LESSON VIII

Modal Propositions and Their Opposition

             21a 34 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.

             21a 38 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 nonwhite." For if this is not so, it will be true to say that "wood" is nonwhite 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."

             21b 12 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, not be seen. But it is impossible that opposed assertions in respect to the same thing be true. Therefore, the negation of "possible to be" is not, "possible not to be."

             21b 19 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.

             1. 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. First, he explains their opposition; secondly, he treats of the consequences of their opposition where he says, Logical sequences result from modals ordered thus, etc. With respect to the first point, he proposes the question he intends to consider and then begins his consideration where he says, Let us grant that of mutually related enunciations, contradictories are those opposed to each other, etc.

             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, for the question has many special difficulties.

             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.

             2. We can speak about things in two ways: in one, 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 [de inesse] enunciations; these 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, "That Socrates run is possible." 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.

             3. 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, "That Socrates run is possible," we do not make the composition of running with Socrates substantial, but we qualify it, asserting that it is possible.

             Consequently, Aristotle in proposing the modes, does not mention the true and false at all, although later on he infers the true and the not true, and assigns the reason for it where he does this.

             4. 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, i.e., 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 be 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, i.e., 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.

             5. 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.

             6. 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, etc.; 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; the necessity of treating them, when he adds, for they have many difficulties of their own.

             7. Then he investigates the opposition of modal enunciations, where he says, Let us grant that of those things that are combined, contradictories are those opposed to each other by being related in a certain way according to "to be" and "not to be," etc. First, he presents the question and in so doing gives arguments for the parts; secondly, he determines the truth, where he says, For it follows from what we have said, either that the same thing is asserted and denied at once of the same subject, etc.

             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; then he argues for the negative part, that the negation must not be added to the verb, where he says, However it seems that the same thing is possible to be and possible not to be, etc.

             8. 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, i.e., of complex things, contradictions are those opposed to each other which are disposed according to "to be" and "not to be," i.e., in one of which "to be" is affirmed and in the other denied.

             9. 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, "Nonman 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."

             10. 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 nonwhite," 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, i.e., 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 nonwhite 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 nonwhite man" will be true to say of it, namely of wood, i.e., "Wood is nonwhite man." This is manifestly false, for wood is neither white man nor nonwhite 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.

             11. He continues his induction with enunciations having an adjective verb: Now if the case is as we have stated it, i.e., 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 (i.e., 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 is not walking." 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."

             12. Then he posits the second part of the induction: And if this is always the case, i.e., 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, i.e., 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 "nonreads."

             13. When he says, However, it seems that the same thing is possible  to be and possible not to be, etc., he argues for the negative part of the question, namely, 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; secondly, the major; finally, the conclusion. The minor is: However, it seems that the same thing is possible to be and possible not to be. 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 (as are 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, i.e., 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 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.

             The major is: But it is impossible that contradictions in respect to the same thing be true. The final conclusion inferred is: Therefore, the negation of "possible to be" is not, "possible not to be" 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 it is 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.

             14. Aristotle establishes the truth with respect to this difficulty where he says, For it follows from what we have said, either that the same thing is asserted and denied at once of the same subject, etc. Since he is investigating two things, i.e., 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; then he determines the truth in relation to the second, namely, that contradiction of modals is made by negation of the mode, where he says, Therefore, the negation of "possible to be" is "not possible to be," etc.

             Hence he says that because of the foresaid reasoning one of these two follows: first, that either the same thing, i.e., one and the same thing is said, i.e., is asserted and denied at once of the same subject, i.e., either two contradictories are verified at once of the same thing, as the first argument concluded; or secondly, that assertions and denials of modals, which are opposed contradictorily are not made by the addition of "to be" or "not to be," i.e., contradiction of modals is not made by the negation of the verb, as the second argument concluded. If the former alternative is impossible, 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, i.e., that the contradiction of modals is not made according to negation of the verb, and the first alternative is to be rejected.