by Aristotle
Clearly, then, for these reasons and also because the attributes mentioned are common to everything and universal, we must first take each of them in hand and discuss it. For the investigation of special attributes comes after that of the common attributes.
[25] To begin then, as we said, with motion.
Some things are in fulfilment only, others in potentiality and in fulfilment—one being a ‘this’, another so much, another such and such, and similarly for the other categories of being. The term ‘relative’ is applied sometimes with reference to [30] excess and defect, sometimes to agent and patient, and generally to what can move and what can be moved. For what can cause movement is relative to what can be moved, and vice versa.
There is no such thing as motion over and above the things. It is always with respect to substance or to quantity or to quality or to place that what changes changes. But it is impossible, as we assert, to find anything common to these which [201a1] is neither ‘this’ nor quantity nor quality nor any of the other predicates. Hence neither will motion and change have reference to something over and above the things mentioned; for there is nothing over and above them.
Now each of these belongs to all its subjects in either of two ways: namely, substance—the one is its form, the other privation; in quality, white and black; in [5] quantity, complete and incomplete. Similarly, in respect of locomotion, upwards and downwards or light and heavy. Hence there are as many types of motion or change as there are of being.
We have distinguished in respect of each class between what is in fulfilment [10] and what is potentially; thus the fulfilment of what is potentially, as such, is motion—e.g. the fulfilment of what is alterable, as alterable, is alteration; of what is increasable and its opposite, decreasable (there is no common name for both), increase and decrease; of what can come to be and pass away, coming to be and passing away; of what can be carried along, locomotion.
That this is what motion is, is clear from what follows: when what is buildable, [15] in so far as we call it such, is in fulfilment, it is being built, and that is building. Similarly with learning, doctoring, rolling, jumping, ripening, aging.
The same thing can be both potential and fulfilled, not indeed at the same time [20] or not in the same respect, but e.g. potentially hot and actually cold. Hence such things will act and be acted on by one another in many ways: each of them will be capable at the same time of acting and of being acted upon. Hence, too, what effects motion as a natural agent can be moved: when a thing of this kind causes motion, it is itself also moved. This, indeed, has led some people to suppose that every mover is [25] moved. But this question depends on another set of arguments, and the truth will be made clear later.20 It is possible for a thing to cause motion, though it is itself incapable of being moved.
It is the fulfilment of what is potential when it is already fulfilled and operates not as itself but as movable, that is motion. What I mean by ‘as’ is this: bronze is potentially a statue. But it is not the fulfilment of bronze as bronze which is motion. [30] For to be bronze and to be a certain potentiality are not the same. If they were identical without qualification, i.e. in definition, the fulfilment of bronze as bronze would be motion. But they are not the same, as has been said. (This is obvious in contraries. To be capable of health and to be capable of illness are not the same; for if they were there would be no difference between being ill and being well. Yet the [201b1] subject both of health and of sickness—whether it is humour or blood—is one and the same.)
We can distinguish, then, between the two—just as colour and visible are different—and clearly it is the fulfilment of what is potential as potential that is [5] motion.
It is evident that this is motion, and that motion occurs just when the fulfilment itself occurs, and neither before nor after. For each thing is capable of being at one time actual, at another not. Take for instance the buildable: the actuality of the buildable as buildable is the process of building. For the actuality must be either [10] this or the house. But when there is a house, the buildable is no longer there. On the other hand, it is the buildable which is being built. Necessarily, then, the actuality is the process of building. But building is a kind of motion, and the same account will apply to the other kinds also. [15]
2 · The soundness of this definition is evident both when we consider the accounts of motion that the others have given, and also from the difficulty of defining it otherwise.
One could not easily put motion and change in another genus—this is plain if [20] we consider where some people put it: they identify motion with difference or inequality or not being; but such things are not necessarily moved, whether they are different or unequal or non-existent. Nor is change either to or from these rather than to or from their opposites.
The reason why they put motion into these genera is that it is thought to be [25] something indefinite, and the principles in the second column21 are indefinite because they are privative: none of them is either a ‘this’ or such or comes under any of the other categories. The reason why motion is thought to be indefinite is that is cannot be classed as a potentiality or as an actuality—a thing that is merely capable [30] of having a certain size is not necessarily undergoing change, nor yet a thing that is actually of a certain size, and motion is thought to be a sort of actuality, but incomplete, the reason for this view being that the potential whose actuality it is is incomplete. This is why it is hard to grasp what motion is. It is necessary to class it with privation or with potentiality or with simple actuality, yet none of these seems [202a1] possible. There remains then the suggested mode of definition, namely that it is a sort of actuality, or actuality of the kind described, hard to grasp, but not incapable of existing.
Every mover too is moved, as has been said—every mover, that is, which is capable of motion, and whose immobility is rest (for when a thing is subject to [5] motion its immobility is rest). For to act on the movable as such is just to move it. But this it does by contact, so that at the same time it is also acted on. Hence motion is the fulfilment of the movable as movable, the cause being contact with what can move, so that the mover is also acted on. The mover will always transmit a form, [10] either a ‘this’ or such or so much, which, when it moves, will be the principle and cause of the motion, e.g. the actual man begets man from what is potentially man.
3 · The solution of the difficulty is plain: motion is in the movable. It is the fulfilment of this potentiality by the action of that which has the power of causing [15] motion; and the actuality of that which has the power of causing motion is not other than the actuality of the movable; for it must be the fulfilment of both. A thing is capable of causing motion because it can do this, it is a mover because it actually does it. But it is on the movable that it is capable of acting. Hence there is a single actuality of both alike, just as one to two and two to one are the same interval, and the steep ascent and the steep descent are one—for these are one and the same, [20] although their definitions are not one. So it is with the mover and the moved.
This view has a dialectical difficulty. Perhaps it is necessary that there should be an actuality of the agent and of the patient. The one is agency and the other patiency; and the outcome and end of the one is an action, that of the other a passion. Since [25] then they are both motions, we may ask: in what are they, if they are different? Either both are in what is acted on and moved, or the agency is in the agent and the patiency in the patient. (If we ought to call the latter also ‘agency’, the word would be used in two senses.)
Now, in the latter case, the motion will be in the mover, for the same account will hold of mover and moved. Hence either every mover will be moved, or, though [30] having motion, it will not be moved.
If on the other hand both are in what is moved and acted on—both the agency and the patiency (e.g. both teaching and learning, though they are two, in the learner), then, first, the actuality of each will not be present in each, and, a second absurdity, a thing wil
l have two motions at the same time. How will there be two [35] alterations of quality in one subject towards one form? The thing is impossible: the actualization will be one.
But (someone will say) it is contrary to reason to suppose that there should be [202b1] one identical actualization of two things which are different in kind. Yet there will be, if teaching and learning are the same, and agency and patiency. To teach will be the same as to learn, and to act the same as to be acted on—the teacher will necessarily be learning everything that he teaches, and the agent will be acted on. [5] It is not absurd that the actualization of one thing should be in another. Teaching is the activity of a person who can teach, yet the operation is performed in something—it is not cut adrift from a subject, but is of one thing in another.
There is nothing to prevent two things having one and the same actualization (not the same in being, but related as the potential is to the actual). [10]
Nor is it necessary that the teacher should learn, even if to act and to be acted on are one and the same, provided they are not the same in respect of the account which states their essence (as raiment and dress), but are the same in the sense in which the road from Thebes to Athens and the road from Athens to Thebes are the same, as has been explained above. For it is not things which are in any way the [15] same that have all their attributes the same, but only those to be which is the same. But indeed it by no means follows from the fact that teaching is the same as learning, that to learn is the same as to teach, any more than it follows from the fact that there is one distance between two things which are at a distance from each other, that being here at a distance from there and being there at a distance from here are one and the same. To generalize, teaching is not the same as learning, or agency as patiency, in the full sense, though they belong to the same subject, the [20] motion; for the actualization of this in that and the actualization of that through the action of this differ in definition.
What then motion is, has been stated both generally and particularly. It is not difficult to see how each of its types will be defined—alteration is the fulfilment of the alterable as alterable (or, more scientifically, the fulfilment of what can act and [25] what can be acted on, as such)—generally and again in each particular case, building, healing. A similar definition will apply to each of the other kinds of motion.
4 · The science of nature is concerned with magnitudes and motion and time, [30] and each of these is necessarily infinite or finite, even if some things are not, e.g. a quality or a point—it is not necessary perhaps that such things should be put under [35] either head. Hence it is incumbent on the person who treats of nature to discuss the infinite and to inquire whether there is such a thing or not, and, if there is, what it is.
[203a1] The appropriateness to the science of this problem is clearly indicated; for all who have touched on this kind of science in a way worth considering have formulated views about the infinite, and indeed, to a man, make it a principle of things.
Some, as the Pythagoreans and Plato, make the infinite a principle as a [5] substance in its own right, and not as an accident of some other thing. Only the Pythagoreans place the infinite among the objects of sense (they do not regard number as separable from these), and assert that what is outside the heaven is infinite. Plato, on the other hand, holds that there is no body outside (the Forms are not outside, because they are nowhere), yet that the infinite is present not only in the objects of sense but in the Forms also.
[10] Further, the Pythagoreans identify the infinite with the even. For this, they say, when it is cut off and shut in by the odd, provides things with the element of infinity. An indication of this is what happens with numbers. If the gnomons are placed round the one, and without the one, in the one construction the figure that [15] results is always different, in the other it is always the same. But Plato has two infinites, the Great and the Small.
The physicists, on the other hand, all of them, regard the infinite as an attribute of a substance which is different from it and belongs to the class of the so-called elements—water or air or what is intermediate between them. Those who make them limited in number never make them infinite in amount. But those who [20] make the elements infinite in number, as Anaxagoras and Democritus do, say that the infinite is continuous by contact—compounded of the homogeneous parts according to the one, of the seedmass of the atomic shapes according to the other.
Further, Anaxagoras held that any part is a mixture in the same way as the whole, on the ground of the observed fact that anything comes out of anything. For [25] it is probably for this reason that he maintains that once upon a time all things were together. This flesh and this bone were together, and so of any thing; therefore all things—and at the same time too. For there is a principle of separation, not only for each thing, but for all. Each thing that comes to be comes to be from a similar body, and there is a coming to be of all things, though not, it is true, at the same time. [30] Hence there must also be a principle of coming to be. One such source there is which he calls Mind, and Mind begins its work of thinking from some principle. So necessarily all things must have been together at a certain time, and must have begun to be moved at a certain time.
Democritus, for his part, asserts that no element arises from another element. [203b1] Nevertheless for him the common body is a principle of all things, differing from part to part in size and in shape.
It is clear then from these considerations that the inquiry concerns the student of nature. Nor is it without reason that they all make it a principle. We cannot say that the infinite exists in vain, and the only power which we can ascribe to it is that [5] of a principle. For everything is either a principle or derived from a principle. But there cannot be a principle of the infinite, for that would be a limit of it. Further, as it is a principle, it is both uncreatable and indestructible. For there must be a point at which what has come to be reaches its end, and also a termination of all passing away. That is why, as we say, there is no principle of this, but it is this which is held [10] to be the principle of other things, and to encompass all and to steer all, as those assert who do not recognize, alongside the infinite, other causes, such as Mind or Friendship. Further they identify it with the Divine, for it is deathless and imperishable as Anaximander says, with the majority of the physicists. [15]
Belief in the existence of the infinite comes mainly from five considerations: From the nature of time—for it is infinite; From the division of magnitudes—for the mathematicians also use the infinite; again, if coming to be and passing away do not give out, it is only because that from which things come to be is infinite; again, [20] because the limited always finds its limit in something, so that there must be no limit, if everything is always limited by something different from itself. Most of all, a reason which is peculiarly appropriate and presents the difficulty that is felt by everybody—not only number but also mathematical magnitudes and what is [25] outside the heaven are supposed to be infinite because they never give out in our thought.
If what is outside is infinite it seems that body also is infinite, and that there is an infinite number of worlds. Why should there be body in one part of the void rather than in another? Grant only that mass is anywhere and it follows that it must be everywhere. Also, if void and place are infinite, there must be infinite body too; for in the case of eternal things what may be is. [30] But the problem of the infinite is difficult: many contradictions result whether we suppose it to exist or not to exist. If it exists, we have still to ask how it exists—as a substance or as the essential attribute of some entity? Or in neither way, yet none the less is there something which is infinite or some things which are infinitely many?
The problem, however, which specially belongs to the physicist is to investigate [204a1] whether there is a sensible magnitude which is infinite.
We must begin by distinguishing the various ways in which the term ‘infinite’ is used: in one way, it is applied to what is incapable of being gone
through, because it is not its nature to be gone through (the way in which the voice is invisible); in another, to what admits of a traversal which cannot be completed, or which can only [5] be completed with difficulty, or what naturally admits of a traversal but does not have a traversal or limit.
Further, everything that is infinite may be so in respect of addition or division or both.
5 · Now it is impossible that the infinite should be a thing which is in itself infinite, separable from sensible objects. If the infinite is neither a magnitude nor an aggregate, but is itself a substance and not an accident, it will be indivisible; for the [10] divisible must be either a magnitude or an aggregate. But if indivisible, then not infinite, except in the way in which the voice is invisible. But this is not the way in which it is used by those who say that the infinite exists, nor that in which we are investigating it, namely as that which cannot be gone through. But if the infinite is [15] accidental, it would not be, qua infinite, an element in things, any more than the invisible would be an element of speech, though the voice is invisible.
Further, how can the infinite be itself something, unless both number and magnitude, of which it is an essential attribute, exist in that way? If they are not substances, a fortiori the infinite is not.
[20] It is plain, too, that the infinite cannot be an actual thing and a substance and principle. For any part of it that is taken will be infinite, if it has parts; for to be infinite and the infinite are the same, if it is a substance and not predicated of a subject. Hence it will be either indivisible or divisible into infinites. But the same [25] thing cannot be many infinites. (Yet just as part of air is air, so a part of the infinite would be infinite, if it is supposed to be a substance and principle.) Therefore the infinite must be without parts and indivisible. But this cannot be true of what is infinite in fulfilment; for it must be a definite quantity.