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This dialogue examined the relation between "han" in Miura Baien's Gengo and Sheffer's stroke in modern mathematical logic. Sheffer's stroke is the NAND operation in mathematical logic. It is expressed as follows: This operation denies that A and B can both be true at the same time. Moreover, NAND is a functionally complete operation. A whole logical system can be constructed from this single operation. In this sense, Sheffer's stroke may be called the smallest logical operator, or a logical atom, in modern logic. In contrast, Baien's "han" in Gengo is not mere opposition. It is a logical cut that divides the undifferentiated "one" into two and thereby generates the structure of the world. Baien thought in terms of "one is immediately one-one." The one is not an isolated unit. Through han, it opens into one-one. From this arise paired concepts such as yin and yang, ki and thing, nature and body, motion and stillness, and universe as space and time. In other words, Baien's han is the first cut by which the world is articulated. It is the fundamental operation for mapping existence. In this respect, there is a deep functional affinity between Baien's han and Sheffer's stroke. Sheffer's stroke generates a logical system in propositional logic by denying simultaneous truth. Baien's han generates the structure of the world in natural philosophy by cutting through incompatibility. In short, Sheffer's stroke is a logical atom for constructing the world of propositions. Baien's han is a logical atom for mapping the world of nature. More Fundamental than Yin-Yang Theory One important point confirmed in this dialogue is that Baien's han is more fundamental than what is usually called yin-yang theory. Yin-yang theory already presupposes the division into yin and yang. It can discuss alternation, circulation, complementarity, and harmony between yin and yang. But it already assumes that yin and yang have been separated. Baien's han belongs to the level before that separation. It concerns the first operation by which the one, not yet divided into yin and yang, becomes divided into yin and yang. Therefore, Baien did not merely develop yin-yang theory. He considered the more fundamental logical cut by which yin and yang first become possible as yin and yang. More Fundamental than Dialectics The same can be said of dialectics. Dialectics presupposes already established opposites: thesis and antithesis, being and non-being, proposition and counter-proposition. It begins from opposites that have already been set up, and then discusses their movement or synthesis. Baien's han, however, is the operation before opposites are established as opposites. It asks how one thing first becomes divided into two and how those two come to stand as mutually opposed terms. Therefore, Baien's han is not a concept inside dialectics. It is a more fundamental logical operation that makes possible the opposites which dialectics itself presupposes. More Fundamental than the Principle of Relativity This logical cut is also more fundamental than the principle of relativity in physics. The principle of relativity presupposes body A and body B, or observer A and observer B, in relative motion. It also presupposes that time and space have already been distinguished in some way. But in order for A and B to be in relative motion, A and B must already be separated. In order for time and space to be relativized, time and space must already be distinguishable. Baien's han belongs to a still deeper level. It divides A and B before A and B are already separated. It divides universe into space and time before space and time have already been distinguished. It makes possible the differentiation of subject and object, ki and thing, nature and body, before these have already been set apart. Thus, the theory of relativity is a physical principle that operates within an already articulated world. Baien's han is a logical-generative principle by which the world itself becomes articulated. Gengo as a Theory of Mapping What became clear through this dialogue is that Gengo is not merely an Edo-period book of natural philosophy. It is a system that logically maps the whole of nature. Baien did not simply list the things of the world as objects. He diagrammed how the world is articulated through cuts, and how it is structured through incompatibilities. In this sense, Gengo is not a catalogue of beings. It is a mapping system for the generation of beings. The basic operation of this mapping is han. Han is not mere opposition or negation. It is a logical cut that opens the undifferentiated one into two, establishes the two as a pair, and then constructs the world through a chain of such pairs. This structure can be connected with modern information science, knowledge representation, graph theory, binary trees, logical operations, and the conceptual structures of AI. In particular, if Sheffer's stroke is understood as a logical atom, then Baien's han can be understood as a logical atom for mapping the world of nature. Significance in World Intellectual History Sheffer's stroke was discovered in modern logic in the early twentieth century. However, long before that, in the Edo period, Miura Baien constructed a system that used the logical cut called han to map the whole of nature. Of course, Baien did not formulate NAND as modern mathematical logic. But he used, as a fundamental principle of nature, the operation by which things cannot simply stand together at the same time, by which mutually incompatible things establish each other, and by which one opens into two. This is not merely yin-yang theory. It is not merely dialectics. It is not the principle of relativity. Rather, it asks about the cut itself, which all of these systems already presuppose. This discovery is important not only for the history of Japanese thought, but also for world intellectual history. Miura Baien, in the Edo period, constructed a theory of mapping the whole of nature by using han as a logical atom. Gengo is a book for reading the world, but it is also a system for operationally mapping the world. Baien's han is the smallest logical operator that drives this system. In this sense, Gengo should be rediscovered in the age of AI as a knowledge representation system that emerged from East Asia. |