When a white horse is not a horse

When a white horse is not a horse is a famous paradox in Chinese philosophy. Around 300 BC, Gongsun Long wrote this dialectic analysis of the question "Can one legitimately assert white horse is not horse?", in a work now named for him, Gongsun Longzi, in a segment called the White Horse Dialogue ".

1. The original text
The White Horse Dialogue Baima Lun constitutes chapter 2 of the eponymous Gongsun Longzi. The purported author, also known as Master Gongsun Long, was counted among the School of Names AKA the Logicians or the Dialecticians in the Hundred Schools of Thought. Most of Gongsuns writings have been lost and the received Gongsun Longzi text only contains six of the supposedly 14 original chapters. Parts of the text are dislocated and some commentators and translators rearrange them for clarity. The dialogue is between two unnamed speakers:
Is "Chinese: 白馬非馬 ; pinyin: Baimǎ fēi mǎ ; literally: white horse is not horse" assertible?
Advocate: It is.
Objector: How?
Advocate: "Horse" is that by means of which one names the shape. "White" is that by means of which one names the color. What names the color is not what names the shape. Hence, one may say "white horse is not horse."
Objector: If there are white horses, one cannot say that there are no horses. If one cannot say that there are no horses, doesnt that mean that there are horses? For there to be white horses is for there to be horses. How could it be that the white ones are not horses?
Advocate: If one wants horses, that extends to yellow or black horses. But if one wants white horses, that does not extend to a yellow or black horses. Suppose that white horses were horses. Then what one wants would be the same. If what one wants were the same, then white would not differ from horse. If what one wants does not differ, then how is it that yellow or black horses are acceptable in one case and unacceptable in the other case? It is clear that acceptable and unacceptable are mutually contrary. Hence, yellow and black horses are the same, one can respond that there are horses, but one cannot respond that there are white horses. Thus, it is evident that white horses are not horses.
This dialogue continues with deliberations over colored and colorless horses and whether white and horse can be separated from white horse.
Other Gongsun Longzi chapters discuss Baima -related concepts of: jian 堅 hard; hardness, and bai 白 white; whiteness, ming 名 name; term, shi 實 solid; true, actual; fact, reality, the abstract zhi 指 finger; pointing; designation; universal like "whiteness", and the concrete wu 物 thing; object; particular like "a white horse".

2. Interpretations and Proposed Solutions
The paradox can be resolved by recognizing that the lack of articles in the Chinese language contributes to semantic ambiguity. Without grammatical articles, it is unclear whether each horse 馬 in the statement "A white horse is not a horse" 白馬非馬 refers to a horse, the desired horse, all horses, or horsekind. This can be seen clearly by expressing the paradox in English using articles: suppose that one desires yellow or black horses, then a white horse would not be the desired horse. The Advocates sophistry in the White Horse Dialogue is due to his confounding a horse with the desired horse.
According to A. C. Graham, this "A white horse is not a horse" paradox plays upon the ambiguity of whether the is in the statement means:
"Is identical to x ".
"Is a member of the class x "; or
In other words, the expression "white horse is not horse" is ambiguous between white horse is not synonymous with horse true, because white horse is more specific than horse, versus "a white horse is not a member of the set of horses" obviously false. The Advocate in the dialogue is asserting a lack of identity between horses and white horses, while the Objector is interpreting the Advocates statement as a claim that the category of horses does not include white ones.
Beyond the inherent semantic ambiguities of baima fei ma, the first line of the White Horse Dialogue obscurely asks ke hu 可乎, Can it be that.?. This dialogue could be an attempted proof that a white horse is not a horse, or a question if such a statement is possible, or both. Bryan W. Van Norden suggests that "the Advocate is only arguing that a white horse is not a horse could be true, given a certain interpretation. He might acknowledge that, in another interpretation, a white horse is a horse.
An alternative interpretation is offered in Feng Youlans History of Chinese Philosophy:
Strictly speaking, names or terms are divided into those that are abstract and those that are concrete. The abstract term denotes the universal, the concrete term the particular. The particular is the denotation, and the universal the connotation, of the term. In western inflected languages there is no difficulty in distinguishing between the particular white or horse and the abstract whiteness or horseness. In Chinese, however, owing to the fact that the written characters are ideographic and pictorial and lack all inflection, there is no possible way, as far as the form of individual words is concerned, of distinguishing between abstract and concrete terms. Thus in Chinese the word designating a particular horse and that designating the universal, horseness, are written and pronounced in the same way. Similarly with other terms, so that such words as horse and white, being used to designate both the concrete particular and the abstract universal, thus hold two values.
However, there are recent histories of Chinese philosophy do not subscribe to Feng Youlans interpretation. Other contemporary philosophers and sinologists who have analyzed the dialogue include Graham, Hansen, Harbsmeier, Thompson, and Van Norden.

3. Historic influence
In the Chinese philosophical tradition, the White Horse Dialogues significance is evident from how many Chinese classic texts directly or indirectly discuss it. The Liezi, which lists and criticizes the paradoxes of Gongsun Long as "perversions of reason and sense", explains "A white horse is not a horse, because the name diverges from the shape."
Two Zhuangzi chapters 17 and 33 mock Gongsun Long, and another 2 combines his zhi 指 attribute and ma 馬 horse notions in the same context:
To use an attribute to show that attributes are not attributes is not as good as using a nonattribute to show that attributes are not attributes. To use a horse to show that a horse is not a horse is not as good as using a non-horse to show that a horse is not a horse, Heaven and earth are one attribute; the ten thousand things are one horse.
The Mengzi 6A4 notes that bai 白 white has different connotations whether one is using it to refer to a graying person who is worthy of respect because of their age or a white horse which should be treated like any other animal:
Mencius said, There is no difference between our pronouncing a white horse to be white and our pronouncing a white man to be white. But is there no difference between the regard with which we acknowledge the age of an old horse and that with which we acknowledge the age of an old man? And what is it which is called righteousness? The fact of a mans being old? Or the fact of our giving honour to his age?
Other early "a white horse is not a horse" references are found in the Hanfeizi 32, Mozi 11B, and Zhanguoce 4.