LESSON III

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

             19b 32 The same is the case when the affirmation is of a name taken universally, as in the following:

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Diagram #4 (Image 4)]]

             19b 35 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.

             19b 36 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   Non-man is not just

 (Affirmation)    (Negation)

 Non-man is not nonjust  Non-man is nonjust

 (Negation)    (Affirmation)

             20a 1 There will be no more opposites than these.

             20a 1 The latter, however, are separate from the former and distinct from them because of the use of "non-man" as a name.

             20a 3 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   Not every man matures

 (Affirmation)    (Negation)

 Not every non-man matures Every non-man matures

 (Negation)    (Affirmation)

             20a 7 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.

             20a 10 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.

             20a 14 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.

COMMENTARY BY CARDINAL CAJETAN

1. 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. He first proposes a similarity between these enunciations and the infinite enunciations already discussed, and then shows their difference where he says, But it is not possible, in the same way as in the former case, that those on the diagonal both be true, etc. Finally, be concludes with the number of oppositions there are between these enunciations where he says, These two pairs, then, are opposed, etc.

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

             2. 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 again, 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 nonjust" and its negation, "Not every man is nonjust." 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 but the particular negative as was stated in the first book.

             3. 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 prolixity 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:

   DIAGRAM OF THE INDEFINITES

 Man is just    Man is not just

 Man is not nonjust   Man is nonjust

 Man is not unjust   Man is unjust

   DIAGRAM OF THE UNIVERSALS

 Every man is just   Not every man is just

 Not every man is nonjust  Every man is nonjust

 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.

             4. When he says, But it is not possible, in the same way as in the former case, that those on the diagonal both be true, etc., he proposes a difference between the universals and the indefinites, i.e., 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, then according to the opinion of others.

             Aristotle means by diagonal enunciations those that are diametrically opposed in the diagram above, i.e., 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.

             5. Enunciations that are similar in quality, and called diagonal because diametrically distant, are dissimilar in truth, then, in the case of indefinites and universals. The indefinites on the corners, both on 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, i.e., 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.

             6. Herminus, however, according to Boethius, 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, i.e., 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 nonjust." 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.

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Diagram #5 (Images 5 and 6)]]

             With enunciations disposed in this way he says their difference is this: that in indefinite enunciations, 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 this follows: the particular is true, therefore its universal contradictory is false. But this does not follow: this universal contradictory is false, therefore its universal contrary, which is the diagonal of the particular assumed, is true. For contraries can be at once false.

             7. 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; for in Aristotle's diagram affirmatives are diagonal to affirmatives and negatives to negatives.

             8. Then Aristotle says, These two pairs, then, are opposed, etc. 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, for 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.

             9. When he says, and there are two other pairs if something is added to "non-man" as a subject, etc., he shows the diversity of enunciations when "is" is added as a third element and the subject is an infinite name. First, he proposes and distinguishes them; secondly, he shows that there are no more opposites than these where he says, There will be no more opposites than these; thirdly, he shows the relationship of these to the others where he says, The latter, however, are separate from the former and distinct from them, etc.

             With respect to the first point, it should be noted that there are three species of absolute [de inesse] 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 nonjust." 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 nonjust." 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 beside the verb "is" to "non-man" as if to a subject, i.e., 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." Then he posits another opposition between those with an infinite subject and an infinite predicate, "Non-man is nonjust," "Non-man is not nonjust."

             10. Then he says, There will be no more opposites than these. Here he points out that there are no more oppositions of enunciations than the ones he has already given. We should note, then, that simple [or absolute] enunciations--of which we have been speaking--in which the verb "is" is explicitly posited whether it is the second or third element added, cannot be more than the twelve posited. 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; and in any order there are four enunciations. And since their subject in any order can be quantified in four ways, i.e., by universality, particularity, singularity, and indefiniteness, these twelve will be increased to forty-eight (four twelves being 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

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Diagram #7 (Image 7)]]

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 co-ordered in a straight line and in the three distinct orders given above.

             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.

             11. Then when he says, The latter, however, are separate from the former and distinct from them, etc., 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, i.e., 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, to be predicated common to a name and a verb, and therefore every subject of an enunciation is subjected as a name.

             12. Next he takes up enunciations in which adjective verbs are posited, when he says, In enunciations in which "is" does not join the predicate to the subject, etc. First, he distinguishes these adjective verbs; secondly, he answers an implied question where he says, We must not say "non-every man," etc.; thirdly, he concludes with their conditions where he says, All else in the enunciations in which "is" does not join the predicate to the subject will be the same, etc.

             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, i.e., 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, i.e., 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, and for the same reason, i.e., 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, such as "matures" or "walks," i.e., 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."

             13. Then he answers an implied question when he says, We must not say "non-every man" but must add the negation to man, etc. First he states the solution of the question, then he proves it where he says, This is evident from the following, etc.

             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."

             14. Where he says, This is evident from the following, etc., 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; when I say, "Every man matures," however, 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.

             15. Two things should be noted here: first, that Aristotle does not say "every" and "no" signify universally, but that the universal is taken universally; secondly, 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 I Posteriorum 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, i.e., of a subject, universally, i.e., 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, i.e., "every" and "no," one of which distributes positively, the other distributes by removing.

             16. When he says All else in enunciations in which "is" does not join the predicate to the subject, etc., 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, i.e., similar to these.