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Wednesday, January 18, 2017

White Horse Not Horse 白馬非馬

About  2,400 years ago,  Chinese logician/philosopher Gongsun Long (公孫龍) made the assertion "white horse not horse". Since classical Chinese lacks indefinite articles, it could read "a white horse is not a horse" which resulted in massive confusions and the entire logician school was dismissed by Confucian mainstream as trivial sophistry.

The dialogue began when someone asked Mr Gongsun: "If a person has a white horse and you say 'white horse not horse', can you say he has no horse then?" (Quite a clever question. By induction, a horse of any color is also not horse. Therefore, horses don't exists!)  

Here's Gongsun Long's reply:

(1) 求馬,黃、黑馬皆可致;求白馬,黃、黑馬不可致。
(2) 使白馬乃馬也,是所求一也。
(3) 所求一者,白馬不異馬也;
(4) 所求不異,如黃、黑馬有可有不可,何也?
(5) 可與不可,其相非明。
(6) 故黃、黑馬一也,而可以應有馬,而不可以應有白馬。
(7) 是白馬之非馬,審矣!

My literal translation (which attempts to retain some of the ambiguity of Classical Chinese, my annotations are bracketed):

(1) When one looks for a horse, a yellow or black horse will do. When one looks for a white horse, a yellow or black horse won't do.
(2) If white horse is same as horse (i.e., we can freely interchange "white horse" and "horse" in the previous sentence), looking for a horse would be the same (as looking for a white horse).

(3) If (2) is true, then it follows that white horse is not different from horse.

(4) If looking for a horse is same as looking for a white horse, why a yellow or black horse won't satisfy the search for a white horse? (violates second half of (1))

(5) The condition is either satisfied or not, but it cannot be contradictory.

(6) Therefore, uniformly,  a yellow or black horse satisfies the condition of a horse, but not the condition of a white horse.

(7) White horse is not (equivalent to) horse,  that much is clear!

After I understand the argument, I can hardly believe the controversies! If you had "New Math" Set Theory in middle school, a simplest Venn diagram of two intersecting sets would make the argument completely self-explanatory. Part of the difficulty is Classical Chinese is very terse, part of the problem could be the Logician School was known to be good debaters and enjoyed making grand and shocking assertions -- sometimes taking advantage of the semantics.

The school was actually called "The School of Names" or  名家 。Unfortunately, almost all their important books were lost. I'd venture to guess the word Name could mean that they grappled with names & substance (名實), or maybe even symbolic logic as in the case the name "horse" is not interchangeable with the name "white horse". Regardless, I cannot but to come to the conclusion Mr. Gongsun was a deep thinker in his time, albeit a show-off.

 Zhuang Zi (莊子) was a (much more famous) contemporary of Gongsun Long, his criticism regarding this argument was:
(1) 以指喻指之非指,不若以非指喻指之非指也;
(2) 以馬喻馬之非馬,不若以非馬喻馬之非馬也。

My literal translation follows. Here I think the word 指 means the property or attribute of a thing, like the horsi-ness of a horse. Literally, the word could be a noun (finger) or a verb (point). Anyway, bear in mind Zhunag Zi is a very esoteric book and my translation is highly unconventional.

(1) Using an attribute to show what it is not, is not as clear as showing what other attribute the attribute in question does not possess.

(2) Using horsi-ness attribute to define what a (white) horse is not, is not as clear as showing not all horses have the whiteness attribute.

Or, simply: It's more clear to say "Not all horses are white, not everything white is a horse". 

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