Ancient Symbolism and Textual Interactions. I: Chuang-Tsu Intertextuality II: Mathematical Inference of the Logicians

Chinese and Japanese Religions
Dr. Lowe
Reaction Paper Two: Ancient Symbolism and Textual Interactions.
I: Chuang-Tsu Intertextuality
II: Mathematical Inference of the Logicians
Kristoffer Martin

Author Note: I will be addressing two separate aspects of Symbolism and Textuality, divided as the subtitles suggest. In the second part of this paper I would ask that words and meanings be taken without subversive correction, many terms maybe new to the reader. Please reference the additional notes on new terms which will be the final page.

I: Chuang-Tzu Intertextuality
Chuang-Tzu utilizes circular symbolism and artifacts to describe the reality of the being and Dao. Many of these circular images describe the contradictions of human nature and thus force the reader to question what the meaning of existence is. In his argument of the “I” (我) he states, “People say to each other ‘I am I [me].’ How do they know that their ‘I’ is the real ‘I’?” He states that a man who is dreaming, and is of another “I” another being, cannot be told apart from the real man. (Chan, 200)
It is this metaphorical persuasion that intrigues and brought followers to his ideals and understanding of Dao. With in his workings these parallels influenced those who were able to understand it and follow the ideals. And from these people arouse other ideas and understandings of Dao. As Chuang-Tzu exerts the ideals and morals, he also expressed ideas of logical process and there in the art of science and mathematics. The philosophical rhetoric of this time used cryptic allegory and metaphor to speak of the ways of the natural world, in hopes of describing and discovering the ways of the after life.
This sentiment is described in Chuang-Tzu’s idea of movement or chi (气).
All species have originative or moving power (chi), when they obtain water they are small like silk. In a place bordering water and land they are like lichens. Thriving on land they become moss…The [insect] qing-ning produces the insect called qieng, qieng produces the horse, and the horse produces men. Man goes back into the originative process of Nature. All things come from the originative of Nature and all things return to it. (Chan 204)
Nature is regarded as the ultimate form, but is also the beginning and end. In this the ultimate goal is to show the connection man has to nature and how it affects and is the being of man. The textual structure consists of artifacts, such as silk, or the insect qing-ning, which common people would know of, and would be known through any variances of stories and common occurrence. His cryptic description continues in how he describes subjectivity and objectivity with the complex artifact of the fish in the Hao River.
Chuang-Tzu and Hui Tzu were taking a leisurely walk along the dam of the Hao River. Chuang Tzu said, “The white fish are swimming at ease. This is the happiness of the Fish.” “You are not fish,” said Hui Tzu, “How do you know its happiness?” “You are not I,” said Chuang-Tzu, “How do you know that I do not know the happiness of the fish?” Hui Tzu said, “Of course I do not know, since I am not you. But you are not the fish, and It is perfectly clear that you do not know the happiness of the fish.” “Let us get at the bottom of the matter,” said Chuang Tzu. “When you asked how I knew the happiness of the fish, you already knew that I knew the happiness of the fish, but asked how. I knew it along the river.” (Chan, 210)
What is interesting here is that there is a pluralized edict in comparison to the fish and the two men. Chuang-Tzu says that he knows the happiness of the fish, because he too is at ease while walking along the river. He is almost joking when speaking to Hui Tzu in this argument, because he points out the relative being of the fish to he and Hui Tzu. The fish become a symbol of that which flows with the river, as the river, as man (or men) flow in the Dao.
Chuang-Tzu’s logical rhetoric later lead to further development of experimental logic in understanding the being of nature and the connection man has to nature. How things work and move and change.
II: Mathematical Inference of the Logicians
Metaphysics is a recursive logic that uses parallels, metaphors, and allegories to attempt to explain the basics of the universe and how it works. From this process of logic modern sciences and mathematics were born. The Chinese Logicians used logic through inference to question the validity of reality and discuss how we determine and understand what we consider nature, Dao, or reality. One such argument on the being of stone is related to the actuality of nullified mathematics and the legitimacy of current mathematics.
Nullified mathematics is different from traditional counters because it changes the validity and basis of math counters altogether. Traditional counters or the common counter define an indifferent absolute zero, and an Nth numerator infinite. That is, the Nth series is 0, 1, 2, 3, 4, 5…etc. However, nullified mathematics begin the counter series with null. Null is the absolute nothing, and is represented in math by brackets []. The counter then follows as such, -1, -0, [], 0, 1, 2… The Logicians explore a similar principle to null in their discussion of hardness and whiteness of stone.
A. “Is it correct that Hardness, whiteness, and stone are three?”
B. “No.”
A. “Is it correct that they are two?”
B. “Yes.”
A. “Why?”
B. “When whiteness but not hardness is perceived, we have a case of two. When hardness but not whiteness is perceived, we have a case of two.”
A. “When whiteness is perceived, it is incorrect to say that there is no whiteness. When hardness is perceived, it is incorrect to say that there is no hardness. The stone is by nature so [hard and white]. Does that not make it three?
B. “When seeing does not perceive hardness but whiteness, there is no hardness to speak of. When touching perceives not whiteness but hardness, there is no whiteness to speak of.”
A. ”If there were no whiteness in the world, one could not see a stone. If there were no hardness in the world, one could not speak of a stone. Hardness, whiteness, and stone do not exclude each other. How could the three be hidden?”
B. “Some are hidden by themselves, [such as whiteness is hidden from touch]. They are not hidden because someone has hidden them.”
A. “Whiteness and hardness are necessary attributes of the stone that pervade each other, how is it possible that they hide themselves?
B. “Whether one perceives the whiteness [of the stone] or perceives the hardness [of the stone] depends on weather one sees or not. Seeing and not seeing are separate from each other. Neither one pervades the other, and therefore they are separate. To be separate means to be hidden.
A. “[The Whiteness] is the whiteness of the stone and [the hardness] is the hardness of the stone. Whether one perceives them or not, the two together [with the stone] make three. They pervade each other as width and length do in a surface. Is this not a [clear] case?”
“Some thing may be white, but whiteness is not fixed on it. Something may be hard, but hardness is not fixed on it. What is not fixed on anything is universal. How can it be the stone?” (Chan, 240-241)
Here the mathematical principle of null comes out. How can one be one, two be two, and so on? Numbers are constructed on this same principle logic; we must compare the nothing and something, which are not the same, hidden from each other, to discover the cardinality of nothing and something.
The hidden aspect of null and nth counters is like the hidden being of hardness from whiteness. When we construct a number we compare a something to null. And the idea of an infinite being finite becomes real. So if we take nothing, and put something next to it, there is no comparison. This cardinality is defined as zero. When we compare the next something, to the first group, we get one. There is only one possible countable comparison. We get the counter of [], nth0, nth1, nth2, etc.
It could be then argued, that the hidden null in traditional counters acts as the hidden connection in traditional thought that makes up the three in the addition of whiteness, hardness, and stone.

New Terms to be considered:
Nullified Mathematics: Null or nullification means the extraction of nothing, or literally nothing. Mathematics that work on the null counter make it the beginning counter, zero becomes a numerator of interjected Nth infinite counters.

Infinite Finites; the principle that any infinite is finite and anything finite is infinite; that is, if we take a length of any line (such as a|———|b) and denote it to be a length of one. It has a given limit, from point A to point B. These limits are a type of null, and this length actually includes the counters 0 and 1. If we divide this length in half, it will continue, mathematically speaking, indefinitely. This in fact is part of a fractalization of nullified mathematics.

Cardinality: The countable comparison between Nth objects, or infinite finite objects. In fact, there is only one truly finite object and that is null, all other counters are an infinite finites.

Chan, Wing-Tsit. Chinese Philosophy. Princeton, New Jersey: Princeton University Press, 1963, 1969, 1973.

Ancient Symbolism and Textual Interactions. I: Chuang-Tsu Intertextuality II: Mathematical Inference of the Logicians


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A discussion of Chuang Tzu philosophy and natural science logic, and the Chinese Logicians Metaphysical logic experiments in comparison to Nullified Mathematics.

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