The essence of modern computers is the engineering instantiation of the Turing Machine theory. They can strictly follow preset syntactic rules (i.e., program logic), but they cannot transcend formal systems to understand the semantics behind those rules. The reason lies in the fact that Turing Machines are defined within the computability scope of first-order predicate logic and cannot solve the decidability issues of their own logical systems. This means: even if a program is executed precisely, the computer cannot “understand” what it is doing—it is only “formally correct.”

Turing himself recognized this in his 1938 paper Systems of Logic Based on Ordinals, where he proposed the Oracle Machine and the transfinite iteration framework of ordinal logic, in an attempt to break out of the closed syntactic system of the Turing Machine and use higher-order logical structures (such as second-order predicate logic) to address the undecidability within first-order logic.

Within this theoretical framework, “semantics” is no longer merely the interpretation of formal symbols but becomes an evolutionary outcome within cross-layered decision structures. This also opens up a new pathway for us to understand human intuition, the generation of meaning, and even systems of collective consensus.

Bitcoin, precisely, is the epoch-making realization of this theoretical idea in reality. It is not an ordinary program but an artificial system that embeds semantics within its syntactic system. Although Bitcoin’s scripting language is a formalized system based on Turing Machine theory, its operational logic relies on the “decision structure” within the consensus process—the distributed oracle network (i.e., miners) making non-formal judgments about “what constitutes a valid transaction.” This structure embodies a “semantic consensus” beyond Turing-style computation: a decentralized decision mechanism that does not depend on a central interpreter.

Therefore, Bitcoin is not just a technical system—it is a paradigm shift from syntax to semantics, from formal systems to emergent consensus. Through engineering practice, it responds to the theoretical challenge raised in Turing’s doctoral thesis, marking the first time humanity has embedded a decidable semantic structure at the foundational layer of an artificial system.