All the limitative Theorems of metamathematics and the
theory of computation suggest that once the ability to
represent your own structure has reached a certain critical
point, that is the kiss of death: it guarantees that you can
never represent yourself totally. Godel's Incompleteness
Theorem, Church's Undecidability Theorem, Turing Halting
Problem, Turski's Truth Theorem-- all have the flavour of some
ancient fairy tale which warns you that "To seek self-knowledge
is to embark on a journey which ... will always be
incomplete, cannot be charted on a map, will never halt,
cannot be described."
-- Douglas R. Hofstadter. Gödel, Escher, Bach: An Eternal
Golden Braid (p. 697).