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.

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