Lecture 2 — The number and relationship of simple enunciations, in which the verb “is” is predicated as a third element and the subject is the finite name not universally taken

19b19. But when “is” is predicated as a third element in the enunciation, there are two oppositions.

19b20. I mean by this that in an enunciation such as “man is just,” the “is” is a third name or verb contained in the affirmation.

19b22. In this case, therefore, there will be four enunciations.

19b23. Two of these will correspond in their sequence (in respect of affirmation and negation) with the privations, but two will not.

19b24. I mean that the “is” will be added either to “just” or to “non-just”; and so also in the case of the negative. Thus there will be four.

19b27. The following diagram will make this clear: man is just—man is not just; man is not not-just—man is not-just. Here "is" and "is not" are added either to "just" or to "not-just." This, then, is the way these are arranged, as we have said in the Analytics.

But when “is” is predicated as a third element. After distinguishing enunciations in which either a finite or an infinite name is posited only on the part of the subject, the Philosopher begins here to distinguish enunciations in which either a finite or an infinite name is posited as the subject and as the predicate.

About this he does two things:

first, he distinguishes these enunciations;

second, he manifests certain things that might be doubtful in relation to them, at: since the negation contrary (20a16; [242]).

About the first he does two things:

first, he deals with enunciations in which the name is predicated with the verb “is”;

second, with those in which other verbs are used, at: in enunciations in which “is" (20a3; [237]).

He distinguishes these enunciations as he did the primary enunciations, according to a triple difference on the part of the subject:

first, he treats those in which the subject is a finite name not taken universally;

second, those in which the subject is a finite name taken universally, at: the same is the case when the affirmation (19b32; [226]);

third, those in which an infinite name is the subject, at: and there are two other pairs (19b36; [234]).

About the first he does three things:

first, he proposes a diversity of oppositions;

second, he concludes as to their number and states their relationship, at: in this case, therefore, there will be four enunciations (19b22; [215]);

third, he exemplifies this with a table.

Concerning the first he does two things:

first, he sets forth what he intends to do;

second, he explains what he had said, at: I mean by this (19b20; [214]).

In relation to the first point two things have to be understood.

First, what he means by: “is” is predicated as a third element in the enunciation (19b19). To clarify this, we must note that the verb “is” itself is sometimes predicated in an enunciation, as in “Socrates is.” By this we intend to signify that Socrates really is. Sometimes, however, “is” is not predicated as the principal predicate, but is joined to the principal predicate to connect it to the subject, as in “Socrates is white.” Here the intention is not to assert that Socrates really is, but to attribute whiteness to him by means of the verb “is.” Hence, in such enunciations, “is” is predicated as added to the principal predicate. It is said to be third not because it is a third predicate, but because it is a third word posited in the enunciation, which together with the name predicated makes one predicate. The enunciation is thus divided into two parts and not three.

Second, we must consider what he means by when “is” is predicated as a third element in the enunciation (19b19), in the mode in which we have explained, there are two oppositions. In the enunciations already treated, in which the name is posited only on the part of the subject, there was one opposition in relation to any subject. For example, if the subject was a finite name not taken universally, there was only one opposition: “man is—man is not.” But when “is” is predicated in addition, there are two oppositions with regard to the same subject corresponding to the difference of the predicate name, which can be finite or infinite. There is the opposition of “man is just—man is not just,” and the opposition, “man is non-just—man is not non-just.” For the negation is effected by applying the negative particle to the verb “is,” which is a sign of a predication.

When he says: I mean by this (19b20), he explains what he said: when “is” is predicated as a third element in the enunciation.

When we say “man is just,” the verb “is” is added to the predicate as a third name or verb in the affirmation. Now, “is,” like any other word, may be called a name, and thus it is a third name—that is, a word. But because, according to common usage, a word signifying time is called a “verb” rather than a “name,” Aristotle adds here, or verb, as if to say that with respect to the fact that it is a third thing, it does not matter whether it is called a name or a verb.

He goes on to say: in this case, therefore, there will be four enunciations (19b22). Here he concludes to the number of the enunciations.

First, he gives the number;

second, their relationship, at: two of which will correspond in their sequence (19b23);

third, the reason for the number, at: I mean that the “is” will be added either to “just” or to “non-just" (19b24; [223]).

Therefore, he first says that since there are two oppositions when “is” is predicated as a third element in the enunciation, and since every opposition is between two enunciations, it follows that there are four enunciations in which “is” is predicated as a third element when the subject is finite and is not taken universally.

When he says: two of which will correspond in their sequence (19b23), he shows their relationship.

Two of these enunciations are related to affirmation and negation according to consequence (or according to correlation or proportion, as it is in the Greek) like privations, but the other two are not.

Because this is said so briefly and obscurely, it has been explained in diverse ways.

Before we take up the various explanations of this passage, there is a general point in relation to it that needs to be clarified. In this kind of enunciation, a name can be predicated in three ways.

We can predicate a finite name and by this we obtain two enunciations, one affirmative and one negative, “man is just” and “man is not just.” These are called simple enunciations.

Or, we can predicate an infinite name, and by this we obtain two other enunciations, “man is non-just” and “man is not non-just.” These are called infinite enunciations.

Finally, we can predicate a privative name, and again we will have two, “man is unjust” and “man is not unjust.” These are called privative.

Now, the passage in question has been explained by some in the following way. Two of the enunciations he has given, those with an infinite predicate, are related to the affirmation and negation of the finite predicate according to consequence or analogy, as are privations, that is, as are those with a privative predicate. For the two with an infinite predicate are related according to consequence to those with a finite predicate but in a transposed way, namely, affirmation to negation and negation to affirmation. That is, “man is non-just,” the affirmation of the infinite predicate, corresponds according to consequence to the negative of the finite predicate, that is, to “man is not just”; the negative of the infinite predicate, “man is not non-just,” corresponds to the affirmative of the finite predicate, that is, to “man is just.” Theophrastus for this reason called those with the infinite predicate “transposed.” The affirmative with a privative predicate also corresponds according to consequence to the negative with a finite predicate, that is, “man is unjust” to “man is not just”; and the negative of the privative predicate to the affirmative of the finite predicate, “man is not unjust” to “man is just.”

These enunciations can therefore be placed in a table in the following way:

Simple: man is just—man is not just.

Infinite: man is not non-just—man is non-just.

Privative: man is not unjust—man is unjust.

This makes it clear that two—those with the infinite predicate—are related to the affirmation and negation of the finite predicate in the way privations are, that is, as those that have a privative predicate. It is also evident that there are two others that do not have a similar consequence, namely, those with an infinite subject, “non-man is just” and “non-man is not just.”

This is the way Herminus explained the words but two will not, that is, by referring it to enunciations with an infinite subject.

This, however, is clearly contrary to the words of Aristotle, for, after giving the four enunciations (two with a finite predicate and two with an infinite predicate), he adds: two of which, but two will not, as though he were subdividing them, which can only mean that both pairs are comprised in what he is saying. He does not include among these the ones with an infinite subject but will mention them later. It is clear, then, that he is not speaking of these here.

Since this exposition is not consonant with Aristotle’s words, others, Ammonius says, have explained this in another way. According to them, two of the four propositions—those of the infinite predicate—are related to affirmation and negation, that is, to the species itself of affirmation and negation, as privations, that is, as privative affirmations and negations. For the affirmation, “man is non-just,” is not an affirmation simply, but relatively, as though according to privation, just as a dead man is not a man simply, but according to privation. The same thing applies to the negative enunciation with an infinite predicate. However, the two enunciations having finite predicates are not related to the species of affirmation and negation according to privation, but simply, for the enunciation “man is just” is simply affirmative, and “man is not just” is simply negative.

But this meaning does not correspond to the words of Aristotle either, for he says further on: this, then, is the way these are arranged, as we have said in the Analytics, but there is nothing in that text pertaining to this meaning.

Ammonius, therefore, interprets this differently and in accordance with what is said in Prior Analytics 1.46, 51b5 about propositions having a finite or infinite or privative predicate.

To make Ammonius’ explanation clear, it must be noted that, as Aristotle himself says, by some power, the enunciation is related to the things of which the whole of what is signified in the enunciation can be truly predicated. The enunciation “man is just,” for example, is related to all those of which in any way “is a just man” can be truly said. So, too, the enunciation “man is not just” is related to all those of which in any way “is not a just man” can be truly said. According to this mode of speaking, it is thus evident that the simple negative is wider than the infinite affirmative which corresponds to it. Thus, “is a non-just man” can truly be said of any man who does not have the habit of justice, but “is not a just man” can be said not only of a man not having the habit of justice, but also of what is not a man at all. For example, it is true to say, “wood is not a just man,” but false to say, “wood is a non-just man.” The simple negative, then, is wider than the infinite affirmative, just as “animal” is wider than “man,” since it is true of more things. For a similar reason, the simple negative is wider than the privative affirmative, for “is an unjust man” cannot be said of what is not man. But the infinite affirmative is wider than the private affirmative, for “is a non-just man” can be truly said of a boy or of any man not yet having a habit of virtue or vice, but “is an unjust man” cannot. And the simple affirmative is narrower than the infinite negative, for “is not a non-just man” can be said not only of a just man, but also of what is not man at all. Similarly, the privative negative is wider than the infinite negative. For “is not an unjust man” can be said not only of a man having the habit of justice and of what is not man at all—of which “is not a non-just man” can be said—but over and beyond this can be said about all men who neither have the habit of justice nor the habit of injustice.

With these points in mind it is easy to explain the present sentence in Aristotle. Two of which, that is, the infinites, will be related to the simple affirmation and negation according to consequence, that is, in their mode of following upon the two simple enunciations, the infinitives will be related as are privations, that is, as the two privative enunciations.

For just as the infinite negative follows upon the simple affirmative, and is not convertible with it (because the infinite negative is wider), so also the privative negative, which is wider, follows upon the simple affirmative and is not convertible. But just as the simple negative follows upon the infinite affirmative, which is narrower and is not convertible with it, so also the simple negative follows upon the privative affirmative, which is narrower and is not convertible. From this it is clear that there is the same relationship, with respect to consequence, of infinites to simple enunciations as there is of privatives.

He goes on to say: but two (19b23), namely, the simple enunciations that are left after the two infinite enunciations have been taken care of, will not, that is to say, they are not related to infinites according to consequence as privatives are related to them. On the one hand, the simple affirmative is narrower than the infinite negative, and the privative negative is wider than the infinite negative. On the other hand, the simple negative is wider than the infinite affirmative, and the privative affirmative narrower than the infinite affirmative. Thus it is clear that simple enunciations are not related to infinites in respect to consequence as privatives are related to infinites.

But although this smoothly explains the words of the Philosopher, the explanation appears a bit forced. For the words of the Philosopher seem to say that diverse relationships will not apply in respect to diverse things. However, in the exposition we have just seen, there is first an explanation of a similitude of relationship to simple enunciations, and then an explanation of a dissimilitude of relationship in respect to infinites.

Porphyry’s simpler exposition of this passage of Aristotle, which Boethius gives, is therefore more suitable. According to Porphyry’s explanation, there is similitude and dissimilitude according to consequence of affirmatives and negatives. Thus Aristotle is saying: of which, that is, the four enunciations we are discussing, two (namely, one simple and one infinite affirmative) will be related according to consequence in regard to affirmation and negation, that is, so that the other negative follows upon one affirmative, for the infinite negative follows upon the simple affirmative and the simple negative upon the infinite affirmative. But two, namely, the negatives, will not, that is, they are not so related to affirmatives that affirmatives follow from negatives. And with respect to both, privatives are related in the same way as the infinites.

Then Aristotle says, I mean that the “is"(19b24). Here he shows how, under these circumstances, we get four enunciations.

We are speaking now of enunciations in which the verb “is” is predicated as added to some finite or infinite name—for instance, as it adjoins “just” in “man is just,” or “non-just” in “man is non-just.” Now, since the negation is not applied to the verb in either of these, each is affirmative. However, there is a negation opposed to every affirmation, as was shown in the first book. Therefore, two negatives correspond to the two foresaid affirmative enunciations, making four simple enunciations.

Then he says: the following diagram will make this clear (19b27). Here he manifests what he has said by a diagrammatic description.

For, as he says, what has been stated can be understood . . .

Continuation of Cajetan

Commentary of Thomas Cajetan on the Remainder of Book 2 of On Interpretation

Lecture 3

The Number and Relationship of Enunciations in Which the Verb “Is” Is Predicated and the Subject Is the Finite Name Taken Universally, or the Infinite Name, and of Those in Which the Adjective Verb is Predicated

19b32. The same is the case when the affirmation is of a name taken universally, as in the following:

Every man is just (Affirmation)

Not every man is just (Negation)

Every man is non-just (Affirmation)

Not every man is non-just (Negation)

19b35. But it is not possible, in the same way as in the former case, that those on the diagonal both be true; it is sometimes possible, however.

19b36. These two pairs, then, are opposed; and there are two other pairs if something is added to “non-man” as a subject. Thus:

Non-man is just (Affirmation)

Non-man is not non-just (Negation)

Non-man is not just (Negation)

Non-man is non-just (Affirmation)

20a1. There will be no more opposites than these.

20a1. The latter, however, are separate from the former and distinct from them because of the use of “non-man” as a name.

20a3. In enunciations in which “is” does not join the predicate to the subject, for example when the verb “matures” or “walks” is used, the same scheme applies, and they are arranged in the same way as when “is” was added. For example:

Every man matures (Affirmation)

Not every man matures (Negation)

Every non-man matures (Affirmation)

Not every non-man matures (Negation)

20a7. We must not say “non-every man” but must add the negation to “man”; for the “every” does not signify a universal but that a universal is taken universally.

20a10. This is evident from the following: “Man matures,” “Man does not mature”; “Non-man matures,” “Non-man does not mature.” For these differ from the former in that they are not taken universally; the “every” and the “no,” then, only signify that the affirmation or negation is of a name universally.

20a14. All else in enunciations in which “is” does not join the predicate to the subject will be the same as in the case in which “is” is the second element.

Having distinguished enunciations in which the subject is an infinite name not taken universally, Aristotle now distinguishes enunciations in which the subject is a finite name taken universally.

About this he does three things.

He first proposes a similarity between these enunciations and the infinite enunciations already discussed;

second, he shows their difference where he says, but it is not possible, in the same way as in the former case (19b35; [229]);

third, he concludes with the number of oppositions there are between these enunciations where he says, these two pairs, then, are opposed (19b36; [233]).

He says first, then, that enunciations in which the affirmation is of a name taken universally are similar to those already discussed.

It is to be noted in relation to Aristotle’s first point that in indefinite enunciations there were two oppositions and four enunciations, the affirmatives inferring the negatives and not being inferred by them, as is clear in the exposition of Ammonius as well as of Porphyry. In enunciations in which the finite name universally taken is the subject there are also two oppositions and four enunciations, the affirmatives inferring the negatives and not the contrary. Hence, enunciations are related in a similar way if the affirmation is made universally of the name taken as the subject. For four enunciations will be made, two with a finite predicate—every man is just, and its negation, not every man is just—and two with an infinite predicate—every man is non-just, and its negation, not every man is non-just. And since any affirmation together with its negation makes one whole opposition, two oppositions are made, as was also said of indefinite enunciations. There might seem to be an objection to his use of particulars when speaking of universal enunciations, but this cannot be objected to, for just as in dealing with indefinite enunciations he spoke of their negations, so now in dealing with universal affirmatives he is forced to speak of their negations. The negation of the universal affirmative, however, is not the universal negative, but the particular negative, as was stated in the first book.

A table will make it evident that the consequence is similar in these and in indefinite enunciations. And lest what is clear be made obscure by verbosity, let us first make a diagram of the indefinites posited in the last lesson, based upon the exposition of Porphyry.

Place the finite affirmative on one side and under it the infinite negative, and under this the privative negative. On the other side put the finite negative first, under it the infinite affirmative, and under this the privative affirmative.

Then, under this diagram, make another similar to it, but of universals. On one side put the universal affirmative of the finite predicate, under it the particular negative of the infinite predicate, and to complete the parallel put the particular negative of the privative predicate under this. On the other side, first put the particular negative of the infinite predicate, under it the universal affirmative of the finite predicate, and under this the universal affirmative of the privative predicate. Thus: [figure: Man is just Man is not just; Man is not non-just Man is non-just; Man is not unjust Man is unjust] [figure: Every man is just Not every man is just; Not every man is non-just Every man is non-just; Not every man is unjust Every man is unjust]

In this disposition of enunciations, the consequence always follows in the second diagram just as it followed in regard to indefinites in the first diagram. This is true if we follow the exposition of Ammonius, in which infinites are related to finites as privatives are related to the same finites, and the finites not related to the infinite middle enunciations as privatives are related to those infinites. It is equally true if we follow the exposition of Porphyry, in which affirmatives infer negatives and not vice versa. That the tables serve both expositions will be clear to one studying them. These universal enunciations, therefore, are related in like manner to indefinite enunciations in three things: the number of propositions, the number of oppositions, and the mode of consequence.

When he says, but it is not possible (19b35), he proposes a difference between the universals and the indefinites, namely, that it is not possible for the diagonals to be true in the case of universals.

First, we will explain these words according to the exposition we believe Aristotle had in mind;

next, according to the opinion of others.

Aristotle means by diagonal enunciations those that are diametrically opposed in the diagram above, namely, the finite affirmative in one corner and the infinite affirmative or the privative in the other; and the finite negative in one corner and the infinite negative or privative in the other.

Enunciations that are similar in quality and called diagonal because diametrically distant are then dissimilar in truth in the case of indefinites and universals. The indefinites on the corners, both in the diagonal of affirmations and the diagonal of negations, can be simultaneously true, as is evident in the table of the indefinite enunciations. This is to be understood in regard to contingent matter. But diagonals of universals are not so related, for angulars on the diagonal of affirmations cannot be simultaneously true in any matter. Those on the diagonal of negations, however, can sometimes be true simultaneously, namely, when they are in contingent matter. In necessary and remote matter it is impossible for both of these to be true. This is the exposition of Boethius, which we believe to be the true one.

However, according to Boethius, Herminus explains this in another way. He takes the oppositions in one way in universals and in another in indefinites, although he holds that there is a likeness between universals and indefinites with respect to the number of enunciations and of oppositions. He arrives at the oppositions of indefinites we have—namely, one between the affirmative and negative finites, and the other between the affirmative and negative infinites.

But he disposes the oppositions of universals in another way, taking one between the finite universal affirmative and finite particular negative—every man is just and not every man is just—and the other between the same finite universal affirmative and the infinite universal affirmative—every man is just and every man is non-just. Between the latter there is contrariety, between the former contradiction.

He also proposes the dissimilarity between universals and indefinites in another way. He does not base the dissimilarity between diagonals of universals and indefinites on the difference between affirmative and negative diagonals of universals, as we do, but on the difference between the diagonals of universals on both sides among themselves. Hence he forms his diagram in this way: under the finite universal affirmative he places the infinite universal affirmative, and on the other side, under the finite particular negative the infinite particular negative. Thus the diagonals are of different quality. He also diagrams the indefinites in this way. [figure of opposition]

With enunciations disposed in this way he says their difference is this: in indefinite enunciations, the one on the diagonal is true as a necessary consequence of the truth of the other, so that the truth of one enunciation infers the truth of its diagonal from wherever you begin.

But there is no such mutual necessary consequence in universals from the truth of one on a diagonal to the other, since the necessity of inference fails in part. If you begin from any of the universals and proceed to its diagonal, the truth of the universal cannot be simultaneous with the truth of its diagonal so as to compel it to truth. For if the universal is true, its universal contrary will be false, since they cannot be at once true; and if this universal contrary is false, its particular contradictory, which is the diagonal of the first universal assumed, will necessarily be true, since it is impossible for contradictories to be at once false. But if, conversely, you begin with a particular enunciation and proceed to its diagonal, the truth of the particular can so stand with the truth of its diagonal that it does not infer its truth necessarily. For it follows that if the particular is true, then its universal contradictory is false. But it does not follow that if this universal contradictory is false, then its universal contrary (which is the diagonal of the particular assumed) is true. For contraries can be at once false.

But the way in which oppositions are taken in this exposition does not seem to be what Aristotle had in mind. He did not intend to speak here of the opposition between finites and infinites, but of the opposition between finites themselves and infinites themselves. For if we meant to explain each mode of opposition, there would not be two but three oppositions:

first, between finites;

second, between infinites;

and third, the one Herminus states between finite and infinite.

Even the diagram Herminus makes is not like the one Aristotle makes at the end of I Priorum, to which Aristotle himself referred us in the last lesson when he said, this, then, is the way these are arranged, as we have said in the Analytics (19b27). For in Aristotle’s diagram, affirmatives are diagonal to affirmatives and negatives to negatives.

Next, Aristotle says, these two pairs, then, are opposed (19b36). Here he concludes to the number of propositions. What he says here can be interpreted in two ways.

In the first way, these designates universals, and thus the meaning is that the finite and infinite universals have two oppositions, which we have explained above.

In the second, these designates enunciations which are finite and infinite with respect to the predicate, whether universal or indefinite, and then the meaning is that these enunciations have two oppositions, one between the finite affirmation and its negation and the other between the infinite affirmation and its negation.

The second exposition seems more satisfactory to me, because the brevity for which Aristotle strove allows for no repetition; hence, in terminating his treatment of the enunciations he had enumerated—those with a finite and infinite predicate according to diverse quantities—he meant to reduce all the oppositions to two.

When he says, and there are two other pairs (19b36), he shows the diversity of enunciations when “is” is added as a third element and the subject is an infinite name.

About this he does three things.

First, he proposes and distinguishes them;

second, he shows that there are no more opposites than these, at: there will be no more opposites than these (20a1; [235]);

third, he shows the relationship of these to the others, at: the latter, however, are separate (20a1; [236]).

With respect to the first point, it should be noted that there are three species of absolute enunciations in which the verb “is” is posited explicitly.

Some have nothing added to the subject—which can be either finite or infinite—beyond the verb, as in man is*, *non-man is.

Some have, besides the verb, something either finite or infinite added to a finite subject, as in man is just*, *man is non-just.

Finally, some have, besides the verb, something either finite or infinite added to an infinite subject, as in non-man is just*, *non-man is non-just.

He has already treated the first two and now intends to take up the last ones. And there are two other pairs, he says, that have something (namely, a predicate) added to non-man beside the verb is, as if to a subject (that is, to an infinite subject). He says as if because the infinite name falls short of the notion of a subject insofar as it falls short of the notion of a name. Indeed, the signification of an infinite name is not properly submitted to composition with the predicate, which is, the third element added, introduces.

Aristotle enumerates four enunciations and two oppositions in this order as he did in the former. In addition, he distinguishes these from the former finiteness and infinity.

First, he posits the opposition between affirmative and negative enunciations with an infinite subject and a finite predicate, non-man is just*, *non-man is not just.

Second, he posits another opposition between those with an infinite subject and an infinite predicate, non-man is non-just, non-man is not non-just.

Then he says, there will be no more opposites than these (20a1). Here he points out that there are no more oppositions of enunciations than the ones he has already given. We should note, then, that there cannot be more simple enunciations than the twelve posited in which the verb “is” is explicitly set down (whether it is the second or third element added). Consequently, their oppositions according to affirmation and negation are only six.

For enunciations are divided into three orders: those with the second element added, those with the third element added to a finite subject, and those with the third element added to an infinite subject. Further, in any order there are four enunciations. And since their subject can be quantified in four ways in any order—namely, by universality, particularity, singularity, and indefiniteness—these twelve will be increased to forty-eight, since four times twelve is forty-eight. Nor is it possible to imagine more than these. Aristotle has only expressed twenty of these, eight in the first order, eight in the second, and four in the third, but through them he intended the rest to be understood.

They are to be enumerated and disposed according to each order so that the primary negation is placed opposite an affirmation in order to make the relation of opposition more evident. Thus, the universal negative should not be ordered as opposite to the universal affirmative, but the particular negative, which is its negation. Conversely, the particular negative should not be ordered as opposite to the particular affirmative, but the universal negative, which is its negation. For a clearer look at their number, all those of similar quantity should be placed in a straight line and in the three distinct orders given above. [insert figure from https://isidore.co/aquinas/PeriHermeneias.htm#B3]

It is evident that there are no more than these, for the subject and the predicate cannot be varied in any other way with respect to finite and infinite. Nor can the finite and infinite subject be varied in any other way, for the enunciation with a second adjoining element cannot be varied with a finite and infinite predicate but only in respect to the subject. This is clear enough. But enunciations with a third adjoining element can be varied in four ways: they may have either a finite subject and predicate, or an infinite subject and predicate, or a finite subject and infinite predicate, or an infinite subject and finite predicate. These variations are all evident in the above table.

Then, when he says, the latter, however, are separate from the former (20a1), he shows the relationship of those we have put in the third order to those in the second order. The former, he says, are distinct from the latter because they do not follow upon the latter, nor conversely. He assigns the reason when he adds: because of the use of “non-man” as a name, that is, the former are separate from the latter because the former use an infinite name in place of a name, since they all have an infinite subject. It should be noted that he says enunciations of an infinite subject use an infinite name as a name, for to be subjected in an enunciation is proper to a name but to be predicated common to a name and a verb; therefore, every subject of an enunciation is subjected as a name.

Next, he takes up enunciations in which adjective verbs are posited, when he says, in enunciations in which “is” (20a3).

About this he does three things.

First, he distinguishes these adjective verbs;

second, he answers an implied question, at: we must not say “non-every man” (20a7; [238]);

third, he concludes with their conditions, at: all else in the enunciations in which “is” does not join (20a14; [241]).

It is necessary to note here that there is a difference between enunciations in which “is” is posited as a second adjoining element and those in which it is posited as a third element. In those with “is” as a second element, oppositions are simple, that is, varied only on the part of the subject by finite and infinite. In those having “is” as a third element, oppositions are made in two ways—on the part of the predicate and on the part of the subject—for both can be varied by finite and infinite. Hence we made only one order of enunciations with “is” as the second element. It had four enunciations quantified in diverse ways, and two oppositions. But enunciations with “is” as a third element must be divided into two orders, because in them there are four oppositions and eight enunciations, as we said above.

Enunciations with adjective verbs are made equivalent in signification to enunciations with “is” as the third element by resolving the adjective verb into its proper participle and “is,” which may always be done because a substantive verb is contained in every adjective verb. For example, “every man runs” signifies the same thing as “every man is running.” Because of this, Boethius calls enunciations having an adjective verb “enunciations of the second adjoining element according to vocal sound, but of the third adjoining element according to power.” He designates them in this manner because they can be resolved into enunciations with a third adjoining element to which they are equivalent.

With respect to the number and oppositions of enunciations, those with an adjective verb formally taken are not equivalent to those with a third adjoining element, but to those in which “is” is posited as the second element. For oppositions cannot be made in two ways in adjectival enunciations, as they are in the case of substantival enunciations with a third adjoining element—namely, on the part of the subject and predicate, because the verb which is predicated in adjectival enunciations cannot be made infinite. Hence oppositions of adjectival enunciations are made simply, that is, only by the subject quantified in diverse ways being varied by finite and infinite—as was done above in substantival enunciations with a second adjoining element for the same reason, namely, because there can be no affirmation or negation without a verb but there can be without a name.

Since the present treatment is not of significations but of the number of enunciations and oppositions, Aristotle determines that adjectival enunciations are to be diversified according to the mode in which enunciations with “is” as the second adjoining element are distinguished. And he says that in enunciations in which the verb “is” is not posited formally, but some other verb is posited (such as “matures” or “walks”)—that is, in adjectival enunciations—the name and verb form the same scheme with respect to the number of oppositions and enunciations as when “is” as a second adjoining element is added to the name as a subject. For these adjectival enunciations, like the ones in which “is” is posited, have only two oppositions: one between the finites, as in “every man runs,” “not every man runs”; the other between the infinites with respect to subject, as in “every non-man runs,” “not every non-man runs.”

Then he answers an implied question when he says, we must not say “non-every man” (20a7).

About this he does two things.

First, he states the solution of the question;

then, he proves it, at: this is evident from the following (20a10; [239]).

The question is this: why is the negation that makes a word infinite never added to the universal or particular sign? For example, when we wish to make “every man runs” infinite, why do we do it in this way: “every non-man runs,” and not in this: “non-every man runs”? He answers the question by saying that to be capable of being made infinite, a name has to signify something universal or singular. “Every” and similar signs, however, do not signify something universal or singular, but that something is taken universally or particularly. Therefore, we should not say “non-every man” if we wish to infinitize (although it may be used if we wish to deny the quantity of an enunciation), but must add the infinitizing negation to “man,” which signifies something universal, and say “every non-man.”

Where he says, this is evident from the following (20a10), he proves that every and similar words do not signify a universal but that a universal is taken universally. His argument is the following. That by which enunciations having or not having the every differ is not the universal; rather, they differ in that the universal is taken universally. But that by which enunciations having and not having the every differ is signified by the every. Therefore, that which is signified by the every is not a universal but that the universal is taken universally. The minor of the argument is evident, though not explicitly given in the text: that in which the having of some term differs from the not having of it, other things being equal, is the signification of that term. The major is made evident by examples. The enunciations “man matures” and “every man matures” differ precisely by the fact that in one there is an “every,” in the other not. However, they do not differ in such a way by this that one is universal, the other not universal, for both have the universal subject, “man.” They differ because in the one in which “every” is posited, the enunciation is of the subject universally, but in the other not universally. For when I say, “man matures,” I attribute maturing to “man” as universal or common, but not to man as to the whole human race; however, when I say, “every man matures,” I signify maturing to be present to man according to all the inferiors. This is evident, too, in the three other examples of enunciations in Aristotle’s text. For example, “non-man matures,” when its universal is taken universally, becomes “every non-man matures”; and so of the others. It follows, therefore, that every and no and similar signs do not signify a universal but only signify that they affirm or deny of man universally.

Two things should be noted here:

first, that Aristotle does not say “every” and “no” signify universally, but that the universal is taken universally;

second, that he adds, they affirm or deny of man.

The reason for the first is that the distributive sign does not signify the mode of universality or of particularity absolutely, but the mode applied to a distributed term. When I say “every man,” the “every” denotes that universality is applied to the term “man.” Hence, when Aristotle says “every” signifies that a universal is taken universally, by the that he conveys the application in actual exercise of the universality denoted by the “every,” just as in Posterior Analytics 1 (71b10) in the definition of “to know” (namely, to know scientifically is to know a thing through its cause and that this is its cause), he signifies by the word “that” the application of the cause.

The reason for the second is to imply the difference between categorematic and syncategorematic terms. The former apply what is signified to the terms absolutely; the latter apply what they signify to the terms in relation to the predicates. For example, in “white man,” the “white” denominates man in himself apart from any regard to something to be added; but in every man, although the “every” distributes “man,” the distribution does not confirm the intellect unless it is understood in relation to some predicate. A sign of this is that when we say “every man runs,” we do not intend to distribute “man” in its whole universality absolutely, but only in relation to “running.” When we say “white man runs,” on the other hand, we designate man in himself as “white” and not in relation to “running.” Therefore, since every and no and the other syncategorematic terms do nothing except determine the subject in relation to the predicate in the enunciation, and this cannot be done without affirmation and negation, Aristotle says that they only signify that the affirmation or negation is of a name (that is, of a subject), universally (that is, they prescribe the affirmation or negation that is being formed), and by this he separates them from categorematic terms. They affirm or deny can also be referred to the signs themselves (that is, every and no); one of these distributes positively, the other distributes by removing.

When he says, all else in enunciations (20a14), he concludes the treatment of the conditions of adjectival enunciations. He has already stated that adjectival enunciations are the same with respect to the number of oppositions as substantival enunciations with “is” as the second element, and has clarified this by a table showing the number of oppositions. Now, since upon this conformity follows conformity both with respect to finiteness of predicates and with respect to the diverse quantity of subjects, and also—if any enunciations of this kind are enumerated—their multiplication in sets of four, he concludes, therefore, also the other things, which are to be observed in them, are to be considered the same, that is, similar to these.

Lecture 4

Some Doubts About What Has Been Said Are Presented and Solved

20a16. Since the negation contrary to “every animal is just” is the one signifying “no animal is just,” it is evident that these will never be at once true, or in reference to the same thing, but the opposites of these will sometimes be true—that is, “not every animal is just” and “some animal is just.”

20a20. Now, the enunciation “no man is just” follows upon the enunciation “every man is non-just”; and “not every man is non-just,” which is its opposite, follows upon “some man is just,” for its opposite (That is, the opposite of “every man.”) must be “some man.”

20a23. And it is also clear with respect to the singular that if a question is asked and a negative answer is the true one, there is also a true affirmation. Take the example, “Is Socrates wise?” and the answer, “No.” Then, “Socrates is non-wise.” But in the case of universals, the affirmative inference is not true, but the negation is true. For example, in the question, “Is every man wise?” and the true answer is “no,” the inference “Then every man is non-wise” is clearly false, but “Not every man is wise” is true. The latter is the opposite, the former the contrary.

20a31. The antitheses in infinite names and verbs, as in “non-man” and “non-just,” might seem to be negations without a name or a verb; they are not, however. For the negation must always be either true or false; but the person who says “non-man” says nothing more than one who says “man,” and he is even further from saying something true or false if something is not added.

20a37. Moreover, “every non-man is just” does not signify the same thing as any of the other enunciations, nor does the opposite of this, “not every non-man is just.”

20a39. But “every non-man is non-just” signifies the same thing as “no non-man is just.”

20b1. When the names and verbs, are transposed, the enunciations signify the same thing—for example, “man is white” and “white is man.”

20b3. For if this is not the case, there will be more than one negation of the same enunciation; but it has been shown that there is only one negation of one affirmation, for the negation of “man is white” is “man is not white”; and if “white is man” is not the same as “man is white,” the negation of it will be “white is not non-man” and “white is not man.” The former, however, is the negation of “white is non-man”; the latter of “man is white.” Therefore, there will be two [negations] of one [affirmation]. It is clear, therefore, that when the name and the verb are transposed, the signification of the affirmation and negation is the same.

Having treated the diversity of enunciations, Aristotle now answers certain questions about them. He takes up six points related to the number of difficulties, which will become evident as we come to them. Since he has said that in universal enunciations the diagonals in one case cannot be at once true but can be in another (for the diagonal affirmatives cannot be at once true but the negatives can), someone might raise a question as to the cause of this diversity. Therefore, it is his intention now to assign the cause of this: namely, that the diagonal affirmatives are contrary to each other, and contraries cannot be at once true in any matter; but the diagonal negatives are subcontraries opposed to these and can be at once true.

About this, he does two things.

He first states the conditions for contraries and subcontraries.

Second, he shows that diagonal affirmatives are contraries and that diagonal negatives are subcontraries, at: now, the enunciation “no man is just" (20a20; [243]).

By way of resumé, therefore, he says that in the first book it was said that the negative enunciation contrary to the universal affirmative every animal is just is no animal is just. It is evident that these cannot be at once true (that is, at the same time), nor of the same thing (that is, of the same subject). But the opposites of these, the subcontraries, can sometimes be at once true, namely, in contingent matter, as in some animal is just and not every animal is just.

When he says, now the enunciation, “no man is just” (20a20), he shows that the diagonal affirmatives previously posited are contraries, the negatives subcontraries.

First, he manifests this from the fact that the infinite universal affirmative and the simple universal negative are equal in meaning, and consequently each of them is contrary to the simple universal affirmative, which is the other diagonal. Hence, he says that the infinite universal affirmative, every man is non-just follows upon the finite universal negative, no man is just, equivalently.

Second, he shows this from the fact that the finite particular affirmative and the infinite particular negative are equal in meaning, and consequently each of these is subcontrary to the simple particular negative, which is the other diagonal. This you can see in the previous diagram. He says, then, that the opposite, not every man is non-just, follows upon the finite particular some man is just equivalently (understanding “the opposite” not of this particular, but of the infinite universal affirmative, for this is its contradictory).

In order to see clearly how these enunciations are equivalent, make a four-sided figure, putting the finite universal negative in one corner and under it the contradictory, the finite particular affirmative. On the other side, put the infinite universal affirmative and under it the contradictory, the infinite particular negative. Now indicate the contradiction between diagonals and the contradiction between collaterals. [insert figure]

This arrangement makes the mutual consequence of the universals in truth and falsity evident, for if one of them is true, its diagonal contradictory is false; and if this is false, its collateral contradictory, which is the other universal, will be true. With respect to the falsity of the particulars, the procedure is the same. Their mutual consequence is made evident in the same way, for if one of them is true, its diagonal contradictory is false, and if this is false, its contradictory collateral (which is the other particular) will be true. The procedure is the same with respect to falsity.

However, a question arises with respect to this. At the end of Prior Analytics 1 (51b5), Aristotle determines from what he has proposed that the judgment of the universal negative and the infinite universal affirmative is not the same. Furthermore, in the second book of the present work, in relation to the phrase of which two are related according to consequence, two are not, Ammonius, Porphyry, Boethius, and St. Thomas say that the simple negative follows upon the infinite affirmative and not conversely. Albert answers this latter difficulty by pointing out that the infinite affirmative follows upon the finite negative when the subject is constant, but the simple negative follows upon the affirmative absolutely. Hence both positions are verified, for with a constant subject there is a mutual consequence between them, but there is not a mutual consequence between them absolutely.

We could also answer this difficulty in this way. In book 2, lectio 2, we were speaking of the infinite enunciation with the whole of what it signified reduced to the form of the predicate, and according to this there was not a mutual consequence, since the finite negative is higher than the infinite affirmative. But here we are speaking of the infinite itself formally taken. Hence St. Thomas, when he introduced the exposition of Ammonius in his commentary on the above passage, said that according to this mode of speaking the simple negative is wider than the infinite affirmative. In the above mentioned text in Prior Analytics 1 (52a36), Aristotle is speaking of finite and infinite enunciations in relation to the syllogism. It is evident, however, that the universal affirmative, whether finite or infinite is only inferred in the first mode of the first figure, while any universal negative whatever is inferred in the second mode of the first figure and in the first and second modes of the second figure.

When he says, and it is also clear with respect to the singular (20a23), he presents a difficulty relating to the varying position of the negation, namely, whether there is a difference as to truth and falsity when the negation is a part of the predicate or a part of the verb. This difficulty arises from what he has just said, namely, that it is of no consequence as to truth or falsity whether you say every man is non-just or every man is not just; yet in one case the negation is a part of the predicate, in the other part of the copula, and this makes a great deal of difference with respect to affirmation and negation. To solve this problem Aristotle makes a distinction: in singular enunciations, the singular negation and infinite affirmation of the same subject are of the same truth, but in universals this is not so. For if the negation of the universal is true, it is not necessary that the infinite affirmation of the universal is true. The negation of the universal is the contradictory particular, but if it is true, (That is, the contradictory particular.) it is not necessary that the subaltern, which is the contrary of the contradictory, be true, for two contraries can be at once false. Hence he says that in singular enunciations it is evident that if it is true to deny the thing asked—that is, if the negation of a singular enunciation, which has been made into an interrogation, is true—there will also be a true affirmation, namely, the infinite affirmation of the same singular will be true. For example, if the question do you think Socrates is wise? has no as a true response, then Socrates is non-wise; that is, the infinite affirmation Socrates is non-wise will be true. But in the case of universals the affirmative inference is not true—that is, from the truth of a negation to a universal affirmative question, the truth of the infinite universal affirmative (which is similar in quantity and quality to the enunciation asked) does not follow. But the negation is true—that is, from the truth of the negative response it follows that its negation is true (that is, the negation of the universal asked, which is the particular negative). Consider, for example, the question do you think every man is wise? If the response no is true, one would be tempted to infer the affirmative similar to the question asked, namely, that every man is non-wise. This, however, does not follow from the negation, for this is false as it follows from that response. Rather, what must be inferred is then not every man is wise. And the reason for both is that the particular enunciation inferred last is the opposite (that is, the contradictory) of the universal question, which, being falsified by the negative response, makes the contradictory of the universal affirmative true, for of contradictories, if one is false the other is true.

Next, when he says, the antitheses in infinite names and verbs (20a31), he raises the third difficulty, namely, whether infinite names or verbs are negations. This question arises from his having said that the negative and infinite are equivalent and from having just said that in singular enunciations it makes no difference whether the negative is a part of the predicate or a part of the verb. For if the infinite name is a negation, then the enunciation having an infinite subject or predicate will be negative and not affirmative. He resolves this question by an interpretation which proves that neither infinite names nor verbs are negations although they seem to be.

About this he does two things.

First, he proposes the solution, saying, the antitheses in infinite names and verbs, that is, words contraposed such as non-man and non-just man and just man—or this may be read as, those (namely, words) corresponding to infinites, that is, corresponding to the nature of infinites, placed in opposition to names or verbs (namely, removing what the names and verbs signify, as in non-man, non-just, and non-runs, which are opposed to man, just, and runs)—would seem at first sight to be quasi-negations without name and verb, because, as related to the names and verbs before which they are placed, they remove them. However, they are not truly negations. He says without a name or a verb because the infinite name lacks the nature of a name and the infinite verb does not have the nature of a verb. He says as though because the infinite name does not fall short of the notion of the name in every way, nor the infinite verb of the nature of the verb. Hence, if it is thought that they are negations, they will be regarded as without a name or a verb, not in every way but as though they were without a name or a verb.

Next, he proves that infinitizing signs of separation are not negations by pointing out that it is always necessary for the negation to be true or false, since a negation is an enunciation of something separated from something. The infinite name, however, does not assert what is true or false. Therefore, the infinite word is not a negation. He manifests the minor when he says that the one who says non-man says nothing more of man than the one who says man. Clearly this is so with respect to what is signified, for non-man adds nothing beyond man; rather, it removes man. Moreover, with respect to a conception of truth or falsity, it is of no more use to say non-man than to say man if something else is not added. Rather, it is less true or false—that is, one who says non-man is more removed from truth and falsity than one who says man, for both truth and falsity depend on composition, and the finite word which posits something is closer to composition than the infinite word, which neither posits nor composes (that is, it implies neither positing nor composition).

When he says, moreover, “every non-man is just” does not signify (20a37), he answers a fourth difficulty, namely, how the earlier statement concerning enunciations having an infinite subject is to be understood. The statement was that the latter, however, are separate from the former and distinct from them because of the use of “non-man” as a name. This is to be understood not just with respect to the enunciations themselves formally, but with respect to the consequence of what is signified. Hence, giving two examples of enunciations with an infinite subject, the universal affirmative and universal negative, he says that neither of these signifies the same thing as any of those, namely, of those having a finite subject. The universal affirmative every non-man is just does not signify the same thing as any of the enunciations with a finite subject, for it does not signify every man is just nor every man is non-just. Nor do the opposite negation, or the universal negative having an infinite subject which is contrarily opposed to the universal affirmative, signify the same thing as enunciations with a finite subject; that is, not every non-man is just and no non-man is just do not signify the same thing as any of those with a finite subject. This is evident from the diversity of subject in the latter and the former.

When he says, but “every non-man is non-just” signifies (20a39), he answers a fifth difficulty, namely, whether there is a consequence among enunciations with an infinite subject. This question arises from the fact that consequences were assigned among them earlier. He says, therefore, that there is a consequence even among these, for the universal affirmative with an infinite subject and predicate and the universal negative with an infinite subject but a finite predicate are equivalent—that is, every non-man is non-just signifies the same thing as no non-man is just. This is also the case in particular infinites and singulars which are similar to the ones already mentioned, for no matter what their quantity, the affirmative with both extremes infinite and the negative with an infinite subject and a finite predicate are always equivalent, as may be easily seen by examples. Hence, Aristotle, in giving the universals, intends the others to be understood from these.

When he says, when the names and verbs are transposed (20b1), he resolves a sixth difficulty: whether the signification of the enunciation is varied because of the transposition of names or verbs. This question arises from his having shown that the transposition of the negation varies the signification of the enunciation. He said that every man is non-just does not signify the same thing as not every man is just. This raises the question as to whether a similar thing happens when we transpose names. Would this vary the enunciation as the transposed negation does?

About this he does two things.

First, he states the solution, saying that transposed names and verbs signify the same thing; for instance, man is white signifies the same thing as white is man. Transposed verbs also signify the same thing, as in man is white and man white is.

Then he proves the solution from the number of contradictory negations when he says, for if this is not the case (20b3). He does this by a reduction to the impossible, and his reasoning is as follows. If this is not so—that is, if transposed names diversify enunciations—there will be two negations of the same affirmation. But in the first book it was shown that there is only one negation of one affirmation. Going, then, from the destruction of the consequent to the destruction of the antecedent, transposed names do not vary the enunciation. To clarify the proof of the consequent, make a figure in which both of the affirmations posited above, with the names transposed are located on one side. Put the two negatives similar to them in respect to terms and position on the opposite side. Then, leaving a little space, under the affirmatives put the affirmation with an infinite subject and under the negatives the negation of it. Mark the contradiction between the first affirmation and the first two negations and between the second affirmation and all three negations, but in the latter case mark the contradiction between it and the lowest negation as not true but imaginary. Mark, also, the contradiction between the third affirmation and negation. [insert figure]

Now we can see how Aristotle proves the consequent. The negation of the affirmation man is white is man is not white. But if the second affirmation, white is man, is not the same as man is white, because of the transposition of the names, its negation (That is, of “white is man.”) will be either of these two: non-man is not white, or white is not man. But each of these has another opposed affirmation than that assigned, namely, than white is man. For one of the negations, namely, non-man is not white, is the negation of non-man is white; the other, white is not man, is the negation of the affirmation man is white, which was the first affirmation. Therefore, whatever negation is given as contradictory to the middle enunciation, it follows that there are two of one—that is, two affirmations of one negation and two negations of one affirmation—which is impossible. And this, as has been said, follows upon an erroneously set up hypothesis, namely, that these affirmations are diverse because of the transposition of names.

Notice first that Aristotle has comprehended other things through these two negations, non-man is not white and white is not man, taken under disjunction to find the negation of the affirmation man is white. It is as though he said that the negation which will be taken will either be the true negation of such an affirmation or some extraneous negation. And whichever is taken, it always follows, given the hypothesis, that there are many negations of one affirmation—one which is the contradictory of it, having equal truth with the one having its name transposed, and the other which you accept as distinct, or you imagine falsely. And conversely, there is a single negation of many affirmations, as is clear in the diagram. Hence, from whichever of these four you begin, you see two opposed to it. It is significant, therefore, that Aristotle concludes indeterminately: therefore, there will be two of one.

Second, note that Aristotle does not consider it important to prove that the contradictory of the first affirmation is the contradictory of the second, and similarly that the contradictory of the second affirmation is the contradictory of the first. This he accepts as self-evident, since they can neither be true at the same time nor false at the same time. This is manifestly clear when a singular term is placed first, for “Socrates is a white man” and “Socrates is not a white man” cannot be maintained at the same time in any mode. You should not be disturbed by the fact that he does not propose these singulars here, for he was undoubtedly aware that he had already stated in the first book which affirmations and negations are contradictories and which are not, and for this reason felt that a careful elaboration of the examples was not necessary here. It is therefore evident that since negations of affirmations with transposed names are not diverse, the affirmations themselves are not diverse, and hence transposed names and verbs signify the same thing.

A doubt does arise, however, about the point Aristotle is making here, for it does not seem true that with transposed names the affirmation is the same. This, for example, is not valid: “Every man is an animal, therefore, every animal is a man.” Nor is the following example with a transposed verb valid: “Man is a rational animal and,” taking “is” as the second element, “therefore, ‘man animal rational is’”; for although it is nugatory as a whole combination, nevertheless it does not follow upon the first.

The answer to this is as follows. Just as there is a twofold transmutation in natural things—namely, local (from place to place) and formal (from form to form)—so in enunciations there is a twofold transmutation: a positional transmutation when a term placed before is placed after (and conversely), and a formal transmutation when a term that was a predicate is made a subject (and conversely, or in whatever mode, simply, and the like). And just as in natural things sometimes a purely local transmutation is made (for instance, when a thing is transferred from place to place, with no other variation made) and sometimes a transmutation is made according to place not simply but with a formal variation (as when a thing passes from a cold place to a hot place), so in enunciations a transmutation is sometimes made which is purely positional, such as when the name and verb are varied only in vocal position, and sometimes a transmutation is made which is at once formal and positional, as when the predicate becomes the subject, or the verb which is the third element added becomes the second. Aristotle’s purpose here was to treat of the purely positional transmutation of names and verbs, as the vocabulary of the transposition indicates; when he says, then, that transposed names and verbs signify the same thing, he intends to imply that if nothing other than the transposition of name and verb takes place in the enunciation, what is said remains the same. Hence, the response to the present objection is clear, for in both examples there is not only a transposition but a transmutation of subject to predicate in one case, and from an enunciation with a third element to one with a second element in the other. The response to similar questions is evident from this.

Lecture 5

Ways in Which an Enunciation May Be Many Rather Than One

20b12. Neither the affirmation nor the negation which affirms or denies one predicate of many subjects or many predicates of one subject is one, unless something one is constituted from the many. I do not use “one” of those things which, although one name may be imposed, do not constitute something one. For example, perhaps man is “animal” and “biped” and “civilized,” but there is also something one formed from these; whereas from “white” and “man” and “walking” there is not. Consequently, if someone affirms something one of these latter there will not be one affirmation, except in vocal sound; on the contrary, there will be many affirmations. Nor will there be one affirmation if someone affirms these of one subject; in this case too there will be many.

20b22. In fact, if dialectical interrogation is a request for an answer—that is, either for the admission of a premise or one part of a contradiction (and a premise is a part of one contradiction)—there would not be one answer in reference to the above predicates. There would not be one answer even if there is a true answer, for there would not be a single question.

20b26. But we have spoken about these things in Topics 8.7. At the same time, it is clear that the question “What is it?” is not a dialectical one. For the dialectical interrogation must provide for choosing whichever part of a contradiction one wishes to enunciate. For this the interrogator must specifically word the question so that the parts of the contradiction are clear; for example, by asking whether man is this or not.

After the Philosopher has treated the diversity in an enunciation arising from the addition of the infinite negation, he explains what happens to an enunciation when something is added to the subject or predicate which takes away its unity.

About this he does two things.

He first determines their diversity;

second, he proves that all the enunciations are many, at: some things predicated separately (20b31; [262]).

About the first he does two things.

First, he outlines their diversity;

second, he determines their consequences, at: in fact, if dialectical interrogation (20b22; [258]).

He begins by taking up something he said in the first book: there is not one affirmative enunciation nor one negative enunciation when one thing is affirmed or denied of many or many of one, if one thing is not constituted from the many. And he explains what he means by the subject or predicate having to be one where he says, I do not use “one” of those things which, although one name may be imposed, do not constitute something one (20b12), that is, a subject or predicate is one not from the unity of the name, but from the unity of what is signified. For when many things are brought together under one name in such a way that what is signified by that name is not one, then the unity is only one of vocal sound. But when one name has been imposed for many, whether for subjective or for integral parts, so that it encloses them in the same signification, then there is unity both of vocal sound and what is signified. In the latter case, unity of the enunciation is not impeded.

Then he adds, for example, perhaps man is “animal” and “biped” and “civilized" (20b12). This, however, is obscure, for it can be understood as an example of the opposite, as if he were saying, I do not mean by “one” such a “one” as the unity of the name imposed upon many from which one thing is not constituted, for instance, “man” as “one” from the parts of the definition, “animal” and “civilized” and “biped.” And to prevent anyone from thinking these are true parts of the definition of the name he interposes perhaps.

Porphyry, however, who is referred to with approval by Boethius, separates these parts of the text. He says Aristotle first states that that enunciation is many in which many are subjected to one (or many are predicated of one) when one thing is not constituted from these. And when he says, for example, perhaps man is, he intends to show that an enunciation is many when many things are subjected or predicated from which one thing is constituted, as in the example man is an animal and civilized and biped, with interjected copulas or a pause such as orators make. They say that he added perhaps to imply that this could happen, but it need not.

While agreeing with the opinion of Porphyry, Boethius, and Albert, we think a more subtle construction can be made of the text. According to it, Aristotle makes four points here.

First, he reviews what an enunciation is in general when he says that the enunciation is many in which one is enunciated of many or many of one. This is unless something one is constituted from the many, as he stated and explained in the first book.

Second, he clarifies the term “one” when he says, I do not use “one” of those things, that is, I call a name “one” not by reason of the unity of vocal sound, but of signification, as was said above.

Third, he manifests by dividing and divides by manifesting the number of ways in which one name may be imposed on many things from which one thing is not constituted. From this he implies the diversity of the multiple enunciation.

And he posits two ways.

First, when one name is imposed upon many things from which one thing is constituted, but not as one thing is constituted from them. In this case, materially and accidentally speaking, the name is imposed on many from which one thing is constituted, but it is formally and per se imposed on many from which one thing is not constituted. For it is not imposed upon them in the respect in which they constitute one thing, as perhaps the name “man” is imposed to signify “animal” and “civilized” and “biped” (which are parts of its definition) not as they are united in the one nature of man in the mode of act and potency, but as they are themselves distinct actualities. Aristotle implies that he is taking these parts of the definition as distinct by the conjunctions and by also adding adversatively, but if there is something one formed from these, as if to say, when, however, it holds that one thing is constituted from these. He adds perhaps because the name man is not imposed to signify its definitive parts as they are distinct. But if it had been so imposed or were imposed, it would be one name imposed on many things from which no one thing is constituted.

And since the judgment with respect to such a name and those many things is the same, the many definitive parts can also be taken in two ways.

First, in the mode of the actual and possible, and thus they constitute one thing; are formally called “many from which one thing is constituted”; are to be pronounced in continuous speech; and make one enunciation, such as “a mortal rational animal is running.” For this is one enunciation, just as is “man is running.”

In the second way, the foresaid parts of the definition are taken as they are distinct actualities, and thus they do not constitute one thing, for one thing is not constituted from two acts as such, as Aristotle says in Metaphysics 7.13 (1039a5). In this case they constitute many enunciations and are pronounced either with conjunctions interposed or with a pause in the rhetorical manner, for example, man is an animal and civilized and biped or man is animal, civilized, biped. Each of these is a multiple enunciation, and so is the enunciation, “Socrates is a man,” if “man” is imposed to signify “animal,” “civilized,” and “biped” as they are distinct actualities.

Aristotle takes up the second way in which one name is imposed on many from which one thing is not constituted where he says, whereas from “white” and “man” and “walking” there is not. Since in no way can any one nature be constituted from man, white, and walking (as there can be from the definitive parts), it is evident that if a name were imposed on these it would be a name that does not signify one thing, as was said in the first book of the name “cloak” imposed for man and horse.

We have, therefore, two modes of the many (that is, the multiple) enunciation, and since both are constituted in two ways, there will be four modes:

first, when one name imposed on many from which one thing is constituted is subjected or predicated as though the name stands for many;

second, when the many from one which one thing is constituted are subjected or predicated as distinct actualities;

third, when one name is imposed for a many from which nothing one is constituted;

the fourth, when many which do not constitute one thing are subjected or predicated.

Note that the enunciation, according to the members of the division by which it has been divided into one and many, can be varied in four ways: one is predicated of one, one of many, many of one, and many of many. Aristotle has not spoken of the last one either because its plurality is clear enough or because, as Albert says, he only intends to treat of the enunciation which is one in some way.

Finally, he concludes with this summary: consequently, if someone affirms something one of these latter there will not be one affirmation, except in vocal sound; on the contrary, there will be many affirmations. Nor will there be one affirmation if someone affirms these of one subject; in this case too there will be many**. For example, “man is white, walking, and musical” implies three affirmations, namely, “man is white” and “is walking” and “is musical.” This is clear from its contradiction, for a threefold negation is opposed to it, corresponding to the threefold affirmation.

Then, when he says, in fact, if dialectical interrogation is a request for an answer (20b22), he proves a posteriori that the foresaid enunciations are many.

About this he does two things.

First, he states an argument to prove this by way of the consequent;

then he proves the antecedent of the given consequent where he says, but we have spoken about these things in Topics 8.7 (20b26; [261]).

Now if dialectical questioning is a request for an answer—either a proposition or one part of a contradiction—none of the foresaid enunciations, put in the form of a question, will have one answer. Therefore, the question is not one, but many. Aristotle first states the antecedent of this argument, at: if dialectical interrogation is a request for an answer (20b22).

To understand this it should be noted that an enunciation, a question, and an answer sound the same. For when we say, “The region of heaven is animated,” we call it an enunciation inasmuch as it enunciates a predicate of a subject, but when it is proposed to obtain an answer we call it an interrogation, and as applied to what was asked we call it a response. Therefore, to prove that there is not one response or one question or one enunciation will be the same thing.

It should also be noted that interrogation is twofold.

One proposes either of the two parts of a contradiction to choose from. This is called “dialectical interrogation” because the dialectician knows the way to prove either part of a contradiction from probable positions.

The other kind of interrogation seeks one determinate response. This is the demonstrative interrogation, for the demonstrator proceeds determinately toward a single alternative.

Note, finally, that it is possible to reply to a dialectical question in two ways.

We may consent to the question either affirmatively or negatively. For example, when someone asks, “Is the region of heaven animated?” we may respond, “It is,” or to the question “Is not God moved?” we may say, “No.” Such a response is called a proposition.

The second way of replying is by destroying. For example, when someone asks “Is the region of heaven animated?” we may respond, “No,” or to the question, “Is not God moved?” we may respond, “He is moved.” Such a response is called “the other part of a contradiction,” because a negation is given to an affirmation and an affirmation to a negation.

Dialectical interrogation, then, according to the exposition just given (which is that of Boethius) is a request for an admission (which is a proposition) or a denial (which is one part of a contradiction).

He adds the proof of the consequent when he says, and a premise is a part of one contradiction (20b22). In relation to this it should be noted that if a dialectical response could be many, it would not follow that a response to a multiple enunciation would not be dialectical. However, if the dialectical response can only be one enunciation, then it follows that a response to a plural enunciation is not a dialectical response, for it is one. (That is, it inclines to one part of a contradiction at a time.) It should also be noted that if an enunciation is a part of many contradictions, it is thereby proven not to be one, for one contradicts only one. But if an enunciation is a part of only one contradiction, it is one by the same reasoning, namely, because there is only one negation of one affirmation, and conversely. Hence Aristotle proves the consequent from the fact that the proposition (that is, the dialectical response), is a part of one contradiction (that is, it is one affirmative or one negative enunciation). It follows from this, as has been said, that there is no dialectical response of a multiple enunciation, and consequently not one response. It should not be overlooked that when he designates a proposition or one part of a contradiction as the response to a dialectical interrogation, it is only of the proposition that he adds that it is one, because the very wording shows the unity of the other. For when you hear one part of a contradiction, you immediately understand one affirmation or negation. He puts the therefore with the antecedent, either implying that this is taken from another place and he will explain in particular afterward, or having changed the structure, he places the sign of the consequent, which should be between the antecedent and consequent, before the antecedent, as when one says, “Therefore, if Socrates runs, he is moved,” for “If Socrates runs, therefore he is moved.” Then the consequent follows that there will not be one answer to this, and the inference of the principal conclusion, for there would not be a single question. For if the response cannot be one, the question will not be one.

He adds, even if there is a true answer (20b22), because someone might think that although one response cannot be given to a plural interrogation when the question concerns something that cannot be affirmed or denied of all of the many—for example, when someone asks, “Is a dog an animal?” no one response can be given, for we cannot truly say of every dog that it is an animal because of the star by that name, nor can we truly say of every dog that it is not an animal, because of the barking dog—nevertheless one response could be given when that which falls under the interrogation can be truly said of all. For example, when someone asks, “Is a dog a substance?” a single response can be given because it can truly be said of every dog that it is a substance, for to be a substance belongs to all dogs. Aristotle adds the phrase, even if there is a true answer, to remove such an erroneous judgment. For even if the response to the multiple enunciation is verified of all, it is nonetheless not one, since it does not signify one thing, nor is it a part of one contradiction. Rather, as is evident, this response has many contradictories.

Where he says, but we have spoken about these things in Topics 8.7 (20b26), he proves the antecedent in two ways.

First, he proves it on the basis of what was said in the Topics;

second, by a sign.

About this he does two things.

First, he gives the sign, saying, at the same time, it is clear that the question (20b26). That is, given the doctrine in the Topics, it is clear (namely, assuming the antecedent that the dialectical interrogation is a request for an affirmative or negative response) that the question “What is it?” is not a dialectical interrogation. For instance, when someone asks, “What is an animal?” he does not interrogate dialectically.

Second, he gives the proof of what was assumed, namely, that the question “What is it?” is not a dialectical question. He states that a dialectical interrogation must offer to the one responding the option of whichever part of the contradiction he wishes. The question “What is it?” does not offer such liberty, for in saying “What is an animal?” the one responding is forced to assign a definition, and a definition is not only determined to one but is also entirely devoid of contradiction, since it affirms neither being nor non-being. Therefore, the question “What is it?” is not a dialectical interrogation. Thus he says, for the dialectical interrogation must provide, that is, from the proposed dialectical interrogation the one responding must be able to choose whichever part of the contradiction he wishes, which the interrogator must specify—that is, he must propose the question in this way: “Is this animal man or not?” so that the wording of the question clearly offers an option to the one answering. Therefore, a sign that a dialectical question is seeking a response of a proposition or of one part of a contradiction is the setting apart of the question “What is it?” from dialectical questions.

Lecture 6

Some Predicates Said Divisively of a Subject Can Be Said Conjointly, Others Not

20b31. Some things predicated separately are such that they unite to form one predicate; others, however, do not. What, then, is the difference? For it is true to say separately of man that he is an animal and that he is biped, and it is also true to say these as one. It is also true to say “man” and “white” separately of him and to say these as one. But if a man is a shoemaker and also good, it is not true to say that he is a good shoemaker.

20b36. For if we hold that whenever each is truly said of a subject, both together must also be true, many absurdities will follow. For example, it is true to say of man that he is man and that he is white; therefore, these two taken together can also be truly said of him; again, if it is true to say that he is white and that he is also the two combined predicates above, he will be white white man; and so to infinity. Or, again, “musical,” “white,” and “walking” may be truly said of man; and these combined many times. Furthermore, if Socrates is Socrates and a man, Socrates is a Socrates man; and if he is man and biped, he is a biped man.

It is clear, therefore, that if anyone says these combinations can always be made simply, many absurd things follow. Now, we will state how this must be resolved.

21a7. Those things that are predicated—taken in relation to that to which they are joined in predication—which are said accidentally, either of the same subject or one another, will not be one. For example, man is white and musical, but whiteness and being musical are not one, for both are accidental to the same thing. Even if it were true to say that whatever is white is musical, musical and white will not be one thing, for that which is musical is white accidentally; consequently, that which is white will not be musical.

21a14. This is the reason “good” and “shoemaker” cannot be combined simply; but “biped” and “animal” can, for these are not accidental.

21a16. Furthermore, predicates that are present in one another cannot be combined simply. This is the reason we cannot combine “white” many times, nor is “man” an “animal-man,” or a “biped-man,” for the notion man includes both biped and animal.

Having explained the diversity of the multiple enunciation, Aristotle now proposes to determine the consequences of this.

He treats this in relation to two questions which he solves.

The second begins at: on the other hand, it is also true (21a18; [273]).

About the first he does three things.

first, he proposes the question,

second, he shows that the question is a reasonable one, at: for if we hold that whenever each is truly said (20b36; [263]).

third, he solves it, at: those things that are predicated (21a7; [264]).

The first question is this: why is it that from some things predicated divisively of a subject an enunciation follows in which they are predicated of the same subject unitedly, and from others not? What is the reason for this diversity? For example, from “Socrates is an animal and he is biped” follows “Therefore, Socrates is a biped animal.” Similarly, from “Socrates is a man and he is white” follows “Therefore, Socrates is a white man.” But from “Socrates is good and he is a lute player,” the enunciation, “Therefore, he is a good lute player” does not follow. Hence in proposing the question Aristotle says, some things, namely, predicates, are so predicated when combined that there is one predicate from what is predicated separately—that is, from some things that are predicated separately, a united predication is made, but from others this is not so. What is the difference between these? From where does such a diversity arise? He adds the examples which we have already cited and applied to the question. Of these examples, the first contains predicates from which something essentially one is formed, namely, “animal” and “biped,” a genus and difference; the second contains predicates from which something accidentally one is formed, namely, “white man”; the third contains predicates from which neither one essentially nor one accidentally is formed, “lute player” and “good,” as will be explained.

When he says, for if we hold that whenever each (20b36), he shows that there truly is such a diversity among predicates and in so doing renders the question reasonable, for if there were not such a diversity among predicates the question would be pointless. He shows this by reasoning leading to an absurdity, that is, to something nugatory. Now, something nugatory is effected in two ways, explicitly and implicitly.

Therefore, he first makes a deduction to the explicitly nugatory;

second, to the implicitly, at: furthermore, if Socrates is Socrates and a man, Socrates is a Socrates man (20b36).

If, he says, there is no difference between predicates, and it is supposed of any of them indifferently that because both are said separately both may be said conjointly, many absurdities will follow. For it is true of some man (say Socrates) to say separately that he is a man and he is white, and therefore he is both together—that is, we may also say conjointly, “Socrates is a white man.” Again, of the same Socrates we can say separately that he is a white man and that he is white, and both together—that is, conjointly, “Socrates is a white white man.” Here the nugatory expression is evident. Further, if of the same Socrates that you again say separately is a “white white man” it will be true and consistent to say that he is white, and following this, if you will not deviate from a similar truth by again repeating this separately (and this will follow to infinity), then Socrates is a “white white white man” to infinity.

The same thing can be shown by another example. If someone says of Socrates that he is “musical,” “white,” and “walking,” since it is also possible to say separately that he is musical, and that he is white, and that he is walking, it will follow that “Socrates is musical, white, walking, musical, white, walking.” And since these can be enunciated many times separately, yet at the same time, the nugatory statement proceeds without end.

Next he makes a deduction to the implicitly nugatory. Since it can be truly said of Socrates separately that he is man and that he is biped, it will follow that Socrates is a biped man, if it is licit to infer conjointly. This is implicitly nugatory because the “biped,” which indirectly expresses the difference of man in act and in understanding, is included in the notion of man. Hence, if we posit the definition of man in place of “man” (which it is licit to do, as Aristotle teaches in Topics 2.2 [110a5]) the nugatory character of the enunciation will be evident, for when we say “Socrates is a biped man,” we are saying “Socrates is a biped biped animal.”

From what has been said it is evident that many absurdities follow if anyone proposes that combinations (or unions of predicates), be made simply, that is, without any distinction. Now, that is, in what follows, we will state how this must be settled. This particular text is not uniformly worded in the manuscripts, but since no discrepancy of thought is involved one may read it as he wishes.

When he says, those things that are predicated (21a7), he solves the proposed question.

About this he does two things.

First, he makes an answer with respect to the instances cited in proposing the question;

second, he solves the problem as related to the instances posited in his proof, at: furthermore, predicates that are present (21a16; [272]).

About the first he does two things:

first, he states the true position;

second, he applies it to the instances, at: this is the reason “good” and “shoemaker” (21a14; [268]).

He settles the question with this distinction: there are two kinds of multiple predicates and subjects. Some are accidental, some per se. If they are accidental, this occurs in two ways: either because both are said accidentally of a third thing or because they are predicated of each other accidentally. Now when the many predicated divisively are in any way accidental, a conjoined predicate does not follow from them; but when they are per se, a conjoined predicate does follow from them.

In answering the question, therefore, Aristotle connects what he is saying with what has gone before: of those things that are predicated and those of which they are predicated, namely, subjects, whichever are said accidentally (by which he intimates the opposite member, namely, per se), either of the same subject, that is, they unite accidentally for the denomination of one third thing, or of one another, that is, they denominate each other accidentally (and by this he posits the members of a two-fold division), these, namely, these many accidentally, will not be one, that is, do not produce a conjoined predication.

He explains both of these by examples.

First, he explains the first (21a7)—when the many are said accidentally of a third—with the example of how man is white and musical divisively. But they are not the same, that is, it does not follow unitedly that man is musical white, for both are accidental to the same third thing.

Then he explains the second member by an example. In it, the many are predicated only of one another. Even if it were true to say white is musical—that is, even if these are predicated accidentally of each other by reason of the subject in which they are united, so that we may say man is white and he is musical, and white is musical—it still does not follow that musical white is predicated as a unity when we say, therefore, man is musical white. He gives as the cause of this that white is said of musical accidentally and conversely.

It must be noted here that although he has enumerated two accidental members, he explains both members by this single example so as to imply that the distinction is not one of different accidental predicates, but of the same predicates compared in different ways. White and musical compared to “man” fall under the first member, but compared with each other, under the second. Hence he has provided diversity of comparison by the plurality of the members, but identity of predicates by the unity of the example.

To make this division evident, it must also be noted that “accidentally” can be taken in two ways.

In one way, it may be taken as it is distinguished from “posterioristic essentiality.” This is not the way it is taken here, for “many predicates accidentally” would then mean that the accidentally determines a conjunction between predicates, and thus the rule would clearly be false, for the first predicates he gave as examples are predicated accidentally in this way, namely, “biped animal,” or “rational animal.” For a difference is not predicated of a genus in any mode of essentiality, and yet Aristotle says in the text that these are not predicated accidentally, and has asserted that he is an animal and biped, therefore he is a biped animal is a good inference. Or it would mean that the “accidentally” determines a conjunction of the predicates with the subject, and thus also the rule would be false, for it is valid to say, “The wall is colored and it is visible,” yet “visible colored” is not per se in the wall.

Accidentally taken in the second way is distinguished from what I call “on its own account,” that is, not because of something else. “Accidentally” then means “through another.” This is the way it is taken here, for whatever things are of such a nature that they are joined because of something else, and not on their own account, do not admit of conjoined inference, because a conjoined inference subjects one to the other, and denotes the things united on their own account as potency and act. Therefore, the sense of the division is this: of many predicates, some are accidental, and some are per se—that is, some are united among themselves on their own account, some on account of another. Those that are per se united infer conjointly; those that are united on account of another do not infer conjointly in any way.

When he says, this is the reason “good” and “shoemaker” cannot be combined simply (21a14), he applies the truth he has stated to the parts of the question.

He applies it first to the second part, that is, why this does not follow: “He is good and he is a shoemaker, therefore he is a good shoemaker,” at: this is the reason “good” and “shoemaker.”

Second, he applies it to the other part of the question, that is, why this follows: “He is an animal and he is biped, therefore he is a biped animal,” at: but “biped” and “animal” can. He adds the reason in the case of the latter: “biped” and “animal” are not predicates accidentally conjoined among themselves, nor in a third thing, but per se.

This also explains the other member of the first division which has not yet been explicitly posited. Notice that he maintains the same judgment is to be made about lute player and good, and musical and white. He has concluded that “white” and “musical” do not infer a conjoined predicate; hence neither do “lute player” and “good” infer “good lute player” simply, that is, conjointly.

There is a reason for saying this. For although there is a difference between musical and white, and goodness and the art of lute-playing, they are also similar. Let us consider their difference first. Goodness is of such a nature that it denominates both a third subject (namely, man) and the art of lute-playing. This is the reason the falsity is clearly discernible when we say “He is good and a lute player, therefore he is a good lute player.” Musical and whiteness, on the other hand, are of such a nature that they denominate only a third subject, and not each other, and hence the error is less obvious in “He is white and he is musical, therefore he is musical white.” Now it is this difference that makes Aristotle’s process of reasoning appear somewhat inconclusive.

However, they are similar. For if identity of predicates is kept in every way that is required for the same things divided to be inferred conjointly, then, just as “musical” does not denominate “whiteness,” nor the contrary, so neither does “goodness” (of which we are speaking when we say “man is good”) denominate the art of lute-playing, nor conversely. For “good” is equivocal, even though by choice, and is therefore said of the perfection of the lute player by means of one notion and of the perfection of man by means of another. For example, when we say, “Socrates is good” we understand moral goodness, which is the goodness of man absolutely (for the analogous term posited simply stands for what is mainly so); but when “good lute player” is inferred, it is not the goodness of morality that is predicated, but the goodness of art. Thus the identity of the terms is not saved. Therefore, Aristotle has adequately and subtly expressed the same judgment about both pairs (“white” and “musical,” and “good” and “lute player”), for the reason here is the same as there.

There is another point that must be mentioned. Aristotle draws three consequences in proposing the question: “He is an animal and biped, therefore he is a biped animal”; “He is a man and white, therefore he is a white man”; and “He is a lute player and good, therefore he is a good lute player.” Then he states that the first two consequences are good, the third not. His intention was to inquire into the cause of this diversity, but in solving the question he mentions only the first and third consequences, leaving the goodness or badness of the second consequence undiscussed. Why is this?

I would say in answer to this that in these few words he has also implied the nature of the second consequence, for there is a more profound meaning to the statement in the text that whiteness and being musical is not one (21a7). It is a meaning that not only indicates what has already been explained but also its cause, and from this the nature of the second consequence is apparent. The reason “white” and “musical” do not infer a conjoined predication is that in conjoined predication one part must be subjected to the other as potency to act such that in some way one thing is formed from them and one is denominated from the other (for the force of the conjoined predication requires this, as we have said above concerning the parts of the definition). “White” and “musical,” however, do not in themselves form one thing per se, as is evident, nor do they form one thing accidentally. For while it is true that as united in a subject they are one in subject accidentally, nevertheless things that are united in one third subject do not form one thing accidentally among themselves:

first, because neither informs the other (which is required for accidental unity of things among themselves, although not in a third thing);

second, because, considered apart from the unity of a subject, which is outside of their notions, there is no cause of unity between them.

Therefore, when Aristotle says that whiteness and being musical are not one (namely, among themselves), in some measure he expresses the reason why a predicate is not conjointly inferred from them. And since the same discipline extends to opposites, the goodness of the second consequence is implied by these words. That is, man and white are related as potency and act (and so whiteness informs, denominates, and forms one thing with “man” on its own account). Therefore, from these taken divisively a conjoined predication can be inferred, namely, “He is man and white, therefore be is a white man,” just as, in the opposite case, it was said that “musical” and “white” do not infer a conjoined predicate because neither informs the other

There is no opposition between the position just stated and the fact that white forms an accidental unity with man. For we did not say that accidental unity of certain things impedes inferring a conjunction from divided things, but that accidental unity of certain things only by reason of a third thing is the one that impedes. Things that are one accidentally only by reason of a third thing have no unity among themselves; and for this reason a conjunction, which implies unity, cannot be inferred, as we have said. But things that are one accidentally on their own account (that is, among themselves)—as, for example, white man—have the necessary unity when taken conjointly because they have unity among themselves. Notice that I have added only. The reason is that if any two are one accidentally (that is, by reason of a third subject), and they not only have unity from this but also on their own account (because one informs the other), then from these taken divisively a conjoined inference can be made. For example, we can infer, “It is a quantity and it is colored, therefore it is a colored quantity,” because color informs quantity.

You can hold as true that this second consequence is good even though Aristotle has not explicitly confirmed it by returning to it, both from the fact that in proposing the question he has claimed it as good and also because there is no instance opposed to it. Moreover, Aristotle has implied that it is only such unity that impedes the conjoined inference where he says: which are said accidentally, either of the same subject or of one another (21a7). By accidentally of the same subject, he posits their unity to be only from union in a third thing (for only these are predicated accidentally of the same subject, as was said). When he adds or of one another—positing mutual accidentality—no unity at all is left between them. Therefore, both kinds of accidental predicates (namely, in a third thing or in one another) that impede a conjoined inference have unity only in a third thing.

Then when he says, furthermore, predicates that are present (21a16), he gives the solution for the instances (both the explicitly nugatory and the implicitly nugatory) cited in the proof. It is not only illicit, he says, to infer a union from divided predicates when these are accidental, but it is illicit when the predicates are present in one another. That is, it is illicit to infer a conjoined predicate from divided predicates when the predicates include one another in such a way that one is included in the formal signification of another intrinsically, or explicitly (as “white” in “white”), or implicitly (as “animal” and “biped” in “man”). Therefore, “white” said repeatedly and divisively does not infer a conjoined predication, nor does “man” divisively enunciated from “animal” or “biped” infer “biped” or “animal” conjoined with man, such that we could say, “Therefore, Socrates is a biped-man” or “animal-man.” For “animal” and “biped” are included in the notion of man in act and in understanding, although implicitly.

The solution of the question, then, is this: the inferring of a conjunction from divided predicates is impeded when there is unity of the many accidentally, only in a third thing, and with a nugatory result. Consequently, where neither of these is found, it will be licit to infer a conjunction from divided predicates. It is to be understood that this applies when the divided predicates are at once true of the same subject.

Lecture 7

Whether From an Enunciation Having Many Conjoined Predicates It Is Licit to Infer an Enunciation That Contains the Same Predicates Divisively

21a18. On the other hand, it is also true to say predicates of something singly; for example, it is true to say that some man is a man, or that some white man is white. However, this is not always the case.

21a21. When something opposed is present in the adjunct, from which a contradiction follows, it will not be true to predicate them singly, but false—for instance, to say that a dead man is a man. When something opposed is not present in the adjunct, however, it is true to predicate them singly.

21a24. Or, rather, when something opposed is present in it, it is never true; but when something opposed is not present, it is not always true. For example, Homer is something, say, a poet. Is it therefore true to say also that Homer is, or not?

21a26. The “is” here is predicated accidentally of Homer, for the “is” is predicated of him with regard to the fact that he is a poet, not in itself.

21a29. Therefore, in whatever predications no contrariety is present when definitions are put in place of the names, and wherein predicates are predicated in itself and not accidentally, it will also be true to predicate each one singly.

21a32. In the case of non-being, however, it is not true to say that because it is a matter of opinion it is something; for the opinion of it is not that it is, but that it is not.

Aristotle now takes up the second question in relation to multiple enunciations.

About this he does three things.

First, he presents it;

second, he solves it, at: when something opposed is present in the adjunct (21a21; [274]);

third, he excludes an error, at: in the case of non-being, however (21a32; [289]).

This is the question: Is it licit to infer from an enunciation having a conjoined predication, enunciations dividing that conjunction? This question is the contrary of the first question. The first asked whether a conjoined predicate could be inferred from divided predicates; the present one asks whether divided predicates follow from conjoined predicates. When he presents the question he says, on the other hand, it is also true to say predicates of something singly, that is, what was previously said conjointly may be said divisively, for example, that some white man is a man, or that some white man is white. That is, from “Socrates is a white man,” follows divisively, “Therefore, Socrates is a man,” and “Therefore, Socrates is white.” However, this is not always the case, that is, sometimes it is not possible to infer divisively from conjoined predicates, for this does not follow: “Socrates is a good lute player; therefore, he is good.” Hence, sometimes it is licit, sometimes not. Note that in inferring each part divisively he takes as an example “white man.” This is significant, for by it he means to imply that his intention is to investigate when each part can be inferred divisively from a conjoined predicate, and not when only one of the two can be inferred.

When he says, when something opposed is present in the adjunct (21a21), he solves the question.

And he does two things.

First, he responds to the negative part of the question, that is, when it is not licit;

second, to the affirmative part, that is, when it is licit, at: therefore, in whatever predications (21a29; [280]).

It should be noted, in relation to the negative part of the question, that a conjoined predicate may be formed in two ways: from opposites and from non-opposites.

Therefore, he shows first that the parts in a conjoined predicate of opposites can never be inferred divisively.

Second, he shows that this is not licit universally in a conjoined predicate of non-opposites, at: or, rather, when something opposed (21a24; [278]).

Aristotle says, then, that when something that is an opposite is contained in the adjacent term, which results in a contradiction between the terms themselves, it is not true, but false, to infer divisively. For example, when we say, “Caesar is a dead man,” it does not follow, “Therefore, he is a man,” because the contradiction between “man” and “dead” which results from adding the “dead” to “man” is opposed to man. For if he is a man, he is not dead, because he is not an inanimate body; and if he is dead, he is not a man, because as dead he is an inanimate body. When something opposed is not present, namely, when there is no such opposition, it is true, that is, it is true to infer divisively. The reason a divided inference does not follow when there is opposition in the added term is that in a conjoined enunciation the other term is destroyed by the opposition of the added term. But that which has been destroyed is not inferred apart from the destruction, which is what the divided inference would signify.

Two questions arise at this point. The first concerns something assumed here: how can it ever be true to make such a statement as “Caesar is a dead man,” since an enunciation cannot be true in which two contradictories are predicated at the same time of something (for this is a first principle)? But “man” and “dead,” as is said in the text, include contradictory opposition, for in man is included life, and in dead, non-life.

The second question concerns the consequent that Aristotle rejects, which appears to be good. The enunciation given as an example predicates terms that are opposed contradictorily. But from an enunciation predicating two contradictory terms, either both can be inferred (because it is equivalent to a copulative enunciation), or neither (because it destroys itself); therefore, both parts seem to follow, since it is false that neither follows.

These two questions can be answered simultaneously. It is one thing to speak of two terms in themselves, and another to speak of them as one stands under the determination of another.

Taken in the first way, “man” and “dead” have a contradiction between them and it is impossible that they be found in the same thing at the same time.

In the second way, however, “man” and “dead” are not opposed, since “man,” changed by the destructive element introduced by “dead,” no longer stands for what it signifies as such, but as determined by the term added, by which what is signified is removed.

Aristotle, in order to imply both, says two things: that they have the opposition upon which contradiction follows if you regard what they signify in themselves; and that one true enunciation is formed from them as in “Socrates is a dead man,” if you regard their conjunction as destructive of one of them. Accordingly, the answer to the two questions is evident. In a case such as this, two contradictories are not enunciated of the same thing at the same time, but one term as it stands under dissolution or transmutation from the other, to which by itself it would be contradictory.

There is also a question about something else that Aristotle says, namely, something opposed is present . . . from which a contradiction follows (21a21). The phrase from which a contradiction follows seems to be superfluous, for contradiction follows upon all opposites, as is evident in discoursing about singulars; for a father is not a son, and white is not black, and one seeing is not blind. Opposites, however, can be taken in two ways: formally (that is, according to what they signify), and denominatively (or subjectively). For example, father and son can be taken for paternity and filiation, or they can be taken for the one who is denominated a father or a son. But, again, since every distinction is made by some opposition, as is said in Metaphysics 10.3 (1054a20), it could be supposed that opposites are wholly distinct.

It must be pointed out, therefore, that although contradiction follows between all opposites or distinct things formally taken, nevertheless, contradiction does not follow upon all opposites denominatively taken. Father and son formally taken infer a mutual negation of one another, for paternity is not filiation and filiation is not paternity, but in respect to what is denominated they do not necessarily infer a contradiction. It does not follow, for example, that “Socrates is a father; therefore, he is not a son,” nor conversely. Aristotle, therefore, in order to establish that not all combined opposites prevent a divided inference (since those having a contradiction applying only formally do not prevent a divided inference, but those having a contradiction both formally and according to the thing denominated do prevent a divided inference) adds, from which a contradiction follows, namely, in the third thing denominated. And appropriately enough he uses the word follows, for the contradiction in the third thing denominated is in a certain way outside of the opposites themselves.

When he says, or, rather, when something opposed is present in it, it is never true (21a24), he explains that the parts cannot universally be inferred divisively in the case of a conjoined predicate in which there is a non-opposite as the third thing denominated.

First, he proposes this, at: or, rather, when something opposed is present in it, that is, opposition between the terms conjoined. This is as if amending what he has just said, namely, it is always false to infer divisively. What he is saying, then, is this: I have said that when there is inherent opposition it is not true but false to infer divisively; but when there is not such opposition it is true to infer divisively; or, even better, when there is opposition it is always false, but when there is not such opposition it is not always true. That is, he modifies what he first said by the addition of always and not always. Then he adds an example to show that division does not always follow from non-opposites: for example, Homer is something, say, a poet. Is it therefore true to say also that Homer “is,” or not? From the conjoined predicate, is a poet, enunciated of Homer, one part, therefore, Homer is, does not follow; yet it is evident that these two conjoined parts, is and poet, do not have the opposition upon which contradiction follows. Therefore, in the case of conjoined non-opposites, a divided inference does not always hold.

When he says, the “is” here is predicated accidentally of Homer (21a26), he proves what he has said. One part of this composite, namely, is, is predicated of Homer in the antecedent conjunction accidentally, that is, by reason of another, namely, with regard to the “poet” which is predicated of Homer; it is not predicated as such of Homer. Nevertheless, this is what is inferred when one concludes therefore, Homer is. To validate his negative conclusion—namely, that it is not always true to infer divisively from conjoined non-opposites—it was sufficient to give one instance of the opposite of the universal affirmative.

To do this, Aristotle introduces that genus of enunciation in which one part of the conjunction is something pertaining to an act of the mind (for we are speaking only of Homer living in his poems in the minds of men). In such enunciations the parts conjoined are not opposed in the third thing denominated; nevertheless, it is not licit to infer each part divisively, for the fallacy of going from the relative to the absolute will be committed. For example, it is not valid to say, “Caesar is praiseworthy, therefore he is,” which is a parallel case, namely, of an effect whose existence requires maintenance. Aristotle will explain in the following sections of the text how the reasoning in the above text is to be understood.

When he says, therefore, in whatever predications no contrariety is present (21a29), he replies to the affirmative part of the question, that is, when it is licit to infer divisively from conjoined predicates. He maintains that two conditions—opposed to what has been said earlier in this portion of the text—must combine in one enunciation in order that such a consequence be effected: there must be no opposition between the parts conjoined, and they must be predicated per se.

He says, then, inferring from what has been said: therefore, in whatever predications, that is, predicates joined in a certain order, no contrariety, in virtue of which contradiction is posited in the third thing denominated (for contraries mutually remove each other from the same thing), is present, or universally, no opposition is present, that is, upon which a contradiction follows in the third thing denominated, when definitions are taken in place of the names.

He says this because it may be the case that the opposition is not apparent from the names alone, as in “dead man,” and again it may be, as in “living dead,” but whether apparent or not it will be evident that we are putting together opposites if we posit the definitions of the names in place of the names. For example, in the case of “dead man,” if we replace “man” and “dead” with their definitions, the contradiction will be evident, for what we are saying is “rational animate body, irrational inanimate body.” In whatever conjoined predicates, then, there is no opposition, and where predicates are predicated per se and not accidentally, in these it will also be true to predicate them singly, that is, say divisively what had been enunciated conjointly.

In order to make this second condition clear, it should be noted that per se can be taken in two ways:

positively, and thus it refers to the essentiality of the first, of the second, and of the fourth mode universally;

or negatively, and thus it means the same as not through something else.

It should also be noted that when Aristotle says of a conjoined predicate that it is predicated “per se,” the per se can be referred to three things:

to the parts of the conjunction among themselves,

to the whole conjunction with respect to the subject,

and to the parts of the conjoined predicate with respect to the subject.

Now if per se is taken positively, although it will not be false, nevertheless in reference to any of these three the meaning will be found to be foreign to the mind of Aristotle. For although these are valid: “He is a risible man; therefore, he is man and he is risible” and “He is a rational animal; therefore, he is animal and he is rational,” nevertheless the opposite kind of predication infers consequences in a similar way. For example, there is no essentiality in “He is a white musician; therefore, he is white and he is a musician”; rather, there is an accidental conjunction, not only between the parts among themselves and between the whole and the subject, but even between the parts and the subject.

It is evident, therefore, that Aristotle is not taking per se positively, for an addition that does not differentiate this kind of predication from the opposed kind of predication would be useless. Why add “per se and not accidentally,” if both those that are per se in the way explained and those that are conjoined accidentally infer divisively? If “per se” is taken negatively, that is, as not through another, and is referred to the parts of the conjoined predicate among themselves, the rule is found to be false. It is not licit, for example, to say, “He is a good lute player, therefore he is good and a lute player”; yet the art of lute-playing and its goodness are conjoined without anything as a medium. And the case is the same if it is referred to the whole conjoined predicate with respect to the subject, as is clear in the same example, for the whole, “good lute player,” does not belong to man on account of another, and yet it does not infer the division, as has already been said. Therefore, “per se” is referred to the parts of the conjoined predicate with respect to the subject, and the meaning is that when the predicates are conjointly predicated per se, that is, not through another (so that each part is predicated of the subject not on account of another but on account of itself and the subject), then a divided predication is inferred from the conjoined predication.

This is the way in which Averroes and Boethius explain this and, explained in this way, a true rule is found, as can easily be manifested inductively. Moreover, the reasoning is compelling. For if the parts of some conjoined predicate so inhere in the subject that neither of them is in it on account of another, their separation produces nothing that could impede the truth of the divided predicates. And this meaning is consonant with the words of Aristotle, for by this he also distinguishes between enunciations in which the conjoined predicate infers a divided predicate, and those in which this consequence is not inherent. For, besides the predicates having opposition in the additional determining element, there are those with a conjoined predicate in which one part is a determination of the other in such a way that only through it does it regard the subject, as is evident in Aristotle’s example, Homer is a poet. The “is” does not regard Homer by reason of Homer himself, but precisely by reason of the poetry he left. Hence it is not licit to infer, “Therefore, Homer is.” The same is true with respect to negative enunciations of this type, for it is not licit to infer from “Socrates is not a wall” that “therefore, Socrates is not.” And the reason is the same: “to be” is not denied of Socrates, but of “wallness” in Socrates.

Accordingly, it is evident how the reasoning in the text above is to be understood. Per se is taken negatively in the way explained here, and “accidentally” as “on account of another.” The accidentally is used with the same signification in solving this and the preceding question. In both he understands “accidentally” to mean conjoined on account of another, but it is referred to diverse things. In the preceding question accidentally determines the way in which two predicates are conjoined among themselves; in the latter question it determines the way in which the part of the conjoined predicate is ordered to the subject. Hence, in the former, white and musician are numbered among the things that are accidental, but in the latter they are not.

This exposition seems a bit dubious, however. For if it is not licit to infer divisively from a conjoined predicate because one part of the conjoined predicate does not regard the subject on account of itself but on account of another part (as Aristotle says of the enunciation, Homer is a poet), it will follow that there will never be a good consequence from the third determinant to the second, since in every enunciation with a third determinant, “is” regards the subject on account of the predicate and not on account of itself.

To make this difficulty clear, we must first note a distinction. It is one thing to treat of the rule when inferring a second determinant from a third determinant, and when not; it is quite another thing when a divided inference is made from a conjoined predicate, and when not. The former is an additional point; the latter is the question we have been inquiring about. The former is compatible with variety of the terms, the latter not. For if one of the terms which is one part of a conjoined predicate will be varied according to signification, or supposition when taken separately, it is not inferred divisively from the conjoined predicate, but the other is.

Second, note this proposition: when a second determinant is inferred from a third, identity of the terms is not kept. This is evident with respect to the term “is.” Indeed, St. Thomas said above that “is” as the second determinant implies one thing and “is” as the third determinant another. The former implies the act of being simply, the latter implies the relationship of inherence, or identity of the predicate with the subject. Therefore, when the second determinant is inferred from the third, one term is varied, and consequently an inference is not made of the divided from the conjoined.

Accordingly, the response to the objection is clear, for although the second determinant can sometimes be inferred from the third, it is never licit for the second to be inferred from the third as divided from conjoined, because you cannot infer divisively when one part is destroyed by that very division. Therefore, let the consequence of the objection be denied and for proof let it be said that the conclusion that such an inference is illicit under the limits of inferences which induce division from a conjoined predicate is good, for this is what Aristotle is speaking of here.

But the objection is raised against this that in the case of “Socrates is white; therefore, he is,” a divided inference can be made as from a conjoined predicate, in virtue of the argument that we can go from what is in the mode of part to its whole as long as the terms remain the same. The answer to this is as follows. It is true that white man is a part in the mode of man (because white diminishes nothing of the notion of man but posits man simply); “is white,” however, is not a part in the mode of “is,” because a part in the mode of its whole is a universal, the condition not diminishing the positing of it simply. But it is evident that “white” diminishes the notion of “is,” and does not posit it simply, for it contracts it to relative being. Hence, when something becomes white, philosophers do not say that it is generated, but generated relatively.

In accordance with this, the objection is raised that in saying, “It is an animal; therefore, it is,” a divided inference is made in virtue of the same argument; for “animal” does not diminish the notion of “is” itself. The answer to this is that if the “is” asserts the truth of a proposition, the fallacy is committed of going from the relative to the absolute; if the “is” asserts the act of being, the inference is good, but it is of the second determinant, not of the third.

There is another doubt, this time about the principle in the exposition. For this follows, “It is a colored quantity, therefore it is a quantity and it is colored.” But “colored” regards the subject through the medium of quantity. Therefore, the exposition given above does not seem to be correct. The answer to this and to similar objections is that “colored” is not so present in a subject by means of quantity that it is its determination, and by reason of such a determination denominates the subject; as “goodness,” for instance, determines the art of lute-playing when we say “He is a good lute player.” Rather, the subject itself is first denominated “colored” and quantity is called “colored” secondarily, although color is received through the medium of quantity. Hence, we made a point of saying earlier that one part of a conjoined predicate is predicated accidentally when it denominates the subject precisely because it denominates the other part. This is not the case here, nor in similar instances.

When he says, in the case of non-being, however (21a32), he excludes the error of those who were satisfied to conclude that what is not, is. This is the syllogism they use: “That which is, is ‘opinionable’; that which is not, is ‘opinionable’; therefore, what is not, is.” Aristotle destroys this process of reasoning by destroying the first proposition, which predicates divisively a part of what is conjoined in the subject, as if it said, “It is ‘opinionable’; therefore, it is.” Hence, assuming the subject of their conclusion, he says, in the case of that which is not, however; and he adds their middle term, because it is a matter of opinion; then he adds the major extreme, it is not true to say that it is something. He then assigns the cause: it is not because it is but rather because it is not that there is such opinion.

Lecture 8

Modal Propositions and Their Opposition

21a34. Having determined these things, we must consider in what way negations and affirmations of the possible and not possible, contingent and not contingent, and of the impossible and necessary are related to each other—a question of considerable difficulty.

21a38. Let us grant that of mutually related enunciations, contradictories are those opposed to each other by being related in a certain way according to “to be” and “not to be.” For example, the negation of “man is” is “man is not,” and not “non-man is”; and of “man is white,” “man is not white,” and not “man is non-white.” For if this is not so, it will be true to say that “wood” is non-white man, since of anything either the affirmation or the negation is true. Now, in those in which “to be” is not the determining word added, that which is said in place of “to be” will effect the same thing. For example, the negation of “man walks” will be “man does not walk,” and not “non-man walks.” The reason, of course, is that there is no difference between “man walks” and “man is walking.” And if this is always the case, then the negation of “possible to be” will be “possible not to be,” and not “not possible to be.”

21b12. However, it seems that the same thing is possible to be and possible not to be. For everything that has the possibility to be cut or to walk has the possibility not to be cut and not to walk, and the reason is that everything that is possible in this way is not always in act, and so the negation will also be inherent in it. For that which could walk could also not walk, and that which could be seen could not be seen. But it is impossible that contradictions in respect to the same thing be true. Therefore, the negation of “possible to be” is not “possible not to be.”

21b19. For it follows from what we have said either that the same thing is asserted and denied at once of the same subject or that assertions and denials of modals are not made by the addition of “to be” or “not to be” respectively. If the former alternative is impossible, the latter must obtain.

Now that he has treated enunciations in which something added to the parts leaves the unity intact on the one hand, and varies it on the other, Aristotle begins to explain what happens to the enunciation when something is added not to its parts, but to its composition.

About this he does two things.

First, he explains their opposition;

second, he treats of the consequences of their opposition, at: logical sequences result from modals ordered thus (22a14; [309]).

About the first he does two things.

First, he proposes the question he intends to consider;

second, he begins his consideration, at: let us grant that of mutually related enunciations (21a38; [296]).

He proposes that we must now investigate the way in which affirmations and negations of the possible and not possible are related. He gives the reason when he adds, a question of considerable difficulty (21a34).

However, before we proceed with the consideration of enunciations that are called modal, we must first see that there are such things as modal enunciations, and which and how many modes render propositions modal; we must also know what their subject is and their predicate, what the modal enunciation itself is, what the order is between modal enunciations and the enunciations already treated, and finally, why a special treatment of them is necessary.

We can speak about things in two ways:

in one way, composing one thing with another;

in the other, declaring the kind of composition that exists between the two things.

To signify these two ways of speaking about things we form two kinds of enunciations.

One kind enunciates that something belongs or does not belong to something. These are called absolute enunciations, which we have already discussed.

The other enunciates the mode of composition of the predicate with the subject. These are called modal, from their principal part, the mode. For when we say, “That Socrates run is possible,” it is not the running of Socrates that is enunciated but the kind of composition there is between running and Socrates—in this case, possible. I have said “mode of composition” expressly, for there are two kinds of mode posited in the enunciation.

One modifies the verb, either with respect to what it signifies, as in “Socrates runs swiftly,” or with respect to the time signified along with the verb, as in “Socrates runs today.”

The other kind modifies the very composition of the predicate with the subject, as in the example, “It is possible that Socrates run.”

The former determines how or when running is in Socrates; the latter determines the kind of conjunction there is between running and Socrates. The former, which affects the actuality of the verb, does not make a modal enunciation. Only the modes that affect the composition make a modal enunciation, the reason being that the composition, as the form of the whole, contains the whole enunciation.

This kind of mode, properly speaking, is fourfold: possible, impossible, necessary, and contingent. True and false are not included because, strictly speaking, they do not seem to modify the composition even though they fall upon the composition itself, as is evident in “That Socrates runs is true,” and “That man is four-footed is false.” For something is said to be modified in the proper sense of the term when it is caused to be in a certain way, not when it comes to be according to its substance. Now, when a composition is said to be true, it is not proposed that it is in a certain way, but that it is. To say, “That Socrates runs is true,” for example, is to say that the composition of running with Socrates is. The case is similar when it is false, for what is said is that it is not; for example, to say, “That Socrates runs is false” is to say that the composition of running with Socrates is not. On the other hand, when the composition is said to be possible or contingent, we are not saying that it is but that it is in a certain way. For example, when we say, “It is possible that Socrates run,” we do not make the composition of running with Socrates substantial, but we qualify it, asserting that it is possible. Consequently, Aristotle does not mention the true and false at all in proposing the modes, although later on he infers the true and the not true, and assigns the reason for it where he does this.

Since the modal enunciation contains two compositions, one between the parts of what is said, the other between what is said and the mode, it must be understood that it is the former composition that is modified, that is, the composition between the parts of what is said, not the composition between what is said and the mode.

This can be seen in an example. In the modal enunciation, “That Socrates be white is possible,” there are two parts: one, “That Socrates be white,” the other, “is possible.” The first is called the dictum because it is that which is asserted by the indicative, namely, “Socrates is white”; for in saying “Socrates is white” we are simply saying that Socrates is white. The second part is called the mode because it is the addition of a restriction. The first part of the modal enunciation consists of a certain composition of Socrates and white; the second part, opposed to the first, indicates a composition from the composition of dictum and mode. Again, the first part, although it has all the properties of an enunciation—subject, predicate, copula, and composition—is, in its entirety, the subject of the modal enunciation; the second part (the mode) is the predicate.

In a modal enunciation, therefore, the composition of the dictum is subjected and modified; for when we say, “That Socrates be white is possible,” it does not signify the kind of conjunction of possibility there is with the dictum “that Socrates be white,” but it implies the kind of composition there is of the parts of the dictum among themselves (that is, of white with Socrates)—namely, that it is a possible composition. The modal enunciation, therefore, does not say that something is present in or not present in a subject, but rather, it enunciates a mode of the dictum. Nor, properly speaking, does it compose according to what is signified, since it is not a composition of the composition; rather, it adds a mode to the composition of the things. Hence the modal enunciation is simply an enunciation in which the dictum is modified.

Because the modal enunciation has everything duplicated, it must not on that account be thought to be many. It enunciates one mode of only one composition, although there are many parts of that composition. The many concurring for the composition of the dictum are like the many that concur to make one subject, of which it was said above that it does not impede the unity of the enunciation. The enunciation, “The house is white,” is also a case in point, for it is not multiple, although a house is built of many parts.

Modal enunciations are rightly treated after the absolute enunciation, for parts are naturally prior to the whole, and knowledge of the whole depends on knowledge of the parts. Moreover, a special discussion of them was necessary because the modal enunciation has its own peculiar difficulties. Aristotle indicates in his text many of the things we have taken up here: the order of modal enunciations, when he says, having determined these things (21a34); what and how many modes there are when he expresses and lists them; the variation of the same mode by affirmation and negation when he says, the possible and not possible, contingent and not contingent; and the necessity of treating them, when he adds, a question of considerable difficulty.

Then he investigates the opposition of modal enunciations, where he says, let us grant that of mutually related enunciations (21a38).

About this he does two things.

First, he presents the question, and in so doing gives arguments for the parts;

second, he determines the truth, at: for it follows from what we have said (21b19; [303]).

The question with respect to the opposition of modals is this: Is a contradiction made in modal enunciations by a negation added to the verb of the dictum, which expresses what is; or is it not, but rather by a negation added to the mode which qualifies?

Aristotle first argues for the affirmative part, that the negation must be added to the verb;

second, he argues for the negative part, that the negation must not be added to the verb, at: however, it seems that the same thing (21b12; [302]).

His first argument is this. If of combined things, contradictions are those related according to “to be” and “not to be” (as is clear inductively in substantive enunciations with a second determinant, in those with a third determinant, and in adjectival enunciations), and all contradictions must be obtained in this way, the contradictory of possible to be will be possible not to be, and not not possible to be. Consequently, the negation must be added to the verb to get opposition in modal enunciations. The consequence is clear, for when we say “possible to be” and possible not to be” the negation falls on “to be.” Accordingly, he says, let us grant that of those things that are combined, that is, of complex things, contradictions are those opposed to each other which are disposed according to “to be” and “not to be,” that is, in one of which “to be” is affirmed and in the other denied.

He goes on to give an induction, beginning with an enunciation having a second determinant. The negation of man is is “man is not,” in which the verb is negated. The negation of “man is” is not non-man is, for this is not the negative but the affirmative of the infinite subject, which is true at the same time as the first enunciation, “man is.”

He continues the induction with substantive enunciations having a third determinant. The negation of the enunciation “man is white” is “man is not white,” in which the verb is negated. The negation is not “man is non-white,” for this is not the negative, but the affirmative of the infinite predicate.

Now, it might be thought that the affirmatives of the finite and infinite predicates are contradictories since they cannot be verified of the same thing because of their opposed predicates.

To obviate this error, Aristotle interposes an argument proving that these two are not contradictories. The nature of contradictories, he reasons, is such that either the assertion (that is, the affirmation) or the negation is verified of anything, for between contradictories no middle is possible. Now the two enunciations that something is white man and is non-white man are per se contradictories. Therefore, they are of such a nature that one of them is verified of anything. For example, it is false to say “is white man” of wood; hence “is non-white man” will be true to say of it (that is, of wood)—“wood is non-white man.” This is manifestly false, for wood is neither white man nor non-white man. Consequently, there is not a contradiction in the case in which each is at once false of the same subject. Therefore, contradiction is effected when the negation is added to the verb.

He continues his induction with enunciations having an adjective verb: now, if the case is as we have stated it (21a38), that is, if contradiction is taken as said above, then in enunciations in which “to be” is not the determining word added (explicitly), that which is said in place of “to be” will effect the same thing with respect to the opposition obtained—that is, the adjective verb that occupies the place of “to be,” inasmuch as the truth of “to be” is included in it, effects the function of the copula. For example, the negation of the enunciation man walks is not non-man walks (for this is the affirmative of the infinite subject), but man does not walk. In this case, as in that of the substantive verb, the negation must be added to the verb, for there is no difference between using the adjective verb, as in “man walks,” and using the substantive verb, as in “man is walking.”

Then he posits the second part of the induction: and if this is always the case (21a38), that is, that contradiction must be gotten by adding the negation to “to be,” we must conclude that the negation of the enunciation that asserts “possible to be” is “possible not to be,” and not “not possible to be.” The consequent of the conclusion is evident, for in “possible not to be” the negation is added to the verb, in “not possible to be,” it is not. At the beginning of this argument, Aristotle said, of those things that are combined, that is, complex things, the contradictions are effected according to “to be” and “not to be.” He said this in reference to the difference between complex and incomplex things, for opposition in the latter is not made by the negation expressing not to be, but by adding the negative to the incomplex thing itself, as in “man” and “non-man,” “reads” and “non-reads.”

When he says, however, it seems that the same thing (21b12), he argues for the negative part of the question—namely, that to get a contradiction in modals, the negation should not be added to the verb. His reasoning is the following: It is impossible for two contradictories to be true at once of the same subject; but “possible to be” and “possible not to be” are verified at once of the same thing; therefore, these are not contradictories. Consequently, contradiction of the modals is not obtained by negation of the verb.

In this reasoning, the minor is posited first, with its proof;

second, the major;

third, the conclusion.

The minor is: however, it seems that the same thing is possible to be and possible not to be (21b12). For instance, everything that has the possibility of being divided also has the possibility of not being divided, and that which has the possibility of walking also has the possibility of not walking. The proof of this minor is that everything that is possible in this way (like “possible to walk” and “to be divided”) is not always in act; for he who is able to walk is not always actually walking, nor is that which can be divided always divided. And so the negation of the possible will also be inherent in it, that is, therefore not only is the affirmation possible but also the negation.

Notice that since the possible is manifold, as will be said further on, Aristotle explicitly adds in this way when he assumes here that that which is possible is not always in act. For it is not true to say of every possible thing that it is not always in act, but only of some, namely, those that are possible in the way in which to walk and to be divided are possible.

Note also that “possible in this way” has two conditions: that it is able to be in act, and that it is not always in act. It follows necessarily, then, that it is true to say of it simultaneously that it is both possible to be and possible not to be. From the fact that it can be in act it follows that it is possible to be; from the fact that it is not always in act it follows that it is possible not to be, for that which not always is, is able not to be.

Aristotle, then, rightly infers from these two: and so the negation of the possible will also be inherent in it; and not just the affirmation, for that which could walk could also not walk and that which could be seen not be seen (21b12).

The major is: but it is impossible that contradictions in respect to the same thing be true (21b12).

The final conclusion inferred is: therefore, the negation of “possible to be” is not “possible not to be” (21b12), because they are true at once of the same thing.

In relation to this part of the text, be careful not to suppose that possible-as-a-mode is always to be taken for possible to either of two alternatives, for this will be shown to be false later on. If you consider the matter carefully, you will see that it was enough for his intention to give as an instance one modal contained under the modals of the possible in order to show that contradiction in modals is not obtained by negation of the verb.

Aristotle establishes the truth with respect to this difficulty where he says, for it follows from what we have said (21b19). Since he is investigating two things—namely, whether contradiction of modals is made by the negation of the verb or not, and whether it is not rather by negation of the mode—he first determines the truth in relation to the first question, namely, that contradiction of modals is not made by negation of the verb;

second, he determines the truth in relation to the second, namely, that contradiction of modals is made by negation of the mode, at: therefore, the negation of “possible to be” is “not possible to be" (21b23; [304]).

Hence he says that because of the foresaid reasoning one of these two follows:

first, that either the same thing, that is, one and the same thing is said or is asserted and denied at once of the same subject (21b19), that is, either two contradictories are verified at once of the same thing, as the first argument concluded;

or that assertions and denials of modals, which are opposed contradictorily are not made by the addition of “to be” or “not to be” (21b19), that is, contradiction of modals is not made by the negation of the verb, as the second argument concluded.

If the former alternative is impossible (21b19), namely, that two contradictories can be true of the same thing at once, the latter, that contradiction of modals is not made according to negation of the verb, must obtain, for impossible things must always be avoided.

His mode of speaking here indicates that there is some obstacle to each alternative. But since in the first the obstacle is an impossibility that cannot be accepted, while in the second the only obstacle is that the negation must fall upon the copula of the enunciation if a negative enunciation is to be formed, and this can be done otherwise than by denying the verb of the dictum, as will be shown later on, then the second alternative must be chosen (namely, that the contradiction of modals is not made according to negation of the verb), and the first alternative is to be rejected.

Lecture 9

In Contradictions of Modal Propositions the Negation Must Be Added to the Modes, Not to the Verb

21b23. Therefore, the negation of “possible to be” is “not possible to be.” The reasoning is the same in regard to “contingent to be,” for its negation is “not contingent to be.” So, too, in the others—that is, the necessary and the impossible.

21b26. For just as “to be” and “not to be” are the determining additions in the former [that is, absolute enunciations] and the things subjected are “white” and “man,” so here “to be” is as the subject and “is possible” and “is contingent” are determining additions; and just as “to be” and “not to be” determine the true [and the false] in the former, in like manner these determine the true [and the false] in regard to what is possible and not possible.

21b33. The negation, then, of “possible not to be” is “not possible not to be.” Therefore, “possible to be” and “possible not to be” would appear to be consequent to each other; for the same thing is “possible to be” and “possible not to be,” since these are not contradictory to each other. But “possible to be” and “not possible to be” are never true at once of the same subject, for they are opposed. Nor are “possible not to be” and “not possible not to be” ever true at once of the same subject.

The case is the same with respect to the necessary. The negation of “necessary to be” is not, “necessary not to be” but “not necessary to be”; and the negation of “necessary not to be,” “not necessary not to be.”

Likewise, the negation of “impossible to be” is not “impossible not to be” but “not impossible to be”; and of “impossible not to be,” “not impossible not to be.”

22a8. And universally, as has been said, “to be” and “not to be” must be posited as the subject, and those that produce affirmation and negation [that is, possible, not possible, contingent, not contingent, and so on] must be joined to “to be” and “not to be.” And these are the words that are to be considered opposed:

possible and not possible; contingent and not contingent; impossible and not impossible; necessary and not necessary; true and not true.

Aristotle now determines where the negation must be placed in order to obtain contradiction in modals.

About this he does four things.

He first determines the truth summarily;

second, he presents the argument for the truth of the position, which is also the answer to the reasoning induced for the opposite position, at: for just as “to be” and “not to be” (21b26; [305]);

third, he makes this truth evident in all the modals, at: the negation, then, of “possible not to be” is “not possible not to be” (21b33; [307]);

fourth, he arrives at a universal rule, at: and universally, as has been said, “to be” and “not to be” (22a8; [308]).

Since the negation must be added either to the verb or to the mode, and it was shown above in virtue of an argument from division that it is not to be added to the verb, he concludes: therefore, the negation of “possible to be” is “not possible to be” (21b23), that is, the mode is negated. The reasoning is the same with respect to enunciations of the contingent, for the negation of “contingent to be” is “not contingent to be.” And the judgment is the same in the others, namely, the necessary and the impossible.

When he says, for just as “to be” and “not to be” are the determining additions (21b26), he gives the argument for the truth of his position. To obtain contradiction among any enunciations the negation must be applied to the determining addition, that is, to the word that joins the predicate with the subject; but in modals the determining additions are the modes; therefore, to get a contradiction in modals, the negation must be added to the mode. The major of the argument is subsumed; the minor is stated in Aristotle’s wording by a further similitude to absolute enunciations. In absolute enunciations the determining additions, namely, the predications, are “to be” and “not to be,” that is, the verb signifying “to be” or “not to be” (for the verb is always a sign of those things that are predicated of another). The things subjected to the determining additions, that is, to which “to be” and “not to be” are applied, are “white,” in “white is, “or man,” in “man is.” This happens in modals in the same way but in a manner appropriate to them. “To be” is as the subject, that is, the dictum signifying “to be” or “not to be” holds the place of the subject; “is possible” and “is contingent,” that is, the modes, are the predicates. And just as in absolute enunciations we determine truth or falsity with “to be” and “not to be,” so in modals with the modes. He makes this point when he says, determining additions, that is, these modes effect truth just as “to be” and “not to be” determine truth and falsity in the others.

Thus the response to the argument for the opposite position, which he gave first, is evident. That argument concluded that the negation should be added to the verb as it is in absolute enunciations. But since the modal enunciates a mode of a dictum—as the absolute enunciation enunciates “to be” or “not to be” (as, for instance, “to be white” of a subject)—the mode holds the same place here that the verb does there. Consequently, the negation falls upon the same thing proportionally here and there, for the proportion of mode to dictum is the same as the proportion of verb to subject.

Again, since truth and falsity follow upon affirmation and negation, the affirmation and negation of an enunciation and its truth and falsity must be controlled by the same thing. In absolute enunciations truth and falsity follow upon “to be” or “not to be”; hence in the modals they follow upon the mode, for that modal is true which modifies the dictum as the composition of the dictum permits, just as that absolute enunciation is true which signifies that something is as it is. Therefore, negation is added here to the mode just as it is added there to the verb, since the power of each is the same with respect to the truth and falsity of an enunciation.

Notice that he calls the modes “determining additions,” that is, predications, as “to be” is in absolute enunciations—understanding by the mode the whole predicate of the modal enunciation, for example, “is possible.” As a sign of this, he expresses the modes themselves verbally when he says, “is possible” and “is contingent” are determining additions. For is contingent and is possible comprise the whole predicate of the modal enunciation.

When he says, the negation, then, of “possible not to be” (21b33), he makes this truth evident in all the modals, namely, the possible, the necessary, and the impossible (the contingent being convertible with the possible). And since any mode makes two modal affirmatives, one having an affirmed dictum and the other having a negated dictum, he shows what the negation of each affirmation is in each mode.

First, he takes those of the possible. The negation of the first affirmative of the possible (the one with an affirmed dictum)—namely, “possible to be”—was assigned as “not possible to be.” Hence, going on to the remaining affirmative of the possible, he says, the negation, then, of “possible not to be” (in which the dictum is negated) is “not possible not to be.” Then he proves this. The contradictory of “possible not to be” is either “possible to be” or “not possible not to be.” But the former, “possible to be,” is not the contradictory of “possible not to be,” for they can be at once true. Hence they are also thought to follow upon each other, for, as was said above, the same thing is possible to be and not to be. Consequently, just as “possible not to be” follows upon “possible to be,” so conversely “possible to be” follows upon “possible not to be.” But the contradictory of “possible to be,” which cannot be true at the same time, is “not possible to be,” for these, as has been said, are opposed. Therefore, the negation of “possible not to be” is “not possible not to be,” for these are never at once true or false.

Note that he says, therefore, “possible to be” and “possible not to be” would appear to be consequent to each other, and not that they do follow upon each other, for it is not true that they follow upon each other universally, but only particularly (as will be said later); this is the reason they appear to follow upon each other simply.

Then he manifests the same thing in the modals of the necessary.

first, in the affirmative with an affirmed dictum: the case is the same with respect to the necessary. The negation of “necessary to be” is not “necessary not to be” (in which the mode is not negated) but, “not necessary to be.”

Next, he adds the affirmative of the necessary with a negated dictum: and the negation of “necessary not to be is “not necessary not to be.”

Next, he takes up the impossible, keeping the same order. The negation of “impossible to be” is not “impossible not to be” but, “not impossible to be,” in which the mode is negated. The negation of the other affirmative, “impossible not to be,” is “not impossible not to be.” The negation, therefore, is always added to the mode.

Then he says, and universally, as has been said (22a8). Here he concludes with the universal rule. As has been said, the dictums denoting “to be” and “not to be” must be posited in the modals as subjects, and the one making this an affirmation and negation—that is, the opposition of contradiction—must be added only to the selfsame mode, not to diverse modes, for the selfsame mode which was previously affirmed must be denied if there is to be a contradiction.

He gives examples of how this is to be done when he adds, and these are the words that are to be considered opposed, that is. affirmations and negations in modals, possible and not possible, contingent and not contingent. Moreover, when he said elsewhere but in another way that the negation must be applied only to the mode, he did not exclude the copula of the mode, but the copula of the dictum. For it is unique to modals that the same opposition is made by adding a negation to the mode and to its verb. The contradictory of “is possible to be,” for instance, is not only “is not possible to be,” but also “not is possible to be.”

There are two reasons, however, for his mentioning the mode rather than the verb:

first, for the reason we have just given, namely, so as to imply that the negation placed after the verb of the mode, the mode having been put first, accomplishes the same thing as if it were placed before the modal verb;

second, because the modal enunciation is never without a mode; hence the negation can always be put on the mode. However, it cannot always be put on the verb of a mode, for the modal enunciation may lack the verb of a mode—as, for example, in “Socrates runs necessarily,” in which case the negation can always be adapted to the verb.

In adding true and not true at the end, he implies that besides the four modes mentioned previously there are others that also determine the composition of the enunciation, for example, “true” and “not true,” “false” and “not false.” Nevertheless, he did not posit these among the modes first given because, as was shown, they do not properly modify.

Lecture 10

The Logical Consequents of the Modals

22a14. Logical sequences result from modals ordered thus. From “possible to be” follows “contingent to be,” and the latter is convertible with the former; “not impossible to be” and “not necessary to be” also follow from “possible to be.” From “possible not to be” follows “contingent not to be,” “not necessary not to be,” and “not impossible not to be.” From “not possible to be” and “not contingent to be” follows “necessary not to be” and “impossible to be.” From “not possible not to be” and “not contingent not to be” follows “necessary to be” and “impossible not to be.” Let us consider these with the help of a table.

22a24. Possible to be—not possible to be

contingent to be—not contingent to be

not impossible to be—impossible to be

not necessary to be—necessary not to be

possible not to be—not possible not to be

contingent not to be—not contingent not to be

not impossible not to be—impossible not to be

not necessary not to be—necessary to be

22a32. Now, the impossible and the not impossible follow contradictorily upon the contingent and the possible and the not contingent and the not possible, but inversely. The negation of “impossible to be” follows upon “possible to be,” and the affirmation of the former follows upon the negation of the latter, that is, “impossible to be” follows upon “not possible to be.” For “impossible to be” is an affirmation, “not impossible to be” a negation.

22a38. Now, we must consider how enunciations predicating necessity are related to these. It is evident that the case here is not the same, for the contraries follow, but their contradictories are separated.

22a39. For the negation of “necessary not to be” is not “not necessary to be,” since both may be true of the same subject, for the necessary not to be is not necessary to be.

22b3. Now, the reason why enunciations predicating necessity do not follow in the same way as the others is that the impossible expresses contrarily the same thing as the necessary. For if it is impossible that this be, it is necessary, not that it be, but necessary that it not be; and if it is impossible that it not be, it is necessary that it be. So, if the impossible and not impossible follow in like manner from the possible and not possible, the necessary and not necessary follow contrarily, since the necessary and the impossible signify the same thing, but (as has been said) inversely.

22b10. Or is it impossible to arrange the contradictions of enunciations predicating necessity in this way? For what is necessary to be, is possible to be (for if not, the negation will follow, since it is necessary either to affirm or deny; and if it is not possible to be, it is impossible to be; therefore, that which is necessary to be is impossible to be, which is absurd). But from “possible to be” follows “not impossible to be,” and from this, “not necessary to be”; and thus what is necessary to be is not necessary to be, which is absurd.

22b17. But, in fact, neither “necessary to be” nor “necessary not to be” follow upon “possible to be.” For “to be possible” admits of two possibilities; but if either “necessary to be” or “necessary not to be” is true, both possibilities will no longer be true. For a thing is at once possible to be and not to be, but if it is necessary to be or not to be, the two alternatives will not be possible. It remains, therefore, that “not necessary not to be” follows upon “possible to be.”

22b23. For this is true also with respect to “necessary to be.” For “not necessary not to be” is the contradictory of what follows upon “not possible to be,” for “not possible to be” is followed by “impossible to be” and by “necessary not to be,” and the negation of this is “not necessary not to be.”

22b26. Thus, these contradictions also follow in the way indicated, and nothing impossible follows when they are thus arranged.

Having established the opposition of modals, Aristotle now intends to determine their consequents.

About this he does two things.

First, he presents the true doctrine;

second, he raises a difficulty, at: but it may be asked (22b29; [327]).

About the first he does two things.

First, he posits the consequents of the opposition of modals according to the opinion of others;

second, he determines the truth by examining and correcting their opinion, at: now the impossible and the not impossible (22a32; [313]).

Before we consider these consequents according to the opinion of others, we must first note that since any mode makes two affirmations to which are opposed two negations, there will be four enunciations according to any one mode, two affirmatives and two negatives. And since there are four modes, there will be sixteen modals. Among these sixteen, from wherever you begin, any one of each mode has only one of each mode following upon it. Hence, to assign the consequents of the modals, we have to take one from each mode and arrange them among themselves to form an order of consequents.

The modals were ordered in this way by the ancients. They disposed them in four orders placing together in each order those that were a consequent to each other. Aristotle speaks of this order when he says, logical sequences follow according to the order in the table below, which is the way in which the ancients posited them (22a14). Henceforth, however, to avoid confusion let us call the affirmative of dictum and mode in any one mode, the simple affirmative, as it is by Averroes, among others; affirmative of mode and negative of dictum, the declined affirmative; negative of mode and not of dictum, the simple negative; negative of both mode and dictum, the declined negative. Hence, simplicity of mode designates affirmation or negation, and so, too, does declination of dictum.

The ancients said, then, that simple affirmation of the contingent (that is, “contingent to be”) follows upon simple affirmation of the possible (that is, “possible to be”), for the contingent is converted with the possible; the simple negative of the impossible also follows upon this (namely, “not impossible to be”); and the simple negative of the necessary (namely, “not necessary to be”). This is the first order of modal consequents.

In the second order they said that the declined negatives of the necessary and impossible (namely, “not necessary not to be” and “not impossible not to be”) follow upon the declined affirmative of the possible and the contingent (namely, “possible not to be” and “contingent not to be”).

In the third order, according to them, the declined affirmative of the necessary (that is, “necessary not to be”) and the simple affirmative of of the impossible (that is, “impossible to be”) follow upon the simple negatives of the possible and the contingent (that is, “not possible to be” and not contingent to be”).

Finally, in the fourth order, the simple affirmative of the necessary (namely, “necessary to be”) and the declined affirmative of the impossible (namely, “impossible not to be”) follow upon the declined negatives of the possible and the contingent (namely, “not possible not to be” and “not contingent not to be”).

To make this ordering more evident, let us consider it with the help of the following table of the consequents of modal enunciations in the four orders posited and ordered by the ancient.

FIRST ORDER
It is possible to be
It is contingent to be
It is not impossible to be
It is not necessary to be

SECOND ORDER
It is possible not to be
It is contingent not to be
It is not impossible not to be
It is not necessary not to be

THIRD ORDER
It is not possible to be
It is not contingent to be
It is impossible to be
It is necessary not to be

FOURTH ORDER
It is not possible not to be
It is not contingent not to be
It is impossible not to be
It is necessary to be

When he says, now, the impossible and the not impossible follow contradictorily (22a32), he determines the truth by examining the foresaid opinion.

About this he does two things.

First, he examines the consequents of enunciations predicating impossibility;

second, those predicating necessity, at: now we must consider how enunciations predicating necessity (22a38; [314]).

From the opinion advanced, then, he concludes with approval that these, the impossible and the not impossible, follow upon the contingent and the possible and the not contingent and the not possible, contradictorily (that is, the contradictories of the impossible follow upon the contradictories of the possible and the contingent), but inversely—that is, not so that affirmation follows upon affirmation and negation upon negation, but inversely, so that negation follows upon affirmation and affirmation upon negation.

He explains this when he says, the negation of “impossible to be” follows upon “possible to be” (22a32), that is, the negation of the impossible (“not impossible to be”) follows upon the affirmation of the possible, and the affirmation of the impossible follows upon the negation of the possible. For the affirmation “impossible to be” follows upon the negation “not possible to be.” In the latter the mode is negated, in the former it is not.

Therefore, the ancients were right in saying that in any order, the consequences of enunciations predicating impossibility are as follows: from affirmation of the possible, negation of the impossible is inferred; and from negation of the possible, affirmation of the impossible is inferred. This is apparent in the diagram.

When he says, now, we must consider how enunciations predicating necessity (22a38), he proposes an examination of the consequents of enunciations predicating necessity in order to determine the truth about them.

About this he does two things.

First, he examines what was said by the ancients;

second, he determines the truth, at: but in fact neither “necessary to be” nor “necessary not to be” (22b17; [321]).

About the first he does four things.

First, he shows what was well said by the ancients and what was badly said. It must be noted in regard to this that, as we have said, there are four enunciations predicating necessity, which differ among themselves in quantity and quality, and thus make up a diagram of opposition in the manner of the absolute enunciations. Two of them are contrary to each other, and two are contradictory to these contraries, as is clear in the diagram below. [figure]

Now the ancients correctly inferred the universal contraries from the possibles, contingents, and impossibles, but incorrectly inferred their contradictories, namely, particulars. This is the reason Aristotle says that it remains to be considered how enunciations predicating necessity are related consequentially to the possible and not possible. From what Aristotle says, it is clear that those predicating necessity do not follow upon the possibles in the same way as those predicating impossibility follow upon the possibles, for all of the enunciations predicating impossibility were correctly inferred by the ancients, but those predicating necessity were not. Two of them, the contraries “necessary to be” and “necessary not to be,” follow (that is, correct consequents were deduced by the ancients in the third and fourth orders); the remaining two, “not necessary not to be” and “not necessary to be,” which are contradictories of the contraries, are outside of the consequents of these, in the second and first orders. Hence, the ancients represented everything correctly in the third and fourth orders, but in the first and second they erred—though not with respect to all things, but only with respect to enunciations predicating necessity.

Second, when he says, for the negation of “necessary not to be” is not “not necessary to be” (22a39), he replies to a tacit objection. This reply could be used to defend the consequent of the enunciation of the necessary made by the ancients in the first order. The tacit objection is this: “not possible to be” and “necessary not to be” follow convertibly in the third order which has already been shown to be correct; therefore, “possible to be” and “not necessary to be” ought to follow upon each other in the first order. The consequent holds, for the contradictories of two that convertibly follow upon each other mutually follow upon each other; but those two follow upon each other convertibly in the third order, and these two in the first order are their contradictories; therefore, those of the first order (namely, “possible to be” and “not necessary to be”) mutually follow upon each other.

Aristotle replies here to this objection by destroying what was assumed in the minor, namely, that the necessary of the first order and the necessary of the third order are contradictories. He says, for the negation of “necessary not to be” (which is in the third order) is not “not necessary to be” (which has been placed in the first order). He also gives the reason: it is possible for both to be true at once of the same subject, which is repugnant to contradictories. For the same thing which is necessary not to be, is not necessary to be; for example, it is necessary that man not be wood and it is not necessary that man be wood. Notice, as will be clear later, that these two, which the ancients posited in the first and third orders, are subalterns and therefore are at once true, when they should be contradictories; hence the ancients were in error.

Boethius and Averroes read both this and the preceding part of the text not reprovingly, but as explanatorily joined together. They say Aristotle explains the quality of the above table with respect to the consequents of enunciations predicating necessity after he has explained in what way those predicating impossibility are related. What Aristotle is saying, then, is that those of the necessary do not follow those of the possible in the same way as those of the impossible follow upon the possible. For contradictories of the impossible follow upon contradictories of the possible, although inversely; but contradictories of the necessary are not said to follow the contradictories of the possible, but rather the contraries of the necessary follow upon them. It is not the contraries among themselves that follow, but contraries in this way: the negation of the necessary is said to follow upon the affirmation of the possible; but what follows on the negation of this possible is not the affirmation of the necessary contradictory to that negative of the necessary following upon the possible, but the contrary of such an affirmation of the necessary. That this is the case is evident in the first and third orders. The sources are negation and affirmation of the possible, and the extremes are “not necessary to be” and “necessary not to be.” But these are not contradictories, for the negation of “necessary not to be” is not “not necessary to be,” for it is possible for them to be at once true of the same thing. “Necessary not to be” is the contrary of the contradictory of “not necessary to be,” which contradictory is “necessary to be.”

In my judgment, however, the first exposition should be accepted and this portion of the text taken as a reproof of the ancients, because the contraries seem to be explained in a forced way by others, whereas our introduction is more in accord with what follows in the next part of the text; in addition, it agrees with Albert’s interpretation.

Third, when he says, now the reason why enunciations (22b3), he shows why enunciations predicating impossibility and necessity do not follow in a similar way upon those predicating possibility. This was the error made by the ancients in both the first and second orders, for in the first order they posited the simple negative of the impossible, and in a similar way the simple negative of the necessary, and in the second order their declined negatives, the reason being that they inferred those predicating impossibility and necessity in a similar way. The cause of this error, then, and the reason why enunciations predicating necessity do not follow the possible in the same way, that is, in a similar mode, as the others, that is, as the impossibles, is that the impossible expresses the same meaning as the necessary, that is, is equivalent to the necessary, contrarily, that is, taken in a contrary mode, and not in the same mode. For if something is impossible to be, we do not infer that therefore it is necessary to be, but that it is necessary not to be. Since, therefore, the impossible and necessary mutually follow each other when their dictums are taken in a contrary mode—and not when their dictums are taken in a similar mode—it follows that the impossible and necessary are not related in the same way to the possible, but in a contrary way. For the negated dictum of the necessary follows upon that possible which follows the affirmed dictum of the impossible, and contrarily. Why this is so will be explained later. Therefore, the ancients erred when they located similar enunciations of the impossible and necessary in the first and in the second orders.

Hence it appears that our exposition is more in conformity with Aristotle. For he introduced this text to manifest these words: it is evident that the case here is not the same (22a38). By taking this meaning, then, these words are made clear through the cause. Moreover, it is evident that here the cause is given of a true dissimilitude between necessaries and impossibles in following the possibles, and not of a dissimilitude falsely held by the ancients, for from a true cause only the truth is concluded. Therefore, in reproving the ancients, it must be understood that a true dissimilitude between the necessary and impossible in following the possible, which they did not heed, has been proposed, and now has been made manifest. It will be clear from what will be said later that the dissimilitude posited by the ancients between the necessary and impossible is falsely posited, for it will be shown that contradictories of the necessary follow contradictories of the possible inversely, and that in this they do not differ from enunciations predicating impossibility. They do differ, however, in the way we have indicated—namely, the dictum of the possibles and of the impossibles following on them is similar, but the dictum of the possibles and of the necessaries following on them is contrary, as will be seen clearly later.

Fourth, when he says, or is it impossible to arrange the contradictions (22b10), he manifests another point he had proposed, namely, that contradictories of enunciations predicating necessity were badly placed according to consequence by the ancients when they ordered them with the contradictory negation to “necessary to be” (namely, “not necessary to be”) in the first order, and the contradictory negation to “necessary not to be” (namely, “not necessary not to be”) in the second.

Aristotle only proves that this mode of consequence is incorrect in the first order, for when this is known the mistake in the second order is readily seen. He does this by an argument leading to an impossibility. “Possible to be” follows upon “necessary to be”; otherwise “not possible to be” would follow, which it manifestly implies. “Not impossible to be” follows upon “possible to be” as is evident, and, according to the ancients, in the first order, “not necessary to be” follows upon “not impossible to be.” Therefore, from first to last, “not necessary to be” follows upon “necessary to be,” which is inadmissible because there is an obvious implication of contradiction. Therefore, it is erroneous to say that “not necessary to be” follows in the first order.

He says, then, that in fact it is impossible to posit contradictions of the necessary according to consequence as the ancients posited them, namely, with the contradictory negation of “necessary to be” (that is, “not necessary to be”) in the first order, and in the second the contradictory negation of “necessary not to be,” (that is, “not necessary not to be”). For “possible to be” follows upon “necessary to be”; if not, that is, if you deny this consequence, the negation of the possible follows upon “necessary to be,” since the possible must either be asserted of the necessary or denied, because there is a true affirmation or a true negation of everything. Therefore, if you say that “possible to be” does not follow upon “necessary to be,” but “not possible to be” does follow, then, since the latter is equivalent to the former (“not possible to be” to “impossible to be”), “impossible to be” follows upon “necessary to be,” and the same thing will be “necessary to be” and “impossible to be,” which cannot be admitted. Consequently, the first inference was good, namely, “it is necessary to be, therefore it is possible to be.” But again, “possible to be” follows upon “not impossible to be,” as is evident in the first order, and according to the ancients, “not necessary to be” follows upon “not impossible to be” in the same first order. Therefore, from first to last we arrive at this: “not necessary to be” follows upon “necessary to be,” which is unlikely, not to say impossible.

There is a doubt about this, for in Prior Analytics 1.13 (32a28, 32b15), it is said that the not necessary follows upon the possible, while here the opposite is said. The possible, however, is taken in two ways:

In one way, commonly, and thus it is higher than the necessary and the contingent to either of two alternatives, as is the case with animal in relation to man and cow. Taken in this way, the not necessary does not follow upon the possible, just as not-man does not follow upon animal.

In another way, it is taken for one part of what is possible commonly, that is, for the possible or contingent to either of two alternatives (namely, for what can be and not be). The not necessary follows upon the possible taken in this way, for what can be and not be is not necessary to be, and likewise is not necessary not to be.

In the Prior Analytics, then, Aristotle is speaking of the possible in particular; here of the possible commonly.

When he says, but in fact neither “necessary to be” nor “necessary not to be” follow (22b17), he determines the truth.

About this he does two things.

First, he determines which enunciation of the necessary follows upon the possible;

second, he orders the consequents of all of the modals, at: thus, these contradictions also follow in the way indicated (22b26; [326]).

Aristotle has reproved the ancients in two ways; on the basis of these two he now proves which enunciation of the necessary follows upon the possible. What he intends to show is that “not necessary not to be” follows upon “possible to be.”

The first argument is taken from a locus of division. “Not necessary to be” does not follow upon possible to be” (as has been proved), but neither does “necessary to be” nor “necessary not to be.” Therefore, “not necessary not to be” follows upon “possible to be,” since there are no more enunciations of the necessary.

He first proposes the remaining two members that are to be excluded from this common division: but in fact neither “necessary to be” nor “necessary not to be” follow upon “possible to be” (22b17).

Second, he proves this. No formal consequent diminishes its antecedent, for if it did, the opposite of the consequent would stand with the antecedent; but both of these, namely, “necessary to be” and “necessary not to be,” diminish “possible to be”; therefore, etc. The major is therefore implied. Hhe gives the proof of the minor when he says that “possible to be” admits of two possibilities, namely, “to be” and “not to be”; but of these, namely, “necessary to be” and “necessary not to be” (whichever should be true), these two (“to be” and “not to be”) will not be true at the same time in potency.

He explains the first point thus: when I say “possible to be,” it is at once possible to be and not to be.

With respect to the second, he adds: if you should say, “necessary to be” or “necessary not to be,” both do not remain (that is, possible to be and not to be do not remain), for if a thing is necessary to be, possibility not to be is excluded, and if it is necessary not to be, possibility to be is removed. Both of these, then, diminish the antecedent, “possible to be,” for it is extended to “to be” and “not to be.”

Third, he concludes that it remains, therefore, that “not necessary not to be” accompanies “possible to be,” and consequently will have to be placed in the first order.

A difficulty arises at this point with respect to his saying that the necessary does not follow upon the possible, since he has also said that the not necessary does not follow upon it. For the necessary and the not necessary are opposed contradictorily, and since of anything there is a true affirmation or negation, it seems impossible to avoid the conclusion that either the necessary or the not necessary follows upon the possible; and since the necessary does not follow, the not necessary must follow, as the ancients said. Furthermore, the difficulty is augmented by the fact that Aristotle just used such a mode of argumentation when, to prove that the possible follows upon the necessary, he said, for if not, the negation will follow (22b10); for it is necessary either to affirm or deny.

In order to resolve this, we must recall the relationship between the possible and the necessary, namely, that the possible is higher than the necessary. Now the superior potentially contains its own inferior and the opposite of it in such a way that neither of them is actually appropriated by the higher, but each is possible to it, as in the case of man and not-man in relation to animal. We must also consider that the proportion of the superior as related to the affirmation and negation of one inferior is the same (which is the proportion of some subject to the affirmative and negative of a future contingent), for it is had by neither of the two, and the potency to either is kept. Accordingly, as in future contingents neither the affirmation nor the negation is determinately true, but under disjunction one is necessarily true (as was concluded at the end of the first book), so neither the affirmation nor negation of the inferior follows upon the affirmation or negation of the superior determinately, but one follows necessarily under disjunction. For instance, neither “it is animal; therefore, it is man,” nor “therefore, it is not man” is valid; but “therefore, it is man or it is not man” is valid. Since, then, the possible is higher than the necessary, Aristotle has correctly determined that neither part of the contradiction of the necessary determinately follows upon the possible. However, he has not said that under disjunction neither follows; for this would be opposed to the first principle that of anything there is a true or false affirmation.

The response to what was added is based upon the same point. Since the necessary is inferior to the possible, and the inferior does not include its superior in potency but in act, the superior must follow determinately upon the inferior; otherwise, the contradiction of it would follow determinately. Hence, because of the dissimilar relationship between the necessary, the possible, and the not possible on the one hand, and between the possible, the necessary, and the not necessary on the other, the movement of the earlier argument to one part of the contradiction determinately was quite right, and the movement here to neither determinately was quite right.

There is another slight difficulty, for it seems that Aristotle takes the possible in a different way in the preceding text and in this. There he takes it commonly as it follows upon the necessary; here he seems to take it specifically for the possible that is indifferent to alternatives, since he says that the possible is at once possible to be and not to be. But in fact Aristotle has used the possible uniformly. Nor are his words at variance, for it is also true to say of the possible as common that it admits of both possibilities, namely, of “to be” and “not to be”:

first, because whatever is verified of its inferior is verified also of its superior, although not in the same mode;

second, because the possible as common determines neither part of the contradiction to itself and consequently admits of either happening, although it does not affirm a potency to each part, as does the possible to either of two alternatives.

The second grounds for proving the same thing corresponds to the tacit objection of the ancients he excluded above: for this, he says, is true also with respect to “necessary to be" (22b23). It should be noted here that Aristotle subsumes under the major cited as a proof for the position of the ancients (namely, contradictories of consequences convertibly following each other mutually follow upon each other) this minor. The contradictories of those following upon each other convertibly in the third order (that is, of “not possible to be” and “necessary not to be”) are “possible to be” and “not necessary not to be” (for they are opposed to them by negation of mode). Therefore, these two (namely, “possible to be” and “not necessary not to be”) follow upon each other and are to be placed in the first order.

Hence, with respect to the basis of the above argument, he says, for this, that is, what has been said, is true, namely, is shown to be true, also with respect to “necessary not to be,” namely, of the opposite of “not necessary not to be,” which is “necessary not to be.” Or, for this, namely, “not necessary not to be,” is true, namely, is the true contradictory of “necessary not to be.”

He gives the minor when he says, for “not necessary not to be” is the contradictory of what follows upon “not possible to be”(22b23).

Then he states this explicitly. “Not possible to be,” which is the source of the third order, is followed by this impossible, namely, “impossible to be,” and by this one of the necessary, namely, “necessary not to be,” of which the negation or contradictory is “not necessary not to be.” And since, other things being equal, the mode is negated, and “possible to be” is (it is understood) the contradictory of “not possible to be,” therefore, these two (namely, “possible to be” and “not necessary not to be”) mutually follow upon each other as contradictories of the two mutually following upon each other.

When he says, thus, these contradictions also follow in the way indicated (22b26), he orders all of the consequents of modals according to his own opinion. He says, then, that these contradictions of the necessary follow those of the possible, according to the foresaid and approved mode of those of the impossible. For just as contradictories of the impossible follow upon contradictories of the possible, although inversely, so contradictories of the necessary follow contradictories of the possible inversely. In the latter, however, as has been said, there is a dissimilarity in that the dictum of the contradictories of the possible and impossible is similar, but the dictum of the contradictories of the possible and necessary is contrary. This can be seen in the following table of the consequents of modal enuniciations posited and ordered by Aristotle according to four orders.

FIRST ORDER
It is possible to be
It is contingent to be
It is not impossible to be
It is not necessary to be

SECOND ORDER
It is possible not to be
It is contingent not to be
It is not impossible not to be
It is not necessary not to be

THIRD ORDER
It is not possible to be
It is not contingent to be
It is impossible to be
It is necessary not to be

FOURTH ORDER
It is not possible not to be
It is not contingent not to be
It is impossible not to be
It is necessary to be

Here you see that there is no difference between Aristotle and the ancients except in the first two orders with respect to those of the necessary. The ancients inverted the position of these, placing the necessary that should have been placed in the first order in the second order, and the one that should have been in the second in the first. Notice, too, that he has ordered them in such a way that the contradictories of those following upon each other convertibly, always follow each other, for each one in the first order is the contradictory of each one in the third order, and similarly, each of the fourth order the contradictory of each in the second. This the ancients did not observe.

Lecture 11

Whether “Possible to Be” Follows Upon “Necessary to Be”

22b29. But it may be asked whether “possible to be” follows upon “necessary to be.” Yet if not, the contradictory, “not possible to be,” would have to follow; or if someone should say that this is not the contradictory, then “possible not to be.” But both of these are false in regard to that which is necessary to be.

22b33. On the other hand, it seems possible for the same thing to be cut and not to be cut, and to be and not to be, and thus it would follow that what is necessary to be is possible not to be, which is false.

22b36. It is evident by now that not every possibility of being or walking is one that admits of opposites. There are those of which this is not true. First of all, this is not true of potentialities which are not according to reason, like fire, which has an irrational potentiality (the power to heat). Potentialities that are in conjunction with reason are capable of more than one and of contraries, but not all irrational potentialities are capable of contraries; as has been said, fire does not have the potentiality to heat and not to heat, nor does anything that always acts have this potentiality. However, even some of the irrational potencies are simultaneously capable of opposites. We have spoken of this in order to show that not every potentiality is a potentiality to opposites, not even all those that are called potentialities according to the same notion.

Now that he has explained the consequents of modals, Aristotle raises a question about one of the points that has already been determined, namely, that the possible follows upon the necessary.

He does two things:

first, he raises the question;

second, he establishes another order of the same consequents from the determination of the present question, at: indeed, the necessary and not necessary may well be (23a18; [341]).

About the first he does two things:

first, he raises the question;

second, he settles it, at: it is evident by now that not every possibility (22b36; [329]).

First, then, he raises the question: but it may be questioned whether “possible to be" follows upon “necessary to be” (22b29).

Second, he argues to the affirmative part: yet if not, the contradictory, “not possible to be” (22b29), would have to follow, as was deduced earlier, for either the affirmation or the negation is true of anything. And if someone should say “not possible to be” is not the contradictory of “possible to be,” because he wants to avoid the conclusion by saying that neither of these follows upon “necessary to be,” this may be conceded, although what he says is false. But then he will have to say that the contradictory of “possible to be” is “possible not to be,” for the contradictory of “possible to be” has to be either “not possible to be” or “possible not to be.” But if he says this, he will fall into another error, for it is false to say it is not possible to be of that which is necessary to be, and it is false to say it is possible not to be. Consequently, neither follows upon it, for no enunciation follows upon an enunciation whose truth it destroys. Therefore, “possible to be” follows upon “necessary to be.”

Third, he argues to the negative part where he says, on the other hand, it seems possible for the same thing (22b33). His argument is as follows. If “possible to be” follows upon “necessary to be,” then, since “possible not to be” follows upon the possible (through conversion to the opposite quality, as is said in Prior Analytics 1.13 [32a31], for the same thing is possible to be and not to be), from first to last it will follow that the necessary is possible not to be, which is clearly false. In this argument, Aristotle supplies a hypothesis opposed to the position that possible to be follows upon necessary to be: on the other hand, it seems possible for the same thing to be cut and not to be cut, such as a garment, and to be and not to be, such as a house. Therefore, from first to last, necessary to be will be possible not to be. But this is false. Therefore, the hypothesis that the possible follows upon the necessary is false.

When he says, it is evident by now that not every possibility of being or walking (22b36), he answers the question he proposed.

First, he manifests the truth simply;

second, he applies it to the question, at: so it is not true to say (23a15; [339]).

First, then, he proposes the truth he is going to explain, at: it is evident by now that not every possibility of being or walking, that is, of operating. He means that not everything possible according to first or second act admits of opposites (that is, has access to opposites); there are some possibles of which it is not true to say that they are capable of opposites.

Then, since the possible arises from potency, he manifests how potency is related to opposites, for it will be clear from this how the possible is related to opposites.

About this he does two things.

First, he manifests this in potencies having the same notion;

second, in those that are called potencies equivocally, at: but some are called potentialities equivocally (23a6 [335]).

About the first he does three things.

First, he manifests how an irrational potency is related to opposites. He says that an irrational potency is not a potency that is capable of opposites.

It must be noted in this connection that active potency, since it is the principle by which we act on something else, is divided into rational and irrational potency, as is said in Metaphysics 9.2 (1046a36). Rational potency operates in connection with reason and choice, like the art of medicine, by which the physician, knowing and willing what is expedient in healing an illness, applies a remedy. Irrational potency operates according to its own natural disposition, not according to reason and liberty; for example, the heat of fire is an irrational potency, because it heats not as it knows and wills, but as its nature requires. In the Metaphysics, a twofold difference between these potencies is assigned which is relevant here.

The first is that an irrational active potency is not capable of two opposites, but is determined to one opposite, whether “opposite” is taken contradictorily or contrarily. For instance, heat cannot heat and not heat, which are opposed contradictorily; nor can it heat and cool, which are contraries, but is determined to heating. Understand this to be per se, for heat can cool accidentally either by destroying the matter of heat (namely, the humid) or through alternation of the contrary. It also has the potentiality not to heat accidentally, if that which can be heated is lacking. A rational potency, on the other hand, is capable of opposites, both contradictorily and contrarily; for by the art of medicine the physician can employ a remedy and not employ it, which are contradictories, and employ healing and harmful remedies, which are contraries.

The second difference is that an irrational active potency necessarily operates when a subject is present and impediments are withdrawn, for heat necessarily heats when a subject that can be heated is present and nothing impedes it. A rational potency, however, does not necessarily operate when a subject is present; for instance, when a sick man is present, the physician is not forced to employ a remedy.

The reasons for these differences are given in the Metaphysics, but let us return to the text. Explaining how an irrational potency is related to opposites, he says, first of all, this is not true, that is, it is not true to say that there is a potency to opposites in those which are not according to reason, namely, whose power is through irrational potencies; as fire which is calefactive, or capable of heating, has this power, that is, this irrational potentiality, since it is not able to cool, nor is it in its power to heat and not to heat. Note that he speaks here of a first kind. This is in relation to a second genus of the possible which he will speak of later, in which there is not a potency to opposites either.

Second, he shows how a rational potency is related to opposites, that is, it is capable of opposites: potentialities that are in conjunction with reason, that is, rational potencies, are capable of contraries (22b36), not only of two, but even of many. For example, a physician can employ many pairs of contraries by the art of medicine and he can abstain from doing or not doing many things. He begins with therefore so as to imply that this follows from what has been said. The argument would be that properties of opposites are opposites; an irrational potency, because it is irrational, does not extend itself to opposites; and therefore a rational potency, because it is rational, has access to opposites.

Third, he explains what he has said about irrational potencies; he will later assign the reason for doing this. He makes the point that what he has said about irrational potentiality, namely, that it is not capable of opposites, is not true universally, but particularly. It should be noted here that irrational potency is divided into active potency, which is the principle of acting, and passive potency, which is the principle of being acted upon; for instance, potency to heat is divided into potentiality to heat and potentiality to be heated. Now it is true that active irrational potencies are not capable of opposites, as was explained. This is not true, however, of passive potencies, for what can be heated can also be cooled, because the matter is the same, or the passive potency of contraries, as is said in On the Heavens 2.7 (286a23). It can also not be heated, since the subject of privation and of form is the same, as is said in Physics 1.7 (189b32).

Therefore, in explaining about irrational potencies, he says that not all irrational potentialities should be understood to be excluded from the capacity of opposites. Those like the potentiality of fire to heat are to be excluded (for it is evident that fire cannot not heat), and, universally, whatever others are potencies of such a kind that they always act, that is, the ones that of themselves cannot not act, but are necessitated by their form always to act. All active irrational potencies are of this kind, as we have explained.

There are others, however, of such a condition that, even though they are irrational (or passive) potencies, are simultaneously capable of certain opposites; for example, air can be heated and cooled. Simultaneously modifies are capable and not opposites. What he means is that the thing simultaneously has a passive potency to each opposite, and not that it has a passive potency to have both opposites simultaneously, for it is impossible to have opposites at one and the same time. Hence it is customary and correct to say that in these there is simultaneity of potency, not potency of simultaneity. Therefore, irrational potency is excluded from the capacity of opposites, not completely, but according to its part, namely, according to active potencies.

Because it might seem superfluous to have added the differences between active and passive irrational potencies, since enough had already been said to show that not every potency is of opposites, Aristotle gives the reason for this. It was not only to make it known that not every potency is of opposites, speaking of potency most commonly, but also that not all that are called potencies according to the same species are capable of opposites. For all irrational potencies are included under one species of irrational potency, and yet not all are capable of opposites, but only the passive potencies. It was not superfluous, therefore, to point out the difference between passive and active irrational potencies, since this was necessary in order to show that not all potencies of the same species are capable of opposites. “This” in the phrase “this has been said” could designate each difference, the one between rational and irrational potencies, and the one between active and passive irrational potencies. The meaning is, then, that we have said this to show that not every potentiality which is said according to the same notion of physical power (namely, because it can be in something as rational and irrational)—not even every potentiality which is contained under the same species, as active and passive under the species irrational—is capable of opposites.

Lecture 12

The Explanation of Potencies That Are Called Such Equivocally and the Determination, Through the Notion of the Impossible, of the Possible that Follows Upon the Necessary

23a6. But some are called potentialities equivocally, for “possible” has more than one meaning. On the one hand, it is that which is true of a thing because it is in act, as walking is possible to someone because he is actually walking, and, in general, possible is said of that which is possible to be because it is already actualized. On the other hand, possible is said of that which can be actualized, as walking is possible to someone because he could walk.

23a11. This latter potentiality is only in that which is movable, but the former is also in the immovable. Now, it is true to say, both of that which is walking already and is actual, and of that which could walk, that it is not impossible that it walk or be.

23a15. So it is not true to say the latter possible [that is, the possible which could be] of what is necessary simply, but it is true to say the former of it. Therefore, since the universal follows upon the part, possible to be follows upon that which necessarily is, though not every kind of possible does.

23a18. Indeed, the necessary and not necessary may well be the principle of all that is or is not and the others must be regarded as consequent to these.

23a21. It is evident, then, from what has been said that that which necessarily is, actually is; and, if eternal things are prior, that actuality is prior to potentiality.

23a23. Some things are actualities without potentiality, namely, the primary substances. Others are actualities with potentiality—those that are prior in nature, but posterior in time. And some never are actualities but are only potentialities.

Aristotle now proposes to show in what way potencies that are called equivocal are related to opposites.

About this he does two things.

First, he explains the nature of this kind of potency;

second, he gives the difference and agreement all between these and the foresaid, where he says, this latter potentiality is only (23a11; [337]).

In Metaphysics 5.12 (1019a15) and 12.1 (1046a4), Aristotle divides potency into those that are called potencies for the same reason, and those that have the name potency for another reason than the aforesaid potencies. The latter are named “potencies” equivocally.

Under the first member are included all active and passive, rational and irrational potencies, for whatever are said to be possible through their active or passive potency are potencies for the same reason, namely, because there is in them the originative force of something active or passive.

Mathematical and logical potencies are included under the second member of this division. That by which a line can lead to a square we call a mathematical potency, for a line constitutes a square when protracted back to itself. That by which two terms can be joined in an enunciation without contradiction is a logical potency. Logical potency also comprises that which is called “potency” because it is.

The latter [mathematical and logical potencies] are named from the former equivocally because they predicate no active or passive capacity; and what is said to be possible in these ways is not termed possible in virtue of having the capacity to do or undergo as in the first case. Hence, since the potencies related to opposites are active or passive, the ones that are called potentialities equivocally are not related to opposites. These, then, are the potencies he speaks of when he says, but some are called potentialities equivocally (23a6), and therefore they are not related to opposites.

To clarify the kind of potency that is called equivocal, he gives the usual division of the possible through which this is known. “Possible,” he says, is not said in one way, but in two.

Something is said to be possible because it is true as in act, that is, inasmuch as it actually is (for example, it is possible to walk when one is already walking), and in general (or universally) that is said to be possible which is possible to be because it is already in act.

Something is said to be possible in the second way not because it actually is, but because it is about to act, that is, because it can act; for instance, it is possible for someone to walk because he is about to walk.

Notice here that by this two-membered division of the possible he makes the division of potency posited above evident a posteriori, for the possible is named from potency. Under the first member of the possible he signifies potencies equivocally; under the second, potencies univocally, that is, active and passive potencies. He means to show, then, that since “possible” is said in two ways, potentiality is also twofold. He explains equivocal potentialities in terms of only one member, namely, those that are called possible because they are, since this was sufficient for his purpose.

When he says, this latter potentiality is only in that which is movable,(23a11), he specifies the difference between each potency. This last potency, (The possible because it can be.) he says, which is called physical potency, is only in things that are movable; but the former is in movable and immovable things. The possible that is named from the potency which can act, but is not yet acting, cannot be found without the mutability of that which is said to be possible in this way. For if that which can act now and is not acting should act, it is necessary that it be changed from rest to operation. On the other hand, that which is called possible because it is requires no mutability in that which is said to be possible in this way, for to be in act, which is the basis of such a possibility, is found in necessary things, in immutable things, and in mobile things. Therefore, the possible which is called logical is more common than the one we customarily call physical.

Then he shows that there is a correspondence between these possibles when he adds that not impossible to be is true of both of these potentialities and possibles. For instance, to walk is not impossible for that which is already walking in act (that is, acting), and it is not impossible for that which could now walk; that is, they agree in that not impossible is verified of both—of either what is said to be possible from the fact that it is in act or of what is said to be possible from the fact that it could be. Consequently, the necessary is verified as possible, for possible follows upon not impossible. The possible that is already in act is the second genus of the possible in which access is not found to both opposites, of which Aristotle spoke when he said, first of all this is not true of the potentialities (22b36). For that which is said to be possible because it is already in act is already determined, since it is supposed as being in act. Therefore, not every possible is the possible of alternatives, whether we speak of the physical possible or the logical.

When he says, so it is not true to say the latter possible (23a6), he applies the truth he has determined to what has been proposed.

First, by way of a conclusion from what has been said, he shows the relationship of each possible to the necessary. So, he says, it is not true to say and predicate this possible (namely physical) which is only in mobile things of the necessary simply, because what is necessary simply cannot be otherwise. The physical possible, however, can be thus and otherwise, as has been said. He adds simply because the necessary is manifold. There is the necessary for well-being and there is also the necessary from supposition, but it is not our business to treat these, only to indicate them. In order, then, to avoid the modes of the necessary that do not have the notion of the necessary perfectly and in every way, he adds simply. Now the physical possible is not verified of this kind of necessary, (That is, of the necessary simply.) but it is true to enunciate the logical possible, the one found in immovable things, of the necessary, since it takes away nothing of the necessity. The argument introduced for the negative part of this question is destroyed by this. The error in that argument was the inference—by way of conversion into the opposite quality—of the possible to both alternatives from the necessary.

Then he replies to the question formally. He states that the affirmative part of the question must be held, namely, that the possible follows upon the necessary, and he assigns the cause. The whole universal follows constructively upon its subjective part; but the necessary is a subjective part of the possible, because the possible is divided into logical and physical and under the logical is comprehended the necessary; therefore, the possible follows upon the necessary. Hence he says, therefore, since the universal follows upon the part (23a15), that is, since the whole universal follows upon its subjective part, to be possible to be, that is, possible, as the whole universal, follows upon that which necessarily is, that is, necessary, as a subjective part.

He adds: though not every kind of possible does (23a15), that is, not every species of the possible follows; just as animal follows upon man, but not in every way, namely, it does not follow upon man according to all its subjective parts, for it is not valid to say, “He is a man, therefore he is an irrational animal.” By this proof of the validity of the affirmative part, Aristotle has explicitly destroyed the reasoning adduced for the negative part, which, as is evident, erred according to the fallacy of the consequent in inferring the possible from the necessary by descending to one species of the possible.

When he says, indeed, the necessary and not necessary (23a18), he disposes the same consequences of modals in another arrangement, placing the necessary before all the other modes.

About this he does two things.

First, he proposes the order of modals;

second, he assigns the cause of the order, at: it is evident, then, from what has been said (23a21; [342]).

Indeed, he says, the necessary and not necessary may well be the principle of the “to be” or “not to be” of all modal enunciations (23a18), that is, the necessary and not necessary is the principle of affirmatives or negatives. And the others—the possible, contingent, and impossible to be—must be considered as consequent to these, namely, to the necessary and not necessary, as seen in the table of the consequents of modal enuniciations according to the four orders, posited and disposed by Aristotle in another appropriate arrangement.

FIRST ORDER
It is necessary to be
It is not possible not to be
It is not contingent not to be
It is impossible not to be

SECOND ORDER
It is necessary not to be
It is not possible to be
It is not contingent to be
It is impossible to be

THIRD ORDER
It is not necessary to be
It is possible not to be
It is contingent not to be
It is not impossible not to be

FOURTH ORDER
It is not necessary not to be
It is possible to be
It is contingent to be
It is not impossible to be

Nothing is changed here except the enunciations predicating necessity. They have been allotted the first place, whereas in the former table they were placed last. When he says may well be, it is not because he is in any doubt, but because he is proposing this here without a determinate proof.

When he says, it is evident, then, from what has been said (23a21), he gives the cause of this order.

First, he gives the reason for placing the necessary before the possible: the sempiternal is prior to the temporal; but “necessary” signifies sempiternal (because it signifies “to be in act,” excluding all mutability and consequently temporality, which is not imaginable without movement) and the possible signifies temporality (since it does not exclude the possibility of being and not being); therefore, the necessary is rightly placed before the possible.

He proposes the minor of this argument when he says that it is evident, then, from what has been said (in treating the necessary) that which is necessarily is totally in act, since it excludes all mutability and potency to the opposite—for if it could be changed into the opposite in any way, then it would not be necessary.

Next, he gives the major, which is in the mode of an antecedent conditional: and if eternal things are prior to temporal (23a21).

Finally, he posits the conclusion: those that are wholly in act in every way (namely, the necessary) are prior to the potential (namely, to possibles), which do not have being in act wholly, although they are compatible with it.

Then, when he says, some things are actualities without potentiality (23a23), he assigns the cause of the whole order established among modals. The grades of the universe are threefold.

Some things are in act without potentiality, that is, not combined with potency. These are the primary substances—not those we have called “first” in the present work because they principally and especially sustain, but those that are first because they are the causes of all things, namely, the Intelligences.

In others, act is accompanied with possibility, as is the case with all mobile things, which, according to what they have of act, are prior in nature to themselves according to what they have of potency, although the contrary is the case in regard to the order of time. According to what they have of potency, they are prior in time to themselves according to what they have of act. For example, according to time, Socrates first was able to be a philosopher, then he actually was a philosopher. In Socrates, therefore, potency precedes act according to the order of time. The converse is the case, however, in the order of nature, perfection, and dignity, for when he actually was a philosopher, Socrates was regarded as prior according to dignity, that is, more worthy and more perfect than when he was potentially a philosopher. Hence, when we consider each order, that is, nature and time, in one and the same thing, the order of potency and act is reversed.

Others never are in act but are only in potency, such as motion, time, the infinite division of magnitude, and the infinite augmentation of number. These, as is said in Metaphysics 9.6 (1048b9–17), never terminate in act, for it is repugnant to their nature. None of them is ever such that something of it is not expected, and consequently they can only be in potency. These, however, must be treated in another place.

This has been said so that, once the order of the universe has been seen, it would be clear that we were imitating it in our present ordering.

The necessary, which signifies “to be in act” without potentiality or mutability, has been placed first, in imitation of the first grade of the universe.

We have put the possible and contingent, both of which signify act with possibility, in the second place in conformity with the second grade of the universe. The possible has been placed before the contingent because the possible relates to act, while the contingent, as the force of the name suggests, relates to the defect of a cause, which pertains to potency, for defect follows upon potency. The order of these is similar to the order in the second part of the universe, where act is prior to potency according to nature, though not according to time.

We have reserved the last place for the impossible because it signifies what never will be, just as the last part of the universe is said to be that which is never in act.

Thus, a beautifully proportioned order is established when the divine is observed.

Since the consequents of modals (namely, those placed under each other) are their equivalents in meaning, and these are produced by the varying position of the negation changing the quality or quantity or both, a few things must be said about their quality and quantity to complete our knowledge of them. The nature of the whole arises from the parts, and therefore we should note the following things about the parts of the modal enunciation. The subject of the modal enunciation asserts to be or not to be, and is a singular dictum, and contains in itself the subject of the dictum. The predicate of a modal enunciation, namely, the mode, is the total predicate (since it explicitly or implicitly contains the verb, which is always a sign of something predicated of another, for which reason Aristotle says that the mode is a determining addition), and contains in itself distributive force according to the parts of time. The necessary and impossible distribute in all time either simply or in a limited way; the possible and contingent distribute according to some time commonly.

As a consequence of these five conditions there is a twofold quality and a threefold quantity in any modal.

The twofold quality results from the fact that both the subject and the predicate of a modal have a verb in them. One of these is called the quality of the dictum, the other the quality of the mode. This is why it was said above that there is an enunciation which is affirmative of mode and not of dictum, and conversely.

Of the threefold quantity of a modal enunciation, one arises from the fact that the subject of the modal contains in it the subject of the dictum. This is called the quantity of the subject of the dictum, and is distinguished into universal, particular, and singular, as in the case of the quantity of an absolute enunciation. For we can say that it is possible that “Socrates,” “some man,” “every man,” or “no man” run.

The second quantity is that of the dictum, which arises from the fact that the subject of one modal is one dictum. This is a unique singularity, for every dictum of a modal is the singular of that universal, namely, the dictum. “That man be white is possible” means that this dictum, “that man be white,” is possible. “This dictum” is singular in quantity, just as “this man” is. Hence, every modal is singular with respect to dictum, although with respect to the subject of the dictum it is universal or particular.

The third quantity is that of the mode, or modal quantity, which arises from the fact that the predicate of the modal, which is the mode, has distributive force. This is distinguished into universal and particular.

Now, there are two things about modal enunciations that must be carefully noted.

The first—which is peculiar to modals—is that the predicate quantifies the modal proposition simply, as it also qualifies it simply. For just as the modal enunciation in which the mode is affirmed is affirmative simply, and negative when the mode is negated, so the modal enunciation in which the mode is universal is universal simply and particular in which the mode is particular. The reason for this is that the modal follows the nature of the mode.

The second thing to be noted (which is the cause of the first) is that the predicate of a modal, which is the mode, not only has the relationship of a predicate to its subject (that is, to “to be” and “not to be”), but also has the relationship to the subject of a distributive syncategorematic term, which has the effect of distributing the subject not according to the quantity of its subjective parts, but according to the quantity of the parts of its time. And rightly so, for just as the proper quantity of the subject of an absolute enunciation varies according to the division or lack of division of its subject (since the subject is a name which signifies in the mode of substance, whose quantity is from the division of the continuous, and therefore the quantifying sign distributes according to the subjective parts), so, because the proper quantity of the subject of a modal enunciation is time (since the subject is a verb, which signifies in the mode of movement, whose proper quantity is time), the quantifying mode distributes the subject, namely, “to be” or “not to be,” according to the parts of time. Hence, we arrive at the subtle point that the quantity of the modal is the quantity of the proper subject of the modal enunciation, namely, of “to be” or “not to be.”

Therefore, a modal enunciation is universal simply when the proper subject is distributed throughout all time, either simply, as in “that man is an animal is necessary or impossible,” or taken in a limited way, as in “that man is running today or until he is running is necessary or impossible.” A modal enunciation is particular in which “to be” or “not to be” is distributed not throughout all time, but commonly throughout some time, as in “that man is an animal is possible or contingent.” This modal quantity is therefore also a property of its subject (in that quantity universally comes from the matter) but is derived from the mode not insofar as it is a predicate (because, as such, it is understood formally), but insofar as it performs a syncategorematic function, which it has in virtue of the fact that it is properly a mode.

Therefore, with respect to their proper quantity, some modals are universal affirmatives, namely, those of the necessary, because they distribute “to be” to all time. Others are universal negatives, namely, those of the impossible because they distribute “to be” to no time. Still others are particular affirmatives, namely, those signifying the possible and contingent, for both of these distribute “to be” to some time. Finally, there are particular negatives, namely, those of the not necessary and not impossible, for they distribute “not to be” to some time. This is similar to the diversity in absolute enunciations from the use of “every,” “no,” “some,” “not all,” and “not none.” Now, since this quantity belongs to modals insofar as they are modals, as has been said, and since Aristotle is now considering them in this particular respect, the modal enunciations that are equivalent, namely, their consequents, are ordered by the different location of the negation, as is the case with absolute enunciations that are equivalent. A negative placed before the mode makes an enunciation equivalent to its contradictory; placed after the mode, namely, with the verb of the dictum, makes it equivalent to its contrary; placed before and after the mode makes it equivalent to its subaltern, as you can see in the last table of consequents given by Aristotle. In that table of oppositions, you see all the mutual consequents, according to one of the three rules for making enunciations equivalent. Consequently, the whole first order of equivalent enunciations is contrary to the second, contradictory to the third, and the fourth is subalternated to it. [insert figure]

Lecture 13

Contrariety of Opinions in the Mind Is Constituted by an Opposition of the True and the False

23a27. There is a question as to whether the contrary of an affirmation is a negation, or whether the contrary of an affirmation is another affirmation; and in the case of speech whether the one saying that no man is just is contrary to the one saying that every man is just, or is the one saying that every man is unjust contrary to the one saying that every man is just. For example, which of these are contraries: “Callias is just,” “Callias is not just,” “Callias is unjust”?

23a32. For if those things that are in vocal sound are determined by those in the intellect, and if in the intellect that opinion is contrary which is about a contrary—for instance, the contrary of “every man is just” is “every man is unjust”—the case must be the same with respect to spoken affirmations. But if in the intellect the contrary opinion is not one which is about a contrary, then in speech the affirmation will not be contrary to the affirmation, but the negation will be. We must therefore consider which false opinion is contrary to a true opinion, whether it is a negation of the true opinion or the opinion affirming a contrary.

What I mean is this: there is a true opinion of that which is good, that it is good, and a false opinion, that it is not good, and another kind, that it is evil. Of the latter two, which one is contrary to the true opinion? And if they are one and the same, which one is the contrary?

23b2. It is false, of course, to suppose that opinions are to be defined as contrary because they are about contraries; for the opinion of that which is good, that it is good, and of that which is evil, that it is evil, are probably the same, and, whether they are many or one are true. Yet good and evil are contraries. However, opinions are not contraries because they are about contraries; rather, they are contrary because they are related contrarily.

23b7. Now, if there is the opinion of that which is good, that it is good, and the opinion that it is not good, and there are other opinions that something that does not belong and could not possibly belong to the good belongs to the good, none of the latter should be posited as the contrary, neither those purporting that what does not belong to the good belongs to it nor those purporting that what belongs to the good does not belong to it, for the opinions that that belongs which does not belong and the opinions that that does not belong which does are infinite.

Now that he has treated the enunciation as it is diversified by an addition made to the terms and by an addition made to its composition (which is the division of the text made by St. Thomas at the beginning of the second book), Aristotle takes up another question about oppositions of enunciations. This question concerns the oppositions that result from something added to the simple enunciation.

About this he does four things.

First, he asks the question;

second, he shows that this question depends upon another, which must be treated first, at: for if those things that are in vocal sound are determined by those in the intellect (23a32; [353];

third, he settles the latter question, at: it is false, course, to suppose that opinions are to be defined (23b2; [356]);

fourth, he replies to the first question, at: if, therefore, this is the case with respect to opinion (24b1; [374]).

The first question he raises is this: is the contrary of an affirmative enunciation the negation of the same predicate or the affirmation of a contrary or privative predicate? Hence he says, there is a question as to whether the contrary of an affirmation is the contradictory negation (23a27), and universally, whether affirmative speech is contrary to negative speech. For instance, is affirmative speech which says every man is just contrary to negative speech which says no man is just, or to the affirmative of the privative predicate, every man is unjust? And similarly, is the affirmation Callias is just contrary to the contradictory negation, Callias is not just, or is it contrary to Callias is unjust, the affirmative of the privative predicate?

Since this question has not been discussed by others, we must begin by noting that there are two things in an enunciation, namely, the enunciation itself (or the signification), and the mode of enunciating or signifying. Hence, a twofold opposition can be made between enunciations, one by reason of the enunciation itself, the other by reason of the mode of enunciating.

If we consider the modes of enunciating, we find two species of opposition among enunciations, namely, contrariety and contradiction. This point was made earlier when opposed enunciations were divided into contraries and contradictories.

There is contradiction by reason of mode of enunciating when the same thing is predicated of the same subject in a contradictory mode; so that just as one of a pair of contradictories posits nothing but only destroys the other, so one enunciation asserts nothing, but only destroys what the other was enunciating. All enunciations that are called contradictories are of this kind; for instance, "every man is just, not every man is just"; "Socrates is just, Socrates is not just." It follows from this that they cannot be at once true or false, just as two contradictories cannot be at once.

There is contrariety between enunciations by reason of mode of enunciating when the same thing is predicated of the same subject in a contrary mode of enunciating; so that just as one of a pair of contraries posits matter common to itself and to the other which is at the extreme distance under that genus—as is evident, for instance, in white and black—so one enunciation posits a subject common to itself and its opposite at the extreme distance under that predicate. All the enunciations in the diagram that are called contrary are of this kind, such as "every man is just, no man is just." These make the subject “man” distant to the greatest degree possible under justice, one enunciating justice to be in man not in just any way, but universally, the other enunciating justice to be absent from man, not in just any way, but universally. For no distance can be greater than the distance between the total number of things having something and none of the total number of things having that thing. It follows that contrary enunciations cannot be at once true, just as contraries cannot be in the same thing at once. They can, however, be false at the same time, just as it is possible that contraries not be in the same thing at the same time.

If we consider the enunciation itself (namely, its signification) according to only one species of opposition, we will find in the whole range of enunciations an opposition of contrariety, namely, an opposition according to truth and falsity. The reason for this is that the significations of two enunciations are positive, and accordingly cannot be opposed either contradictorily or privatively because the other extreme of both of these oppositions is formally non-being. And since significations are not opposed relatively, as is evident, the only way they can be opposed is contrarily.

The contrariety spoken of here consists in this: of two enunciations, one is not compatible with the other either in truth or falsity—presupposing always the conditions for contraries, that they are about the same thing and at once. It can be shown that such opposition is contrariety from the nature of the conceptions of the soul when composing and dividing, each of which is an enunciation. Adequate conceptions of the soul are opposed to inadequate conceptions only contrarily, and inadequate conceptions, if each cancels the other, are also called contraries. It is from this that St. Thomas proves, in ST I, Q. 17, that the true and false are contrarily opposed. Therefore, as in the conceptions of the soul, so in enunciations, adequate significations are contrarily opposed to inadequate (that is, true to false); and the inadequate (or the false) are also contrarily opposed among themselves if it happens that they are not compatible, supposing always the conditions for contraries. There is, therefore, in enunciations a twofold contrariety, one by reason of mode, the other by reason of signification, and only one contradiction, that by reason of mode. To avoid confusion, let us call the first contrariety modal and the second formal. We may call contradiction modal, not to avoid confusion (since it is unique), but for propriety of expression. Formal contrariety is found between all contradictory enunciations, since one contradictory always excludes the other. It is also found between all modally contrary enunciations in regard to truth, since they cannot be at once true. However, it is not found between the latter in regard to falsity, since they can be at once false.

Aristotle in this question is speaking of the contrariety of enunciations that extends to contraries modally and to contradictories. This is evident from what he says in the beginning and at the end of the question. In the beginning, he proposes both contradictories when he says, whether the contrary of an affirmation is a negation (23a27); and contraries modally, when he says, or whether the contrary of an affirmation is another affirmation. It is evident, too, from the examples immediately added. At the end, he explicitly divides what he has concluded to be contrary to a true universal affirmative, into the modally contrary universal negative and the contradictory. It is clear at once that this division would be false unless it comprised the contrary formally. Since he takes contrariety in this way, the question must be understood with respect to formal contrariety of enunciations. This is a very subtle question which must be treated but has not been thus far.

The question, therefore, is this: whether the formal contrary of the true affirmative is the false negative of the same predicate or the false affirmative of the privative predicate (that is, of the contrary)? The meaning of the question is now clear, and it is evident why he does not ask about any other oppositions of enunciations—no other opposition is found in them formally. It is also evident that he is taking contrariety properly and strictly, notwithstanding the fact that such contrariety is found among contradictories modally and contraries modally. St. Thomas has already pointed out that this question arises from the fact that something is added to the simple enunciation, for as far as simple enunciations are concerned (that is, those with only a second determinant), there is no occasion for the question. When, however, something is added, namely a predicate, to the simple enunciation, that is, to the subject and the substantive verb, the question arises as to whether what ought to be added in contrary enunciations is the selfsame predicate with a negation added to the verb or a contrary (that is, privative) predicate without a negation added to the verb.

When Aristotle says, for if those things that are in vocal sound (23a32), he shows where we have to begin in order to settle this question.

And he does two things.

First, he shows that the question depends on another question, namely, whether a true opinion (that is, a conception of the soul in the second operation of the intellect) is contrary to a false negative opinion of the same predicate, or to a false affirmative of the contrary (or privative) predicate.

Then he gives the reason why the former question depends on this. Vocal enunciations follow upon mental as adequate effects upon proper causes and as the signified upon adequate signs. So, in this the nature of each is similar.

He begins, then, with the reason for this dependence (23a32): for if those things that are in vocal sound are determined by those in the intellect (as was said in the beginning of the first book) and if those opinions are contrary in the soul which affirm contrary predicates about the same subject, (for example, the mental enunciations, every man is just, every man is unjust), then in affirmations that are in vocal sound, the case must be the same. The contraries will be two affirmatives about the same subject with contrary predicates. But if in the soul this is not the case—namely, that opinions with contrary predicates constitute contrariety in mental enunciations—then the contrary of a vocal affirmation will not be a vocal affirmation with a contrary predicate. Rather, the contrary of an affirmation will be the negation of the same predicate.

The first question, then, depends on this question as an effect upon its cause. For this reason, and by way of a conclusion to what he has just been saying, he adds the second question, which must be treated first so that once the cause is known the effect will be known: we must therefore consider to which false opinion the true opinion is contrary, whether it is to the false negation or to the false affirmation that it is to be judged contrary (23a32). And in order to propose the question by examples, he says, what I mean is this: there are three opinions of a good, such as of life. One is a true opinion, that it is good (for instance, that life is good). The other is a false negative, that it is not good (for instance, that life is not good). Still another, likewise false, is the affirmative of the contrary, that it is evil (for instance, that life is evil). The question is, then, which of these false opinions is contrary to the true one.

Then he adds, the question, and if there is one, is either one the contrary (23a32). This passage can be read in three ways.

It can be read inquiringly so that it is a part of the question, and then the meaning is: which of these false opinions is contrary to the true opinion, and is there one of these by which the contrary to the true one is effected? For since one is contrary to one other, as is said in Metaphysics 10.1 (1055a19), in asking which of these is the contrary we are also asking whether one of them is the contrary.

This can also be read adversatively, and then the meaning is: which of these is the contrary, given that we know it is not both but one by which the contrariety is effected?

This can be read in a third way by dividing the first clause, and if it is one, from the second clause, is either one the contrary. The first part is then read assertively, the second inquiringly, and the meaning is: which of these two false opinions is contrary to the true opinion if the two false opinions differ as to consequence, and also if both are one (that is, united to each other indivisibly)?

Boethius explains this passage in the last way. He says that Aristotle adds these words because of immediate contraries, in which the contrary does not differ from the privative, for the difference between mediate and immediate contraries is that in the former the contrary is not inferred from the privative. For example, this is not valid: “A colored body is not white, therefore it is black”—for it could be red. In immediate contraries, on the other hand, it is valid to infer the contrary from the privative; for instance, “An animal is not healthy, therefore it is ill; number is not even, therefore it is odd.” Therefore, Aristotle intends to show here that when we ask which of these false opinions (namely, negative and affirmative contraries) is contrary to the true affirmative, we are asking universally whether these two false opinions follow each other indivisibly or not.

When he says, it is false, of course, to suppose (23b2), he proceeds with the second question.

About this he does four things.

First, he shows that contrariety of opinions is not determined by the contrariety of the matter involved, but rather by the opposition of true and false;

second, he shows that there is not contrariety of opinions in just any opposites according to truth and falsity, at: now if there is the opinion of that which is good, that it is good (23b7; [357]);

third, he determines that contrariety of opinions is concerned with the per se first opposites according to truth and falsity for three reasons, at: rather, those opinions in which there is fallacy (23b13; [358]);

fourth, he shows that this determination is true of all, at: it is evident that it will make no difference (24a3; [373]).

Aristotle says, then, proposing the conclusion he intends to prove, that it is false to suppose that opinions are to be defined or determined as contrary because they are about contrary objects.

He gives two arguments for this.

Contrary opinions are not the same opinion; but opinions about contraries are probably the same opinion; therefore, opinions are not contrary from the fact that they are about contraries.

Also, contrary opinions are not simultaneously true; but opinions about contraries, whether many or one, are sometimes true simultaneously; therefore, opinions are not contraries because they are about contraries.

Having supposed the majors of these arguments, he posits a manifestation of each minor at the same time.

In relation to the first argument, he says, for the opinion of that which is good, that it is good, and of that which is evil, that it is evil are probably the same (23b2).

In relation to the second argument he adds: and, whether many or one, are true (23b2).

He uses probably, an adverb expressing doubt and disjunction, because this is not the place to determine whether the opinion of contraries is the same opinion, and because in some way the opinion is the same and in some way not. In the case of habitual opinion, the opinion of contraries is the same, but in the case of an actual opinion it is not. One mental composition is actually made in conceiving that a good is good and another in conceiving that an evil is evil, although we know both by the same habit, the former per se and first, the latter secondarily, as is said in Metaphysics 9.4 (1051a4).

Then he adds that good and evil—which are used for the manifestation of the minor—are contraries even when the contrariety is taken strictly in moral matters, and so in using this our exposition is apposite.

Finally, he draws the conclusion. Opinions are not contraries because they are about contraries, but rather because they are contraries (23b2), that is, opinions are to be considered as contrary from the fact that they enunciate contrarily and adverbially (namely, in a contrary mode)—that is, they enunciate truly and falsely. Thus the first argument is clear.

When he says, now, if there is the opinion of that which is good, that it is good (23b7), he takes up the second point. Since he has just said that contrariety of opinions is taken according to their opposition of truth and falsity, he goes on to show that not just any opposites according to truth and falsity are contraries. This is his argument. Four opinions can be held about a good such as justice: that justice is good, that it is not good, that it is avoidable, that it is not desirable. Of these, the first is true, the rest false. The three false ones are diverse. The first denies the same predicate the true one affirmed; the second affirms something which does not belong to the good; the third denies what belongs to the good, but something other than the true one affirmed. Now if all opinions opposed as to truth and falsity are contraries, then not only are there many contraries to one true opinion, but an infinite number. But this is impossible, for one is contrary to one other. The consequence holds because infinite false opinions about one thing, similar to those cited, can be imagined; such opinions would affirm of it what does not belong to it and deny what is joined to it in some way. Both kinds are indeterminate and without number. We can think, for instance, that justice is a quantity, that it is a relation, that it is this and that; and likewise we can think that it is not a quality, is not desirable, is not a habit.

Hence, from what was said above in proposing the question, Aristotle infers a plurality of false opinions opposed to one true opinion: now if there is the opinion of that which is good, such as justice, that it is good; and there is a false opinion denying the same thing, namely, that it is not good; and besides these a third opinion, false also, affirming that some other thing belongs to justice that does not belong and cannot belong to it (for instance, that justice is avoidable or that it is illicit); and a fourth opinion, also false, that denies something other than the true opinion affirms, something, however, which does belong to justice (for instance, that it is not a quality, that it is not a virtue), then none of these other false enunciations are to be posited as the contrary of the true opinion. To explain what he is designating by of these others, he adds, neither those purporting that what is not, is, as opinions of the third order do, nor those purporting that what is, is not, as opinions of the fourth order signify. Then he adds the reason these cannot be posited as the contrary of the true opinion: for both the opinions that that is which is not, and that which is not, is, are infinite, as was shown above. Therefore, not just any opinions opposed according to truth and falsity are contraries. Thus the second argument is clear.

Lecture 14

The Opposition of True and False that Constitutes Contrariety of Opinions Is Opposition According to Affirmation and Negation of the Same Predicate of the Same Subject

23b13. Rather, those opinions in which there is fallacy must be posited as contrary to true opinions. Now, the things from which fallacies arise are the things from which generations arise. But generations are from opposites; therefore, so are fallacies.

23b15. Now, if that which is good is both good and not evil, the former per se, the latter accidentally (for it is accidental to that which is good not to be evil), and the true opinion which is a per se opinion of a thing is more true, then the false opinion which is a per se opinion is also more false. But the opinion that that which is good is not good is a false opinion about what belongs in itself to a good, and the opinion that it is evil is a false opinion concerning what belongs to it accidentally. Therefore, the opinion of the negation of the good will be more false than the opinion affirming a contrary. Now, the one who holds the contrary opinion about each thing is most mistaken; for contraries are those that differ most with respect to the same thing. If, then, of two opinions one is the contrary, but the opinion of the negation is more contrary, it is evident that it must be the contrary. The opinion that that which is good is evil, however, is implicative; for probably along with this opinion one must understand that the good is not good.

23b27. Further, if this necessarily holds in a similar way in all other cases, it would seem that what we have said is correct; for the opposition of contradiction either holds everywhere or nowhere. Now, in the case where there is no contrary, that opinion is false which is the opposite of the true opinion; for instance, he who thinks man is not man thinks falsely. If, then, these are contraries, the others in which there is contradiction are also contraries.

23b33. Again, the opinions of that which is good, that it is good, and of that which is not good, that it is not good, are parallel; so also are the opinions of that which is good, that it is not good, and of that which is not good, that it is good. What, then, would be the contrary of a true opinion that that which is not good is not good? It is not the opinion saying that it is evil. This might be at the same time true, and a true opinion is never contrary to a true opinion; for some things that are not good are evil, and therefore it is possible for both opinions to be true. Nor is the opinion that it is not evil the contrary, for this too might be true, since something could be at one and the same time not good and not evil. It remains, therefore, that the contrary of an opinion that that which is not good is not good, is the false opinion that that which is not good is good; for the former is true. Therefore, also the opinion that that which is good is not good is contrary to the opinion that that which is good is good.

24a3. It is evident that it will make no difference if we posit the affirmation universally, for the universal negation will be the contrary. For instance, the contrary of the opinion that everything that is good is good, is that nothing that is good is good. For the opinion that that which is good is good, if the good is taken universally, is the same as the opinion that whatever is good is good; and this is no different from the opinion that everything that is good is good. And the same is the case with respect to the not good.

24b1. If, therefore, this is the case with respect to opinion, and affirmations and negations in vocal sound are signs of those in the soul, it is evident that the contrary of the affirmation is the negation of the same subject universally. For example, the contrary of the enunciation “everything good is good” is “nothing good is good,” or of “every man is good” is “no man is good.” The contradictories, on the other hand, are “not everything good is good,” and “not every man is good.”

24b6. It is evident, too, that true cannot be contrary to true, either in opinion or in contradiction. For contraries are about opposites, and while it is possible for the same thing to be said truly about contraries, it is not possible for contraries to belong at once to the same subject.

Aristotle has just completed a subtle investigation in which he has shown that contrariety of matter does not constitute contrariety of opinion, nor does just any kind of opposition of true and false, but some opposition of true and false does. Now he intends to determine what kind of opposition of true and false it is that constitutes contrariety of opinions, for this will answer the question directly. He maintains that only opposition of opinions according to affirmation and negation of the same thing of the same thing (and so on) constitutes their contrariety. Accordingly, as the response to the question, he intends to prove the following conclusion: opinions opposed according to affirmation and negation of the same thing of the same thing are contraries; and consequently, opinions opposed according to affirmation of contrary predicates of the same subject are not contraries, for if these were contraries, the true affirmative would have two contraries, which is impossible, since one is contrary to one other.

Aristotle uses three arguments to prove this conclusion.

The first one is as follows. Those opinions in which there is fallacy first are contraries. Opinions opposed according to affirmation and negation of the same predicate of the same subject are those in which there is fallacy first. Therefore, these are contraries.

The sense of the major is this: opinions which first in the order of nature are the limits of fallacy (that is, of deception or error) are contraries; for when someone is deceived or errs, there are two limits, the one from which he turns away and the one toward which he turns. In the text the major of the argument is posited first: rather, those opinions in which there is fallacy must be posited as contrary to true opinions (23b13). By uniting this part of the text adversatively with what was said previously, Aristotle implies that not just any of the number of opinions enumerated are contraries, but those in which there is fallacy first in the manner we have explained.

Then he gives this proof of the minor: those things from which generations are and from which fallacies are, are the same proportionally; generations are from opposites according to affirmation and negation; therefore, fallacies, too, are from opposites according to affirmation and negation (which was assumed in the minor). Hence he posits the major of this prosyllogism: now the things from which fallacies arise, namely, limits, are the things from which generations arise (23b13)—although proportionally. Under it he posits the minor: but generations are from opposites, that is, according to affirmation and negation. Finally, he concludes, therefore, also fallacies, that is, they are from opposites according to affirmation and negation of the same thing of the same thing.

This proof will be more evident from the following. Knowledge and fallacy, or error, bring about the same thing in the intellect’s progression as generation and corruption do in nature’s progression. For just as natural perfections are acquired by generations and perish by corruptions, so intellectual perfections are acquired by knowledge and lost by errors or deceptions. Accordingly, just as generation and corruption are between affirmation and negation as proper terms, as is said in Physics 5.1 (224b35), so both to know something and to be deceived about it is between affirmation and negation as proper terms. Consequently, what one who knows attains first in the second operation of the intellect is affirmation of the truth, and what he rejects per se and first is the negation of it. In like manner, what he who is deceived loses per se and first is affirmation of the truth, and acquires first is negation of the truth. Therefore, Aristotle is correct in maintaining that the terms between which there is generation first and between which there is fallacy first are the same, because with respect to both, the terms are affirmation and negation.

When he says, now, if that which is good is both good and not evil (23b15), he intends to prove the major of the principal argument. He has already shown that the opinions in which there is fallacy first are affirmation and negation, and therefore in place of the major to be proved (that is, opinions in which it there is fallacy first are contraries) he uses his conclusion—which has already been shown to be equivalent—that opinions opposed according to affirmation and negation of the same thing are contraries. Thus with his customary brevity he at once proves the major, responds directly to the question, and applies it to what he has proposed. In place of the major, then, he proves the conclusion principally intended, namely, that opinions opposed according to affirmation and negation of the same thing are contraries, and not those opposed according to affirmation of contraries about the same thing.

His argument is as follows. A true opinion and the opinion that is more false in respect to it are contrary opinions, but opinions opposed according to affirmation and negation are the true opinion and the opinion that is more false in respect to it; therefore, opinions opposed according to affirmation and negation are contraries.

The major is proved thus. Those things that are most distant in respect to the same thing are contraries; but the true and the more false are most distant in respect to the same thing, as is clear.

The proof of the minor is that the opposite according to negation of the same thing of the same thing is per se false in relation to the true affirmation of it. But a per se false opinion is more false than any other, since each thing that is per se such is more such than anything that is such by reason of something else.

Accordingly, returning to the opinions already given in proposing the question so as to show his intention more clearly by example, he begins with the proof of the minor. There are four opinions, of which two are true, “a good is good” and “a good is not evil”; and two are false, “a good is not good” and “a good is evil.” It is evident that the first is true by reason of itself and the second accidentally, that is, by reason of another, for not to be evil is added to that which is good. Hence, “a good is not evil” is true because a good is good, and not contrarily. Therefore, the first of these opinions, which is per se true, is more true than the second, for in each genus that which per se is true is more true. The two false opinions are to be judged in the same way. The more false is the one that is per se false. The first of them, the negative, “a good is not good,” in relation to the affirmative, “a good is good,” is per se false, not false by reason of another. The second, the affirmative of the contrary, “a good is evil,” in relation to the same opinion, is false accidentally, that is, by reason of another (for “a good is evil” is not immediately falsified by the true opinion, “a good is good,” but mediately through the other false opinion “a good is not good”). Therefore, the negation of the same thing is more false in respect to a true affirmation than the affirmation of a contrary. This was assumed in the minor.

As was pointed out above, Aristotle returns to the opinions already posited, and infers the first two true opinions: now, if that which is good is both good and not evil (23b15), and if what the first opinion says is true per se, that is, by reason of itself; and what the second opinion says is true accidentally (since it is accidental or added to the good not to be evil); and if in each order that which is per se true is more true, then that which is per se false is more false, since, as has been shown, the true also is of this nature—namely, that the more true is that which per se is true. Therefore, of the two false opinions proposed in the question, namely, “a good is not good,” and “a good is evil,” the one saying that what is good is not good, namely, the negative, is an opinion positing what is per se false—that is, by reason of itself it contains falsity in it. The other false opinion, the one saying it is evil—namely, the affirmative contrary in respect to the affirmation saying that a good is good—is false accidentally, that is, by reason of another.

Then he gives the minor: therefore, the opinion of the negation of the good will be more false than the opinion affirming a contrary (23b15).

Next, he posits the major, the one who holds the contrary judgment about each thing is most mistaken (23b15), that is, in relation to the true judgment the contrary is more false. This was assumed in the major. He gives as the proof of this: for contraries are those that differ most with respect to the same thing, for nothing differs more from a true opinion than the more false opinion in respect to it.

Finally, he directly approaches the question. If (for “since”), then, of two opinions (namely, false opinions—the negation of the same thing and the affirmation of a contrary), one is the contrary of the true affirmation, and the contradictory opinion (that is, the negation of the same thing of the same thing), is more contrary according to falsity (namely, is more false), it is evident that the false opinion of negation will be contrary to the true affirmation, and conversely. The opinion saying that what is good is evil (that is, the affirmation of a contrary) is not the contrary but implies it, that is, it implies in itself the opinion contrary to the true opinion (namely, “a good is not good”). The reason for this is that the one conceiving the affirmation of a contrary must conceive that the same thing of which he affirms the contrary is not good. If, for example, someone conceives that life is evil, he must conceive that life is not good, for the former necessarily follows upon the latter and not conversely. Hence, affirmation of a contrary is said to be implicative, but negation of the same thing of the same thing is not implicative. This concludes the first argument.

The general rule about the contrariety of opinions that Aristotle has given here (namely, that contrary opinions are those opposed according to affirmation and negation of the same thing of the same thing) is accurate both in itself and in the propositions assumed for its proof. Many questions may arise, however, as a consequence of this doctrine and its proof.

First of all, all philosophers hold that opposition according to affirmation and negation constitutes contradiction, not contrariety. How, then, can Aristotle maintain that opinions opposed in this way are contraries? The difficulty is augmented by the fact that he has said that those opinions in which there is fallacy first are contraries, yet he adds that they are opposed as the terms of generation are, which he establishes to be opposed contradictorily. In addition, there is a difficulty as to the way in which the assertion of St. Thomas, which we used above, is true, namely, that no two opinions are opposed contradictorily, since here it is explicitly said that some are opposed according to affirmation and negation.

The second question involves his assumption that the contrary of each true opinion is per se false. This does not seem to be true, for according to what was determined previously, the contrary of the true opinion “Socrates is white” is “Socrates is not white.” But this is not per se false, for the opposed affirmation is true accidentally, and hence its negation is false accidentally. Falsity is accidental to such an enunciation because, being in contingent matter, it can be changed into a true one.

A third difficulty arises from the fact that Aristotle says the contradictory opinion is not contrary (23b15). He seems to be proposing, according to this, that both the opinion of the negation and of a contrary are contrary to a true affirmation. Consequently, he is either positing two opinions contrary to one or he is not taking contrariety strictly, although we showed above that he was taking contrariety properly and strictly.

In order to answer all of the difficulties in regard to the first argument, it must be noted that opinions, or intellectual conceptions in the second operation, can be taken in three ways:

in one way, according to what they are absolutely;

in a second, according to the things they represent absolutely;

in a third, according to the things they represent, as they are in opinions.

We will omit the first since it does not belong to the present consideration.

If they are taken in the second way, that is, according to the things represented, there can be opposition of contradiction, of privation, and of contrariety among them. The mental enunciation “Socrates sees,” according to what it represents, is opposed contradictorily to “Socrates does not see”; privatively to “Socrates is blind”; and contrarily to “Socrates is purblind.” Aristotle points out the reason for this in Categories 10 (12a35): not only is blindness privation of sight but to be blind is also a privation of to be seeing, and so of others.

Opinions taken in the third way, that is, as the things represented through opinions are in the opinions, have no opposition except contrariety; for opposites as they are in opinions, whether represented contradictorily or privatively or contrarily, only admit of the opposition that can be found between two real beings, for opinions are real beings. The rule is that whatever belongs to something according to the being which it has in another belongs to it according to the mode and nature of that in which it is, and not according to what its own nature would require. Now, between real beings only contrariety is found formally. (I am omitting here the consideration of relative opposition.) Therefore, opinions taken in this mode, if they are opposed, represent contrariety, although not all are contraries properly. Only those differing most in respect to truth and falsity about the same thing are contraries properly. Now Aristotle proved that these are judgments affirming and denying the same thing of the same thing. Therefore, these are the true contraries. The rest are called contraries by reduction to these.

From this the answer to the objections is clear. We grant that affirmation and negation in themselves constitute contradiction. In actual judgments, affirmation and negation cause contrariety between opinions because of the extreme distance they posit between real beings, namely, true opinion and false opinion about the same thing. And these two stand at the same time: those in which there is fallacy first are opposed as the terms of generation are, and yet they are contraries by the use of the foresaid distinction—for they are opposed contradictorily as terms of generation according to the things represented, but they are contraries insofar as they have in themselves those contradictories and hence differ most. It is also evident that there is no disagreement between Aristotle and St. Thomas, for we have shown that it is true that some opinions are opposed according to affirmation and negation if we consider the things represented, as is said here.

It will be noted, however, by those of you who are more penetrating and advanced in your thinking, that between opposite opinions there is something of true motion when a change is made from the affirmed to the affirmed; but according to the order of representation there is a certain similitude to generation and corruption so long as the change is bounded by affirmation and negation. Consequently, fallacy or error may be regarded in different ways.

Sometimes it has the aspect of both movement and change. This is the case when someone changes his opinion from a true one to one that is per se false, or conversely.

Sometimes change alone is imitated. This happens when someone arrives at a false opinion apart from a former true opinion.

Sometimes, however, there is movement in every respect. This is the case when reason passes from the true affirmation to the false affirmation of a contrary about the same thing.

However, since the first root of being in error is the opposition of affirmation and negation, Aristotle is correct in saying that those in which there is fallacy first are opposed as are the terms of generation.

With respect to the second question, I say that there is an equivocation of the term “per se false” and “per se true” in the objection. Opinion, as well as enunciation, can be called per se true or false in two ways.

In one way, it can be called per se true in itself. This is the case in respect to all opinions and enunciations that are in accordance with the modes of essentiality enumerated in Posterior Analytics 1.4 (73a34–73b15). Similarly, they can be said to be per se false according to the same modes. An example of this would be “man is not an animal.” Per se true or false is not taken in this mode in the rule about contrariety of opinions and enunciations, as the objection concludes. For if this were needed for contrariety of opinions, there could not be contrary opinions in contingent matter, which is false.

Second, an opinion or enunciation can be said to be per se true or false in respect to its opposite: per se true with respect to its opposite false opinion, and per se false with respect to its opposite true opinion. Accordingly, to say that an opinion is per se true with regard to its opposite is to say that on its own account and not on account of another it is verified by the falsity of its opposite. Similarly, to say that an opinion is per se false with regard to its opposite means that on its own account and not on account of another it is falsified by the truth of the opposite. For example, the opinion that is per se false in respect to the true opinion “Socrates is running” is not “Socrates is sitting,” since the falsity of the latter does not immediately follow from the former, but mediately from the false opinion, “Socrates is not running.” It is the latter opinion that is per se false in relation to “Socrates is running,” since it is falsified on its own account by the truth of the opinion “Socrates is running,” and not through an intermediary. Similarly, the per se true opinion in respect to the false opinion “Socrates is four-footed” is not “Socrates is two-footed,” for the truth of the latter does not by itself make the former false; rather, it is through “Socrates is not four-footed” as a medium, which is per se true in respect to “Socrates is four-footed”; for “Socrates is not four-footed” is verified on its own account by the falsity of “Socrates is four-footed,” as is evident. We are using “per se true” and “per se false” in this second mode in propounding the rule concerning contrariety of opinions and enunciations. Thus it is universally true in all matter that the true opinion and the per se false opinion in relation to it, and the false opinion and the per se true in relation to it are contraries.

Consequently, the response to the objection is clear, for it results from taking “per se true” and “per se false” in the first mode.

The answer to the third difficulty is the following. Since there is no other opposition but contrariety between opinions pertaining to each other, Aristotle (since he chose to use limited terms) has been forced to say that one is more contrary than another, which implies that both have opposition of contrariety in respect to a true opinion. However, he determines immediately that only one of them, the negative opinion, is contrary to a true affirmation, when he adds, it is evident that it must be the contrary (23b15). What he says, then, is that each, i.e., both negation of the same thing and affirmation of a contrary, is contrary to a true affirmation, and that only one of them, i.e., the negation, is contrary. Both of these statements are true, for both contrarieties are caused by an opposition contrary to the affirmation, as was said, but not uniformly. The opinion of negation is contrary first and per se, the opinion of affirmation of a contrary, secondarily and accidentally, i.e., through another, namely, by reason of the negative opinion, as has already been shown. There is a parallel to this in natural things: both black and red are contrary to white, the former first, the latter reductively, i.e., inasmuch as red is reduced to black in a motion from white to red, as is said in Physics 5.5 (229b15). However, the second statement, i.e., that only one of them, the negation, is contrary, is true simply, for the most distant extremes of one extent are contraries absolutely. Nov,, there are only two extremes of one distance and since between opinions pertaining to each other true affirmation is at one extreme, the remaining extreme must be granted to only one false opinion, i.e., to the one that is most distant from the true opinion. This has been proved to be the negative opinion. Only this one, then, is contrary to that absolutely speaking. Other opposites are contrary by reason of this one, as was said of those in between. Therefore, Aristotle has not posited many opinions contrary to one, nor used contrariety in a broad sense, both of which were maintained by the objector.

When Aristotle says, further, if this necessarily holds (23b27), he gives the second argument to prove that the negation of the same thing is contrary to the affirmation, and not the affirmation of a contrary. If opinions are necessarily related in a similar way (that is, in the same way) in other matters, that is, in such a way that affirmation and negation of the same thing are contraries in other matter, it would seem that what we have said about the opinions of that which is good and that which is evil is correct, namely, that the contrary of the affirmation of that which is good is not the affirmation of evil but the negation of good.

He proves this consequence when he adds: for the opposition of contradiction either holds everywhere or nowhere (23b27), that is, in every matter one part of a contradiction must be judged contrary to its affirmation—or nowhere, that is, in no matter. For if there is a general art which deals with contrary opinions, contrary opinions must be taken everywhere and in every matter in one and the same mode. Consequently, if in any matter, negation of the same thing of the same thing is the contrary of the affirmation, then in all matter negation of the same thing of the same thing will be the contrary of the affirmation.

Since he intends in his proof to conclude from the position of the antecedent, Aristotle affirms the antecedent through its cause: in matter in which there is not a contrary, such as substance and quantity (which have no contraries, as is said in Categories 5 [3b24] and 6 [5b10]), the one contradictorily opposed to the true opinion is per se false. For example, he who thinks that a man such as Socrates is not a man is per se mistaken with regard to one who thinks that Socrates is a man.

Then he affirms the antecedent formally and concludes directly from the position of the antecedent to the position of the consequent. If, then, these (23b27), namely, affirmation and negation in matter which lacks a contrary, are contraries, all other contradictions must be judged to be contraries.

When he says, again, the opinions of that which is good (23b33), he begins the third argument to prove the same thing. The two opinions of that which is good—that it is good, and that it is not good—are related in the same way as the two opinions of that which is not good—that it is not good and that it is good—namely, the opposition of contradiction is kept in both. The first opinion of each combination is true, the second false. Hence with respect to the first true opinions of each combination he proposes this major: again, the opinions of that which is good, that it is good, and of that which is not good, that it is not good, are parallel. With respect to the second false judgment of each combination he adds: so also are the opinions of that which is good, that it is not good, and of that which is not good, that it is good. This is the major.

But the contrary of the true opinion of that which is not good, namely, the true opinion “that which is not good is not good,” is not “that which is not good is evil,” nor “that which is not good is not evil,” which have a contrary predicate, but the opinion that that which is not good is good, which is its contradictory. Therefore, the contrary of the true opinion of that which is good, namely, the true opinion “that which is good is good,” will also be its contradictory, “that which is good is not good,” and not the affirmation of the contrary “that which is good is evil.” Hence he adds the minor which we have already stated: what, then, would be the contrary of the true opinion asserting that that which is not good is not good?

The contrary of it is not the opinion which asserts the contrary predicate affirmatively, “that which is not good is evil,” because these two are sometimes at once true. But a true opinion is never contrary to a true opinion. That these two are sometimes at once true is evident from the fact that some things that are not good are evil. Take injustice; it is something not good, and it is evil. Therefore, contraries would be true at one and the same time, which is impossible. But neither is the contrary of the above true opinion the one asserting the contrary predicate negatively, “that which is not good is not evil,” and for the same reason. These will also be true at the same time. For example, a chimera is something not good, and it is true to say of it simultaneously that it is not good and that it is not evil.

There remains the third part of the minor: the contrary of the true opinion that that which is not good is not good is the opinion that it is good, which is the contradictory of it.

Then he concludes as he intended: the opinion that a good is not good is contrary to the opinion that a good is good, that is, its contradictory. Therefore, it must be judged that contradictions are contraries in every matter.

When he says, it is evident that it will make no difference (24a3), he shows that the truth he has determined is extended to opinions of every quantity. The case has already been stated in respect to indefinites, particulars, and singulars. On this point their status is alike, for indefinites and particulars, unless they stand for the same thing, as is the case in singulars, are not opposed by way of affirmation and negation, since they are at once true. Therefore he turns his attention to those of universal quantity. It is evident, he says, that it will make no difference with respect to the proposed question if we posit the affirmations universally, for the contrary of the universal affirmative is the universal negative, and not the universal affirmation of a contrary. For example, the contrary of the opinion that everything that is good is good is the opinion that nothing that is good (namely, no good) is good. He manifests this by the nominal definition of universal affirmative: for the opinion that that which is good is good, if the good is universal, that is, the universal opinion “Every good is good,” is the same, that is, is equivalent to the opinion that whatever is good is good. Consequently, its negation is the contrary I have stated, “nothing which is good is good,” that is, “no good is good.” The case is similar with respect to the not good. The universal negation of the not good is opposed to the universal affirmation of the not good, as we have stated with respect to the good.

When he says, if, therefore, this is the case with respect to opinion (24b1), he returns to the question first advanced, to reply to it, for he has now completed the second on which the first depends.

About this he does two things.

First, he replies to the question;

second, he manifests a point in the solution of a preceding difficulty, at: it is evident, too, that true cannot be contrary to true (24b6; [378]).

About the first he does two things.

First, he replies directly to the question, saying, if, therefore, contrariety is such in the case of opinions (24b1), and affirmations and negations in vocal sound are signs of affirmations and negations in the soul, it is evident that the contrary of the affirmation, that is, of the affirmative enunciation, is the negation of the same subject. In other words, the negative enunciation of the same predicate of the same subject will be the contrary, and not the affirmative enunciation of a contrary. Thus the response to the first question—whether the contrary of the affirmative enunciation is its negative or the contrary affirmative—is clear. The answer is that the negative is the contrary.

Second, he divides negation as it is contrary to affirmation, that is, into the universal negation and the contradictory: the universal negation, is contrary to the affirmation (24b1). In order to state this division by way of example he relates one enunciation to one enunciation: the contrary of the universal affirmative enunciation “every good is good” or “every man is good” is the universal negative “no good is good” or “no man is good.” Again, relating one to one, he says that the contradictory negation contrary to the universal affirmation is “not every man is good” or “not everything good is good.” Thus he posits both members of the division and makes the division evident.

A difficulty arises at this point which we cannot disregard. If the contrary of the universal affirmative is a twofold negation, namely, the universal and the contradictory, either there are two contraries to one affirmation or Aristotle is using “contrariety” in a broad sense, although we showed that this was not the case through of an earlier passage of the text. The difficulty is augmented by the fact that Aristotle said in the passage immediately preceding that it makes no difference if we take the universal negation as contrary to the universal affirmation, that is, as one of its negations. Hence, the conclusion cannot be avoided that in the mode in which Aristotle speaks of contrariety here, there are two contrary negations to the universal affirmative.

To clear up this difficulty we must note that it is one thing to speak of the contrariety between the negation of some universal affirmative in relation to the affirmation of a contrary, and another to speak of that same universal negative in relation to the negation contradictory to the same affirmative. For example, the four enunciations of which we are now speaking are the universal affirmative, the contradictory, the universal negative, and the universal affirmation of a contrary: “every man is just,” “not every man is just,” “no man is just,” “every man is unjust.” Notice that although all the rest are contrary to the first in some way, there is a great difference between the contrariety of each to the first.

The last one, the affirmation of a contrary, is contrary to the first by reason of the preceding universal negation, for it is false not per se, but by reason of that negation, that is, it is implicative, as Aristotle has already proved.

The third, the universal negation, is not per se contrary to the first either. It is contrary by reason of the second, the contradictory negation, and for the same reason, namely, it is not per se false in respect to the truth of the affirmation but is implicative, for it contains the contradictory negation “not every man is just,” by means of which it is made false in respect to the truth of the affirmation. The reason for this is that the falsity of the contradictory negation is prior absolutely to the falsity of the universal negation, for the whole is more composite and posterior as compared to its parts. There is, therefore, an order among these three false enunciations.

Only the contradictory negation is simply contrary to the true affirmation, for it is per se false simply in respect to the affirmation; the affirmative of the contrary is per accidens contrary, since it is per accidens false; the universal negation, which is a medium partaking of the nature of each extreme, is per se contrary and per se false as related to the affirmation of a contrary, but is per accidens false and per accidens contrary as related to the contradictory negation; just as red in a motion from red to black takes the place of white, and in a motion from red to white takes the place of black, as is said in Physics 5.5 (229b15). Therefore, it is one thing to speak of the universal negation in relation to affirmation of a contrary and another to speak of it in relation to the contradictory negation. If we are speaking of it in the first way, the universal negation is per se contrary and per se false; if in the second, it is not per se false or contrary to the affirmation.

Since Aristotle is now treating the question of whether the contrary of a true affirmation is the affirmation of a contrary or the negation, and not the question as to which of the negations is contrary to a true affirmation—as is clear in the whole progression of the question—his answer is that both negations are contrary to the true affirmation without distinction, and that affirmation of a contrary is not. His intention is to manifest the diversity between the negation and the affirmation of a contrary inasmuch as they are contrary to a true affirmation. He does not intend to say that both negations are contrary simply, for this is not the difficulty in question here, but the former is.

With respect to his saying that it makes no difference if we posit the universal negation, the same point applies, for in regard to showing that affirmation of a contrary is not contrary to a true affirmation, which is the question at issue here, it makes no difference which negation is posited. It would make a great deal of difference, however, if we wished to discuss which negation was contrary to a true affirmation. It is evident, then, that Aristotle’s discussion of the true contrariety of enunciations is very subtle, for he has posited one to one contraries in every matter and quantity, and affirmed that contradictions are contraries simply.

When he says, it is evident, too, that true cannot be contrary to true (24b6), he returns to a statement he has already made in order to prove it. It is evident, too, from what has been said, that true cannot be contrary to true, either in mental opinion or in contradiction, that is, in vocal enunciation. He gives as the cause of this that contraries are opposites about the same thing; consequently, true enunciations and opinions about diverse things cannot be contraries. However, it is possible for all true enunciations and opinions about the same thing to be verified at the same time, inasmuch as the things signified or represented by them belong to the same thing at the same time; otherwise, they are not true. Consequently, not all true enunciations and opinions about the same thing are contraries, for it is not possible for contraries to be in the same thing at the same time. Therefore, no true opinion or enunciation, whether it is about the same thing or is about another, is contrary to another.

We conclude the commentary on this book Peri Hermenias, 1496 A.D., on the feast of St. Thomas Aquinas. Glory and honor to God for allowing me to bring this work, so long left unfinished, to completion.