The gödelian foundations of self-reference, the liar and incompleteness: Arms race in complex strategic innovation

Self-referential calculations of oppositional or contrarian structures and the necessity to innovate to outsmart hostile agents in an arms race are ubiquitous in socio-economic systems, immunology and evolutionary biology. However, such phenomena with strategic innovation, which entails novel actions beyond listable sets, are outside the ambit of extant game theory. How can strategic innovation with novel actions be a Nash equilibrium of a game? Based on the only known Gödel- Turing-Post (GTP) axiomatic framework on meta-analyses of offline simulations that involve recursive operations on encoded information, we show that mutually mentalising agents capable of such offline simulations can "think outside the box" and embark on an arms race in novelty or surprises. A key logical ingredient of this is the self-referential encoding of a proposition on mutual negation or opposition, often referred to as the Gödel sentence. The only recursive best response function of a two-person game with an oppositional structure that can implement strategic innovation in a lock-step formation of an arms race is the productive function of the Emil Post set theoretic proof of the Gödel incompleteness result.