Aristotle · a new plain-English translation from the original language
1| "Principle" is said, in one sense, of that from which a person would first be moved with respect to the thing — for instance, of a length or a road, starting from this point is one principle, and from the opposite end another; [1013a] and of that from which each thing would best come about — for instance of learning, one must sometimes begin not from the first point and the principle of the thing itself but from wherever one would most easily learn; and of that from which a thing first comes to be, this being present within it, as the keel is of a ship and the foundation of a house, and among animals some suppose it to be the heart, others the brain, others whatever else happens to be of that sort; and of that from which a thing first comes to be, this not being present within it, and from which motion and change naturally begin, as the child comes from the father and the mother, and the fight from the verbal abuse; and of that by whose choice the things that are moved are moved and the things that change, change, as for instance the offices in cities and the ruling powers and kingships and tyrannies are called principles, and so are the crafts, and among these especially the architectonic ones. Further, that from which a thing is first knowable is also called a principle of the thing, as for instance the hypotheses are of demonstrations. Causes are spoken of in an equal number of ways:
2| for all causes are principles. Common, then, to all principles is this: to be the first point from which a thing either is, or comes to be, or is known. Of these, some are present within the thing, others are outside it. That is why nature is a principle, and the element, and thought, and choice, and substance, and that for the sake of which something is; for of many things both the coming to know and the motion have as their principle the good and the fine. "Cause" is spoken of, in one way, as that out of which something comes to be, this being present within it, as the bronze is of the statue and the silver of the bowl, and the genera of these; in another way, as the form and the pattern, and this is the account of the essence, and the genera of this — as for instance of the octave the ratio two to one, and number in general — and the parts that are in the account. Further, as that from which the first principle of change or of rest comes, as for instance the one who deliberated is a cause, and the father is a cause of the child, and in general the maker is a cause of the thing made and the changer of the thing changed. Further, as the end: this is that for the sake of which something is, as for instance health is the cause of walking.
3| For why does he walk? We say: in order to be healthy. And having said this, we think we have given the cause. And so too with all the things that come to be along the way toward the end once something else has set them in motion, [1013b] as thinning, or purging, or drugs, or instruments are causes of health: for all these exist for the sake of the end, but they differ from one another in that some are instruments and others are actions. The causes, then, are spoken of in about that many ways, but since causes are spoken of in many ways, it results that there are also many causes of the same thing, and not accidentally — for instance both the art of statue-making and the bronze are causes of the statue, not in virtue of anything else but in that it is a statue, though not in the same way, but the one as matter, the other as that from which the motion comes; and things can also be causes of one another, as for instance exertion is a cause of good condition, and good condition of exertion, but not in the same way — the one as end, the other as principle of motion. Further, the same thing is the cause of contraries: for what, being present, is the cause of this thing, we sometimes blame, being absent, for the contrary, as for instance we blame the pilot's absence for the capsizing, whose presence was the cause of safety; both the presence and the privation are causes, as sources of motion. All the causes just mentioned fall under four ways, the most evident ones. For the elements of syllables, and the matter of manufactured things, and fire and earth and all such things among bodies, and the parts of a whole, and the premises of a conclusion, are causes as that out of which a thing comes.
4| Of these, some are causes as the substrate, for example the parts, others as the essence — the whole, the composition, and the form. The seed, the doctor, the one who deliberated, and in general the agent — all these are causes as that from which the change or the rest originates. Others are causes as the end and the good of the other things: for that for the sake of which tends to be the best and the end of the other things, and it makes no difference whether we call it, itself, a good or an apparent good. These, then, are the causes, and this many in kind, but the ways in which causes are spoken of are numerically many, though when summed up these too are fewer. For causes are spoken of in many ways, and even among causes of the same kind, one is prior and another posterior to another, as the doctor and the expert are both causes of health, and the double and number are both causes of the octave, and in general whatever contains any particular thing is a cause of it. Further, causes are spoken of as the accidental attribute and the genera of these, as, for example, in a different way Polyclitus and in a different way the sculptor are causes of a statue, because it is accidental to the sculptor to be Polyclitus.
5| [1014a] And also the things that contain the accidental attribute, as, for example, man is the cause of a statue, or, more generally, animal, because Polyclitus is a man and man is an animal. And among accidental causes too, some are more remote and others nearer, as, for example, if the white one or the musical one were said to be the cause of the statue, and not only Polyclitus or man. And besides all these, both the things spoken of in their own right and the things spoken of accidentally are spoken of, some as being capable, others as actually operating — for example, the builder, or the building builder, as cause of the thing being built. And the same will be said of the things of which these causes are the causes, as, for example, of this statue, or of a statue, or of an image in general; and of this bronze, or of bronze, or of matter in general; and likewise in the case of accidental attributes. Further, both these and those will be spoken of in combination, as, for example, not Polyclitus, nor the sculptor, but Polyclitus the sculptor. But nevertheless all these are, in number, six, though each is spoken of in two ways: either as the particular or as the genus, or as the accidental attribute or as the genus of the accidental attribute, or as these in combination, or as spoken of simply; and all are spoken of either as actually operating or as in accordance with a potentiality.
6| And they differ to this extent: the causes that are actually operating and the particular causes exist and cease to exist at the same time as the things of which they are the causes — as, for example, this man healing exists together with this man being healed, and this builder together with this thing being built — whereas the causes spoken of in accordance with a potentiality do not always do so; for the house and the builder do not perish at the same time. An element is said to be that out of which a thing is composed as a primary constituent, indivisible in kind into another kind — as, for example, the elements of an utterance are those out of which the utterance is composed and into which it is ultimately divided, while those are no longer divisible into other utterances differing in kind from themselves; but even if they are divided, their parts are of the same kind, as the part of water is water, but not so with the part of a syllable. Similarly, those who speak of the elements of bodies mean the things into which bodies are divided as their ultimate constituents, while those are no longer divisible into other things differing in kind; and whether such things are one or several, these are what they call elements. And in a similar way the elements of geometrical figures are so called, and in general the elements of demonstrations; for the primary demonstrations, present within a number of other demonstrations,
7| [1014b] these are called the elements of demonstrations, and the primary syllogisms of this kind are those made from three terms through one middle term. And by transference people also call by the name element whatever, being one and small, is useful for many purposes; that is why what is small and simple and indivisible is called an element. Hence it has come about that the most universal things are thought to be elements, because each of them, being one and simple, is present in many things, either in all or in most, and because some think that the one and the point are principles. Since, then, what are called genera are universal and indivisible (for there is no single account of them), some call the genera elements, and more so than the differentia, because the genus is more universal; for whatever the differentia belongs to, the genus follows as well, but whatever the genus belongs to, the differentia does not belong to all of it. Common to all cases is that the element of each thing is the first constituent present within it. Nature is spoken of, in one sense, as the coming-to-be of growing things — as if one were to pronounce the upsilon with a lengthened sound — and in another sense as the first thing out of which a growing thing grows, this being present within it; further, as that from which the primary motion in each of the things that exist by nature originates, being present in it as such:
8| Things are said to grow when they receive increase through something else by touching and growing together with it, or growing onto it, as embryos do; growing-together differs from mere touching, for in the case of touching there need be nothing else besides the contact, whereas in things that have grown together there is some one and the same thing in both which, instead of mere contact, produces a growing-together and makes them one in respect of continuity and quantity, though not in respect of quality. Further, nature is spoken of as the first thing out of which any of the things that exist by nature either is or comes to be, this thing being unformed and unchangeable out of its own potentiality — as, for example, in the case of a statue and bronze utensils, the bronze is called the nature, and in the case of wooden things, the wood; and likewise in the other cases; for each thing consists of these, the primary matter being preserved throughout. In this way people also say that the elements of the things that exist by nature are their nature — some saying fire, others earth, others air, others water, others some other such thing, others some of these, and others all of them. Further, in another sense, nature is spoken of as the substance of the things that exist by nature, as, for example, those who say that nature is the primary composition,
9| [1015a] or, as Empedocles says, that nature is of none of the things that are, but only mixture and separation of the things mixed exist, and nature is merely a name given to these by human beings (Empedocles, fr. 8). Hence too, whatever exists or comes to be by nature, even when the thing already exists out of which it is natural for it to come to be or to exist, we say does not yet have its nature unless it has its form and shape. So what exists by nature is what comes from both of these together — for example, animals and their parts; and nature is both the primary matter (and this in two senses: either what is primary relative to the thing itself, or what is primary absolutely — as, for example, in the case of bronze works, bronze is primary relative to them, but water is perhaps primary absolutely, if all meltable things are water) and the form, that is, the substance; and this is the end of the coming-to-be. Indeed, by an extension of the term, every substance whatsoever is now called nature because of this, since nature too is a kind of substance. From what has been said, then, nature in the primary sense, and the sense properly so called, is the substance of things that have within themselves, as such, a principle of motion; for matter is called nature because it is receptive of this principle, and comings-to-be and growings are called motions because they proceed from this principle.
10| And this is the principle of motion in things that exist by nature, present within them in some way, either potentially or as a realization. The necessary is said to be that without which it is not possible to live, as a contributing cause — for example, breathing and food are necessary for an animal, since it is impossible to exist without these — and also that without which the good cannot exist or come to be, or without which the bad cannot be got rid of or removed (for example, drinking the medicine is necessary in order not to be ill, and sailing to Aegina is necessary in order to recover the money). Further, there is the forced and force: this is what impedes and hinders contrary to impulse and choice; for what is forced is called necessary, and hence also painful, as Evenus too says: 'for every necessary thing is by nature grievous'; and force is a kind of necessity, as Sophocles also says: 'but force compels me to do this'; and necessity is thought to be something that cannot be persuaded otherwise, and rightly so, for it is opposed to motion in accordance with choice and reasoning. Further, what cannot be otherwise we say is necessarily so; and it is in accordance with this sense of the necessary that all the other things too are, in a way, all called necessary: for what is forced is called necessary either as making something happen or as undergoing something at that time,
11| [1015b] when the impulse cannot proceed because of the compelling force, so that this is a necessity because of which there is no other way — and it is the same way with the joint causes of living and of the good. For when it is not possible for the good to exist here, or for living and being to exist there, without certain things, these are necessary, and this cause is a kind of necessity. Again, demonstration deals with necessary things, because it is not possible for the thing demonstrated to be otherwise, if it has been demonstrated without qualification; and the causes of this are the primary premises, if it is impossible for the things from which the syllogism proceeds to be otherwise. Now of some things something else is the cause of their being necessary, but of others nothing is, and rather it is because of these that other things exist of necessity. So that what is primarily and properly necessary is the simple: for this does not admit of being in more than one way, so that it cannot be one way and then another — for then it would already be in more than one way. If, then, there are certain eternal and unmoved things, nothing is forced or contrary to nature for them. One thing is said to be one in one sense accidentally, in another sense in its own right. Accidentally, for example, Coriscus and the musical, and musical Coriscus (for it is the same thing to say Coriscus and the musical, and musical Coriscus), and the musical and the just, and musical Coriscus and just Coriscus:
12| for all these are said to be one accidentally, the just and the musical because they are attributes of one substance, the musical and Coriscus because the one is an attribute of the other; and likewise, in a way, musical Coriscus is one with Coriscus because one of the parts of the account is an attribute of the other, namely the musical is an attribute of Coriscus; and musical Coriscus is one with just Coriscus because a part of each is an attribute of the same one thing. Similarly, whether the accident is predicated of a genus or of one of the universal names, for example that man is the same thing as musical man — either because musical is an attribute of man, which is one substance, or because both are attributes of some particular thing, for example Coriscus. Except that both do not belong in the same way, but the one, presumably, as a genus and within the substance, the other as a state or affection of the substance. All the things, then, that are called one accidentally are called so in this way; but of the things called one in their own right, some are called so because they are continuous, for example a bundle by a binding and pieces of wood by glue:
13| [1016a] and a line, even if it is bent, provided it is continuous, is called one, just as each of the parts is, for example a leg or an arm. And of these very things, those continuous by nature are more one than those continuous by craft. A thing is called continuous when its motion is one in its own right and cannot be otherwise; and it is one when it is undivided, and undivided with respect to time. Things are continuous in their own right when they are not one by contact; for if you were to posit pieces of wood touching one another, you would not say these are one, either one piece of wood or one body or any other continuous thing. Things that are continuous in a full sense are called one even if they have a bend, and still more those that have no bend, for example the shin or the thigh rather than the leg, because it is possible for the motion of the leg not to be one. And the straight line is more one than the bent; but the bent line, the one having an angle, we call both one and not one, because it is possible for its motion to be not simultaneous and also to be simultaneous; whereas that of the straight line is always simultaneous, and no part of it having magnitude is at rest while another is in motion, as is the case with the bent line. Again, in another sense a thing is called one because the substrate is undifferentiated in form; and things are undifferentiated of which the form is undivided as perceived by the senses:
14| and the substrate is either the first or the last in relation to the end; for wine is called one, and water one, insofar as it is undivided in form, and all liquids are called one, for example oil and wine, and all things that melt, because the ultimate substrate of all of them is the same — for all these are water or air. And things are also called one of which the genus is one, differing by opposite differentiae — and all these are called one because the genus, which is the substrate for the differentiae, is one (for example horse, man, dog are one something because all are animals), and in a way rather similar to how the matter is one. And these things are sometimes called one in this way, but sometimes the higher genus is said to be the same — if the species are the last in the genus — namely the genus above these, for example the isosceles and the equilateral are the same and one figure because both are triangles, but they are not the same triangles. Again, things are called one whose account, stating the essence, is undivided in relation to another account that makes clear what the thing's essence is (for every account, taken by itself, is divisible). For in this way both what has grown and what is diminishing are one, because the account is one, just as with plane figures the account of the form is one.
15| [1016b] And in general, those things of which the thought that thinks the essence is undivided, and cannot separate the thing either in time or in place or in account, are most of all one, and among these, those that are substances. For universally, whatever has no division, insofar as it has none, is on that account called one — for example, if insofar as it is man it has no division, it is one man; if insofar as it is animal, one animal; if insofar as it is a magnitude, one magnitude. Now most things are called one because they either do or have or undergo or stand in relation to some other thing that is one; but the things called one in the primary sense are those whose substance is one, and one either by continuity or in form or in account. For we count as more than one either things that are not continuous, or things whose form is not one, or things whose account is not one. Again, in one sense we say a thing is one, whatever it is, if it is a quantity and continuous; in another sense we say it is not, unless it is somehow a whole, and this it is not unless it has a form that is one — for example we would not say we see it as equally one if we saw the parts of a shoe put together in just any way, unless it were through their continuity, but rather if put together so as to be a shoe and already have some one form:
16| and this is why the line of the circle is, above all, the most one of lines, because it is whole and complete. And to be one is to be a certain principle of number; for the first measure is a principle, since that by which we first come to know each genus is the first measure of that genus. The one, then, is the principle of what is knowable about each thing. But the one is not the same in all genera; for in one place it is the quarter-tone, in another the vowel or the consonant; and of weight it is something else, and of motion something else again. But everywhere the one is undivided either in quantity or in form. Now of what is undivided in quantity, that which is undivided in every way and has no position is called a unit; that which is undivided in every way and has position is a point; that which is divisible in one direction is a line; that which is divisible in two directions is a plane; and that which is divisible in every way and in three directions in respect of quantity is a body. And conversely, that which is divisible in two directions is a plane, that which is divisible in one direction is a line, and that which is not divisible at all in quantity is a point and a unit — the one without position being a unit, the one with position a point. Again, some things are one in number, some in form, some in genus, some by analogy: in number, those whose matter is one; in form, those whose account is one; in genus, those that have the same figure of predication; and by analogy, whatever stands to one thing as another thing stands to a third.
17| And the later always follows on the earlier: for example, whatever is one in number is also one in species, but not everything one in species is one in number; [1017a] but everything one in species is also one in genus, while not everything one in genus is one in species, but rather by analogy; and not everything one by analogy is one in genus. It is also clear that the many will be spoken of as opposed to the one, in ways corresponding to the ways the one is spoken of: some things are called many because they are not continuous, others because their matter is divisible in respect of form — either the primary matter or the last — and others because there are several accounts stating the essence. Being is spoken of partly accidentally, partly in its own right. Accidentally, for example, we say the just man is musical, and the man is musical, and the musical is a man, speaking in much the same way as when we say the musical builds, because it is accidental to the builder to be musical, or to the musical to be a builder (for 'this is that' signifies that this is accidental to that); and so too in the cases mentioned: for when we say the man is musical, and the musical is a man, or the white is musical, or this is white, in one case it is because both are accidental to the same thing, in another because it is accidental to a thing that is, and in the case of the musical man, because the musical is accidental to this man (and in the same way we also speak of the not-white as being, because that to which it is accidental itself is). So the things said to be accidentally are said to be so either because both belong to the same existing thing, or because they belong to something that is, or because the thing itself is that to which belongs the thing of which it is itself predicated.
18| Things are said to be in their own right in as many ways as the figures of predication signify: for in as many ways as being is spoken of, in that many ways it signifies being. Since, then, of things predicated some signify what a thing is, others of what quality, others of what quantity, others a relation, others doing or being acted on, others where, others when, being signifies the same as each of these: for it makes no difference to say 'the man is being-well' or 'the man is-well', nor 'the man is walking' or 'is cutting' rather than 'the man walks' or 'cuts', and likewise in the other cases. Further, 'to be' and 'is' signify that a thing is true, and 'not to be' that it is not true but false — likewise with affirmation and negation: for example, that Socrates is musical signifies that this is true, or that Socrates is not white, that this is true; but 'the diagonal is commensurable' signifies that this is false.
19| [1017b] Further, 'to be' and 'being' signify, of the things spoken of, that which can be said potentially and that which can be said actually: for we say that a thing sees both when it is capable of seeing potentially and when it is seeing actually, and likewise that a thing knows both when it is capable of using the knowledge and when it is using it, and that a thing is at rest both when rest already belongs to it and when it is capable of being at rest. And likewise with substances: for we say that Hermes is in the stone, and the half is in the line, and that grain not yet ripe is grain. When a thing is already possible and when it is not yet, must be determined elsewhere. Substance is spoken of as the simple bodies — for example earth, fire, water, and the like — and bodies in general, and the things composed of these, both animals and divine beings, and the parts of these; all these are called substance because they are not said of a subject, but the other things are said of them. In another way, substance is whatever is the cause of being, present within such things as are not said of a subject — for example the soul in the case of an animal. Further, whatever parts are present within such things, bounding them and signifying a this, and whose removal removes the whole — for example, as some say, the surface is substance of body, and the line of the surface.
20| And in general, number seems to some to be of this kind (for when it is removed, they say, nothing is, and it bounds everything). Further, the essence — whose account is a definition — this too is called the substance of each thing. It follows, then, that substance is spoken of in two ways: as the ultimate subject, which is no longer said of anything else, and as whatever is a this and separable — and of this kind in each case is the shape and the form. Things are called the same partly accidentally, as when the white and the musical are called the same because they are accidental to the same thing, and man and musical because the one is accidental to the other, and the musical man is called the same as man because the musical is accidental to the man; and each of these is called the same as this one, and this one the same as each of those — for the man and the musical are both said to be the same as the musical man, and this in turn is said to be the same as them (which is why none of these is said universally: for it is not true to say that every man is the same as the musical, since universal terms belong in their own right, while accidents do not belong in their own right;
21| [1018a] but of particulars it is said without qualification: for Socrates and musical Socrates seem to be the same; but 'Socrates' is not said of many, and so we do not say 'every Socrates' as we say 'every man'). Some things, then, are called the same in this way, but others are called the same in their own right, in as many ways as the one is: for things whose matter is one, either in species or in number, are called the same, and things whose substance is one; so that it is clear that sameness is a kind of oneness of the being either of more than one thing, or of a thing treated as more than one — as when someone calls a thing the same as itself, for then he treats it as two. Things are called different whose forms are more than one, or their matter, or the account of their substance; and in general 'different' is spoken of as opposed to 'the same'. Things are called distinct which, while being the same something, are different — not only in number but in species or genus or by analogy; further, things whose genus is different, and contraries, and whatever has otherness in its substance. Things are called similar which have undergone entirely the same affections, and those which have undergone more of the same affections than different ones, and those whose quality is one; and, of the contraries in respect of which alteration is possible, whatever has more of them, or the more decisive ones, is similar in virtue of this.
22| Opposed to the similar are the dissimilar. Things called opposed are: contradiction, contraries, relatives, privation and possession, and the extremes from which and into which generations and destructions occur; and whatever cannot be present at the same time in that which is receptive of both is said to be opposed — either the things themselves, or that from which they are. For grey and white do not belong to the same thing at the same time; that is why the things from which they come are opposed. Things are called contrary which, differing in genus, cannot be present at the same time in the same thing; and things that differ most among those in the same genus; and things that differ most among those in the same recipient; and things that differ most among those falling under the same power; and those whose difference is greatest, either without qualification, or in genus, or in species. Other things are called contrary — some because they have such contraries, others because they are receptive of them, others because they are productive or affective of them, or are producing or undergoing them, or are losses or acquisitions, or are possessions or privations of them. And since the one and being are spoken of in many ways, it necessarily follows that the other terms spoken of in relation to them also do so — so that the same and the different and the contrary do too, so that each is different according to each category.
23| Things are called different in species which, being of the same genus, are not subordinate to one another, [1018b] and which, being in the same genus, have a differentia, and which have a contrariety in their substance; and contraries are different in species from one another, either all of them or those called so primarily; and things are different in species whose accounts are different even in the ultimate species of the genus (for example, man and horse are undivided in genus, but their accounts are different); and so are things which, though in the same substance, have a differentia. Things called the opposites of these are the same in species. Some things are called prior and posterior on the ground that there is some first thing and starting point in each genus, by being nearer to some determinate starting point, either without qualification and by nature, or in relation to something, or in some place, or by certain agents — for example, some things are prior in place by being nearer, either by nature to some determinate place (for example, the middle or the extreme) or to some chance place, while what is farther off is posterior; others are prior in time, and this in two ways (some by being farther from the now, as with things that have already happened — for example, the Trojan War is prior to the Persian Wars, because it is farther removed from the now; others by being nearer to the now, as with things that are going to happen — for example, the Nemean games are prior to the Pythian, because they are nearer to the now, the now being used as a starting point and a first thing):
24| others are prior in respect of motion (for what is nearer to the first mover is prior — for example a child is prior to a man; and this too is in a way a starting point without qualification); others in respect of capacity (for what exceeds in capacity is prior, that is, the more powerful; and a thing of this sort is one on whose choice the other, posterior thing must necessarily follow, so that if the first does not cause motion the second does not move, while if the first does cause motion the second moves — and the choice is a starting point); others in respect of order (these are things which, in relation to some one determinate thing, stand apart from one another according to some ratio — for example, the man next to the leader is prior to the one three places off, and the second-from-last string is prior to the last; for in the one case the leader is the starting point, in the other the middle string is). These things, then, are called prior in this way; but there is another way, that of being prior in knowledge, as also being called prior without qualification. And of these, again, things prior in account and things prior in perception differ: for according to account the universals are prior, but according to perception the particulars are. And according to account the accident is prior to the whole — for example, the musical is prior to the musical man, since the account will not be whole without the part; and yet it is not possible for the musical to exist without some musical person existing. Again, the affections of prior things are themselves called prior — for example, straightness is prior to smoothness:
25| for the one is an affection of a line in its own right, the other of a surface. [1019a] These things, then, are called prior and posterior in this way; but other things are so called in respect of nature and substance, namely all such as admit of being without other things, while those other things cannot be without them — a division Plato used. (Since being is spoken of in many ways: first, the substrate is prior, and this is why substance is prior; then, in another way, things are prior according to potentiality and according to actuality — for some things are prior in potentiality, others in actuality; for example, in potentiality the half is prior to the whole, and the part to the whole, and the matter to the substance, but in actuality they are posterior, since it is only when the whole has been broken up that they will exist in actuality.) In a certain way, then, all the things called prior and posterior are so called according to these senses: for some things, in respect of coming to be, can exist apart from the others — for example the whole in relation to the parts — while others, in respect of perishing, can exist apart from the others — for example the part in relation to the whole. And likewise with the rest. Capacity is spoken of, in one sense, as a starting point of motion or change that is in another thing, or in the thing itself insofar as it is other — for example, the art of building is a capacity that does not exist in the thing being built, whereas the art of medicine, being a capacity, might exist in the person being healed, though not insofar as he is being healed. The starting point of change or motion in general, then, when it is in another thing, or in the thing itself insofar as it is other, is called capacity; and the starting point of being acted on by another thing, or by the thing itself insofar as it is other, is also called capacity (for it is in virtue of this that what is acted on is acted on in some way — sometimes we say a thing is capable of undergoing anything whatever that happens to it, sometimes not in respect of every affection, but only if the affection is for the better):
26| again, capacity is the capacity of doing this well, that is, according to choice: for sometimes we say of those who could only walk or speak, but not well, or not as they had chosen, that they are not able to speak or walk; and likewise in the case of being acted on. Again, all those states in virtue of which things are wholly unaffected, or unchangeable, or not easily moved for the worse, are called capacities: for a thing is broken, and crushed, and bent, and altogether destroyed, not by being able but by not being able and by falling short in something; and things are unaffected by such things which are only hardly and slightly affected, on account of a capacity, and by being able, and by being in a certain state. Since capacity is spoken of in so many ways, the capable too will be spoken of, in one sense, as that which has a starting point of motion or change (for even what stands still is capable of something) in another thing, or in itself insofar as it is other; in another sense, if some other thing has such a capacity over it,
27| [1019b] in another sense, if it has the capacity to change into anything whatever, whether for the worse or for the better (for even what is being destroyed seems to be capable of being destroyed — otherwise it would not have been destroyed, if it were incapable of it; but as it is, it has some disposition and cause and starting point of such an affection; and sometimes it seems to be so by having something, sometimes by being deprived of something; and if privation is in a way a state, everything would be capable by having something; but if not, then a thing is capable in one sense by having some state and starting point, and, in another sense, homonymously, by having the privation of this, if it is possible to have such a privation — but if not, then only homonymously); and in another sense, by not having in it, or in what is other than it, a capacity or starting point that is destructive of it. Further, all these are so called either because the thing would merely happen to come to be or not come to be, or because it would happen well. For even in things without soul such a capacity is present, for example in instruments: for they say that one lyre is capable of being sounded, and another capable of nothing, if it is not tuneful. Incapacity is a privation of capacity, and of such a starting point as has been described, either altogether, or in the case of a thing naturally fitted to have it, or even at the time when it is already naturally fitted to have it:
28| for they would not say in the same way that a child and a man and a eunuch are unable to beget. Again, corresponding to each of the two capacities there is an opposed incapacity, both to the capacity that merely causes motion and to the capacity that causes motion well. And so some things are called incapable in accordance with this incapacity, others in a different way, along with capable and incapable in this further sense: a thing is impossible of which the contrary is necessarily true (for example, it is impossible for the diagonal to be commensurable, because this is false, and its contrary is not only true but necessarily true, namely that it is incommensurable; so the commensurable is not only false but necessarily false); the contrary of this, the possible, holds when it is not necessary that the contrary be false — for example, it is possible for a man to be sitting, since it is not necessarily false that he is not sitting. The possible, then, means in one sense, as has been said, what is not necessarily false; in another, what is true; in another, what admits of being true. (It is by metaphor that capacity is spoken of in geometry.) These things, then, are called possible not in accordance with capacity in the strict sense; but all the things that are called possible in accordance with capacity are so called with reference to the one primary sense:
29| [1020a] This is a principle of change in another thing, or in the thing itself as other. For other things are called potential because some of them have some such power in another, some do not have it, and some have it in a certain way. And likewise for the incapable. So that the governing definition of the primary sense of potentiality would be: a principle capable of producing change in another thing, or in the thing itself as other. Quantity means what is divisible into constituent parts, each or every one of which is by nature some one thing and a this. A plurality is a quantity if it is countable, a magnitude if it is measurable. A plurality means what is divisible potentially into non-continuous parts, a magnitude what is divisible into continuous parts. Of magnitude, that which is continuous in one dimension is length, in two breadth, in three depth. Of these, plurality bounded is number, length is a line, breadth is a surface, depth is a body. Further, some things are called quantities in their own right, others accidentally, for instance the line is a quantity in its own right, the musical is a quantity accidentally. Of those in their own right, some belong to the substance, for instance the line is a quantity of this sort (for it is present in the account that states what a thing is), while others are affections and states of a substance of this kind, for instance the much and the little, the long and the short, the broad and the narrow, the deep and the shallow, the heavy and the light, and other such things.
30| The large and the small, and larger and smaller, both said in their own right and said relative to one another, are affections of quantity in their own right; but these names are also transferred to other things. Of the things called quantities accidentally, some are called so in the way it was said the musical and the white are quantities because that to which they belong is a quantity, others as motion and time are called quantities: for these too are called a certain amount and continuous, because the things of which these are affections are divisible. I mean not the thing that is moved but the distance it was moved through: for because that is a quantity, motion too is a quantity, and time is a quantity because motion is. Quality is said in one way of the differentia of substance, for instance man is a certain sort of animal because two-footed, the horse because four-footed, and a circle is a certain sort of figure because it has no angles — quality here being the differentia relative to substance;
31| [1020b] — quality is said in this one way, then, as the differentia of substance; in another way as applied to unchangeable things, the objects of mathematics, as numbers are of a certain quality, for instance the composite numbers, which are not only in one dimension but of which the plane and the solid are copies (these are the numbers that are so-many-times-so-many, or so-many-times-so-many-times-so-many), and generally whatever belongs to the substance apart from quantity: for the substance of each thing is what it is taken once, for instance of the number six it is not what it is taken twice or three times but what it is taken once, for six taken once is six. Further, quality includes all the affections of changeable substances, for instance hotness and coldness, whiteness and blackness, heaviness and lightness, and all such things, in respect of which bodies are also said to be altered when they change. Further, it includes quality in respect of virtue and vice, and generally the bad and the good. Quality, then, would be spoken of in roughly two ways, and of these one is the most proper: for the primary quality is the differentia of substance (and the quality found in numbers is a part of this, being a certain differentia of substances, though of substances either not changing or not qua changing), while the other sense covers the affections of things that are changing, qua changing, and the differentiae of motions.
32| Virtue and vice are a part of these affections: for they make plain the differentiae of the motion and the activity, in respect of which things that are in motion act or are acted upon well or badly. For what is capable of being moved or of acting in this way is good, what is capable in this other and contrary way is bad. The good and the bad signify quality especially in the case of ensouled things, and among these especially in those that have choice. Relative things are called so in one way as the double is relative to the half and the triple to the third, and generally the multiple to what it is a multiple of, and the exceeding to what it exceeds; in another way as the productive of heat is relative to what can be heated, and the cutting to what can be cut, and generally the active to the passive; in another way as the measurable is relative to the measure, the knowable to knowledge, and the perceptible to perception. Things are called relative in the primary sense according to number, either simply or determinately, either relative to themselves or to one — for instance the double is a determinate number relative to one, while the multiple is relative to one according to number, though not determinately, being, say, this number or that;
33| [1021a] while the sesquialterate is relative to the subsesquialterate according to a determinate number relative to a number; and the superparticular is relative to the subsuperparticular according to an indeterminate number, as the multiple is relative to one; and the exceeding is relative to the exceeded altogether indeterminately in respect of number: for number is commensurable, and of what is not commensurable there is no number spoken of, but the exceeding is, relative to the exceeded, just so much and something more, and this is indeterminate: for it may be either equal or not equal, whichever happens to be the case. All these relatives, then, are spoken of according to number and are affections of number; and further the equal and the like and the same are spoken of relative in another way (for all these are spoken of in respect of the one: things are the same whose substance is one, alike whose quality is one, equal whose quantity is one; and the one is the principle and measure of number, so that all these are called relative according to number, though not in the same way); and the active and the passive are called relative according to an active and a passive power and the activities of these powers, for instance what is capable of heating is relative to what can be heated because it has the capacity, and again what is heating is relative to what is being heated, and what is cutting to what is being cut, as things actually engaged in activity.
34| Of the things spoken of according to number there are no activities, except in the way spoken of elsewhere; but relatives according to motion have no such activities. Of the relatives according to a capacity, some are also spoken of according to times, as what has produced is relative to what has been produced, and what will produce to what will be produced. For it is in this way too that a father is called father of a son: the one has produced something, the other has undergone something. Further, some relatives are so according to a privation of capacity, as the incapable and whatever is spoken of in this way, for instance the invisible. Now the things spoken of as relative according to number and according to capacity are all relative in that the very thing they are is spoken of as belonging to another, and not in that something else is relative to it; but the measurable and the knowable and the thinkable are called relative in that something else is spoken of as relative to them. For the thinkable signifies that there is a thought of it, but the thought is not relative to that of which it is the thought (for then the same thing would have been said twice); and likewise sight is the sight of something, not of that of which it is the sight (though that too would be true to say), but relative to color or to some other such thing. In the other way the same thing would be said twice, namely that sight is of that of which it is the sight.
35| [1021b] Of things called relative in their own right, some are called so in this way, others because their genera are of this kind — for example medicine is among the relatives because its genus, knowledge, is thought to be relative; further, whatever things are called relative according to the properties they have, for example equality because the equal is relative, and likeness because the like is relative. Others are relative accidentally, for example a man is relative because it is accidental to him to be double something, and this is one of the relatives; or the white is relative if it is accidental to the same thing to be both double and white. Complete is said of one thing in the sense that outside which nothing can be found, not even one part (for example the complete time of each thing is that outside of which no time belonging to it can be found which is a part of that time), and of that which, in respect of virtue and excellence, has no excess relative to its kind, for example a complete doctor and a complete flute-player, when they lack nothing according to the form of their proper virtue (and by this transference we speak the same way even of bad things, calling a complete swindler and a complete thief, since we also call them good — a good thief and a good swindler; and virtue is a kind of completion —
36| for each thing is complete then, and every substance is complete then, when in respect of the form of its proper virtue it lacks no part of its natural magnitude): further, things to which the end belongs — an end that is worthwhile — are called complete, since it is by having the end that they are complete; so that, since the end is one of the extreme things, we also, by transference, speak of a thing as completely ruined and completely destroyed, when nothing is missing from the destruction and the evil but it is at the extreme; hence too the ending of life is called, by transference, an end, because both are extremes; and the end also means that for the sake of which, when this is an extreme. Things, then, called complete in their own right are called so in this many ways: some in that they lack nothing in respect of what is good, and have no excess, and nothing can be found outside them; others, in general, in that they have no excess in their own genus and there is nothing outside them.
37| [1022a] The other things are now called complete in accordance with these, either by producing something of this sort, or by having it, or by being fitted to it, or by being related in some way or other to the things called complete in the primary sense. Limit is said of the extreme of each thing, and of that outside which nothing first can be found, and within which everything first is contained, and whatever is the form of a magnitude or of a thing having magnitude, and the end of each thing (and this is that toward which motion and action tend, and not that from which — though sometimes it is both, both that from which and that toward which, and also that for the sake of which), and the substance of each thing and the essence of each thing; for this is the limit of knowledge, and if of knowledge, then also of the thing. So it is clear that in as many ways as the principle is spoken of, in that many ways the limit is spoken of too, and in still more ways; for the principle is a kind of limit, but not every limit is a principle. 'In virtue of which' is said in many ways: in one way, the form and the substance of each thing, for example that in virtue of which a thing is good is the good itself; in another, that in which a thing first naturally comes to be, for example color in a surface. So what is called 'in virtue of which' in the primary sense is the form, and in a secondary sense it is as the matter of each thing and the substrate proper to each thing.
38| In general, 'in virtue of which' will apply in as many senses as the cause; for it is said in virtue of what he has come, or for the sake of what he has come, and in virtue of what someone has reasoned falsely or has drawn a valid conclusion, or what is the cause of the syllogism or of the false reasoning. Further, 'in virtue of which' is said in respect of position, in virtue of which he stands or in virtue of which he walks; for all these signify place and position. So 'in its own right' must also be said in many ways. For in one sense the essence of each thing is in its own right, for example Callias is in his own right Callias, and so is the essence of Callias; in another sense, whatever belongs in the account of what a thing is, for example Callias is in his own right an animal, for animal is present in the account, since Callias is a kind of animal. Further, if something has received an attribute in itself, first, or in some part of itself — for example a surface is white in its own right, and a man lives in his own right, for the soul is a part of the man, and it is in the soul primarily that life resides. Further, that of which there is no other cause; for of man there are many causes — animal, two-footed — but nevertheless man is a man in his own right. Further, whatever belongs to a thing alone, and insofar as it belongs to it alone, is separate and in its own right.
39| [1022b] Disposition is said of the arrangement of what has parts, whether in respect of place, or of capacity, or of form; for there must be some position, as indeed the name 'disposition' itself indicates. State is said, in one sense, as being a kind of activity of the haver and the thing had, like an action or a motion (for whenever one thing acts and another is acted upon, there is a making between them; so too between the one having clothing and the clothing had there is a having-state) — and it is clear that this sort of state cannot itself have a state, for it would go on to infinity, if what is had could itself have the having; but in another sense, state is said of the disposition in accordance with which the thing disposed is disposed well or badly, and either in its own right or in relation to something else — for example health is a state, for it is a disposition of this kind. Further, state is said of a thing if it is a part of such a disposition; hence too the virtue of the parts is a kind of state. Affection is said, in one sense, of a quality in respect of which alteration is possible, for example white and black, sweet and bitter, heaviness and lightness, and all other such things; in another sense, of the actualizations of these — the alterations already under way. Further, more particularly than these, the harmful alterations and motions, and especially the painful injuries.
40| Further, the magnitudes of misfortunes and painful things are called affections. Privation is said, in one sense, when a thing does not have something that it is natural to have, even if it is not itself the kind of thing naturally suited to have it — for example a plant is said to be deprived of eyes; in another sense, when a thing that is naturally suited to have something, either itself or its genus, does not have it — for example a blind man is deprived of sight in a different way than a mole is, the mole in respect of its genus, the man in his own right. Further, when a thing that is naturally suited to have something, and at the time when it is natural for it to have it, does not have it; for blindness is a kind of privation, but a person is not called blind at every age, but only if he does not have sight at the age when it is natural to have it. Likewise too in respect of that in which, and in virtue of which, and in relation to which, and in the manner in which it is naturally suited to have something, if it does not have it. Further, the forcible removal of anything is called privation. And in as many ways as the negations formed with 'a-' are said, in that many ways privations too are said; for the unequal is so called because it lacks equality, which it is naturally suited to have, the invisible both because it has no color at all and because it has it only faintly, and the footless both because it lacks feet altogether and because it has poor ones. Further, also by having little of something, for example the stoneless (fruit):
41| [1023a] This is being in a poor condition in some way. Again, things are said to lack something by not having it easily or not having it well — for instance, the uncuttable is called so not only because it is not cut but because it is not cut easily or well. Again, by not having it at all: for a person is not called blind for lacking sight in one eye, but only if lacking it in both; that is why not everyone is good or bad, just or unjust, but there is also an intermediate. "To have" is said in many ways: in one way, to lead according to one's own nature or according to one's own impulse — that is why a fever is said to "have" a person, and tyrants are said to have their cities, and those wearing clothes are said to have their clothing. In another way, it is said of that in which something is present as in a receptacle, as the bronze has the form of the statue and the body has the disease. In another way, as the container has the things contained: for that in which something is, as a container, is said to be "had" by it — for instance we say the vessel has the liquid, the city has people, and the ship has sailors; and in this way too the whole has its parts. Again, what prevents something from moving or acting according to its own impulse is said to "have" that very thing — as the pillars are said to have the weights resting on them, and as the poets make Atlas have the sky, on the ground that it would otherwise fall upon the earth, as some of the natural philosophers also say.
42| In this same way, what holds things together is said to have the things it holds together, since each of them would otherwise separate according to its own impulse. And "to be in something" is spoken of in a similar way and follows upon "to have." "To be from something" is said, in one way, of that from which a thing is as from matter, and this in two ways — either according to the first genus or according to the last species: for instance in one sense all meltable things are from water, in another sense the statue is from bronze. In another way, it is said of the first originating principle of motion — for instance, "from what did the fight arise? From abuse, because this was the starting point of the fight." In another way, it is said of the composite, from the matter and the form, as the parts are from the whole, and the verse is from the Iliad, and the stones are from the house: for the form is an end, and what has attained its end is complete. And other things are said to be from the part as the form is, as man is from "two-footed" and the syllable from the letter — for this is different from the way the statue is from bronze.
43| [1023b] For the composite substance is from perceptible matter, but the form too is from the matter of the form. So some things are said to be from something in this way, others if something holds according to a part of these ways — as the child is from father and mother, and plants are from earth, because it is from some part of them. In another way, something is said to be "from" that after which it comes in time — as night is from day, and winter from fair weather, because the one comes after the other. Of these, some are so called because they have a change into one another, as the cases just mentioned, while others are so called only by mere succession in time — as the voyage is said to be "from the equinox" because it took place after the equinox, and the Thargelia are "from" the Dionysia because they come after the Dionysia. "Part" is said, in one way, of that into which a quantity may be divided in any way whatsoever (for what is taken away from a quantity, insofar as it is a quantity, is always called a part of it — for instance two is called in a way a part of three); in another way, only of the things that measure such things exactly — hence two is in one sense said to be a part of three, and in another sense not. Again, a "part" is said of that into which the form might be divided apart from quantity, and these too are called parts of it.
44| That is why the species are said to be parts of the genus. Again, parts are that into which the whole is divided, or of which it is composed — whether the whole is the form, or that which has the form — for instance, of the bronze sphere or the bronze cube, the bronze is a part (this is the matter in which the form is), and the angle is a part. Again, the elements in the account that makes each thing clear are also parts of the whole; that is why the genus too is called a part of the species, though in another sense the species is a part of the genus. A "whole" is said of that from which none of the parts is missing, of which it is naturally called a whole, and of that which contains the things contained in such a way that they are some one thing; and this in two ways — either as each part being one, or as the one being composed out of these. For the universal, and what is called universal as being a certain whole, is universal in this sense: that it contains many things by being predicated of each and by all of them being one, as each one — for instance man, horse, god, because all are animals. But the continuous and limited is a whole when it is some one thing composed of several parts present in it, above all potentially, and if not, actually. Of these themselves, the things that are so by nature are more truly wholes than those that are so by craft, just as we said in the case of the one — on the ground that wholeness is a kind of oneness.
45| [1024a] Further, quantity possesses a starting point, a midpoint, and a final point: wherever arrangement makes no difference, the thing is called "all," and wherever arrangement does make a difference, it is called "whole." Whatever admits of both is called both "whole" and "all"; and these are things whose nature remains the same through transposition, but whose shape does not — for instance wax and a garment: for these are called both whole and all, since they have both. But water and liquids and number are called "all," while "whole number" and "whole water" are not said, except by metaphor. Things are called "all" in the case where the "all" is applied to them as to one thing; "all" in the plural is applied to them as to things divided — "all this number," "all these units." "Maimed" is not said of just any quantity, but it must be a quantity that is both divisible and a whole. For the number two is not maimed when one unit is taken from the other (for the deficiency and the remainder are never equal), nor is any number whatever maimed in this way at all: for the substance too must remain — if a cup is maimed, it must still be a cup; but the number is no longer the same number. Besides this, even if the parts are unlike, not even these wholes are in every case maimed (for a number is, in a sense, such as to have unlike parts too, as two, three); but in general, things whose position makes no difference are not maimed at all, as water or fire — rather, the things that can be maimed must be such as have a position by virtue of their substance.
46| Again, they must be continuous: for a harmony too, though composed of unlike parts and having a position, does not become maimed. Besides this, not even the things that are wholes are maimed by the privation of just any part whatsoever. For it must not be either the dominant parts of the substance, or parts occupying just any location — for instance, if the cup is pierced, it is not maimed, but if the handle or some extremity is removed, it is; and a man is not maimed if he loses flesh or the spleen, but if he loses some extremity — and not every extremity either, but one that, when wholly removed, does not grow back. That is why bald men are not maimed. "Genus" is said, in one sense, when the coming-to-be of things having the same form is continuous — as it is said "as long as the human race exists," meaning as long as their coming-to-be is continuous; and in another sense, of that from which they derive as from the first thing that set them in motion into being — for it is in this way that some are called Greeks by race and others Ionians, because the former are from Hellen and the latter from Ion as the first begetter; and people are called a race more from the begetter than from the matter (for they are also called a race from the female, as those "from Pyrrha").
47| [1024b] Again, as the plane is the genus of plane figures and the solid of solids: for each of the figures is a plane of a certain kind, or a solid of a certain kind; and this is the substrate for the differentiae. Again, as in definitions the first thing present, which is stated in the answer to "what it is," is the genus, of which the qualities are called the differentiae. So genus is spoken of in this many ways: one, in respect of continuous generation of the same form; another, in respect of the first thing that produced motion, being of the same form; another, as matter — for that of which the differentia and the quality are predicated is the substrate, which we call matter. Things are said to differ in genus when their first substrate is different, and neither is resolved into the other, nor are both resolved into the same thing — for example, form and matter differ in genus, and so do all the things spoken of according to a different figure of the category of being (for some signify what a thing is, among beings, others a quality, others as was distinguished earlier); for none of these are resolved either into one another or into some one thing. Falsity is spoken of, in one way, as a false state of affairs, and of this, one kind consists in not being put together, or in being impossible to put together (as when it is said that the diagonal is commensurable, or that you are sitting —
48| for of these the one is always false, the other only sometimes; for in this way these things are not-beings), while others are things that indeed are, but are naturally such as to appear either not as they are, or as things that do not exist (for example, a sketch in perspective, and dreams — for these are indeed something, but not what they produce the appearance of). States of affairs, then, are called false in this way, either by not existing, or by the appearance arising from them being of what does not exist. A statement is false which is a statement of things that are not, insofar as it is false; hence every statement is false of something other than that of which it is true — for example, the statement of a circle is false of a triangle. Of each thing there is, in one sense, a single statement — that of its essence — but in another sense there are many, since the thing itself and the thing itself as modified are somehow the same, for example Socrates and musical Socrates (but the false statement is, without qualification, a statement of nothing). Hence Antisthenes held, foolishly, that nothing should be predicated except by its own proper statement, one of one; from which it followed that there could be no contradiction, and scarcely even falsehood. But it is possible to speak of each thing not only by its own statement but also by that of something else — falsely, indeed, and altogether so, but in a way also truly, just as eight is double by the statement of two.
49| [1025a] Things, then, are called false in this way; and a false man is one who is ready and inclined toward such statements, not for some other reason but for their own sake, and one who is apt to produce such statements in others — just as we say that things are false which produce a false appearance. Hence the argument in the Hippias misleads, in taking it that the same man is both false and true. For it takes as false the man who is capable of lying (and this is the man who has knowledge and is prudent); and further, that the man who is voluntarily bad is better than one who is bad involuntarily. But it arrives at this falsely by induction — for the man who limps voluntarily is better than the man who limps involuntarily — calling the limping an act of imitation; whereas if a man is actually lame voluntarily, he is presumably worse, just as with character, so too here. An accident is said of what belongs to something and can truly be said of it, yet neither of necessity nor for the most part — as when someone digging a hole for a plant finds a treasure. This finding of the treasure is then accidental to the man digging the hole: for it does not follow from that by necessity, nor does one generally find a treasure when planting. And a man might be both musical and pale; but since this comes about neither of necessity nor for the most part, we call it accidental.
50| So then, since there is what belongs to a thing, and belongs to a particular thing, and some of these also belong somewhere and at some time, whatever belongs to a thing but not because it was this, or now, or here, will be accidental. Nor indeed is there any determinate cause of the accidental, but a chance one; and this is indeterminate. It happened to someone to arrive at Aegina if he did not arrive there in order to go there, but was driven off course by a storm, or was seized by pirates. This accident has come about, or is, but not qua itself, but qua something else: for the storm was the cause of his not arriving where he was sailing to, and that was Aegina. But accident is also spoken of in another way, namely whatever belongs to each thing in its own right without being in its substance — for example, having its angles equal to two right angles belongs to the triangle. And these can be eternal, but none of the former can. The account of this is given elsewhere.