

The famous Bulgariann writer Yordan Radichkov's works are interpreted philosophically. The genre of philosophical and literary criticism is utilized. Any great writer referring to considerable questions of human life and being, and thus, philosophical. A few short stories, plays, and novels of Radichkov (1929-2004) are interpreted accordingly their philosophical content.

Стаття присвячена томістичній філософській антропології. Основний предмет якої структура буття особи. До розгляду взято аспект людського існування у світі "осіб" та "речей". The article is devoted thomistic philosophical anthropology. The basic topic of which is a structure of person being. The aspect of human existence is examined in the world of "persons" and "things".

Обсъден е преходът към пазарна икономика в Русия: от края на СССР до първия мандат на Путин, както и песпективите за социално-икономическо и политическо развитие.