All men naturally desire knowledge. An indication of this is our esteem for the senses; for apart from their use we esteem them for their own sake, and most of all the sense of sight. Not only with a view to action, but even when no action is contemplated, we prefer sight, generally speaking, to all the other senses.

The reason of this is that of all the senses sight best helps us to know things, and reveals many distinctions.

Now animals are by nature born with the power of sensation, and from this some acquire the faculty of memory, whereas others do not.

Accordingly the former are more intelligent and capable of learning than those which cannot remember.

Such as cannot hear sounds (as the bee, and any other similar type of creature) are intelligent, but cannot learn; those only are capable of learning which possess this sense in addition to the faculty of memory.

Thus the other animals live by impressions and memories, and have but a small share of experience; but the human race lives also by art and reasoning.

It is from memory that men acquire experience, because the numerous memories of the same thing eventually produce the effect of a single experience.

Experience seems very similar to science and art,

but actually it is through experience that men acquire science and art; for as Polus rightly says, "experience produces art, but inexperience chance."

Art is produced when from many notions of experience a single universal judgement is formed with regard to like objects.

To have a judgement that when Callias was suffering from this or that disease this or that benefited him, and similarly with Socrates and various other individuals, is a matter of experience; but to judge that it benefits all persons of a certain type, considered as a class, who suffer from this or that disease (e.g. the phlegmatic or bilious when suffering from burning fever) is a matter of art.

It would seem that for practical purposes experience is in no way inferior to art; indeed we see men of experience succeeding more than those who have theory without experience.

The reason of this is a that experience is knowledge of particulars, but art of universals; and actions and the effects produced are all concerned with the particular. For it is not man that the physician cures, except incidentally, but Callias or Socrates or some other person similarly named, who is incidentally a man as well.

So if a man has theory without experience, and knows the universal, but does not know the particular contained in it, he will often fail in his treatment; for it is the particular that must be treated.

Nevertheless we consider that knowledge and proficiency belong to art rather than to experience, and we assume that artists are wiser than men of mere experience (which implies that in all cases wisdom depends rather upon knowledge);

and this is because the former know the cause, whereas the latter do not. For the experienced know the fact, but not the wherefore; but the artists know the wherefore and the cause. For the same reason we consider that the master craftsmen in every profession are more estimable and know more and are wiser than the artisans,

because they know the reasons of the things which are done; but we think that the artisans, like certain inanimate objects, do things, but without knowing what they are doing (as, for instance, fire burns);

only whereas inanimate objects perform all their actions in virtue of a certain natural quality, artisans perform theirs through habit. Thus the master craftsmen are superior in wisdom, not because they can do things, but because they possess a theory and know the causes.

In general the sign of knowledge or ignorance is the ability to teach, and for this reason we hold that art rather than experience is scientific knowledge; for the artists can teach, but the others cannot.

Further, we do not consider any of the senses to be Wisdom. They are indeed our chief sources of knowledge about particulars, but they do not tell us the reason for anything, as for example why fire is hot, but only that it

hot.

It is therefore probable that at first the inventor of any art which went further than the ordinary sensations was admired by his fellow-men, not merely because some of his inventions were useful, but as being a wise and superior person.

And as more and more arts were discovered, some relating to the necessities and some to the pastimes of life, the inventors of the latter were always considered wiser than those of the former,

because their branches of knowledge did not aim at utility.

Hence when all the discoveries of this kind were fully developed, the sciences which relate neither to pleasure nor yet to the necessities of life were invented, and first in those places where men had leisure. Thus the mathematical sciences originated in the neighborhood of Egypt, because there the priestly class was allowed leisure.

The difference between art and science and the other kindred mental activities has been stated in theEthics

; the reason for our present discussion is that it is generally assumed that what is called Wisdom

is concerned with the primary causes and principles, so that, as has been already stated, the man of experience is held to be wiser than the mere possessors of any power of sensation, the artist than the man of experience, the master craftsman than the artisan; and the speculative sciences to be more learned than the productive.

Thus it is clear that Wisdom is knowledge of certain principles and causes.

Since we are investigating this kind of knowledge, we must consider what these causes and principles are whose knowledge is Wisdom. Perhaps it will be clearer if we take the opinions which we hold about the wise man.

We consider first, then, that the wise man knows all things, so far as it is possible, without having knowledge of every one of them individually; next, that the wise man is he who can comprehend difficult things, such as are not easy for human comprehension (for sense-perception, being common to all, is easy, and has nothing to do with Wisdom); and further that in every branch of knowledge a man is wiser in proportion as he is more accurately informed and better able to expound the causes.

Again among the sciences we consider that that science which is desirable in itself and for the sake of knowledge is more nearly Wisdom than that which is desirable for its results, and that the superior is more nearly Wisdom than the subsidiary; for the wise man should give orders, not receive them; nor should he obey others, but the less wise should obey him.

Such in kind

and in number are the opinions which we hold with regard to Wisdom and the wise. Of the qualities there described the knowledge of everything must necessarily belong to him who in the highest degree possesses knowledge of the universal, because he knows in a sense all the particulars which it comprises. These things, viz. the most universal, are perhaps the hardest for man to grasp, because they are furthest removed from the senses.

Again, the most exact of the sciences are those which are most concerned with the first principles; for those which are based on fewer principles are more exact than those which include additional principles; e.g., arithmetic is more exact than geometry.

Moreover, the science which investigates causes is more instructive than one which does not, for it is those who tell us the causes of any particular thing who instruct us. Moreover, knowledge and understanding which are desirable for their own sake are most attainable in the knowledge of that which is most knowable. For the man who desires knowledge for its own sake will most desire the most perfect knowledge,

and this is the knowledge of the most knowable, and the things which are most knowable are first principles and causes; for it is through these and from these that other things come to be known, and not these through the particulars which fall under them.

And that science is supreme, and superior to the subsidiary, which knows for what end each action is to be done; i.e. the Good in each particular case, and in general the highest Good in the whole of nature.

Thus as a result of all the above considerations the term which we are investigating falls under the same science, which must speculate about first principles and causes; for the Good, i.e. the

, is one of the causes.

That it is not a productive science is clear from a consideration of the first philosophers.

It is through wonder that men now begin and originally began to philosophize; wondering in the first place at obvious perplexities, and then by gradual progression raising questions about the greater matters too, e.g. about the changes of the moon and of the sun, about the stars and about the origin of the universe.

Now he who wonders and is perplexed feels that he is ignorant (thus the myth-lover is in a sense a philosopher, since myths are composed of wonders);

therefore if it was to escape ignorance that men studied philosophy, it is obvious that they pursued science for the sake of knowledge, and not for any practical utility.

The actual course of events bears witness to this; for speculation of this kind began with a view to recreation and pastime, at a time when practically all the necessities of life were already supplied. Clearly then it is for no extrinsic advantage that we seek this knowledge; for just as we call a man independent who exists for himself and not for another, so we call this the only independent science, since it alone exists for itself.

For this reason its acquisition might justly be supposed to be beyond human power, since in many respects human nature is servile; in which case, as Simonides

says, "God alone can have this privilege," and man should only seek the knowledge which is within his reach.

Indeed if the poets are right and the Deity is by nature jealous,

it is probable that in this case He would be particularly jealous, and all those who excel in knowledge unfortunate. But it is impossible for the Deity to be jealous (indeed, as the proverb

says, "poets tell many a lie"), nor must we suppose that any other form of knowledge is more precious than this; for what is most divine is most precious.

Now there are two ways only in which it can be divine. A science is divine if it is peculiarly the possession of God, or if it is concerned with divine matters. And this science alone fulfils both these conditions; for (a) all believe that God is one of the causes and a kind of principle, and (b) God is the sole or chief possessor of this sort of knowledge. Accordingly, although all other sciences are more necessary than this, none is more excellent.

The acquisition of this knowledge, however, must in a sense result in something which is the reverse of the outlook with which we first approached the inquiry. All begin, as we have said, by wondering that things should be as they are, e.g. with regard to marionettes, or the solstices, or the incommensurability

of the diagonal of a square; because it seems wonderful to everyone who has not yet perceived the cause that a thing should not be measurable by the smallest unit.

But we must end with the contrary and (according to the proverb)

the better view, as men do even in these cases when they understand them;

for a geometrician would wonder at nothing so much as if the diagonal were to become measurable.

Thus we have stated what is the nature of the science which we are seeking, and what is the object which our search and our whole investigation must attain.

It is clear that we must obtain knowledge of the primary causes, because it is when we think that we understand its primary cause that we claim to know each particular thing. Now there are four recognized kinds of cause. Of these we hold that one is the essence or essential nature of the thing (since the "reason why" of a thing is ultimately reducible to its formula, and the ultimate "reason why" is a cause and principle); another is the matter or substrate; the third is the source of motion; and the fourth is the cause which is opposite to this, namely the purpose or "good";

for this is the end of every generative or motive process. We have investigated these sufficiently in the Physics

;

however, let us avail ourselves of the evidence of those who have before us approached the investigation of reality and philosophized about Truth. For clearly they too recognize certain principles and causes, and so it will be of some assistance to our present inquiry if we study their teaching; because we shall either discover some other kind of cause, or have more confidence in those which we have just described.

Most of the earliest philosophers conceived only of material principles as underlying all things. That of which all things consist, from which they first come and into which on their destruction they are ultimately resolved, of which the essence persists although modified by its affections—this, they say, is an element and principle of existing things. Hence they believe that nothing is either generated or destroyed, since this kind of primary entity always persists. Similarly we do not say that Socrates comes into being

when he becomes handsome or cultured, nor that he is destroyed when he loses these qualities; because the substrate, Socrates himself, persists.

In the same way nothing else is generated or destroyed; for there is some one entity (or more than one) which always persists and from which all other things are generated.

All are not agreed, however,

as to the number and character of these principles. Thales,

the founder of this school of philosophy,

says the permanent entity is water (which is why he also propounded that the earth floats on water). Presumably he derived this assumption from seeing that the nutriment of everything is moist, and that heat itself is generated from moisture and depends upon it for its existence (and that from which a thing is generated is always its first principle). He derived his assumption, then, from this; and also from the fact that the seeds of everything have a moist nature, whereas water is the first principle of the nature of moist things.

There are some

who think that the men of very ancient times, long before the present era, who first speculated about the gods, also held this same opinion about the primary entity. For they

represented Oceanus and Tethys to be the parents of creation, and the oath of the gods to be by water— Styx,

as they call it. Now what is most ancient is most revered, and what is most revered is what we swear by.

Whether this view of the primary entity is really ancient and time-honored may perhaps be considered uncertain; however, it is said that this was Thales' opinion concerning the first cause. (I say nothing of Hippo,

because no one would presume to include him in this company, in view of the paltriness of his intelligence.)

Anaximenes

and Diogenes

held that air is prior to water, and is of all corporeal elements most truly the first principle. Hippasus

of Metapontum and Heraclitus

of Ephesus hold this of fire; and Empedocles

—adding earth as a fourth to those already mentioned—takes all four. These, he says, always persist, and are only generated in respect of multitude and paucity, according as they are combined into unity or differentiated out of unity.

Anaxagoras of Clazomenae—prior to Empedocles in point of age, but posterior in his activities—says that the first principles are infinite in number. For he says that as a general rule all things which are, like fire and water,

homoeomerous, are generated and destroyed in this sense only, by combination and differentiation; otherwise they are neither generated nor destroyed, but persist eternally.

From this account it might be supposed that the only cause is of the kind called "material." But as men proceeded in this way, the very circumstances of the case led them on and compelled them to seek further; because if it is really true

that all generation and destruction is out of some one entity or even more than one,

does this happen, and what is the cause?

It is surely not the substrate itself which causes itself to change. I mean, e.g., that neither wood nor bronze is responsible for changing itself; wood does not make a bed, nor bronze a statue, but something else is the cause of the change. Now to investigate this is to investigate the second type of cause: the source of motion, as we should say.

Those who were the very first to take up this inquiry, and who maintained that the substrate is one thing, had no misgivings on the subject; but some of those

who regard it as one thing, being baffled, as it were, by the inquiry, say that that one thing (and indeed the whole physical world) is immovable in respect not only of generation and destruction (this was a primitive belief and was generally admitted) but of all other change. This belief is peculiar to them.

None of those who maintained that the universe is a unity achieved any conception of this type of cause, except perhaps Parmenides

; and him only in so far as he admits, in a sense, not one cause only but two.

But those who recognize more than one entity, e.g. hot and cold, or fire and earth, are better able to give a systematic explanation, because they avail themselves of fire as being of a kinetic nature, and of water, earth, etc., as being the opposite.

After these thinkers and the discovery of these causes, since they were insufficient to account for the generation of the actual world, men were again compelled (as we have said) by truth itself to investigate the next first principle.

For presumably it is unnatural that either fire or earth or any other such element should cause existing things to be or become well and beautifully disposed; or indeed that those thinkers should hold such a view. Nor again was it satisfactory to commit so important a matter to spontaneity and chance.

Hence when someone

said that there is Mind in nature, just as in animals, and that this is the cause of all order and arrangement, he seemed like a sane man in contrast with the haphazard statements of his predecessors.

We know definitely that Anaxagoras adopted this view; but Hermotimus

of Clazomenae is credited with having stated it earlier. Those thinkers, then, who held this view assumed a principle in things which is the cause of beauty, and the sort of cause by which motion is communicated to things.

It might be inferred that the first person to consider this question was Hesiod, or indeed anyone else who assumed Love or Desire as a first principle in things; e.g. Parmenides. For he says, where he is describing the creation of the universe, “ Love she

created first of all the gods . . . ” And Hesiod says,

“ First of all things was Chaos made, and then/Broad-bosomed Earth . . ./And Love, the foremost of immortal beings, ” thus implying that there must be in the world some cause to move things and combine them.

The question of arranging these thinkers in order of priority may be decided later. Now since it was apparent that nature also contains the opposite of what is good, i.e. not only order and beauty, but disorder and ugliness;

and that there are more bad and common things than there are good and beautiful: in view of this another thinker introduced Love and Strife

as the respective causes of these things—

because if one follows up and appreciates the statements of Empedocles with a view to his real meaning and not to his obscure language, it will be found that Love is the cause of good, and Strife of evil. Thus it would perhaps be correct to say that Empedocles in a sense spoke of evil and good as first principles, and was the first to do so—that is, if the cause of all good things is absolute good.

These thinkers then, as I say, down to the time of Empedocles, seem to have grasped two of the causes which we have defined in the Physics

: the material cause and the source of motion; but only vaguely and indefinitely. They are like untrained soldiers in a battle, who rush about and often strike good blows, but without science; in the same way these thinkers do not seem to understand their own statements, since it is clear that upon the whole they seldom or never apply them.

Anaxagoras avails himself of Mind as an artificial device for producing order, and drags it in whenever he is at a loss to explain

some necessary result; but otherwise he makes anything rather than Mind the cause of what happens.

Again, Empedocles does indeed use causes to a greater degree than Anaxagoras, but not sufficiently; nor does he attain to consistency in their use.

At any rate Love often differentiates and Strife combines: because whenever the universe is differentiated into its elements by Strife, fire and each of the other elements are agglomerated into a unity; and whenever they are all combined together again by Love, the particles of each element are necessarily again differentiated.

Empedocles, then, differed from his predecessors in that he first introduced the division of this cause, making the source of motion not one but two contrary forces.

Further, he was the first to maintain that the so-called material elements are four—not that he uses them as four, but as two only,

treating fire on the one hand by itself, and the elements opposed to it—earth, air and water—on the other, as a single nature.

This can be seen from a study of his writings.

Such, then, as I say, is his account of the nature and number of the first principles.

Leucippus,

however, and his disciple Democritus

hold that the elements are the Full and the Void—calling the one "what is" and the other "what is not." Of these they identify the full or solid with "what is," and the void or rare with "what is not" (hence they hold that what is not is no less real than what is,

because Void is as real as Body); and they say that these are the material causes of things.

And just as those who make the underlying substance a unity generate all other things by means of its modifications, assuming rarity and density as first principles of these modifications, so these thinkers hold that the "differences"

are the causes of everything else.

These differences, they say, are three: shape, arrangement, and position; because they hold that what is differs only in contour, inter-contact, and

.

(Of these contour means shape, inter-contact arrangement, and inclination position.) Thus, e.g., A differs from N in shape, AN from NA in arrangement, and Z from N

in position.

As for motion, whence and how it arises in things,

they casually ignored this point, very much as the other thinkers did. Such, then, as I say, seems to be the extent of the inquiries which the earlier thinkers made into these two kinds of cause.

At the same time, however, and even earlier the so-called

Pythagoreans applied themselves to mathematics, and were the first to develop this science

; and through studying it they came to believe that its principles are the principles of everything.

And since

are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analogues

of what is and comes into being—such and such a property of number being

,

and such and such

or

, another

, and similarly, more or less, with all the rest—and since they saw further that the properties and ratios of the musical scales are based on numbers,

and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe,

they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion

or number. Whatever analogues to the processes and parts of the heavens and to the whole order of the universe they could exhibit in numbers and proportions, these they collected and correlated;

and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nine

that are visible, they make the "antichthon"

the tenth.

We have treated this subject in greater detail elsewhere

; but the object of our present review is to discover from these thinkers too what causes they assume and how these coincide with our list of causes.

Well, it is obvious that these thinkers too consider number to be a first principle, both as the material

of things and as constituting their properties and states.

The elements of number, according to them, are the Even and the Odd. Of these the former is limited and the latter unlimited; Unity consists of both

(since it is both odd and even)

; number is derived from Unity; and numbers, as we have said, compose the whole sensible universe.

Others

of this same school hold that there are ten principles, which they enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) Square and Oblong.

Apparently Alcmaeon of Croton speculated along the same lines, and either he derived the theory from them or they from him; for [Alcmaeon was contemporary with the old age of Pythagoras, and]

his doctrines were very similar to theirs.

He says that the majority of things in the world of men are in pairs; but the contraries which he mentions are not, as in the case of the Pythagoreans, carefully defined, but are taken at random, e.g. white and black, sweet and bitter, good and bad, great and small.

Thus Alcmaeon only threw out vague hints with regard to the other instances of contrariety,

but the Pythagoreans pronounced how many and what the contraries are. Thus from both these authorities

we can gather thus much, that the contraries are first principles of things; and from the former, how many and what the contraries are.

How these can be referred to our list of causes is not definitely expressed by them, but they appear to reckon their elements as material; for they say that these are the original constituents of which Being is fashioned and composed.

From this survey we can sufficiently understand the meaning of those ancients who taught that the elements of the natural world are a plurality. Others, however, theorized about the universe as though it were a single entity; but their doctrines are not all alike either in point of soundness or in respect of conformity with the facts of nature.

For the purposes of our present inquiry an account of their teaching is quite irrelevant, since they do not, while assuming a unity, at the same time make out that Being is generated from the unity as from matter, as do some physicists, but give a different explanation; for the physicists assume motion also, at any rate when explaining the generation of the universe; but these thinkers hold that it is immovable. Nevertheless thus much is pertinent to our present inquiry.

It appears that Parmenides conceived of the Unity as one in definition,

but Melissus

as materially one. Hence the former says that it is finite,

and the latter that it is infinite.

But Xenophanes,

the first exponent of the Unity (for Parmenides is said to have been his disciple), gave no definite teaching, nor does he seem to have grasped either of these conceptions of unity; but regarding the whole material universe he stated that the Unity is God.

This school then, as we have said, may be disregarded for the purposes of our present inquiry; two of them, Xenophanes and Melissus, may be completely ignored, as being somewhat too crude in their views. Parmenides, however, seems to speak with rather more insight. For holding as he does that Not-being, as contrasted with Being, is nothing, he necessarily supposes that Being is one and that there is nothing else (we have discussed this point in greater detail in thePhysics

); but being compelled to accord with phenomena, and assuming that Being is one in definition but many in respect of sensation, he posits in his turn two causes, i.e. two first principles, Hot and Cold; or in other words, Fire and Earth.

Of these he ranks Hot under Being and the other under Not-being.

From the account just given, and from a consideration of those thinkers who have already debated this question, we have acquired the following information. From the earliest philosophers we have learned that the first principle is corporeal (since water and fire and the like are bodies); some of them assume one and others more than one corporeal principle, but both parties agree in making these principles material. Others assume in addition to this cause the

, which some hold to be one and others two.

Thus down to and apart from the Italian

philosophers the other thinkers have expressed themselves vaguely on the subject, except that, as we have said, they actually employ two causes, and one of these—the source of motion —some regard as one and others as two. The Pythagoreans, while they likewise spoke of two principles, made this further addition, which is peculiar to them: they believed, not that the Limited and the Unlimited are separate entities, like fire or water or some other such thing, but that the Unlimited itself and the One itself are the essence of those things of which they are predicated, and hence that number is the essence of all things.

Such is the nature of their pronouncements on this subject. They also began to discuss and define the "what" of things; but their procedure was far too simple. They defined superficially, and supposed that the essence of a thing is that to which the term under consideration first applies—e.g. as if it were to be thought that "double" and "2" are the same, because 2 is the first number which is double another.

But presumably "to be double a number" is not the same as "to be the number 2." Otherwise, one thing will be many—a consequence which actually followed in their system.

This much, then, can be learned from other and earlier schools of thought.

The philosophies described above were succeeded by the system of Plato,

which in most respects accorded with them, but contained also certain peculiar features distinct from the philosophy of the Italians.

In his youth Plato first became acquainted with Cratylus

and the Heraclitean doctrines—that the whole sensible world is always in a state of flux,

and that there is no scientific knowledge of it—and in after years he still held these opinions.

And when Socrates, disregarding the physical universe and confining his study to moral questions, sought in this sphere for the universal and was the first to concentrate upon definition, Plato followed him and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing.

These entities he called "Ideas,"

and held that all sensible things are named after

them sensible and in virtue of their relation to them; for the plurality of things which bear the same name as the Forms exist by participation in them. (With regard to the "participation," it was only the term that he changed; for whereas the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation—merely a change of term.

As to what this "participation" or "imitation" may be, they left this an open question.)

Further, he states that besides sensible things and the Forms there exists an intermediate class, the

,

which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique.

Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things.

Accordingly the material principle is the "Great and Small," and the essence is the One, since the numbers are derived from the "Great and Small" by participation in the the One.

In treating the One as a substance instead of a predicate of some other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in stating that the numbers are the causes of Being in everything else; but it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the "Great and Small." He is also peculiar in regarding the numbers as distinct from sensible things, whereas they hold that things themselves are numbers, nor do they posit an intermediate class of mathematical objects.

His distinction of the One and the numbers from ordinary things (in which he differed from the Pythagoreans) and his introduction of the Forms were due to his investigation of logic (the earlier thinkers were strangers to Dialectic)

; his conception of the other principle as a duality to the belief that numbers other than primes

can be readily generated from it, as from a matrix.

The fact, however, is just the reverse, and the theory is illogical; for whereas the Platonists derive multiplicity from matter although their Form generates only once,

it is obvious that only one table can be made from one piece of timber, and yet he who imposes the form upon it, although he is but one, can make many tables. Such too is the relation of male to female: the female is impregnated in one coition, but one male can impregnate many females. And these relations are analogues of the principles referred to.

This, then, is Plato's verdict upon the question which we are investigating. From this account it is clear that he only employed two causes

: that of the essence, and the material cause; for the Forms are the cause of the essence in everything else, and the One is the cause of it in the Forms.

He also tells us what the material substrate is of which the Forms are predicated in the case of sensible things, and the One in that of the Forms—that it is this the duality, the "Great and Small." Further, he assigned to these two elements respectively the causation of good

and of evil; a problem which, as we have said,

had also been considered by some of the earlier philosophers, e.g. Empedocles and Anaxagoras.

We have given only a concise and summary account of those thinkers who have expressed views about the causes

and reality, and of their doctrines. Nevertheless we have learned thus much from them: that not one of those who discuss principle or cause has mentioned any other type than those which we we have distinguished in the Physics.

Clearly it is after these types that they are groping, however uncertainly.

Some speak of the first principle as material, whether they regard it as one or several, as corporeal or incorporeal: e.g. Plato speaks of the "Great and Small"; the Italians

of the Unlimited; Empedocles of Fire, Earth, Water and Air; Anaxagoras of the infinity of homoeomeries.

All these have apprehended this type of cause; and all those too who make their first principle air or water or "something denser than fire but rarer than air"

(for some have so described the primary element). These, then, apprehended this cause only, but others apprehended the

—e.g. all such as make Love and Strife, or Mind, or Desire a first principle.

As for the

or

, nobody has definitely introduced it;

but the inventors of the Forms express it most nearly. For they do not conceive of the Forms as the

of sensible things (and the One as the matter of the Forms), nor as producing the

(for they hold that they are rather the cause of immobility and tranquillity); but they adduce the Forms as the

of all other things, and the One as that of the Forms.

The

towards which actions, changes and motions tend they do in a way treat as a cause, but not in this sense, i.e. not in the sense in which it is naturally a cause. Those who speak of Mind or Love assume these causes as being something good; but nevertheless they do not profess that anything exists or is generated

of them, but only that motions originate from them.

Similarly also those who hold that Unity or Being is an entity of this kind state that it is the cause of existence, but not that things exist or are generated for the sake of it. So it follows that in a sense they both assert and deny that the Good is a cause; for they treat it as such not absolutely, but incidentally.

It appears, then, that all these thinkers too (being unable to arrive at any other cause) testify that we have classified the causes rightly, as regards both number and nature. Further, it is clear that all the principles must be sought either along these lines or in some similar way.

Let us next examine the possible difficulties arising out of the statements of each of these thinkers, and out of his attitude to the first principles.

All those who regard the universe as a unity, and assume as its matter some one nature, and that corporeal and extended, are clearly mistaken in many respects. They only assume elements of corporeal things, and not of incorporeal ones, which also exist. They attempt to state the causes of generation and destruction, and investigate the nature of everything; and at the same time do away with the cause of motion.

Then there is their failure to regard the

or formula as a cause of anything; and further their readiness to call any one of the simple bodies—except earth—a first principle, without inquiring how their reciprocal generation is effected. I refer to fire, water, earth and air. Of these some are generated from each other by combination and others by differentiation;

and this difference is of the greatest importance in deciding their relative priority. In one way it might seem that the most elementary body is that from which first other bodies are produced by combination;

and this will be that body which is rarest and composed of the finest particles.

Hence all who posit Fire as first principle will be in the closest agreement with this theory. However, even among the other thinkers everyone agrees that the primary corporeal element is of this kind. At any rate none of the Monists thought earth likely to be an element—obviously on account of the size of its particles—

but each of the other three has had an advocate; for some name fire as the primary element, others water, and others air.

And yet why do they not suggest earth too, as common opinion does? for people say "Everything is earth."

And Hesiod too says

that earth was generated first of corporeal things—so ancient and popular is the conception found to be. Thus according to this theory anyone who suggests any of these bodies other than fire, or who assumes something "denser than air but rarer than water,"

will be wrong.

On the other hand if what is posterior in generation is prior in nature, and that which is developed and combined is posterior in generation, then the reverse will be the case; water will be prior to air, and earth to water. So much for those who posit

cause such as we have described.

The same will apply too if anyone posits more than one, as e.g. Empedocles says that matter consists of four bodies;

objections must occur in his case also, some the same as before, and some peculiar to him. First, we can see things being generated from each other in a way which shows that fire and earth do not persist as the same corporeal entity. (This subject has been treated in my works on Natural Science.

) Again with regard to the cause of motion in things, whether one or two should be assumed, it must not be thought that his account is entirely correct or even reasonable.

And in general those who hold such views as these must of necessity do away with qualitative alteration; for on such a theory cold will not come from hot nor hot from cold, because to effect this there must be something which actually takes on these contrary qualities: some single element which becomes both fire and water—which Empedocles denies.

If one were to infer that Anaxagoras recognized two

elements, the inference would accord closely with a view which, although he did not articulate it himself, he must have accepted as developed by others.

To say that originally everything was a mixture is absurd for various reasons,

but especially since (a) it follows that things must have existed previously in an unmixed state; (b) it is contrary to nature for

to mix with

; (c) moreover affections and attributes would then be separable from their substances (because what is mixed can also be separated). At the same time, if one were to follow his doctrine carefully and interpret its meaning, perhaps it would be seen to be more up-to-date;

because when nothing was yet differentiated, obviously nothing could be truly predicated of that substance—e.g. that it was white or black or buff or any other color. It must necessarily have been colorless, since otherwise it would have had one of these colors.

Similarly by the same argument it had no taste or any other such attribute; for it cannot have had any quality or magnitude or individuality. Otherwise some particular form would have belonged to it; but this is impossible on the assumption that everything was mixed together, for then the form would have been already differentiated, whereas he says that everything was mixed together except Mind, which alone was pure and unmixed.

It follows from this that he recognizes as principles the One (which is simple and unmixed) and the Other, which is such as we suppose the Indeterminate to be before it is determined and partakes of some form. Thus his account is neither correct nor clear,

but his meaning approximates to more recent theories and what is now more obviously true.

However, these thinkers are really concerned only with the theories of generation and destruction and motion (for in general it is only with reference to this aspect of reality that they look for their principles and causes).

Those, however, who make their study cover the whole of reality, and who distinguish between sensible and non-sensible objects, clearly give their attention to both kinds; hence in their case we may consider at greater length what contributions, valuable or otherwise, they make to the inquiry which is now before us.

The so-called Pythagoreans employ abstruser principles and elements than the physicists. The reason is that they did not draw them from the sensible world; for mathematical objects, apart from those which are connected with astronomy, are devoid of motion.

Nevertheless all their discussions and investigations are concerned with the physical world. They account for the generation of the sensible universe,

and observe what happens in respect of its parts and affections and activities, and they use up their principles and causes in this connection, as though they agreed with the others—the physicists—that reality is just so much as is sensible and is contained in the so-called "heavens."

All the same, as we have said,

the causes and principles which they describe are capable of application to the remoter class of realities as well, and indeed are better fitted to these than to their physical theories.

But as to how there is to be motion, if all that is premissed is Limit and the Unlimited, and Odd and Even, they do not even hint; nor how, without motion and change, there can be generation and destruction, or the activities of the bodies which traverse the heavens.

And further, assuming that it be granted to them or proved by them that

is composed of these factors, yet how is it to be explained that some bodies are light, and others have weight? For in their premisses and statements they are speaking just as much about sensible as about mathematical objects; and this is why they have made no mention of fire or earth or other similar bodies, because, I presume, they have no separate explanation of sensible things.

Again, how are we to understand that number and the modifications of number are the causes

of all being and generation, both in the beginning and now, and at the same time that there is no other number than the number of which the universe is composed?

Because when they make out that Opinion and Opportunity are in such and such a region, and a little above or below them Injustice and Separation or Mixture, and when they state as proof of this that each of these abstractions is a number; and that also in this region there is already a plurality of the magnitudes composed of number, inasmuch as these modifications of number correspond to these several regions,—is the number which we must understand each of these abstractions to be the same number which is present in the sensible universe, or another kind of number?

Plato at least says that it is another. It is true that he too supposes that numbers are both these magnitudes and their causes; but in his view the causative numbers are intelligible and the others sensible.

The Pythagoreans, then, may be dismissed for the present, for it is enough to touch upon them thus briefly.

As for those who posit the Forms as causes,

in the first place in their attempt to find the causes of things in our sensible world, they introduced an equal number of other entities—as though a man who wishes to count things should suppose that it would be impossible when they are few, and should attempt to count them when he has added to them. For the Forms are as many as, or not fewer than, the things in search of whose causes these thinkers were led to the Forms; because corresponding to each thing there is a synonymous entity apart from the substances (and in the case of non-substantial things there is a One over the Many

), both in our everyday world and in the realm of eternal entities.

Again, not one of the arguments by which we

try to prove that the Forms exist demonstrates our point: from some of them no necessary conclusion follows, and from others it follows that there are Forms of things of which we hold that there are no Forms.

For according to the arguments from the sciences

there will be Forms of all things of which there are sciences

; and according to the "One-over-Many" argument,

of negations too; and according to the argument that "we have some conception of what has perished," of perishable things; because we have a mental picture of these things.

Again, of Plato's more exact arguments some establish Ideas of relations,

which we do not hold to form a separate genus;

and others state the "Third Man."

And in general the arguments for the Forms do away with things which are more important to us exponents of the Forms than the existence of the Ideas;

for they imply that it is not the Dyad that is primary, but Number

; and that the relative is prior to the absolute

; and all the other conclusions in respect of which certain persons, by following up the views held about the Ideas, have gone against the principles of the theory.

Again, according to the assumption by which we hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances, but also in the case of all other things; and there are sciences not only of substances but of other things as well; and there are a thousand other similar consequences); but according to logical necessity, and from the views generally held about them, it follows that if the Forms are participated in, then there can only be Ideas of substances. For they are not participated in qua accidents; each Form can only be participated in in so far as it is not predicated of a subject.

I mean, e.g., that if anything participates in "absolute Doubleness" it participates also in "eternal," but only accidentally; because it is an

of Doubleness to be eternal.

Thus the Forms must be substance. But the same names denote substance in the sensible as in the Ideal world;

otherwise what meaning will there be in saying that something exists beside the particulars, i.e. the unity comprising their multiplicity?

If the form of the Ideas and of the things which participate in them is the same, they will have something in common (for why should Duality mean one and the same thing in the case of perishable "twos"

and the "twos" which are many but eternal,

and not in the case of the Idea of Duality and a particular "two"?); but if the form is not the same, they will simply be homonyms; just as though one were to call both Callias and a piece of wood "man," without remarking any property common to them.

Above all we might examine the question what on earth the Forms contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them.

Again, they are no help towards the

of other things

(for they are not the substance of things, otherwise they would be

things), nor to their existence, since they are not present in the things which partake of them. If they were, it might perhaps seem that they are causes, in the sense in which the admixture of white causes a thing to be white;

but this theory, which was first stated by Anaxagoras

and later by Eudoxus

and others, is very readily refutable, for it is easy to adduce plenty of impossibilities against such a view. Again, other things are not

in any accepted sense

from the Forms.

To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the Ideas

Besides, anything may both be and become like something else without being imitated from it; thus a man may become just like Socrates whether Socrates exists or not,

and even if Socrates were eternal, clearly the case would be the same. Also there will be several "patterns," and hence Forms, of the same thing; e.g. "animal" and "two-footed" will be patterns of "man," and so too will the Idea of Man.

Further, the Forms will be patterns not only of sensible things but of themselves (e.g. genus in the sense of genus of species), and thus the same thing will be both pattern and copy.

Further, it would seem impossible that the substance and the thing of which it is the substance exist in separation; hence how can the Ideas, if they are the substances of things, exist in separation from them?

It is stated in the Phaedo

that the Forms are the causes both of existence and of generation.

Yet, assuming that the Forms exist, still the things which participate in them are not generated unless there is something to impart motion; while many other things

generated (e.g. house, ring) of which we hold that there are no Forms. Thus it is clearly possible that all other things may both exist and be generated for the same causes as the things just mentioned.

Further, if the Forms are numbers, in what sense will they be causes? Is it because things are other numbers, e.g. such and such a number Man, such and such another Socrates, such and such another Callias? then why are those numbers the causes of these? Even if the one class is eternal and the other not, it will make no difference.

And if it is because the things of our world are ratios of numbers (e.g. a musical concord), clearly there is some one class of things of which they are ratios. Now if there is this something, i.e. their

, clearly the numbers themselves will be ratios of one thing to another.

I mean, e.g., that if Callias is a numerical ratio of fire, earth, water and air, the corresponding Idea too will be a number of certain other things which are its substrate. The Idea of Man, too, whether it is in a sense a number or not, will yet be an arithmetical ratio of certain things,

and not a mere number; nor, on these grounds, will any Idea be a number.

Again, one number can be composed of several numbers, but how can one Form be composed of several Forms? And if the one number is not composed of the other numbers themselves, but of their constituents (e.g. those of the number 10,000), what is the relation of the units? If they are specifically alike, many absurdities will result, and also if they are not (whether (a) the units in a given number are unlike, or (b) the units in each number are unlike those in every other number).

For in what can they differ, seeing that they have no qualities? Such a view is neither reasonable nor compatible with our conception of units.

Further, it becomes necessary to set up another kind of number (with which calculation deals), and all the objects which are called "intermediate" by some thinkers.

But how or from what principles can these be derived? or on what grounds are they to be considered intermediate between things

and Ideal numbers? Further, each of the units in the number 2 comes from a prior 2; but this is impossible.

Further, why should a number , taken together, be one thing? And further, in addition to the above objections, if the units are unlike, they should be treated as the thinkers who assume two or four elements treat those elements; for not one of them applies the term "element" to the common substrate, e.g. body, but to fire and earth—whether there is a common substrate (i.e. body) or not.

As it is, the One is spoken of as though it were homogeneous, like fire or water. But if this is so, the numbers will not be substances. And if there is an absolute One which is a principle, clearly the term "one" is ambiguous; otherwise this is impossible.

When we wish to refer substances to their principles we derive lines

from "Long and Short," a kind of "Great and Small"; and the plane from "Wide and Narrow," and the solid body from "Deep and Shallow." But in this case how can the plane contain a line,

or the solid a line and a plane? for "Wide and Narrow" and "Deep and Shallow" are different genera. Nor is Number contained in these objects (because "Many and Few" is yet another class); and in the same way it is clear that none of the other higher genera will be contained in the lower. Nor, again, is the Broad the genus of which the Deep is a species; for then body would be a kind of plane.

Further, how will it be possible for figures to contain points?

Plato steadily rejected this class of objects as a geometrical fiction, but he recognized "the beginning of a line," and he frequently assumed this latter class, i.e. the " indivisible lines."

But these must have some limit; and so by the same argument which proves the existence of the line, the point also exists.

In general, although Wisdom is concerned with the cause of visible things, we have ignored this question (for we have no account to give of the cause from which change arises),

and in the belief that we are accounting for their substance we assert the existence of other substances; but as to

the latter are the substances of the former, our explanation is worthless—for "participation," as we have said before,

means nothing.

And as for that which we can see to be the cause in the sciences, and through which all mind and all nature works—this cause

which we hold to be one of the first principles—the Forms have not the slightest bearing upon it either. Philosophy has become mathematics for modern thinkers,

although they profess

that mathematics is only to be studied as a means to some other end.

Further, one might regard the substance which they make the material substrate as too mathematical, and as being a predicate and differentia of substance or matter rather than as matter itself, I mean the "Great and Small," which is like the "Rare and Dense" of which the physicists speak,

holding that they are the primary differentiae of the substrate; because these qualities are a species of excess and defect.

Also with regard to motion, if the "Great and Small" is to constitute motion, obviously the Forms will be moved; if not, whence did it come? On this view the whole study of physics is abolished. And what is supposed to be easy, to prove that everything is One, does not follow; because from their exposition

it does not follow, even if you grant them all their assumptions that everything is One, but only that there is an absolute One—

and not even this, unless you grant that the universal is a class; which is impossible in some cases.

Nor is there any explanation of the lines, planes and solids which "come after" the Numbers

: neither as to how they exist or can exist, nor as to what their importance is. They cannot be Forms (since they are not numbers) or Intermediates (which are the objects of mathematics) or perishables; clearly they form yet another fourth class.

In general, to investigate the elements of existing things without distinguishing the various senses in which things are said to exist is a hopeless task;

especially when one inquires along these lines into the nature of the elements of which things are composed. For (a) we cannot surely conceive of the elements of activity or passivity or straightness; this is possible, if at all, only in the case of substances. Hence to look for, or to suppose that one has found, the elements of

that exists, is a mistake.

(b) How

one apprehend the elements of

? Obviously one could not have any previous knowledge of anything; because just as a man who is beginning to learn geometry can have previous knowledge of other facts, but no previous knowledge of the principles of that science or of the things about which he is to learn, so it is in the case of all other branches of knowledge.

Hence if there is a science which embraces everything

(as some say), the student of it can have no previous knowledge at all. But all learning proceeds, wholly or in part, from what is already known; whether it is through demonstration or through definition—since the parts of the definition must be already known and familiar. The same is true of induction.

On the other hand, assuming that this knowledge should turn out to be innate,

it is astonishing that we should possess unawares the most important of the sciences. Further, how is one to

of what elements things consist? how is it to be established?

Even this presents a difficulty, because the facts might be disputed, as happens in the case of certain syllables—for some say that ZA is composed of S, D and A, while others say that it is a distinct sound and not any one of those which are familiar to us.

Further, how can one gain knowledge of the objects of a particular sense-perception without possessing that sense? Yet it should be possible, that if the elements of which all things consist, as composite sounds consist of their peculiar

elements, are the same.

Thus it is obvious, from the statements of earlier thinkers also, that all inquiry is apparently directed towards the causes described in the Physics,

and that we cannot suggest any other cause apart from these. They were, however, only vaguely conceived; and although in one sense they have all been stated before, in another they have not been stated at all.

For the earliest philosophy speaks falteringly, as it were, on all subjects; being new and in its infancy. Even Empedocles says that bone exists by virtue of its ratio,

which is the definition or essence of a thing.

But by similar reasoning both flesh and every other thing,

or else nothing at all, must be ratio; for it must be because of this, and not because of their matter—which he calls fire, earth, water and air—that flesh and bone and every other thing exists.

If anyone else had stated this, he would necessarily have agreed, but his own statement was not clear.

These and similar points have been explained already. We will now return to the difficulties which might be raised about these same questions, for they may throw some light upon subsequent difficulties.

The study of Truth is in one sense difficult, in another easy. This is shown by the fact that whereas no one person can obtain an adequate grasp of it, we cannot

fail in the attempt;

each thinker makes some statement about the natural world, and as an individual contributes little or nothing to the inquiry; but a combination of all conjectures results in something considerable.

Thus in so far as it seems that Truth is like the proverbial door which no one can miss,

in this sense our study will be easy; but the fact that we cannot, although having some grasp of the whole, grasp a particular part, shows its difficulty. However, since difficulty also can be accounted for in two ways, its cause may exist not in the objects of our study but in ourselves:

just as it is with bats' eyes in respect of daylight, so it is with our mental intelligence in respect of those things which are by nature most obvious.

It is only fair to be grateful not only to those whose views we can share but also to those who have expressed rather superficial opinions. They too have contributed something; by their preliminary work they have formed our mental experience.

If there had been no Timotheus,

we should not possess much of our music; and if there had been no Phrynis,

there would have been no Timotheus. It is just the same in the case of those who have theorized about reality: we have derived certain views from some of them, and they in turn were indebted to others.

Moreover, philosophy is rightly called

a knowledge of Truth. The object of theoretic knowledge is truth, while that of practical knowledge is action; for even when they are investigating

a thing is so, practical men study not the eternal principle but the relative and immediate application.

But we cannot know the truth apart from the cause. Now every thing through which a common quality is communicated to other things is itself of all those things in the highest degree possessed of that quality (e.g. fire is hottest, because it is the cause of heat in everything else); hence that also is most true which causes all subsequent things to be true.

Therefore in every case the first principles of things must necessarily be true above everything else—since they are not merely

true, nor is anything the cause of their existence, but they are the cause of the existence of other things,—and so as each thing is in respect of existence, so it is in respect of truth.

Moreover, it is obvious that there is some first principle, and that the causes of things are not infinitely many either in a direct sequence or in kind. For the material generation of one thing from another cannot go on in an infinite progression (e.g. flesh from earth, earth from air, air from fire, and so on without a stop); nor can the source of motion (e.g. man be moved by air, air by the sun, the sun by Strife,

with no limit to the series).

In the same way neither can the Final Cause recede to infinity—walking having health for its object, and health happiness, and happiness something else: one thing always being done for the sake of another.

And it is just the same with the Formal Cause. For in the case of all intermediate terms of a series which are contained between a first and last term, the prior term is necessarily the cause of those which follow it; because if we had to say which of the three is the cause, we should say "the first." At any rate it is not the last term, because what comes at the end is not the cause of anything. Neither, again, is the intermediate term, which is only the cause of one

(and it makes no difference whether there is one intermediate term or several, nor whether they are infinite or limited in number). But of series which are infinite in this way, and in general of the infinite, all the parts are equally intermediate, down to the present moment. Thus if there is no first term, there is no cause at all.

On the other hand there can be no infinite progression downwards

(where there is a beginning in the upper direction) such that from fire comes water, and from water earth, and in this way some other kind of thing is always being produced. There are two senses in which one thing "comes from" another—apart from that in which one thing is said to come

another, e.g. the Olympian "from"

the Isthmian games—either as a man comes from a child as it develops, or as air comes from water.

Now we say that a man "comes from" a child in the sense that that which

become something comes from that which

becoming: i.e. the perfect from the imperfect. (For just as "becoming" is always intermediate between being and not-being, so is that which is becoming between what is and what is not. The learner is becoming informed, and that is the meaning of the statement that the informed person "comes from" the learner.)

On the other hand A comes from B in the sense that water comes from air by the destruction of B. Hence the former class of process is not reversible

(e.g. a child cannot come from a man, for the result of the process of becoming is not the thing which is becoming, but that which exists after the process is complete. So day comes from early dawn, because it is after dawn; and hence dawn does not come from day). But the other class is reversible.

In both cases progression to infinity is impossible; for in the former the intermediate terms must have an end, and in the second the process is reversible, for the destruction of one member of a pair is the generation of the other. At the same time the first cause, being eternal, cannot be destroyed; because, since the process of generation is not infinite in the upper direction, that cause which first, on its destruction, became something else, cannot possibly be eternal.

Further, the Final cause of a thing is an

, and is such that it does not happen for the sake of some thing else, but all other things happen for its sake. So if there is to be a last term of this kind, the series will not be infinite; and if there is no such term, there will be no Final cause. Those who introduce infinity do not realize that they are abolishing the nature of the Good (although no one would attempt to do anything if he were not likely to reach some limit);

nor would there be any intelligence in the world, because the man who has intelligence always acts for the sake of something, and this is a limit, because the

is a limit.

Nor again can the Formal cause be referred back to another fuller definition;

for the prior definition is always closer, and the posterior is not; and where the original definition does not apply, neither does the subsequent one.

Further, those who hold such a view do away with scientific knowledge, for on this view it is impossible to know anything until one comes to terms which cannot be analyzed.

Understanding, too, is impossible; for how can one conceive of things which are infinite in this way? It is different in the case of the line, which, although in respect of divisibility it never stops, yet cannot be conceived of unless we make a stop (which is why, in examining an infinite

line, one cannot count the sections).

Even matter has to be conceived under the form of something which changes,

and there can be nothing which is infinite.

In any case the concept of infinity is not infinite.

Again, if the kinds of causes were infinite in

it would still be impossible to acquire knowledge; for it is only when we have become acquainted with the causes that we assume that we know a thing; and we cannot, in a finite time, go completely through what is additively infinite.

The effect of a lecture depends upon the habits of the listener; because we expect the language to which we are accustomed,

and anything beyond this seems not to be on the same level, but somewhat strange and unintelligible on account of its unfamiliarity; for it is the familiar that is intelligible. The powerful effect of familiarity is clearly shown by the laws, in which the fanciful and puerile survivals prevail, through force of habit, against our recognition of them.

Thus some people will not accept the statements of a speaker unless he gives a mathematical proof; others will not unless he makes use of illustrations; others expect to have a poet adduced as witness. Again, some require exactness in everything, while others are annoyed by it, either because they cannot follow the reasoning or because of its pettiness; for there is something about exactness which seems to some people to be mean, no less in an argument than in a business transaction.

Hence one must have been already trained how to take each kind of argument, because it is absurd to seek simultaneously for knowledge and for the method of obtaining it; and neither is easy to acquire. Mathematical accuracy is not to be demanded in everything, but only in things which do not contain matter.

Hence this method is not that of natural science, because presumably all nature is concerned with matter. Hence we should first inquire what nature is; for in this way it will become clear what the objects of natural science are [and whether it belongs to one science or more than one to study the causes

and principles of things].

It is necessary, with a view to the science which we are investigating, that we first describe the questions which should first be discussed. These consist of all the divergent views which are held about the first principles; and also of any other view apart from these which happens to have been overlooked.

Now for those who wish to get rid of perplexities it is a good plan to go into them thoroughly; for the subsequent certainty is a release from the previous perplexities, and release is impossible when we do not know the knot. The perplexity of the mind shows that there is a "knot" in the subject; for in its perplexity it is in much the same condition as men who are fettered: in both cases it is impossible to make any progress.

Hence we should first have studied all the difficulties, both for the reasons given and also because those who start an inquiry without first considering the difficulties are like people who do not know where they are going; besides, one does not even know whether the thing required has been found or not.

To such a man the

is not clear; but it is clear to one who has already faced the difficulties.

Further, one who has heard all the conflicting theories, like one who has heard both sides in a lawsuit, is necessarily more competent to judge.

The first difficulty is concerned with the subjects

which we discussed in our prefatory remarks. (1.) Does the study of the causes belong to one science or to more than one?

(2.) Has that science only to contemplate the first principles of substance, or is it also concerned with the principles which all use for demonstration—e.g. whether it is possible at the same time to assert and deny one and the same thing, and other similar principles?

And if it is concerned with substance, (3.) is there one science which deals with all substances, or more than one; and if more than one, are they all cognate, or should we call some of them "kinds of Wisdom" and others something different?

This too is a question which demands inquiry: (iv.) should we hold that only sensible substances exist, or that there are other besides? And should we hold that there is only one class of non-sensible substances, or more than one (as do those who posit the Forms and the mathematical objects as intermediate between the Forms and sensible things)?

These questions, then, as I say, must be considered; and also (v.) whether our study is concerned only with substances,

or also with the essential attributes of substance;

and further, with regard to Same and Other, and Like and Unlike and Contrariety, and Prior and Posterior, and all other such terms which dialecticians try to investigate, basing their inquiry merely upon popular opinions; we must consider whose province it is to study all of these.

Further, we must consider all the essential attributes of these same things, and not merely what each one of them is, but also whether each one has one opposite

; and (vi.) whether the first principles and elements of things are the genera under which they fall or the pre-existent parts into which each thing is divided; and if the genera, whether they are those which are predicated ultimately of individuals, or the primary genera—e.g., whether "animal" or "man" is the first principle and the more independent of the individual.

Above all we must consider and apply ourselves to the question (7.) whether there is any other cause

besides matter, and if so whether it is dissociable from matter, and whether it is numerically one or several; and whether there is anything apart from the concrete thing (by the concrete thing I mean matter together with whatever is predicated of it) or nothing; or whether there is in some cases but not in others; and what these cases are.

Further, (8.) we must ask whether the first principles are limited in number or in kind

—both those in the definitions and those in the substrate—and (ix.) whether the principles of perishable and of imperishable things are the same or different; and whether all are imperishable, or those of perishable things are perishable.

Further, there is the hardest and most perplexing question of all: (x.) whether Unity and Being (as the Pythagoreans and Plato maintained) are not distinct, but are the substance of things; or whether this is not so, and the substrate is something distinct

(as Empedocles holds of Love,

another thinker

of fire, and another

of water or air

);

and (xi.) whether the first principles are universal or like individual things

; and (12.) whether they exist potentially or actually; and further whether their potentiality or actuality depends upon anything other than motion

; for these questions may involve considerable difficulty.

Moreover we must ask (13.) whether numbers and lines and figures and points are substances in any sense, or not; and if they are, whether they are separate from sensible things or inherent in them.

With regard to these problems not only is it difficult to attain to the truth, but it is not even easy to state all the difficulties adequately.

(1.) Firstly, then, with respect to the first point raised: whether it is the province of one science or of more than one to study all the kinds of causes.

How can

science comprehend the first principles unless they are contraries? Again, in many things they are not all present.

How can a principle of motion be in immovable things? or the "nature of the Good"? for everything which is good in itself and of its own nature is an

and thus a cause, because for its sake other things come to be and exist; and the

and

is the end of some action, and all actions involve motion; thus it would be impossible either for this principle to exist in motionless things or for there to be any

Good.

Hence in mathematics too nothing is proved by means of this cause, nor is there any demonstration of the kind "because it is better or worse"; indeed no one takes any such consideration into account.

And so for this reason some of the sophists, e.g. Aristippus,

spurned mathematics, on the ground that in the other arts, even the mechanical ones such as carpentry and cobbling, all explanation is of the kind "because it is better or worse," while mathematics takes no account of good and bad.

On the other hand if there are several sciences of the causes, and a different one for each different principle, which of them shall we consider to be the one which we are seeking, or whom of the masters of these sciences shall we consider to be most learned in the subject which we are investigating?

For it is possible for all the kinds of cause to apply to the same object; e.g. in the case of a house the source of motion is the art and the architect; the final cause is the function; the matter is earth and stones, and the form is the definition. Now to judge from our discussion some time ago

as to which of the sciences should be called Wisdom, there is some case for applying the name to each of them.

Inasmuch as Wisdom is the most sovereign and authoritative kind of knowledge, which the other sciences, like slaves, may not contradict, the knowledge of the

and of the

resembles Wisdom (since everything else is for the sake of the

); but inasmuch as it has been defined as knowledge of the first principles and of the most knowable, the knowledge of the essence will resemble Wisdom.

For while there are many ways of understanding the same thing, we say that the man who recognizes a thing by its being something knows more than he who recognizes it by its not being something; and even in the former case one knows more than another, and most of all he who knows

it is, and not he who knows its size or quality or natural capacity for acting or being acted upon.

Further, in all other cases too, even in such as admit of demonstration,

we consider that we know a particular thing when we know

it is (e.g. what is the squaring of a rectangle? answer, the finding of a mean proportional to its sides; and similarly in other instances); but in the case of generations and actions and all kinds of change, when we know the source of motion.

This is distinct from and opposite to the

. Hence it might be supposed that the study of each of these causes pertained to a different science.

(2.) Again, with respect to the demonstrative principles as well, it may be disputed whether they too are the objects of one science

or of several.

By demonstrative I mean the axioms from which all demonstration proceeds, e.g. "everything must be either affirmed or denied," and "it is impossible at once to be and not to be," and all other such premisses. Is there one science both of these principles and of substance, or two distinct sciences? and if there is not one, which of the two should we consider to be the one which we are now seeking?

It is not probable that both subjects belong to one science; for why should the claim to understand these principles be peculiar to geometry rather than to any other science? Then if it pertains equally to any science, and yet cannot pertain to all,

comprehension of these principles is no more peculiar to the science which investigates substances than to any other science.

Besides, in what sense can there in be a science of these principles? We know already just what each of them is; at any rate other sciences employ them as being known to us.

If, however there is a demonstrative science of them, there will have to be some underlying genus, and some of the principles will be derived from axioms, and others will be unproved

(for there cannot be demonstration of everything), since demonstration must proceed from something, and have some subject matter, and prove something. Thus it follows that there is some one genus of demonstrable things; for all the demonstrative sciences employ axioms.

On the other hand, if the science of substance is distinct from the science of these principles, which is of its own nature the more authoritative and ultimate?

The axioms are most universal, and are the first principles of everything. And whose province will it be, if not the philosopher's, to study truth and error with respect to them?

(3.) And in general, is there one science of all substances, or more than one?

if there is not one, with what sort of substance must we assume that this science is concerned?

On the other hand, it is not probable that there is one science of all substances; for then there would be one demonstrative of all attributes—assuming that every demonstrative science

proceeds from accepted beliefs and studies the essential attributes concerned with some definite subject matter.

Thus to study the essential attributes connected with the same genus is the province of the same science proceeding from the same beliefs. For the subject matter belongs to one science, and so do the axioms, whether to the same science or to a different one; hence so do the attributes, whether they are studied by these sciences themselves or by one derived from them.

(v.) Further, is this study concerned only with substances, or with their attributes as well?

I mean, e.g., if the solid is a kind of substance, and so too lines and planes, is it the province of the same science to investigate both these and their attributes, in every class of objects about which mathematics demonstrates anything, or of a different science?

If of the same, then the science of substance too would be in some sense demonstrative; but it does not seem that there is any demonstration of the "what is it?" And if of a different science, what will be the science which studies the attributes of substance? This is a very difficult question to answer.

(iv.) Further, are we to say that only sensible substances exist, or that others do as well? and is there really only one kind of substance, or more than one

(as they hold who speak of the Forms and the Intermediates, which they maintain to be the objects of the mathematical sciences)?

In what sense we Platonists hold the Forms to be both causes and independent substances has been stated

in our original discussion on this subject. But while they involve difficulty in many respects, not the least absurdity is the doctrine that there are certain entities apart from those in the sensible universe, and that these are the same as sensible things except in that the former are eternal and the latter perishable.

For Platonists say nothing more or less than that there is an absolute Man, and Horse, and Health; in which they closely resemble those who state that there are Gods, but of human form; for as the latter invented nothing more or less than eternal men, so the former simply make the Forms eternal sensibles.

Again, if anyone posits Intermediates distinct from Forms and sensible things, he will have many difficulties;

because obviously not only will there be lines apart from both Ideal and sensible lines, but it will be the same with each of the other classes.

Thus since astronomy is one of the mathematical sciences, there will have to be a heaven besides the sensible heaven, and a sun and moon, and all the other heavenly bodies.

But how are we to believe this? Nor is it reasonable that the heaven should be immovable; but that it should move

is utterly impossible.

It is the same with the objects of optics and the mathematical theory of harmony; these too, for the same reasons, cannot exist apart from sensible objects. Because if there are intermediate objects of sense and sensations, clearly there will also be animals intermediate between the Ideal animals and the perishable animals.

One might also raise the question with respect to what kind of objects we are to look for these sciences. For if we are to take it that the only difference between mensuration and geometry is that the one is concerned with things which we can perceive and the other with things which we cannot, clearly there will be a science parallel to medicine (and to each of the other sciences), intermediate between Ideal medicine and the medicine which we know.

Yet how is this possible? for then there would be a class of healthy things apart from those which are sensible and from the Ideally healthy. Nor, at the same time, is it true that mensuration is concerned with sensible and perishable magnitudes; for then it would perish as they do. Nor, again, can astronomy be concerned with sensible magnitudes or with this heaven of ours;

for as sensible lines are not like those of which the geometrician speaks (since there is nothing sensible which is straight or curved in that sense; the circle

touches the ruler not at a point, but as Protagoras used to say in refuting the geometricians), so the paths and orbits of our heaven are not like those which astronomy discusses, nor have the symbols of the astronomer the same nature as the stars.

Some, however, say that these so-called Intermediates between Forms and sensibles do exist: not indeed separately from the sensibles, but in them. It would take too long to consider in detail all the impossible consequences of this theory, but it will be sufficient to observe the following.

On this view it is not logical that only this should be so; in clearly it would be possible for the Forms also to be in sensible things; for the same argument applies to both. Further, it follows necessarily that two solids must occupy the same space; and that the Forms cannot be immovable, being present in sensible things, which move.

And in general, what is the object of assuming that Intermediates exist, but only in sensible things? The same absurdities as before will result: there will be a heaven besides the sensible one, only not apart from it, but in the same place; which is still more impossible.

Thus it is very difficult to say, not only what view we should adopt in the foregoing questions in order to arrive at the truth, but also in the case of the first principles (vi.) whether we should assume that the genera, or the simplest constituents of each particular thing, are more truly the elements and first principles of existing things. E.g., it is generally agreed that the elements and first principles of speech are those things of which, in their simplest form, all speech is composed; and not the common term "speech"; and in the case of geometrical propositions we call those the "elements"

whose proofs are embodied in the proofs of all or most of the rest.

Again, in the case of bodies, both those who hold that there are several elements and those who hold that there is one call the things of which bodies are composed and constituted first principles. E.g., Empedocles states that fire and water and the other things associated with them are the elements which are present in things and of which things are composed; he does not speak of them as genera of things.

Moreover in the case of other things too, if a man wishes to examine their nature

he observes, e.g., of what parts a bed consists and how they are put together; and then he comprehends its nature. Thus to judge from these arguments the first principles will not be the genera of things.

But from the point of view that it is through definitions that we get to know each particular thing, and that the genera are the first principles of definitions, the genera must also be the first principles of the things defined.

And if to gain scientific knowledge of things is to gain it of the species after which things are named, the genera are first principles of the species. And apparently some even of those

who call Unity or Being or the Great and Small elements of things treat them as genera.

Nor again is it possible to speak of the first principles in both senses.

The formula of substance is one; but the definition by genera will be different from that which tells us of what

a thing is composed.

Moreover, assuming that the genera are first principles in the truest sense, are we to consider the

genera to be first principles, or the final terms predicated of individuals? This question too involves some dispute.

For if universals are always more truly first principles, clearly the answer will be "the highest genera," since these are predicated of everything. Then there will be as many first principles of things

as there are primary genera, and so both Unity and Being will be first principles and substances, since they are in the highest degree predicated of all things.

But it is impossible for either Unity or Being to be one genus of existing things. For there must

differentiae of each genus, and each differentia must be

; but it is impossible either for the species of the genus to be predicated of the specific differentiae, or for the genus to be predicated without its species.

Hence if Unity or Being is a genus, there will be no differentia Being or Unity.

But if they are not genera, neither will they be first principles, assuming that it is the genera that are first principles. And further, the intermediate terms, taken together with the differentiae, will be genera, down to the individuals; but in point of fact, although some are thought to be such, others are not. Moreover the differentiae are more truly principles than are the genera; and if they also are principles, we get an almost infinite number of principles, especially if one makes the ultimate genus a principle.

Moreover, if Unity is really more of the nature of a principle, and the indivisible is a unity, and every thing indivisible is such either in quantity or in kind, and the indivisible in kind is prior to the divisible, and the genera are divisible into species, then it is rather the lowest predicate that will be a unity (for "man" is not the genus

of individual men).

Further, in the case of things which admit of priority and posteriority, that which is predicated of the things cannot exist apart from them. E.g., if 2 is the first number, there will be no Number apart from the species of number; and similarly there will be no Figure apart from the species of figures. But if the genera do not exist apart from the species in these cases, they will scarcely do so in others; because it is assumed that genera are most likely to exist in these cases.

In individuals, however, there is no priority and posteriority. Further, where there is a question of better or worse, the better is always prior; so there will be no genus in these cases either.

From these considerations it seems that it is the terms predicated of individuals, rather than the genera, that are the first principles. But again on the other hand it is not easy to say in what sense we are to understand these to be principles;

for the first principle and cause must be apart from the things of which it is a principle, and must be able to exist when separated from them. But why should we assume that such a thing exists

alongside of the individual, except in that it is predicated universally and of all the terms? And indeed if this is a sufficient reason, it is the more universal concepts that should rather be considered to be principles; and so the primary genera will be the principles.

In this connection there is a difficulty which is the hardest and yet the most necessary of all to investigate, and with which our inquiry is now concerned. (7.) If nothing exists apart from individual things, and these are infinite in number, how is it possible to obtain knowledge of the numerically infinite? For we acquire our knowledge of all things only in so far as they contain something universal, some one and identical characteristic.

But if this is essential, and there must be something apart from individual things, it must be the genera; either the lowest or the highest; but we have just concluded that this is impossible.

Further, assuming that when something is predicated of matter there is in the fullest sense something apart from the concrete whole, if there is something, must it exist apart from

concrete wholes, or apart from some but not others, or apart from none?

If nothing exists apart from individual things, nothing will be intelligible; everything will be sensible, and there will be no knowledge of anything—unless it be maintained that sense-perception is knowledge. Nor again will anything be eternal or immovable, since sensible things are all perishable and in motion.

Again, if nothing is eternal, even generation is impossible; for there must be something which becomes something, i.e. out of which something is generated, and of this series the ultimate term must be ungenerated; that is if there is any end to the series and generation cannot take place out of nothing.

Further, if there is generation and motion, there must be limit too. For (a) no motion is infinite, but every one has an end; (b) that which cannot be completely generated cannot begin to be generated, and that which has been generated must

as soon as it has been generated.

Further, if matter exists apart in virtue of being ungenerated, it is still more probable that the substance, i.e. that which the matter is at any given time becoming, should exist. And if neither one nor the other exists, nothing will exist at all. But if this is impossible, there must be something, the shape or form, apart from the concrete whole.

But again, if we assume this, there is a difficulty: in what cases shall we, and in what shall we not, assume it? Clearly it cannot be done in all cases; for we should not assume that a particular house exists apart from particular houses.

Moreover, are we to regard the essence of all things, e.g. of men, as one? This is absurd; for all things whose essence is one are one.

Then is it many and diverse? This too is illogical. And besides, how does the matter become each individual one of these things, and how is the concrete whole both matter and form?

(8.) Further, the following difficulty might be raised about the first principles. If they are one in kind, none of them will be one in number, not even the Idea of Unity or of Being. And how can there be knowledge unless there is some universal term?

On the other hand if they are numerically one, and each of the principles is one, and not, as in the case of sensible things, different in different instances (e.g. since a given syllable is always the same in kind, its first principles are always the same in kind, but only in kind, since they are essentially different in number)—if the first principles are one, not in this sense, but numerically, there will be nothing else apart from the elements; for "numerically one" and "individual" are identical in meaning. This is what we mean by "individual": the numerically one; but by "universal" we mean what is predicable of individuals.

Hence just as, if the elements of language

were limited in number, the whole of literature would be no more than those elements—that is, if there were not two nor more than two of the same .

(ix.) There is a difficulty, as serious as any, which has been left out of account both by present thinkers and by their predecessors: whether the first principles of perishable and imperishable things are the same or different. For if they are the same, how is it that some things are perishable and others imperishable, and for what cause?

The school of Hesiod, and all the cosmologists, considered only what was convincing to themselves, and gave no consideration to us. For they make the first principles Gods or generated from Gods, and say that whatever did not taste of the nectar and ambrosia became mortal—clearly using these terms in a sense significant to themselves;

but as regards the actual applications of these causes their statements are beyond our comprehension. For if it is for pleasure that the Gods partake of them, the nectar and ambrosia are in no sense causes of their existence; but if it is to support life, how can Gods who require nourishment be eternal?

However, it is not worth while to consider seriously the subtleties of mythologists; we must ascertain

by cross-examining those who offer demonstration of their statements why exactly things which are derived from the same principles are some of an eternal nature and some perishable. And since these thinkers state no reason for this view, and it is unreasonable that things should be so, obviously the causes and principles of things cannot be the same.

Even the thinker who might be supposed to speak most consistently, Empedocles, is in the same case; for he posits Strife as a kind of principle which is the cause of destruction, but none the less Strife would seem to produce everything except the One; for everything except God

proceeds from it.

At any rate he says

From which grew all that was and is and shall be

In time to come: the trees, and men and women,

The beasts and birds and water-nurtured fish,

And the long-living Gods.

And it is obvious even apart from this;

for if there had not been Strife in things, all things would have been one, he says; for when they came together "then Strife came to stand outermost."

Hence it follows on his theory that God, the most blessed being, is less wise than the others, since He does not know all the elements; for He has no Strife in Him, and knowledge is of like by like:

By earth (he says) we earth perceive, by water water,

By air bright air, by fire consuming fire,

Love too by love, and strife by grievous strife.

But—and this is the point from which we started—thus much is clear: that it follows on his theory that Strife is no more the cause of destruction than it is of Being. Nor, similarly, is Love the cause of Being; for in combining things into one it destroys everything else.

Moreover, of the actual process of change he gives no explanation, except that it is so by nature:

But when Strife waxing great among the members

Sprang up to honor as the time came round

Appointed them in turn by a mighty oath,

as though change were a necessity; but he exhibits no cause for the necessity.

However, thus much of his theory is consistent: he does not represent some things to be perishable and others imperishable, but makes everything

perishable except the elements. But the difficulty now being stated is why some things are perishable and others not, assuming that they are derived from the same principles.

The foregoing remarks may suffice to show that the principles cannot be the same.

If however they are different, one difficulty is whether they too are to be regarded as imperishable or as perishable. For if they are perishable, it is clearly necessary that they too must be derived from something else, since everything passes upon dissolution into that from which it is derived. Hence it follows that there are other principles prior to the first principles;

but this is impossible, whether the series stops or proceeds to infinity. And further, how can perishable things exist if their principles are abolished? On the other hand if the principles are imperishable, why should some imperishable principles produce perishable things, and others imperishable things? This is not reasonable; either it is impossible or it requires much explanation.

Further, no one has so much as attempted to maintain different principles; they maintain the same principles for everything.

But they swallow down the difficulty which we raised first

as though they took it to be trifling.

But the hardest question of all to investigate and also the most important with a view to the discovery of the truth, is whether after all Being and Unity are substances of existing things, and each of them is nothing else than Being and Unity respectively, or whether we should inquire what exactly Being and Unity are, there being some other nature underlying them.

Some take the former, others the latter view of the nature of Being and Unity. Plato and the Pythagoreans hold that neither Being nor Unity is anything else than itself, and that this is their nature, their essence being simply Being and Unity.

But the physicists, e.g. Empedocles, explain what Unity is by reducing it to something, as it were, more intelligible—or it would seem that by Love Empedocles means Unity; at any rate Love is the cause of Unity in all things. Others identify fire and others air with this Unity and Being of which things consist and from which they have been generated.

Those who posit more numerous elements also hold the same view; for they too must identify Unity and Being with all the principles which they recognize.

And it follows that unless one assumes Unity and Being to be substance in some sense, no other universal term can be substance; for Unity and Being are the most universal of all terms,

and if there is no absolute Unity or absolute Being, no other concept can well exist apart from the so-called particulars. Further, if Unity is not substance, clearly number cannot be a separate characteristic of things; for number is units, and the unit is simply a particular kind of one.

On the other hand, if there is absolute Unity and Being, their substance must be Unity and Being; for no other term is predicated universally of Unity and Being, but only these terms themselves. Again, if there is to be absolute Being and absolute Unity, it is very hard to see how there can be anything else besides these; I mean, how things can be more than one.

For that which is other than what is, is not; and so by Parmenides' argument

it must follow that all things are one, i.e. Being.

In either case there is a difficulty; for whether Unity is not a substance or whether there is absolute Unity, number cannot be a substance.

It has already been stated why this is so if Unity is not a substance; and if it is, there is the same difficulty as about Being. For whence, if not from the absolute One or Unity, can there be another one? It must be not-one; but all things are either one, or many of which each is one. Further, if absolute Unity is indivisible, by Zeno's axiom it will be nothing.

For that which neither when added makes a thing greater nor when subtracted makes it smaller is not an existent thing, he says

; clearly assuming that what exists is spatial magnitude. And if it is a spatial magnitude it is corporeal, since the corporeal exists in all dimensions, whereas the other magnitudes, the plane or line, when added to a thing in one way will increase it, but when added in another will not; and the point or unit will not increase a thing in any way whatever.

But since Zeno's view is unsound, and it is possible for a thing to be indivisible in such a way that it can be defended even against his argument (for such a thing

when added will increase a thing in number though not in size)—still how can a

be composed of one or more such indivisible things? It is like saying that the line is composed of points.

Moreover, even if one supposes the case to be

such that number is generated, as some say, from the One itself and from something else which is not one, we must none the less inquire why and how it is that the thing generated will be at one time number and at another magnitude, if the not-one was inequality and the same principle in both cases.

For it is not clear how magnitude can be generated either from One and this principle, or from a number and this principle.

(13.) Out of this arises the question whether numbers, bodies, planes and points are substances or not. If not, the question of what Being is, what the substances of things are, baffles us; for modifications and motions and relations and dispositions and ratios do not seem to indicate the substance of anything; they are all predicated of a substrate, and none of them is a definite thing.

As for those things which might be especially supposed to indicate substance—water, earth, fire and air, of which composite bodies are composed—

their heat and cold and the like are modifications, not substances; and it is only the body which undergoes these modifications that persists as something real and a kind of substance.

Again, the body is less truly substance than the plane, and the plane than the line, and the line than the unit or point; for it is by these that the body is defined, and it seems that they are possible without the body, but that the body cannot exist without them.

This is why the vulgar and the earlier thinkers supposed that substance and Being are Body, and everything else the modifications of Body; and hence also that the first principles of bodies are the first principles of existing things; whereas later thinkers with a greater reputation for wisdom supposed that substance and Being are numbers.

As we have said, then, if these things are not substance, there is no substance or Being at all; for the attributes of these things surely have no right to be called existent things. On the other hand, if it be agreed that lines and points are more truly substance than bodies are, yet unless we can see to what

of bodies they belong (for they cannot be in sensible bodies) there will still be no substance.

Further, it is apparent that all these lines are divisions of Body, either in breadth

or in depth or in length. Moreover every kind of shape is equally present in a solid, so that if "Hermes is not in the stone,"

neither is the half-cube in the cube as a determinate shape.

Hence neither is the plane; for if any kind of plane were in it, so would that plane be which defines the half-cube. The same argument applies to the line and to the point or unit. Hence however true it may be that body is substance, if planes, lines and points are more truly substance than Body is, and these are not substance in any sense, the question of what Being is and what is the substance of things baffles us.

Because, in addition to the above arguments, absurd results follow from a consideration of generation and destruction; for it seems that if substance, not having existed before, now exists, or having existed before, subsequently does not exist it suffers these changes in the process of generation and destruction. But points, lines and planes, although they exist at one time and at another do not, cannot be in process of being either generated or destroyed;

for whenever bodies are joined or divided,

at one time, when they are joined one surface is instantaneously produced, and at another, when they are divided, two. Thus when the bodies are combined the surface does not exist but has perished; and when they are divided, surfaces exist which did not exist before. (The indivisible point is of course never divided into two.) And if they

generated and destroyed, from what are they generated?

It is very much the same with "the present moment" in time. This too cannot be generated and destroyed; but nevertheless it seems always to be different, not being a substance. And obviously it is the same with points, lines and planes, for the argument is the same; they are all similarly either limits or divisions.

In general one might wonder why we should seek for other entities apart from sensible things and the Intermediates:

e.g., for the Forms which we Platonists assume.

If it is for the reason that the objects of mathematics, while differing from the things in our world in another respect, resemble them in being a plurality of objects similar in form, so that their principles cannot be numerically determined (just as the principles of all language in this world of ours are determinate not in number but in kind—unless one takes such and such a particular syllable

or sound, for the principles of these are determinate in number too—

and similarly with the Intermediates, for in their case too there is an infinity of objects similar in form), then if there is not another set of objects apart from sensible and mathematical objects, such as the Forms are said to be, there will be no substance which is one both in kind and in number, nor will the principles of things be determinate in number, but in kind only.

Thus if this is necessarily so, it is necessary for this reason to posit the Forms also. For even if their exponents do not articulate their theory properly, still this is what they are trying to express, and it must be that they maintain the Forms on the ground that each of them is a substance, and none of them exists by accident.

On the other hand, if we are to assume that the Forms exist, and that the first principles are one in number but not in kind, we have already stated

the impossible consequences which must follow.

(12.) Closely connected with these questions is the problem whether the elements exist potentially or in some other sense.

If in some other sense, there will be something else prior to the first principles.

For the potentiality is prior to the actual cause, and the potential need not necessarily always become actual. On the other hand, if the elements exist potentially, it is possible for nothing to exist; for even that which does not yet exist is capable of existing. That which does not exist may come to be, but nothing which cannot exist comes to be.

(xi.) Besides the foregoing problems about the first principles we must also raise the question whether they are universal or such as we describe the particulars to be. For if they are universal, there will be no substances; for no common term denotes an individual thing, but a type; and substance is an individual thing.

But if the common predicate be hypostatized as an individual thing, Socrates will be several beings: himself, and Man, and Animal—that is, if each predicate denotes one particular thing.

These then are the consequences if the principles are universal. If on the other hand they are not universal but like particulars, they will not be knowable; for the knowledge of everything is universal. Hence there will have to be other universally predicated principles prior to the first principles, if there is to be any knowledge of them.

There is a science which studies Being qua Being, and the properties inherent in it in virtue of its own nature. This science is not the same as any of the so-called particular sciences, for none of the others contemplates Being generally qua Being; they divide off some portion of it and study the attribute of this portion, as do for example the mathematical sciences.

But since it is for the first principles and the most ultimate causes that we are searching, clearly they must belong to something in virtue of its own nature. Hence if these principles were investigated by those also who investigated the elements of existing things, the elements must be elements of Being not incidentally, but qua Being. Therefore it is of Being qua Being that we too must grasp the first causes.

The term "being" is used in various senses, but with reference to one central idea and one definite characteristic, and not as merely a common epithet. Thus as the term "healthy" always relates to health (either as preserving it or as producing it or as indicating it or as receptive of it),

and as "medical" relates to the art of medicine (either as possessing it or as naturally adapted for it or as being a function of medicine)—and we shall find other terms used similarly to these—

so "being " is used in various senses, but always with reference to one principle. For some things are said to "be" because they are substances; others because they are modifications of substance; others because they are a process towards substance, or destructions or privations or qualities of substance, or productive or generative of substance or of terms relating to substance, or negations of certain of these terms or of substance. (Hence we even say that not-being

not-being.)

And so, just as there is one science of all healthy things, so it is true of everything else. For it is not only in the case of terms which express one common notion that the investigation belongs to one science, but also in the case of terms which relate to one particular characteristic; for the latter too, in a sense, express one common notion. Clearly then the study of things which

being, also belongs to one science.

Now in every case knowledge is principally concerned with that which is primary, i.e. that upon which all other things depend, and from which they get their names. If, then, substance is this primary thing, it is of substances that the philosopher must grasp the first principles and causes.

Now of every single class of things, as there is one perception,

so there is one science: e.g., grammar, which is one science, studies all articulate sounds.

Hence the study of all the species of Being qua Being belongs to a science which is generically one, and the study of the several species of Being belongs to the specific parts of that science.

Now if Being and Unity are the same, i.e. a single nature, in the sense that they are associated as principle and cause are, and not as being denoted by the same definition (although it makes no difference but rather helps our argument if we understand them in the same sense),

since "one man" and "man" and "existent man" and "man" are the same thing, i.e. the duplication in the statement "he is a man and an

man" gives no fresh meaning (clearly the concepts of humanity and existence are not dissociated in respect of either coming to be or ceasing to be), and similarly in the case of the term "one," so that obviously the additional term in these phrases has the same significance, and Unity is nothing distinct from Being;

and further if the substance of each thing is one in no accidental sense, and similarly is of its very nature something which is—then there are just as many species of Being as of Unity. And to study the essence of these species (I mean, e.g., the study of Same and Other and all the other similar concepts—

roughly speaking all the "contraries" are reducible to this first principle;

but we may consider that they have been sufficiently studied in the "Selection of Contraries"

) is the province of a science which is generically one.

And there are just as many divisions of philosophy as there are kinds of substance; so that there must be among them a First Philosophy and one which follows upon it.

For Being and Unity at once entail genera, and so the sciences will correspond to these genera. The term "philosopher" is like the term "mathematician" in its uses; for mathematics too has divisions—there is a primary and a secondary science, and others successively, in the realm of mathematics.

Now since it is the province of one science to study opposites, and the opposite of unity is plurality, and it is the province of one science to study the negation and privation of Unity, because in both cases we are studying Unity, to which the negation (or privation) refers, stated either in the simple form that Unity is not present, or in the form that it is not present in a particular class; in the latter case Unity is modified by the differentia, apart from the content of the negation (for the negation of Unity is its absence); but in privation there is a substrate of which the privation is predicated.—

The opposite of Unity, then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness, Dissimilarity, Inequality and everything else which is derived from these or from Plurality or Unity—

fall under the cognizance of the aforesaid science. And one of them is Oppositeness; for this is a form of Difference, and Difference is a form of Otherness.

Hence since the term "one" is used in various senses, so too will these terms be used; yet it pertains to one science to take cognizance of them all. For terms fall under different sciences, not if they are used in various senses, but if their definitions are neither identical nor referable to a common notion.

And since everything is referred to that which is primary, e.g. all things which are called "one" are referred to the primary "One," we must admit that this is also true of Identity and Otherness and the Contraries. Thus we must first distinguish all the senses in which each term is used, and then attribute them to the primary in the case of each predicate, and see how they are related to it; for some will derive their name from possessing and others from producing it, and others for similar reasons.

Thus clearly it pertains to one science to give an account both of these concepts and of substance (this was one of the questions raised in the "Difficulties"

), and it is the function of the philosopher to be able to study all subjects.

If this is not so, who is it who in will investigate whether " Socrates" and " Socrates seated" are the same thing; or whether one thing has one contrary, or what the contrary is, or how many meanings it has?

and similarly with all other such questions.

Thus since these are the essential modifications of Unity qua Unity and of Being qua Being, and not qua numbers or lines or fire, clearly it a pertains to that science

to discover both the essence and the attributes of these concepts.

And those who investigate them err, not in being unphilosophical, but because the substance, of which they have no real knowledge, is prior. For just as number qua number has its peculiar modifications, e.g. oddness and evenness, commensurability and equality, excess and defect, and these things are inherent in numbers both considered independently and in relation to other numbers; and as similarly other peculiar modifications are inherent in the solid and the immovable and the moving and the weightless and that which has weight; so Being qua Being has certain peculiar modifications, and it is about these that it is the philosopher's function to discover the truth. And here is evidence of this fact.

Dialecticians and sophists wear the same appearance as the philosopher, for sophistry is Wisdom in appearance only, and dialecticians discuss all subjects,

and Being is a subject common to them all; but clearly they discuss these concepts because they appertain to philosophy.

For sophistry and dialectic are concerned with the same class of subjects as philosophy, but philosophy differs from the former in the nature of its capability and from the latter in its outlook on life. Dialectic treats as an exercise what philosophy tries to understand, and sophistry seems to be philosophy; but is not.

Further, the second column of contraries is privative, and everything is reducible to Being and Not being, and Unity and Plurality; e.g. Rest falls under Unity and Motion under Plurality. And nearly everyone agrees that substance and existing things are composed of contraries; at any rate all speak of the first principles as contraries—

some as Odd and Even,

some as Hot and Cold,

some as Limit and Unlimited,

some as Love and Strife.

And it is apparent that all other things also are reducible to Unity and Plurality (we may assume this reduction);

and the principles adduced by other thinkers fall entirely under these as genera.

It is clear, then, from these considerations also, that it pertains to a single science to study Being qua Being; for all things are either contraries or derived from contraries, and the first principles of the contraries are Unity and Plurality. And these belong to one science, whether they have reference to one common notion or not. Probably the truth is that they have not; but nevertheless even if the term "one" is used in various senses, the others will be related to the primary sense (and similarly with the contraries)—

even if Being or Unity is not a universal and the same in all cases, or is not separable from particulars (as it presumably is not; the unity is in some cases one of reference and in others one of succession). For this very reason it is not the function of the geometrician to inquire what is Contrariety or Completeness or Being or Unity or Identity or Otherness, but to proceed from the assumption of them.

Clearly, then, it pertains to one science to study Being qua Being, and the attributes inherent in it qua Being; and the same science investigates, besides the concepts mentioned above, Priority and Posteriority, Genus and Species, Whole and Part, and all other such concepts.

We must pronounce whether it pertains to the same science

to study both the so-called axioms in mathematics and substance, or to different sciences. It is obvious that the investigation of these axioms too pertains to one science, namely the science of the philosopher; for they apply to all existing things, and not to a particular class separate and distinct from the rest. Moreover all thinkers employ them—because they are axioms of Being qua Being, and every genus possesses Being—

but employ them only in so far as their purposes require; i.e., so far as the genus extends about which they are carrying out their proofs. Hence since these axioms apply to all things qua Being (for this is what is common to them), it is the function of him who studies Being qua Being to investigate them as well.

For this reason no one who is pursuing a particular inquiry—neither a geometrician nor an arithmetician—attempts to state whether they are true or false; but some of the physicists did so, quite naturally; for they alone professed to investigate nature as a whole, and Being.

But inasmuch as there is a more ultimate type of thinker than the natural philosopher (for nature is only a genus of Being), the investigation of these axioms too will belong to the universal thinker who studies the primary reality.

Natural philosophy is a kind of Wisdom, but not the primary kind.

As for the attempts of some of those who discuss how the truth should be received, they are due to lack of training in logic; for they should understand these things before they approach their task, and not investigate while they are still learning.

Clearly then it is the function of the philosopher, i.e. the student of the whole of reality in its essential nature, to investigate also the principles of syllogistic reasoning. And it is proper for him who best understands each class of subject to be able to state the most certain principles of that subject; so that he who understands the modes of Being qua Being should be able to state the most certain principles of all things.

Now this person is the philosopher, and the most certain principle of all is that about which one cannot be mistaken; for such a principle must be both the most familiar (for it is about the unfamiliar that errors are always made), and not based on hypothesis.

For the principle which the student of any form of Being must grasp is no hypothesis; and that which a man must know if he knows anything he must bring with him to his task.

Clearly, then, it is a principle of this kind that is the most certain of all principles. Let us next state

this principle is.

"It is impossible for the same attribute at once to belong and not to belong

to the same thing and in the same relation"; and we must add any further qualifications that may be necessary to meet logical objections. This is the most certain of all principles, since it possesses the required definition;

for it is impossible for anyone to suppose that the same thing is and is not, as some imagine that Heraclitus says

—for what a man says does not necessarily represent what he believes.

And if it is impossible for contrary attributes to belong at the same time to the same subject (the usual qualifications must be added to this premiss also), and an opinion which contradicts another is contrary to it, then clearly it is impossible for the same man to suppose at the same time that the same thing is and is not; for the man who made this error would entertain two contrary opinions at the same time.

Hence all men who are demonstrating anything refer back to this as an ultimate belief; for it is by nature the starting-point of all the other axioms as well.

There are some, however, as we have said, who both state themselves that the same thing can be and not be,

and say that it is possible to hold this view. Many even of the physicists adopt this theory. But we have just assumed that it is impossible at once to be and not to be, and by this means we have proved that this is the most certain of all principles.

Some, indeed, demand to have the law proved, but this is because they lack education

; for it shows lack of education not to know of what we should require proof, and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity, so that even so there would be no proof.

If on the other hand there are some things of which no proof need be sought, they cannot say what principle they think to be more self-evident. Even in the case of this law, however, we can demonstrate the impossibility by refutation, if only our opponent makes some statement. If he makes none, it is absurd to seek for an argument against one who has no arguments of his own about anything, in so far as he has none; for such a person, in so far as he is such, is really no better than a vegetable.

And I say that proof by refutation differs from simple proof in that he who attempts to prove might seem to beg the fundamental question, whereas if the discussion is provoked thus by someone else, refutation and not proof will result.

The starting-point for all such discussions is not the claim that he should state that something is or is not so

(because this might be supposed to be a begging of the question), but that he should say something significant both to himself and to another (this is essential if any argument is to follow; for otherwise such a person cannot reason either with himself or with another);

and if this is granted, demonstration will be possible, for there will be something already defined. But the person responsible is not he who demonstrates but he who acquiesces; for though he disowns reason he acquiesces to reason. Moreover, he who makes such an admission as this has admitted the truth of something apart from demonstration [so that not everything will be "so and not so"].

Thus in the first place it is obvious that this at any rate is true: that the term "to be" or "not to be" has a definite meaning; so that not everything can be "so and not so." Again, if "man" has one meaning, let this be "two-footed animal."

By "has one meaning" I mean this: if X means "man," then if anything is a man, its humanity will consist in being X. And it makes no difference even if it be said that "man" has several meanings, provided that they are limited in number;

for one could assign a different name to each formula.

For instance, it might be said that "man" has not one meaning but several, one of which has the formula "two-footed animal," and there might be many other formulae as well, if they were limited in number; for a particular name could be assigned to each for formula.

If on the other hand it be said that "man" has an infinite number of meanings, obviously there can be no discourse; for not to have one meaning is to have no meaning, and if words have no meaning there is an end of discourse with others, and even, strictly speaking, with oneself; because it is impossible to think of anything if we do not think of one thing; and even if this were possible, one name might be assigned to that of which we think.

Now let this name, as we said at the beginning, have a meaning; and let it have one meaning. Now it is impossible that "being man" should have the same meaning as "not being man," that is, if "man" is not merely predicable of one subject but has one meaning

(for we do not identify "having one meaning" with "being predicable of one subject," since in this case "cultured" and "white" and "man" would have one meaning, and so all things would be one; for they would all have the same meaning). And it will be impossible for the same thing to be and not to be, except by equivocation, as e.g. one whom we call "man"

others might call "not-man";

but the problem is whether the same thing can at once be and not be "man," not in

, but in

. If "man" and "not-man" have not different meanings, clearly "not being a man" will mean nothing different from "being a man"; and so "being a man" will be "not being a man"; they will be one.

For "to be one" means, as in the case of "garment" and "coat," that the formula is one. And if "being man" and "being not-man" are to be one, they will have the same meaning; but it has been proved above that they have different meanings. If then anything can be truly said to be "man," it must be "two-footed animal"; for this is what "man" was intended to mean.

And if this is necessarily so, it is impossible that at the same time the same thing should not be "two-footed animal." For "to be necessarily so" means this: that it is impossible not to be so. Thus it cannot be true to say at the same time that the same thing is and is not man.

And the same argument holds also in the case of not being man;

because "being man" and "being not-man" have different meanings if "being white" and "being man" have different meanings (for the opposition is much stronger in the former case so as to produce different meanings).

And if we are told that "white" too means one and the same thing,

we shall say again just what we said before,

that in that case all things, and not merely the opposites, will be one. But if this is impossible, what we have stated follows; that is, if our opponent answers our question; but if when asked the simple question he includes in his answer the negations, he is not answering our question.

There is nothing to prevent the same thing from being "man" and "white" and a multitude of other things; but nevertheless when asked whether it is true to say that X is man, or not, one should return an answer that means one thing, and not add that X is white and large. It is indeed impossible to enumerate all the infinity of accidents; and so let him enumerate either all or none.

Similarly therefore, even if the same thing is ten thousand times "man" and "not-man," one should not include in one's answer to the question whether it is "man" that it is at the same time also "not-man," unless one is also bound to include in one's answer all the other accidental things that the subject is or is not.

And if one does this, he is not arguing properly.

In general those who talk like this do away with substance and essence,

for they are compelled to assert that all things are accidents, and that there is no such thing as "being essentially man" or "animal." For if there is to be such a thing as "being essentially man," this will not be "being not-man" nor "not-being man" (and yet these are negations of it); for it was intended to have one meaning, i.e. the substance of something.

But to denote a substance means that the essence is that and nothing else; and if for it "being essentially man" is the same as either "being essentially not-man" or "essentially not-being man," the essence will be something else.

Thus they are compelled to say that nothing can have such a definition as this, but that all things are accidental; for this is the distinction between substance and accident: "white" is an accident of "man," because although he is white, he is not white in essence.

And since the accidental always implies a predication about some subject, if all statements are accidental, there will be nothing primary about which they are made;

so the predication must proceed to infinity. But this is impossible, for not even more than two accidents can be combined in predication. An accident cannot be an accident of an accident unless both are accidents of the same thing.

I mean, e.g., that "white" is "cultured" and "cultured" "white" merely because both are accidents of a man. But it is not in this sense—that both terms are accidents of something else—that Socrates is cultured. Therefore since some accidents are predicated in the latter and some in the former sense, such as are predicated in the way that "white" is of Socrates cannot be an infinite series in the upper direction; e.g. there cannot be another accident of "white Socrates," for the sum of these predications does not make a single statement.

Nor can "white " have a further accident, such as "cultured"; for the former is no more an accident of the latter than vice versa; and besides we have distinguished that although some predicates are accidental in this sense, others are accidental in the sense that "cultured" is to Socrates; and whereas in the former case the accident is an accident of an accident, it is not so in the latter; and thus not all predications will be of accidents.

Therefore even so there will be something which denotes substance. And if this is so, we have proved that contradictory statements cannot be predicated at the same time.

Again, if all contradictory predications of the same subject at the same time are true, clearly all things will be one.

For if it is equally possible either to affirm or deny anything of anything, the same thing will be a trireme and a wall and a man; which is what necessarily follows for those who hold the theory of Protagoras.

For if anyone thinks that a man is not a trireme, he is clearly not a trireme; and so he also is a trireme if the contradictory statement is true.

And the result is the dictum of Anaxagoras, "all things mixed together"

; so that nothing truly exists. It seems, then, that they are speaking of the Indeterminate; and while they think that they are speaking of what exists, they are really speaking of what does not; for the Indeterminate is that which exists potentially but not actually.

But indeed they must admit the affirmation or negation of any predicate of any subject, for it is absurd that in the case of each term its own negation should be true, and the negation of some other term which is not true of it should not be true. I mean, e.g., that if it is true to say that a man is not a man, it is obviously also true to say that he is or is not a trireme.

Then if the affirmation is true, so must the negation be true; but if the affirmation is not true the negation will be even truer than the negation of the original term itself.

Therefore if the latter negation is true, the negation of "trireme" will also be true; and if this is true, the affirmation will be true too.

And not only does this follow for those who hold this theory, but also that it is not necessary either to affirm or to deny a statement.

For if it is true that X is both man and not-man, clearly he will be neither man nor not-man; for to the two statements there correspond two negations, and if the former is taken as a single statement compounded out of two, the latter is also a single statement and opposite to it.

Again, either this applies to all terms, and the same thing is both white and not-white, and existent and non-existent, and similarly with all other assertions and negations; or it does not apply to all, but only to some and not to others.

And if it does not apply to all, the exceptions will be admitted

; but if it does apply to all, again either (a) the negation will be true wherever the affirmation is true, and the affirmation will be true wherever the negation is true, or (d) the negation will be true wherever the assertion is true, but the assertion will not always be true where the negation is true.

And in the latter case there will be something which definitely is not, and this will be a certain belief; and if that it is not is certain and knowable, the opposite assertion will be still more knowable. But if what is denied can be equally truly asserted, it must be either true or false to state the predicates separately and say, e.g.,

that a thing is white, and again that it is not-white.

And if it is not-true to state them separately, our opponent does not say what he professes to say, and nothing exists; and how can that which does not exist speak or walk?

And again all things will be one, as we said before,

and the same thing will be "man" and "God" and "trireme" and the negations of these terms.

For if it is equally possible to assert or deny anything of anything, one thing will not differ from another; for if anything does differ, it will be true and unique. And similarly even if it is possible to make a true statement while separating the predicates, what we have stated follows. Moreover it follows that all statements would be true and all false; and that our opponent himself admits that what he says is false. Besides, it is obvious that discussion with him is pointless, because he makes no real statement.

For he says neither "yes" nor "no," but "yes and no"; and again he denies both of these and says "neither yes nor no"; otherwise there would be already some definite statement.

Again, if when the assertion is true the negation is false, and when the latter is true the affirmation is false, it will be impossible to assert and deny with truth the same thing at the same time.

But perhaps it will be said that this is the point at issue.

Again, is the man wrong who supposes that a thing is so or not so, and he who supposes both right? If he is right, what is the meaning of saying that "such is the nature of reality"?

And if he is not right, but is more right than the holder of the first view, reality will at once have a definite nature, and this will be true, and not at the same time not-true.

And if all men are equally right and wrong, an exponent of this view can neither speak nor mean anything, since at the same time he says both "yes" and "no." And if he forms no judgement, but "thinks" and "thinks not" indifferently, what difference will there be between him and the vegetables?

Hence it is quite evident that no one, either of those who profess this theory or of any other school, is really in this position.

Otherwise, why does a man walk to Megara and not stay at home, when he thinks he ought to make the journey? Why does he not walk early one morning into a well or ravine, if he comes to it, instead of clearly guarding against doing so, thus showing that he does

think that it is equally good and not good to fall in? Obviously then he judges that the one course is better and the other worse.

And if this is so, he must judge that one thing is man and another not man,

and that one thing is sweet and another not sweet. For when, thinking that it is desirable to drink water and see a man, he goes to look for them, he does not look for and judge all things indifferently; and yet he should, if the same thing were equally man and not-man.

But as we have said, there is no one who does not evidently avoid some things and not others. Hence, as it seems, all men form unqualified judgements, if not about all things, at least about what is better or worse.

And if they do this by guesswork and without knowledge, they should be all the more eager for truth; just as a sick man should be more eager for health than a healthy man; for indeed the man who guesses, as contrasted with him who knows, is not in a healthy relation to the truth.

Again, however much things may be "so and not so," yet differences of degree are inherent in the nature of things. For we should not say that 2 and 3 are equally even; nor are he who thinks that 4 is 5, and he who thinks it is 1000, equally wrong: hence if they are not equally wrong, the one is clearly less wrong, and so more right.

If then that which has more the nature of something is nearer to that something,

there will be some truth to which the more true is nearer. And even if there is not, still there is now something more certain and true, and we shall be freed from the undiluted doctrine which precludes any mental determination.

From the same view proceeds the theory of Protagoras, and both alike must be either true or false. For if all opinions and appearances are true, everything must be at once true and false; for many people form judgements which are opposite to those of others, and imagine that those who do not think the same as themselves are wrong: hence the same thing must both be and not be.

And if this is so, all opinions must be true; for those who are wrong and those who are right think contrarily to each other. So if reality is of this nature, everyone will be right.

Clearly then both these theories proceed from the same mental outlook. But the method of approach is not the same for all cases; for some require persuasion and others compulsion.

The ignorance of those who have formed this judgement through perplexity is easily remedied, because we are dealing

not with the theory but with their mental outlook; but those who hold the theory for its own sake can only be cured by refuting the theory as expressed in their own speech and words.

This view comes to those who are perplexed from their observation of sensible things. (1.) The belief that contradictions and contraries can be true at the same time comes to them from seeing the contraries generated from the same thing.

Then if what is not cannot be generated, the thing must have existed before as both contraries equally—just as Anaxagoras says

that everything is mixed in everything; and also Democritus, for he too says

that Void and Plenum are present equally in any part, and yet the latter

, and the former

.

To those, then, who base their judgement on these considerations, we shall say that although in one sense their theory is correct, in another they are mistaken. For "being" has two meanings, so that there is a sense in which something can be generated from "not-being," and a sense in which it cannot; and a sense in which the same thing can at once be and not be; but not in the same respect. For the same thing can "be" contraries at the same time potentially, but not actually.

And further, we shall request them to conceive another kind also of substance of existing things, in which there is absolutely no motion or destruction or generation.

And (2.) similarly the theory that there is truth in appearances has come to some people from an observation of sensible things.

They think that the truth should not be judged by the number or fewness of its upholders; and they say that the same thing seems sweet to some who taste it, and bitter to others; so that if all men were diseased or all insane, except two or three who were healthy or sane, the latter would seem to be diseased or insane, and not the others.

And further they say that many of the animals as well get from the same things impressions which are contrary to ours, and that the individual himself does not always think the same in matters of sense-perception. Thus it is uncertain which of these impressions are true or false; for one kind is no more true than another, but equally so. And hence Democritus says

that either there is no truth or we cannot discover it.

And in general it is because they suppose that thought is sense-perception, and sense-perception physical alteration, that they say that the impression given through sense-perception is necessarily true; for it is on these grounds that both Empedocles and Democritus and practically all the rest have become obsessed by such opinions as these.

For Empedocles says that those who change their bodily condition change their thought:

For according to that which is present to them doth thought increase in men.

And in another passage he says:

And as they change into a different nature, so it ever comes to them to think differently.

And Parmenides too declares in the same way:

For as each at any time hath the temperament of his many-jointed limbs, so thought comes to men. For for each and every man the substance of his limbs is that very thing which thinks; for thought is that which preponderates.

There is also recorded a saying of Anaxagoras to some of his disciples, that things would be for them as they judged them to be.

And they say that in Homer too clearly held this view, because he made Hector,

when he was stunned by the blow, lie with thoughts deranged—thus implying that even those who are "out of their minds" still think, although not the same thoughts. Clearly then, if both are kinds of thought, reality also will be "both so and not so."

It is along this path that the consequences are most difficult; for if those who have the clearest vision of such truth as is possible (and these are they who seek and love it most) hold such opinions and make these pronouncements about the truth, surely those who are trying to be philosophers may well despair; for the pursuit of truth will be "chasing birds in the air."

But the reason why these men hold this view is that although they studied the truth about reality, they supposed that reality is confined to sensible things, in which the nature of the Indeterminate, i.e. of Being in the sense which we have explained,

is abundantly present. (Thus their statements, though plausible, are not true;

this form of the criticism is more suitable than that which Epicharmus

applied to Xenophanes.) And further, observing that all this indeterminate substance is in motion, and that no true predication can be made of that which changes, they supposed that it is impossible to make any true statement about that which is in all ways and entirely changeable.

For it was from this supposition that there blossomed forth the most extreme view of those which we have mentioned, that of the professed followers of Heraclitus, and such as Cratylus held, who ended by thinking that one need not say anything, and only moved his finger; and who criticized Heraclitus for saying that one cannot enter the same river twice,

for he himself held that it cannot be done even once.

But we shall reply to this theory also that although that which is changeable supplies them, when it changes, with some real ground for supposing that it "is not," yet there is something debatable in this; for that which is shedding any quality retains something of that which is being shed, and something of that which is coming to be must already exist.

And in general if a thing is ceasing to be, there will be something there which

; and if a thing is coming to be, that from which it comes and by which it is generated must

; and this cannot go on to infinity. But let us leave this line of argument and remark that quantitative and qualitative change are not the same.

Let it be granted that there is nothing permanent in respect of quantity; but it is by the

that we recognize everything. And again those who hold the theory that we are attacking deserve censure in that they have maintained about the whole material universe what they have observed in the case of a mere minority of sensible things.

For it is only the realm of sense around us which continues subject to destruction and generation, but this is a practically negligible part of the whole; so that it would have been fairer for them to acquit the former on the ground of the latter than to condemn the latter on account of the former.

Further, we shall obviously say to these thinkers too the same as we said some time ago

; for we must prove to them and convince them that there is a kind of nature that is not moved

(and yet those who claim that things can at once be and not be are logically compelled to admit rather that all things are at rest than that they are in motion; for there is nothing for them to change into, since everything exists in everything).

And as concerning reality, that not every appearance is real, we shall say, first, that indeed the perception, at least of the proper object of a sense, is not false, but the impression we get of it is not the same as the perception.

And then we may fairly express surprise if our opponents raise the question whether magnitudes and colors are really such as they appear at a distance or close at hand, as they appear to the healthy or to the diseased; and whether heavy things are as they appear to the weak or to the strong; and whether truth is as it appears to the waking or to the sleeping.

For clearly they do not really believe the latter alternative—at any rate no one, if in the night he thinks that he is at Athens whereas he is really in Africa, starts off to the Odeum.

And again concerning the future (as indeed Plato says

) the opinion of the doctor and that of the layman are presumably not equally reliable, e.g. as to whether a man will get well or not.

And again in the case of the senses themselves, our perception of a foreign object and of an object proper to a given sense, or of a kindred object and of an actual object of that sense itself, is not equally reliable

; but in the case of colors sight, and not taste, is authoritative, and in the case of flavor taste, and not sight. But not one of the senses ever asserts at the same time of the same object that it is "so and not so."

Nor even at another time

does it make a conflicting statement about the quality, but only about that to which the quality belongs. I mean, e.g., that the same wine may seem, as the result of its own change or of that of one's body, at one time sweet and at another not; but sweetness, such as it is when it exists, has never yet changed, and there is no mistake about it, and that which is to be sweet is necessarily of such a nature.

Yet all these theories destroy the possibility of anything's existing by necessity, inasmuch as they destroy the existence of its essence; for "the necessary" cannot be in one way and in another; and so if anything exists of necessity, it cannot be "both so and not so."

And in general, if only the sensible exists, without animate things there would be nothing; for there would be no sense-faculty.

That there would be neither sensible qualities nor sensations is probably true

(for these depend upon an effect produced in the percipient), but that the substrates which cause the sensation should not exist even apart from the sensation is impossible.

For sensation is not of itself, but there is something else too besides the sensation, which must be prior to the sensation;

because that which moves is by nature prior to that which is moved, and this is no less true if the terms are correlative.

But there are some, both of those who really hold these convictions and of those who merely profess these views, who raise a difficulty; they inquire who is to judge of the healthy man, and in general who is to judge rightly in each particular case. But such questions are like wondering whether we are at any given moment asleep or awake;

and all problems of this kind amount to the same thing. These people demand a reason for everything. They want a starting-point, and want to grasp it by demonstration; while it is obvious from their actions that they have no conviction. But their case is just what we have stated before

; for they require a reason for things which have no reason, since the starting-point of a demonstration is not a matter of demonstration.

The first class, then, may be readily convinced of this, because it is not hard to grasp. But those who look only for cogency in argument look for an impossibility, for they claim the right to contradict themselves, and lose no time in doing so.

Yet if not everything is relative, but some things are self-existent, not every appearance will be true; for an appearance is an appearance to someone. And so he who says that all

appearances are true makes everything relative.

Hence those who demand something cogent in argument, and at the same time claim to make out a case, must guard themselves by saying that the appearance is true; not in itself, but

it appears, and at, the time when it appears, and in the

and

. And if they make out a case without this qualification, as a result they will soon contradict themselves;

for it is possible in the case of the same man for a thing to appear honey to the sight, but not to the taste, and for things to appear different to the sight of each of his two eyes, if their sight is unequal. For to those who assert (for the reasons previously stated

) that appearances are true, and that all things are therefore equally false and true, because they do not appear the same to all, nor always the same to the same person, but often have contrary appearances at the same time

(since if one crosses the fingers touch says that an object is two, while sight says that it is only one

), we shall say "but not to the same sense or to the same part of it in the same way and at the same time"; so that with this qualification the appearance will be true.

But perhaps it is for this reason that those who argue not from a sense of difficulty but for argument's sake are compelled to say that the appearance is not true in itself, but true to the percipient;

and, as we have said before, are compelled also to make everything relative and dependent upon opinion and sensation, so that nothing has happened or will happen unless someone has first formed an opinion about it; otherwise clearly all things would not be relative to opinion.

Further, if a thing is one, it is relative to one thing or to something determinate. And if the same thing is both a half and an equal, yet the equal is not relative to the double.

If to the thinking subject "man" and the object of thought are the same, "man" will be not the thinking subject but the object of thought; and if each thing is to be regarded as relative to the thinking subject, the thinking subject will be relative to an infinity of specifically different things.

That the most certain of all beliefs is that opposite statements are not both true at the same time, and what follows for those who maintain that they are true, and why these thinkers maintain this, may be regarded as adequately stated. And since the contradiction of a statement cannot be true at the same time of the same thing, it is obvious that contraries cannot apply at the same time to the same thing.

For in each pair of contraries one is a privation no less than it is a contrary—a privation of substance. And privation is the negation of a predicate

to some defined genus. Therefore if it is impossible at the same time to affirm and deny a thing truly, it is also impossible for contraries to apply to a thing at the same time; either both must apply in a modified sense, or one in a modified sense and the other absolutely.

Nor indeed can there be any intermediate between contrary statements, but of one thing we must either assert or deny one thing, whatever it may be. This will be plain if we first define truth and falsehood. To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false.

But neither what is nor what is not is said not to be

to be. Further, an intermediate between contraries will be intermediate either as grey is between black and white, or as "neither man nor horse" is between man and horse. If in the latter sense, it cannot change (for change is from not-good to good, or from good to not-good);

but in fact it is clearly always changing; for change can only be into the opposite and the intermediate. And if it is a true intermediate, in this case too there would be a kind of change into white not from not-white; but in fact this is not seen.

Further, the understanding either affirms or denies every object of understanding or thought (as is clear from the definition

)

whenever it is right or wrong. When, in asserting or denying, it combines the predicates in one way, it is right; when in the other, it is wrong.

Again, unless it is maintained merely for argument's sake, the intermediate must exist beside all contrary terms; so that one will say what is neither true nor false. And it will exist beside what is and what is not; so that there will be a form of change beside generation and destruction.

Again, there will also be an intermediate in all classes in which the negation of a term implies the contrary assertion; e.g., among numbers there will be a number which is neither odd nor not-odd. But this is impossible, as is clear from the definition.

Again, there will be an infinite progression, and existing things will be not only half as many again, but even more.

For again it will be possible to deny the intermediate in reference both to its assertion and to its negation, and the result will be something

; for its essence is something distinct.

Again, when a man is asked whether a thing is white and says "no," he has denied nothing except that it is , and its not-being is a negation.

Now this view has occurred to certain people in just the same way as other paradoxes have also occurred; for when they cannot find a way out from eristic arguments, they submit to the argument and admit that the conclusion is true.

Some, then, hold the theory for this kind of reason, and others because they require an explanation for everything. In dealing with all such persons the starting-point is from definition;

and definition results from the necessity of their meaning something; because the formula, which their term implies, will be a definition.

The doctrine of Heraclitus, which says that everything is and is not,

seems to make all things true; and that of Anaxagoras

seems to imply an intermediate in contradiction, so that all things are false; for when things are mixed, the mixture is neither good nor not-good; and so no statement is true.

It is obvious from this analysis that the one-sided and sweeping statements which some people make cannot be substantially true—some maintaining that nothing is true (for they say that there is no reason why the same rule should not apply to everything as applies to the commensurability of the diagonal of a square

), and some that everything is true.

These theories are almost the same as that of Heraclitus. For the theory which says that all things are true and all false also makes each of these statements separately;

so that if they are impossible in combination they are also impossible individually. And again obviously there are contrary statements, which cannot be true at the same time. Nor can they all be false, although from what we have said, this might seem more possible.

But in opposing all such theories we must demand, as was said in our discussion above,

not that something should be or not be, but some significant statement; and so we must argue from a definition, having first grasped what "falsehood" or "truth" means. And if to assert what is true is nothing else than to deny what is false, everything cannot be false; for one part of the contradiction must be true.

Further, if everything must be either asserted or denied, both parts cannot be false; for one and only one part of the contradiction is false. Indeed, the consequence follows which is notorious in the case of all such theories, that they destroy themselves;

for he who says that everything is true makes the opposite theory true too, and therefore his own untrue (for the opposite theory says that his is not true); and he who says that everything is false makes himself a liar.

And if they make exceptions, the one that the opposite theory alone is not true, and the other that his own theory alone is not false,

it follows none the less that they postulate an infinite number of true and false statements. For the statement that the true statement is true is also true; and this will go on to infinity.

Nor, as is obvious, are those right who say that all things are at rest; nor those who say that all things are in motion. For if all things are at rest, the same things will always be true and false, whereas this state of affairs is obviously subject to change; for the speaker himself once did not exist, and again he will not exist. And if all things are in motion, nothing will be true, so everything will be false; but this has been proved to be impossible.

Again, it must be that which

that changes, for change is from something into something. And further, neither is it true that all things are at rest or in motion sometimes, but nothing continuously; for there is something

which always moves that which is moved, and the "prime mover" is itself unmoved.

"Beginning"

means: (a) That part of a thing from which one may first move; eg., a line or a journey has one beginning

, 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

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

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

and

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

and the other as the

. 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

, and the other as

of

.

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

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

sense. Of these some are causes as substrate: e.g. the parts; and others as

: 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

and

of the others; for the final cause tends to be the greatest good and

of the rest.

Let it be assumed that it makes no difference whether we call it "good" or "apparent good." In

, then, there are these four classes of cause.

The

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

and

, some are termed causes in a

and others in an

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

of the causes; e.g. to

statue, or

statue, or generally an image; and to

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.

man giving medical treatment with

man recovering his health, and

builder with

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

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

of

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

, 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

in the substance, and the other as

or

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

. 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

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 . 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

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

; 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,

.)

These, then, are the senses in which things are said to "be" accidentally: either because both predicates belong to the same subject, which

; or because the predicate belongs to the subject, which

; or because the subject to which belongs that of which it is itself predicated itself

.

(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" 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

"a seeing thing." And in the same way we call "understanding" both that which

use the understanding, and that which

; 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

, 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

. 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

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

are different from the prior in

. 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

something, and sometimes because it is

of something; but if privation is in a sense a state or "habit," everything will be "potent" through

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

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

. 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

or

;

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" 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

which motion and action proceed, and not the end

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

, and in the secondary sense, as it were, the

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

, "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

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

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 (

-). 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" 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 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" , 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

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" is used: (a) When there is a continuous generation of things of the same type; e.g., "as long as the human

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

; (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

, 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

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

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" 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.

It is the principles and causes of the

that we are seeking; and clearly of the things which are qua being. There is a cause of health and physical fitness; and mathematics has principles and elements and causes; and in general every intellectual science or science which involves intellect deals with causes and principles, more or less exactly or simply considered.

But all these sciences single out some existent thing or class, and concern themselves with that; not with Being unqualified, nor qua Being, nor do they give any account of the essence; but starting from it, some making it clear to perception, and others assuming it as a hypothesis, they demonstrate, more or less cogently, the essential attributes of the class with which they are dealing.

Hence obviously there is no demonstration of substance or essence from this method of approach, but some other means of exhibiting it. And similarly they say nothing as to whether the class of objects with which they are concerned exists or not; because the demonstration of its essence and that of its existence belong to the same intellectual process.

And since physical science also happens to deal with a genus of Being

(for it deals with the sort of substance which contains in itself the principle of motion and rest), obviously it is neither a practical nor a productive science.

For in the case of things produced the principle of motion (either mind or art or some kind of potency) is in the producer; and in the case of things done the will is the agent—for the thing done and the thing willed are the same. Thus if every intellectual activity is either practical or productive or speculative, physics will be a speculative science; but speculative about that kind of Being which can be moved, and about formulated substance for the most part only qua inseparable from matter.

But we must not fail to observe

the essence and the formula exist, since without this our inquiry is ineffectual.

Now of things defined, i.e. of essences, some apply in the sense that "snub" does, and some in the sense that "concave" does. The difference is that "snub" is a combination of form with matter; because the "snub" is a concave

, whereas concavity is independent of sensible matter.

Now if all physical terms are used in the same sense as "snub"—e.g. nose, eye, face, flesh, bone, and in general animal; leaf, root, bark, and in general vegetable (for not one of these has a definition without motion; the definition invariably includes matter)—it is clear how we should look for and define the essence in physical things, and why it is the province of the physicist to study even some aspects of the soul, so far as it is not independent of matter.

It is obvious, then, from these considerations, that physics is a form of speculative science. And mathematics is also speculative; but it is not clear at present whether its objects are immutable and separable from matter; it is clear, however, that some branches of mathematics study their objects qua immutable and qua separable from matter. Obviously it is the province of a speculative science to discover whether a thing is eternal and immutable and separable from matter;

not, however, of physics (since physics deals with mutable objects) nor of mathematics, but of a science prior to both. For physics deals with things which exist separately but are not immutable; and some branches of mathematics deal with things which are immutable, but presumably not separable, but present in matter; but the primary science treats of things which are both separable and immutable.

Now all causes must be eternal, but these especially; since they are the causes of what is visible of things divine. Hence there will be three speculative philosophies: mathematics, physics, and theology—

since it is obvious that if the divine is present anywhere, it is present in this kind of entity; and also the most honorable science must deal with the most honorable class of subject.

The speculative sciences, then, are to be preferred to the other sciences, and "theology" to the other speculative sciences. One might indeed raise the question whether the primary philosophy is universal or deals with some one genus or entity; because even the mathematical sciences differ in this respect—geometry and astronomy deal with a particular kind of entity, whereas universal mathematics applies to all kinds alike.

Then if there is not some other substance besides those which are naturally composed, physics will be the primary science; but if there is a substance which is immutable, the science which studies this will be prior to physics, and will be primary philosophy, and universal in this sense, that it is primary. And it will be the province of this science to study Being qua Being; what it is, and what the attributes are which belong to it qua Being.

But since the simple term "being" is used in various senses, of which we saw that one was

, and another

(not-being being used in the sense of "false"); and since besides these there are the categories, e.g. the "what," quality, quantity, place, time, and any other similar meanings;

and further besides all these the

and

: since the term "being" has various senses, it must first be said of what "is" accidentally, that there can be no speculation about it.

This is shown by the fact that no science, whether practical, productive or speculative, concerns itself with it. The man who produces a house does not produce all the attributes which are accidental to the house in its construction; for they are infinite in number. There is no reason why the house so produced should not be agreeable to some, injurious to others, and beneficial to others, and different perhaps from every other existing thing; but the act of building is productive of none of these results.

In the same way the geometrician does not study the accidental attributes of his figures, nor whether a triangle is different from a triangle the sum of whose angles is equal to two right angles. And this accords with what we should reasonably expect, because "accident" is only, as it were, a sort of name. Hence in a way Plato

was not far wrong in making sophistry deal with what is nonexistent;

because the sophists discuss the accident more, perhaps, than any other people—whether "cultured" and "grammatical,"

and "cultured Coriscus" and "Coriscus,"

are the same or different; and whether everything that is, but has not always been, has come into being, so that if a man who is cultured has become grammatical,

he has also, being grammatical, become cultured

; and all other such discussions. Indeed it seems that the accidental is something closely akin to the nonexistent.

This is clear too from such considerations as the following: of things which

in other senses there is generation and destruction, but of things which

accidentally there is not.

Nevertheless we must state further, so far as it is possible, with regard to the accidental, what its nature is and through what cause it exists. At the same time it will doubtless also appear why there is no science of it.

Since, then, there are among existing things some which are invariable and of necessity (not necessity in the sense of compulsion,

but that by which we mean that it cannot be otherwise

), and some which are not necessarily so, nor always, but usually: this is the principle and this the cause of the accidental. For whatever is neither always nor usually so, we call an accident.

E.g., if in the dog-days

we have storm and cold, we call it an accident; but not if we have stifling and intense heat, because the latter always or usually comes at this time, but not the former. It is accidental for a man to be white (since this is neither always nor usually so), but it is not accidental for him to be an animal.

It is by accident that a builder restores to health, because it is not a builder but a doctor who naturally does this; but the builder happened accidentally to be a doctor. A confectioner, aiming at producing enjoyment, may produce something health-giving; but not in virtue of his confectioner's art. Hence, we say, it was accidental; and he produces it in a sense, but not in an unqualified sense.

For there are potencies which produce other things, but there is no art or determinate potency of accidents, since the cause of things which exist or come to be by accident is also accidental.

Hence, since not everything is or comes to be of necessity and always, but most things happen usually, the accidental must exist. E.g., the white man is neither always nor usually cultured; but since this sometimes happens, it must be regarded as accidental. Otherwise, everything must be regarded as of necessity.

Therefore the cause of the accidental is the matter, which admits of variation from the usual.

We must take this as our starting-point: Is everything either "always" or "usually"? This is surely impossible. Then besides these alternatives there is something else: the fortuitous and accidental. But again, are things

so, but nothing

, or are there things which are eternal? These questions must be inquired into later

;

but it is clear that there is no science of the accidental—because all scientific knowledge is of that which is

or

so. How else indeed can one learn it or teach it to another? For a fact must be defined by being so always or usually; e.g., honey-water is usually beneficial in case of fever.

But science will not be able to state the exception to the rule: when it is not beneficial—e.g. at the new moon; because that which happens at the new moon also happens either always or usually; but the accidental is contrary to this. We have now explained the nature and cause of the accidental, and that there is no science of it.

It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destruction

; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will A be, or not? Yes, if B happens; otherwise not. And B will happen if C does.

It is clear that in this way, as time is continually subtracted from a limited period, we shall come to the present.

Accordingly So-and-so will die by disease or violence if he goes out; and this if he gets thirsty; and this if something else happens; and thus we shall come to what is the case now, or to something which has already happened. E.g. "if he is thirsty"; this will happen if he is eating pungent food, and this is either the case or not.

Thus of necessity he will either die or not die. And similarly if one jumps over to the past, the principle is the same; for this—I mean that which has just happened—is already present in something. Everything, then, which is to be, will be of necessity; e.g., he who is alive must die—for some stage of the process has been reached already; e.g., the contraries are present in the same body—but whether by disease or violence is not yet determined; it depends upon whether so-and-so happens.

Clearly, then, the series goes back to some starting-point, which does not go back to something else. This, therefore, will be the starting-point of the fortuitous, and nothing else is the cause of its generation. But to what sort of starting-point and cause this process of tracing back leads, whether to a material or final or moving cause, is a question for careful consideration.

So much, then, for the accidental sense of "being"; we have defined it sufficiently. As for "being" qua truth, and "not-being" qua falsity, since they depend upon combination and separation,

and taken together are concerned with the arrangement of the parts of a contradiction (since the true has affirmation when the subject and predicate are combined, and negation where they are divided; but the false has the contrary arrangement.

How it happens that we combine or separate in thought is another question. By "combining or separating in thought" I mean thinking them not as a succession but as a unity

); for "falsity" and "truth" are not in

—the good, for example, being true, and the bad false—but in

; and with regard to simple concepts and essences there is no truth or falsity even in thought;

—what points we must study in connection with being and not-being in this sense, we must consider later. But since the combination and separation exists in thought and not in things, and this sense of "being" is different from the proper senses (since thought attaches or detaches essence or quality or quantity or some other category), we may dismiss the accidental and real senses

of "being."

For the cause of the one is indeterminate and of the other an affection of thought;

and both are connected with the remaining genus of "being," and do not indicate any objective reality. Let us therefore dismiss them, and consider the causes and principles of Being itself qua Being. [We have made it clear in our distinction of the number of senses in which each term is used that "being" has several senses.]

The term "being" has several senses, which we have classified in our discussion

of the number of senses in which terms are used. It denotes first the "

" of a thing, i.e. the individuality; and then the quality or quantity or any other such category. Now of all these senses which "being" has, the primary sense is clearly the "what," which denotes the

(because when we describe the quality of a particular thing we say that it is "good or bad," and not "five feet high" or "a man"; but when we describe

it is, we say not that it is "white" or "hot" or "five feet high," but that it is "a man" or "a god"), and all other things are said to "be" because they are either quantities or qualities or affections or some other such thing.

Hence one might raise the question whether the terms "to walk" and "to be well" and "to sit" signify each of these things as "being," or not; and similarly in the case of any other such terms; for not one of them by nature has an independent existence or can be separated from its substance. Rather, if anything it is the

which walks or sits or is well that is existent.

The reason why these things are more truly existent is because their subject is something definite; i.e. the substance and the individual, which is clearly implied in a designation of this kind, since apart from it we cannot speak of "the good" or "sitting." Clearly then it is by reason of the substance that each of the things referred to exists.

Hence that which

primarily, not in a qualified sense but absolutely, will be substance.

Now "primary" has several meanings; but nevertheless substance is primary in all senses, both in definition and in knowledge and in time. For none of the other categories can exist separately, but substance alone;

and it is primary also in definition, because in the formula of each thing the formula of substance must be inherent; and we assume that we know each particular thing most truly when we know

"man" or "fire" is—

rather than its quality or quantity or position; because we know each of these points too when we know

the quantity or quality is.

Indeed, the question which was raised long ago, is still and always will be, and which always baffles us—"What is Being?"—is in other words "What is substance?" Some say that it is one

; others, more than one; some, finite

; others, infinite.

And so for us too our chief and primary and practically our only concern is to investigate the nature of "being" in the sense of substance.

Substance is thought to be present most obviously in bodies. Hence we call animals and plants and their parts substances, and also natural bodies, such as fire, water, earth, etc., and all things which are parts of these or composed of these, either of parts or them or of their totality; e.g. the visible universe and its parts, the stars and moon and sun.

We must consider whether (a) these are the only substances, or (b) these and some others, or (c) some of these, or (d) some of these and some others, or (e) none of these, but certain others. Some

hold that the bounds of body—i.e. the surface, line, point and unit—are substances, and in a truer sense than body or the solid.

Again, some

believe that there is nothing of this kind besides sensible things, while others believe in eternal entities more numerous and more real than sensible things.

Thus Plato posited the Forms and the objects of mathematics as two kinds of substance, and as a third the substance of sensible bodies;

and Speusippus

assumed still more kinds of substances, starting with "the One," and positing principles for each kind: one for numbers, another for magnitudes, and then another for the soul. In this way he multiplies the kinds of substance. Some

again hold that the Forms and numbers have the same nature, and that other things—lines and planes—are dependent upon them; and soon back to the substance of the visible universe and sensible things.

We must consider, then, with regard to these matters, which of the views expressed is right and which wrong; and what things are substances; and whether there are any substances besides the sensible substances, or not; and how sensible substances exist; and whether there is any separable substance (and if so, why and how) or no substance besides the sensible ones. We must first give a rough sketch of what substance is.

The term "substance" is used, if not in more, at least in four principal cases; for both the essence and the universal and the genus are held to be the substance of the particular, and fourthly the substrate. The substrate is that of which the rest are predicated, while it is not itself predicated of anything else. Hence we must first determine its nature,

for the primary substrate is considered to be in the truest sense substance.

Now in one sense we call the

the substrate; in another, the

; and in a third, the combination of the two. By matter I mean, for instance, bronze; by shape, the arrangement of the form; and by the combination of the two, the concrete thing: the statue. Thus if the form is prior to the matter and more truly existent, by the same argument it will also be prior to the combination.

We have now stated in outline the nature of substance—that it is not that which is predicated of a subject, but that of which the other things are predicated. But we must not merely define it so, for it is not enough. Not only is the statement itself obscure, but also it makes matter substance; for if matter is not substance, it is beyond our power to say what else is.

For when everything else is removed, clearly nothing but matter remains; because all the other things are affections, products and potencies of bodies, and length, breadth and depth are kinds of quantity, and not substances. For quantity is not a substance; rather the substance is that to which these affections primarily belong.

But when we take away length and breadth and depth we can see no thing remaining, unless it be the something bounded by them; so that on this view matter must appear to be the only substance.

By matter I mean that which in itself is neither a particular thing nor a quantity nor designated by any of the categories which define Being.

For there is something of which each of these is predicated, whose being is different from that of each one of the categories; because all other things are predicated of substance, but this is predicated of matter. Thus the ultimate substrate is in itself neither a particular thing nor a quantity nor anything else. Nor indeed is it the negations of these; for the negations too will only apply to it accidentally.

If we hold this view, it follows that matter is substance. But this is impossible; for it is accepted that separability and individuality belong especially to substance. Hence it would seem that the form and the combination of form and matter are more truly substance than matter is.

The substance, then, which consists of both—I mean of matter and form—may be dismissed, since it is posterior and obvious. Matter too is in a sense evident. We must consider the third type, for this is the most perplexing.

Now it is agreed that some sensible things are substances, and so we should begin our inquiry in connection with these.

It is convenient to advance to the more intelligible

; for learning is always acquired in this way, by advancing through what is less intelligible by nature to what is more so. And just as in actions it is our task to start from the good of the individual and make absolute good good for the individual,

so it is our task to start from what is more intelligible to oneself and make what is by nature intelligible intelligible to oneself.

Now that which is intelligible and primary to individuals is often but slightly intelligible, and contains but little reality; but nevertheless, starting from that which is imperfectly intelligible but intelligible to oneself, we must try to understand the absolutely intelligible; advancing, as we have said, by means of these very things which are intelligible to us.

Since we distinguished at the beginning

the number of ways in which substance is defined, and since one of these appeared to be essence, we must investigate this.

First, let us make certain linguistic statements about it.

The essence of each thing is that which it is said to be per se. "To be you" is not "to be cultured," because you are not of your own nature cultured. Your essence, then, is that which you are said to be

of your own nature. But not even all of this is the essence; for the essence is not that which is said to be per se in the sense that whiteness is said to belong to a surface,

because "being a surface" is not "being white."

Nor is the essence the combination of both, "being a white surface." Why? Because the word itself is repeated.

Hence the formula of the essence of each thing is that which defines the term but does not contain it. Thus if "being a white surface" is the same as "being a smooth surface," "white" and "smooth" are one and the same.

But since in the other categories too there are compounds with substance (because there is a substrate for each category, e.g. quality, quantity, time, place and motion), we must inquire whether there is a formula of the essence of each one of them; whether these compounds, e.g. "white man," also have an essence. Let the compound be denoted by X.

What is the essence of X?

"But this is not even a per se expression." We reply that there are two ways in which a definition can be not per se true of its subject: (a) by an addition, and (b) by an omission.

In one case the definition is not per se true because the term which is being defined is combined with something else; as if, e.g., in defining whiteness one were to state the definition of a white man. In the other, because something else (which is not in the definition) is combined with the subject; as if, e.g., X were to denote "white man," and X were defined as "white." "White man" is white,

but its essence is not "to be white." But is "to be X" an essence at all?

Surely not. The essence is an individual type; but when a subject has something distinct from it predicated of it, it is not an individual type. E.g., "white man" is not an individual type; that is, assuming that individuality belongs only to substances. Hence essence belongs to all things the account of which is a definition.

We have a definition, not if the name and the account signify the same (for then all accounts would be definitions; because any account can have a name, so that even "the

" will be a definition), but if the account is of something primary. Such are all statements which do not involve the predication of one thing of another.

Hence essence will belong to nothing except species of a genus, but to these only; for in these the predicate is not considered to be related to the subject by participation or affection, nor as an accident. But of everything else as well, if it has a name, there will be a formula of

—that X belongs to Y; or instead of a simple formula one more exact—but no definition, nor essence.

Or perhaps "definition," like the "what," has more than one sense. For the "what" in one sense means the substance and the individual,

and in another each one of the categories: quantity, quality, etc.

Just as "is" applies to everything, although not in the same way, but primarily to one thing and secondarily to others; so "what it is" applies in an unqualified sense to substance, and to other things in a qualified sense. For we might ask also what quality "is," so that quality also is a "what it is"; not however without qualification, but just as in the case of not-being some say by a verbal quibble that not-being "is"—not in an unqualified sense, but "is" not-being—so too with quality.

Now although we must also consider how we should express ourselves in each particular case, it is still more important to consider what the facts are. Hence now, since the language which we are using is clear, similarly essence also will belong primarily and simply to substance, and secondarily to other things as well; just as the "what it is" is not essence simply, but the essence of a quality or quantity.

For it must be either by equivocation that we say that these things

, or by adding and subtracting qualifications, as we say that the unknowable is known

; since the truth is that we use the terms neither equivocally nor in the same sense, but just as we use the term "medical" in

to one and the same thing;

but not

one and the same thing, nor yet equivocally. The term "medical" is applied to a body and a function and an instrument, neither equivocally nor in one sense, hut in relation to one thing.

However, in whichever way one chooses to speak of these things, it matters nothing; but this point is clear: that the primary and unqualified definition, and the essence, belong to substances. It is true that they belong equally to other things too, but not

. For if we assume this, it does not necessarily follow that there is a definition of anything which means the same as any formula; it must mean the same as a particular kind of formula, i.e. the formula of one thing—

one not by continuity like the Iliad, or things which are arbitrarily combined, but in one of the proper senses of "one." And "one" has the same variety of senses as "being." "Being" means sometimes the individual thing, sometimes the quantity, sometimes the quality. Hence even "white man" will have a formula and definition; but in a different sense from the definition of "whiteness" and "substance."

The question arises: If one denies that a formula involving an added determinant is a definition, how can there be a definition of terms which are not simple but coupled? Because they can only be explained by adding a determinant.

I mean, e.g., there is "nose" and "concavity" and "snubness," the term compounded of the two, because the one is present in the other. Neither "concavity" nor "snubness" is an accidental, but a per se affection of the nose.

Nor are they attributes in the sense that "white" is of Callias or a man, because Callias is white and is by accident a man; but in the sense that "male" is an attribute of animal, and equality of quantity, and all other attributes which we say belong per se.

That is, all things which involve the formula or name of the subject of the affection, and cannot be explained apart from it. Thus "white" can be explained apart from "man," but not "female" apart from "animal." Thus either these terms have no essence or definition, or else they have it in a different sense, as we have said.

But there is also another difficulty about them. If "snub nose" is the same as "concave nose," "snub" will be the same as "concave." But if not, since it is impossible to speak of "snub" apart from the thing of which it is a per se affection (because "snub" means a concavity in the nose), either it is impossible to call the nose snub, or it will be a tautology, "concave-nose nose" because "snub nose" will equal "concave-nose nose."

Hence it is absurd that such terms as these should have an essence. Otherwise there will be an infinite regression; for in "snub-nose nose" there will be yet another nose.

Clearly, then, there is definition of substance alone. If there were definition of the other categories also, it would have to involve an added determinant, as in the case of the qualitative; and of the odd, for this cannot be defined apart from number; nor can "female" apart from "animal."

By "involving an added determinant" I mean descriptions which involve a tautology, as in the above examples. Now if this is true, there will be no definition of compound expressions either; e.g., "odd number." We fail to realize this because our terms are not used accurately. If on the other hand there are definitions of these too, either they are defined in a different way, or, as we have said, "definition" and "essence" must be used in more than one sense;

thus in one sense there will be no definition of anything, and nothing will have an essence, except substances; and in another those other things will have a definition and essence. It is obvious, then, that the definition is the formula of the essence, and that the essence belongs either

to substances, or especially and primarily and simply.

We must inquire whether the essence is the same as the particular thing, or different. This is useful for our inquiry about substance; because a particular thing is considered to be nothing other than its own substance, and the essence is called the substance of the thing.

In accidental predications, indeed, the thing itself would seem to be different from its essence;

e.g., "white man" is different from "essence of white man." If it were the same, "essence of man" and "essence of white man" would be the same. For "man" and "white man" are the same, they say, and therefore "essence of white man" is the same as "essence of man."

But perhaps it is not necessarily true that the essence of accidental combinations is the same as that of the simple terms; because the extremes of the syllogism are not identical with the middle term in the same way.

Perhaps it might be thought to follow that the accidental extremes are identical; e.g. "essence of white" and "essence of cultured"; but this is not admitted.

But in per se expressions, is the thing necessarily the same as its essence, e.g., if there are substances which have no other substances or entities prior to them, such as some hold the Ideas to be?

For if the Ideal Good is to be different from the essence of good, and the Ideal Animal and Being from the essence of animal and being,

there will be other substances and entities and Ideas besides the ones which they describe; and prior to them, if essence is substance. And if they are separate from each other, there will be no knowledge of the Ideas, and the essences will not exist

(by "being separate" I mean if neither the essence of good is present in the Ideal Good, nor "being good" in the essence of good); for it is when we know the essence of it that we have knowledge of a thing. And it is the same with other essences as with the essence of good; so that if the essence of good is not good, neither will the essence of being "be," nor the essence of one be one.

Either all essences exist alike, or none of them; and so if not even the essence of being "is," neither will any other essence exist. Again that to which "essentially good" does not apply cannot be good. Hence "the good" must be one with the essence of good, "the beautiful" with the essence of beauty, and so with all terms which are not dependent upon something else, but self-subsistent and primary.

For it is enough if this is so, even if they are not Forms; or perhaps rather even if they are. (At the same time it is clear also that if the Ideas are such as some hold, the substrate will not be substance; for the Ideas must be substances, but not involving a substrate, because if they did involve one they would exist in virtue of its participation in them.)

That each individual thing is one and the same with its essence, and not merely accidentally so,

is apparent, not only from the foregoing considerations, but because to have knowledge of the individual is to have knowledge of its essence; so that by setting out examples it is evident that both must be identical.

But as for the accidental term, e.g. "cultured" or "white," since it has two meanings, it is not true to say that the term itself is the same as its essence; for both the accidental term and that of which it is an accident are "white," so that in one sense the essence and the term itself are the same, and in another they are not, because the essence is not the same as "the man" or "the white man," but it is the same as the affection.

The absurdity will be apparent also if one supplies a name for each essence; for then there will be another essence besides the original one, e.g. the essence of "horse" will have a further essence. Yet why should not some things be identified with their essence from the outset,

if essence is substance? Indeed not only are the thing and its essence one, but their formula is the same,

as is clear from what we have just stated; for it is not by accident that the essence of "one," and "the one," are one.

Moreover, if they are different, there will be an infinite series; for the essence of "one" and "the one" will both exist; so that in that case too the same principle will apply.

Clearly, then, in the case of primary and self-subsistent terms, the individual thing and its essence are one and the same.

It is obvious that the sophistical objections to this thesis are met in the same way as the question whether Socrates is the same as the essence of Socrates; for there is no difference either in the grounds for asking the question or in the means of meeting it successfully. We have now explained in what sense the essence is, and in what sense it is not, the same as the individual thing.

Of things which are generated, some are generated naturally, others artificially, and others spontaneously; but everything which is generated is generated by something and from something and becomes something. When I say "becomes something" I mean in any of the categories; it may come to be either a particular thing or of some quantity or quality or in some place.

Natural generation is the generation of things whose generation is by nature.

That from which they are generated is what we call matter; that by which, is something which exists naturally; and that which they become is a man or a plant or something else of this kind, which we call substance in the highest degree.

All things which are generated naturally or artificially have matter; for it is possible for each one of them both to be and not to be, and this possibility is the matter in each individual thing.

And in general both that from which and that in accordance with which they are generated, is nature; for the thing generated, e.g. plant or animal, has a nature. And that by which they are generated is the so-called "formal" nature, which has the same form as the thing generated (although it is in something else); for man begets man.

Such is the generation of things which are naturally generated; the other kinds of generation are called productions. All productions proceed from either art or potency or thought.

Some of them are also generated spontaneously and by chance in much the same way as things which are naturally generated; for sometimes even in the sphere of nature the same things are generated both from seed and without it.

We shall consider cases of this kind later.

Things are generated artificially whose form is contained in the soul (by "form" I mean the essence of each thing, and its primary substance);

for even contraries have in a sense the same form.

For the substance of the privation is the opposite substance; e.g., health is the substance of disease; for disease is the absence of health, and health is the formula and knowledge in the soul. Now the healthy subject is produced as the result of this reasoning: since health is so-and-so, if the subject is to be healthy, it must have such-and-such a quality, e.g. homogeneity; and if so, it must have heat.

And the physician continues reasoning until he arrives at what he himself finally can do; then the process from this point onwards, i.e. the process towards health, is called "production." Therefore it follows in a sense that health comes from health and a house from a house; that which has matter from that which has not (for the art of medicine or of building is the

of health or the house). By substance without matter I mean the essence.

In generations and motions part of the process is called cogitation, and part production—that which proceeds from the starting-point and the form is cogitation, and that which proceeds from the conclusion of the cogitation is production. Each of the other intermediate measures is carried out in the same way. I mean, e.g., that if A is to be healthy, his physical condition will have to be made uniform. What, then, does being made uniform entail? So-and-so;

and this will be achieved if he is made hot. What does this entail? So-and-so; now this is potentially present, and the thing is now in his power.

The thing which produces, and from which the process of recovering health begins, is the form in the soul, if the process is artificial; if spontaneous, it is whatever is the starting-point of the production for the artificial producer; as in medical treatment the starting-point is, perhaps, the heating of the patient; and this the doctor produces by friction. Heat in the body, then, is either a part of health, or is followed (directly or through several intermediaries) by something similar which is a part of health. This is the ultimate thing, namely that produces, and in this sense is a part of, health—or of the house

(in the form of stones)

or of other things. Therefore, as we say, generation would be impossible if nothing were already existent. It is clear, then, that some part must necessarily pre-exist; because the matter is a part, since it is matter which pre-exists in the product and becomes something.

But then is matter part of the formula? Well, we define bronze circles in both ways; we describe the matter as bronze, and the form as such-and-such a shape; and this shape is the proximate genus in which the circle is placed.

The bronze circle, then, has its matter in its formula. Now as for that from which, as matter, things are generated, some things when they are generated are called not "so-and-so," but "made of so-and-so"; e.g., a statue is not called stone, but made of stone. But the man who becomes healthy is not called after that from which he becomes healthy. This is because the generation proceeds from the privation and the substrate, which we call matter (e.g., both "the man" and "the invalid" become healthy),

but it is more properly said to proceed from the privation; e.g., a man becomes healthy from being an invalid rather than from being a man. Hence a healthy person is not called an invalid, but a man, and a healthy man. But where the privation is obscure and has no name—e.g. in bronze the privation of any given shape, or in bricks and wood the privation of the shape of a house—the generation is considered to proceed from these materials, as in the former case from the invalid.

Hence just as in the former case the subject is not called that from which it is generated, so in this case the statue is not called wood, but is called by a verbal change not wood, but wooden; not bronze, but made of bronze; not stone, but made of stone; and the house is called not bricks, but made of bricks.

For if we consider the matter carefully, we should not even say without qualification that a statue is generated from wood, or a house from bricks; because that from which a thing is generated should not persist, but be changed. This, then, is why we speak in this way.

Now since that which is generated is generated

something (by which I mean the starting-point of the process of generation), and

something (by which let us understand not the privation but the matter; for we have already distinguished the meanings of these), and

something (i.e. a sphere or circle or whatever else it may be); just as the craftsman does not produce the substrate, i.e. the bronze, so neither does he produce the sphere; except accidentally, inasmuch as the bronze sphere is a sphere, and he makes the former.

For to make an individual thing is to make it out of the substrate in the fullest sense. I mean that to make the bronze round is not to make the round or the sphere, but something else; i.e. to produce this form in another medium. For if we make the form, we must make it out of something else; for this has been assumed.

E.g., we make a bronze sphere; we do this in the sense that from A, i.e. bronze, we make B, i.e. a sphere.

If, then, we make the spherical form itself, clearly we shall have to make it in the same way; and the processes of generation will continue to infinity.

It is therefore obvious that the form (or whatever we should call the shape in the sensible thing) is not generated—generation does not apply to it— nor is the essence generated; for this is that which is induced in something else either by art or by nature or by potency.

But we do cause a bronze sphere to be, for we produce it from bronze and a sphere; we induce the form into this particular matter, and the result is a bronze sphere. But if the essence of sphere in general is generated, something must be generated from something; for that which is generated will always have to be divisible, and be partly one thing and partly another; I mean partly matter and partly form.

If then a sphere is the figure whose circumference is everywhere equidistant from the center, part of this will be the medium in which that which we produce will be contained, and part will be in that medium; and the whole will be the thing generated, as in the case of the bronze sphere. It is obvious, then, from what we have said, that the thing in the sense of form or essence is not generated, whereas the concrete whole which is called after it is generated; and that in everything that is generated matter is present, and one part is matter and the other form.

Is there then some sphere besides the particular spheres, or some house besides the bricks? Surely no individual thing would ever have been generated if form had existed thus independently.

Form means "of such a kind"; it is not a definite individual, but we produce or generate from the individual something "of such a kind"; and when it is generated it is an individual "of such a kind."

The whole individual, Callias or Socrates, corresponds to "this bronze sphere," but "man" and "animal" correspond to bronze sphere in general.

Obviously therefore the cause which consists of the Forms (in the sense in which some speak of them, assuming that there are certain entities besides particulars), in respect at least of generation and destruction, is useless; nor, for this reason at any rate, should they be regarded as self-subsistent substances.

Indeed in some cases it is even obvious that that which generates is of the same kind as that which is generated—not however identical with it, nor numerically one with it, but formally one—e.g. in natural productions (for man begets man), unless something happens contrary to nature, as when a horse sires a mule. And even these cases are similar; for that which would be common to both horse and ass, the genus immediately above them, has no name; but it would probably be both, just as the mule is both.

Thus obviously there is no need to set up a form as a pattern (for we should have looked for Forms in these cases especially, since living things are in a special sense substances); the thing which generates is sufficient to produce, and to be the cause of the form in the matter. The completed whole, such-and-such a form induced in this flesh and these bones, is Callias or Socrates. And it is different from that which generated it, because the matter is different but identical in form, because the form is indivisible.

The question might be raised why some things are generated both artificially and spontaneously—e.g. health—and others not; e.g. a house. The reason is that in some cases the matter—which is the starting-point of the process in the production and generation of artificial things, and in which some part of the result is already existent—is such that it can initiate its own motion, and in other cases it is not; and of the former kind some can initiate motion in a particular way, and some cannot. For many things can move themselves, but not in a particular way, e.g. so as to dance.

It is impossible, then, for any things whose matter is of this kind (e.g. stones) to be moved in

particular way except by something else; but in

particular way it is possible. And it is so with fire.

For this reason some things cannot exist apart from the possessor of the art, and others can;

because the motion can be initiated by those things which do not indeed possess the art, but can themselves be moved either by other things which do not possess the art, or by the motion from the part of the product which pre-exists in them.

It is clear also from what we have said that in a sense all artificial things are generated either from something which bears the same name (as is the case with natural objects) or from a part of themselves which bears the same name as themselves (e.g. a house from a house, inasmuch as it is generated by mind; for the art is the form), or from something which contains some part; that is if the generation is not accidental; for the direct and independent cause of the production is a part of the product.

Heat in the motion produces heat in the body; and either this is health or a part of health, or a part of health or health accompanies it. And this is why heat is said to produce health, because it produces that of which health is a concomitant and consequence. Therefore as essence is the starting-point of everything in syllogisms (because syllogisms start from the "what" of a thing), so too generation proceeds from it.

And it is the same with natural formations as it is with the products of art. For the seed produces just as do those things which function by art. It contains the form potentially,

and that from which the seed comes has in some sense the same name as the product (for we must not expect that all should have the same name in the sense that "man" is produced by "man"—since woman is also produced by man); unless the product is a freak. This is why a mule is not produced by a mule.

Those natural objects which are produced, like artificial objects, spontaneously, are those whose matter can also initiate for itself that motion which the seed initiates. Those whose matter cannot do this cannot be generated otherwise than by their proper parents.

It is not only with reference to substance that our argument shows that the form is not generated; the same argument is common in its application to all the primary divisions, i.e. quantity, quality and the other categories.

For just as the bronze sphere is generated, but not the sphere nor the bronze; and as in the case of bronze, if it is generated the form and matter are not (because they must always pre-exist), so it is too with the "what" and the quality and quantity and the other categories similarly; for it is not the quality that is generated, but the wood of that quality; nor is it the size, but the wood or animal of that size.

But a peculiarity of substance may be gathered from this: that some other substance must pre-exist in actuality which produces it; e.g. an animal, if an animal is being generated; but a quality or quantity need not pre-exist otherwise than potentially.

Since a definition is a formula, and every formula has parts; and since the formula is related to the thing in the same way as the part of the formula to the part of the thing, the question

now arises: Must the formula of the parts be contained in the formula of the whole, or not? It seems clear that it is so in some cases, but not in others.

The formula of the circle does not include that of the segments, but the formula of the syllable includes that of the letters. And yet the circle is divisible into its segments in just the same way as the syllable into its letters.

Again, if the parts are prior to the whole, and the acute angle is part of the right angle, and the finger part of the animal, the acute angle will be prior to the right angle, and the finger to the man.

But it is considered that the latter are prior; for in the formula the parts are explained from them; and the wholes are prior also in virtue of their ability to exist independently. The truth probably is that "part" has several meanings, one of which is "that which measures in respect of quantity." However, let us dismiss this question and consider of what, in the sense of parts, substance consists.

If then matter, form, and the combination of the two are distinct, and if both matter and form and their combination are substance, there is one sense in which even matter may be called "part" of a thing; and another in which it is not, but the only parts are those elements of which the formula of the form consists. E.g., flesh is not a part of concavity, because flesh is the matter in which concavity is induced; but it is a part of snubness. And bronze is part of the statue as a concrete whole, but not of the statue in the sense of form.

We may speak of the form (or the thing as having a form) as an individual thing, but we may never so speak of that which is material by itself. This is why the formula of the circle does not contain that of the segments, whereas the formula of the syllable does contain that of the letters; for the letters are parts of the formula of the form; they are not matter; but the segments are parts in the sense of matter in which the form is induced. They approximate, however, more closely to the form than does the bronze when roundness is engendered in bronze.

But there is a sense in which not even all the letters will be contained in the formula of the syllable; e.g. particular letters on wax

or sounds in the air; for these too are part of the syllable in the sense that they are its sensible matter.

For even if the line is divided and resolved into its halves, or if the man is resolved into bones and muscles and flesh,

it does not follow that they are composed of these as parts of their essence, but as their matter; and these are parts of the concrete whole, but not of the form, or that to which the formula refers. Hence they are not in the formulae.

Accordingly in some cases the formula will include the formula of such parts as the above, but in others it need not necessarily contain their formula, unless it is the formula of the concrete object. It is for this reason that some things are composed of parts in the sense of principles into which they can be resolved, while others are not.

All things which are concrete combinations of form and matter (e.g. "the snub" or the bronze circle) can be resolved into form and matter, and the matter is a part of them; but such as are not concrete combinations with matter, but are without matter—whose formulae refer to the form only—cannot be resolved; either not at all, or at least not in this way.

Thus these material components are principles and parts of the concrete objects, but they are neither parts nor principles of the form. For this reason the clay statue can be resolved into clay, and the sphere into bronze, and Callias into flesh and bones, and the circle too into segments, because it is something which is combined with matter.

For we use the same name for the absolute circle and for the particular circle, since there is no special name for the particular circles.

We have now stated the truth; nevertheless let us recapitulate and state it more clearly. All constituents which are parts of the formula, and into which the formula can be divided, are prior to their wholes—either all or some of them. But the formula of the right angle is not divisible into the formula of an acute angle, but vice versa; since in defining the acute angle we use the right angle, because "the acute angle is less than a right angle."

It is the same with the circle and the semicircle; for the semicircle is defined by means of the circle. And the finger is defined by means of the whole body; for a finger is a particular kind of part of a man. Thus such parts as are material, and into which the whole is resolved as into matter, are posterior to the whole; but such as are parts in the sense of parts of the formula and of the essence as expressed in the formula, are prior; either all or some of them.

And since the soul of animals (which is the substance of the living creature) is their substance in accordance with the formula, and the form and essence of that particular kind of body (at least each part, if it is to be properly defined, will not be defined apart from its function; and this will not belong to it apart from perception

); therefore the parts of the soul are prior, either all or some of them, to the concrete animal; and similarly in other individual cases.

But the body and its parts are posterior to this substance, and it is not the substance, but the concrete whole, which is resolved into these parts as into matter. Therefore in one sense these parts are prior to the concrete whole, and in another not; for they cannot exist in separation. A finger cannot in every state be a part of a living animal; for the dead finger has only the name in common with the living one.

Some parts are contemporary with the whole: such as are indispensable and in which the formula and the essence are primarily present; e.g. the heart or perhaps the brain,

for it does not matter which of them is of this nature. But "man" and "horse" and terms which are applied in this way to individuals, but universally, are not substance, but a kind of concrete whole composed of

particular formula and

particular matter regarded as universal. But individually Socrates is already composed of ultimate matter; and similarly in all other cases.

A part, then, may be part of the form (by form I mean essence), or of the concrete whole composed of form and matter, or of the matter itself. But only the parts of the form are parts of the formula, and the formula refers to the universal;

for "circle" is the same as "essence of circle," and "soul" the same as "essence of soul."

But when we come to the concrete thing, e.g. this circle—which is a particular individual, either sensible or intelligible (by intelligible circles I mean those of mathematics,

and by sensible those which are of bronze or wood)—of these individuals there is no definition;

we apprehend them by intelligence or perception; and when they have passed from the sphere of actuality it is uncertain whether they exist or not, but they are always spoken of and apprehended by the universal formula. But the matter is in itself unknowable. Some matter is sensible and some intelligible; sensible, such as bronze and wood and all movable matter; intelligible, that which is present in sensible things not qua sensible, e.g. the objects of mathematics.

We have now discussed the case of the whole and part, and of prior and posterior. But we must answer the question, when we are asked which is prior—the right angle and circle and animal, or that into which they are resolved and of which they are composed, i.e. their parts—by saying that neither is

prior.

For if the soul also

the animal or living thing, or the soul of the individual

the individual, and "being a circle"

the circle, and "being a right angle" or the essence of the right angle

the right angle, then we must admit that the whole in one sense is posterior to the part in one sense:

e.g. to the parts in the formula and the parts of a particular right angle

(since both the material right angle of bronze and the right angle included by individual lines are posterior to their parts), but the immaterial angle is posterior to the parts in the formula, but prior to the parts in the individual. We must not give an unqualified answer. And if the soul is not the animal but something else, even so we must say that some wholes are prior and some are not, as has been stated.

The question naturally presents itself, what sort of parts belong to the form and what sort belong not to it but to the concrete object. Yet if this is not plain it is impossible to define the particular; because the definition refers to the universal and the form. Therefore if it is not clear what kind of parts are material and what kind are not, the formula of the thing will not be clear either.

In the case of things which can be seen to be induced in specifically different materials, as, e.g., a circle is in bronze and stone and wood, it seems clear that these things, the bronze and the stone, are in no sense part of the essential substance of the circle, because it is separable from them.

As for things which are not visibly separable, there is no reason why the same should not apply to them; e.g., if all the circles that had ever been seen were bronze;

for the bronze would be none the less no part of the form, but it is difficult to separate it in thought.

For example, the form of "man" is always manifested in flesh and bones and elements of this kind; then are these actually parts of the form and formula, or are they not so, but matter, though since the form is not induced in other materials, we cannot separate it?

Now since this seems to be possible, but it is not clear

, some thinkers

are doubtful even in the case of the circle and the triangle, considering that it is not proper to define them by lines and continuous space, but that all these are to the circle or triangle as flesh or bone is to man, and bronze or stone to the statue; and they reduce everything to numbers, and say that the formula of "line" is the formula of 2.

And of the exponents of the Forms, some make 2 the Ideal line, and some the form of the line

; for they say that in some cases the form and that of which it is the form, e.g. 2 and the form of 2, are the same; but in the case of "line" this is no longer so.

It follows, then, that there is one form of many things whose form is clearly different (a consequence which confronted the Pythagoreans too

), and that it is possible to make one supreme Form of everything, and not to regard the rest as forms.

In this way, however, all things would be one.

Now we have stated that the question of definitions involves some difficulty, and have shown why this is so. Hence to reduce everything in this way and to dispose of the matter is going too far; for some things are presumably a particular form in particular matter, or particular things in a particular state.

And the analogy in the case of the living thing which the younger Socrates

used to state is not a good one; for it leads one away from the truth, and makes one suppose that it is possible for a man to exist without his parts, as a circle does without the bronze. But the case is not similar; for the animal is sensible and cannot be defined without motion, and hence not unless its parts are in some definite condition;

for it is not the hand in

condition that is a part of a man, but only when it can perform its function, and so has life in it. Without life in it it is not a part.

And with respect to mathematical objects, why are the formulae of the parts not parts of the formulae of the whole; e.g., why are the formulae of the semicircles not parts of the formula of the circle? for they are not sensible.

Probably this makes no difference; because there will be matter even of some things which are not sensible.

Indeed there will be matter in some sense in everything which is not essence or form considered independently, but a particular thing. Thus the semicircles will be parts not of the universal circle but of the particular circles, as we said before

—for some matter is sensible, and some intelligible.

It is clear also that the soul is the primary substance, and the body matter; and "man" or "animal" is the combination of both taken universally. And " Socrates" or "Coriscus" has a double sense, that is if the soul too can be called Socrates (for by Socrates some mean the soul and some the concrete person); but if Socrates means simply

soul and

body, the individual is composed similarly to the universal.

Whether there is some other material component of these substances besides their matter, and whether we should look for some further substance in them, such as numbers or something of that kind, must be considered later.

It is with a view to this that we are trying to determine the nature of sensible substances, since in a sense the study of sensible substances belongs to physics or secondary philosophy; for the physicist must know not only about the matter, but also about the substance according to the formula; this is even more essential.

And in the case of definitions, in what sense the elements in the formula are parts of the definition, and why the definition is one formula (for the thing is clearly one,

but in virtue of what is it one, seeing that it has parts?); this must be considered later.

We have stated, then, in a general account which covers all cases, what essence is, and how it is independent; and why the formula of the essence of some things contains the parts of the thing defined, while that of others does not; and we have shown that the material parts of a thing cannot be present in the formula of the substance (since they are not even parts of the substance in that sense, but of the concrete substance; and of this in one sense there is a formula, and in another sense there is not.

There is no formula involving the matter, for this is indeterminate; but there is a formula in accordance with the primary substance, e.g., in the case of a man, the formula of the soul; because the substance is the indwelling form, of which and of the matter the so called concrete substance is composed. E.g., concavity is such a form, since from this and "nose" is derived "snub nose" and "snubness"—for "nose" will be present twice over in these expressions);

but in the concrete substance, e.g. snub nose or Callias, matter will be present too.

We have stated also that the essence and the individual are in some cases the same,

as in the case of the primary substances; e.g. crookedness and "essence of crookedness," if this is primary.

By primary I mean that which does not imply the presence of something in something else as a material substrate. But such things as are material or are compounded with matter are not the same as their essence; not even if they are accidentally one, e.g. Socrates and "cultured"; for these are only accidentally the same.

Now let us first deal with definition, in so far as it has not been dealt with in the Analytics; for the problem stated there

has a bearing upon our discussion of substance. The problem I mean is this: what constitutes the unity of the thing of which we say that the formula is a definition? E.g., in the case of man, "two-footed animal"; for let us take this as the formula of "man."

Why, then, is this a unity and not a plurality, "animal" and "two-footed"? For in the case of "man" and "white" we have a plurality when the latter does not refer to the former, but a unity when it does refer to it, and the subject, "man," has an attribute; for then they become a unity and we have "the white man."

But in the case before us one term does not partake of the other; the genus is not considered to partake of its differentiae, for then the same thing would be partaking simultaneously of contraries,

since the differentiae by which the genus is distinguished are contrary. And even if it does partake of them, the same argument applies, since the differentiae are many; e.g. terrestrial, two-footed, wingless.

Why is it that these are a unity and not a plurality? Not because they are present in one genus, for in that case all the differentiae of the genus will form a unity. But all the elements in the definition must form a unity, because the definition is a kind of formula which is one and defines substance, so that it must be a formula of one particular thing; because the substance denotes one thing and an individual, as we say.

We must first

examine definitions which are reached by the process of division.

For there is nothing else in the definition but the primary genus and the differentiae; the other genera consist of the primary genus together with the differentiae which are taken with it. E.g., the primary genus is "animal"; the next below it, "two-footed animal"; and again, "two-footed wingless animal"; and similarly also if the expression contains more terms still.

In general it does not matter whether it contains many or few terms, nor, therefore, whether it contains few or two. Of the two one is differentia and the other genus; e.g., in "two-footed animal" "animal" is genus, and the other term differentia.

If, then, the genus absolutely does not exist apart from the species which it includes, or if it exists, but only as matter (for speech is genus and matter, and the differentiae make the species, i.e. the letters, out of it), obviously the definition is the formula composed of the differentiae.

But further we must also divide by the differentia of the differentia. E.g., "having feet" is a differentia of "animal"; then in turn we must discover the differentia of "animal having feet" qua "having feet." Accordingly we should not say that of "that which has feet" one kind is winged and another wingless, (that is if we are to speak correctly; if we say this it will be through incapability), but only that one kind is cloven-footed and another not; because these are differentiae of "foot," since cloven-footedness is a kind of footedness.

And thus we tend always to progress until we come to the species which contain no differentiae. At this point there will be just as many species of foot as there are differentiae, and the kinds of animals having feet will be equal in number to the differentiae. Then, if this is so,

obviously the ultimate differentia will be the substance and definition of the thing, since we need not state the same things more than once in definitions, because this is superfluous.

However, it does happen; for when we say "footed two-footed animal" we have simply said "animal having feet, having two feet." And if we divide this by its proper division, we shall be stating the same thing several times, as many times as there are differentiae.

If, then, we keep on taking a differentia of a differentia, one of them, the last, will be the form and the substance. But if we proceed with reference to accidental qualities—e.g. if we divide "that which has feet" into white and black—there will be as many differentiae as there are divisions. It is therefore obvious that the definition is the formula derived from the differentiae, and strictly speaking from the last of them.

This will be clear if we change the order of such definitions, e.g. that of man, saying "two-footed footed animal"; for "footed" is superfluous when we have already said "two-footed." But there is no question of order in the substance; for how are we to think of one part as posterior and the other prior?

With regard, then, to definitions by division, let this suffice as a preliminary statement of their nature.

Since the subject of our inquiry is substance, let us return to it. Just as the substrate and the essence and the combination of these are called substance, so too is the universal. With two of these we have already dealt, i.e. with the essence

and the substrate

; of the latter we have said that it underlies in two senses—either being an individual thing (as the animal underlies its attributes), or as matter underlies the actuality.

The universal also is thought by some

to be in the truest sense a cause and a principle. Let us therefore proceed to discuss this question too; for it seems impossible that any universal term can be substance.

First, the substance of an individual is the substance which is peculiar to it and belongs to nothing else; whereas the universal is common; for by universal we mean that which by nature appertains to several things.

Of what particular, then, will the universal be the substance? Either of all or of none. But it cannot be the substance of all; while, if it is to be the substance of one, the rest also will be that one; because things whose substance is one have also one essence and are themselves one.

Again, substance means that which is not predicated of a subject, whereas the universal is always predicated of some subject.

But perhaps although the universal cannot be substance in the sense that essence is, it can be present in the essence, as "animal" can be present in "man" and "horse."

Then clearly there is in some sense a formula of the universal. It makes no difference

even if there is not a formula of everything that is in the substance; for the universal will be none the less the substance of something; e.g., "man" will be the substance of the man in whom it is present. Thus the same thing will happen again

; e.g. "animal" will be the substance of that in which it is present as peculiar to it.

Again, it is impossible and absurd that the individual or substance, if it is composed of anything, should be composed not of substances nor of the individual, but of a quality; for then non-substance or quality will be prior to substance or the individual. Which is impossible; for neither in formula nor in time nor in generation can the affections of substance be prior to the substance, since then they would be separable.

Again, a substance will be present in "Socrates," who is a substance; so that it will be the substance of two things. And in general it follows that if "man" and all terms used in this way are substance, none of the elements in the formula is the substance of anything, nor can it exist apart from the species or in anything else; I mean, e.g., that neither "animal" nor any other element of the formula can exist apart from the particular species.

If we look at the question from this standpoint it is obvious that no universal attribute is substance; and it is also clear from the fact that none of the common predicates means "so-and-so,"

but "such and-such." Otherwise amongst many other awkward consequences we have the "third man."

Again, it is clear in this way too. Substance can not consist of substances actually present in it; for that which is actually two can never be actually one, whereas if it is potentially two it can be one. E.g., the double consists of two halves—that is, potentially; for the actualization separates the halves.

Thus if substance is one, it cannot consist of substances present in it even in this sense, as Democritus rightly observes; he says that it is impossible for two to come from one, or one from two, because he identifies substance with the atoms.

Clearly then the same will also hold good in the case of number (assuming that number is a composition of units, as it is said to be by some); because either 2 is not 1, or there is not

a unit in it.

The consequence involves a difficulty; for if no substance can consist of universals, because they mean "of such a kind," and not a particular thing; and if no substance can be actually composed of substances, every substance will be incomposite, and so there will be no formula of any substance.

But in point of fact it is universally held, and has been previously stated,

that substance is the only or chief subject of definition; but on this showing there is no definition even of substance. Then there can be no definition of anything; or rather in a sense there can, and in a sense cannot. What this means will be clearer from what follows later.

From these same considerations it is clear also what consequence follows for those who maintain that the Forms are substances and separable, and who at the same time make the species consist of the genus and the differentiae. If there are Forms, and if "animal" is present in the man and the horse, it is either numerically one and the same with them, or not.

(In formula they are clearly one; for in each case the speaker will enunciate the same formula.) If, then, there is in some sense an Absolute Man, who is an individual and exists separately, then the constituents, e.g. "animal" and "two-footed," must have an individual meaning and be separable and substances. Hence there must be an Absolute Animal too.

(i) Then if the "animal" which is in the horse and the man is one and the same, as you are one and the same with yourself,

how can the one which in things that exist separately be one, and why should not this "animal" also be separated from itself? Again, if it is to partake of "two-footed" and of "many-footed," an impossibility follows; for contrary attributes will belong to it although it is one and individual.

But if it does not, in what sense is it that one calls an animal "two-footed" or "terrestrial"? Perhaps the terms are "combined" and "in contact" or "mixed." But all these expressions are absurd.

(2) "But there is a different 'animal' in each species." Then there will be practically an infinity of things of which "animal" is the substance, since it is not in an accidental sense that "man" is derived from "animal."

Again, the Absolute Animal will be a plurality. For (a) the "animal" in each species will be the substance of that species, since the species is called after it and no other thing. Otherwise "man" would be derived from that other thing, which would be the genus of "man." (b) Further, all the constituents of "man" will be Ideas. Then, since nothing can be the Idea of one thing and the substance of another (for this is impossible),

each and every "animal" in the various species will be the Absolute Animal.

Further, from what will these Forms be derived, and how can they be derived from the Absolute Animal? Or how can "the animal," whose very essence is "animal," exist apart from the Absolute Animal? And further, in the case of sensible things both these and still more absurd consequences follow. If, then, these consequences are impossible, clearly there are not Forms of sensible things in the sense in which some hold that there are.

Since substance is of two kinds, the concrete thing and the formula (I mean that one kind of substance is the formula in combination with the matter, and the other is the formula in its full sense), substances in the former sense admit of destruction, for they also admit of generation. But the formula does not admit of destruction in the sense that it is ever

destroyed, since neither does it so admit of generation (for the essence of house is not generated, but only the essence of

house); formulae

, and

, independently of generation and destruction; for it has been shown

that no one either generates or creates them.

For this reason also there is no definition or demonstration of particular sensible substances, because they contain matter whose nature is such that it can both exist and not exist. Hence all the individual instances of them are perishable.

If, then, the demonstration and definition of necessary truths requires scientific knowledge, and if, just as knowledge cannot be sometimes knowledge and sometimes ignorance (it is opinion that is of this nature), so too demonstration and definition cannot vary (it is opinion that is concerned with that which can be otherwise than it is)—

then clearly there can be neither definition nor demonstration of individual sensible substances.

For (a) things which perish are obscure to those who have knowledge of them when they are removed from the sphere of their perception, and (b) even though their formulae are preserved in the soul, there will no longer be either definition or demonstration of them. Therefore in cases relating to definition, when we are trying to define any individual, we must not fail to realize that our definition may always be upset; because it is impossible to define these things.

Nor, indeed, can any Idea be defined; for the Idea is an individual, as they say, and separable; and the formula must consist of words, and the man who is defining must not coin a word, because it would not be comprehensible. But the words which are in use are common to all the things which they denote; and so they must necessarily apply to something else as well. E.g., if a man were to define you, he would say that you are an animal which is lean or white or has some other attribute, which will apply to something else as well.

And if it should be said that there is no reason why all the attributes separately should not belong to several things, and yet in combination belong to this alone, we must reply, (1.) that they also belong to both the elements; e.g., "two-footed animal" belongs both to "animal" and to "two-footed" (and in the case of eternal elements this is even necessarily so; since they are prior to the compound, and parts of it.

Indeed they are also separable, if the term "man" is separable—for either neither can be separable, or both are so.

If neither, the genus will not exist apart from the species, or if it is so to exist, so will the differentia); (2.) that "animal" and "two-footed" are prior in being to "two-footed animal," and that which is prior to something else is not destroyed together with it.

Again, if the Ideas are composed of Ideas (for constituents are less composite than that which they compose), still the elements of which the Idea is composed (e.g. "animal" and "two-footed") will have to be predicated of many particulars. Otherwise, how can they be known? For there would be an Idea which cannot be predicated of more than one thing. But this is not considered possible; every Idea is thought to admit of participation.

Thus, as we have said,

the impossibility of defining individuals is hard to realize when we are dealing with eternal entities, especially in the case of such as are unique, e.g. the sun and moon. For people go wrong not only by including in the definition attributes on whose removal it will still be sun—e.g., "that which goes round the earth," or "night-hidden " (for they suppose that if it stops or becomes visible

it will no longer be sun; but it is absurd that this should be so, since "the sun "denotes a definite substance)—they also mention attributes which may apply to something else; e.g., if another thing with those attributes comes into being, clearly it will be a sun. The formula, then, is general;

but the sun was supposed to be an individual, like Cleon or Socrates.

Why does not one of the exponents of the Ideas produce a definition of them? If they were to try, it would become obvious that what we have just said is true.

It is obvious that even of those things which are thought to be substances the majority are potentialities; both the parts of living things (for none of them has a separate substantial existence; and when they are separated, although they still exist, they exist as matter), and earth, fire and air; for none of these is one

—they are a mere aggregate before they are digested and some one thing is generated from them.

It might be supposed very reasonably that the parts of living things and the corresponding parts of their vital principle are both, i.e. exist both actually and potentially, because they contain principles of motion derived from something in their joints; and hence some animals

live even when they are divided. Nevertheless it is only potentially that all of them will exist when they are one and continuous by nature and not by force or concretion; for this sort of thing is malformation.

And since "unity" has the same variety of senses as "being," and the substance of Unity is one, and things whose substance is numerically one are numerically one, evidently neither Unity nor Being can be the substance of things, just as neither "being an element" or "principle" can be the substance;

but we ask what the principle is so that we may refer to something more intelligible.

Now of these concepts Being and Unity are more nearly substance than are principle, element and cause; but not even the former are quite substance, since nothing else that is common is substance; for substance belongs to nothing except itself and that which contains it and of which it is the substance.

Again, Unity cannot exist in many places at the same time, but that which is common is present in many things at the same time. Hence it is clear that no universal exists in separation apart from its particulars. The exponents of the Forms are partly right in their account when they make the Forms separate; that is, if the Forms are substances, but they are also partly wrong, since by "Form" they mean the "one-over-many."

The reason for this is that they cannot explain what are the imperishable substances of this kind which exist besides particular sensible substances; so they make them the same in kind as perishable things (for these we know); i.e., they make "Ideal Man" and "Ideal Horse," adding the word "Ideal" to the names of sensible things.

However, I presume that even if we had never seen the stars,

none the less there would be eternal substances besides those which we knew; and so in the present case even if we cannot apprehend what they are, still there must be eternal substances of some kind.

It is clear, then, both that no universal term is substance and that no substance is composed of substances.

As for what and what sort of thing we mean by substance, let us explain this by making, as it were, another fresh start. Perhaps in this way we shall also obtain some light upon that kind of substance which exists in separation from sensible substances. Since, then, substance is a kind of principle and cause, we had better pursue our inquiry from this point.

Now when we ask why a thing is, it is always in the sense "why does A belong to B?"

To ask why the cultured man is a cultured man is to ask either, as we have said, why the man is cultured, or something else. Now to ask why a thing is itself is no question; because when we ask the reason of a thing the fact must first be evident; e.g., that the moon suffers eclipse;

and "because it is itself" is the one explanation and reason which applies to all questions such as "why is man man?" or "why is the cultured person cultured?" (unless one were to say that each thing is indivisible from itself, and that this is what "being one" really means);

but this, besides being a general answer, is a summary one.

We may, however, ask why a man is an animal of such-and-such a kind.

It is clear, then, that we are not asking why he who is a man is a man; therefore we are asking why A, which is predicated of B, belongs to B. (The fact that A does belong to B must be evident, for if this is not so, the question is pointless.) E.g., "Why does it thunder?" means "why is a noise produced in the clouds?" for the true form of the question is one thing predicated in this way of another.

Or again, "why are these things, e.g. bricks and stones, a house?" Clearly then we are inquiring for the cause (i.e., to speak abstractly, the essence); which is in the case of some things, e.g. house or bed, the

, and in others the prime mover—for this also is a cause. We look for the latter kind of cause in the case of generation and destruction, but for the former also in the case of existence.

What we are now looking for is most obscure when one term is not predicated of another;

e.g. when we inquire what man is; because the expression is a simple one not analyzed into subject and attributes. We must make the question articulate before we ask it; otherwise we get something which shares the nature of a pointless and of a definite question.

Now since we must know that the fact actually exists, it is surely clear that the question is "why is the

so-and-so?" e.g. "why are these materials a house?" Because the essence of house is present in them. And this matter, or the body containing this particular form, is man. Thus what we are seeking is the cause (i.e. the form) in virtue of which the matter is a definite thing; and this is the substance of the thing.

Clearly then in the case of simple entities

inquiry and explanation are impossible; in such cases there is a different mode of inquiry.

Now since that which is composed of something in such a way that the whole is a unity; not as an aggregate is a unity, but as a syllable is

—the syllable is not the letters, nor is BA the same as B and A; nor is flesh fire and earth; because after dissolution the compounds, e.g. flesh or the syllable, no longer exist; but the letters exist, and so do fire and earth.

Therefore the syllable is some particular thing; not merely the letters, vowel and consonant, but something else besides. And flesh is not merely fire and earth, or hot and cold, but something else besides.

Since then this something else must be either an element or composed of elements,

(a) if it is an element, the same argument applies again; for flesh will be composed of

and fire and earth, and again of another element, so that there will be an infinite regression. And (b) if it is composed of elements, clearly it is composed not of one (otherwise it will itself be that element) but of several; so that we shall use the same argument in this case as about the flesh or the syllable.

It would seem, however, that this "something else" is something that is not an element, but is the cause that

matter is flesh and

matter a syllable, and similarly in other cases.

And this is the substance of each thing, for it is the primary cause of its existence. And since, although some things are not substances, all substances are constituted in accordance with and by nature, substance would seem to be this "nature," which is not an element but a principle.

An element is that which is present as matter in a thing, and into which the thing is divided; e.g., A and B are the elements of the syllable.

We must now draw our conclusions from what has been said, and after summing up the result, bring our inquiry to a close. We have said

that the objects of our inquiry are the causes and principles and elements of substances. Now some substances are agreed upon by all; but about others certain thinkers have stated individual theories.

Those about which there is agreement are natural substances: e.g. fire, earth, water, air and all the other simple bodies; next, plants and their parts, and animals and the parts of animals; and finally the sensible universe and its parts; and certain thinkers individually include as substances the Forms and the objects of mathematics.

And arguments show that there are yet other substances: the essence and the substrate.

Again, from another point of view, the genus is more nearly substance than the species, and the universal than the particulars

; and there is a close connection between the universal and genus and the Ideas, for they are thought to be substance on the same grounds.

And since the essence is substance, and definition is the formula of the essence, we have therefore systematically examined definition and essential predication.

And since the definition is a formula, and the formula has parts,

we have been compelled to investigate "parts," and to discover what things are parts of the substance, and what are not; and whether the parts of the substance are also parts of the definition.

Further, then, neither the universal nor the genus is substance.

As for the Ideas and the objects of mathematics (for some say that these exist apart from sensible substances) we must consider them later.

But now let us proceed to discuss those substances which are generally accepted as such.

Now these are the sensible substances, and all sensible substances contain matter.

And the substrate is substance; in one sense matter (by matter I mean that which is not actually, but is potentially, an individual thing); and in another the formula and the specific shape (which is an individual thing and is theoretically separable); and thirdly there is the combination of the two, which alone admits of generation and destruction,

and is separable in an unqualified sense—for of substances in the sense of formula some are separable

and some are not.

That matter is also substance is evident; for in all opposite processes of change there is something that underlies those processes; e.g., if the change is of

, that which is now in one place and subsequently in another; and if the change is of

, that which is now of such-and-such a size, and subsequently smaller or greater; and if the change is of

, that which is now healthy and subsequently diseased.

Similarly, if the change is in respect of

, there is something which is now in course of generation, and subsequently in course of destruction, and which is the underlying substrate, now as

individual thing, and subsequently as deprived of its individuality. In this last process of change the others are involved, but in either one or two

of the others it is not involved; for it does not necessarily follow that if a thing contains matter that admits of change of place, it also contains matter that is generable and destructible.

The difference between absolute and qualified generation has been explained in the Physics.

Since substance in the sense of substrate or matter is admittedly substance, and this is potential substance, it remains to explain the nature of the actual substance of sensible things. Now Democritus

apparently assumes three differences in substance; for he says that the underlying body is one and the same in material, but differs in figure, i.e. shape; or inclination, i.e. position; or intercontact, i.e. arrangement.

But evidently there are many differences; e.g. some things are defined by the way in which their materials are combined, as, for example, things which are unified by mixture, as honey-water; or by ligature, as a faggot; or by glue, as a book; or by clamping, as a chest; or by more than one of these methods. Other things are defined by their position, e.g. threshold and lintel (for these differ in being situated in a particular way);

and others by place , e.g. the winds; others by time, e.g. dinner and breakfast; and others by the attributes peculiar to sensible things, e.g. hardness and softness, density and rarity, dryness and humidity. Some are distinguished by some of these differences, and others by all of them; and in general some by excess and some by defect.

Hence it is clear that "is" has the same number of senses; for a thing "is" a threshold because it is situated in a particular way, and "to be a threshold" means to be situated in this particular way, and "to be ice" means to be condensed in this particular way. Some things have their being defined in all these ways: by being partly mixed, partly blended, partly bound, partly condensed, and partly subjected to all the other different processes; as, for example, a hand or a foot.

We must therefore comprehend the various kinds of differences—for these will be principles of being—i.e. the differences in degree, or in density and rarity, and in other such modifications, for they are all instances of excess and defect.

And if anything differs in shape or in smoothness or roughness, all these are differences in straightness and curvature. For some things mixture will constitute being,

and the opposite state not-being.

From this it is evident that if substance is the cause of the existence of each thing, we must look among these "differences" for the cause of the being of each thing.

No one of them, nor the combination of any two of them, is substance, but nevertheless each one of them contains something analogous to substance. And just as in the case of substances that which is predicated of the matter is the actuality itself, so in the other kinds of definition it is the nearest approximation to actuality. E.g., if we have to define a threshold, we shall call it "a piece of wood or stone placed in such-and-such a way"; and we should define a house as "bricks and timber arranged in such-and-such a way";

or again in some cases there is the final cause as well. And if we are defining ice, we shall describe it as "water congealed or condensed in such-and-such a way"; and a harmony is "such-and-such a combination of high and low"; and similarly in the other cases.

From this it is evident that the actuality or formula is different in the case of different matter; for in some cases it is a combination, in others a mixture, and in others some other of the modes which we have described.

Hence in defining the nature of a house, those who describe it as stones, bricks and wood, describe the potential house, since these things are its matter; those who describe it as "a receptacle for containing goods and bodies," or something else to the same effect, describe its actuality; but those who combine these two definitions describe the third kind of substance, that which is composed of matter and form.

For it would seem that the formula which involves the differentiae is that of the form and the actuality,

while that which involves the constituent parts is rather that of the matter. The same is true of the kind of definitions which Archytas

used to accept; for they are definitions of the combined matter and form. E.g., what is "windlessness?" Stillness in a large extent of air; for the air is the matter, and the stillness is the actuality and substance.

What is a calm? Levelness of sea. The sea is the material substrate, and the levelness is the actuality or form.

From the foregoing account it is clear what sensible substance is, and in what sense it exists; either as matter, or as form and actuality, or thirdly as the combination of the two.

We must not fail to realize that sometimes it is doubtful whether a name denotes the composite substance or the actuality and the form—e.g. whether "house" denotes the composite thing, "a covering made of bricks and stones arranged in such-and-such a way," or the actuality and form, "a covering"; and whether "line" means "duality in length" or "duality"

; and whether "animal" means "a soul in a body" or "a soul"; for the soul is the substance and actuality of some body.

The term "animal" would be applicable to both cases; not as being defined by one formula, but as relating to one concept. These distinctions are of importance from another point of view, but unimportant for the investigation of sensible substance;

because the essence belongs to the form and the actualization.

Soul and essence of soul are the same, but man and essence of man are not, unless the soul is also to be called man; and although this is so in one sense, it is not so in another.

It appears, then, upon inquiry into the matter,

that a syllable is not derived from the phonetic elements plus combination, nor is a house bricks plus combination. And this is true; for the combination or mixture is not derived from the things of which it is a combination or mixture,

nor, similarly, is any other of the "differences." E.g., if the threshold is defined by its position, the position is not derived from the threshold, but rather vice versa. Nor, indeed, is man "animal"

"two-footed"; there must be something which exists besides these, if they are matter; but it is neither an element nor derived from an element, but the substance; and those who offer the definition given above are omitting this and describing the matter.

If, then, this something else is the cause of a man's being, and this is his substance, they will not be stating his actual substance.

Now the substance must be either eternal or perishable without ever being in process of perishing, and generated without ever being in process of generation. It has been clearly demonstrated elsewhere

that no one generates or creates the form; it is the individual thing that is created, and the compound that is generated.

But whether the substances of perishable things are separable or not is not yet at all clear

; only it is clear that this is impossible in some cases,

i.e. in the case of all things which cannot exist apart from the particular instances; e.g. house or implement.

Probably, then, neither these things themselves, nor anything else which is not naturally composed, are substances; for their nature is the only substance which one can assume in the case of perishable things.

Hence the difficulty which perplexed the followers of Antisthenes

and others similarly unlearned has a certain application; I mean the difficulty that it is impossible to define

a thing is (for the definition, they say, is a lengthy formula), but it

possible actually to teach others what a thing

; e.g., we cannot say

silver is, but we can say that it is like tin.

Hence there can be definition and formula of one kind of substance, i.e. the composite, whether it is sensible or intelligible; but not of its primary constituents, since the defining formula denotes something predicated of something, and this must be partly of the nature of matter and partly of the nature of form.

It is also obvious that, if numbers are in any sense substances, they are such in this sense, and not, as some

describe them, aggregates of units. For (a) the definition is a kind of number, since it is divisible, and divisible into indivisible parts (for formulae are not infinite); and number is of this nature.

And (b) just as when any element which composes the number is subtracted or added, it is no longer the same number but a different one, however small the subtraction or addition is;

so neither the definition nor the essence will continue to exist if something is subtracted from or added to it. And (c) a number must be something in virtue of which it is a unity (whereas our opponents cannot say what makes it one); that is, if it is a unity.

For either it is not a unity but a kind of aggregate, or if it is a unity, we must explain what makes a unity out of a plurality. And the definition is a unity; but similarly they cannot explain the definition either. This is a natural consequence, for the same reason applies to both, and substance is a unity in the way which we have explained, and not as some thinkers say: e.g. because it is a kind of unit or point; but each substance is a kind of actuality and nature.

Also (d) just as a number does not admit of variation in degree, so neither does substance in the sense of form; if any substance does admit of this, it is substance in combination with matter.

Let this suffice as a detailed account of the generation and destruction of so-called substances, in what sense they are possible and in what sense they are not; and of the reference of things to number.

As regards material substance, we must not fail to realize that even if all things are derived from the same primary cause, or from the same things as primary causes

; i.e. even if all things that are generated have the same matter for their first principle, nevertheless each thing has some matter peculiar to it; e.g., "the sweet" or "the viscous" is the proximate matter of mucus, and "the bitter" or some such thing is that of bile—

although probably mucus and bile are derived from the same ultimate matter.

The result is that there is more than one matter of the same thing, when one thing is the matter of the other; e.g., mucus is derived from "the viscous"; and from "the sweet," if "the viscous" is derived from "the sweet"; and from bile, by the analysis of bile into its ultimate matter. For there are two senses in which X comes from Y; either because X will be found further on than Y in the process of development, or because X is produced when Y is analyzed into its original constituents.

And different things can be generated by the moving cause when the matter is one and the same, e.g. a chest and a bed from wood. But some different things must necessarily have different matter; e.g., a saw cannot be generated from wood, nor does this lie in the power of the moving cause, for it cannot make a saw of wool or wood.

If, then, it is possible to make the same thing from different matter, clearly the art, i.e. the moving principle, is the same; for if both the matter and the mover are different, so too is the product.

So whenever we inquire what the cause is, since there are causes in several senses, we must state all the possible causes.

E.g., what is the material cause of a man? The menses. What is the moving cause? The semen. What is the formal cause? The essence. What is the final cause? The end.

(But perhaps both the latter are the same.) We must, however, state the most proximate causes. What is the matter? Not fire or earth, but the matter proper to man.

Thus as regards generable natural substances we must proceed in this manner, if we are to proceed correctly; that is, if the causes are these and of this number, and it is necessary to know the causes. But in the case of substances which though natural are eternal the principle is different. For presumably some of them have no matter; or no matter of this kind, but only such as is spatially mobile.

Moreover, things which exist by nature but are not substances have no matter; their substrate is their substance. E.g., what is the cause of an eclipse; what is its matter? It has none; it is the moon which is affected. What is the moving cause which destroys the light? The earth. There is probably no final cause. The formal cause is the formula; but this is obscure unless it includes the efficient cause.

E.g., what is an eclipse? A privation of light; and if we add "caused by the earth's intervention," this is the definition which includes the cause. In the case of sleep it is not clear what it is that is proximately affected. Is it the animal? Yes; but in respect of what, and of what proximately? The heart, or some other part. Again, by what is it affected? Again, what is the affection which affects that part, and not the whole animal? A particular kind of immobility?

Yes; but in virtue of what affection of the proximate subject is it this?

Since some things both are and are not, without being liable to generation and destruction

—e.g. points,

if they exist at all; and in general the forms and shapes of things (because white does not come to be, but the wood becomes white, since everything which comes into being comes from something and becomes something)—not all the contraries

can be generated from each other. White is not generated from black in the same way as a white man is generated from a black man; nor does everything contain matter, but only such things as admit of generation and transformation into each other.

And such things as, without undergoing a process of change, both are and are not, have no matter.

There is a difficulty in the question how the matter of the individual is related to the contraries. E.g., if the body is potentially healthy, and the contrary of health is disease, is the body potentially both healthy and diseased? And is water potentially wine and vinegar? Probably in the one case it is the matter in respect of the positive state and form, and in the other case in respect of privation and degeneration which is contrary to its proper nature.

There is also a difficulty as to why wine is not the matter of vinegar, nor potentially vinegar (though vinegar comes from it), and why the living man is not potentially dead. In point of fact they are not; their degeneration is accidental,

and the actual matter of the living body becomes by degeneration the potentiality and matter of the dead body, and water the matter of vinegar; for the one becomes the other just as day becomes night.

All things which change reciprocally in this way must return into the matter; e.g., if a living thing is generated from a dead one, it must first become the matter, and then a living thing; and vinegar must first become water, and then wine.

With regard to the difficulty which we have described

in connection with definitions and numbers, what is the cause of the unification? In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some

; inasmuch as even in bodies sometimes contact is the cause of their unity, and sometimes viscosity or some other such quality.

But a definition is

account, not by connection, like the Iliad , but because it is a definition of one thing.

What is it, then, that makes "man" one thing, and why does it make him one thing and not many, e.g. "animal" and "two-footed," especially if, as some say, there is an Idea of "animal" and an Idea of "two-footed"?

Why are not these Ideas "man," and why should not man exist by participation, not in any "man," but in two Ideas, those of "animal" and "two-footed"?

And in general "man" will be not one, but two things—"animal" and "two-footed." Evidently if we proceed in this way, as it is usual to define and explain, it will be impossible to answer and solve the difficulty.

But if, as we maintain, man is part matter and part form—the matter being potentially, and the form actually man—, the point which we are investigating will no longer seem to be a difficulty. For this difficulty is just the same as we should have if the definition of X

were "round bronze"; for this name would give a clue to the formula, so that the question becomes "what is the cause of the unification of 'round' and 'bronze'?"

The difficulty is no longer apparent, because the one is matter and the other form. What then is it (apart from the active cause) which causes that which exists potentially to exist actually in things which admit of generation? There

no other cause of the potential sphere's being an actual sphere; this was the essence of each.

Some matter is intelligible and some sensible, and part of the formula is always matter and part actuality; e.g., the circle is a plane figure.

But such thing

as have no matter, neither intelligible nor sensible, are ipso facto each one of them essentially something one;

just as they are essentially something existent: an individual substance, a quality, or a quantity. Hence neither "existent" nor "one" is present in their definitions. And their essence is ipso facto something one, just as it is something existent.

Hence also there is no other cause of the unity of any of these things, or of their existence; for each one of them is one and "existent" not because it is contained in the genus "being" or "unity," nor because these genera exist separately apart from their particulars, but ipso facto.

It is because of this difficulty that some thinkers

speak of "participation," and raise the question of what is the cause of participation, and what participation means; and others speak of "communion"; e.g., Lycophron

says that knowledge is a communion of the soul with "knowing"; and others call life a combination or connection of soul with body.

The same argument, however, applies in every case; for "being healthy" will be the "communion" or "connection" or "combination" of soul and health; and "being a bronze triangle" a "combination" of bronze and triangle; and "being white" a "combination" of surface and whiteness. The reason for this is that people look for a unifying formula, and a difference, between potentiality and actuality.

But, as we have said,

the proximate matter and the shape are one and the same; the one existing potentially, and the other actually.

Therefore to ask the cause of their unity is like asking the cause of unity in general; for each individual thing is one, and the potential and the actual are in a sense one. Thus there is no cause other than whatever initiates the development from potentiality to actuality. And such things as have no matter are all, without qualification, essential unities.

We have now dealt with Being in the primary sense, to which all the other categories of being are related; i.e. substance. For it is from the concept of substance that all the other modes of being take their meaning; both quantity and quality and all other such terms; for they will all involve the concept of substance, as we stated it in the beginning of our discussion.

And since the senses of being are analyzable

not only into substance or quality or quantity, but also in accordance with potentiality and actuality and function, let us also gain a clear understanding about potentiality and actuality; and first about potentiality in the sense which is most proper to the word, but not most useful for our present purpose—

for potentiality and actuality extend beyond the sphere of terms which only refer to motion.

When we have discussed this sense of potentiality we will, in the course of our definitions of actuality,

explain the others also.

We have made it plain elsewhere

that "potentiality" and "can" have several senses.

All senses which are merely equivocal may be dismissed; for some are used by analogy, as in geometry,

and we call things possible or impossible because they "are" or "are not" in some particular way. But the potentialities which conform to the same type are all principles, and derive their meaning from one primary sense of potency, which is the source of change in some other thing, or in the same thing qua other.

One kind of potentiality is the power of being affected; the principle in the patient itself which initiates a passive change in it by the action of some other thing, or of itself qua other. Another is a positive state of impassivity in respect of deterioration or destruction by something else or by itself qua something else; i.e. by a transformatory principle—for all these definitions contain the formula of the primary sense of potentiality.

Again, all these potentialities are so called either because they merely act or are acted upon in a particular way, or because they do so

. Hence in their formulae also the formulae of potentiality in the senses previously described are present in some degree.

Clearly, then, in one sense the potentiality for acting and being acted upon is one

(for a thing is "capable" both because it itself possesses the power of being acted upon, and also because something else has the power of being acted upon by it);

and in another sense it is not; for it is partly in the patient (for it is because it contains a certain principle, and because even the matter is a kind of principle, that the patient is acted upon; i.e., one thing is acted upon by another: oily stuff is inflammable, and stuff which yields in a certain way is breakable, and similarly in other cases)—

and partly in the agent; e.g. heat and the art of building: the former in that which produces heat, and the latter in that which builds. Hence in so far as it is a natural unity, nothing is acted upon by itself; because it is one, and not a separate thing.

"Incapacity" and "the incapable" is the privation contrary to "capacity" in this sense; so that every "capacity" has a contrary incapacity for producing the same result in respect of the same subject.

Privation has several senses

—it is applied (1.) to anything which does not possess a certain attribute; (2.) to that which would naturally possess it, but does not; either (a) in general, or (b) when it would naturally possess it; and either (1) in a particular way, e.g. entirely, or (2) in any way at all. And in some cases if things which would naturally possess some attribute lack it as the result of constraint, we say that they are "deprived."

Since some of these principles are inherent in inanimate things, and others in animate things and in the soul and in the rational part of the soul,

it is clear that some of the potencies also will be irrational and some rational. Hence all arts, i.e. the productive sciences, are potencies; because they are principles of change in another thing, or in the artist himself qua other.

Every rational potency admits equally of contrary results, but irrational potencies admit of one result only. E.g., heat can only produce heat, but medical science can produce disease and health. The reason of this is that science is a rational account, and the same account explains both the thing and its privation, though not in the same way; and in one sense it applies to both, and in another sense rather to the actual fact.

Therefore such sciences must treat of contraries—essentially of the one, and non-essentially of the other; for the rational account also applies essentially to the one, but to the other in a kind of accidental way, since it is by negation and removal that it throws light on the contrary. For the contrary is the primary privation,

and this is the removal of that to which it is contrary.

And since contrary attributes cannot be induced in the same subject, and science is a potency which depends upon the possession of a rational formula, and the soul contains a principle of motion, it follows that whereas "the salutary" can only produce health, and "the calefactory" only heat, and "the frigorific" only cold,

the scientific man can produce both contrary results.

For the rational account includes both, though not in the same way; and it is in the soul, which contains a principle of motion, and will therefore, by means of the same principle, set both processes in motion, by linking them with the same rational account. Hence things which have a rational potency produce results contrary to those of things whose potency is irrational

; for the results of the former are included under one principle, the rational account.

It is evident also that whereas the power of merely producing (or suffering) a given effect is implied in the power of producing that effect

, the contrary is not always true; for that which produces an effect well must also produce it, but that which merely produces a given effect does not necessarily produce it well.

There are some, e.g. the Megaric school,

who say that a thing only has potency when it functions, and that when it is not functioning it has no potency. E.g., they say that a man who is not building cannot build, but only the man who is building, and at the moment when he is building; and similarly in the other cases.

It is not difficult to see the absurd consequences of this theory. Obviously a man will not be a builder unless he is building, because "to be a builder" is "to be capable of building"; and the same will be true of the other arts.

If, therefore, it is impossible to possess these arts without learning them at some time and having grasped them,

and impossible not to possess them without having lost them at some time (through forgetfulness or some affection or the lapse of time; not, of course, through the destruction of the object of the art,

because it exists always), when the artist ceases to practice his art, he will not possess it;

and if he immediately starts building again, how will he have re-acquired the art?

The same is true of inanimate things. Neither the cold nor the hot nor the sweet nor in general any sensible thing will exist unless we are perceiving it (and so the result will be that they are affirming Protagoras' theory

). Indeed, nothing will have the faculty of sensation unless it is perceiving, i.e. actually employing the faculty.

If, then, that is blind which has not sight, though it would naturally have it, and when it would naturally have it, and while it still exists, the same people will be blind many times a day; and deaf too.

Further, if that which is deprived of its potency is incapable, that which is not happening will be incapable of happening; and he who says that that which is incapable of happening

or

, will be in error, for this is what "incapable" meant.

Thus these theories do away with both motion and generation; for that which is standing will always stand, and that which is sitting will always sit; because if it is sitting it will not get up, since it is impossible that anything which is incapable of getting up should get up.

Since, then, we cannot maintain this, obviously potentiality and actuality are different. But these theories make potentiality and actuality identical;

hence it is no small thing that they are trying to abolish.

Thus it is possible that a thing may be capable of being and yet not be, and capable of not being and yet be; and similarly in the other categories that which is capable of walking may not walk, and that which is capable of not walking may walk.

A thing is capable of doing something if there is nothing impossible in its having the actuality of that of which it is said to have the potentiality. I mean, e.g., that if a thing is capable of sitting and is not prevented from sitting, there is nothing impossible in its actually sitting; and similarly if it is capable of being moved or moving or standing or making to stand or being or becoming or not being or not becoming.

The term "actuality," with its implication of "complete reality," has been extended from motions, to which it properly belongs, to other things; for it is agreed that actuality is properly motion.

Hence people do not invest non-existent things with motion, although they do invest them with certain other predicates. E.g., they say that non-existent things are conceivable and desirable, but not that they are in motion. This is because, although these things do not exist actually, they will exist actually;

for some non-existent things exist potentially; yet they do not exist, because they do not exist in complete reality.

Now if, as we have said, that is possible which does not involve an impossibility, obviously it cannot be true to say that so-and-so is possible, but will not be, this view entirely loses sight of the instances of impossibility.

I mean, suppose that someone—i.e. the sort of man who does not take the impossible into account—were to say that it is possible to measure the diagonal of a square, but that it will not be measured, because there is nothing to prevent a thing which is capable of being or coming to be from neither being nor being likely ever to be.

But from our premisses this necessarily follows: that if we are to assume that which is not, but is possible, to be or to have come to be, nothing impossible must be involved. But in this case something impossible will take place; for the measuring of the diagonal is impossible.

The false is of course not the same as the impossible; for although it is false that you are now standing, it is not impossible.

At the same time it is also clear that if B must be real if A is, then if it is possible for A to be real, it must also be possible for B to be real; for even if B is not necessarily possible, there is nothing to prevent its being possible. Let A, then, be possible. Then when A was possible, if A was assumed to be real, nothing impossible was involved; but B was necessarily real too.

But ex hypothesi B was impossible. Let B be impossible.

Then if B is impossible, A must also be impossible. But A was by definition possible. Therefore so is B.

If, therefore, A is possible, B will also be possible; that is if their relation was such that if A is real, B must be real.

Then if, A and B being thus related, B is not possible on this condition, A and B will not be related as we assumed; and if when A is possible B is necessarily possible, then if A is real B must be real too. For to say that B must be possible if A is possible means that if A is real at the time when and in the way in which it was assumed that it was possible for it to be real, then B must be real at that time and in that way.

Since all potencies are either innate, like the senses, or acquired by practice, like flute-playing, or by study, as in the arts, some—such as are acquired by practice or a rational formula—we can only possess when we have first exercised them

; in the case of others which are not of this kind and which imply passivity, this is not necessary.

Since anything which is possible is something possible at some time and in some way, and with any other qualifications which are necessarily included in the definition; and since some things can set up processes rationally and have rational potencies, while others are irrational and have irrational potencies; and since the former class can only belong to a living thing, whereas the latter can belong both to living and to inanimate things: it follows that as for potencies of the latter kind, when the agent and the patient meet in accordance with the potency in question, the one must act and the other be acted upon; but in the former kind of potency this is not necessary, for whereas each single potency of the latter kind is productive of a single effect, those of the former kind are productive of contrary effects,

so that one potency will produce at the same time contrary effects.

But this is impossible. Therefore there must be some other deciding factor, by which I mean

or

. For whichever of two things an animal desires decisively it will do, when it is in circumstances appropriate to the potency and meets with that which admits of being acted upon. Therefore everything which is rationally capable, when it desires something of which it has the capability, and in the circumstances in which it has the capability, must do that thing.

Now it has the capability when that which admits of being acted upon is present and is in a certain state; otherwise it will not be able to act. (To add the qualification "if nothing external prevents it" is no longer necessary; because the agent has the capability in so far as it is a capability of acting; and this is not in all, but in certain circumstances, in which external hindrances will be excluded;

for they are precluded by some of the positive qualifications in the definition.)

Hence even if it wishes or desires to do two things or contrary things simultaneously, it will not do them, for it has not the capability to do them under these conditions, nor has it the capability of doing things simultaneously, since it will only do the things to which the capability applies and under the appropriate conditions.

Since we have now dealt with the kind of potency which is related to motion, let us now discuss actuality; what it is, and what its qualities are. For as we continue our analysis it will also become clear with regard to the potential that we apply the name not only to that whose nature it is to move or be moved by something else, either without qualification or in some definite way, but also in other senses; and it is on this account that in the course of our inquiry we have discussed these as well.

"Actuality" means the presence of the thing, not in the sense which we mean by "potentially." We say that a thing is present potentially as Hermes is present in the wood, or the half-line in the whole, because it can be separated from it; and as we call even a man who is not studying "a scholar" if he is capable of studying. That which is present in the opposite sense to this is present actually.

What we mean can be plainly seen in the particular cases by induction; we need not seek a definition for every term, but must comprehend the analogy: that as that which is actually building is to that which is capable of building,

so is that which is awake to that which is asleep; and that which is seeing to that which has the eyes shut, but has the power of sight; and that which is differentiated out of matter to the matter; and the finished article to the raw material.

Let actuality be defined by one member of this antithesis, and the potential by the other.

But things are not all said to exist actually in the same sense, but only by analogy—as A is in B or to B, so is C in or to D; for the relation is either that of motion to potentiality, or that of substance to some particular matter.

Infinity and void and other concepts of this kind are said to "be" potentially or actually in a different sense from the majority of existing things, e.g. that which sees, or walks, or is seen.

For in these latter cases the predication may sometimes be truly made without qualification, since "that which is seen" is so called sometimes because it is seen and sometimes because it is capable of being seen; but the Infinite does not exist potentially in the sense that it will ever exist separately in actuality; it is separable only in knowledge. For the fact that the process of division never ceases makes this actuality exist potentially, but not separately.

Since no action which has a limit is an end, but only a means to the end, as, e.g., the process of thinning;

and since the parts of the body themselves, when one is thinning them, are in motion in the sense that they are not already that which it is the object of the motion to make them, this process is not an action, or at least not a complete one, since it is not an end; it is the process which includes the end that is an action.

E.g., at the same time we see and have seen, understand and have understood, think and have thought; but we cannot at the same time learn and have learnt, or become healthy and be healthy. We are living well and have lived well, we are happy and have been happy, at the same time; otherwise the process would have had to cease at some time, like the thinning-process; but it has not ceased at the present moment; we both are living and have lived.

Now of these processes we should call the one type motions, and the other actualizations.

Every motion is incomplete—the processes of thinning, learning, walking, building—these are motions, and incomplete at that. For it is not the same thing which at the same time is walking and has walked, or is building and has built, or is becoming and has become, or is being moved and has been moved, but two different things; and that which is causing motion is different from that which has caused motion.

But the same thing at the same time is seeing and has seen, is thinking and has thought. The latter kind of process, then, is what I mean by actualization, and the former what I mean by motion.

What the actual is, then, and what it is like, may be regarded as demonstrated from these and similar considerations.

We must, however, distinguish when a particular thing exists potentially, and when it does not; for it does not so exist at any and every time.

E.g., is earth potentially a man? No, but rather when it has already become semen,

and perhaps not even then; just as not

can be healed by medicine, or even by chance, but there is some definite kind of thing which is capable of it, and this is that which is potentially healthy.

The definition of that which as a result of thought comes, from existing potentially, to exist actually, is that, when it has been willed, if no external influence hinders it, it comes to pass; and the condition in the case of the patient, i.e. in the person who is being healed, is that nothing in him should hinder the process. Similarly a house exis