Chapter 9

The concept and possibility of operation

1201. When we conceive a determined ens, we simultaneously conceive an act, that is, the act of its existence. This act is simple and lasts as long as the ens. It is, therefore, one of the acts we call 'immanent'.

1202. But is conceiving an ens and conceiving the act of its existence one and the same?
The act of the existence of an ens does not differ from the ens itself except through certain relationships which our mind adds to it.

1. When we say act, we add to it a relationship with potency, to which the concept of act is correlative through opposition.

2. When we say ens, we conceive a completed, finalised act. When, however, we say act of being, we conceive mentally or imagine we conceive the entire path by which an ens has been unnatured. In the act itself, we distinguish a certain kind of principle (the initial act), a means, and an end in which the being rests as complete and absolute. This explains certain sayings of philosophers, such as 'in an act, there is not yet act', and so on.

3. Moreover, the act itself of being is conceived by us as preceded or followed necessarily by certain other immanent acts, as we shall explain soon.

1203. When an ens is constituted with all its necessary, immanent acts, we then think, as a result of our experience, that the ens now has its complete act of existence and that it moves towards other acts which are also called its actions and operations. The act of existence and even the immanent acts which normally accompany it are usually called first acts; subsequent acts are usually called transient, second acts.

1204. The nature of the transient act consists in the passage made by an ens from one state to another. This may happen in an instant, or last for a while in some continuous motion. The characteristic of the transient act, therefore, is passage; it is unceasing motion.

1205. An immanent act is one that endures along with an ens until there is some kind of substantial change. Amongst immanent acts, the act of existence is certainly the first, as we said.
Nevertheless, we do find, other than the act through which a given being exists, other immanent acts which can be divided into two classes.

1. Immanent acts which precede (not in chronological order, but in the intrinsic order of ennaturation) the act of being. For example, we saw that the act of being proper to human nature, that is, the act of the rational principle, results from two preceding acts (as it were, from its form and its matter). One of these acts is the intellective act, the other the act of the fundamental animal-feeling. These acts also are immanent.

2. Immanent acts which follow the act of being, but which are indivisibly joined with it. For example, the stable accidents of a substance, such as, habits.

1206. There are, therefore, three classes of immanent acts: 1. those which precede the act of being in an ens; 2. the act of being; and 3. those which are subsequent to the act of being and remain stable.

1207. Moreover, analysis and abstraction often split up an act further as a result of the different relationships under which they consider it. Consequently, immanent acts are multiplied in language and in human conception.

1208. Great minds first began to raise highly difficult questions in Italy, the homeland of dialectic. Here, it was first understood that it was not as easy to explain as to accept what the whole world admitted, that is, operations of entia as transient acts. It was not easy to reconcile these acts with other truths administered by human thought. But truth, as we know, cannot be split in two or contradict itself.

1209. The difficulty, clearly perceived by the ancient Italian philosophers, was relative to the popular concept of transient acts, according to which 'the transient act, continually changing, endures for some time.' This concept of continual change involved insuperable difficulties which, when subjected to extremely subtle dialectic by the illustrious school of Elea, disturbed the whole field of philosophy. The battle, which flared up on several occasions, always ended through exhaustion on the part of the adversaries, never as a result of some decisive victory. It seems to me that these arguments contain something solid. Five of them can profitably be used against the continuity of an act.

Arguments against continual change presupposed in the transient act

1210. I. Argument. - If, during its transient act, an ens changes continually, none of the states which it undergoes successively during these changes has duration of any kind whatsoever. But that which does not endure, is not. Consequently, none of its successive states is. Hence, the concept of continual change is absurd.

1211. II. Argument. - If the transient act, taken as a whole, has some duration, during which an ens changes its state continually, the number of the successive states it takes does not exist, because a number of instances does not exist. For example, take any number of instances you wish that, put together, may form some duration.(117) If there is no number of states for the ens to pass through, it is absurd to think that it can pass through them. To pass through different states, there must be a determined number of states because there is nothing given in nature which is not determined. Hence, continual change involves absurdity. It is, therefore, impossible.

1212. III. Argument. - But perhaps a given duration is actually divisible ad infinitum. If this were so, it would be possible to have an infinite number (this is certainly absurd despite its being affirmed by great men such as Leibniz!). In this case, I would have to ask if each of this infinite number of parts (into which, it is claimed, duration can be divided) endures a short time or no time at all. It must be one or the other. If each part endures, we would need an infinite time to move through an infinite number of durations, no matter how small they may be. In this case, the transient act would never be completed. This is one of Zeno's arguments against continuous motion [App., no. 7]. If, however, each part of the duration does not in any way endure but is an instant, the transient act would have no duration, which is against the hypothesis. Infinite instants, each of which has a duration equal to zero, give only a duration equal to zero when added together.

1213. IV. Argument - Bodies which move with continuous motion can never move with different speeds. If we suppose that a body is not stationary anywhere, it must pass from one place to another at the greatest speed; we cannot conceive any speed greater than that which passes without cessation from one place to another because it does not lose even the slightest time in passing.

1214. V. Argument - I take this argument from the time which motion requires to communicate itself to all parts of a body. Almost all physicists hold as indubitable that this communication requires time; it is not done in an instant. This, for example, is the reason why a bullet fired from a gun makes a hole in a plank. The extreme velocity of the bullet breaks the cohesion of the parts of the wood which it strikes. The time the bullet takes to do this is less than the time required for the motion to be communicated to the whole plank which, therefore, remains stationary. This indubitable fact provides two arguments which prove equally that motion is not continuous.

The first of these arguments affirms that if motion were communicated without pause to the places through which it passes, the total time employed would have to be nothing because the sum of so many zeros equals zero. In fact, an instant does not endure; it has zero duration only. But because this argument is similar to the preceding, I consider it simply as confirmation of what has gone before.

The second argument, however, is new and runs as follows. My supposition is that we have a perfectly hard body which receives an impetus to motion from another perfectly hard, moving body. The first body does not move until the impetus has been communicated successively to all its parts. For this communication to take place, some time is required, as we have seen. The length of time depends on the size of the two bodies and the speed of the body which imparts the impetus. During this time, the hard body receiving the impetus resists the moving body which provides the impetus. For a brief moment, the moving body is halted; then, both bodies, the one which strikes and the one which is struck, continue to move according to the laws of motion.

Here we have an undoubted case of rest during the seemingly continuous movement of the first body. We have, therefore, motion, then rest for a moment, then motion again. But according to the law of inertia a body when at rest remains at rest unless there is a new cause of motion. The fact that we have indicated is opposed to this law. We have to say, therefore, that there is some kind of pause and rest which harmonises very well with the motion we think continuous, and to which we apply the law of inertia.(118) Moreover, if the body which is struck is unable to move until the impetus has been propagated to all its parts, and if the propagation of the impetus is not halted at any point (as supposed by those who believe motion to be continuous), motion would be impossible. If communicated to a point in an instant, it would either produce movement immediately or, if there were some obstacle to motion, it would be smothered and wiped out. In fact, it is necessary for the impetus to be retained in the individual parts and points of the body for the whole time needed for all the parts to acquire the same impetus, and thus be moved together. Each part of the body, therefore, which receives the impetus waits for some time before beginning its effective motion. After this time, motion begins.

Consequently, the communication of motion itself, but not of the impetus [App., no. 8], is made to each part of the struck body in a given time, not in an instant. But all bodies, however small, have some continuous extended element. The same thing must happen in all of them, therefore. Motion is not communicated to any body in an instant, but with some interval of rest.
What can we say about these arguments? - As far as I can see, they are insoluble. Each contains a demonstration that the transient act is not carried out by means of continual change, but in instants between each of which there is some duration. I have already demonstrated this when I denied the continuity of real movement,(119) despite its phenomenal continuity.

1215. Minds unaccustomed to philosophical speculation have immense difficulty in conceiving how the movement of some real being, that is, change in the transient act, is not continual. People tend to believe in the phenomena of their senses to such an extent that they cannot think anything as possible which does not appear to their senses. It is not to be wondered, therefore, that we hear so often: 'Observation shows us that movement is continuous and, as you yourself constantly say, we cannot go against facts which we observe.' It is very difficult to convince people that observation cannot decide the question under discussion. We are dealing with something beyond all sensible observation - something which cannot be proved by observation. As we know, every size smaller than a given measure escapes our sense.

1216. Let us imagine that I succeed in persuading these people that observation can tell us nothing about those measurements of space, of time, and of motion which are so small, as they must be in our case, that human sensitivity is unable to perceive them,(120) or at least that no mental advertence is capable of considering them in feeling, even if feeling provided them. People would then ask: 'How therefore is it possible to conceive a transient act or some real movement done at intervals?' This question, however, is not drawn from observation, but from reasoning which considers the possibility of non-sensible things. It would be sufficient to reply that there is nothing to demonstrate the impossibility of what we have suggested, even if we do not know how to explain the way it occurs. Moreover, if there are two opposite opinions and we have shown the absurdity of one, but not of the other, we have to hold the second and reject the first. It would be sufficient, I say. Nevertheless, it would not persuade the majority who have little faith in what reason demonstrates. To assist such weakness of spirit, which withholds simple, firm assent to speculative proofs contrasting with sensible appearances, I shall first show that sight, to which we normally give credence when it gives or seems to give witness to the continuity of the motion of a body (the same reasoning can then be applied to the other senses) does not and cannot properly speaking witness to the continuity of motion.

1217. It is indeed a fact acknowledged by all physicists and provided by experience that sight sensations have some duration in the optic sensory. They do not pass in an instant. If this were not a truth of indubitable experience, the necessity of duration could be demonstrated by considering that sensations which had no duration could not exist. But we do not need such a proof from reason.

However, although all optic sensations last some time, people normally think them instantaneous because their duration is very limited. But, granted the truth that every optic sensation has some tiny duration, it follows inevitably that the eye cannot witness in any way to continuous movement because it cannot testify to what it does not see. Continuous movement is in fact a continual change of place in such a way that a body never comes to halt in any place. If continuous movement were to be seen, the eye would have to have a succession of different sensations, each of which possesses no duration at all. But this is not what happens. When a person thinks he sees a body in continuous movement, the eye experiences only a series of sensations. Each of these sensations follows on from another (or with an insensible interval); each of them lasts a small time. Hence even phenomenal motion, which is sensible to the eye, is reduced to a series of states of what is movable. Each of these states lasts a little time. The mistake is in our mental advertence when, by neglecting to observe those minute durations, we suppose that one follows another without any interruption [App., no. 9].

Starting from these principles, natural scientists eventually invented some ingenious gadgets with which they made it seem to the eye that a body was moving. They did this simply by successively placing before sight a certain number of bodies, each of which appeared with the same form in places very near each other. The body which appeared first seemed no distance at all from the succeeding body. But all these equal bodies presented successively to sight in extreme proximity are taken for a single body moving with continuous motion. This device enables us to compose any apparent motion whatsoever, linear or circular, etc., although the body which apparently moves is not in fact identical, but a complex of several equal bodies seen in different places and representing the motion that we take for continuous.

1218. This experiment alone is a sufficient reply to the somewhat indiscreet question: 'How is it possible for a body to pass from one place to another without moving continuously through all the intermediate spaces?' The question is sufficiently answered when we demonstrate the possibility of motion's appearing continuous to sight without actually being such. This possibility has been demonstrated provided we have proved the fact in a single case.
Nevertheless, I want to offer another experiment, one amongst many provided by physics, principally astronomy.

When a person passes in front of a mirror, the movement of the image corresponds to the motion of the person. Both motions seem continuous. But how does the apparent motion of the image come about? It certainly does not pass from one place to another. This appearance is produced by means of continually new rays of light which depict ever-new images, that is, physically different images, on the mirror when previous images have vanished; nevertheless, the same image seems to walk and pass in front of the mirror. Hence, the phenomenon of the continuity of motion can be explained without any absolute necessity that all the points of a given, moving body should touch the intermediate points of the space through which the body passes, or seems to pass.

1219. A time will come perhaps when we will be able to appeal in favour of this teaching to intermittent light, suspected by some physicists although not fully demonstrated. For the moment, I want to offer a final objection.

1220. The examples I have used show clearly that the phenomenon of continuous motion can arise without any actual motion. This comes about as equal, multiple bodies are substituted successively for one another. This applies also to equal, multiple operations. Now, is it possible that moving bodies do not retain their identity, as Leibniz said? He supposed that the full and empty areas of space were made up of immovable matter, which constituted infinite space. This matter hardened itself, as it were, successively, and thus appeared as an identical, moving body.

This supposition, although extraordinary to normal thought which restricts itself to the phenomenon without investigating reasons and causes, has never been shown absurd, still less factually false. It is a metaphysical question which leaves physical things as they are, whatever solution is given. Consequently, it can scarcely be proved true or false with physical arguments.

1221. Leaving aside an examination of Leibniz's supposition, I want to ask if the elements making up the identity of a body have been clearly defined. This is a more difficult question than appears at first sight. I shall deal with it briefly here, but in a way sufficient for our purpose. Two things are distinguished in body: extension and force. When a body moves, it is certain that extension is changed; the body changes place, and one place, which is always outside another, is never identical with the other. This truth may not be understood if we are prejudiced by the thought that a body carries around its own extension, as though extension could be moved from one place to another, or as though the extension of a body and that of the place occupied by the body were two extensions rather than a single, extremely simple extension. It is the measure of quantity of extension, which is always preserved identical by a body, which leads our thought in this direction. Extension itself, however, changes. It constantly takes on another extension, although one of equal measure with that previously present. Because the different extensions in which the body successively expands are totally equal in size and uniform in quality, the illusion is easily aroused of some extension adhering to and carried around by the body.

1222. The identity of body, therefore, cannot consist in any element except bodily force. This, however, is only the term of an act of the hidden agent I have called corporeal principle, which can only be simple. But the identity of the term of an act consists in this: the term is equal in everything. We are looking for a specific identity in relationship with the act, because the term is constituted by this essential relationship. Thus, if I smell a rose one hundred times, these acts although numerically different have a specifically identical term. They always terminate in the same sensation of the scent of the rose, granted that this sensation is invariable. In all these acts, we have no other sensation than that of the scent of the rose. This scent is referred to multiple acts.

Now, the corporeal principle is simple and as such can embrace the whole of space in a single moment (as we have seen in the case of the sentient principle). In our case, if the corporeal principle were to actuate a body intermittently, it could make the body appear successively in tightly packed places in such a way that these places appeared continuous and uninterrupted. Thus, the body would appear to move with continuous movement, although this would not in fact be the case. Nevertheless, it would be the same body because it is a totally equal term of the intermittent acts of the simple, corporeal principle. The individual diversity that the body could possess would be wholly indiscernible. If, however, we were dissatisfied with maintaining a specific identity for each body, and required numerical identity, there would be no difficulty. The sensiferous force could be considered as an identical power of the corporeal principle, a power which operated intermittently and in a way unobservable by sense.

1223. My conclusion is that transient acts are formed in an instant, or are a complex of lesser acts formed in very close instants between which there is a tiny duration totally unobservable by human beings.

Notes

(117) Aristotle knew that the continuum in space, in time, and in motion cannot result from an aggregate of indivisible things. The great philosopher's argument for this can be found in the sixth book of Physics , and is worth reading.

(118) If we suppose the body which is struck to be of immense size, the two bodies will be halted for a noticeable period. Indeed, this respite can last as long as we wish because we can imagine the body which is struck to be as big as we like.

(119) NE , vol. 2, 813-819.

(120) Sense, in perceiving the continuum in space (where it is certainly found) also perceives as a result every small space assignable in a space of significant dimension. This, however, does not mean that it perceives every minimum space separated and isolated from a greater space.