by Aristotle
Let this, then, suffice to show that the most indisputable of all beliefs is that contradictory statements are not at the same time true, and what consequences follow from the denial of this belief, and why people do deny it. Now since it is [15] impossible that contradictories should be at the same time true of the same thing, obviously contraries also cannot belong at the same time to the same thing. For of the contraries, no less than of the contradictories, one is a privation—and a privation of substance; and privation is the denial of a predicate to a determinate genus. If, then, it is impossible to affirm and deny truly at the same time, it is also [20] impossible that contraries should belong to a subject at the same time, unless both belong to it in particular relations, or one in a particular relation and one without qualification.
7 · But on the other hand there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate. This is clear, in the first place, if we define what the true and the false are. To say of what is [25] that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true; so that he who says of anything that it is, or that it is not, will say either what is true or what is false; but neither what is nor what is not is said to be or not to be.—Again, either the intermediate between the contradictories [30] will be so in the way in which grey is between black and white, or as that which is neither man nor horse is between man and horse. If it were of the latter kind, it could not change, for change is from not-good to good, or from good to not-good; but as a matter of fact it evidently always does, for there is no change except to opposites and to their intermediate. But if it is really intermediate, in this way too there is a difficulty—there would have to be a change to white, which was not [1012a1] from not-white; but as it is, this is never seen.—Again, the understanding either affirms or denies every object of understanding or reason—this is obvious from the definition—whenever it is true or false. When it connects in one way by assertion or negation, it is true, and when it does so in the other way, it is false.—Again, there [5] must be an intermediate between all contradictories, if one is not arguing merely for the sake of argument; so that it will be possible for a man to say what is neither true nor untrue. And there will be a middle between that which is and that which is not, so that there will also be a kind of change intermediate between generation and destruction.—Again, in all classes in which the negation of an attribute means the [10] assertion of its contrary, even in these there will be an intermediate; for instance, in the sphere of numbers there will be number which is neither odd nor not-odd. But this is impossible, as is obvious from the definition.—Again, the process will go on ad infinitum, and the number of realities will be not only made half as great again, but even greater. For again it will be possible to deny this intermediate with reference both to its assertion and to its negation, and this new term will be some [15] definite thing; for its substance is something different.—Again, when a man, on being asked whether a thing is white, says ‘no’, he has denied nothing except that it is; and its not being is a negation.
Some people have acquired this opinion as other paradoxical opinions have been acquired; when men cannot refute eristical arguments, they give in to the [20] argument and agree that the conclusion is true. This, then, is why some argue in such fashion; others do so because they demand a reason for everything. And the starting-point in dealing with all such people is definition. Now the definition rests on the necessity of their meaning something; for the formula, of which the word is a [25] sign, becomes its definition.—The doctrine of Heraclitus, that all things are and are not, seems to make everything true, while that of Anaxagoras, that there is an intermediate between the terms of a contradiction, seems to make everything false; for when things are mixed, the mixture is neither good nor not-good, so that one cannot say anything that is true.
8 · In view of these distinctions it is obvious that the one-sided theories which [30] some people express about all things cannot be valid—on the one hand the theory that nothing is true (for, they say, there is nothing to prevent every statement from being like the statement ‘the diagonal of a square is commensurate with the side’),—on the other hand the theory that everything is true.—These views are practically the same as that of Heraclitus; for that which says that all things are true and all are false also makes each of these statements separately, so that since [1012b1] they are impossible, the double statement must be impossible too.—Again, there are obviously contradictories which cannot be at the same time true. Nor on the other hand can all statements be false; yet this would seem more possible in view of [5] what has been said.—But against all such arguments we must postulate, as we said above, not that something is or is not, but that people mean something, so that we must argue from a definition, having got what falsity or truth means. If that which it is true to affirm is nothing other than that which it is false to deny, it is impossible [10] that all statements should be false; for one side of the contradiction must be true.—Again, if it is necessary with regard to everything either to assert or to deny it, it is impossible that both should be false; for it is one side of the contradiction that is false.—Further, all such arguments are exposed to the often-expressed objection, [15] that they destroy themselves. For he who says that everything is true makes the statement contrary to his own also true, so that his own is not true (for the contrary statement denies that it is true), while he who says everything is false makes himself also false.—And if the former person excepts the contrary statement, saying it alone is not true, while the latter excepts his own as being alone not false, none the less they are driven to postulate the truth or falsehood of an infinite number of [20] statements; for that which says the true statement is true, is true, and this process will go on to infinity.
Evidently again those who say all things are at rest are not right, nor are those who say all things are in movement. For if all things are at rest, the same statements will always be true and the same always false,—but they obviously are not; for he [25] who makes a statement himself at one time was not and again will not be. And if all things are in motion, nothing will be true; everything therefore will be false. But it has been shown that this is impossible. Again, it must be that which is that changes; for change is from something to something. But again it is not the case that all things are at rest or in motion sometimes, and nothing for ever; for there is [30] something which always moves the things that are in motion, and the first mover must itself be unmoved.
BOOK V (Δ)
1 · We call an origin1 (1) that part of a thing from which one would start first, e.g. a line or a road has an origin in either of the contrary directions. (2) That from which each thing would best be originated, e.g. we must sometimes begin to [1013a1] learn not from the first point and the origin of the thing, but from the point from which we should learn most easily. (3) That from which (as an immanent part) a thing first arises, e.g. as the keel of a ship and the foundation of a house, while in [5] animals some suppose the heart, others the brain, others some other part, to be of this nature. (4) That from which (not as an immanent part) a thing first arises, and from which the movement or the change naturally first proceeds, as a child comes from the father and the mother, and a fight from abusive language. (5) That by whose choice that which is moved is moved and that which changes changes, e.g. the [10] magistracies in cities, and oligarchies and monarchies and tyrannies, are called origins, and so are the arts, and of these especially the architectonic arts. (6) That from which a thing can first be known; for this also is called the origin of the thing, [15] e.g. the hypotheses are the origins of demonstrations. (Causes are spoken of in an equal number of senses; for all causes are origins.) It is common, then, to all to be the first point from which a thing either is or comes to be or is known; but of these some are immanent in the thing and others are outside. Therefore the nature of a thing is an origin, and so are the el
ements of a thing, and thought and choice, and [20] substance, and that for the sake of which—for the good and the beautiful are the origin both of the knowledge and of the movement of many things.
2 · We call a cause (1) that from which (as immanent material) a thing [25] comes into being, e.g. the bronze of the statue and the silver of the saucer, and the classes which include these. (2) The form or pattern, i.e. the formula of the essence, and the classes which include this (e.g. the ratio 2:1 and number in general are causes of the octave) and the parts of the formula. (3) That from which the change [30] or the freedom from change first begins, e.g. the man who has deliberated is a cause, and the father a cause of the child, and in general the maker a cause of the thing made and the change-producing of the changing. (4) The end, i.e. that for the sake of which a thing is, e.g. health is the cause of walking. For why does one walk? We [35] say ‘in order that one may be healthy’, and in speaking thus we think we have given the cause. The same is true of all the means that intervene before the end, when [1013b1] something else has put the process in motion (as e.g. thinning or purging or drugs or instruments intervene before health is reached); for all these are for the sake of the end, though they differ from one another in that some are instruments and others are actions.
These, then, are practically all the senses in which causes are spoken of, and as [5] they are spoken of in several senses it follows that there are several causes of the same thing, and in no accidental sense, e.g. both the art of sculpture and the bronze are causes of the statue not in virtue of anything else but qua statue; not, however, in the same way, but the one as matter and the other as source of the movement. And [10] things can be causes of one another, e.g. exercise of good condition, and the latter of exercise; not, however, in the same way, but the one as end and the other as source of movement.—Again, the same thing is sometimes cause of contraries; for that which when present causes a particular thing, we sometimes charge, when absent, with the contrary, e.g. we impute the shipwreck to the absence of the steersman, [15] whose presence was the cause of safety; and both—the presence and the privation—are causes as sources of movement.
All the causes now mentioned fall under four senses which are the most obvious. For the letters are the causes of syllables, and the material is the cause of manufactured things, and fire and earth and all such things are the causes of bodies, [20] and the parts are causes of the whole, and the hypotheses are causes of the conclusion, in the sense that they are that out of which these respectively are made; but of these some are cause as substratum (e.g. the parts), others as essence (the whole, the synthesis, and the form). The semen, the physician, the man who has deliberated, and in general the agent, are all sources of change or of rest. The [25] remainder are causes as the end and the good of the other things; for that, for the sake of which other things are, is naturally the best and the end of the other things; let us take it as making no difference whether we call it good or apparent good.
These, then, are the causes, and this is the number of their kinds, but the [30] varieties of causes are many in number, though when summarized these also are comparatively few. Causes are spoken of in many senses, and even of those which are of the same kind some are causes in a prior and others in a posterior sense, e.g. both the physician and the professional man are causes of health, and the ratio 2:1 and number are causes of the octave, and the classes that include any particular cause are always causes of the particular effect. Again, there are accidental causes and the classes which include these, e.g. while in one sense the sculptor causes the [35] statue, in another sense Polyclitus causes it, because the sculptor happens to be Polyclitus; and the classes that include the accidental cause are also causes, e.g. a [1014a1] man—or in general an animal—is the cause of the statue, because Polyclitus is a man, and a man is an animal. Of accidental causes also some are more remote or nearer than others, as, for instance, if the white and the musical were called causes [5] of the statue, and not only Polyclitus or a man. But besides all these varieties of causes, whether proper or accidental, some are called causes as being able to act, others as acting, e.g. the cause of the house’s being built is the builder, or the builder when building.—The same variety of language will be found with regard to the [10] effects of causes, e.g. a thing may be called the cause of this statue or of a statue or in general of an image, and of this bronze or of bronze or of matter in general; and similarly in the case of accidental effects. Again, both accidental and proper causes may be spoken of in combination, e.g. we may say not ‘Polyclitus’ nor ‘the sculptor’, [15] but ‘Polyclitus the sculptor’.
Yet all these are but six in number, while each is spoken of in two ways; for (1) they are causes either as the individual, or as the class that includes the individual, or as the accidental, or as the class that includes the accidental, and these either as combined, or as taken simply; and (2) all may be taken as acting or as having a capacity. But they differ inasmuch as the acting causes and the individuals exist, or [20] do not exist, simultaneously with the things of which they are causes, e.g. this particular man who is curing, with this particular man who is recovering health, and this particular builder with this particular thing that is being built; but this is not always so with potential causes; for the house does not perish at the same time as the builder. [25]
3 · We call an element that which is the primary component immanent in a thing, and indivisible in kind into other kinds, e.g. the elements of speech are the parts of which speech consists and into which it is ultimately divided, while they are no longer divided into other forms of speech different in kind from them. If they are divided, their parts are of the same kind, as a part of water is water (while a part of [30] the syllable is not a syllable). Similarly those who speak of the elements of bodies mean the things into which bodies are ultimately divided, while they are no longer divided into other things differing in kind; and whether the things of this sort are one or more, they call these elements. The elements of geometrical proofs, and in [35] general the elements of demonstrations, have a similar character; for the primary demonstrations, each of which is implied in many demonstrations, are called [1014b1] elements of demonstrations; and the primary deductions, which have three terms and proceed by means of one middle, are of this nature.
People also transfer the word ‘element’ from this meaning and apply it to that which, being one and small, is useful for many purposes; for which reason the small [5] and simple and indivisible is called an element. Hence come the facts that the most universal things are elements (because each of them being one and simple is present in a plurality of things, either in all or in as many as possible), and that unity and the point are thought by some to be first principles. Now, since the so-called genera are [10] universal and indivisible (for there is no formula of them), some say the genera are elements, and more so than the differentia, because the genus is more universal; for where the differentia is present, the genus accompanies it, but where the genus is, the differentia is not always. It is common to all the meanings that the element of [15] each thing is the first component immanent in each.
4 · We call nature (1) the genesis of growing things—the meaning which would be suggested if one were to pronounce the υ in φὑσις long. (2) The primary immanent element in a thing, from which its growth proceeds. (3) The source from which the primary movement in each natural object is present in it in virtue of its [20] own essence. Those things said to grow which derive increase from something else by contact and organic unity, or organic adhesion as in the case of embryos. Organic unity differs from contact; for in the latter case there need not be anything besides the contact, but in organic unities there is something identical in both parts, which [25] makes them grow together instead of merely touching, and be one in respect of continuity and quantity, though not of quality.—(4) Nature is the primary matter of which any non-natural object consists or out of which it is made, which cannot be modified or changed from its own potency,
as e.g. bronze is said to be the nature of a [30] statue and of bronze utensils, and wood the nature of wooden things; and so in all other cases; for when a product is made out of these materials, the first matter is preserved throughout. In this way people call the elements of natural objects also their nature, some naming fire, others earth, others air, others water, others [35] something else of the sort, and some naming more than one of these, and others all of them.—(5) Nature is the substance of natural objects, as with those who say the [1015a1] nature is the primary mode of composition, or as Empedocles says:—