Thoughts on reading Basic Writings by Zhuangzi as translated by Burton Watson.

Here I have attempted to compile a portion of Zhuangzi’s thoughts on epistemological and ontological questions that arise in the study of mathematics.

On The Law of the Excluded Middle

Everything has its “that,” everything has its “this.” Fromthe point of view of “that,” you cannot see it; but throughunderstanding, you can know it. So I say, “that” comes outof “this,” and “this” depends on “that”—which is to say that“this” and “that” give birth to each other… Therefore thesage does not proceed in such a way but illuminates all inthe light of Heaven. He, too, recognizes a “this” but a“this” that is also “that,” a “that” that is also “this.” His“that” has both a right and a wrong in it; his “this,” too, hasboth a right and a wrong in it… A state in which “this” and “that” nolonger find their opposites is called the hinge of the Way.When the hinge is fitted into the socket, it can respondendlessly. Its right, then, is a single endlessness, and itswrong, too, is a single endlessness. So I say, the best thingto use is clarity. (35)

Now I am going to make a statement here. I don’t knowwhether or not it fits into the category of other people’sstatements. But whether it fits into their category orwhether it doesn’t, it obviously fits into some category. Soin that respect, it is no different from their statements.However, let me try making my statement. (38)

On Proofs of Indirection

To use a horse to show that ahorse is not a horse is not as good as using a non-horse toshow that a horse is not a horse. (35)

“The fish trap exists because of the fish; once you’vegotten the fish, you can forget the trap. The rabbit snareexists because of the rabbit; once you’ve gotten the rabbit,you can forget the snare. Words exist because of meaning;once you’ve gotten the meaning, you can forget the words.Where can I find a man who has forgotten words so I canhave a word with him? (141)

On Computational Complexity

Ziqi of Nanbo was wandering around the Hill of Shangwhen he saw a huge tree there, different from all the rest. Athousand teams of horses could have taken shelter under it,and its shade would have covered them all. Ziqi said, “Whattree is this? It must certainly have some extraordinaryusefulness!” But looking up, he saw that the smaller limbswere gnarled and twisted, unfit for beams or rafters, andlooking down, he saw that the trunk was pitted and rottenand could not be used for coffins. He licked one of theleaves, and it blistered his mouth and made it sore. Hesniffed the odor, and it was enough to make a man drunk forthree days. “It turns out to be a completely unusable tree,”said Ziqi, “and so it has been able to grow this big. Aha!—itis this unusableness that the Holy Man makes use of!” (60)

“Calculate what man knows, and it cannot compare withwhat he does not know… Yet mantakes something so small and tries to exhaust thedimensions of something so large! (100)

On Data Sparsity

Therefore great wisdom observes both far and near, and forthat reason, it recognizes small without considering itpaltry, recognizes large without considering it unwieldy, forit knows that there is no end to the weighing of things. (99)

Ruo of the North Sea said, “If from the standpoint of theminute, we look at what is large, we cannot see to the end.If from the standpoint of what is large, we look at what isminute, we cannot distinguish it clearly. The minute is thesmallest of the small, the gigantic is the largest of thelarge, and it is therefore convenient to distinguish betweenthem. (100)