Book 5

Beginning means: (a) That part of a thing from which one may first move; eg., a line or a journey has one beginning here, and another at the opposite extremity. (b) The point from which each thing may best come into being; e.g., a course of study should sometimes be begun not from what is primary or from the starting-point of the subject, but from the point from which it is easiest to learn. (c) That thing as a result of whose presence something first comes into being; e.g., as the keel is the beginning of a ship, and the foundation that of a house, and as in the case of animals some thinkers suppose the heart to be the beginning, others the brain, and others something similar, whatever it may be. (d) That from which, although not present in it, a thing first comes into being, and that from which motion and change naturally first begin, as the child comes from the father and mother, and fighting from abuse. (e) That in accordance with whose deliberate choice that which is moved is moved, and that which is changed is changed; such as magistracies, authorities, monarchies and despotisms.

(f) Arts are also called beginnings, especially the architectonic arts. (g) Again, beginning means the point from which a thing is first comprehensible, this too is called the beginning of the thing; e.g. the hypotheses of demonstrations. (Cause can have a similar number of different senses, for all causes are beginnings.)

It is a common property, then, of all beginnings to be the first thing from which something either exists or comes into being or becomes known; and some beginnings are originally inherent in things, while others are not. Hence nature is a beginning, and so is element and understanding and choice and essence and final cause —for in many cases the Good and the Beautiful are the beginning both of knowledge and of motion.

Cause means: (a) in one sense, that as the result of whose presence something comes into being—e.g. the bronze of a statue and the silver of a cup, and the classes which contain these; (b) in another sense, the form or pattern; that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 and number in general is the cause of the octave—and the parts of the formula.

(c) The source of the first beginning of change or rest; e.g. the man who plans is a cause, and the father is the cause of the child, and in general that which produces is the cause of that which is produced, and that which changes of that which is changed. (d) The same as end; i.e. the final cause; e.g., as the end of walking is health.

For why does a man walk? To be healthy, we say, and by saying this we consider that we have supplied the cause. (e) All those means towards the end which arise at the instigation of something else, as, e.g. fat-reducing, purging, drugs and instruments are causes of health; for they all have the end as their object, although they differ from each other as being some instruments, others actions.

These are roughly all the meanings of cause, but since causes are spoken of with various meanings, it follows that there are several causes (and that not in an accidental sense) of the same thing. E.g., both statuary and bronze are causes of the statue; not in different connections, but qua statue. However, they are not causes in the same way, but the one as material and the other as the source of motion. And things are causes of each other; as e.g. labor of vigor, and vigor of labor—but not in the same way; the one as an end, and the other as source of motion.

And again the same thing is sometimes the cause of contrary results; because that which by its presence is the cause of so-and-so we sometimes accuse of being, by its absence, the cause of the contrary—as, e.g., we say that the absence of the pilot is the cause of a capsize, whereas his presence was the cause of safety.

And both, presence and privation, are moving causes.

Now there are four senses which are most obvious under which all the causes just described may be classed.

The components of syllables; the material of manufactured articles; fire, earth and all such bodies; the parts of a whole; and the premisses of a syllogistic conclusion; are causes in the material sense. Of these some are causes as substrate: e.g. the parts; and others as essence: the whole, and the composition, and the form.

The seed and the physician and the contriver and in general that which produces, all these are the source of change or stationariness. The remainder represent the end and good of the others; for the final cause tends to be the greatest good and end of the rest.

Let it be assumed that it makes no difference whether we call it good or apparent good. In kind, then, there are these four classes of cause.

The modes of cause are numerically many, although these too are fewer when summarized.

For causes are spoken of in many senses, and even of those which are of the same kind, some are causes in a prior and some in a posterior sense; e.g., the physician and the expert are both causes of health; and the ratio 2:1 and number are both causes of the octave; and the universals which include a given cause are causes of its particular effects.

Again, a thing may be a cause in the sense of an accident, and the classes which contain accidents; e.g., the cause of a statue is in one sense Polyclitus and in another a sculptor, because it is an accident of the sculptor to be Polyclitus. And the universal terms which include accidents are causes; e.g., the cause of a statue is a man, or even, generally, an animal; because Polyclitus is a man, and man is an animal.

And even of accidental causes some are remoter or more proximate than others; e.g., the cause of the statue might be said to be white man or cultured man, and not merely Polyclitus or man.

And besides the distinction of causes as proper and accidental, some are termed causes in a potential and others in an actual sense; e.g., the cause of building is either the builder or the builder who builds.

And the same distinctions in meaning as we have already described will apply to the effects of the causes; e.g. to this statue, or a statue, or generally an image; and to this bronze, or bronze, or generally material. And it is the same with accidental effects. Again, the proper and accidental senses will be combined; e.g., the cause is neither Polyclitus nor a sculptor but the sculptor Polyclitus.

However, these classes of cause are in all six in number, each used in two senses. Causes are (1.) particular, (2.) generic, (3.) accidental, (4.) generically accidental; and these may be either stated singly or (5, 6) in combination; and further they are all either actual or potential.

And there is this difference between them, that actual and particular causes coexist or do not coexist with their effects (e.g. this man giving medical treatment with this man recovering his health, and this builder with this building in course of erection); but potential causes do not always do so; for the house and the builder do not perish together.

Element means (a) the primary immanent thing, formally indivisible into another form, of which something is composed. E.g., the elements of a sound are the parts of which that sound is composed and into which it is ultimately divisible, and which are not further divisible into other sounds formally different from themselves. If an element be divided, the parts are formally the same as the whole: e.g., a part of water is water; but it is not so with the syllable.

(b) Those who speak of the elements of bodies similarly mean the parts into which bodies are ultimately divisible, and which are not further divisible into other parts different in form. And whether they speak of one such element or of more than one, this is what they mean.

(c) The term is applied with a very similar meaning to the elements of geometrical figures, and generally to the elements of demonstrations; for the primary demonstrations which are contained in a number of other demonstrations are called elements of demonstrations. Such are the primary syllogisms consisting of three terms and with one middle term.

(d) The term element is also applied metaphorically to any small unity which is useful for various purposes; and so that which is small or simple or indivisible is called an element.

(e) Hence it comes that the most universal things are elements; because each of them, being a simple unity, is present in many things—either in all or in as many as possible. Some too think that unity and the point are first principles.

(f) Therefore since what are called genera are universal and indivisible (because they have no formula), some people call the genera elements, and these rather than the differentia, because the genus is more universal. For where the differentia is present, the genus also follows; but the differentia is not always present where the genus is. And it is common to all cases that the element of each thing is that which is primarily inherent in each thing.

Nature means: (a) in one sense, the genesis of growing things—as would be suggested by pronouncing the υ of φύσις long—and (b) in another, that immanent thing from which a growing thing first begins to grow. (c) The source from which the primary motion in every natural object is induced in that object as such. All things are said to grow which gain increase through something else by contact and organic unity (or adhesion, as in the case of embryos).

Organic unity differs from contact; for in the latter case there need be nothing except contact, but in both the things which form an organic unity there is some one and the same thing which produces, instead of mere contact, a unity which is organic, continuous and quantitative (but not qualitative).

Again, nature means (d) the primary stuff, shapeless and unchangeable from its own potency, of which any natural object consists or from which it is produced; e.g., bronze is called the nature of a statue and of bronze articles, and wood that of wooden ones, and similarly in all other cases.

For each article consists of these natures, the primary material persisting. It is in this sense that men call the elements of natural objects the nature, some calling it fire, others earth or air or water, others something else similar, others some of these, and others all of them.

Again in another sense nature means (e) the substance of natural objects; as in the case of those who say that the nature is the primary composition of a thing, or as Empedocles says: Of nothing that exists is there nature, but only mixture and separation of what has been mixed; nature is but a name given to these by men.

Hence as regards those things which exist or are produced by nature, although that from which they naturally are produced or exist is already present, we say that they have not their nature yet unless they have their form and shape.

That which comprises both of these exists by nature; e.g. animals and their parts. And nature is both the primary matter (and this in two senses: either primary in relation to the thing, or primary in general; e.g., in bronze articles the primary matter in relation to those articles is bronze, but in general it is perhaps water—that is if all things which can be melted are water) and the form or essence, i.e. the end of the process, of generation. Indeed from this sense of nature, by an extension of meaning, every essence in general is called nature, because the nature of anything is a kind of essence.

From what has been said, then, the primary and proper sense of nature is the essence of those things which contain in themselves as such a source of motion; for the matter is called nature because it is capable of receiving the nature, and the processes of generation and growth are called nature because they are motions derived from it. And nature in this sense is the source of motion in natural objects, which is somehow inherent in them, either potentially or actually.

Necessary means: (a) That without which, as a concomitant condition, life is impossible; e.g. respiration and food are necessary for an animal, because it cannot exist without them. (b) The conditions without which good cannot be or come to be, or without which one cannot get rid or keep free of evil—e.g., drinking medicine is necessary to escape from ill-health, and sailing to Aegina is necessary to recover one’s money.

(c) The compulsory and compulsion; i.e. that which hinders and prevents, in opposition to impulse and purpose. For the compulsory is called necessary, and hence the necessary is disagreeable; as indeed Evenus says: For every necessary thing is by nature grievous.

And compulsion is a kind of necessity, as Sophocles says: Compulsion makes me do this of necessity.

And necessity is held, rightly, to be something inexorable; for it is opposed to motion which is in accordance with purpose and calculation. (d) Again, what cannot be otherwise we say is necessarily so.

It is from this sense of necessary that all others are somehow derived; for the term compulsory is used of something which it is necessary for one to do or suffer only when it is impossible to act according to impulse, because of the compulsion: which shows that necessity is that because of which a thing cannot be otherwise; and the same is true of the concomitant conditions of living and of the good. For when in the one case good, and in the other life or existence, is impossible without certain conditions, these conditions are necessary, and the cause is a kind of necessity.

(e) Again, demonstration is a necessary thing, because a thing cannot be otherwise if the demonstration has been absolute. And this is the result of the first premisses, when it is impossible for the assumptions upon which the syllogism depends to be otherwise.

Thus of necessary things, some have an external cause of their necessity, and others have not, but it is through them that other things are of necessity what they are.

Hence the necessary in the primary and proper sense is the simple, for it cannot be in more than one condition. Hence it cannot be in one state and in another; for if so it would ipso facto be in more than one condition. Therefore if there are certain things which are eternal and immutable, there is nothing in them which is compulsory or which violates their nature.

The term one is used (1.) in an accidental, (2.) in an absolute sense. (1.) In the accidental sense it is used as in the case of Coriscus and cultured and cultured Coriscus (for Coriscus and cultured and cultured Coriscus mean the same);

and cultured and upright and cultured upright Coriscus. For all these terms refer accidentally to one thing; upright and cultured because they are accidental to one substance, and cultured and Coriscus because the one is accidental to the other.

And similarly in one sense cultured Coriscus is one with Coriscus, because one part of the expression is accidental to the other, e.g. cultured to Coriscus; and cultured Coriscus is one with upright Coriscus, because one part of each expression is one accident of one and the same thing. It is the same even if the accident is applied to a genus or a general term; e.g., man and cultured man are the same, either because cultured is an accident of man, which is one substance, or because both are accidents of some individual, e.g. Coriscus.

But they do not both belong to it in the same way; the one belongs presumably as genus in the substance, and the other as condition or affection of the substance. Thus all things which are said to be one in an accidental sense are said to be so in this way.

(2.) Of those things which are said to be in themselves one, (a) some are said to be so in virtue of their continuity; e.g., a faggot is made continuous by its string, and pieces of wood by glue; and a continuous line, even if it is bent, is said to be one, just like each of the limbs; e.g. the leg or arm. And of these things themselves those which are naturally continuous are one in a truer sense than those which are artificially continuous.

Continuous means that whose motion is essentially one, and cannot be otherwise; and motion is one when it is indivisible, i.e. indivisible in time. Things are essentially continuous which are one not by contact only; for if you put pieces of wood touching one another you will not say that they are one piece of wood, or body, or any other continuous thing.

And things which are completely continuous are said to be one even if they contain a joint, and still more those things which contain no joint; e.g., the shin or the thigh is more truly one than the leg, because the motion of the leg may not be one.

And the straight line is more truly one than the bent. We call the line which is bent and contains an angle both one and not one, because it may or may not move all at once; but the straight line always moves all at once, and no part of it which has magnitude is at rest while another moves, as in the bent line.

(b) Another sense of one is that the substrate is uniform in kind.

Things are uniform whose form is indistinguishable to sensation; and the substrate is either that which is primary, or that which is final in relation to the end. For wine is said to be one, and water one, as being something formally indistinguishable. And all liquids are said to be one (e.g. oil and wine), and melted things; because the ultimate substrate of all of them is the same, for all these things are water or vapor.

(c) Things are said to be one whose genus is one and differs in its opposite differentiae. All these things too are said to be one because the genus, which is the substrate of the differentiae, is one (e.g., horse, man and dog are in a sense one, because they are all animals); and that in a way very similar to that in which the matter is one.

Sometimes these things are said to be one in this sense, and sometimes their higher genus is said to be one and the same (if they are final species of their genus)—the genus, that is, which is above the genera of which their proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same figure (because they are both triangles), but not the same triangles.

(d) Again, things are said to be one when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable 〈into genus and differentiae〉. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one.

And in general those things whose concept, which conceives the essence, is indistinguishable and cannot be separated either in time or in place or in definition, are in the truest sense one; and of these such as are substances are most truly one. For universally such things as do not admit of distinction are called one in so far as they do not admit of it; e.g., if man qua man does not admit of distinction, he is one man; and similarly if qua animal, he is one animal; and if qua magnitude, he is one magnitude.

Most things, then, are said to be one because they produce, or possess, or are affected by, or are related to, some other one thing; but some are called one in a primary sense, and one of these is substance. It is one either in continuity or in form or in definition; for we reckon as more than one things which are not continuous, or whose form is not one, or whose definition is not one.

Again, in one sense we call anything whatever one if it is quantitative and continuous; and in another sense we say that it is not one unless it is a whole of some kind, i.e. unless it is one in form (e.g., if we saw the parts of a shoe put together anyhow, we should not say that they were one — except in virtue of their continuity; but only if they were so put together as to be a shoe, and to possess already some one form).

Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete.

The essence of one is to be a kind of starting point of number; for the first measure is a starting point, because that by which first we gain knowledge of a thing is the first measure of each class of objects. The one, then, is the starting-point of what is knowable in respect of each particular thing. But the unit is not the same in all classes, for in one it is the quarter-tone, and in another the vowel or consonant; gravity has another unit, and motion another. But in all cases the unit is indivisible, either quantitatively or formally.

Thus that which is quantitatively and qua quantitative wholly indivisible and has no position is called a unit; and that which is wholly indivisible and has position, a point; that which is divisible in one sense, a line; in two senses, a plane; and that which is quantitatively divisible in all three senses, a body.

And reversely that which is divisible in two senses is a plane, and in one sense a line; and that which is in no sense quantitatively divisible is a point or a unit; if it has no position, a unit, and if it has position, a point.

Again, some things are one numerically, others formally, others generically, and others analogically; numerically, those whose matter is one; formally, those whose definition is one; generically, those which belong to the same category; and analogically, those which have the same relation as something else to some third object.

In every case the latter types of unity are implied in the former: e.g., all things which are one numerically are also one formally, but not all which are one formally are one numerically; and all are one generically which are one formally, but such as are one generically are not all one formally, although they are one analogically; and such as are one analogically are not all one generically.

It is obvious also that many will have the opposite meanings to one. Some things are called many because they are not continuous; others because their matter (either primary or ultimate) is formally divisible; others because the definitions of their essence are more than one.

Being means (1.) accidental being, (2.) absolute being. (1.) E.g., we say that the upright person is cultured, and that the man is cultured, and that the cultured person is a man; very much as we say that the cultured person builds, because the builder happens to be cultured, or the cultured person a builder; for in this sense X is Y means that Y is an accident of X.

And so it is with the examples cited above; for when we say that the man is cultured and the cultured person is a man or the white is cultured or the cultured is white, in the last two cases it is because both predicates are accidental to the same subject, and in the first case because the predicate is accidental to what is; and we say that the cultured is a man because the cultured is accidental to a man.

(Similarly not-white is said to be, because the subject of which not-white is an accident, is.) These, then, are the senses in which things are said to be accidentally: either because both predicates belong to the same subject, which is; or because the predicate belongs to the subject, which is; or because the subject to which belongs that of which it is itself predicated itself is.

(2.) The senses of essential being are those which are indicated by the figures of predication; for being has as many senses as there are ways of predication. Now since some predicates indicate (a) what a thing is, and others its (b) quality, (c) quantity, (d) relation, (e) activity or passivity, (f) place, (g) time, to each of these corresponds a sense of being.

There is no difference between the man is recovering and the man recovers; or between the man is walking or cutting and the man walks or cuts; and similarly in the other cases.

(3.) Again, to be and is mean that a thing is true, and not to be that it is false.

Similarly too in affirmation and negation; e.g., in Socrates is cultured is means that this is true; or in Socrates is not-white that this is true; but in the diagonal is not commensurable is not means that the statement is false. (4.) Again, to be 〈or is 〉 means that some of these statements can be made in virtue of a potentiality and others in virtue of an actuality.

For we say that both that which sees potentially and that which sees actually is a seeing thing. And in the same way we call understanding both that which can use the understanding, and that which does; and we call tranquil both that in which tranquillity is already present, and that which is potentially tranquil.

Similarly too in the case of substances. For we say that Hermes is in the stone, and the half of the line in the whole; and we call corn what is not yet ripe. But when a thing is potentially existent and when not, must be defined elsewhere.

Substance means (a) simple bodies, e.g. earth, fire, water and the like; and in general bodies, and the things, animal or divine, including their parts, which are composed of bodies. All these are called substances because they are not predicated of any substrate, but other things are predicated of them.

(b) In another sense, whatever, being immanent in such things as are not predicated of a substrate, is the cause of their being; as, e.g., the soul is the cause of being for the animal.

(c) All parts immanent in things which define and indicate their individuality, and whose destruction causes the destruction of the whole; as, e.g., the plane is essential to the body (as some hold) and the line to the plane. And number in general is thought by some to be of this nature, on the ground that if it is abolished nothing exists, and that it determines everything.

(d) Again, the essence, whose formula is the definition, is also called the substance of each particular thing.

Thus it follows that substance has two senses: the ultimate subject, which cannot be further predicated of something else; and whatever has an individual and separate existence. The shape and form of each particular thing is of this nature.

The same means (a) accidentally the same. E.g., white and cultured are the same because they are accidents of the same subject; and man is the same as cultured, because one is an accident of the other; and cultured is the same as man because it is an accident of man; and cultured man is the same as each of the terms cultured and man, and vice versa; for both man and cultured are used in the same way as cultured man, and the latter in the same way as the former.

Hence none of these predications can be made universally. For it is not true to say that every man is the same as the cultured; because universal predications are essential to things, but accidental predications are not so, but are made of individuals and with a single application. Socrates and cultured Socrates seem to be the same; but Socrates is not a class-name, and hence we do not say every Socrates as we say every man.

Some things are said to be the same in this sense, but (b) others in an essential sense, in the same number of senses as the one is essentially one; for things whose matter is formally or numerically one, and things whose substance is one, are said to be the same. Thus sameness is clearly a kind of unity in the being, either of two or more things, or of one thing treated as more than one; as, e.g., when a thing is consistent with itself; for it is then treated as two.

Things are called other of which either the forms or the matter or the definition of essence is more than one; and in general other is used in the opposite senses to same.

Things are called different which, while being in a sense the same, are other not only numerically, but formally or generically or analogically; also things whose genus is not the same; and contraries; and all things which contain otherness in their essence.

Things are called like which have the same attributes in all respects; or more of those attributes the same than different; or whose quality is one. Also that which has a majority or the more important of those attributes of something else in respect of which change is possible (i.e. the contraries) is like that thing. And unlike is used in the opposite senses to like.

The term opposite is applied to (a) contradiction; (b) contraries; (c) relative terms; (d) privation; (e) state; (f) extremes; e.g. in the process of generation and destruction. And (g) all things which cannot be present at the same time in that which admits of them both are called opposites; either themselves or their constituents. Grey and white do not apply at the same time to the same thing, and hence their constituents are opposite.

Contrary means: (a) attributes, generically different, which cannot apply at the same time to the same thing. (b) The most different attributes in the same genus; or (c) in the same subject; or (d) falling under the same faculty. (e) Things whose difference is greatest absolutely, or in genus, or in species.

Other things are called contrary either because they possess attributes of this kind, or because they are receptive of them, or because they are productive of or liable to them, or actually produce or incur them, or are rejections or acquisitions or possessions or privations of such attributes.

And since one and being have various meanings, all other terms which are used in relation to one and being must vary in meaning with them; and so same, other and contrary must so vary, and so must have a separate meaning in accordance with each category.

Things are called other in species (a) which belong to the same genus and are not subordinate one to the other; or (b) which are in the same genus and contain a differentia; or (c) which contain a contrariety in their essence.

(d) Contraries, too (either all of them or those which are called so in a primary sense), are other in species than one another; and (e) so are all things of which the formulae are different in the final species of the genus (e.g., man and horse are generically indivisible, but their formulae are different); and (f) attributes of the same substance which contain a difference. The same in species has the opposite meanings to these.

Prior and posterior mean: (1.) (a) In one sense (assuming that there is in each genus some primary thing or starting-point) that which is nearer to some starting-point, determined either absolutely and naturally, or relatively, or locally, or by some agency; e.g., things are prior in space because they are nearer either to some place naturally determined, such as the middle or the extreme, or to some chance relation; and that which is further is posterior.

(b) In another sense, prior or posterior in time. Some things are prior as being further from the present, as in the case of past events (for the Trojan is prior to the Persian war, because it is further distant from the present); and others as being nearer the present, as in the case of future events (for the Nemean are prior to the Pythian games because they are nearer to the present, regarded as a starting-point and as primary).

(c) In another sense, in respect of motion (for that which is nearer to the prime mover is prior; e.g., the boy is prior to the man). This too is a kind of starting point in an absolute sense. (d) In respect of potency; for that which is superior in potency, or more potent, is prior. Such is that in accordance with whose will the other, or posterior, thing must follow, so that according as the former moves or does not move, the latter is or is not moved. And the will is a starting-point.

(e) In respect of order; such are all things which are systematically arranged in relation to some one determinate object. E.g., he who is next to the leader of the chorus is prior to him who is next but one, and the seventh string is prior to the eighth; for in one case the leader is the starting-point, and in the other the middle string.

In these examples prior has this sense; but (2.) in another sense that which is prior in knowledge is treated as absolutely prior; and of things which are prior in this sense the prior in formula are different from the prior in perception. Universals are prior in formula, but particulars in perception. And in formula the attribute is prior to the concrete whole: e.g. cultured to the cultured man; for the formula will not be a whole without the part.

Yet cultured cannot exist apart from some cultured person.

Again, (3.) attributes of prior subjects are called prior; e.g., straightness is prior to smoothness, because the former is an attribute of the line in itself, and the latter of a surface.

Some things, then, are called prior and posterior in this sense; but others (iv.) in virtue of their nature and substance, namely all things which can exist apart from other things, whereas other things cannot exist without them. This distinction was used by Plato. (And since being has various meanings, (a) the substrate, and therefore substance, is prior; (b) potential priority is different from actual priority.

Some things are prior potentially, and some actually; e.g., potentially the half-line is prior to the whole, or the part to the whole, or the matter to the substance; but actually it is posterior, because it is only upon dissolution that it will actually exist.)

Indeed, in a sense all things which are called prior or posterior are so called in this connection; for some things can exist apart from others in generation (e.g. the whole without the parts), and others in destruction (e.g. the parts without the whole). And similarly with the other examples.

Potency means: (a) the source of motion or change which is in something other than the thing changed, or in it qua other. E.g., the science of building is a potency which is not present in the thing built; but the science of medicine, which is a potency, may be present in the patient, although not qua patient.

Thus potency means the source in general of change or motion in another thing, or in the same thing qua other; or the source of a thing’s being moved or changed by another thing, or by itself qua other (for in virtue of that principle by which the passive thing is affected in any way we call it capable of being affected; sometimes if it is affected at all, and sometimes not in respect of every affection, but only if it is changed for the better).

(b) The power of performing this well or according to intention; because sometimes we say that those who can merely take a walk, or speak, without doing it as well as they intended, cannot speak or walk. And similarly in the case of passivity.

(c) All states in virtue of which things are unaffected generally, or are unchangeable, or cannot readily deteriorate, are called potencies. For things are broken and worn out and bent and in general destroyed not through potency but through impotence and deficiency of some sort; and things are unaffected by such processes which are scarcely or slightly affected because they have a potency and are potent and are in a definite state.

Since potency has all these meanings, potent (or capable) will mean (a) that which contains a source of motion or change (for even what is static is potent in a sense) which takes place in another thing, or in itself qua other. (b) That over which something else has a potency of this kind. (c) That which has the potency of changing things, either for the worse or for the better (for it seems that even that which perishes is capable of perishing; otherwise, if it had been incapable, it would not have perished. As it is, it has a kind of disposition or cause or principle which induces such an affection.

Sometimes it seems to be such as it is because it has something, and sometimes because it is deprived of something; but if privation is in a sense a state or habit, everything will be potent through having something; and so a thing is potent in virtue of having a certain habit or principle, and also in virtue of having the privation of that habit, if it can have privation; and if privation is not in a sense habit, the term potent is equivocal).

(d) A thing is potent if neither any other thing nor itself qua other contains a potency or principle destructive of it. (e) All these things are potent either because they merely might chance to happen or not to happen, or because they might do so well. Even in inanimate things this kind of potency is found; e.g. in instruments; for they say that one lyre can be played, and another not at all, if it has not a good tone.

Impotence is a privation of potency—a kind of abolition of the principle which has been described—either in general or in something which would naturally possess that principle, or even at a time when it would naturally already possess it (for we should not use impotence —in respect of begetting—in the same sense of a boy, a man and a eunuch). Again, there is an impotence corresponding to each kind of potency; both to the kinetic and to the successfully kinetic.

Some things are said to be impotent in accordance with this meaning of impotence, but others in a different sense, namely possible and impossible. Impossible means: (a) that whose contrary is necessarily true; e.g., it is impossible that the diagonal of a square should be commensurable with the sides, because such a thing is a lie, whose contrary is not only true but inevitable. Hence that it is commensurable is not only a lie but necessarily a lie.

And the contrary of the impossible, i.e. the possible, is when the contrary is not necessarily a lie; e.g., it is possible that a man should be seated, for it is not necessarily a lie that he should not be seated. Possible, then, means in one sense, as we have said, that which is not necessarily a lie; in another, that which is true; and in another, that which may be true.

(The power in geometry is so called by an extension of meaning.)

These are the senses of potent which do not correspond to potency. Those which do correspond to it all refer to the first meaning, i.e. a source of change which exists in something other than that in which the change takes place, or in the same thing qua other.

Other things are said to be potent because something else has such a potency over them; others because it does not possess it; others because it possesses it in a particular way. The term impotent is similarly used. Thus the authoritative definition of potency in the primary sense will be a principle producing change, which is in something other than that in which the change takes place, or in the same thing qua other.

Quantity means that which is divisible into constituent parts, each or every one of which is by nature some one individual thing. Thus plurality, if it is numerically calculable, is a kind of quantity; and so is magnitude, if it is measurable. Plurality means that which is potentially divisible into non-continuous parts; and magnitude that which is potentially divisible into continuous parts. Of kinds of magnitude, that which is continuous in one direction is length; in two directions, breadth; in three, depth.

And of these, plurality, when limited, is a number; length, a line; breadth, a plane; depth, a body. Again, some things are essentially quantitative, but others only accidentally; e.g. the line is essentially, but cultured accidentally quantitative.

And of the former class some are quantitative in virtue of their substance, e.g. the fine (because the definition which describes it is quantitative in some form); and others are attributes and conditions of a substance of this kind— e.g., much and little, long and short, broad and narrow, deep and shallow, heavy and light, etc.

Moreover, great and small, and greater and smaller, whether used absolutely or relatively to one another, are essential attributes of quantity; by an extension of meaning, however, these terms are also applied to other things.

Of things called quantitative in an accidental sense, one kind is so called in the sense in which we said above that cultured or white is quantitative—because the subject to which they belong is quantitative; and others in the sense that motion and time are so called—for these too are said in a sense to be quantitative and continuous, since the subjects of which they are attributes are divisible. I mean, not the thing moved, but that through or along which the motion has taken place; for it is because the latter is quantitative that the motion is quantitative, and because the motion is quantitative that the time is also.

Quality means (a) in one sense, the differentia of essence; e.g., a man is an animal of a certain quality because he is two-footed; and so is a horse, because it is four-footed. Also a circle is a geometrical figure of a certain quality, because it has no angles; which shows that the essential differentia is quality.

In this one sense, then, quality means differentia of essence; but (b) in another it is used as of immovable and mathematical objects, in the sense that numbers are in a way qualitative—e.g. such as are composite and are represented geometrically not by a line but by a plane or solid (these are products respectively of two and of three factors)—and in general means that which is present besides quantity in the essence. For the essence of each number is that which goes into it once; e.g. that of 6 is not what goes twice or three times, but what goes once; for 6 is once 6.

(c) All affections of substance in motion in respect of which bodies become different when they (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and lightness, etc. (d) The term is used with reference to goodness and badness, and in general to good and bad.

Thus there are, roughly speaking, two meanings which the term quality can bear, and of these one is more fundamental than the other. Quality in the primary sense is the differentia of the essence; and quality in numbers falls under this sense, because it is a kind of differentia of essences, but of things either not in motion or not qua in motion. Secondly, there are the affections of things in motion qua in motion, and the differentiae of motions.

Goodness and badness fall under these affections, because they denote differentiae of the motion or functioning in respect of which things in motion act or are acted upon well or badly. For that which can function or be moved in such-and-such a way is good, and that which can function in such-and-such a way and in the contrary way is bad. Quality refers especially to good and bad in the case of living things, and of these especially in the case of such as possess choice.

Things are called relative (a) In the sense that the double is relative to the half, and the triple to the third; and in general the many times greater to the many times smaller, and that which exceeds to the thing exceeded. (b) In the sense that the thing which heats or cuts is relative to the thing heated or cut; and in general the active to the passive. (c) In the sense that the measurable is relative to the measure, and the knowable to knowledge, and the sensible to sensation.

(a) In the first sense they are said to be numerically relative; either simply, or in a definite relation to numbers or to 1. E.g., the double in relation to 1 is a definite number; the many times as great is in a numerical relation to 1, but not in a definite relation such as this or that;

the relation of that which is 1.5 times something else to that something is a definite numerical relation to a number; and that which is (n+1)/n times something else is in an indefinite relation to a number, just as the many times as great is in an indefinite relation to 1.

The relation of that which exceeds to that which is exceeded is numerically quite indefinite, for number is commensurate, and is not predicated of the incommensurate; whereas that which exceeds, in relation to that which is exceeded, is so much plus something more; and this something more is indefinite, for it is indifferently equal or not equal to the so much.

Thus not only are all these things said to be relative in respect of number, but also the equal and like and same, though in another way: for all these terms are used in respect of one. Things are the same whose essence is one; like whose quality is one; equal whose quantity is one. Now one is the starting-point and standard of number; and so all these relations involve number, though not all in the same way.

(b) Active and passive things are called relative in virtue of an active or passive potentiality or actualization of the potentialities; e.g., that which can heat is called relative to that which can be heated, because it can heat; and again the thing heating is called relative to the thing heated, and the thing cutting to the thing cut, because their potentialities are actualized. Numerical relations, on the other hand, are not actualized (except as has been described elsewhere); they have no actualizations in respect of motion.

Of things potentially relative, some are further relative in respect of particular times; as, e.g., that which has made or will make is relative to that which has been or will be made. It is in this way that a father is called father of a son; the one has acted, and the other has been acted upon, in a particular way. Again, some things are relative in virtue of a privation of their potentiality; such is the impossible and all similar terms, e.g. the invisible.

Thus relative terms which involve number and potentiality are all relative because their very essence contains a reference to something else; but not because something else is related to their essence. But (c) that which is measurable or knowable or thinkable is called relative because something else is related to its essence.

For thinkable signifies that there is a thought which thinks it; but thought is not relative to that of which it is the thought (for then the same thing would have been said twice). And similarly sight is the sight of something; not of that of which it is the sight, although this is of course true—it is relative to some color or other similar thing.

To describe it in the other way— the sight of the object of sight —would be to say the same thing twice. Things, then, which are called relative of their own nature are so called, some in these senses, and others because the classes which contain them are of this kind. E.g., medicine is reckoned as relative because its genus, science, is thought to be a relative thing.

Further, there are the properties in virtue of which the things which possess them are called relative; e.g., equality is relative because the equal is relative, and similarity because the similar is relative. Other things are accidentally relative; e.g., a man is relative because he happens to be double something else, and double is a relative term; or white is relative if the same thing happens to be white as well as double.

Perfect 〈or complete 〉 means: (a) That outside which it is impossible to find even a single one of its parts; e.g., the complete time of each thing is that outside which it is impossible to find any time which is a part of it. (b) That which, in respect of goodness or excellence, cannot be surpassed in its kind; e.g., a doctor and a musician are perfect when they have no deficiency in respect of the form of their peculiar excellence.

And thus by an extension of the meaning we use the term in a bad connection, and speak of a perfect humbug and a perfect thief; since indeed we call them good — e.g. a good thief and a good humbug.

(c) And goodness is a kind of perfection. For each thing, and every substance, is perfect when, and only when, in respect of the form of its peculiar excellence, it lacks no particle of its natural magnitude. (d) Things which have attained their end, if their end is good, are called perfect; for they are perfect in virtue of having attained the end.

Hence, since the end is an ultimate thing, we extend the meaning of the term to bad senses, and speak of perishing perfectly or being perfectly destroyed, when the destruction or calamity falls short in no respect but reaches its extremity. Hence, by an extension of the meaning, death is called an end, because they are both ultimate things. And the ultimate object of action is also an end.

Things, then, which are called perfect in themselves are so called in all these senses; either because in respect of excellence they have no deficiency and cannot be surpassed, and because no part of them can be found outside them; or because, in general, they are unsurpassed in each particular class, and have no part outside. All other things are so called in virtue of these, because they either produce or possess something of this kind, or conform to it, or are referred in some way or other to things which are perfect in the primary sense.

Limit means: (a) The furthest part of each thing, and the first point outside which no part of a thing can be found, and the first point within which all parts are contained. (b) Any form of magnitude or of something possessing magnitude.

(c) The end of each thing. (This end is that to which motion and action proceed, and not the end from which. But sometimes it is both the end from which and the end to which, i.e. the final cause.) (d) The reality or essence of each thing; for this is the limit of our knowledge of it, and if it is a limit of the knowledge, it is also a limit of the thing. Thus it is obvious that limit has not only as many senses as beginning but even more; because the beginning is a kind of limit, but not every limit is a beginning.

That in virtue of which has various meanings. (a) The form or essence of each individual thing; e.g., that in virtue of which a man is good is goodness itself. (b) The immediate substrate in which a thing is naturally produced; as, e.g., color is produced in the surface of things. Thus that in virtue of which in the primary sense is the form, and in the secondary sense, as it were, the matter of each thing, and the immediate substrate.

And in general that in virtue of which will exist in the same number of senses as cause. For we say indifferently in virtue of what has he come? or for what reason has he come? and in virtue of what has he inferred or inferred falsely? or what is the cause of his inference or false inference? (And further, there is the positional sense of καθ’ ὅ, in which he stands, or in which he walks; all these examples denote place or position.)

Hence in virtue of itself must also have various meanings. It denotes (a) The essence of each particular; e.g., Callias is in virtue of himself Callias and the essence of Callias. (b) Everything contained in the definition; e.g., Callias is in virtue of himself an animal, because animal is present in the definition, since Callias is a kind of animal.

(c) Any attribute which a thing has received directly in itself or in any of its parts; e.g., the surface is white in virtue of itself; and man lives in virtue of himself, because the soul is a part of the man, and life is directly contained in it. (d) That which has no other cause. Man has many causes: animal, twofooted, etc.; but nevertheless man is in virtue of himself man. (e) All things which belong to a thing alone and qua alone; and hence that which is separate is in virtue of itself.

Disposition means arrangement of that which has parts, either in space or in potentiality or in form. It must be a kind of position, as indeed is clear from the word, disposition.

Having means (a) In one sense an activity, as it were, of the haver and the thing had, or as in the case of an action or motion; for when one thing makes and another is made, there is between them an act of making. In this way between the man who has a garment and the garment which is had, there is a having. Clearly, then, it is impossible to have a having in this sense; for there will be an infinite series if we can have the having of what we have.

But (b) there is another sense of having which means a disposition, in virtue of which the thing which is disposed is disposed well or badly, and either independently or in relation to something else. E.g., health is a state, since it is a disposition of the kind described. Further, any part of such a disposition is called a state; and hence the excellence of the parts is a kind of state.

Affection means (a) In one sense, a quality in virtue of which alteration is possible; e.g., whiteness and blackness, sweetness and bitterness, heaviness and lightness, etc. (b) The actualizations of these qualities; i.e. the alterations already realized. (c) More particularly, hurtful alterations and motions, and especially hurts which cause suffering. (d) Extreme cases of misfortune and suffering are called affections.

We speak of privation: (a) In one sense, if a thing does not possess an attribute which is a natural possession, even if the thing itself would not naturally possess it; e.g., we say that a vegetable is deprived of eyes. (b) If a thing does not possess an attribute which it or its genus would naturally possess. E.g., a blind man is not deprived of sight in the same sense that a mole is; the latter is deprived in virtue of its genus, but the former in virtue of himself.

(c) If a thing has not an attribute which it would naturally possess, and when it would naturally possess it (for blindness is a form of privation; but a man is not blind at any age, but only if he lacks sight at the age when he would naturally possess it), and similarly if it lacks an attribute in the medium and organ and relation and manner in which it would naturally possess it.

(d) The forcible removal of anything is called privation. (e) Privation has as many senses as there are senses of negation derived from the negative affix (ἀ -). For we call a thing unequal because it does not possess equality (though it would naturally do so); and invisible either because it has no color at all or because it has only a faint one; and footless either because it has no feet at all or because it has rudimentary feet.

Again, a negative affix may mean having something in a small degree —e.g. stoneless — that is, having it in some rudimentary manner. Again, it may mean having it not easily or not well; e.g., uncutable means not only that which cannot be cut, but that which cannot be cut easily or well. And again, it may mean not having a thing at all; for it is not the one-eyed man, but the man who lacks sight in both eyes, who is called blind. Hence not every man is good or bad, moral or immoral; there is also the intermediate state.

To have 〈or possess 〉 is used in various senses. (a) To direct in accordance with one’s own nature or impulse; whence we say that fever possesses a man, and despots possess cities, and people who wear clothes possess them. (b) We speak of anything as having in which, as receptive material, something is present. E.g., the bronze has the shape of the statue, and the body has the disease.

(c) In the sense that the container holds the contained; for when A is contained in B, we say that A is held by B. E.g., we say that the vessel holds the liquid, and the city holds men, and the ship holds sailors, and so too that the whole holds the parts.

(d) The same term is applied to that which prevents anything from moving or acting in accordance with its own impulse; as pillars hold 〈up〉 the weights which are imposed upon them, and as the poets make Atlas hold up the heaven, because otherwise it would fall upon the earth (as some of the physicists maintain also).

It is in this sense that we say that that which holds together holds what it holds together; because otherwise the latter would disperse, each part in accordance with its own impulse.

To be in a thing is used similarly in senses corresponding to those of to have.

To come from something means: (a) In one sense, to come from something as matter, and this in two ways: in respect either of the primary genus or of the ultimate species. E.g., in the one sense everything liquefiable comes from water, and in the other the statue comes from bronze.

(b) To come from something as the first moving principle; e.g., from what comes fighting? From abuse; because this is the beginning of a fight. (c) To come from the combination of matter and form (as the parts come from the whole, and the verse from the Iliad, and the stones from the house); for the shape is an end, and that is a complete thing which has attained its end.

(d) In the sense that the form is made out of the part of its definition; as, e.g., man is made out of two-footed and the syllable out of its element (this is a different way from that in which the statue is made out of the bronze; for the composite entity is made out of perceptible material, but the form is also made out of the material of the form).

These, then, are some of the meanings of from 〈or out of 〉, but (e) sometimes one of these senses only partially applies; e.g., the child comes from the father and mother, and plants from the earth, because they come from some part of those things. (f) It means after in time; e.g., we say that night comes from day, and storm from fine weather, because one comes after the other.

And we speak thus of some of these things in view of their alternation with each other, as in the examples just mentioned, and of others in view merely of their succession in time; e.g., the voyage was made from the equinox, meaning that it was made after it; and the Thargelia are from the Dionysia, meaning after the Dionysia.

Part means: (a) That into which a quantity can be in any way divided; for that which is taken from a quantity qua quantity is always called a part of that quantity—e.g., we call 2 part (in a sense) of 3. (b) In another sense the term is only applied to those parts in sense (a) which measure the whole; hence in one sense we call 2 part of 3, and in another not.

Again, (c) those divisions into which the form, apart from quantity, can be divided, are also called parts of the form. Hence species are called parts of their genus. (d) That into which the whole (either the form or that which contains the form) is divided, or of which it is composed. E.g., of a bronze sphere or cube not only is the bronze

(i.e. the material which contains the form) a part, but also the angle. (e) The elements in the definition of each thing are also called parts of the whole. Hence the genus is even called a part of the species, whereas in another sense the species is part of the genus.

Whole means: (a) That from which no part is lacking of those things as composed of which it is called a natural whole. (b) That which so contains its contents that they form a unity; and this in two ways, either in the sense that each of them is a unity, or in the sense that the unity is composed of them.

For (i) the universal, or term generally applied as being some whole thing, is universal in the sense that it contains many particulars; because it is predicated of each of them, and each and all of them (e.g. man, horse, god) are one; because they are all living things. And (2) that which is continuous and limited is a whole when it is a unity composed of several parts (especially if the parts are only potentially present in it; but otherwise even if they are present actually).

And of these things themselves, those which are so naturally are more truly wholes than those which are so artificially; just as we said of the one, because wholeness is a kind of oneness. Again, since a quantity has a beginning, middle and end, those to which position makes no difference we describe as all, and those to which position makes a difference we describe as whole, and those to which both descriptions can be applied, as both all and whole.

These are all things whose nature remains the same in transposition, but whose shape does not; e.g. wax or a coat. They are described as both whole and all; for they have both characteristics. Water, however, and all liquids, and number, are described as all; we do not speak of a whole number or whole water except by an extension of meaning. Things are described as all in the plural qua differentiated which are described as all in the singular qua one; all this number, all these units.

We do not describe any chance quantity as mutilated; it must have parts, and must be a whole. The number 2 is not mutilated if one of its 1’s is taken away—because the part lost by mutilation is never equal to the remainder—nor in general is any number mutilated; because the essence must persist. If a cup is mutilated, it must still be a cup; but the number is no longer the same.

Moreover, not even all things which have dissimilar parts are mutilated; for a number has in a sense dissimilar as well as similar parts—e.g. 2, 3. But in general of things whose position makes no difference, e.g. water or fire, none is mutilated;— to be mutilated, things must be such as have their position according to their essence.

Further, they must be continuous; for a musical scale is composed of dissimilar parts, and has position; but it does not become mutilated. Moreover, even things which are wholes are not mutilated by the removal of any of their parts; the parts removed must be neither proper to their essence nor in any chance location. E.g., a cup is not mutilated if a hole is made in it, but only if the handle or some projection is broken;

and a man is not mutilated if he loses flesh or his spleen, but if he loses some extremity; and not every extremity, but only such as cannot grow again when completely removed. Hence bald people are not mutilated.

The term genus 〈or race 〉 is used: (a) When there is a continuous generation of things of the same type; e.g., as long as the human race exists means as long as the generation of human beings is continuous. (b) Of anything from which things derive their being as the prime mover of them into being. Thus some are called Hellenes by race, and others Ionians, because some have Hellen and others Ion as their first ancestor.

(Races are called after the male ancestor rather than after the material. Some derive their race from the female as well; e.g. the descendants of Pyrrha.) (c) In the sense that the plane is the genus of plane figures, and the solid of solids (for each one of the figures is either a particular plane or a particular solid); i.e., that which underlies the differentiae.

(d) In the sense that in formulae the first component, which is stated as part of the essence, is the genus, and the qualities are said to be its differentiae. The term genus, then, is used in all these senses—(a) in respect of continuous generation of the same type; (b) in respect of the first mover of the same type as the things which it moves; (c) in the sense of material. For that to which the differentia or quality belongs is the substrate, which we call material.

Things are called generically different whose immediate substrates are different and cannot be resolved one into the other or both into the same thing. E.g., form and matter are generically different, and all things which belong to different categories of being; for some of the things of which being is predicated denote the essence, others a quality, and others the various other things which have already been distinguished. For these also cannot be resolved either into each other or into any one thing.

False means: (i) false as a thing; (a) because it is not or cannot be substantiated; such are the statements that the diagonal of a square is commensurable, or that you are sitting. Of these one is false always, and the other sometimes; it is in these senses that these things are not facts.

(b) Such things as really exist, but whose nature it is to seem either such as they are not, or like things which are unreal; e.g. chiaroscuro and dreams. For these are really something, but not that of which they create the impression. Things, then, are called false in these senses: either because they themselves are unreal, or because the impression derived from them is that of something unreal.

(2.) A false statement is the statement of what is not, in so far as the statement is false. Hence every definition is untrue of anything other than that of which it is true; e.g., the definition of a circle is untrue of a triangle. Now in one sense there is only one definition of each thing, namely that of its essence; but in another sense there are many definitions, since the thing itself, and the thing itself qualified (e.g. Socrates and cultured Socrates) are in a sense the same.

But the false definition is not strictly a definition of anything. Hence it was foolish of Antisthenes to insist that nothing can be described except by its proper definition: one predicate for one subject; from which it followed that contradiction is impossible, and falsehood nearly so. But it is possible to describe everything not only by its own definition but by that of something else; quite falsely, and yet also in a sense truly—e.g., 8 may be described as double by the definition of 2.

Such are the meanings of false in these cases. (3.) A false man is one who readily and deliberately makes such statements, for the sake of doing so and for no other reason; and one who induces such statements in others—just as we call things false which induce a false impression. Hence the proof in the Hippias that the same man is false and true is misleading;

for it assumes (a) that the false man is he who is able to deceive, i.e. the man who knows and is intelligent; (b) that the man who is willingly bad is better. This false assumption is due to the induction; for when he says that the man who limps willingly is better than he who does so unwillingly, he means by limping pretending to limp. For if he is willingly lame, he is presumably worse in this case just as he is in the case of moral character.

Accident 〈or attribute 〉 means that which applies to something and is truly stated, but neither necessarily nor usually; as if, for example, while digging a hole for a plant one found a treasure. Then the finding of treasure is an accident to the man who is digging the hole; for the one thing is not a necessary consequence or sequel of the other, nor does one usually find treasure while planting.

And a cultured man might be white; but since this does not happen necessarily or usually, we call it an accident. Thus since there are attributes and subjects, and some attributes apply to their subjects only at a certain place and time, any attribute which applies to a subject, but not because it was a particular subject or time or place, will be an accident.

Nor is there any definite cause for an accident, but only a chance, i.e. indefinite, cause. It was by accident that X went to Aegina if he arrived there, not because he intended to go there but because he was carried out of his course by a storm, or captured by pirates.

The accident has happened or exists, but in virtue not of itself but of something else; for it was the storm which was the cause of his coming to a place for which he was not sailing—i.e. Aegina.

Accident has also another sense, namely, whatever belongs to each thing in virtue of itself, but is not in its essence; e.g. as having the sum of its angles equal to two right angles belongs to the triangle. Accidents of this kind may be eternal, but none of the former kind can be. There is an account of this elsewhere.