A White Horse is not a Horse

No, not that one. That one's really not a horse. I mean to refer to a philosophical argument from China's Warring States period. The author is somewhat like Socrates, in that he questions the basic uses of language and points out difficulties in how our concepts apply to the world. He is unlike Socrates, if the historians are right, in that he did this chiefly for fun. For Socrates, these philosophical problems were the most important thing in the world -- literally worth dying for, if Plato's treatment of Socrates' defense and death are accurate.

For Gongsun Long, they were a way of entertaining at court. He offered five proofs that 'white horse is not horse.' You can read them all, and a careful analysis of them, at the link above. Here are two of the proofs by themselves, for you to wrestle with before you click through to read the analysis.

Argument 2.
If someone seeks a horse, then it's admissible to deliver a brown or a black horse. If someone seeks a white horse, then it's inadmissible to deliver a brown or a black horse. Suppose white horse were indeed horse. In that case, what the person seeks in those two cases would be one and the same. What he seeks being one and the same is the white one not being different from horse. If what he seeks is not different, then how is it that the brown or black horse are in the one case admissible and in the other inadmissible? Admissible and inadmissible, that they contradict each other is clear. So brown and black horses are one and the same in being able to answer to “having horse” but not to “having white horse.” This confirms that white horse is not horse.

Argument 5.
“White” does not fix what is white.… As to “white horse,” saying it fixes what is white. What fixes what is white is not white. “Horse” selects or excludes none of the colors, so brown or black horses can all answer. “White horse” selects some color and excludes others; brown and black horses are all excluded on the basis of color, and so only white horse alone can answer. Excluding none is not excluding some. Therefore white horse is not horse.

The translation is a bit confusing here. When he says "'white' does not fix what is white," he means that asking for a "white" thing doesn't tell you what kind of thing is supposed to be white. You fix the issue of just what is white not when you specify white, but when you specify the kind of thing you want. This is the same issue that caused Aristotle to divide the world into substances (like horses) and attributes (like being white). So it's not an idle thing to notice; Aristotle hung his basic ontology on the same point.