LESSON XII

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

             23a 6 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.

             23a 11 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.

             23a 15 So it is not true to say the latter possible [i.e., 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.

             23a 18 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.

             23a 21 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.

             23a 23 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.

             1. Aristotle now proposes to show in what way potencies that are called equivocal are related to opposites. He first explains the nature of this kind of potency, and then gives the difference and agreement between these and the foresaid, where he says, This latter potentiality is only in that which is movable, but the former is also in the immovable, etc.

             In V and IX Metaphysicae, 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 the active or passive potency they have, are potencies for the same reason, i.e., 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, and therefore they are not related to opposites.

             2. 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, i.e., inasmuch as it actually is; for example, it is possible to walk when one is already walking, and in general, i.e., 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, i.e., 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, i.e., 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.

             3. When he says, This latter potentiality is only in that which is movable, but the former is also in the immovable, etc., he specifies the difference between each potency. This last potency, he says, [possible because it can be] 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.

             4. 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, e.g., to walk is not impossible for that which is already walking in act, i.e., 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 which are not according to reason, etc. 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.

             5. When he says, So it is not true to say the latter possible of what is necessary simply, etc., 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 [i.e., 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.

             6. 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. Next, 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, i.e., since the whole universal follows upon its subjective part, to be possible to be, i.e., possible, as the whole universal, follows upon that which necessarily is, i.e., necessary, as a subjective part. He adds: though not every kind of possible does, i.e., not every species of the possible follows; just as animal follows upon man, but not in every way, i.e., 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.

             7. When he says, Indeed the necessary and not necessary may well be the principle of all that is or is not, etc., he disposes the same consequences of modals in another arrangement, placing the necessary before all the other modes. First he proposes the order of modals and then assigns the cause of the order where he says, It is evident, then, from what has been said that that which necessarily is, actually is, etc.

             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, i.e., the necessary and not necessary is the principle of affirmatives or negatives. And the others, i.e., the possible, contingent, and impossible to be must be considered as consequent to these, i.e., to the necessary and not necessary.

THE CONSEQUENTS OF MODAL ENUNCIATIONS ACCORDING TO THE FOUR ORDERS, POSITED AND DISPOSED BY ARISTOTLE IN ANOTHER APPROPRIATE

ARRANGEMENT

 FIRST ORDER     THIRD ORDER

It is necessary to be   It is not necessary to be

It is not possible not to be  It is possible not to be

It is not contingent not to be It is contingent not to be

It is impossible not to be  It is not impossible not to be

 SECOND ORDER     FOURTH ORDER

It is necessary not to be  It is not necessary not to be

It is not possible to be   It is possible to be

It is not contingent to be  It is contingent to be

It is impossible 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.

             8. When he says, It is evident, then, from what has been said that that which necessarily is, actually is, etc., 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, It is evident, then, from what has been said in treating the necessary, that that which necessarily is, 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, etc. Finally, he posits the conclusion: those that are wholly in act in every way, namely necessary, are prior to the potential, i.e., to possibles, which do not have being in act wholly although they are compatible with it.

             9. Then he says, Some things are actualities without potentiality, namely, the primary substances, etc. Here 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, i.e., 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, i.e., more worthy and more perfect than when he was potentially a philosopher. Hence, when we consider each order, i.e., 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, e.g., motion, time, the infinite division of magnitude, and the infinite augmentation of number. These, as is said in IX Metaphysicae, 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.

             10. This has been said so that once the order of the universe has been seen it should appear 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 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 whereas 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.

             11. Since the consequents of modals, i.e., 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.

             12. 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 'Socrates,' 'some man,' 'every man,'" or "'no man,' run is possible."

             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, i.e., dictum. "That man be white is possible" means "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, i.e., the mode, has distributive force. This is distinguished into universal and particular.

             13. 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, i.e., the mode, not only has the relationship of a predicate to its subject (i.e., 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, i.e., "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 "while 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, universally, quantity 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.

             14. Therefore, with respect to their proper quantity, some modals are universal affirmatives, i.e., those of the necessary because they distribute "to be" to all time. Others are universal negatives, i.e., those of the impossible because they distribute "to be" to no time. Still others are particular affirmatives, i.e., those signifying the possible and contingent, for both of these distribute "to be" to some time. Finally, there are particular negatives, i.e., 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, i.e., 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, i.e., 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.

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TABLE OF OPPOSITION OF EQUIPOLLENT MODALS

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