A Foray into the Characteristica Universalis

One of the most consistent themes that emerged from Western interactions with the Chinese character is the idea of an algebra of ideas. Without diving into labyrinthian debates about whether the Sinoglyphs are pictographic, ideographic, or some other description invented by idle philosophers, it is safe to say that some Chinese characters behave like compounds, composed of components - atoms - and the meaning of the whole is associated with the components.

Now the Sinoglyphs, be they used by the Cantonese, the Shanghainese, the Hokkien, the Taiwanese, the Japanese, the Koreans, the Sichuanese, the Vietnamese, the Zhuang, and so on, are not anywhere near to being an algebra of thought by any serious measure. Though there were of course isolated examples amongst their repetoire of inventions that point us to how things might have been.

There were many folks who tried to gestate the characteristica universalis - an algebra of human thought - and many of them wandered in the twilight zone between artifical and constructed languages, formalistic logic, and abstract algebra. But I would say none had as much insight as Leibniz.

Suppose we consider the traditional, Aristotelian definition of man as a “rational animal”. We might consider man as a concept composed of “rational” and “animal”. In other words “rational” constitutes man. Here, “rational” and “animal” are atomic terms - they are prime. So, Leibniz assigned animal = 2, rational = 3. The composite concept of man can then be represented as the represented as the expression 2 * 3, or 6.

We can express this symbolically:

“rational” constitutes man ⇔ rational | man.

“animal” constitutes man ⇔ animal | man.

man is a rational animal ⇔ man = rational * animal

It is very interesting to note that this assignation of prime numbers to conceptual atoms by Leibniz was repeated by Gödel again in his proofs of his Incompleteness Theorems. This is slightly different from the encoding of characters with numbers in Unicode and ASCII, for the numbering employed herein is just natural numbers, which leaves no room in between numbers for composites. In fact, Unicode and ASCII are just a blind order of symbols, whereas the characteristica universalis is supposed to represent some underlying structure of the universe of concepts. In other words, the characterstica universalis is to represent a universe of concepts.

There is another time for us to talk about Gödel’s Incopleteness Theorem’s relationship with prime number. What’d I’d like to point out is that the words “rational”, “animal”, and “man”, can actually be replaced by Chinese characters, and by combining them on paper, according to the reasonable composition rules of Chinese character composition, you end up with the following statement.

By representing “rational” as 黹 and “animal” with 兽, and “man” as 人, we can translate the above as

“rational” constitutes man ⇔ rational | man ⇔ 黹｜人

“animal” constitutes man ⇔ animal | man. 兽｜人

man is a rational animal ⇔ man = rational * animal ⇔ 黹兽 = 人

If we treat 黹兽 as a individually standing character, it might have well been one that existed in reality as a historical artifact. Many Chinese have had very obscure but very distinct variants in history, in which the composition of the variant had demonstrated or advanced an alternative understanding to the meaning of character - or rather the underlying referent of the character - the underlying ontology or metaphysic of the referent of the character. The Taoists have some of the most ingenius inventions. 天 = 靝, or as represented here, where 青氣 = 天，萬丈 = 長，山水土 = 地，多年 = 久

There seems to be some kind of proto-logic here. And this logic seems to emerge from an origin completely different to western (i.e. modern logic) emerged from. This proto-logic here seemed to emerge from writing, a manipulation of symbols, and not from spoken language. And the writing it which it emerged from doesn’t seem to be a language at all. It seemed to be a pure, aesthetic mush, with some system of rules of how valid patterns are to be generated.

One can go slightly further and argue that there might be interesting results of applying Gödel’s Incompleteness Theorem to the the matured logic that one could extract from this proto logic. If “rationality” could be represented by 2 but also 黹, and “animal” could be represented by 3 but also 兽 , and “man” represented by 6 and 人, and you can have use numbers to represent logical symbols and predicates, and you can eventually encode entire propositions that talk about numbers in numbers, you can equivalently use sinoglyphs to encode entire propositions that talk about sinoglyphs. The question then is, what would the first incompleteness theorem say in its cousin version in sinoglyphs? If I recall correctly, the first incompleteness theorem says, “you can say stuff about numbers that are true, but you can neither prove nor disprove them”. What’s the sinoglyph equivalent? “You can say stuff about sinoglyphs that are true, but you can neither prove nor disprove them”?