Lecture 10 — The proposition’s division on the part of the subject; affirmation and negation in universal and indefinite propositions

17a38. Since some of the things we are concerned with are universal and others singular—by “universal,” I mean that which is of such a nature as to be predicated of many, and by “singular,” that which is not (for example “man” is universal, “Plato” singular)—

17b1. we have to enunciate either of a universal or of a singular that something belongs or does not belong to it.

17b3. If, then, it is universally enunciated of a universal that something belongs or does not belong to it, the enunciations will be contraries. By “universally enunciated of a universal,” I mean such enunciations as “every man is white” or “no man is white.”

17b6. On the other hand, when the enunciations are of a universal but not universally enunciated, they are not contraries, although it is possible for the things signified to be contraries.

17b8. I mean by “enunciated of a universal but not universally” such enunciations as “man is white” or “man is not white.”

17b10. For, while “man” is a universal, it is not used as universal in the enunciation, for “every” does not signify the universal but signifies that it is taken “universally.”

17b12. But as regards the predicate, the universal universally predicated is not true; for no affirmation will be true in which a universal predicate is predicated universally, such as “every man is every animal.”

Since some of the things we are concerned with. The Philosopher has just said that contradiction is the opposition of the affirmation and negation of the same thing of the same subject. Following upon this, he distinguishes the diverse oppositions of affirmation and negation, the purpose being to know what true contradiction is.

And here he does two things:

first, he states a division of enunciation which is necessary in order to assign the difference of these oppositions;

second, he begins to manifest the different oppositions where he says: if, then, it is universally enunciated of a universal (17b3; [128]).

The division he gives is taken from the difference of the subject; therefore, about the first he does two things:

first, he divides the subject of enunciations;

second, he concludes with the division of enunciation, at: we have to enunciate either of a universal or of a singular (17b1; [125]).

Now, the subject of an enunciation is a name or something taken in place of a name. A name is a vocal sound significant by convention of simple thought, which, in turn, is a likeness of the thing.

Hence, Aristotle distinguishes the subject of enunciation by a division of things. He says that of things, some are universals, others singulars (17a38).

He then explains the members of this division in two ways.

First, he defines them, saying that the universal is that which is of such a nature as to be predicated of many, and that the singular is that which is not to be predicated of many, but of one alone.

Then he manifests them by example when he says that “man” is universal, “Plato” singular.

There is a difficulty about this division, for the Philosopher proves in Metaphysics (Metaphysics, bk. 7, ch. 14, 1039a23.) that the universal is not something existing outside of the thing; and in the Categories, (Categories, ch. 5, 2a11.) he says that second substances are only in first substances, that is, singulars. Therefore, the division of things into universals and singulars does not seem to be consistent, since according to him there are no things that are universal; on the contrary, all things are singular.

The things divided here, however, are things as signified by names—which names are subjects of enunciations. Now, Aristotle has already said that names signify things only through the mediation of the intellect; therefore, this division must be taken as a division of things as apprehended by the intellect. Now, in fact, whatever is joined together in things can be distinguished by the intellect when one of them does not belong to the notion of the other. In any singular thing, we can consider what is proper to the thing insofar as it is this thing—for instance, what is proper to Socrates or to Plato insofar as he is this man.

We can also consider that in which it agrees with certain other things, as that Socrates is an animal, or man, or rational, or risible, or white. Accordingly, when a thing is denominated from what belongs only to this thing insofar as it is this thing, the name is said to signify a singular. When a thing is denominated from what is common to it and to many others, the name is said to signify a universal since it signifies a nature or some disposition which is common to many. Immediately after giving this division of things, then—not of things absolutely as they are outside of the soul, but as they are referred to the intellect—Aristotle defines the universal and the singular through the act of the intellective soul as that which is such as to be predicated of many or of only one, and not according to anything that pertains to the thing (that is, as if he were affirming such a universal outside of the soul, an opinion relating to Plato’s teaching).

There is a further point we should consider in relation to this portion of the text. The intellect apprehends the thing—understood according to the thing’s essence or definition. This is the reason Aristotle says (On the Soul, bk. 3, ch. 4, 429b10.) that the proper object of the intellect is what the thing essentially is. Now, sometimes the proper nature of some understood form is not repugnant to being in many but is impeded by something else, either by something occurring accidentally (for instance, if all men but one were to die), or because of the condition of matter. The sun, for instance, is only one not because it is repugnant to the notion of the sun to be in many according to the condition of its form, but because there is no other matter capable of receiving such a form. This is the reason Aristotle did not say that the universal is that which is predicated of many, but that which is of such a nature as to be predicated of many.

Now, since every form which is so constituted as to be received in matter is communicable to many matters, there are two ways in which what is signified by a name may not be of such a nature as to be predicated of many:

in one way, because a name signifies a form as terminated in this matter (for example, as in the name “Socrates” or “Plato,” which signifies human nature as it is in this matter);

in another way, because a name signifies a form which is not constituted to be received in matter and consequently must remain in itself one and singular. Whiteness, for example, would be only one if it were a form not existing in matter, and consequently singular. This is the reason the Philosopher says that if there were separated species of things, as Plato held, they would be individuals. (Metaphysics bk. 7, ch. 6, 1045a36–1045b7.)

It could be objected that the name “Socrates” or “Plato” is of such a kind as to be predicated of many, since there is nothing to prevent their being applied to many.

The response to this objection is evident if we consider Aristotle’s words. Notice that he divides things into universal and particular, not names. It should be understood from this that what is said to be universal not only has a name that can be predicated of many, but that what is signified by the name is of such a nature as to be found in many. Now, this is not the case in the above-mentioned names, for the name of “Socrates” or “Plato” signifies human nature as it is in this matter. If one of these names is imposed on another man, it will signify human nature in other matter, and it will be a different signification. Consequently, it will be equivocal, not universal.

When he says: we have to enunciate either of a universal or of a singular (17b1), he infers the division of the enunciation.

Since something is always enunciated of something, and of things some are universals and some singulars, it follows that sometimes it will be enunciated that something belongs or does not belong to something universal, sometimes to something singular. The construction of the sentence was interrupted by the explanation of universal and singular, but now we can see the meaning: ***since some of the things we are concerned with are universal and others singulars **. *. . we have to enunciate either of a universal or of a singular that something belongs or does not belong to it.

In relation to the point being made here, we have to consider the four ways in which something is enunciated of the universal.

On the one hand, the universal can be considered as though separated from singulars, whether subsisting in itself (as Plato held), or according to the being it has in the intellect (as Aristotle held). Considered thus, something can be attributed to it in two ways.

Sometimes we attribute something to it which pertains only to the operation of the intellect, such as when we say man (whether the universal, the genus, or the species) is predicable of many. For the intellect forms intentions of this kind and attributes them to the nature understood according as it compares the nature to the things outside of the mind.

But sometimes we attribute something to the universal thus considered (that is, as it is apprehended by the intellect as one) which does not belong to the act of the intellect but to the being that the nature apprehended has in things outside of the soul, such as when we say, “Man is the noblest of creatures.” For this truly belongs to human nature as it is in singulars, since any single man is more noble than all irrational creatures; yet all singular men are not one man outside of the mind, but only in the apprehension of the intellect, and the predicate is attributed to it in this way (that is, as to one thing).

On the other hand, we attribute something to the universal as in singulars in another way, and this is twofold.

Sometimes it is in view of the universal nature itself, such as when we attribute something to it that belongs to its essence, or follows upon the essential principles, as in “Man is an animal,” or “Man is risible.”

Sometimes it is in view of the singular in which the universal is found; for instance, when we attribute something to the universal that pertains to the individual, as in “Man walks.”

Moreover, something is attributed to the singular in three ways:

in one way, as it is subject to the intellect, as when we say, “Socrates is a singular,” or “predicable of only one”;

in another way, by reason of the common nature, as when we say, “Socrates is an animal”;

in the third way, by reason of itself, as when we say, “Socrates is walking.”

The negations are varied in the same number of ways, since everything that can be affirmed can also be denied, as was said above.

This is the third division the Philosopher has given of the enunciation.

The first was the division of the enunciation into one simply and one by conjunction. This is an analogous division into those things of which one is predicated primarily and consequently, for one is divided according to the prior and posterior into simple and composite.

The second was the division of enunciation into affirmation and negation. This is a division of genus into species, for it is taken from the difference of the predicate to which a negation is added. The predicate is the formal part of the enunciation, and hence such a division is said to pertain to the quality of the enunciation. By “quality,” I mean essential quality, for in this case the difference signifies the quality of the essence.

The third division is based upon the difference of the subject as predicated of many or of only one, and is therefore a division that pertains to the quantity of the enunciation, for quantity follows upon matter.

Aristotle shows next how enunciations are opposed in diverse ways according to the diversity of the subject, at: if, then, it is universally enunciated of a universal (17b3).

And here he does two things:

first, he distinguishes the diverse modes of opposition in enunciations;

second, he shows how these diverse oppositions are related in different ways to truth and falsity, at: hence in the case of the latter it is impossible that both be at once true (17b23; [148]).

First, then, he distinguishes the diverse modes of opposition. Since these depend upon a diversity in the subject, we must first consider the latter diversity. Now, the universal can be considered either in abstraction from singulars or as it is in singulars, and by reason of this something is attributed in diverse modes to the universal, as we have already said. To designate diverse modes of attribution, certain words have been conceived which may be called determinations or signs, and which designate that something is predicated in this or that mode.

But first we should note that since it is not commonly apprehended by all men that universals subsist outside of singulars, there is no word in common speech to designate the mode of predicating in which something is thus said of a universal in abstraction from singulars. Plato, who held that universals subsist outside of singulars, did, however, invent certain determinations to designate the way in which something is attributed to the universal as it is outside of singulars. With respect to the species “man,” he called the separated universal subsisting outside of singulars “man in itself” or “man itself,” and he designated other such universals in like manner.

However, the universal as it is in singulars does fall within the common apprehension of men, and accordingly certain words have been conceived to signify the mode of attributing something to the universal taken in this way.

As was said above, this happens in two ways.

Sometimes, something is attributed to the universal in view of the universal nature itself; for this reason, it is said to be predicated of the universal universally—that is, it belongs to the universal according to the whole multitude in which it is found. The word “every” has been devised to designate this in affirmative predications. It designates that the predicate is attributed to the universal subject with respect to the whole of what is contained under the subject. In negative predications, the word “no” has been devised to signify that the predicate is removed from the universal subject according to the whole of what is contained under it. Hence, saying “nullus,” or “none,” in Latin is like saying “non ullus,” or “not any.” In Greek, ουδεις, “none,” is like ουδε εις, “not one,” for not a single one is understood under the universal subject from which the predicate is not removed.

Sometimes, something is either attributed to or removed from the universal in view of the particular. To designate this in affirmative enunciations, the words “some” or “a certain one” has been devised. We designate by this that the predicate is attributed to the universal subject by reason of the particular. “Some” or “a certain one,” however, do not signify the form of any singular determinately; rather, they designate the singular under a certain indetermination. The singular so designated is therefore called the vague individual. In negative enunciations, there is no designated word, but “not all” can be used. Just as “no,” then, removes universally because it signifies the same thing as if we were to say “not any” (that is, “not some”), so also “not all” removes particularly inasmuch as it excludes universal affirmation.

There are, therefore, three kinds of affirmations in which something is predicated of a universal:

in one, something is predicated of the universal universally, as in “every man is an animal”;

in another, something is predicated of the universal particularly, as in “some man is white”;

in the third, something is predicated of the universal without a determination of universality or particularity. Enunciations of this kind are customarily called “indefinite.”

There are the same number of opposed negations.

In the case of the singular, although something is predicated of it in a different respect (as was said above), nevertheless, the whole is referred to its singularity because the universal nature is individuated in the singular. Therefore, it makes no difference as far as the nature of singularity is concerned whether something is predicated of the singular by reason of the universal nature, as in “Socrates is a man,” or belongs to it by reason of its singularity.

If we add the singular to the three already mentioned, there will be four modes of enunciation pertaining to quantity: universal, particular, indefinite, and singular.

Aristotle assigns the diverse oppositions of enunciations according to these differences.

The first opposition is based on the difference of universals and indefinites; the second on the difference of universals and particulars, the latter being treated where he says: affirmation is opposed to negation in the way I call contradictory (17b16; [143]).

About the first he does three things:

first, he treats of the opposition of universal propositions to each other;

second, the opposition of indefinite enunciations, at: when the enunciations are of a universal (17b6; [136]);

third, he excludes a doubt, at: in the predicate, however, the universal (17b12; [140]).

He says first (17b3), then, that if someone enunciates universally of a universal subject (namely, according to the content of its universality) that it is (that is, affirmatively), or is not (that is, negatively), these enunciations will be contrary; as when we say, “every man is white—no man is white.”

And the reason is that the things that are most distant from each other are said to be contraries. For a thing is not said to be black only because it is not white, but because over and beyond “not being white”—which signifies the remotion of white commonly—is added black, the extreme in distance from white. What is affirmed by the enunciation, “every man is white,” then, is removed by the negation, “not every man is white.” The negation, therefore, removes the mode in which the predicate is said of the subject which the word “every” designates. But over and beyond this remotion, the enunciation, “no man is white,” which is most distant from “every man is white,” adds total remotion, and this belongs to the notion of contrariety. He therefore appropriately calls this opposition contrariety.

When he says: on the other hand, when the enunciations are of a universal (17b6), he shows what kind of opposition there is between affirmation and negation in indefinite enunciations.

First, he states the point;

second, he manifests it by an example, at: I mean by “enunciated of a universal but not universally” (17b8).

Finally, he gives the reason for this when he says: for while “man” is a universal, it is not used as a universal (17b10).

He says first, then, that when something is affirmed or denied of a universal subject, but not universally, the enunciations are not contrary but the things that are signified may be contraries.

He clarifies this with examples, at: I mean by “enunciated of a universal but not universally” (17b8).

Note in relation to this that what he said just before this was when . . . of universals but not universally enunciated (17b6), and not, when . . . of universals particularly, because he only intends to speak of indefinite enunciations, not of particulars. He manifests this by the examples he gives. When we say, “man is white,” and, “man is not white,” the universal subjects do not make them universal enunciations.

He gives as the reason for this, that although man, which stands as the subject, is universal, the predicate is not predicated of it universally because the word “every” is not added, which does not itself signify the universal, but the mode of universality—namely, that the predicate is said universally of the subject. Therefore, when “every” is added to the universal subject, it always signifies that something is said of it universally.

This whole exposition relates to what he had been saying: on the other hand, when the enunciations are of a universal but not universally enunciated, they are not contraries (17b6).

Immediately after this, he adds: although it is possible for the things signified to be contraries (17b6), and although this is obscure, he does not explain it. It has therefore been interpreted in different ways. Some related it to the contrariety of truth and falsity proper to enunciations of this kind. For such enunciations may be simultaneously true, such as “man is white” and “man is not white,” and thus not be contraries, for contraries mutually destroy each other. On the other hand, one may be true and the other false, such as “man is an animal” and “man is not an animal,” and thus by reason of what is signified seem to have a certain kind of contrariety.

But this does not seem to be related to what Aristotle has said:

first, because the Philosopher has not yet taken up the point of truth and falsity of enunciations;

second, because this very thing can also be said of particular enunciations.

Others, following Porphyry, relate this to the contrariety of the predicate. For sometimes the predicate may be denied of the subject because of the presence of the contrary in it, as when we say, “Man is not white,” because he is black. Thus it could be the contrary that is signified by “is not white.” This is not always the case, however, for we remove something from a subject even when it is not a contrary that is present in it but some mean between contraries, as in saying, “Someone is not white” because he is pale; or when there is a privation of act or habit or potency, as in saying, “Someone is non-seeing” because he lacks the power of sight or has an impediment so that he cannot see, or even because something is not of such a nature as to see, as in saying, “A stone does not see.” It is therefore possible for the things signified to be contraries, but the enunciations themselves not to be; for, as is said near the end of this book, opinions that are about contraries are not contrary (for example, an opinion that something is good and an opinion that something is evil).

This does not seem to relate to what Aristotle has proposed either, for he is not treating here of contrariety of things or opinions, but of contrariety of enunciations. For this reason it seems better here to follow the exposition of Alexander.

According to his exposition, in indefinite enunciations it is not determined whether the predicate is attributed to the subject universally (which would constitute contrariety of enunciations), or particularly (which would not constitute contrariety of enunciations). Accordingly, enunciations of this kind are not contrary in mode of expression. However, sometimes they have contrariety by reason of what is signified, that is, when something is attributed to a universal in virtue of the universal nature, although the universal sign is not added, as in “man is an animal” and “man is not an animal,” for in virtue of what is signified these enunciations have the same force as “every man is an animal” and “no man is an animal.”

When he says: but as regards the predicate, the universal universally predicated is not true (17b12), he precludes a certain difficulty.

He has already stated that there is a diversity in the opposition of enunciations because of the universal being taken either universally or not universally on the part of the subject. Someone might think, as a consequence, that a similar diversity would arise on the part of the predicate—that is, that the universal could be predicated both universally and not universally. To exclude this, he says that in the case in which a universal is predicated it is not true that the universal is predicated universally.

There are two reasons for this.

The first is that such a mode of predicating seems to be repugnant to the predicate in relation to its status in the enunciation; for, as has been said, the predicate is a quasi-formal part of the enunciation, while the subject is a material part of it. Now, when a universal is asserted universally, the universal itself is taken according to the relationship it has to the singulars contained under it, and when it is asserted particularly, the universal is taken according to the relationship it has to some one of what is contained under it. Thus both pertain to the material determination of the universal. This is why it is not appropriate to add either the universal or particular sign to the predicate, but rather to the subject; for it is more appropriate to say, “No man is an ass” than “Every man is no ass”; likewise, it is more proper to say, “Some man is white” than “Man is some white.” However, sometimes philosophers put the particular sign next to the predicate to indicate that the predicate is in more than the subject, and this especially when they have a genus in mind and are investigating the differences which complete the species. There is an instance of this in On the Soul 2.1, 412a22, where Aristotle says that the soul is a certain act.

The other reason is related to the truth of enunciations. This has a special place in affirmations, which would be false if the predicate were predicated universally. Hence to manifest what he has stated, he adds, for there is no affirmation in which, that is, truly, a universal predicate will be predicated universally, that is, in which a universal predicate is used to predicate universally—for example, “every man is every animal.” If this could be done, the predicate “animal,” according to the singulars contained under it, would have to be predicated of the singulars contained under “man.” But such predication could not be true, whether the predicate is in more than the subject or is convertible with the subject, for then any one man would have to be all animals or all risible beings, which is repugnant to the notion of the singular, which is taken under the universal.

The truth of the enunciation, “every man is susceptible of every discipline” is not an instance that can be used as an objection to this position, for it is not “discipline” that is predicated of man, but “susceptible of discipline.” It would be repugnant to truth if it were said that “every man is everything susceptible of discipline.”

On the other hand, although the negative universal sign or the particular affirmative sign are more appropriately posited on the part of the subject, it is not repugnant to truth if they are posited on the part of the predicate, for such enunciations may be true in some matter. The enunciation, “every man is no stone,” for example, is true, and so is “every man is some animal.” But the enunciation, “every man is every animal,” in whatever matter it occurs, is false.

There are other enunciations of this kind that are always false, such as “some man is every animal” (which is false for the same reason as “every man is every animal” is false). And if there are any others like these, they are always false; and the reason is the same in every case. And, therefore, in rejecting the enunciation, “every man is every animal,” the Philosopher meant it to be understood that all similar enunciations are to be rejected.