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Keywords:

  • Jordan block;
  • dissipative structure;
  • Gödel's incompleteness theorem;
  • self-referential systems;
  • structure-matter dilemma;
  • artificial intelligence

Abstract

In 1986, Seel and Ladik asked, which role Gödel's incompleteness theorem should have in a basic theory of biology. Recently, the author has tried to collect the conditions, which such a meta-theory must fulfill. A further argument concerned the deeper connection between classical canonical forms of so-called (triangular) Jordan blocks in the description of open quantal systems far from equilibrium and those of self-referential contradictions and paradoxes in philosophy and mathematical logic. Related examples were quoted from the emergence of self-organization in so-called dissipative structures with applications to both fundamental- and of higher order levels of organization. To bring this analogy closer together, we have developed a quantum logical formalism, describing such a Gödelian situation, via the characterization of a well-defined “truth matrix.” In this setting, the modus operandi of exploiting self-referential traits and paradoxical inconsistencies emphasize the possibility of a meta-code in complicated enough (biological) systems. In conclusion, we will revisit situations were the aforementioned self-referential property, together with the laws of physics and chemistry will guide our understanding of biology. We will finally consider subsequent implications on the various positions on artificial intelligence. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010