by Aristotle
Since there is a science of being qua being and capable of existing apart, we must consider whether this is to be regarded as the same as natural science or rather [30] as different. Natural science deals with the things that have a principle of movement in themselves; mathematics is theoretical, and is a science that deals with things that are at rest, but its subjects cannot exist apart. Therefore about that which can exist apart and is unmovable there is a science different from both of these, if there is a substance of this nature (I mean separable and unmovable), as we [35] shall try to prove there is. And if there is such a kind of thing in the world, here must surely be the divine, and this must be the first and most important principle. Evidently, then, there are three kinds of theoretical sciences—natural science, [1064b1] mathematics, theology. The class of theoretical sciences is the best, and of these themselves the last named is best; for it deals with the highest of existing things, and each science is called better or worse in virtue of its proper object. [5]
One might raise the question whether the science of being qua being is to be regarded as universal or not. Each of the mathematical sciences deals with some one determinate class of things, but universal mathematics applies alike to all. Now if natural substances are the first of existing things, natural science must be the first [10] of sciences; but if there is another entity and substance, separable and unmovable, the science of it must be different and prior to natural science, and universal because it is prior.
8 · Since things are said to be, without qualification, in several ways, of [15] which one is being by accident, we must consider first that which is in this sense. Evidently none of the traditional sciences busies itself about the accidental. For neither does building consider what will happen to those who are to use the house (e.g. whether they will have a painful life in it or not), nor does weaving, or [20] shoemaking, or the confectioner’s art, do the like; but each of these sciences considers only what is peculiar to it, i.e. its proper end. And as for the argument that when he who is musical becomes lettered he will be both at once, not having been [25] both before; and that which is, not having always been, must have been coming to be; therefore he must have been at once becoming musical and lettered,—this none of the recognized sciences considers, but only sophistic; for this alone busies itself about the accidental, so that Plato was not wrong when he said that the sophist spends his time on non-being.
[30] That a science of the accidental is not even possible, will be evident if we try to see what the accidental really is. We say that everything either is always and of necessity (necessity not in the sense of violence, but that which we appeal to in [35] demonstrations), or is for the most part, or is neither for the most part, nor always and of necessity, but merely as it chances; e.g. there might be cold in the dog-days, but this occurs neither always and of necessity, nor for the most part, though it [1065a1] might happen sometimes. The accidental, then, is what occurs, but not always nor of necessity, nor for the most part. Now we have said what the accidental is, and it is obvious why there is no science of such a thing; for all science is of that which is [5] always or for the most part, but the accidental is in neither of these classes.
Evidently there are not causes and principles of the accidental, of the same kind as there are of what is in its own right; for if there were, everything would be of necessity. If A is when B is, and B is when C is, and if C exists not by chance but of [10] necessity, that of which C was cause will exist of necessity, down to the last mentioned of the things caused (but this was supposed to be accidental). Therefore all things will be of necessity, and chance and the possibility of a thing’s either occurring or not occurring are removed entirely from the range of events. And if the [15] cause be supposed not to exist but to be coming to be, the same results will follow; everything will occur of necessity. For tomorrow’s eclipse will occur if A occurs, and A if B occurs, and B if C occurs; and in this way if we subtract time from the limited time between now and tomorrow we shall come sometime to the already existing [20] condition. Therefore since this exists, everything after this will occur of necessity, so that all things occur of necessity.
As to that which is in the sense of being true or of being by accident, the former depends on a combination in thought and is an affection of thought (which is the reason why it is the principles, not of that which is in this sense, but of that which is outside and can exist apart, that are sought); and the latter is not necessary but [25] indeterminate (I mean the accidental); and of such a thing the causes are unordered and indefinite.
The ‘for the sake of something’ is found in events that happen by nature or as the result of thought. It is chance when one of these events happens by accident. For as a thing may exist, so it may be a cause, either by its own nature or by accident. [30] Chance is a cause accidentally among those of events that happen for the sake of something which are in accordance with choice. Therefore chance and thought are concerned with the same sphere; for choice cannot exist without thought. The causes from which chance results might happen are indeterminate; therefore chance is obscure to human calculation and is a cause by accident, but in the unqualified sense a cause of nothing. It is good or bad luck when the result is good or [1065b1] evil; and prosperity or misfortune when the scale is large.
Since nothing accidental is prior to the essential, neither are accidental causes prior. If, then, chance or spontaneity is a cause of the heavens, reason and nature are causes before it.
9 · Some things exist only actually, some potentially, some potentially and [5] actually—some as beings, some as quantities, others in the other categories. There is no movement apart from things; for change is always according to the categories of being; and there is nothing common to these and in no one category; but each of the categories belongs to all its subjects in either of two ways (e.g. ‘thisness’—for [10] one kind of it is form, and the other is privation; and as regards quality one kind is white and the other black, and as regards quantity one kind is complete and the other incomplete, and as regards spatial movement one is upwards and the other downwards, or one thing is light and another heavy); so that there are as many kinds of movement and change as of being. Each kind of thing being divided into the [15] potential and the fulfilled, I call the actuality of the potential as such, movement. That what we say is true, is plain from the following facts. When the buildable, in so far as we call it such, exists actually, it is being built, and this is the process of building. Similarly with learning, healing, and rolling, walking, leaping, ageing, ripening. Movement takes place when the fulfillment itself exists, and neither [20] earlier nor later. The fulfillment then, of that which is potentially, when it is fulfilled and actual, not qua itself, but qua movable, is movement. By qua I mean this: bronze is potentially a statue; but yet the fulfillment of bronze, qua bronze, is [25] not movement. For it is not the same to be bronze and to be a certain potentiality. If it were absolutely the same in its formula, the fulfillment of bronze would have been a movement. But it is not the same. This is evident in the case of contraries; for to be capable of health and to be capable of illness are not the same; for if they were, health and illness would have been the same. (It is that which underlies and is [30] healthy or sick, whether it is moisture or blood, that is one and the same.) And since they are not the same, as colour and the visible are not the same, it is the fulfillment of the potential as such, that is movement. Evidently it is this, and movement takes place when the fulfillment itself exists, and neither earlier nor later. For each thing is capable of being sometimes actual, sometimes not, e.g. the buildable qua [1066a1] buildable; and the actuality of the buildable qua buildable is building. For the actuality is either this—building—or the house. But when the house exists, it is no longer buildable; the buildable is being built. The actuality then must be the [5] building, and the building is a movement. And the same account applies to all other movements.
That what we have said is right, is evident from what all othe
rs say about movement, and from the fact that it is not easy to define it otherwise. For firstly one cannot put it in another class. This is evident from what people say. Some call it [10] difference and inequality and the unreal; none of these, however, is necessarily moved, and further, change is not to these nor from these but rather from opposite to opposite. The reason why people put movement in these classes is that it is thought to be something indefinite, and the principles on one side of the list of contraries are indefinite because they are privative, for none of them is either a ‘this’ [15] or a ‘such’ or in any of the other categories. And the reason why movement is thought to be indefinite is that it cannot be classed either with the potentiality of things or with their actuality, for neither that which is capable of being of a certain [20] quantity, nor that which is actually of a certain quantity, is moved of necessity. And movement is thought to be an actuality, but incomplete; the reason is that the potential, whose actuality it is, is incomplete. And therefore it is hard to grasp what movement is; for it must be classed either with privation or with potentiality or with absolute actuality, but evidently none of these is possible. Therefore what remains is [25] that it must be what we said—actuality, i.e. actuality in the sense we have defined—which is hard to understand but capable of existing.
And evidently movement is in the movable; for it is the fulfillment of this by that which is capable of causing movement. And the actuality of that which is capable of causing movement is no other than that of the movable. For it must be [30] the fulfillment of both. For a thing is capable of causing movement because it can do this, and is a mover because it is active; but it is on the movable that it is capable of acting, so that the actuality of both alike is one, just as there is the same interval from one to two as from two to one, and as the ascent and the descent are one, but being them is not one; the case of the mover and the moved is similar.
[35] 10 · The infinite is either that which is incapable of being traversed because it is not its nature to be traversed (as the voice is invisible), or that which admits only of incomplete traverse or scarcely admits of traverse, or that which, though it naturally admits of traverse, is not traversed or limited; further, a thing may be [1066b1] infinite in respect of addition or of subtraction or of both. The infinite cannot be a separate, independent thing. For if it is neither a spatial magnitude nor a plurality, but infinity itself is its substance and not an accident, it will be indivisible; for the [5] divisible is either magnitude or plurality. But if indivisible, it is not infinite, except as the voice is invisible; but people do not mean this, nor are we examining this sort of infinite, but the infinite as untraversable. Further, how can an infinite exist by itself, unless number and magnitude also exist by themselves,—since infinity is an attribute of these? Further, if the infinite is an accident of something else, it cannot [10] be qua infinite an element in things, as the invisible is not an element in speech, though the voice is invisible. And evidently the infinite cannot exist actually. For then any part of it that might be taken would be infinite; for to be infinite and the infinite are the same, if the infinite is substance and not predicated of a subject. Therefore it is either indivisible, or if it can be divided, it is divisible into infinite [15] parts; but the same thing cannot be many infinites, yet as a part of air is air, so a part of the infinite would be infinite, if the infinite is a substance and a principle. Therefore it must be inseparable and indivisible. But the actually infinite cannot be indivisible; for it must be a quantity. Therefore infinity belongs to a subject [20] incidentally. But if so, as we have said, it cannot be a principle, but rather that of which it is an accident—the air or the even number.
This inquiry is universal; but that the infinite is not among sensible things, is evident from the following argument. If the formula of body is that which is bounded by planes, there cannot be an infinite body either sensible or intelligible; nor a separate and infinite number, for number or that which has a number can be [25] counted. The following considerations drawn from natural science make matters clear: the infinite can neither be composite nor simple. For it cannot be a composite body, since the elements are limited in multitude. For the contraries must be equal and no one of them must be infinite; for if one of the two bodies falls at all short of the other in capacity, the finite will be destroyed by the infinite. And that each [30] should be infinite is impossible. For body is that which has extension in all directions, and the infinite is the boundlessly extended, so that the infinite body will be infinite in every direction. Nor can the infinite body be one and simple—neither, as some say, something which is apart from the elements, from which they generate [35] these (for there is no such body apart from the elements; for everything can be resolved into that of which it consists, but no such thing is observed except the simple bodies), nor fire nor any other of the elements. For apart from the question [1067a1] how any of them could be infinite, the universe, even if it is finite, cannot either be or become one of them, as Heraclitus says all things sometime become fire. The same argument applies to the One, which the natural philosophers posit besides the [5] elements. For everything changes from the contrary, e.g. from hot to cold.
Further, every sensible body is somewhere, and whole and part have the same proper place, e.g. the whole earth and part of the earth. Therefore if the infinite body is homogeneous, it will be unmovable or it will be always moving. But the latter is impossible; for why should it rather move down than up or anywhere else? [10] E.g. if there is a clod, where will this move or rest? The proper place of the body which is homogeneous with it is infinite. Will the clod occupy the whole place, then? And how? When then is its rest or its movement? It will either rest everywhere, and then it cannot move; or it will move everywhere, and then it cannot be still. But if the infinite body has unlike parts, the proper places of the parts are unlike also, and, [15] firstly, the body of the universe is not one except by contact, and, secondly, the parts will be either finite or infinite in kind. Finite they cannot be; for then those of one kind will be infinite and those of another will not (if the universe is infinite), e.g. fire or water would be infinite, but such an infinite part would be destruction to its [20] contrary. But if the parts are infinite and simple, their places also are infinite and the elements will be infinite; and if this is impossible, and the places are finite, the universe also must be limited.
In general, there cannot be an infinite body and also a proper place for all bodies, if every sensible body has either weight or lightness. For it must move either towards the middle or upwards, and the infinite—either the whole or the [25] half—cannot do either; for how will you divide it? Or how will part of the infinite be up and part down, or part extreme and part middle? Further, every sensible body is in a place, and there are six kinds of place, but these cannot exist in an infinite body. [30] In general, if there cannot be an infinite place, there cannot be an infinite body; for that which is in a place is somewhere, and this means either up or down or in one of the other directions, and each of these is a limit.
The infinite is not the same in the sense that it is one thing whether exhibited in magnitude or in movement or in time, but the posterior among these is called [35] infinite in virtue of its relation to the prior, i.e. a movement is called infinite in virtue of the distance covered by the spatial movement or alteration or growth, and a time is called infinite because of the movement which occupies it.
[1067b1] 11 · Of things which change, some change in an accidental sense, like that in which the musical may be said to walk, and others are said, without qualification, to change, because something in them changes, i.e. the things that change in parts; the body becomes healthy, because the eye does. But there is something which is by its [5] own nature moved primarily, and this is the essentially movable. The same distinction is found in the case of the mover; for it causes movement either in an accidental sense or in respect of a part of itself or essentially. There is something that primarily causes movement; and there is
something that is moved, also the time in which it is moved, and that from which and that into which it is moved. But the [10] forms and the affections and the place, which are the terminals of the movement of moving things, are unmovable, e.g. knowledge or heat; it is not heat that is a movement, but heating. Change which is not accidental is found not in all things, but between contraries, and their intermediates, and between contradictories. We may convince ourselves of this by induction.
[15] That which changes changes either from subject into subject, or from non-subject into non-subject, or from subject into non-subject, or from non-subject into subject. (By subject I mean that which is expressed by an affirmative term.) [20] Therefore there must be three changes; for that from non-subject into non-subject is not change; for the terms are neither contraries nor contradictories, because there is no opposition. The change from non-subject into contradictory subject is generation—absolute change absolute generation, and partial change partial generation; and the change from subject to non-subject is destruction—absolute change absolute destruction, and partial change partial destruction. If, then, ‘that which is [25] not’ has several senses, and movement can attach neither to that which implies putting together or separating, nor to that which implies potentiality and is opposed to that which is without qualification (true, the not-white or not-good can be moved incidentally, for the not-white might be a man; but that which is not a ‘this’ at all [30] can in no way be moved), that which is not cannot be moved, and if this is so, generation cannot be movement; for that which is not is generated. For even if we admit to the fullest that its generation is accidental, yet it is true to say that not-being is predicable of that which is generated absolutely. (Similarly rest cannot [35] belong to that which is not.) These difficulties, then, follow, and also this, that everything that is moved is in a place, but that which is not is not in a place; for then it would be somewhere. Nor is destruction movement; for the contrary of movement [1068a1] is movement or rest, but the contrary of destruction is generation. Since every movement is a change, and the kinds of change are the three named above, and of these those in the way of generation and destruction are not movements, and these are the changes from a thing to its contradictory, only the change from subject into [5] subject can be movement. And the subjects are either contrary or intermediate; for even privation must be regarded as contrary, and is expressed by a positive term, e.g. ‘naked’ or ‘toothless’ or ‘black’.