Aristotle · a new plain-English translation from the original language
1| That wisdom is a kind of knowledge concerned with principles is clear from the earlier books, in which we raised difficulties about it in relation to what others have said about the principles. One might raise the difficulty whether wisdom should be supposed to be one science or many. For if one, a single science is always of contraries, but the principles are not contraries. But if it is not one, of what sort must we suppose these sciences to be? Again, does it belong to one science or to several to study the principles of demonstration? For if to one, why to this one rather than to any other? But if to several, what sort of sciences must we suppose these to be? Again, is it a science of all substances or not? For if not of all, it is hard to say of which. But if one science is of all, it is unclear how the same science can be of several things. Again, is demonstration concerned only with substances, or also with their accidents? For if there is demonstration about accidents, there is none about substances. But if the two are different, which is which, and which of them is wisdom? Insofar as it is demonstrative, wisdom is the science of accidents; insofar as it is concerned with what is primary, it is the science of substances. But neither should we suppose that the science we are seeking is concerned with the causes discussed in the works on nature. For it is not concerned with the that-for-the-sake-of-which (for the good is of this kind, and this belongs to things that can be done and to things that are in motion; and this is what moves first — for that is the character of an end — but the first mover is not among the unmoved things). And in general it is a difficulty whether the science now being sought is concerned with sensible substances, or not, but with certain others.
2| [1059b] For if it is concerned with others, it would be concerned either with the forms or with the objects of mathematics. Now that the forms do not exist is clear (yet even if one supposes them to exist, it is a difficulty why what holds for the objects of mathematics does not hold likewise for the other things of which there are forms; I mean that they place the objects of mathematics between the forms and sensible things, as a kind of third class besides the forms and the things here, but there is no third man besides the form itself and the individual men, nor a third horse. But if, on the other hand, they do not exist as they say, what must we suppose the objects the mathematician deals with to be? For certainly not the things here; none of these is such as the mathematical sciences seek.) Nor, again, is the science now being sought concerned with the objects of mathematics (for none of them is separate); but neither is it concerned with sensible substances, for they are perishable. And in general one might raise the difficulty, to what science it belongs to raise the problem about the matter of the objects of mathematics. For it does not belong to natural science, since the whole business of the natural scientist is with things that have in themselves a principle of motion and rest; nor yet to the science that studies demonstration and knowledge;
3| for that science makes precisely this class its subject of inquiry. It remains, then, that the philosophy now before us should conduct the inquiry concerning them. One might raise the difficulty whether the science being sought should be supposed to be concerned with the principles which some call elements; for everyone supposes these to be present in composite things. But it would seem, rather, that the science being sought must be a science of universals; for every account and every science is of universals and not of the ultimate individuals, so that on this view it would be a science of the primary genera. And these would turn out to be being and the one; for these above all would be supposed to embrace all existing things, and to resemble principles most closely, because they are first by nature; for if these are destroyed, the rest are destroyed along with them, since everything is both being and one. But insofar as it is necessary, if one supposes them to be genera, that their differentiae should partake of them, and no differentia partakes of its genus, in this respect it would not seem right to suppose them to be genera, or principles either. Further, if what is simpler is more a principle than what is less so, and the ultimate members derived from the genus are simpler than the genera (for they are indivisible, while the genera are divided into several differing species), the species would seem to be more a principle than the genera.
4| But insofar as the species are destroyed along with the genera, the genera would seem to resemble principles more; for what destroys other things along with itself is a principle. [1060a] These, then, and others like them, are the questions that involve difficulty. Again, must we suppose something to exist besides the individuals, or not, and is the science being sought a science of these individuals? But these are infinite in number. Now what exists besides the individuals is genera or species, but the science now being sought is a science of neither of these. Why this is impossible has been stated. For in general it is a difficulty whether we should suppose some substance to exist separately besides the sensible substances, the things here, or not, but rather that these are the things that exist, and that wisdom is concerned with these. For we seem to be seeking some other substance, and this is our task before us, I mean to see whether there is something separate, existing in its own right and belonging to none of the sensible things. Again, if besides the sensible substances there is some other substance, besides which of the sensible things must we suppose it to exist? For why should one suppose it to exist besides men rather than besides horses or the other animals, or indeed besides inanimate things generally? Yet to construct other eternal substances equal in number to the sensible and perishable substances would seem to fall outside what is reasonable. But if the principle now being sought is not separate from bodies, what other than matter could one suppose it to be rather?
5| Yet matter does not exist in actuality, but only in potentiality. And it would seem that the form, or shape, is a more authoritative principle than matter; but this is perishable, so that there is, in general, no eternal substance that is separate and exists in its own right. But this is absurd; for it seems that some such principle and substance is, and is sought by nearly the most refined thinkers, as actually existing. For how will there be order unless something eternal, separate, and abiding exists? Further, if there is some such substance and principle, of the nature we are now seeking, and this is one and the same for all things, both the eternal and the perishable, it is a difficulty why, since the principle is the same, some of the things falling under the principle are eternal and others are not eternal (for this is absurd). But if the principle of perishable things is one and that of eternal things another, then, if the principle of perishable things is also eternal, we will face the same difficulty (for why, since the principle is eternal, are not the things falling under it also eternal?); and if it is perishable, then some other principle is required for it, and another again for that one, and this proceeds to infinity. But if, on the other hand, one supposes the principles that seem most of all to be unmoved — being and the one — first, if neither of them signifies a particular this and a substance,
6| [1060b] how will they be separate and exist in their own right? Yet it is principles of this kind — eternal and primary — that we are seeking. But if each of them does signify a particular this and a substance, then all existing things are substances; for being is predicated of all things (and the one of some), but it is false that all existing things are substances. Further, for those who say that the first principle is the one, and that this is a substance, and who generate number first out of the one and matter, and assert that this number is substance, how can what they say be true? For how must one conceive the dyad, and each of the remaining composite numbers, as being one? For on this point they say nothing, nor is it easy to say. But if one is to suppose lines, or what comes next after them (I mean the primary surfaces), to be principles, these at any rate are not separate substances, but are cuts and divisions, some of surfaces, some of bodies (and points are cuts and divisions of lines), and further, they are the limits of these same things; and all of these belong to other things, and none of them is separate. Again, how must we suppose there to be a substance of the one and of the point? For there is generation of every substance, but there is none of a point.
7| For the point is a division. There is a further puzzle: every science is of the universal and of such-and-such a kind, but substance is not of the universal, but rather a this and something separable, so that if there is a science of the principles, how must one suppose the principle to be a substance? Further, is there anything beside the concrete whole or not (I mean the matter and what goes along with it)? For if there is not, then all things in matter are perishable; but if there is something, it would be the form and the shape. So on what things this holds and on what it does not, it is hard to determine — for in some cases it is clear that the form is not separable, for example that of a house. Further, are the principles the same in species or in number? For if they are one in number, all things will be the same. Since the science of the philosopher is of being qua being, universally and not of a part of it, but being is spoken of in many ways and not in a single way: if, then, it is spoken of homonymously, with nothing in common, it does not fall under one science (for there is not one genus of such things), but if it is spoken of according to something common, it would fall under one science.
8| It seems, then, that being is spoken of in the way just described, in the way that the medical and the healthy are spoken of: for we speak of each of these too in many ways. [1061a] Each is spoken of in this way because the one is referred somehow to the science of medicine, another to health, another in some other way, but each is referred to the same thing. For a medical account and a medical scalpel are so called because the one belongs to the science of medicine, the other is useful to it. And likewise with the healthy: the one because it is a sign of health, the other because it is productive of it. And the same pattern holds in the remaining cases. In this same way all being too is spoken of: for it is because it is an affection or a state or a disposition or a motion or something else of this kind belonging to being qua being that each of these is called being. Since every being is referred back to some one common thing, each of the contrarieties too will be referred back to the primary differentiae and contrarieties of being, whether the primary differentiae of being are plurality and unity, or likeness and unlikeness, or some others — let these be taken as already examined. It makes no difference whether the reference of being is made to being or to the one. For even if they are not the same but are distinct, still they convert with one another:
9| for what is one is in some way also being, and what is being is one. Since it belongs to one and the same science to study all contraries, and each of them is spoken of in terms of privation — though one might raise a puzzle as to how some of them, between which there is something intermediate, are spoken of in terms of privation, as with the unjust and the just — in all such cases the privation must be posited not of the whole account but of the last species: for example, if the just person is, by a certain state, obedient to the laws, the unjust person will not in every way be deprived of the whole account, but will fall short in some respect regarding obedience to the laws, and it is in this respect that the privation will belong to him; and the same holds in the other cases as well. And just as the mathematician conducts his study by way of abstraction (for having stripped away everything perceptible, he studies things — for instance weight and lightness and hardness and its contrary, and further heat and cold and the other perceptible contrarieties — and leaves only the quantitative and the continuous, in one dimension, or two, or three, and studies the affections of these insofar as they are quantitative and continuous, and studies them under no other aspect; and for some he examines their positions relative to one another and what belongs to these positions,
10| [1061b] for others their commensurabilities and incommensurabilities, and for others their ratios — yet all the same we posit geometry as one and the same science of all of these), in this same way matters stand also with regard to being. For it belongs to no science other than philosophy to study the things that belong to being insofar as it is being, and its contrarieties qua being. For to natural science one would assign the study of things not insofar as they are beings, but rather insofar as they partake of motion; while dialectic and sophistic are indeed concerned with the accidents of beings, but not insofar as they are beings, nor with being itself insofar as it is being. It remains, then, that it is the philosopher, insofar as things are beings, who is engaged in studying the matters described. Since being as a whole, though spoken of in many ways, is spoken of with reference to some one common thing, and the contraries are spoken of in the same way (for they are referred back to the primary contrarieties and differentiae of being), and things of this sort admit of falling under one science, the puzzle stated at the outset would be resolved — I mean the one in which it was asked how there could be some single science of things that are many and different in genus. And since the mathematician too makes special use of the common axioms, it would belong to first philosophy to study the principles of these as well.
11| For that when equals are taken away from equals the remainders are equal is common to all quantities, but mathematics, taking off a certain part of its proper matter, makes its study about that — for instance about lines or angles or numbers or some other of the quantities — not insofar as they are beings, but insofar as each of them is continuous in one, two, or three dimensions; whereas philosophy does not examine particular things insofar as something belongs accidentally to each of them, but studies each of them insofar as it is a being, with regard to being. The same relation holds between natural science and mathematics: for natural science studies the accidents and the principles of beings insofar as they are in motion, and not insofar as they are beings (whereas we have said that first science is the science of these insofar as their underlying subjects are beings, and not insofar as they are something else): hence both this science and mathematics must be posited as parts of wisdom. Now there is among beings a certain principle about which it is not possible to be deceived, but about which one must always do the opposite — I mean, speak the truth — namely, that it is not possible for the same thing to be and not be at one and the same time,
12| [1062a] and the other things opposed to one another in this same way. And concerning such things there is no demonstration without qualification, but there is demonstration directed against a particular person: for it is not possible to construct a syllogism of this very thing from some more credible principle, though this is required if there is to be demonstration without qualification. Against the person who asserts the opposed statements, in order to show him that he is wrong, one must take hold of something of such a kind that it will be the same as saying that it is not possible for the same thing to be and not be at one and the same time, yet will not seem to be the same — for only in this way could it be demonstrated against the one who claims that opposed statements can both be true of the same thing. Now those who are going to share an argument with one another must understand something in common; for if this does not happen, how will there be any communication of argument between them? Each of the names, then, must be intelligible and signify something — and not many things, but only one; and if it signifies more than one thing, one must make clear which of these the name is being applied to. So the person who says that this both is and is not is denying what he asserts, so that he is saying that the name does not signify what it signifies — and this is impossible. So if 'being this' signifies something, it is impossible for the contradiction to be true.
13| Further, if the name signifies something, and this is truly asserted, then this must be so of necessity; and what is of necessity cannot ever not be. Therefore it is not possible for opposed affirmations and denials to be true of the same thing. Further, if the affirmation is no more true than the denial, then one who says "man" will be no more speaking truly than one who says "not-man." And it would seem that one who says the man is not a horse speaks no less truly — indeed just as truly — as one who says he is not a man, so that one who says the same thing is a horse will also speak truly (for it was assumed that opposed statements are equally true). It follows, then, that the same thing is both a man and a horse, or any other animal. Now there is no demonstration of these points without qualification, but there is a demonstration directed against the person who maintains them. And indeed, if one questioned Heraclitus himself in this way, one would quickly force him to agree that opposed statements can never be true of the same things. But as it is, not understanding what he himself is saying, he adopted this opinion. And in general, if what he says is true, then not even this very statement could be true,
14| [1062b] I mean the claim that it is possible for the same thing, at one and the same time, both to be and not to be. For just as, when the affirmation and the denial are taken separately, the affirmation is no more true than the denial, in the same way, when both are taken together and combined as if they were a single affirmation, the whole — taken as posited in an affirmation — will be no more true than the denial. Further, if it is impossible to truly affirm anything, then even this very statement — that no affirmation is true — would be false. But if there is something that can truly be affirmed, then what is said by those who raise these objections and who altogether abolish discourse would be refuted. Similar to what has been said is also the statement made by Protagoras. For he too said that man is the measure of all things, meaning nothing other than that whatever seems so to each person is fixedly so. But if this is granted, it follows that the same thing both is and is not, and is bad and good, and likewise for all the other things said according to opposed statements, because a given thing often appears fine to some people and the opposite to others, and what appears to each is the measure. This difficulty would be resolved if we examine where the starting point of this belief came from.
15| For it seems to have arisen for some from the opinion of the natural philosophers, and for others from the fact that not everyone knows the same things about the same objects, but a given thing appears pleasant to some and the opposite to others. For the doctrine that nothing comes to be from what is not, but everything from what is, is a belief nearly common to all who write about nature. Since, then, what is not white comes to be — from something that was entirely white and in no way not white, but has now come to be not white — what comes to be not white would come to be from the not-white not existing; so that, on their view, it would come to be from what is not, unless the same thing were at once white and not white. But it is not hard to resolve this difficulty, for it has been stated in the Physics how things that come to be come to be from what is not and how from what is. But to give equal weight to the opinions and appearances of people who dispute with each other is foolish. For it is clear that one of the two parties must be mistaken. This is evident from what happens in perception: the same thing never appears sweet to some and the opposite to others,
16| [1063a] unless in the one group the sense organ and the faculty that judges the flavors in question has been damaged and impaired. And this being so, we must suppose that the one group is the measure, and not suppose the other group to be. And I say the same in the case of good and bad, and fine and shameful, and other things of this sort. For claiming this is no different from claiming that what appears to those who press a finger under their eye, and thereby make one thing appear as two, must be two because that is how many it appears to be, and then again one — for to those who do not disturb their sight, the one thing appears one. And in general it is absurd to base our judgment about truth on the fact that the things down here appear to change and never remain the same. For we must hunt for the truth among things that always stay the same and undergo no change, and such are the things in the universe. For these do not appear one way at one time and different at another, but are always the same and share in no change. Further, if there is motion, there is also something that moves, and everything moves from something to something; the thing moving, then, must be in that from which it will move and not be in it, and must move toward this other thing and come to be in it — and, on their own principle, the two sides of a contradiction cannot both be true together.
17| And if the things here flow and are continuously in motion with respect to quantity, and someone were to grant this even though it is not true, why should they not remain stable with respect to quality? For it seems that they are led to predicate contradictory pairs of the same thing chiefly from supposing that quantity does not remain stable in bodies, and that is why the same thing is supposed to be four cubits long and not to be. But substance depends on quality, and this belongs to the determinate nature, while quantity belongs to the indeterminate. Further, why, when a doctor prescribes this particular food, do people take it? For why is this any more bread than it is not bread? So that it would make no difference whether one eats it or not. But as it is, they take it as speaking truly about it and as this being the very food prescribed. And yet they should not, if no nature among perceptible things remains fixed but all are always changing and flowing. Further, if we are always altering and never remain the same, what is surprising about our never perceiving the same things, just as with the sick—
18| [1063b] (for in their case too, because their bodily condition is not disposed the same way as when they were healthy, the things perceived do not appear the same to them — though the perceptible things themselves are not on that account undergoing any change at all, but produce different, not the same, sensations in the sick; and presumably it must be the same way, if the change we have described in us occurs). But if we do not change but continue to be the same, there would be something that remains stable. Now against those who raise the difficulties just stated purely from argument, and who refuse to posit anything and demand no further argument for this refusal, it is not easy to resolve the difficulty. For it is in this way — by positing something — that every argument and every demonstration comes about; by positing nothing, they abolish discourse and reasoned argument altogether, so that against such people there is no argument to be had; but against those who raise difficulties out of the traditional puzzles, it is easy to meet them and to resolve what produces the difficulty in their arguments. This is clear from what has been said. So it is evident from these considerations that it is not possible for opposed statements about the same thing to be true at one and the same time, nor for contraries, since every contrariety is stated in terms of privation — and this becomes clear when one traces the accounts of contraries back to their starting point.
19| And likewise, none of the intermediates can be predicated of one and the same subject either: for if the subject is white and we say it is neither black nor white, we shall be speaking falsely, for it follows that it is white and is not white; for one of the two conjuncts will be true of it, and this is the contradictory of "white." So it is not possible to speak truly either following Heraclitus or following Anaxagoras; for otherwise it will follow that contraries are predicated of the same thing. For when Anaxagoras says that in everything there is a portion of everything, he is saying that a thing is no more sweet than bitter, or than any other of the remaining contraries, given that in everything, everything is present not merely potentially but actually and separated out. Likewise, it is not possible for all statements to be either false or true, both because of many other difficulties that would result from this position, and because, if all statements are false, then not even the person who says this very thing will be speaking truly, whereas if all are true, then the person who says they are all false will not be speaking falsely. But every science seeks certain principles and causes concerning each of the objects of knowledge that fall under it,
20| [1064a] for example, medicine and gymnastics, and each of the rest of the productive and mathematical sciences. For each of these, having marked off some genus for itself, occupies itself with that genus as something that exists and is, but not qua being; that is a different science, distinct from these sciences. Each of the sciences mentioned, having grasped in some way the what-it-is within its own genus, tries to demonstrate the rest of its subject matter more loosely or more strictly. Some grasp the what-it-is through perception, others by hypothesis; hence it is clear from such an induction that there is no demonstration of substance and of the what-it-is. Now since there is a science of nature, it is clear that it will be different both from the practical and from the productive sciences. For in the case of the productive sciences, the principle of motion is in the maker and not in the thing made, and this is either some craft or some other capacity; and likewise in the case of the practical sciences, the motion is not in the thing done but rather in the agents. But the science of the natural philosopher concerns things that have within themselves a principle of motion. It is clear from this, then, that natural science must be neither practical nor productive but theoretical (for it must fall into one of these genera):
21| Since it is necessary for each of the sciences, in some way, to know the what-it-is and to use this as a principle, we must not fail to notice how the natural philosopher should define things, and how the account of substance is to be taken—whether as the account of the snub, or rather as that of the concave. For of these, the account of the snub is stated together with the matter of the thing, while the account of the concave is stated apart from the matter; for snubness occurs in a nose, and so its account is considered together with the nose—for the snub is a concave nose. It is clear, then, that the account of flesh and of eye and of the remaining parts must always be given together with the matter. Now since there is a science of being qua being and separable, we must examine whether this science is to be posited as the same as natural science, or rather as a different one. Natural science concerns things that have a principle of motion in themselves; mathematics is theoretical and concerns things that are at rest, but it is not about separable things. About what is separable and unmoved, then, there is some other science, different from both of these, if indeed there exists a substance of this kind—I mean one that is separable and unmoved—which we shall try to demonstrate.
22| And if indeed there is some such nature among the things that are, it is there, presumably, that the divine would be found too, and this would be the first and most authoritative principle. [1064b] It is clear, then, that there are three kinds of theoretical sciences: natural science, mathematics, and theology. Now the class of the theoretical sciences is the best, and of these themselves the one last named is best; for it concerns the most honorable of the things that are, and each science is called better or worse in accordance with its proper object of knowledge. One might raise the question whether the science of being qua being should be posited as universal or not. For each of the mathematical sciences concerns some one delimited genus, while the universal science is common to all. Now if natural substances are the first among the things that are, then natural science would be the first of the sciences; but if there is another nature and substance, separable and unmoved, then the science of it must also be different, and prior to natural science, and universal by being prior. And since what is, simply speaking, is said in several ways, one of which is called being by accident, we must first examine being in this sense. That none of the traditional sciences occupies itself with the accidental is clear (for neither does the science of building consider what will happen to those who will use the house—for example, whether they will live in it unpleasantly or the opposite—nor does weaving, nor shoemaking, nor cookery; each of these sciences considers only what is proper to it in its own right, and this is its proper end;
23| nor does it consider the musical and the literate—nor, concerning a man who is musical, the fact that, on becoming literate, he will at the same time be both, not having been both before; for what does not always exist comes to be, so that he came to be musical and literate at the same time. But none of the sciences that are acknowledged to exist inquires into this, except sophistic; for this alone occupies itself with the accidental, and hence Plato was not wrong in saying that the sophist spends his time on what is not. That it is not even possible for there to be a science of the accidental will be clear to anyone who tries to see what the accidental actually is. We say that everything that is, is either always and of necessity (necessity not in the sense called forced, but in the sense we use with respect to demonstrations), or for the most part, or neither for the most part nor always and of necessity, but as it chances—for example, cold weather might occur during the dog-days, but this happens neither always and of necessity nor for the most part, though it might happen sometimes, by accident.
24| [1065a] The accidental, then, is what comes to be, but not always, nor of necessity, nor for the most part. What the accidental is, then, has been stated; and it is clear why there is no science of such a thing—for every science concerns what is always the case or what is for the most part, and the accidental falls under neither of these. That the causes and principles of what is by accident are not of the same kind as those of what is in its own right is clear; for otherwise everything would happen of necessity. For if this exists because that exists, and that because of something else, and this is not as it chances but of necessity, then that of which this was the cause will also be of necessity, right up to the last thing spoken of as the thing caused (and this was the accidental one), so that everything will be of necessity, and both what happens either way and the possibility of a thing's both coming to be and not coming to be are completely eliminated from among the things that come to be. And even if the cause supposed is not something existing but something coming to be, the same result will follow; for everything will come to be of necessity. For tomorrow's eclipse will occur if such-and-such occurs, and that if something else occurs, and that again if something else; and in this way, subtracting time from the finite stretch running from now until tomorrow, one will eventually arrive at what already exists, so that, since this exists, everything after it will happen of necessity—so that everything comes to be of necessity.
25| Being as true, and being by accident: one of these lies in a combination made by thought, an affection belonging to thought (which is why principles are not sought for being in this sense, but for being that is outside the mind and separable); the other is not necessary but indeterminate—I mean being by accident. Of such a thing the causes are disorderly and unlimited. What happens for the sake of something occurs either among the things that come to be by nature or from thought; and chance is present whenever one of these comes about by accident. For just as being is in one sense in its own right and in another by accident, so too is cause. Chance is a cause by accident among the things done for the sake of something in accordance with choice; hence chance and thought concern the same things, for choice does not occur without thought. The causes from which the effects of chance may arise are indeterminate; hence chance is unclear to human calculation, and is a cause by accident, but of nothing simply speaking. Chance is called good or bad according as the outcome is good or bad; good fortune and misfortune concern the magnitude of these.
26| [1065b] Since nothing accidental is prior to what is in its own right, accidents are not causes either; so if chance or the automatic is the cause of the heavens, intellect and nature are prior as causes. Now some things are actuality only, some are potentiality, and some are both potentiality and actuality — some being (a substance), some a quantity, some one of the remaining categories. There is no motion apart from things: for a thing always changes with respect to the categories of being, and there is nothing common to these that does not itself fall under some one category. Each category belongs to everything in two ways (for instance the this-something — for one is its form and the other its privation; and with respect to quality, one is white and the other black; and with respect to quantity, one is complete and the other incomplete; and with respect to locomotion, one is up and the other down, or light and heavy): so that there are as many species of motion and change as there are of being. Since in each genus a distinction is drawn between what is potentially and what is actually, I call motion the actuality of what is potentially, insofar as it is such. That we speak truly is clear from this: whenever the buildable, in the sense in which we call it such, is in actuality, it is being built, and this is building —
27| likewise learning, healing, walking, leaping, aging, ripening. And motion occurs precisely when this actuality itself occurs, and neither before nor after. The actuality, then, of what is potentially, when it is in actuality and active — not insofar as it is itself but insofar as it is movable — is motion. I mean 'insofar as' in this sense: bronze is potentially a statue, yet the actuality of bronze, insofar as it is bronze, is not motion. For being bronze and being a certain potentiality are not the same; since if they were simply the same in account, the actuality of bronze would be a kind of motion. But they are not the same (this is clear in the case of contraries: being able to be healthy and being able to be sick are not the same — for otherwise being healthy and being sick would be the same — while the underlying subject that is both healthy and diseased, whether it is moisture or blood, is the same and one). Since, then, they are not the same — just as color and the visible are not the same — the actuality of what is potential, insofar as it is potential, is motion. That this is what motion is, then, and that motion occurs precisely when this actuality itself occurs, and neither before nor after, is clear (for it is possible for each thing at one time to be active and at another not,
28| [1066a] for instance the buildable insofar as it is buildable, and the activity of the buildable insofar as it is buildable is building; for it must be either this — the building, the activity — or the house; but when there is a house, there is no longer anything buildable, whereas the buildable is being built; the activity, then, must necessarily be the building, and building is a kind of motion, and the same account holds for the other motions): that this has been stated correctly is clear from what others say about motion, and from the fact that it is not easy to define it otherwise. For no one could place it in any other genus; this is clear from what people say: some posit otherness, inequality, and not-being, none of which is necessarily in motion, nor indeed does change go into these or out of these any more than into or out of their opposites. The reason they place motion under these is that motion seems to be something indefinite, and the principles of this other column are indefinite because they are privative; for none of them is a this-something or a such-and-such, nor does it fall under any of the remaining categories. The reason motion seems to be indefinite is that it cannot be placed either under the potentiality of things or under their actuality:
29| for what is capable of being a quantity is not necessarily in motion, nor is what is actually a quantity; and motion seems to be a kind of actuality, but an incomplete one — the reason being that the potentiality of which it is the actuality is incomplete. And this is why it is hard to grasp what motion is: for it must be placed either under privation, or under potentiality, or under simple actuality, and none of these appears to admit it; so what remains is the account given — that it is, as we said, both actuality and not actuality, hard to see but nonetheless possible. And it is clear that motion is in the movable thing; for it is the realization of this thing, brought about by what can move it. And the activity of what can move it is not a different activity. For there must be a single realization of both: a thing is capable of moving by its power, and moving by its activity, but this activity belongs to the movable; so that in the same way the activity of both is one, just as the same interval is one whether reckoned from one to two or from two to one, and the uphill and the downhill are the same, though their being is not one; and likewise with the mover and the moved. Now the infinite is either what cannot be traversed because it is not of a nature to be traversed at all — as a sound is invisible — or what has a passage that has no end, or one that can barely be traversed, or one which, though of a nature to have a passage or a limit, does not have one;
30| or again what has a passage only by addition, or by subtraction, or by both. [1066b] Now it cannot be something separate, existing in its own right; for if it has neither magnitude nor multitude, but the infinite itself is a substance and not an accident, it will be indivisible (for what is divisible is either a magnitude or a multitude); and if it is indivisible, it is not infinite, unless it is infinite in the way a sound is invisible — but that is not what people mean, nor is it what we are inquiring into, but rather the infinite as that which cannot be traversed. Again, how can the infinite exist in its own right, unless number and magnitude also do, of which the infinite is an attribute? Again, if it exists accidentally, it would not be an element of things insofar as it is infinite, just as the invisible is not an element of speech, even though sound is invisible. And it is clear that the infinite cannot exist in actuality. For then any part of it that is taken would be infinite (for being infinite and being an infinite thing are the same, if the infinite is a substance and not said of a subject); so that it is either indivisible, or divisible into infinitely many parts, if it is divisible at all; but it is impossible for the same thing to be many infinites (for just as air is a part of air, so an infinite would be a part of an infinite, if the infinite is a substance and a principle); it must therefore be unpartitioned and indivisible. But it is impossible for what exists in actuality to be infinite (for it must be a quantity); it exists, then, accidentally.
31| But if this is so, it has been said that it cannot be a principle, but rather that thing to which infinity is an accident — the air, say, or the even. This inquiry, then, is general; but that the infinite does not exist among perceptible things is clear from the following. If the account of body is that which is bounded by planes, then there could be no infinite body, either perceptible or intelligible, nor a number that is infinite when taken as separate; for a number is what is counted, or what has a number. And from the point of view of natural science it is clear from the following: an infinite body could be neither composite nor simple. It will not be a composite body, if the elements are limited in multitude (for the contraries must be equal, and not one of them infinite; for if the power of either body falls short in any degree, the finite will be destroyed by the infinite; and it is impossible for each element to be infinite, since body is what has extension in every direction, and the infinite is what is extended without limit, so that if the infinite is a body, it will be infinite in every direction): nor can the infinite body be one and simple, either as some say, existing beside the elements from which they generate these (for there is no such body beside the elements — for everything is dissolved into that from which it is, and this does not appear to exist beside the simple bodies),
32| [1067a] Nor is it fire, nor any other of the elements. For apart from the fact that none of them can be infinite, it is impossible for the whole—even if it is finite—either to be, or to become, one of them, as Heraclitus says that all things at some time become fire. The same argument applies also to the One that the natural philosophers posit alongside the elements: for everything changes from a contrary, for example from hot to cold. Further, every perceptible body is somewhere, and the whole and the part have the same place—for example, of earth—so that if it is uniform in kind, it will either be motionless or always in motion, and this is impossible (for why should it move down rather than up, or anywhere else? For instance, if it were a clod of earth, where would it move to, or where would it stay? For the place of the body akin to it is infinite: will it then occupy the whole place? And how? What, then, is its staying still and its motion? Either it will stay everywhere—so it will not move at all—or it will move everywhere—so it will never come to rest): but if the whole is not uniform, the places too are not uniform, and, in the first place, the body of the whole is not one except by contact, and further, these kinds will be either finite or infinite in species. Now they cannot be finite (for then some will be infinite and some not, if the whole is infinite—for example, fire or water; and such a thing is destruction for the contraries):
33| but if they are infinite and simple, the places too are infinite, and there will be infinite elements; and if this is impossible, and the places are finite, then the whole too must necessarily be finite. In general, it is impossible for body to be infinite and also for there to be infinite place for bodies, if every perceptible body has either weight or lightness: for it will move either toward the middle or upward, and it is impossible for the infinite—whether the whole of it or half of it, either way—to undergo this: for how will you divide it? Or how will the infinite have a part below and a part above, or an extremity and a middle? Further, every perceptible body is in a place, and there are six species of place, and it is impossible for these to exist in an infinite body. And in general, if it is impossible for place to be infinite, body too is impossible: for what is in a place is somewhere, and this means either up or down or one of the rest, and each of these is a kind of limit. The infinite is not the same thing in magnitude and in motion and in time, as if it were a single nature; rather, the later is spoken of in accordance with the earlier—for example, motion is called infinite in accordance with the magnitude over which the thing moves, or is altered, or grows, and time is called infinite because of the motion.
34| [1067b] Of that which changes, one thing changes accidentally, as when the musical man walks; another is said to change without qualification because something belonging to it changes—things that change part by part are said to change in this way (for the body is healed because the eye is healed), and there is something that is moved first, in its own right, and this is what is movable in its own right. And likewise there is something similar on the side of the mover: one thing moves accidentally, another part by part, another in its own right; and there is something that moves first; and there is the thing moved, and further, the time in which, and the state from which and the state into which. The forms and affections and the place into which the things moved are moved are themselves unmoved—for example, knowledge and heat: for it is not heat that is a motion, but the process of heating. Non-accidental change does not occur in all things, but among contraries, and their intermediates, and in contradiction; and the proof of this is from induction. What changes, changes either from a subject into a subject, or from a not-subject into a not-subject, or from a subject into a not-subject, or from a not-subject into a subject (by "subject" I mean what is indicated by affirmation), so that there must necessarily be three kinds of change:
35| for change from a not-subject into a not-subject is not a case of change at all: for there is neither contrariety nor contradiction, since there is no opposition. Now the change from a not-subject into a subject, according to contradiction, is coming-to-be—unqualified coming-to-be when it is unqualified, coming-to-be of a certain thing when it is of a certain thing; and that from a subject into a not-subject is destruction—unqualified when unqualified, of a certain thing when of a certain thing. If, then, "what is not" is said in several ways, and neither what is not in the sense of composition or division can be moved, nor what is not potentially—that which is opposed to what is without qualification (for what is not-white or not-good can nevertheless be moved accidentally, for the not-white might be a man; but what is without qualification not a "this" cannot be moved in any way)—it is impossible for what is not to be moved (and if this is so, then coming-to-be cannot be a motion either: for what is not comes to be; for even if it comes to be in the highest degree accidentally, still it is true to say that "what is not" holds of what comes to be without qualification): and likewise for being at rest. These, then, are the difficulties that result; and also, if everything that is moved is in a place, but what is not is not in a place—for otherwise it would be somewhere.
36| Nor, then, is destruction a motion: for what is contrary to a motion is a motion or a state of rest, but what is contrary to coming-to-be is destruction. [1068a] Since every motion is a kind of change, and the changes spoken of are three, and of these, those concerned with coming-to-be and destruction are not motions, and these are the ones according to contradiction, it must be that the change from a subject into a subject is the only motion. And the subjects are either contraries or intermediates (for let privation too be counted as a contrary), and they are indicated by affirmation, for example the naked, the toothless, and the black. If, then, the categories are divided into substance, quality, place, acting or being acted on, relation, and quantity, there must necessarily be three kinds of motion: of quality, of quantity, of place; but not with respect to substance, because nothing is contrary to substance, nor with respect to relation (for it is possible that, when one of two related things changes, the statement about the other becomes false though the other has not changed at all, so that the motion in these cases is accidental), nor with respect to what acts and what is acted on, or what moves and what is moved, because there is no motion of a motion, nor coming-to-be of a coming-to-be, nor, in general, change of a change. For there are two ways in which there could be a motion of a motion: either as of a subject (for example, a man is moved because he changes from white to black, so that in the same way motion too would be heated or cooled or change place or grow—but this is impossible, for change is not one of the things that are subjects), or because some other subject changes, by a change, from that change into another form—for example, a man changing from sickness into health.
37| But not even this is possible, except accidentally. For every motion is a change from one thing into another, and coming-to-be and destruction likewise; except that these are changes into opposites in one way, and motion in another way. At the same time, then, a thing changes from health into sickness, and also from this very change into another. It is clear, then, that when it has fallen sick, it will have changed into some further change or other (for it is possible for it to be at rest), and further, always into some change that is not just any chance one; and that further change too will be from something into something else, so that the change that is opposite to falling sick will be the recovery of health—but only accidentally: for example, it changes from remembering into forgetting because that to which the remembering belongs changes, at one time into knowledge, at another into ignorance. Further, it will go on to infinity, if there is to be a change of a change and a coming-to-be of a coming-to-be. For if the later exists, the earlier must exist too: for example, if unqualified coming-to-be was at some time coming to be, then that which was coming to be was also coming to be:
38| [1068b] so that what is coming to be was not yet coming to be without qualification, but was something coming to be, or was already coming to be. And this too was at some point coming to be, so that at that time it was not yet coming to be. But since among an infinite series there is no first term, there will be no first term here either, and so no term next to it. Therefore nothing can come to be, or be moved, or change at all. Again, motion and rest, and coming to be and passing away, are contraries of the same thing, so that what is coming to be, once it has come to be as a coming-to-be, is at that point passing away — for it is not passing away either immediately upon coming to be, or later, since what is passing away must exist. Again, matter must underlie what comes to be and what changes. What, then, will play the role that an alterable body or a soul plays — that is, what is it that is the coming-to-be, as a motion or a coming-to-be? And further, what is it that things are moved into? For there must be a motion or coming-to-be of this thing from this into this. How, then? For there will not be a learning of learning, and so no coming-to-be of coming-to-be. But since coming-to-be belongs neither to substance, nor to the relative, nor to acting and being acted on, it remains that motion is with respect to quality, quantity, and place (for each of these admits of contrariety); and by quality I mean not the quality within substance (for the differentia too is a quality) but the affective quality, in virtue of which a thing is said to be acted on or to be incapable of being acted on.
39| The unmoved is: what is wholly incapable of being moved; what starts moving only with difficulty over a long time or slowly; and what is naturally such as to be moved and capable of being moved but is not being moved when, where, and as it is naturally such to be moved — which last I call being at rest, among things unmoved alone, since rest is the contrary of motion, and so would be a privation in what is receptive of motion. Things are together in place when they are in one primary place, and separate when they are in a different one; things touch when their extremities are together; the intermediate is that which a changing thing naturally arrives at before reaching the point it changes to last, when it changes continuously in accordance with its nature; contrary in place is what is furthest apart along a straight line; and consecutive is that which, coming after the starting point — the order being fixed by position or by form or in some other way — has nothing between it and that to which it is consecutive, among things of the same genus, for example lines to a line, or units to a unit, or houses to a house (nothing prevents there being something between of another kind). For the consecutive is consecutive to something, and is posterior to it — for one is not consecutive to two, nor is the first of the month consecutive to the second.
40| [1069a] Contiguous is whatever, being consecutive, touches. And since every change is among opposites, and these are contraries or a contradiction, and there is nothing intermediate in a contradiction, it is clear that the intermediate lies among contraries. The continuous is a species of the contiguous. I call it continuous when the limit of each of two things, at which they touch and are held together, becomes one and the same, so that it is clear that the continuous occurs among those things out of which some one thing is naturally constituted by their junction. And it is clear that the consecutive is prior (for what is consecutive does not touch, but what touches is consecutive; and if a thing is continuous it touches, but if it touches it is not yet continuous; and where there is no contact, there is no growing-together either). Hence a point is not the same as a unit, for touching belongs to points but not to units — to these belongs only being consecutive; and of the one there is something between, of the other not.