The School of Names is a group of philosophers in ancient China, who liked to discuss infinity and to enjoy seemingly contradictory propositions as regards infinity. The fact that they played with a variety of contradictions makes them look like the sophists or the Eleatics in ancient Greece. Concerning infinity, there can be found another thinker in the Middle Ages in West, Nicholas of Cusa, who, just like the School of Names, made the most use of the dialectics of infinity. They, the School of Names and Nicholas of Cusa, in my opinion, share more than just similarities in their opinions on infinity. Now, let’s see what we can find in them.
We will begin with the School of Names first. The philosophers are mainly three, Deng Xi, Hui Shi, and Gongsun Long. The founder of the school is thought to be Deng Xi. He is said to have said, just like Protagoras, that everything has two opposite sides, and he discussed infinity. Hui Shi is rumored to have had a wide variety of knowledge, and have enjoyed contradictory statements, which cannot be applied to reality. Gongsun Long, who leapt from category to category and, together with Zeno of Elea, stopped the motion on the earth, contributed to the development of the logic of the School of Names, insufficiently though.
The books by Deng Xi and Hui Shi haven’t been found by now, and that by Gongsun Long has so carelessly been copied that there are too many mistakes and errors in it for us to rightly and justly interpret his philosophical concepts. Their theses can be read in the books by certain thinkers of other schools, only in the form of fragmental conclusions. Therefore, it is hard to see who said what and how the propositions are explained and concluded. But we can at least make some guesses.
I’m going to write about Deng Xi first. Deng Xi may have been the first philosopher in ancient China to make a major breakthrough in the philosophical discussion of infinity, uncovering some of the contradictory aspects which infinity harbors.
Deng Xi, Contradictory Theses on Infinity
Infinity is a strange idea, one of the hardest to catch a clear image of. As a matter of fact, we, as a finite being, can by no means arrive at infinity; if we reach it, infinity is no longer infinite. However, the fact that, no matter how long and how far we go for it, we never reach infinity, definitely shows that we are infinitely moving to infinity: A finite being can never arrive at infinity; it just goes infinitely on and on to infinity; through the negation of infinity appears infinity as infinity.
The following two propositions can be thought of as Deng Xi’s, described a bit figuratively.
You will never finish cutting a whip into halves day by day.
Extensionless things cannot be piled up, and yet they will be as high as one thousand miles.
It is said that Chinese people like to express the abstract in a concrete manner, so ‘never finish cutting a whip into halves day by day’ and ‘one thousand miles,’ are both concrete and figurative expressions of infinity, which is abstract.
In the first statement, you find infinity because you are eternally, or infinitely, cutting a whip. To be in the eternal cutting means to be in the middle of ever cutting; you are in the middle of the cutting, and you haven’t finished anything, nor have you got anywhere, so, logically, you haven’t reached infinity; paradoxically, it is in this eternal doing that you find yourself caught in the infinite.
In the second statement, infinity is described both as ‘dimensionless things’ and as ‘one thousand miles.’ The former means infinity in smallness, the latter in height or largeness; to pile up something is something finite; so the proposition means a transition from infinity to finiteness and, once again, to infinity. One thousand miles, a finite number though a symbol of infinity, is suggestive of the possibility that you can get to the infinite and see what it really is. In a sense, we can and cannot reach the infinite; infinity is both reachable and unreachable. The propositions of Deng Xi implies that we can not only reach but also cannot reach infinity. Infinity is contradictory in itself.
Hui Shi, the Perspective of Infinity
Next comes Hui Shi. Hui Shi is one of the successors of Deng Xi. He views all from the viewpoint of infinity. Infinity makes everything the same. Think about Tokyo and London, which are far apart; seen from high above in a satellite, they are nearer; viewed from on the surface of the moon, they look much closer; the farther and higher you are from the two cities, the closer they appear. How about from infinity? Ideally, they occupy one and the same place. All the differences in distance dissolves into just one spot.
This dissolution does not apply only to space; the same goes for time. Today I’m in Tokyo and planning to go to London tomorrow. I know today is not the same as tomorrow; today I’m in Tokyo, tomorrow I’ll be in London; today and tomorrow are different, just as Tokyo and London are. However, ten years from now, I may confuse today with tomorrow; a thousand years from now, I’m sure I won’t mind mixing today with tomorrow; from infinity, I bet today and tomorrow will share the same instant, just as Tokyo and London are one and the same from the infinity of space. Hence Hui Shi’s propositions:
I know the center of the world; it is to the north of the farthest northern country, and at the same time it is to the south of the farthest southern country.
I left for Yue today and arrived there yesterday.
The sun is rising the highest, and at the same time it is setting. A living thing is born, and at the same time it is dead.
The first thesis means that any two places from the viewpoint of infinity shares the same spot. The second is that any two moments from the perspective of the infinite is just one moment. The third one, the same.
Gongsun Long, Category Mixture in the Eye of Infinity
The last Chinese philosopher I treat here is Gongsun Long, who, with intention, from the perspective of infinity, mixed the superordinate and the subordinate of the same category, and the subordinates among different categories: He jumped from category to category, which I’d like to term category leap.
A white horse is not a horse.
A chicken has ‘leg’, the right leg and the left leg; a chicken has three legs.
All is completely the same and completely different simultaneously.
A white horse is included in the group of horses, in which are found not only white ones but also black and yellow ones. A white horse is not the same as the horse as such. A white horse is just one subordinate of the category of the horse. They, a white horse and a horse, belong to the different levels of the same category.
‘Leg’ is the superordinate of legs in general, and the right leg and the left leg are each the subordinates of ‘leg.’ They belong to the different levels of the same category, like a horse and a white horse. However, from the viewpoint of the infinite superordinate, they can be found at the same level of the category. Since they are horizontally the same, they can be counted altogether. This is because infinity, including the infinity of category, dissolves all the differences of every finite thing.
What Gongsun Long asserts, in the proposition that all is the same and different simultaneously, is that the superordinate and the subordinate is different in our ordinary categorical sense, but at the same time no different from the viewpoint of infinity, just as God in Nicholas of Cusa’s thought system behaves both in the universal and particular fashion.
Time, Space and Category
Time and place each have a hierarchical order. Tokyo is one of the cities in Japan, Japan a country including all the cities of Japan, big and small. So, in terms of category of space, Japan is the superordinate of Tokyo, Tokyo the subordinate of Japan, either occupying different level of the category. Yet from the perspective of infinity of space, they are one and the same. Infinity dissolves all the differences concerning the category of space.
April is one month of Spring, the former included by the latter; April is one of the subordinates of Spring, the superordinate. December is, on the contrary, one month of winter, so April and December each constitute different categories. Yet the infinite eye sees them in one and the same instant. There cannot be found any difference between April, Spring, December, or Winter. No subordinate, no superordinate, no difference.
From this dissolution of all the differences in category of time and space, we can infer that not only time and space but everything other than them may lose the differences in category from the perspective of infinity.
If you look for a white horse, it won’t do to have either a white one or a yellow one; you look for a white one, so you won’t get what you want if a horse is black or yellow. However, if you look for a horse, then any horse, be it white or yellow or black, will be good enough; it doesn’t make any difference which color it has. But it won’t suffice if you get an elephant or a tiger. What if you deadly want to get a four-legged animal? Then any horse, white or yellow or black, any elephant, or any tiger will do, since they are four-legged. But a crow or a salmon won’t be enough. The superordinate embraces all its subordinates, which means that the more subordinate a thing is, the more it includes. From the infinite superordinate, anything will be its member, all the differentiations dissolved.
Nicholas of Cusa; Time, Space, and Category from the Eye of Infinite Being
Nicholas of Cusa is a big fan of the idea of Infinity, or God. He believes that Infinity dissolves all the differences in time, place, and category, though simultaneously differentiating the differences. Concerning time, according to Cusa, when we read a page of a book, we see the words one by one successively, which takes a certain amount of time. How long it takes to finish reading one page differs from person to person. A careful and slow reader takes longer, while a fast and passionate one shorter. On the other hand, God sees and understands the page at once, taking no time, and yet He goes at the pace of each one of us; He goes fast with a fast reader, and at the same time He reads slowly side by side with a slower one. Cusa wonders at His command of time, saying, “Simultaneously－from eternity and beyond all passing of time－You have viewed all books that have been written and that can be written, and You have read them at once; but You also now read them successively, in accompaniment of all who are reading them.”[De Visione Dei, chap.8]
Each and every one of the things in the world occupies its own time and space, and has its own unique features, distinguishing itself from other beings. Yet, from the perspective of infinity, all are just the same, dissolving into one.
How about the differences in place? Wherever we put ourselves, that infinite and loving Being is still watching us in the equal distance. Every spot lies in the same distance from Him, overlapping without any gap. All we have to do is, “draw near to the icon of God and situate yourself first in the east, then in the south, and finally in the west. The icon’s gaze looks at you in equal measure in every region and does not desert you no matter where you are.”[ibid. chap.4]
And category. Considering the appearance of a human being, how one looks differs from time to time. At one time a loving and glad look is seen, and at another time a sad and angry one found, in one and the same person. Or we can say that a look differs according as a person is a boy, an adult, or an old man. However, Absolute Sight, the superordinate of all the looks of human beings, “encompasses all modes in such way that it encompasses each mode.”[ibid. chap.2] Absolute Sight is a loving and glad look and at the same time is a sad and angry look; Absolute Sight is the look of a boy, of an adult, and of an old man as well. These looks differ but from the viewpoint of the absolutely, or infinitely, superordinate look, they are one as one. What Cusa regards as Absolute Look is not God, but I think we can say that it is something infinite.
Infinity integrates and dissolves all the distinctions of time, place, and and category. Which idea can be found in both East and West.
The propositions of the School of Names can be found in Stanford Encyclopedia of Philosophy.
Nicholas of Cusa’s writing can be read here.