Godelian Structures and Self-Organization in Biological Systems

作者：Brandas Erkki J^*

来源：International Journal of Quantum Chemistry, 2011, 111(7-8): 1321-1332.

DOI：10.1002/qua.22616

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

In 1986, Seel and Ladik asked, which role Godel'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 Godelian 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.

• 出版日期2011-7