February 19, 2011

道 = U, The Metaphysical Side

For a long time, I've treated 道 (as a noun) as the universe of discourse (U) and treat most literature on 道 as a primitive approach to logical reasoning in a pre-logical society (that is, one where formal logic and deductive proof was not actively developed). I have only discussed my justification for this kind of move in small circles because my intention was to reinterpret the entire Daodejing as a formal treatise of a sort that would earn it more attention from mainstream Analytic philosophers. I've called it a "set-theoretic reading" (you know, like a Marxist reading, just not stupid). The treatise remains a stunted work in progress, though I didn't see any harm in presenting a nice outline version of a major assumption of such a work for early criticism and commentary. That said, here goes...

Most of my justifications for claiming that 道 is U follow from the many comments that discuss features that 道 has or lacks, which I read in an attempt to understand 道 as a set. These are a few of my observations in that attempt:
  • 道 is infinite and the forefather of everything.
"Tao is a hollow vessel, And its use is inexhaustible!
Fathomless! Like the fountain head of all things."
-- Daodejing, 4:1~4:2 (trans. Lin Yutang)
I've deemed this "hollow" and "inexhausible" container (沖) talk as one about the 道 as something such that it does not merely inject to the natural number line, that there are, crudely, infinitely many things which are of 道. If 道 really is U, then it would be a "source of everything" or an "ancestor to everything," at least in the sense that everything about which we could possibly have a discourse would be a subset of or element of U.
  • 道 is abstract, and its empirically known subsets are not 道.
"The tao that can be described is not the eternal Tao."
-- Daodejing 1:1 (trans. Chan)
Chan's translation simplifies a matter very well. When they discuss 道 as a verb (as in "可道"), most translators often translate it to some sort of (often presumed) illocutionary act -- referring, addressing, describing, speaking, telling. This is less than mundane activity for Laozi, since it's practically a litmus test for determining if something is 道, or rather 常道 ("the eternal Tao"). If 道 is U, then Laozi outlining a basic fact about U, that none of its subsets except for those that equal U are U.

My interpretation further presumes that Laozi's "describing" (道, v.) refers to "describing from our five senses." In a pre-logical world, the abstraction of U would always appear as exist "before" the existence of everything else and of anything that we could see, or smell, or taste... The Daodejing offers that kind of treatment. 道, the U, is the source of everything; but more, it doesn't have any of the features of the things that we can access with our five senses.
  • 道 is the union of all possible contraries (whereas the intersection of them would be the empty set, ∅, or "nothing").
"The movement of the Tao By contraries proceeds; And weakness marks the course Of Tao's mighty deeds."
-- Daodejing, 40:1 (trans. James Legge)
"The things of this world come from something; something comes from nothing."
-- Daodejing, 40:2 (trans. Red Pine)
Legge's flowery translation does favorably portray the set-theoretic reading of these lines. The "contraries" (反) are the "action" or "proceedings" (動) of 道, since failing to account for complements of subsets of U would not generate U. People sometimes allude this first sentence to Taijitu, that of complementary forces working together (and seeing the 道 as U would make that move easier) and determining the nature of everything in nature, and for lay primitive theory, that is probably plenty adequate. However, what convinces me more that they're discussing an abstraction prior to set theory is the line that follows it: "Everything comes from something" (that is, everything that we can know is a subset of 道, of U, but also from subsets of 道 or U). "Something comes from nothing," though, interprets more openly under the presumption that 道 is U. There are things that we can derive from the empty set, such as all of the theorems of logic and the definition for natural numbers. However, it's a stretch to believe that Laozi or any pre-Han Chinese thinker had any such thoughts. Instead, thinking prior to a formal means of understanding subsets and nested sets, we may claim that our denotations for things don't "come from" anywhere. They're just presumptions, just in the way that U is a presumption. We need to assume U for discourse on any topic, just as ancient Chinese thinkers need to assume 道 for their discourse on references to make sense. Our noises and scribbles have to correspond to referents, and the collection of those references, in a pre-logical China, would be some part of 道.
  • There are narrowed 道, such as a "Way of the heavens" (天之道) and a "Way of mankind" (人之道). In logic, we can stipulate a narrower U (certain sets of numbers, for instance), but it is still defined as a union of all of the sets and elements that would still fit the definition.
"Heaven's Way (Tao) is good at conquest without strife:
Rewarding (vice and virtue) without words,
Making its appearance without call,
Achieving results without obvious design."
-- Daodejing, 73:3 (trans. Lin Yutang)
The ability to make stipulations like this allows Chinese thinkers to discuss other philosophical areas, especially ethics and politics. However, these metaphysical areas and ethical areas connect together in a very special way for Daoists, especially when it comes to pursuits of 天之道 and 非道, that is, those unchanging and overarching principles the guide our mortal world (and that is, pursuit of truth).

The defense of such a link is not foreign to us. Spinoza, Kant, and Wittgenstein derive their ethical stances from highly (logically) formal considerations of "the world"; and it would not be out of place for the philosophers of ancient China to appeal to an impartial, all-pervasive force (namely, 道) which would inform their ethos, as well. This is the approach that I will take when I approach the Ethical/Political Side, the sense that one could make of Laozi's ethics from a set-theoretic reading of the text.

February 13, 2011

Yang Zhu Does Not Acknowledge the Hooded Man

Earlier, I found a link to someone who was reading Yang Zhu for his language learning (Spanish-Chinese). Something struck me about that passage that reminded me of a rather prevalent paradox in the Western literature -- the Hooded Man. Both are interesting probes at the logic behind reference, particularly about knowledge of references.

The Hooded Man is one of the classic Sorites paradoxes that was introduced by Eubulides of Miletus in the 300's BCE. It has various renditions, but since I'm going to invoke Yang Zhu's parable, I'm going to make it match more closely to his story:
"You say that your dog knows you, but you came in wearing black clothes and he did not know you."
This is the problem that angers Yang Bu in the related parable, which Yang Zhu manages to reason to his brother to calm him:
"Yang Chu said [to Yang Bu]: 'Do not beat him [your dog]. You are no wiser than he. For, suppose your dog went away white and came home black, do you mean to tell me that you would not think it strange?'"
-- Liezi, 8:26 (trans. Lionel Giles)
What I find intriguing about these passages is that Eubilides is proposing a sort of linguistic or logical error to which we are prone, that he is criticizing our misuse of language or our faulty reasoning to express what we mean clearly. Yang Zhu's story is quite different, though. Yang Zhu is using this exact reasoning to show that such claims are not errors, but exactly correct expectations that follow from a straightforward reasoning. Thus, for Yang Zhu, no paradox exists here, just a difference in the two's understanding of reference.

Let's explore this more by using a descriptive theory of reference. The descriptive theory of reference is the theory (attributed largely to Bertrand Russell's essay, "On Denoting") to which Yang Zhu appears to be appealing. In it, our reference to Yang Bu is just relating to all of the things which he uses to define Yang Bu, which we can simplify to mean a variable for which a series of propositions are necessary to isolate just that one element.

We could say, then, that Yang Zhu is assuming the following: "x is (=) Yang Bu only if [P1(...x...) ∧ ... ∧ Pn(...x...)]", where P's are predicate that contains x as an argument. For the Yangist position, referring to Yang Bu is just referring to that x. In "proper names," we usually stipulate a few overlooked definiens, like that there is exactly one x to which the predicates apply, or that it refers to only those features that isolate him from other referents (including, perhaps, that he was named that). The problem is that different people have different definiens which may not always isolate the referent properly. In this case, it is that Yang Bu's dog thinks, "x is Yang Bu only if, among other things, x wears white clothes." He wasn't wearing white when he returned, so his dog barked at him because the dog thought that he wasn't Yang Bu.

What Yang Zhu explains to Yang Bu is that his anger is hypocritical because he reasons in exactly the same way. Yang Bu probably thinks, "x is Yang Bu's dog only if, among other things, he has white fur." The issue of reference, then, could be corrected with some reconsideration of those necessary conditions so that our imprecise communication matches our more precise intentions. (This interestingly turns us to the Heap paradox, which, despite its name, also has a straightforward rebuttal.)

The Hooded Man version, however, does not seem to employ this kind of reasoning. Instead, it makes a criticism of a different sort: "If x is (=) Yang Bu (a), then his dog knows him. x is still Yang Bu even if he wears black clothes, and yet his dog doesn't know him." These two sentences appear to contradict each other, but in fact, they do not. The paradox arises because of an ambiguity in the word to know, which Yang Zhu's explanation to Yang Bu correctly addresses.

But does this cohere with the original passage? We can read the original passage with some definitional contexts, and it doesn't appear to be the case at first glance. The ancient Chinese '知' is equally ambiguous with modern English's to know, unlike Spanish's conocer or saber.

A reading of the 白話 doesn't disambiguate, either, and Mandarin does have a means to disambiguate to know even more than the Latin languages do (including one for techne, one for episteme, and one for acquaintance)...
-- 新譯列子讀本, p.286
...so what avoids this supposed paradox and leads us to the more obvious conclusion?

It seems that both instances are changing the referent to what they didn't know. In the Hooded Man version, the dog doesn't know that Yang Bu is (=) the man in the black clothes. In Yang Zhu's version, the dog doesn't know that Yang Bu changed his clothes after he left. Because Yang Zhu accepted the dog's ignorance of a situation, and thus a failure of recognition, rather than ignorance of fixed entities (as Yang Bu did), it never occurs to Yang Zhu to think of this situation as paradoxical.

February 02, 2011

Yang Zhu, Yang Bu, and the Dog...in Spanish

A (presently anonymous) Spanish blogger and Chinese enthusiast has posted a Spanish translation of a rather popular Yangist anecdote from the 說附 chapter of the Liezi (26). Below is Lionel Giles's English translation of the passage (with links to the whole book's translation here):
"Yang Chu's younger brother, named Pu, went out one day wearing a suit of white clothes. It came on to rain, so that he had to change and came back dressed in a suit of black. His dog failed to recognize him in this garb, and rushed out at him, barking. This made Yang Pu angry, and he was going to give the dog a beating, when Yang Chu said: 'Do not beat him. You are no wiser than he. For, suppose your dog went away white and came home black, do you mean to tell me that you would not think it strange?"
-- Liezi, 8:26 (trans. Lionel Giles)
I have some thing to say about this passage and its possible relevance to the "the Hooded Man" Sorites paradox. Expect one in the coming weeks.