A white horse is not a horse.

The last time I was reading the Zhoangdze, I got sidetracked by footnotes about the following 白馬論:

  • “A white horse is not a horse.”

This is apparently attributable to Gongsun Long 公孙龙, a Chinese philosopher of the 3rd century B.C. = Era of Warring States 战国时代. How could such a wack philosopher be worth dignifying with a mention in the  庄子?

Juang Tzu

I got my answer from page 40 of James Gleick’s The Information. Like most ancient debates, this all relates back to Bill Clinton and Monica Lewinsky.

  • Big Bill Clinton, Rhodes Scholar: “That depends what the meaning of the word is, is.”

Too true, my man.

As Bill Thurston pointed out, students of mathematics regularly use the = symbol when it’s not appropriate (maybe an or or or set comprehension is what’s needed) just because it’s the only “connecting word” they know. But the meaning of “is” is too multifarious to always translate to the = symbol. For more tools of how to think about what exactly we’re saying with “is”, check out two papers I’ve linked on this site: Barry Mazur’s When is a thing equal to some other thing? and John Baez + James Dolan’s From Finite Sets to Feynman Diagrams.

You might have thought I would stoop to a seductive pic of Ms Lewinsky, but I'm too good for that. Here's an ancient map of China, Warring States period.

Back to the ancient Chinese stuff. What 公孫龍 was trying to say, was that

  • "white horse" “horse”

in the sense of the = sign. The = sign means you can freely substitute one thing for another—to the point of ridiculousness if you wish—without distorting the truth value. But using Gleick’s example,

  • “Lana doesn’t like white horses” does not mean “Lana doesn’t like horses”

Really "white horse" ⊂ "horse", a white horse is a kind of horse, but that means in an object-oriented programming sense we’re talking about class inheritance, not ===.

Now afore you go runnin afeart that the English | Chinese language is being shoehorned into mathematical symbology, read a couple sentences of Quine. In this case a bit of set theory and technical statements like “The set of all referents satisfying the criteria X also satisfy the criteria Y”, and thinking about alternatives to = like  and , actually makes our English-language thinking clearer.


UPDATE: Jeremy Tran explains that:

[As] I understand it. For “is ≡”, we use the phrase 一樣, while for “is ⊂”, we have 一種. These two concepts are relatively distinct from each other. The ‘proper’ translations for the two are “the same” and “a type of”, respectively. But often, those two are translated into English simply as “is”, which can lead to issues.

My Chinese isn’t exactly the best, so hopefully I haven’t made any big mistakes. But this is the gist of it. 😀

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