‍I. Starting Point: Where Does Meaning Come From?

How do we understand “meaning” and “subjectivity”? A profound philosophical perspective suggests that they do not arise from isolated events but from a chain of historical responsibility formed between events. Every event in life—a lunch today, a conversation in the afternoon—is formally independent, governed by its own “syntax” rules. Yet it is precisely these independent events that connect past and future, with later ones taking responsibility for earlier ones, together constructing a coherent and meaningful whole—namely, “who we are.”

This structure can be abstractly called a “historical semantic chain.” In contrast, each individual event resembles a first-order predicate system: a closed, rule-consistent “syntactic island” whose internal logic cannot endow itself with meaning beyond its boundaries.

II. The Limits of Computation: Soulless Machines

This philosophical model finds a perfect reflection in computer science. Computers, or their theoretical model—the Turing Machine—are classic first-order systems. They excel at executing preset algorithms (syntax) but do not comprehend the true meaning (semantics) of the data. As critics point out, computers are “purely syntactic,” lacking “subjectivity” and “intentionality,” because they are passive executors, not active entities capable of taking responsibility for their own history.

This limitation can be precisely described in logic using the Π₂ formula:(∀x)(∃y) R(x,y)

This formula expresses a structural commitment across time:“For every (∀) given challenge x, there exists (∃) a response y such that the relationship R(x,y) holds.”

It is a guarantee of sustained satisfiability—a closed, first-order Turing machine that only exists in the “present” cannot make such historical commitments.

III. Turing’s Vision: Transcending Systems through “Oracle” and “Iteration”

To break through the ceiling of first-order systems, Alan Turing, in his 1938 Ph.D. thesis, proposed two revolutionary concepts that gave formal systems the ability to construct history and meaning:

• ‍Oracle Turing Machine:An external higher-order “oracle” is added to the standard Turing machine. This oracle acts like an external judge capable of directly deciding problems unsolvable within the first-order system. It introduces a higher-dimensional judgment to the closed system from “beyond the domain.”‍
• Transfinite Iteration:A sequence of continuously evolving systems (S₀ → S₁ → S₂ → …) is constructed. In this sequence, each new system reflects upon, enhances, and affirms the previous one. This renders the system no longer static but capable of self-transcendence by accumulating and affirming its own history.
  

Turing’s scheme essentially introduces “historical awareness” and “external supervision” into formal systems—both of which are key to generating meaning and making Π₂-type commitments.

IV. Bitcoin’s Realization: A Working Philosophical Model

Astonishingly, the abstract theory Turing proposed nearly a century ago finds a remarkably concrete realization in Bitcoin’s blockchain structure. The Bitcoin network, as a whole, perfectly solves the Π₂ structural problem, thereby constructing a global consensus system without centralized trust.

We can establish the following clear correspondences:

V. Conclusion: From Syntactic Islands to the Semantic Continent

Bitcoin’s success is essentially a leap from syntax to semantics.

• Syntactic Level: Verification of individual transactions, calculation of individual block hashes (mining)—these are isolated, Turing-computable first-order tasks.

• Semantic Level: By linking independent blocks into a history-bearing chain via hash pointers, and by externally validating the chain’s uniqueness and legitimacy through a decentralized consensus mechanism (oracle), a higher-order architecture emerges.
  

It is precisely this architecture—combining historical continuity (chain structure) and external adjudication (consensus mechanism)—that allows countless independent computational acts (syntactic islands) to converge into a globally consensual, indelible meaning system (semantic continent).

From the philosophical inquiry into “responsibility,” to Turing’s exploration of computational boundaries, to Bitcoin’s reconstruction of “trust,” we witness an unbroken logical thread: True meaning and consensus do not arise from the self-consistency of closed systems but from an open, continuously evolving structure capable of bearing history and taking responsibility for history.