Lesson 4: Opposition and Order


In this fourth lesson we are going to finish our discussion of the logic of the first operation. Let us just recall some basic points. The logic of the first operation aims at understanding what something is, and the means to this is the definition of the thing. But we saw that we need tools to construct a good definition. In the second lesson we discussed the most basic tools, the predicables, especially genus, species, and difference. In the third lesson, we looked at the categories, the highest genera. In this lesson we will cover a tool that relates to specific difference, opposition, and one that helps us put a whole tree together, the tool of order.

The Kinds of Opposition

First, we need to see why opposites are tools for specific difference. Recall the function of the specific difference in the definition. Every definition must include all of the species, but only that species. The genus makes sure that every member of the species is included, and the specific difference makes sure nothing outside the species is included. That is, the specific difference must exclude every member of the other species under the genus. For example, if "rational" is the specific difference of man, it must exclude every beast from the species man. Otherwise, it would not be "defining," drawing a border, between the species man and everything else in the genus.

The sum of the specific differences under a genus, however, must include everything that is included under the genus. Consequently, the specific differences must exhaust the genus and must ensure that the species under the genus do not overlap. For example, the genus animal has two basic species, man and beast, with two specific differences, rational and irrational. These two differences exhaust the genus, because every animal is either rational or irrational, and they prevent overlap between the species, because no animal is both rational and irrational. We could not use brown and four-legged as the specific differences under animal, first because some animals are neither brown nor four-legged, and so the genus is not exhausted, and second because some animals are both brown and four legged, so that the species would overlap. The specific differences must exhaust the genus without allowing species to overlap.

If we ask what kinds of terms are related to each other in such a way that no two species can possess both, yet both together exhaust the genus of those species, Aristotle answers that such terms are called opposites. He takes up this topic in chapter 10 of the Categories. But before he determines exactly what kinds of opposites will work, and how they work, Aristotle gives a general account of opposition and its kinds.

Aristotle identifies four kinds of opposites, and then gives examples of each. Opposites are either correlatives, or contraries, or privatives and positives (also called privation and possession), or the affirmed and the denied (also called contradictory terms). He gives the following examples of each:

An instance of the use of the word "opposite" with reference to correlatives is afforded by the expressions "double" and "half;" with reference to contraries by "bad" and "good." Opposites in the sense of privatives and positives are "blindness" and "sight;" in the sense of affirmatives and negatives, the statements "he sits," "he does not sit."

He then goes on to discuss each kind of opposition in detail. The first kind he defines are the correlatives, which we briefly considered in our discussion of relation. There we found that every relative term implies another relative term that works in the opposite direction. For example, the term "double" implies the correlative "half." Thus, four is the double of two because two is half of four. The two relations together are called correlatives and they constitute a kind of opposition. "Double" and "half" and "parent" and "offspring" are pairs of correlative opposites.

While the opposition between correlatives is important in theology, and we are not wasting our time talking about it, it is not going to be useful for specific differences. An example will explain this. The number four is double of the number two, while it is half of the number eight. Thus, the number four possesses both correlatives, though in relation to different things. Each thing under a genus, however, should be able to have only one of the differences which divide the genus, otherwise the species will overlap. If the opposite "double" and "half" were the specific differences dividing the species number, then four would belong to both species, since it is both double and half. Thus, correlatives would not often be used as the specific differences under a genus.

So we move on the second kind of opposition, that between contraries, for example, between the good and the bad. St. Thomas defines contraries as "what are most different in the same genus." For example, black and white are as different as colors can be. But what is true about contraries is that they often, though not always, have intermediates. For example, black and white are not the only colors. Rather, there are other colors, such as red and yellow, which are between black and white. Contraries, precisely because they are the most different within a genus, often have intermediate states come between them.

Can the specific differences of things be contraries? Contraries clearly do not have the same problem as correlatives of allowing the species to overlap: a thing can only possess one of the contraries, never both. But contraries have another problem: when they admit of intermediates, they do not exhaust the genus to be divided. For example, we could not divide the genus animal through the differences black and white because animals comes in a large variety of intermediate colors: the differences would not exhaust the genus. Thus, contraries, at least those that have intermediates, will not make good specific differences.

We must be careful about the word "contrary." Aristotle sometimes uses the word "contrary" as if it were synonymous with opposite. That is, he uses the name of the species for the genus. There is something right about this: contraries are the most opposite opposites, and when someone asks for examples of opposites, we usually give contraries. But this means that we need to be cautious when we come upon the word contrary: we should ask ourselves whether Aristotle or St. Thomas means contraries in particular, or whether they are just referring to opposites in general.

The third kind of opposition is that between privation and possession, or privatives and positives as our translation has it. Aristotle identifies the distinguishing mark of privation and possession:

Privatives and positives have reference to the same subject. Thus, sight and blindness have reference to the eye.

Taking his example, we can say that blindness is the privation, sight the possession. Blindness, of course, implies the lack of sight, or not-seeing. Yet I cannot attribute blindness to everything that lacks sight: it would be strange say that the rock or my footstool is blind. We do not call them blind because we do not expect them to see. Thus, what Aristotle means by saying that privation and possession have reference to the same subject is that the privation is only attributed to those subjects which can have the possession. The privation is the lack of the possession in the natural subject of that possession.

Can privation and possession be the opposition at the basis of specific difference? It seems that they can. This kind of opposition differs from that of the correlatives because a subject can only have one of them, either the privation or the possession, but not both. For example, the eye cannot both be blind and seeing. Thus, taking these opposites as differences will prevent overlapping species. Privation and possession differ from contraries because they have no intermediates: there is no middle between blind and seeing for the eye. So it seems that the opposition of privation and possession is both non-overlapping and exhaustive and is an appropriate basis for specific differences.

Finally, there is the opposition between affirmatives and negatives, which St. Thomas calls contradictory opposition. At first, it looks like Aristotle's discussion of this kind of opposition is out of place: this is not an opposition between simple expressions, but statements, which are complex expressions: he sits and he is not sitting are statements. Aristotle's answer is that this is not really an example of contradictory opposition, but is only like an example of contradictory opposition. He explains:

That which is affirmed and denied is not itself affirmation or denial. . . . For as the affirmation is opposed to the denial, as in the two statements "he sits" and "he does not sit," so also the thing which constitutes he matter of the statement in one case is opposed to that in the other, his sitting . . . to his not sitting.

He is saying that the two statements, he sits and he does not sit, refer to two different states, sitting and non-sitting, and that the latter two are really examples of contradictory expressions. We could say that contradictory expressions are simple expressions which indicate the presence and absence of something, and are always expressed in terms of a positive word and a negative one. For example, sitting is the positive opposite which expresses presence, and not-sitting is negative and expresses absence. Just as with the two statements one is true and the other false, so with contradictory terms it is always the case that one belongs and the other does not.

Like privation and possession, the opposition between contradictories is non-overlapping: something cannot have both contradictories. Further, it is exhaustive: everything in the genus has either one or the other of the contradictories. The difficulty for contradictories is that they are more universal than any genus, while privation and possession are not. That is, the privation can only apply to what can have the possession, to something in a given genus, but the negative contradictory can apply to everything that is or could be, even to things which could never have the positive contradictory. For example, I cannot call a rock blind, but I can certainly say that a rock is non-seeing. Thus, the opposites seeing and non-seeing, since one applies to everything that is, are more universal than the opposites blind and seeing.

Because contradictories are so universal, they are less fit to be differences than privation and possession. Privation and possession are more suitable precisely because they remain within the genus, while contradictories spill outside the genus. For example, we can understand the specific differences which divide animal as a privation and possession: beasts lack reason, man has it, and the nature of animal, the genus, is the proper subject for reason. But the contradictories, rational and non-rational, are much broader. Not only are some animals non-rational, but so is everything in the material universe except man, including such things as colors and shapes.

Although contradictories are a little too broad to use as specific differences, they are still important. We should notice that contradictories are the most basic kind of opposition because they are always implied in the previous two kinds of opposition. For example, black and white are contraries, but black certainly implies non-white. Thus, the contradictories white and non-white are hidden within the contraries white and black. In the same way, the contradictories not-seeing and seeing are hidden within the privation and possession, blindness and sight.

Our discussion of the opposites has been more extensive than necessary for understanding specific differences, but that is because the subject has a more universal utility. Every distinction has its basis in some kind of opposition, but distinction is one of the first activities of philosophy: St. Thomas says that he who would philosophize must distinguish. Thus, knowing the opposites helps all philosophizing. Furthermore, distinction comes before order: we cannot order what we cannot distinguish. Therefore, the topic of opposition should prepare us to understand our next topic, order.

Order and the Relations of Prior and Posterior

Order is a relation of the prior and posterior, or of what comes before and after, so in chapter 12 of the Categories, Aristotle covers the different meanings of the term "prior" or before. He assigns four meanings to it, priority in time, being, knowledge, and goodness. Let us briefly look at each kind.

Prior in time is the most familiar meaning of prior. Whatever is older than another comes before that other in time. For example, a house built in the year 1500 is older than one built in 2000, so that the building of the first is prior in time to the building of the second.

Prior in being is more difficult to understand. Aristotle writes:

Secondly, one thing is said to be prior to another when the sequence of their being cannot be reversed, as one is prior to two.

What Aristotle means when he says that the sequence of their being cannot be reversed is that the first can exist without the second, but the second cannot exist without the first. His example uses numbers of things: I can have one cow, and not have two cows, but I cannot have two cows without also having one. The possession of one cow is prior in being to the possession of two, even if I bought both cows at the same time. Another example: God did not have to make creatures; God can exist without creatures, but creatures cannot exist without God. Thus, God is prior in being to creatures.

Notice that being prior in being says nothing about time. I can buy both cows at the same time, and yet there is a priority of having one cow to having two. God is entirely outside time, which He has created. Therefore, God is not prior to creatures in time. Yet God is still prior to creatures in being because he can exist without them, but the sequence cannot be reversed.

The third meaning of "prior" is like the second: just as a first is prior to a second in being because it can exist without the second, but the second cannot exist without the first, so also one thing is prior another in knowledge when the first can be known without the second being known, while the second cannot be known unless the first is already known. For example, a child learning to count may know how to count to five without being able to count to ten, but if he can count to ten he can also count to five. Five is prior to ten in our knowledge.

We should notice that what is prior in knowledge is not always the same as what is prior in being. For example, God is prior to creatures in being, but creatures are prior to God in the order of our knowledge. That is, a man may know much about creatures, and nothing about God, but he cannot know nothing about creatures and know something about God because God is known through His creation. Therefore, prior in being and prior in knowledge, while defined in parallel ways, are not the same thing.

The last main meaning of prior is that which is prior in goodness. Aristotle means that what is better is prior in goodness. This may seem a strange use of the term, but there are a couple of ordinary expressions which show that Aristotle is right to give it this meaning. First, the champions in any sport always boast that they are number one. By number one they are indicating that they are first, prior to all the other teams. Why are they first? Because they are the best, and the better is prior to the worse. Moreover, we tell people to get their priorities straight, to put first things first. A man who desires wealth more than virtue has his priorities mixed up. Why? Because virtue is better than wealth, and should be prior to it, but he thinks wealth is better than, prior to, virtue. So we do use the term prior to mean better than. There is an order of goodness.

The knowledge of the kinds of order is vital to all of philosophy. As Aristotle says, the task of the wise man is to order, and one cannot order without knowing order and its kinds. Moreover, one of these kinds of priority is especially important to definition: the order of knowledge. When we are looking for the definition of a thing, we usually find not one, but many genera which apply to it. Man is not only an animal, he is a living thing, a body, and a substance. The question is: in what order are these attributed to man? How should I order the genera in man's definition. Aristotle answers: according to the order of knowledge. The highest, most remote genus is the one which is first known, and the intermediates are ordered according to that knowledge. I cannot know what an animal is without knowing what a living thing is, but I can know what a living thing is without knowing exactly what an animal is. Living thing is therefore prior in knowledge to animal, and is the higher genus. Thus, the knowledge of order is useful for defining.


We have covered almost all of the fundamentals of the logic of the first operation. The first operation aims at definition, which we discussed in our second lesson. In the third, we talked about the categories, which are tools that help us to use the tool of genus in our definitions. In this lecture, we have discussed opposition and order, which are useful for determining both differences and genera. There is one more topic to cover in the logic of the first operation: the use of analogy. In our next lesson we will discuss the logic of analogy, and then we will move on to the logic of the second operation of the intellect, which is the understanding the true and the false.


How are the following terms opposed?

1. Black -- white
2. Hot -- cold
3. Rational -- irrational
4. Black -- non-black
5. Deaf -- hearing
6. Quadruple -- one-fourth
7. Parent -- offspring
8. Odd -- even
9. Cause -- effect
10. Lame -- able-bodied

In what way(s) is the first term prior to the second?

1. God -- creatures
2. Creatures -- God
3. One -- two
4. Baby -- man
5. Man -- baby
6. Ignorant man -- wise man
7. Wise man -- ignorant man
8. Plants -- animals
9. B.C. -- A.D.
10. Socrates -- picture of Socrates


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