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The capacity for subtle self reflection is a defining characteristic of human consciousness. The power of a mathematical system can be measured by the level of self reflection or iteration definable within the system. Gödel's proof shows there is no finite limit to the levels of subtle self reflection in finite systems.
Higher levels of self reflection seem to be associated with higher levels of conscious experience. Evolution creates such structures because they have survival value. They allow better prediction of the consequences of one's actions. Gödel's result suggests that unbounded creative evolution of self reflection and consciousness is possible only if diversity expands without limit.