The ordinal logic system proposed by Turing in his doctoral thesis attempts to break through G ö del incompleteness through super poor iteration. But the problem is that it lacks uniqueness and convergence. Anyone can build an ordinal chain, but cannot form a global consensus. 2/ In other words, Turing's system cannot recursively converge and does not have a universally recognized 'unique main chain'. This makes it impossible to become a deterministic computing or consensus system in practice. 3/ In the 1990s, Nash proposed a transformation: Introducing the introspection mechanism of game theory into ordinal logic, the system is self constrained through Nash equilibrium and converges to a unique canonical chain. 4/ Nash called it a hierarchical introspective logical system. Essentially, it is still ordinal logic, but through dynamic game introspection, it solves the Turing version of the "non uniqueness" problem. 5/ There are two types of incompleteness that need to be distinguished here: G ö del (1931): Static logic incompleteness → self referential. Turing/Church (1936+): Dynamic computation is undecidable → derived from processes. 6/ Nash's Contribution (1990s): At the level of dynamic game theory, the global self referential problem is eliminated through introspection. The system is able to form internal completeness during evolution, breaking through the constraints of static logic. 7/ The implementation project of this theory is Bitcoin (2009). The principle of longest chain=hierarchical introspection logic Competition of miners' computing power=dynamic game field Forking is balanced and eliminated → converges to a unique chain 8/ Therefore, Bitcoin is not a simple distributed ledger. It is the realization of Nash's transformation of the Turing ordinal logic system: A hierarchical logic system that achieves a unique main chain through dynamic game introspection. Summary: Turing proposed ordinal logic, but without unique convergence Nash (1990s) → Introducing game introspection and converging to the main chain Bitcoin (2009) → Engineering Implementation, Forming Global Consensus and Time Order