Lesson 2: The Universal and the Predicables


In our first lecture, we went over the importance of logic and we looked at the whole of logic. Logic was divided into three parts according to the three operations of the intellect, simple apprehension, composing and dividing, and discursive reasoning. In this lesson we will get into the details of the logic of the first operation. Our task today is to look at the Isogoge of Porphyry, which introduces to us the terms Aristotle uses in his Categories. Since Porphyry begins his introduction with the problem of the universal, our first task today is to look at that problem.

The Problem of the Universal

Let us begin by looking at what the term universal means. I can make the following statements: Fido is a dog, Spot is a dog, and Rover is a dog. Fido, Spot and Rover are different individuals, but I can say the same thing about each of them, that he is a dog. So the word dog, even though it is one word, can be said of, predicated of, many different individuals. I can say about many things that each is a dog. That is what we mean when we say that dog is a universal word. The universal is one thing predicated of many.

The universal immediately brings up a problem, perhaps the most important philosophical problem of early medieval philosophy. It asks, what does the universal word signify, what does it point to?

It was one of the first problems addressed by Plato, and he gives it the following solution. The universal, he says, signifies a Form which exists in another world, which the individuals in this world participate in. For example, if we take the universal term dog, Plato says that it actually points to a Form of dogness which exists in another world, the realm of Forms. The individual dogs, Fido, Spot and Rover, participate in that Form of dogness, and are called dogs because of that participation. Plato makes the universal the most real kind of thing.

The medieval nominalists go to the opposite extreme in their solution of the problem. They said that the universal word was just a word, and nothing more, and that it points to nothing other than the individuals. The universal is just a way of collecting the individuals into a group or set. To use the same example, the nominalists denied that there was a Form of dogness, and that individuals participated in that Form. They said that only individuals dogs exist. The word dog was simply a convenient ways of collecting Fido, Spot, and Rover into a group.

Porphyry begins the Isogoge with this problem, and the many medieval commentaries on the Isogoge are often largely attempts to solve the problem. We will next look at Porphyry's careful formulation of the problem.

Porphyry writes:

I shall refuse to say whether genus and species [these are two kinds of universal] are subsistent or located only in naked concepts. And if subsistent, whether they are corporeal or incorporeal, and if incorporeal whether separate from sensible things or subsisting in them or around them. That business is very deep and requires a greater examination.

We can sum up Porphyry's presentation of the problem of universals as follows: 1) Are the universals real or imaginary? 2) If real, are they physical things or incorporeal things? 3) If they are incorporeal, do they exist separately from bodies, or do they exists in physical things?

Porphyry himself, quite rightly, refuses to solve the problem in his treatise, because he sees that the solution belongs to a higher science, namely, metaphysics. In fact, St. Thomas provides the solution to this problem in his metaphysical treatise, On Being and Essence. Still, a careful consideration of the problem even without the solution is useful in logic. Considering the problem helps us to know what we are talking about when we refer to universal words. The subject of the logic of the first operation is primarily concerned with the universal word and understanding what it means.

Need for a Logic of the First Operation

Now from what I have said so far it might seem unnecessary to have any logic for the first operation. After all, the problem of universals cannot be solved by the science of logic, and the simple apprehension of what something is, which is the action of the first operation, seems not to need any direction. We either know what something is, or we don't know it. If the first operation needs no direction from reason, then no part of logic will be concerned with it. Logic is just the art which directs the operations of reasoning.

There is a quote from Plato's Meno which explains why we need a logic for the first operation. Meno, immediately upon finding Socrates, confronts him with this difficult question: Can you tell us, Socrates, Whether virtue is acquired by teaching or by practice, and if by neither, whether it comes to man by nature or in some other way? Socrates responds:

O Meno, I confess with shame that I know literally nothing about virtue, and when I do not know the what of anything, how can I know its properties? How could I tell, Meno, whether you were fair or the opposite of fair, rich and noble, or the reverse of rich and noble, if I did not know you?

This is the point that Plato makes in this passage. Meno wants to jump immediately to the question of whether virtue has certain attributes, characteristics, but Socrates replies that we must ask a previous question, what virtue is. If we do not know the answer to the question, 'What is it?' then we cannot know the answer to the question, 'What properties does it have?' What is clear is that Socrates is not merely ignorant of the meaning of the Greek word, arete, which we translate as virtue. Rather, he has only a vague idea of what virtue is, but before he assigns properties to virtue he needs a distinct idea of what virtue is.

Even in the first operation of the intellect there is a progress in knowledge, a progress in which we begin with a vague, an indistinct idea of what something is, and move towards a more distinct idea of what it is. That distinct idea is necessary for reasoning about the properties of the thing. We need a logic, therefore, which directs us so that we proceed correctly from the indistinct idea to the distinct idea.

The process of moving from the vague to the distinct knowledge of what a thing is is the process of defining. A definition is the way in which the first operation of reason is perfected, and so it is the fundamental concern of the first part of logic. Another way to understand the example is this: Meno asks whether virtue has a certain property, but Socrates responds by asking Meno for a definition of virtue.

Lessons on Definition

Meno is not daunted, and offers to give that definition, and his proposed definitions and Socrates' criticisms of them take up most of the first part of the Meno. What we are going to do now is to look at Meno's definitions and Socrates' criticisms in order to get our first understanding of the requirements of a good definition.

Meno first defines virtue as follows:

Let us take first the virtue of a man. He should know first how to administer the state and in the administration of it to benefit his friends and harm his enemies. The woman's virtue, if you wish to know about that, is also easily described. Her duty is to order and keep what is indoors, and to obey her husband. Every age, every position of life, young or old, slave or free, has a different virtue.

Socrates replies to this definition as follows:

How fortunate I am, Meno! I ask you for one virtue, and you give me a swarm of them. . . . But the virtues, no matter how many and how different they may be, have a common nature which makes them all virtues. Now this, he who would answer the question, what is virtue, would do well to have his eye fixed.

I think that we can take this lesson from Meno's first attempt to define virtue. Meno, when asked for a definition of virtue, begins to describe all the different kinds of virtue. But Socrates wants to know what all those different kinds of virtue have in common. When we are looking for a definition, we are looking for something common to all the things defined. We are looking for one nature.

Meno, finally understanding that lesson, proceeds to give a definition of virtue that is one. He says:

If you want to have one definition of them all, I know not what to say except that virtue is the power of governing mankind.

Meno has made progress. He gives a definition of virtue that does not split virtue into parts, but talks about the whole of it. Socrates points out, however, that this definition of virtue also does not work. He says:

Does this definition for virtue include all virtue? Is the virtue the same in the child and the slave, Meno? Can the child govern his father, or the slave his master?

We learn a second lesson about definition from Meno's second definition. A definition of a thing not only should not split the thing into parts, but it also must apply to all the parts, to every one of the things defined. As we saw before, the definition of virtue cannot simply be a list of the virtues of a man or a woman, the old or the young, the slave or the free, but neither can it leave any of these virtues out. It has to apply to the virtue of a man, of a woman, of the old and young, slave and free. Meno's does not, because it has to do with governing, and governing does not apply to the child or the slave.

Despite the fact that this definition for virtue does not work, Socrates lets it go by because he thinks that he can learn another lesson from it. He says to Meno:

You say that virtue is the power of governing. Should you not add, justly and not unjustly?

And Meno replies:

Yes, Socrates, I agree there, for justice is virtue.

And Socrates replies:

Is justice virtue, Meno, or a virtue?

Now Meno has committed another mistake with this definition. He still has one common definition, it is now the power of governing justly, but the problem is that justice is one of the parts that ought to be underneath virtue, justice is a virtue. Socrates points out that a good definition cannot put a part which falls under the whole into the definition of the whole. That would make the definition of the part circular. For example, if justice is a part of virtue, and it is also in the definition of virtue, when I try to define justice I will find that justice will fall into its own definition. But clearly, if a definition is trying to explain what something is, it cannot assume that you already know what it is.

Meno takes his last definition of virtue from a poet who says:

Virtue is the desire for good things, and the power of attaining them.

This definition avoids the pitfalls which wrecked the three previous definitions. It gives one nature, it applies to all of the things defined, and it does not include in the definition a part which fall under the whole. But Socrates still objects:

Do not all men, my dear sir, desire good things? . . . Then according to your definition, virtue would seem to be the power of attaining good. But is any mode of acquisition, even if unjust and dishonest, equally to be deemed virtue?

Socrates is showing us here that the poet's definition of virtue fails because it applies to men who are not virtuous. For example, the tyrant, like all men, desires the good things in life, and he also has the power of attaining them. Yet like Meno we would deny that the tyrant is virtuous. The definition of virtue must not only apply to all the things defined, but also only to them.

From all these examples we can gather a list of rules which every definition has to obey. First, every definition has to give a common nature, not simply a list of parts or kinds coming underneath the thing defined. Second, every definition must apply to every part under the thing defined. Third, the definition cannot include a part or kind which is underneath the thing defined. Such a definition would be circular. Finally, the definition has to exclude what is outside the thing defined. The definition includes everything in it, excludes everything outside of it.

The etymology of the word definition makes these points clear. Define comes from the Latin word finis, which means limit or boundary. The boundary of a field, for example, contains the whole field and excludes everything outside the field. In the same way, the definition is the boundary of a term: it includes everything which the term applies to, and excludes everything it does not apply to.

What Plato has done for us in the Meno is to sum up the rules of definition. He has given us some idea of how we go from a vague understanding of something to a distinct one. Yet it is one thing to state the rules, and another to obey them. How do we obey these rules, how do we find good definitions? In this and the two succeeding lessons we are going to acquire a set of tools which will help us make good definitions.

The Predicables

We can compare what we are going to do with the art of building. A builder may have the art of building, he may know how to make a good house, and he may have all the proper material and still be unable to make the house because he does not have the right tools. If he does not have a saw and hammer, the blueprints and lumber are useless. We are in the same position with regard to definition. We know now what a good definition is, what rules it must obey, but we still lack the tools which we must use to actually make the definition. These tools fall into two classes: the predicables, which are given to us in Porphyry's Isogoge, and the beginnings of all definitions, which are given in Aristotle's Categories. In the rest of today's lesson, we are going to return to the Isogoge and get the tools we need to make good definitions.

In the Isogoge Porphyry defines the five predicables. They are called the predicables because they are the different ways in which one term can be predicated of, said of, many things. Notice that we are not talking about actual predication here, which is discussed in the second part of logic, but the ability to be predicated. Since the universal is defined as what can be predicated of many things, we can say that the predicables are different ways of being universal.

There are five predicables: genus, species, difference, property, and accident. We are going to concentrate on the first three since they are most important for definition. We will discuss the last two more briefly.

Porphyry works up to his explanation of genus by looking at its etymology. The first meaning of genus is family or clan. The Kennedys would be a famous American clan, and many of them are called Kennedy because that was the name of their Patriarch, Joseph Kennedy. But certain universal terms are related to each other in the same way in which a member of a clan is related to its patriarch. For example, the terms dog, cat, and horse are all universal terms in their own right, but they all have one term predicated of them, animal. Just as John, Robert, and Edward are all Kennedys, so dog, cat, and horse are all animals. And since animal is like the clan or family that dogs, cats, and horses belong to, we can extend the meaning of the term genus and say that animal is the genus of dogs, cats, and horses.

Porphyry then gives the following strictly logical definition of the term genus:

A genus is that which is predicated in answer to "what is it?" of many differing in species; for example, animal of man and beast.

It is interesting that he has brought the word species into the definition of genus, before we know what species is. He does this because genus and species are correlative terms, and therefore must be defined in relation to each other. The next thing, then is to talk about the meaning of the term species.

Again Porphyry gives the etymology of the term. The English word comes straight from the Latin, but the Latin word species is related to speculare, which means to look. This, the species is the look of the thing, its outward appearance. The Greek word eidos has a similar history. Thus, the first meaning that Porphyry assigns to the word species is visible form. Since we tend to divide things into kinds by their visible forms, species comes to mean a kind of thing. Thus, we say that dog, horse and cat are species of animals, meaning they are kinds of animals.

Porphyry then gives the following, strictly logical, definition:

Species is what is arranged under genus and of which genus is predicated in answer to "what is it?"

The explanations of both genus and species both refer to the question, 'What is it?' We have seen the question, What is it?' before because it is the question which asks for the definition of a thing. This is the case because the terms genus and species are closely related to definition. The genus answers the question 'What is it?' about the species, the species must have that question asked about itself, and the answer must include the genus. We can say this: the very nature of the genus/species relationship requires that the genus be in the definition for the species.

What role does the genus play in the definition? We saw that every definition must signify a common nature, some one thing which all the things defined have in common. The tool of genus assures that we have some one common nature. For example, the definition of the dog must point to one nature which all dogs have. But all dogs have the one nature of being animals. Therefore, the genus gives us that common nature.

But the genus cannot be the whole definition of the species. The genus includes what the species excludes. For example, the animal is related to dog as genus to species. The species dog excludes horses, but the genus animal does not, since every horse is also an animal. We saw before, however, that definitions must exclude everything outside what is being defined. Thus, the definition of the species must exclude everything outside the species: for example, the definition of the dog must exclude everything which is not a dog. Therefore, the definition of any species must include something more than the genus.

The other part of the definition of the species is called the difference. The word difference comes from two Latin words, ferre and dis, which combined mean carry away. A difference is what carries one thing away from another, and a specific difference is what carries one species under a genus away from the other species under that same genus. For example, men, dogs, and cats are all animals, but man is carried away from the other species under the genus animal by this difference: man is rational.

Thus, Porphyry gives the following definition of the specific difference:

Difference is predicated in answer to, 'Of what kind?' of those differing in species. Or, difference is what naturally separates those under a genus.

To take another example: living thing is a genus which has two species, plant and animal. The specific differences having sensation and lacking sensation are what divide that genus into its species. Thus, if someone asks what kind of living thing a plant is, the correct response gives the specific difference: a plant is a living thing lacking sensation. If someone asks what kind of animal man is, we say that man is a rational animal. Thus, the specific difference divides the genus and answers the question of what kind? of the species under that genus.

Now we have the first tools we need to build a good definition. A good definition, we saw before, must give a common nature, one thing that applies to everything defined, and must exclude those things not defined. The species is a common nature. The genus of that species includes everything that possesses that common nature. The difference excludes everything that does not possess that common nature. Thus, the definition of a species is made by combining a genus and a specific difference.

There is one more thing to say about genus and species. Porphyry writes:

The summum genus is that genus above which there is no higher genus. The infima species is that species below which there is no lower species. But between the summum genus and the infima species are others which may be taken as genera or species -- depending on how you look at it.

We compared the relations of genus and species to family relations, and Porphyry is describing a kind of family tree of genus and species. Since the relation of genus to species is like father to son, we put the genus above the species on a tree. But the genus itself has a common nature, and we might ask for its definition. Then we must find the genus of the original genus. Then the original genus becomes a species under a higher genus. When we get to the top of the tree, we find a genus which is just a genus, and is not a species. When we get to the bottom of the tree, we find a species which is just a species, and not a genus.

Chart 1

Chart 1 illustrates Porphyry's example. At the top of the tree is substance, which is a genus but not a species. Therefore, it is a summum (or highest) genus. It is divided into two species, body and spirit, by the differences taking up space and not taking up space. The species body is a genus to species underneath it, living thing and non-living thing. In this case, the differences are contained in the very names, living and non-living. Living thing is the genus of plant and animal, and the differences which divide it are having sensation and not having sensation. Finally, animal is a genus for man and beast, with the differences being rational and irrational. There are no species under man, merely individuals. Thus, man is an infima (or lowest) species. We can then give a fully spelled-out definition of man: man is a substance which takes up space, is living, sensitive, and rational.

We need to discuss briefly the last two predicables, property and accident. Neither of these will be used to form a definition, at least the strictest kind of definition, but the distinction between them is important for understanding the third operation of the intellect. Property is from the Latin for one's own. Thus, the car that I buy and keep is my property, since it is mine and no one else's. Things that belong to others, like my neighbor's car, or things that are held in common, like the road which I drive on, are not my property. The word has the following meaning in logic: a property is an attribute which belongs only to a species, to all of that species, and all of the time. For example, the ability to laugh is a property of man: only man can laugh, every man can laugh, and every man retains the ability to laugh all the time. We can take another example from geometry: only triangles have angles that add up to 180 degrees, all triangles have that attribute, and have it all the time.

Finally, the predicable of accident includes any other way of being universally related to a subject. Since the genus, species, and difference are always essentially related to their subjects, they cannot fail to belong to them. Although property is not essential to its subject, it still belongs to it necessarily. An attribute is called an accident when it does not belong necessarily to its subject. This is indicated by the word itself, which comes from the Latin accidere, which means to happen. The accident is what happens to belong to the subject.


Genus, species, difference, property, and accident are the five predicables. The first three are great tools for definition, but they are not enough by themselves. The process of defining is complete only when we can spell out all the differences back to the highest genus. But we do not yet know what the highest genera are. Is there one highest genus, or are there many? What are the highest genera? Where do we find the differences that separate genera into species? How do we put the lower genera in their proper order? In the Categories Aristotle answers these questions. He determines that there is not one highest genus, but rather there are ten. He then gives us the tools for determining the specific differences. Finally, he will indicate how the intermediate genera should be ordered under the highest ones. We will discuss Aristotle's Categories in the next two lessons. Exercises


1. Organize the following terms into a tree of genera and species:

curvilinear figure
rectilinear figure
geometrical figure
isosceles triangle
scalene triangle

2. Write definitions for each of the terms, except the term at the top of the tree.

3. Describe the relation that the predicate has to the subject.

For example: Man is an animal. GENUS
Triangles are rectilinear figures.
Triangles are three-sided.
Man is rational.
A tragedy is a drama.
A tragedy is sad.
Logic directs reason.
Logic is an art.
Socrates is a man.
Socrates is tan.
Some men are tan.


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