Lesson 3: The Categories


Since in this lesson we are beginning to read Aristotle himself, which is what we will do for the rest of the course, I thought that I would first outline the goals we have in going over Aristotle. The first goal is to make you able to read Aristotle's logic itself. I do not mean that you will be able to read it easily, since no one can read him easily. It always takes a great deal of effort and concentration to read Aristotle with understanding. And I do not say "understand him completely" because few do. Rather, our goal is to enable you to read Aristotle himself with some understanding, to at least give you a start at seeing what he is talking about. The second goal is to enable you to actually use Aristotle's logic. That is, use it in your own study, in your own process of learning.

Last time I talked about the predicables, and I made a comparison between them and the tools used for building. The predicables are some of the tools we need to build a good definition, just as the builder needs a hammer and saw to build a house. I want to keep using that idea of tool. We can say this: everything that we are studying in logic is a tool that the mind can use to come to understand things. They are tools we use to read philosophy and theology, to read Aristotle and St. Thomas with understanding, and to think about the subjects which they are writing about. And they are tools we can use to speak and write and teach in an orderly way.

St. Thomas is a good example. He constantly uses these tools. When he is reading Aristotle, that is, commenting on Aristotle's writings, he is constantly pointing to the logical structure of Aristotle's arguments. When he is teaching theology in his own right, he constantly uses these tools. The Summa Theologiae is filled with the use of logical tools. In the later exercises we will go back and look at passages from the Summa in which St. Thomas is using these tools. We can see that our knowledge of these tools is going to help us to understand what St. Thomas writes.

Distinctions at the Beginning of the Categories

Now let's get back to the Categories itself. Recall that in our last lecture we saw that the mind needs definitions: the first operation of the intellect moves from a vague to a distinct knowledge of what something is through making a definition. We also saw that we needed tools to make a definition, specifically the genus, species, and difference. Then we asked at the end of our last lecture how we would find these things, how do we find the genus and difference. The answers are given in the Categories. The main part of the Categories is concerned with finding genus, the latter part with finding specific differences. In today's lecture we will focus on the first part of the Categories, that concerned with genus. Our next lecture will take up the tools which help us find differences.

The tradition divides the Categories into three parts: the pre-categories, the categories themselves, and the post-categories. The pre-categories contains the distinctions we need to make before we can understand the categories themselves. That part is short, compared to the much longer discussion Aristotle undertakes of the categories themselves. In the post-categories Aristotle gives the tools which are concerned with difference. Notice that when Aristotle goes through the pre- and post-categories, he makes points which have an application beyond their use in the Categories. For example, in the post-categories he makes distinctions about order which go beyond the aims of simple definition. Since those kinds of distinctions are so universally important in the intellectual life, I will focus on them.

Aristotle makes three distinctions before he deals with the categories themselves, then he enunciates a law, and third he begins to discuss the categories. Let us first look at those three distinctions, followed by a brief comment on that law, and more extensive comments on each category.

The first distinction is between the univocal and equivocal use of a word. A first approach to this distinction is easy to make, but extremely important. Let us look at how Aristotle explains it:

Things are said to be named equivocally when, though they have a common name, the definition corresponding with the name is different for each.

Then Aristotle gives an example to explain what this means. He says that a man, such as Socrates, and a picture of a man in a painting can both be called "animal." That is, I can point at Socrates and truly and appropriately say, "that is an animal." I can point at the picture of Socrates and say, "that is an animal." The same term, one name, animal, is used both times. The difference is that the meaning, the definition, of the term "animal" is different in the two cases. In the first, animal means "sensitive living thing." In the second, it means "image of a sensitive living thing." This is an equivocal use of a name.

The Aristotle goes on to explain the univocal use of a word:

On the other hand, things are said univocally which have both the name and the definition answering to the name in common.

We can use the example of man and cow. I can say with truth that man is an animal and that cows are animals. The term "animal" is the same name, it is used twice, and it has the same meaning in both cases: sensitive living thing. A man and a cow are both animals for the same reason.

This is not a hard distinction to make, but let us go on to the second distinction between the simple and composite. Here Aristotle does not give us a definition, but only examples:

Forms of speech are either simple or composite. Examples of the latter are such expressions as man runs, man wins, of the former, man, ox, runs, wins.

That is, "The man runs" is a composite expression, but its parts, "man" and "runs" are simple expressions. Aristotle will define more precisely the simple and composite later, but I want to say just one more thing about this distinction. Aristotle uses very neat words to express this distinction. What we have translated as "composite" literally means "interwoven," while what we translated as simple means "without interweaving." That is, sometimes when we use words, we weave them together with other words, while at other times we use them by themselves, without weaving them together with other words. This image of weaving words together will be very helpful for discussing the second and third operations of the intellect.

The third distinction is a distinction between things predicated of others and things present in other things. Before we explain this distinction, we should go back to explain the word "category." Categories is the name of the book, but it is in this context that Aristotle first uses that word. First we can say that "category" is just the Greek equivalent for the Latin-based word "predicate." Now the highest genera are rightly called categories because they are always predicates and never subjects. That is, a species is a subject which can have a definition predicated of it. That definition includes a genus and a difference. But that genus is usually itself a species, and it can have another genus predicated of it. Only when we get to the highest genera do we have a genus which has not other genus predicated of it: it is a predicate only, not a subject. Thus, the highest genera can be called predicates simply, or categories.

Another way to look at the word, perhaps more interesting, is to consider its etymology. The Greek word category has for its first meaning "accusation." It means "to speak against in the public assembly." For example, publicly labeling someone a thief is accusing him, and in the Greek, categorizing him. So we can look at the highest genera as accusations against their subjects: man is "accused" of being a substance, color is "accused" of being a quality.

There are predicates, and there are things that, while not quite predicates, seem to function in much the same way. This is what Aristotle is trying to distinguish here. Let us look at an example. There are two English words that are closely related, brown and brownness. I can say, "The coat is brown," and I have predicated brown of coat. I cannot say, however, "The coat is brownness." That sentence does not seem even to make sense. I can, however, use the word "brownness" to say something similar: "The coat has, or possesses, brownness." This is the distinction Aristotle is pointing to when he distinguishes what is predicated of another from what is present in another. When we say that the subject is the other term, that other term is being predicated of the subject. When we say that the subject has the other term, that other term is present in the subject. In our example, "brown" is predicated of the coat, "brownness" is present in it.

These distinctions are at the beginning of the Categories because they enable us to narrow down what the book Categories is about. The book is about words, but what kind of words? Are they words that are used with many different meanings of their subjects, equivocally, or with the same meaning, univocally? Remember, the definition includes a genus because the genus guarantees that the definition points out one common nature. That does not happen if the genus is a word used equivocally. Since the categories are the ultimate, the highest genera, and they have to be predicated of their species according to the same meaning, the categories must be words used univocally. For example, animal is not a genus for man and the picture of an man, even though both are called animal. I would make animal the genus for man and beast, because the word would have the same meaning in both cases. Because the categories is about the highest genera, it is about words used univocally of all the species under them.

Second, are the categories simple expressions, or complex expressions? If the highest genera were complex expressions, they would need to be explained by something prior because complexity always has a cause. The complex expression cannot be understood without accounting for its simple parts. For example, the expression "man runs" would have to be explained through an analysis of "man" and "runs." It could not be a highest genus. Thus, the categories are not going to be complex, but simple expressions.

Third, are the categories predicated of, or present in, the species? Clearly the categories must be predicated of the species. We say that the species is the genus, not has the genus. Animal is the genus of man, and we say that man is an animal, not that he has animal. Thus, the categories are going to be names that are simple, that are used univocally of the species below them, and that are predicated of them, not present in them. Thus, the three distinctions narrow down the subject of the book Categories.

Finally there is a law which Aristotle states:

When one thing is predicated of another, all that which is predicable of the predicate will also be predicable of the subject.

He does not argue for the law, he simply gives an example. If I say Socrates is a man, and man is an animal, then by this law it is clear that Socrates is also an animal. This law shows us that the ultimate genera are not just useful for defining the very general things that come right below them. They are useful for defining every single species down to the lowest. We have already seen an example of this law at work: we said in our discussion of the Isogoge that man is an animal, and that animal is a living thing. Thus, we also said that man was a living thing. If the process is carried out to it conclusion, we reach the highest genus of substance. Thus, we defined man as a substance with three dimensions, life, sensation, and reason. Without Aristotle's law, we could not fully spell out the definition of man like this.

The Categories Themselves

I have not by any means exhausted the contents of the pre-categories, but we have understood enough to move on to the categories themselves. We said this before: Aristotle does not think that there is one highest genus, but many. St. Thomas explains why, but we are not yet in a position to understand that account. Let us simply note that Aristotle assigns ten highest genera:

Expressions that are in no way composite signify substance, quantity, quality, relation, place, time, position, outfit, action, or being acted upon.

Then he gives example of each:

To sketch my meanings roughly, examples are man or horse, of quantity such terms as two cubits long or three cubits long, of quality such attributes as white, grammatical. Double, half, and greater falls under the category of relation; in the marketplace, in the Lyceum, under that of place; yesterday, last year under that of time. Lying, sitting are terms indicating position, shod and armed outfit, to lance, to cauterize action; to be lanced, to be cauterized being acted upon.

First Aristotle notes that all of these express the understanding of the first operation of the intellect, since none of them by themselves signify the true or the false.

Aristotle does not just give us a list of examples, but rather goes over some of the categories in detail. Six of them he talks about briefly, but he talks about four, substance, quantity, relation, and quality in detail. In the rest of this lecture I would like to go over these four important categories.

First, consider substance. It is a highest genus, so it has no definition in the strict sense, but Aristotle does more than give examples of it. He distinguishes two different ways in which the term is used. He uses the distinction between predicable of and present in a subject to make the distinction between the ways in which the term substance is used. In the first and strictest way in which the term is used, substance is that which is neither predicable of nor present in a subject. For example, I do not say about anything else that it is Socrates. The most I can say is that Socrates is Socrates, or that man is Socrates, but that is not predicating Socrates of another thing, it is simply predicating Socrates of himself. Neither can I say about anything else that it has Socrates. I do not say that another has Socrates in the sense in which Socrates would be present in a subject as a characteristic of that subject. Now if we ask ourselves what logical role the term Socrates plays, since it is neither a predicate nor like a predicate, the answer is that Socrates is just a subject for predicates. That is what it means to be a substance in the first and strictest sense of that term. Substance is the ultimate subject of all predication.

This seems strange because we are looking for the categories, which are the highest genera, which are all predicates. Now we seem to be saying that substance is not a predicate at all. Aristotle's answer is that there is another sense of the term substance. We know that substance in the first sense has other things predicated of it. Some of them, such as tan or pale, do not answer the question "What is it?" about the substance, but other ones, such as "man" and "animal" do. Those predicates which answer the question "What is it?" about substance in the strictest sense are also called substance, though in a second way. Aristotle writes:

Substance in the truest and first and most definite sense of the word is that which is neither predicable of a subject nor present in a subject . . . But in a secondary sense those thing are called substance within which, as species, the primary substances are included; also, those which as genera include the species.

For example, Socrates is substance in the first sense, since he is not present in nor predicated of anything. But when asked the question, "What is Socrates?" I answer by saying "Socrates is a man." Man is therefore also a substance, though in a secondary sense. When asked what a man is, I answer "animal." Thus, the genus of man, animal, is also a substance in a secondary sense.

We said before that there are other things predicated of the primary substances, such as tan or pale, which are not secondary substances because they do not answer the question "what is it?" about the primary substances. Nevertheless, the fact that such things can be predicated of substances points out another distinguishing feature of substance: while remaining numerically one and the same, it is capable of admitting contrary qualities. That is, only substances directly undergo change. The other categories determine the way in which substances change. For example, pale and tan belong to the category of quality. When Socrates undergoes the process of tanning, we say that he has changed: first he was pale, now he is tan. Paleness and tanness did not change, they are the qualities which Socrates loses and gains in order that he might change. The fact that substance is the direct subject of a change, that it goes from one contrary to another, is one of its distinguishing characteristics.

The Accidents

The category of substance includes only one kind of predicate, that which answers the question, "What is it?" about primary substances. But since primary substances are the ultimate subjects of all other predicates, we group the other nine categories under the heading of accident, defined as what happens to a substance. Since the different accidents "happen" to their substances in different ways, we cannot say that "accident is a category." It is rather a word used equivocally to point out a kind of likeness between the other nine categories.

The first accident Aristotle discusses in the Categories is quantity. We can describe quantity by saying that it answers the question "How much?" or "How many?" Aristotle does not distinguish different meanings of the term, as he did with substance. Rather, he first distinguishes the species that fall immediately under this genus. The two species of quantity are the discrete and the continuous.

We will leave aside the formal definitions of these and simply explain what the terms mean. Discrete quantity is that which cannot be infinitely divided. For example, whole numbers are discrete quantities because I can only divide them down to the number one: if I tried to divide the one, I would leave the realm of whole number. Continuous quantities are those which can be infinitely divided. For example, length is a continuous quantity since, no matter how much I divide a length, I can still divide the parts and I'll still have length. He gives other examples: time is a continuous quantity, the syllable is discrete quantity because they are called long and short.

What is common to all quantity and is a distinguishing characteristic of it is that I call quantities equal and unequal. For example, I can say that twelve inches equals a foot, five time five equals twenty-five. If I use the word "equal" outside the realm of quantity, if, for example, I say that all men are equal, I am using the term "equal" in an extended sense. In the strict sense, only quantities are equal to each other.

After quantity, Aristotle takes up the category of relation. A complete treatment would require the consideration of many subtle points, but we will consider the more obvious facts. First, the way we translate the name of this category can be deceptive: relation is a very abstract term, but the Greek term Aristotle uses is concrete: pros ti, which would translate literally as "to something." Things are called relative when they are named in relation to another. For example, superior is a relative term because we cannot just say that something is superior and be understood: we have to say that it is superior to something. And a quantity is not just half, it is half of another quantity. Thus, a term which is only properly used when there is a reference to another is said relatively.

Every relative term implies a reference to another, the correlative of the original term. The superior is superior to another, and that other is inferior to it. Superior and inferior are correlative terms. The half is half of another, which other is double of it, and so half and double are correlative terms. Every relative has a correlative.

But not every relative term is simply a relation. Some terms, while they are said relatively, fall primarily into some other genus. They belong to another category, but because they imply a relation they are often spoken of as if they were relations. For example, knowledge is actually in the category of quality, but it is said relatively: knowledge is knowledge of something, and that something is knowable through knowledge. Thus, relative terms are of two kinds: first, relations themselves; second, things that fall into other categories but imply a relation.

The next category Aristotle discusses in quality. Maybe the best way in English to explain the word is to say that it answers the question, "Is it such a thing?" or "What is the thing like?"

Aristotle points out four species of quality: disposition, capacity, sense qualities, and shape. By shape he means terms such as straight, curved, square or round. By sense qualities he is referring to the objects of the five senses, such as color, sound, temperature, etc. By capacity he is referring to abilities, talents. Some people have the quality of swiftness because they have the capacity to run quickly. Finally, dispositions differ from capacities because they imply, not just an ability to do something, but an inclination to do it. For example, virtue is a disposition because it implies an inclination to do good actions. Swiftness is a capacity because it only implies the ability to run fast: the swift man might be lazy and disinclined to use his ability.

Since the different is the opposite of the like, this category has the characteristic of admitting of contraries: many, though not all, qualities have a contrary. For example, black and white are contraries, hot and cold are contraries, fast and slow are contraries, virtue and vice are contraries. All of them are also qualities. Qualities also often vary in degree. For example, hot is the contrary of cold, but one thing can be hotter than another. Virtue and vice are contrary qualities, but one man can be more virtuous than another. This makes qualities unlike substances and quantities, which neither have contraries nor vary in degree. These marks are not unique to quality, since they are also found in actions.

We can easily note the distinguishing characteristic of this category. If the category of quality tells us what something is like, then things are said to be like each other because they have the same qualities. Coal is like tar because both are black, Socrates is like Cato because both are virtuous. Blackness and virtue are qualities. Whenever we use the term likeness in its strict sense, we are speaking about qualities.


Aristotle says little about the other categories. He notes that action and being acted upon have contraries and vary in degree, like qualities, but otherwise with the last six categories he is content to give examples. His account, however, has been an important tool in our quest for good definitions. We now know what the highest genera are, and thus where our search for definition comes to an end, or we might say, has its beginning. But the search for definitions requires more than the highest genera: it also requires tools that will give us the specific differences completing our definitions. Those tools come in the post-categories, and we will discuss them in our next lecture.


State whether the word in bold is used univocally or equivocally.

1. Man is an animal.
Dogs are animals.

2. The Los Angeles Dodgers are a baseball club.
A baseball bat is a kind of club.

3. Albert was in eighth grade.
Albert received good grades in school.

4. I bought a tent at the general store.
Kmart is a discount department store.

5. The music was coming from the stereo speakers.
Alan Keyes is an inspiring speaker.

6. He put a bit in the horse's mouth.
But he waited a bit before he tried to ride the horse.

7. Logic directs reason in its actions.
Reason always proceeds from the known to the unknown.

8. Fido is a dog.
Spot is a dog.

9. Metaphysics is a science.
Astronomy is a science.

10. The RNC is an arm of the Republican Party.
The wing is the arm of a bird.

Into which category does each of the following terms fall?

eighty meters


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