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What do we mean when we talk about categories? A category is a group of things that have common features; in other words, a category composes at least one superordinate and its subordinates, the former shared by the latter in some sense. For example, there is a category if I say a bulldog and a chihuahua are dogs, a bulldog and a chihuahua being the subordinates and the dog the superordinate, and a bulldog and a chihuahua sharing the dog-ness. In a Platonic sense, dog-ness is what Plato might call a Form, and the dog-ness is partaken of by a bulldog and a chihuahua.

In my opinion, Socrates, Plato, and Gilbert Ryle make a clear distinction between the superordinate and the subordinate, while Charles Darwin, in the evolutionary terms, may treat them basically in the same way but a bit differently at times. Ancient Chinese philosopher Gongsun Long, on the other hand, sometimes deals with the superordinate and the subordinate likewise and sometimes otherwise. Which seems to show the existence of the categorical hierarchy and its fragility and changeability. This instability of the category is akin to the idea of evolution, Darwin’s lifelong theme, which suggests more or less similarities between Darwin’s logic and Gongsun Long’s. Now let’s see the banquet of the geniuses.

In the Western history of thought, the hierarchical order of the category seems to have been made clear first in the discussion by Socrates and his interlocutors, in their attempt at the definition of the ethical term, such as courage. Let’s delve into what they talk about.

In Laches by Plato, Socrates wishes to know what goodness is. However, he thinks it quite tough to give its definition, and therefore proposes to one of his interlocutors, Laches, that he go into the idea of bravery, one aspect of goodness, since it seems easier to do so. Just as Descartes advocates dividing a philosophical issue into parts for examination, so does Socrates advise Laches to argue part of goodness, bravery, for a starter. When Laches defines bravery as being a soldier standing and fighting in combat without making off, Socrates objects that Laches’s definition of bravery is given in a very narrow sense; it just pertains to military and not to human life in general. What Socrates wants to know is not the definition of courage in military, but that in every dimension of human life.

Then enter Nicias, another interlocutor, suggesting that courage is knowledge; to be courageous is to know what you should fear and hope for in all aspects of human life; to fear is to expect a future evil and to hope for a future good. Then Socrates adds, saying that to know to the full, which constitutes the bravery in the truest sense of the word, is to know not only things to be feared and hoped for, but also those in the past and the present. Therefore, to be truly courageous is to know what is to be, is, and was feared and hoped for in the future, present, and past. Which should be regarded as the whole goodness, not courage, which is just part of it. Nicias tries to define courage, ending up in finding out goodness and not bravery.

What’s the problem here at all? What they find out is not so much the definition of courage as the definition itself. To give a definition of any concept we first of all have to not mix the hypernym and the hyponyms of a category, which Socrates’ interlocutors carelessly confuse, and which Socrates wisely distinguishes. Overlooking them difference between the including and the included, we are certain to hit an impasse. This is what may be called Socratic Aporia. Aporia is the inevitable result of the failure to discriminate the difference between a hypernym and its hyponyms. It is a category mistake.

What’s the problem here at all? What they find out is not so much the definition of courage as the definition itself. To give a definition of any concept we first of all have to not mix the hypernym and the hyponyms of a category, which Socrates’s interlocutors carelessly couldn’t, and which Socrates wisely evaded. Overlooking them, we are certain to hit an impasse. This is what you call Socratic Aporia. Aporia is the inevitable result of the failure to discriminate the difference between the including and the included. It is a category mistake.

We can say “A white horse is a horse,” but we cannot think a white horse and a horse to be identical; a white horse is included in a group of horses. We cannot think a hen has three legs, because it is true that a hen has the leg, the right leg and the left leg, mentioning ‘leg‘ three times, but what the proposition means is that the first leg means the abstract superordinate, only in theory, while the second and the third legs mean the concrete subordinate legs, in reality; you cannot count the three legs in the same way, since the first one and the latter ones belong to the different levels of the category. These two mistakes can be named the Vertical Category Mistake since the including and the included are confused. We cannot mention a whiskered hook either because whiskers belong to a group of the living things, but hooks don’t; they, a whisker and a hook, constitute different categories. This one can be called the Horizontal Category Mistake.

Category mistake is what Gilbert Ryle deals with in The Concept of Mind. In the book is found some examples of the category mistakes: It occurs when a foreigner visiting Oxford is shown a number of colleges, libraries, and so on, and asks where the University is. In fact, the University cannot be shown in the same way that colleges and libraries are, since they belong to the different levels of the category, the University subsuming colleges and libraries and the like. We can think this is the vertical category mistake. Another category mistake is found when a philosopher ascribes physical concepts to mental phenomena, confusing mind and body, and believes that just as bodies are governed by rigid mechanical laws, so are minds by rigid non-mechanical laws. Which is a big mistake since minds and bodies constitute different categories. This is the horizontal category mistake.

Some of Gongsun Long’s propositions are worth consideration when we think about category. The following theses are what this logician in ancient China contends:

A white horse is not a horse.
A hen has three legs.
Hooks have whiskers.
An orphaned calf has never had a mother cow.

He realizes that there is a hierarchical category order: A white horse is not a horse because of the following reason; if ordered to bring a horse we can bring a white or a black horse, but if ordered to bring a white horse, we can a white one but not a black one: A white horse is not a horse. Which may suggest the existence of the hierarchical category order. And the order is stable: An orphaned calf, since it is orphaned, logically speaking, should never have had a mother; if it has a mother cow, then it cannot be orphaned. And the order is at the same time unstable: A hen has three legs because it has the leg, the right leg and the left leg. This thesis can be likened to the example that when I drink wine every night, a red wine and a white wine, it means that I have three wines every night; wine, a red wine, and a white wine, a mixture of a superordinate and its subordinates, wine and a red wine and a white wine. This Ryle would surely rebut, calling it a category mistake, and it should be viewed as a vertical one. Which objection Gongsun Long ignores, supposing it might happen. The mistake is not really a mistake. Another instance that the category order is unstable: Hooks have whiskers. Since a hook is an inanimate object and whiskers belong to a certain group of animate objects, it cannot be the case that whiskers grows on a hook, and yet Gongsun Long thinks it could. Which is because the nonliving things and the living things can be fused. A category mistake in the terms of Ryle, a horizontal one. Which protest Gongsun Long neglects, thinking it might occur. In short, Gongsun Long assumes that the hierarchical category order is existent, stable and unstable, and changeable. People might reject his propositions as paradoxical, but aren’t paradoxes traditional toys for philosophers?

Unfortunately for reasonable rationalists, Charles Darwin may argue for Gongsun’s opinion that there can be the superordinate and the subordinates at the same level, a vertical category mistake but not necessarily mistaken. This can be shown by the Darwin’s idea of evolution, especially of the evolution of the Darwin’s finches on and off the Galapagos Islands. To make a long story short, let’s suppose there are two species of finches on the Galapagos Islands, where Darwin did the full research on them. He could simply say, “The finch comes in two forms: There is a finch living on the earth, eating on plants, with a big bill. And there is a finch living in trees, feeding on insects, with a small bill.” What if you ask, “How many finches are there on the islands?” Well, Ryle and Socrates would answer, there are two: The first finch in Darwin’s comment is the superordinate, the second and the third the subordinates, and they belong to the different levels of the category, with Ryle adding, if you think there are three, you make a category mistake: Ryle may claim two physical species of finches to be the included, and the finch as such is the including, so he may continue, why not draw a line between them? After all, just as Oxford as such is not a college or a library or a laboratory or a playing field, the finch itself is not a physical finch found on the earth. And Plato might say, the first finch means finch-ness, a metaphysical entity of the physical finches on the islands. It’s just an abstract concept, a Form he calls it, and it is found only in our mind and doesn’t exist on the earth at all. It is not possible that a hen has three legs, only two. However, Darwin, hearing and smiling at these words, might say that it is highly probable that there are three finches on the earth. A finch came for some reason to the islands, developing, according to the wide variety of circumstances, into two forms. Hence the three kinds of finches, the ancestor and its descendants. A category mistake is not necessarily a mistake; a hen has three legs. I’d like to dub this idea the vertical category change, not mistake.

We may think category confusion is impossible. For example, a tailed human seems impossible since anthropoid primates, humans included, don’t wear tails when some animals, like dogs and cats, do. Just like a whiskered hook, a tailed human is a confusion of a human and a nonhuman attribute, so it is a category mistake. However, homology, an area of biology, shows us that humans seem to share sort of a tail, a coccyx or a tailbone, with tailed animals, through evolution: A common ancestor had some structure which was to undergo divergent evolution into a coccyx now a vestigial organ of a human and a tail of a dog or a cat. Therefore, what seems impossible at first can, in the eye of science, be in fact not impossible. Science is more than just inconsistency: Humans have a tail, or hooks have whiskers, which is called by Ryle a category mistake, or a horizontal one, but as a matter of fact it is the horizontal category change, which is not always impossible.

Socrates, Plato, and Ryle’s concept of category is closed and static, while that of Gongsun Long and Darwin is open and dynamic; the former’s category is rigid, logical and artificial; the latter’s concerns life itself. Socrates, Plato, and Ryle may believe the category remains the same, which Gongsun Long and Darwin doubt and refute, saying, there are times when category changes.

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