Cursus Philosophicus Thomisticus, Secunda Pars Philosophiae Naturalis

The unity of alteration can be considered either under the character of a change, insofar as it destroys one terminus and produces another, or under the character of motion, which includes both changes: that is, whether there is one motion or one or more changes. Continuity in alteration can be considered in three ways: first, with respect to the subject in which it exists, namely, insofar as a quality is spread through continuous parts of a subject; second, with respect to time, insofar as the alteration is contained without any interruption in duration; third, on the part of the form, namely, insofar as the form is not introduced wholly and indivisibly only in an instant, but some of it continuously over time and some of it in an instant.

On the unity of alteration.

I say, then, first: Alteration, as a motion, is one, but it includes two changes: one that corrupts the terminus from which, the other that acquires the terminus toward which.

That these two changes occur is clear from what we said above when treating generation and corruption,¹ which involve these two changes, and in q. 14 of the Physics, art. 2,² where we showed that these changes are necessary for motion, because in motion there is a transition from something to something, and consequently one thing is acquired and another corrupted. That the motion is one is clear, because it is one transition and way from subject to subject, that is, from one positive terminus to another positive terminus, between which there is a range and distance or contrariety. This range is one when there are only two termini between which the motion takes place. Such a range is found in alteration, since it is a transition from one contrary to another; therefore, there is one motion. For the same reason there is one action, because there is one agent and one patient, and consequently one procession of causality.

But you will say: Why do substantial generation and corruption likewise, being two changes, not make one motion as they do in qualities?

It is answered that changes do not produce motion unless some positive distance or contrariety to be overcome is grounded between the positive termini themselves, and not merely a being or nonbeing to be changed. The reason is that in a change, precisely as a change, only the acquisition of some being anew is intended; consequently, on the side of the terminus from which, it per se requires only nonbeing or privation. If this privation is joined to some positive form, that is incidental to such a change, insofar, namely, as the privation is found joined to some form. But in motion, not only is acquiring being anew intended; a distance between the termini over which it occurs must also be overcome, and these termini must be positive. For there is no range between the privative and the positive, since they are opposed without a middle as being and nonbeing; and if anything is found in between, it is by reason of some presupposed positive thing. Contraries, however, have a middle through which they are positively distant and opposed. Hence, since no range of contrariety such as is found in qualities is considered between substantial forms—because from participation in substantial forms as extremes no middle is participated in or tempered, nor is there a more or less in one and the same form—there is no distance and contrariety between substantial forms that grounds motion, as there is between qualities.

Secondly, you will object against the conclusion: For it follows from it that intensification and remission are not two motions, although in art. 1 we said that they are two species of motion.

The consequence is proved as follows: When there is motion from heat of degree one to heat of degree seven, there is an intensification of the heat that is acquired and a remission of the cold that is lost; as much cold is lost as heat is acquired. Therefore, that change of the cold is a remission, and yet there is only one motion, since there is only one way and one terminus acquired and one lost. Otherwise, whenever a quality is intensified there would be two motions: one from less heat to more, the other a remission of cold from more to less.

It is answered that intensification and remission are in themselves distinct motions, like increase and decrease, ascent and descent. They are contrary when they concern the same form, for example, intensifying or lessening heat. When they concern different forms, for example, intensifying heat and lessening cold, these motions are either disparate, if the forms themselves have no order and connection with one another, or coordinated, if the forms themselves are successive in relation to one another, so that one lessens or expels the other. However, when a motion of intensification is found that corrupts or attenuates cold, it is not per se a motion of remission, because it is not per se a lessening, but follows as a consequence insofar as it is the corruption of the cold present in the subject. Yet because this is incidental with respect to the intensification of heat, that motion is not called a remission, nor does it occur in the manner of a motion, but in the manner of a change that corrupts some of the cold consequentially and incidentally, as heat is intensified. Motion does not take its species, nor is it constituted as motion, according to what is incidental and consequential, but according to what is per se and on the side of the terminus toward which; it does not take it merely from the side of the terminus from which. Therefore, when heat is intensified, although there is a lessening of cold, there is not a motion of remission, because that lessening of cold belongs precisely to the side of the terminus from which, as the terminus that is changed and destroyed and stands in succession to the acquisition of heat; it is not a motion per se that lessens, whose terminus toward which would be the lessening of cold. Thus it is not per se a motion of remission, but a change that destroys cold, not one that per se lessens and tempers it. Sometimes, however, intensification can occur without the remission of its opposite, as in the intensification of light, which already presupposes that darkness has been expelled, and in the intensification of charity, which presupposes that sin has been expelled through charity's first introduction. Hence intensification is not always joined to a remission, even as a change that occurs incidentally.

On the continuity of alteration.

I say, secondly: Alteration that is truly motion is continuous, as opposed to discrete, if we attend to the continuity that occurs through the extension of a quality in the parts of a continuum, whether through the duration of time or through the intensification of the form.

We say “as opposed to discrete motion” because if we take “continuous” to mean perpetual and without ceasing, then alteration is not continuous in that sense, but very often ends and is interrupted. Thus, although a quality can be produced in an instant, as when the final disposition is formed, nevertheless, when it occurs through true motion, it occurs neither in an instant nor through many instantaneous actions, such that nothing of the quality is produced between one instant and another and there is only a disposition for production to occur in an instant, as some have thought. The opposite view, however, is commonly held, as can be seen in Magister Báñez on Book 1 of On Generation, ch. 4, q. 6, “On Alteration”; in the Carmelite Course, disp. 2, “On Alteration,” q. 10; in the Coimbra commentary on Book 1 of On Generation, ch. 4, q. 2, art. 2; and by others.

We must therefore prove two things: first, that alteration cannot occur in an instant, but has succession in temporal duration; second, that in the extension or intensification of a quality, something of the quality is produced not only at instants but also in the intervening time between one instant and another, and that the altering action does not cease.

The first was proved by us in q. 21 of the Physics, art. 2,³ because successive motion does not exist in an instant, since, precisely insofar as it is successive, it is not indivisible. For every succession implies one part after another; therefore, it implies divisibility and thus does not coexist with, or receive its measure from, instantaneous duration.

This also follows from the teaching of Saint Thomas, Summa theologiae I, q. 53, art. 3, as we also adduced there: it cannot be the case that some subject rests under one form for the whole of a period of time and, in the final instant of that period, is under another form, as though it had been changed into it in the completed state. Therefore, motion can never be completed in a single instant, so that before that instant there is none of the motion and in the final instant there is the motion and its terminus, that is, the having-been-moved. For there cannot be a having-been-moved unless some being-moved precedes it, that is, some tendency to acquire that form and expel the opposite form. But for the subject to rest throughout the preceding period, it must be under one form in such a way that it is neither on the way to that form's corruption nor tending toward another, but is in the same state now as before. Therefore, it cannot be the case that something is changed in the final instant while no being-moved precedes it throughout the period, but only rest.

This is also apparent in instantaneous changes, if they occur according to the order and manner of nature. Some motion precedes, either by way of disposition or by way of application, as is clear in substantial generation and illumination. For substantial generation depends on a preceding alteration, which is motion. Similarly, a luminous body does not naturally illuminate a space where it did not illuminate before unless it is newly produced there or newly brought there. If it is newly brought there, local motion precedes; if it is newly produced there through natural generation, as when fire is made, alteration precedes. Thus, in the natural order, nothing is ever placed under a new form, even instantaneously, unless some motion precedes. If, however, by divine power something is produced or created suddenly without any preceding disposition or motion, that does not belong to the natural manner of operation of which we are speaking here. So too it is no wonder that Christ's body is placed under the species of bread at some instant, although no motion toward it preceded, because this occurs by supernatural power, not in the natural way. For this reason, Saint Thomas, at the cited place, proves that an angel cannot move in an instant while resting in another place throughout the preceding time. If an angel exists in another place throughout a complete instant, without any time or motion, at rest, then the instant of its existence in one place must differ from the instant of its existence in another, so that it rests in one place not throughout a period of time but throughout an instant, and in another instant is in another place. But then the departure from one place, which occurs in an instant through the final state of being, and the beginning of another, which occurs in another instant, are measured not by one instant but by two. Thus that discrete motion occurs not in an instant but in instants. Hence motion, even discrete motion, is never verified in a single instant.

The second point to be proved in this conclusion is that, if motion is continuous with a continuity belonging to the form, in this sense: if some of the form is produced in an instant, some of it is also acquired in time, and the action and continuation of the form do not cease between one instant and another. Some deny this part. Yet it follows from Saint Thomas in II Sentences, dist. 5, q. 2, art. 1,⁴ where he proves that the dispositions for substantial generation precede the introduction of the form in time, because alteration is continuous motion, and therefore its beginning and middle precede the introduction of the form. Hence alteration occurs in time and is not discrete across instants. The holy Doctor posits the same continuity of alteration through the intermediate time between two instants in Quodlibet 9, art. 9.⁵ It can also be seen in his commentary on Book 1 of On Generation, lect. 24,⁶ on text 84,⁷ and in his commentary on Book 5 of the Physics, lect. 7.⁸ It is taken from the Philosopher in the same Book 5 of the Physics, text 39,⁹ where he says “that every motion is continuous, and that it must be one and continuous simply.”

The reason is this: Either some motion continues between two instants, so that the action does not cease and the subject does not rest, or all motion and the action producing the quality cease between one instant and another. If the first, then that motion and flux between instants cannot be understood without some flowing form, which in an instant has a having-been-moved, or exists in the completed state, while in time, that is, in motion, it exists in a process of becoming and being moved; for motion is not something apart from the things toward which it is motion. Thus, if motion really occurs between one instant and another, a form really exists, being identified with that motion as with a flowing terminus that successively passes from nonbeing to being. If the second is asserted, it is impossible: if a quality is produced in this instant and the motion ceases immediately afterward, while something is produced in the next instant, that thing will not have been acquired through motion or alteration, which is motion, but through another action distinct from succession and motion, and no such action is apparent. Moreover, between one instant and another the agent is duly applied so as to act, and the patient is capable of receiving and is unimpeded, no less than in the following instant; for, as we assume, the patient has not changed from its disposition between instants, nor the agent from its activity. How, then, is the agent suspended from acting between instants? Finally, in local motion one does not cease moving between instants, because one gradually passes from one place to another through the middle and overcomes the distance between two places. Therefore, similarly, the distance and contrariety between qualities and their degrees of intensity must be overcome through the succession and continuation of motion, by producing something between instants.

Nor can it be said that between instants the agent produces something, but not the form, for example heat, rather some disposition toward heat, such as rarefaction or the like. For besides the fact that there is no disposition toward heat, since heat itself is a first quality, even if this were granted, the same argument applies to that disposition. Either it is a quality or it is not. If it is not a quality, one cannot specify what it is or to which category it belongs; or, if it is a mode of the same quality, what mode is it besides intensification and remission? For if these are produced in time, then the motion of intensification is continuous. But if that disposition is a quality, for example rarefaction, then some quality is already produced between instants, and consequently the same reasoning applies to heat itself.

You will say: Although motion is continuous in the intensification of a quality and something is produced between instants, nevertheless, when the alteration is from one quality to another, for example from white to black, what quality is produced between instants, since the intermediate quality is not produced divisibly but indivisibly? For it is a true species of quality, having indivisible being and terminating the having-been-moved. It is answered that when one passes from white to black through an intermediate quality, for example pale, then between instants pallor occurs imperfectly, insofar as whiteness begins to fade and fall away from its perfection: whiteness is in the process of being corrupted, which is pallor in the process of becoming. This occurs between instants because that corruption of whiteness and acquisition of pallor have a range; thus, a part of that range occurs in time and is completed in the completed state at some instant.

On the indivisibles of alteration.

Since a continuum consists of connected parts, which are joined by certain indivisibles, it is necessary to explain how these indivisibles occur in qualities and in successive alteration.

It is answered that the indivisibles of a quality must be considered according to its different modes of indivisibility. For one finds divisibility of extension by reason of the subject's quantity, divisibility of motion by reason of succession, and finally divisibility of form according to more and less in intensification and remission.

As to the first, just as accidents have quantitative extension through quantity, which affects substance and extends it and the accidents in it, so through quantity a quality is made extended and divisible; consequently, through quantity it will also have indivisibles that connect this quantitative divisibility. And just as substance has neither divisibility nor indivisibles except through quantity, as was proved in Book 6 of the Physics, q. 20,¹⁰ and in q. 16 of the Logic,¹¹ so neither do quality and other materially extended accidents have indivisibles of this extension except through quantity; for in this respect the same reasoning applies to them and to substance.

As to the second, we say that in alteration, insofar as it is motion, there are indivisibles as in other motions: namely, the indivisibles are the very having-been-moved states in the succession of the quality, which terminate or connect the succession of motion itself, as we explained in q. 20 of the Physics, art. 1.¹² This having-been-moved, as is drawn from Saint Thomas, Summa theologiae I, q. 53, art. 3, is explained by the fact that the mobile is not in the same disposition at every instant of the time in which it is moved. Thus, insofar as that disposition is in the process of becoming, it is said to be in the process of being moved; insofar as it is terminatively in the completed state, it is said to have been moved, and then the disposition is different. Accordingly, whether this having-been-moved consists in some indivisible in which it is completed and terminated, or in some other mode or respect, that which formally constitutes the having-been-moved is what constitutes the mobile in one disposition after another terminatively and in the completed state: all the parts that are in the process of becoming through time are in the completed state at an instant, and from that completed state follows another process of becoming of another part, which is in the completed state at another instant, continuing up to the final instant at which it stops. Thus a quality, by successively inducing different having-been-moved states, constitutes different successive indivisibles of the motion of alteration.

As to the third, namely the indivisibles of the quality or form itself that is acquired through alteration, a difficulty can arise within the same quality, when it is intensified or lessened: must this divisible range of intensification or remission connect and join its parts through certain indivisibles? This pertains to the following question, where we will treat the intensification and remission of qualities.

A difficulty can also arise as to whether, in the very range or distance found between two contrary qualities, through which the transition from one to the other takes place (as pale, green, blue, and so forth are posited between white and black), indivisibles must also be posited by which this divisible range and distance is joined together. Yet in this there appears to be no reason to posit indivisibles, because these species are not continuous with one another, nor do they have parts of the same nature that need to be joined by different indivisibles; for they are different colors or other intermediate qualities. Within the species of color there is a range from an imperfect and incipient color to another perfect intermediate color, and from that to another, up to the extreme, with the corruption of the prior color, which is expelled. Then no indivisible is acquired to join the parts, but rather a certain determinate species. Yet because it is intermediate and imperfect, it prepares the way and transition to another, which arises from the tempering and mean of the other; therefore it forms a range to be overcome by motion, not one to be joined by indivisibles.

The arguments are solved.

First you will object against the continuity of alteration: The motion of alteration in intensification cannot be continuous; therefore, the conclusion, which speaks of every alteration, is false. The antecedent is proved: What is produced through such a motion is some mode of ever-greater rootedness in the subject. But such modes are indivisible in themselves, as will be proved in the following question; therefore, they cannot terminate motion, since terminating it requires some divisibility and range in the terminus, so that a part of the terminus corresponds to a part of the motion, and an indivisible terminus to an indivisible motion.

It is confirmed, because every part of the motion truly and properly produces something. Therefore, something in the terminus of the motion must correspond to every part of the motion itself, and thus the terminus must have prior and posterior parts. Therefore, if every degree is something indivisible, at least formally the whole degree is produced by the first part of the motion, and nothing will be left for another part or the middle to produce.

It is answered that there is no contradiction in the parts of motion terminating at something indivisible, insofar as it is the terminus of the parts, just as the parts of a line terminate at an indivisible point. Similarly, in motion all the parts of motion terminate at the very having-been-moved, because all the parts of motion are in the process of becoming with respect to it. Indeed, every terminus must be indivisible and terminate divisible parts, not by inhering in each one singly and adequately, but inadequately in some indeterminate one, as we said in q. 20 of the Physics, art. 2,¹³ and thus, although it is not adequate to them informatively, it is adequate to them terminatively, since it is the terminus of them all. Thus, in a quality when it is intensified, some degree or terminus is acquired through motion. Although it is indivisible in itself, as a terminus, it nevertheless implies divisibility virtually, insofar as it presupposes parts and is their terminus. Therefore, divisibility is not required in the terminus in itself and formally, but by reason of the parts it terminates and that must be acquired successively through motion.

To the confirmation, it is answered that every part of motion produces something, namely that having-been-moved, but not every part of motion produces it adequately. Although that terminus is indivisible in itself, it terminates several things that can stand under it and regard it as their completed state. If it had prior and posterior parts, it would not be their terminus but their equal.¹⁴ Nor does the first part of motion produce the entire indivisible, or having-been-moved: both because there is no first part of motion there, where all the parts are indeterminate and confused, and because that middle portion produces the terminus inadequately, that is, as a partial becoming of it, not as its entire becoming.

Secondly, it is argued: In alteration and intensification there is not only one terminus, but several, which are acquired as the same action continues; therefore, there cannot be one motion, because there is not one terminus from which its unity can be taken. The antecedent is clear, because while the motion of alteration continues, several termini are produced, for example, several degrees in intensification or several intermediate qualities in alteration from one species to another. Therefore, the terminus is not one, and consequently neither is the motion; thus it will not be continuous.

It is confirmed: If alteration were continuous motion and lasted, for example, an hour, then at the end of the hour an infinite quality would have been produced, because there are infinitely many instants and consequently infinitely many having-been-moved states. Therefore, if intensification occurs throughout that hour, those infinitely many are attained, each of which increases the intensity and degree; consequently, at the end of the hour the quality would become infinite.

It is answered that in continuous alteration there is one adequate terminus, although there are several inadequate termini. The adequate terminus has unity by reason of the last terminus at which the motion stops and to which the others are ordered. So too, in local motion, when several places are reached up to the last, the unity of that continuous motion is taken from that last place; and therefore it is one simply, because it terminates simply in one, as we explained more fully in q. 19 of the Physics.¹⁵ Thus, at any instant a different inadequate place can be acquired. Between one instant and another, however, there is a transition from place to place, and then one is said to be in a place as in the process of changing, not in the having-been-moved, about which we spoke more fully there.

To the confirmation, it is answered first that the argument proceeds even if alteration is discrete motion, because just as within an hour there are infinitely many divisible parts, so there are infinitely many indivisible instants, in the same way as there are infinitely many parts. Therefore, although there is no motion or action between instants, the same difficulty remains: how does that intensification of the quality occur in the infinitely many instants contained within an hour, without becoming infinite? The answer, then, is that this infinity of instants and of the infinitely many parts contained in every continuum is potential infinity, not actual infinity, because it is an infinity contained and exhausted in aliquot and finite parts; therefore it is finite in actuality and only infinite potentially, as we showed more fully in q. 15¹⁶ and q. 20 of the Physics.¹⁷ For something to be actually infinite, it must consist of infinitely many aliquot parts, since those parts must be equal to a third thing and must not overlap one another. But those infinitely many parts are proportional, indeterminate, and overlapping one another, as we explained in the cited places. Instants, or indivisibles, are related in the same way: they multiply in the continuum together with the parts themselves and in the same manner. Hence they yield only potential infinity, that is, because the divisibility of the whole can be designated infinitely from any part; and so from the fact that intensification lasts for the whole hour it follows only that the quality has infinitely many potential parts and, similarly, indivisibles, but finitely many in actuality, since they are contained within the finite bounds of an hour.

Third, it is argued: If alteration is continuous motion, it cannot begin through a first being, but must begin through a last nonbeing, as other motions do; but this is impossible. Therefore, the conclusion follows.

The minor is proved as follows: If it begins through a last nonbeing, it is true to say, “Now the agent is not altering; immediately afterward it will alter.” At that “now,” then, either the agent is duly applied to the patient, in which case there is no reason it would not act once that application is posited; or it is not duly applied, in which case it will not act immediately afterward either, because the whole application cannot be completed immediately afterward, since it is divisible, being made through motion and in a divisible part. Thus, immediately afterward it will not be wholly applied in the completed state, and therefore the action will not follow. It is likewise unreasonable that a quality, which is a permanent thing, should not begin through a first being, especially since it is a determinate disposition in which a minimum must be assigned, and consequently something definite and determinate; therefore it must begin through a first being. Finally, it is confirmed that this seems to be Aristotle's intention in Book 8 of the Physics, text 23,¹⁸ where he says that “to say that the continuous is altered is to oppose the evident facts,” and adds that “alteration does not occur part by part like freezing, but suddenly, as when a stone is excavated by the last drop”—something that is evidently not continuous motion. Saint Thomas affirms the same in his commentary on the same place, lect. 5,¹⁹ in his commentary on Book 6 of the Physics, lect. 5,²⁰ in Summa contra Gentiles II, ch. 49, and elsewhere.

It is answered that without doubt alteration, like other motions, and the quality produced through it, begins through a last nonbeing. In reply to the proof, it is said that whether the agent's application to motion occurs in an instant or not, its being actually applied belongs to the having-been-moved and is in an instant. Yet it does not begin intrinsically in that instant, and so the inference does not properly follow: “The agent is actually applied in this instant; therefore, action or motion is intrinsically in this instant.” For it does not follow that the action is intrinsically in this instant unless the action itself is instantaneous; it is enough that it begin extrinsically, because it will occur immediately afterward. Therefore, motion need not follow upon the very being-applied except according to its nature: if something is applied in an instant, motion is not intrinsically given in that instant but immediately afterward, and thus it begins extrinsically in that instant, just as a heavy body, when generated upward, begins to move in that same instant not intrinsically but extrinsically. In fact, however, there is no first being-applied, just as there is no first having-been-moved in motion; for application is made through motion.

As to the claim that a quality is a permanent thing and therefore must begin through a first being, I distinguish. It is a permanent thing when it exists determinately in the completed state: I grant this; when it is in flux and becoming: I deny it. Or, secondly: that it is a permanent thing beginning in a permanent manner: I deny; beginning in a flowing and successive manner, after the manner of motion: I grant. In that case it conforms to its manner of coming to be, which is through motion, not to its proper manner of being, which it has in the completed state. A quality that is a disposition toward a substantial form, however, must express something determinate under that state of disposition, especially when speaking of the ultimate disposition. For other dispositions can have a range and indivisibility; that one, then, will begin in an instant, not in the manner of motion.

To the confirmation, it is answered that in the cited places Aristotle and Saint Thomas intend only to argue against certain ancient philosophers who held that everything is always moving and never at rest: alteration is not continuous motion, that is, it does not last perpetually, though this does not mean that it is discrete for as long as it lasts. When he says that alteration does not occur part by part but suddenly, this is understood of alteration with respect to its final effect and disposition, not of alteration absolutely and in itself.