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 The questions discussed in chs. 10-12 arise out of the consideration of essence as definition. 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 i.e.
written on a waxed tablet. 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 Which implies soul. ); 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, Cf. Aristot. Met. 5.1.1. 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 this particular formula and this 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, i.e., something very similar to the Platonic "intermediates." Cf.
Introduction. 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. See Aristot. Met. 13.2, 3. 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 absolutely prior. For if the soul also is the animal or living thing, or the soul of the individual is the individual, and "being a circle" is the circle, and "being a right angle" or the essence of the right angle is 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 when, some thinkers The Pythagoreans. 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 The distinction seems to be that given in Aristot. Met.
8.3.1. Some held that the line, considered absolutely, is simply "twoness"; others that it is "twoness in length."; 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 Cf. Aristot. Met. 1.5.17. ), 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 A "disciple" of the great Socrates; one of the speakers in the Politicus Plat. Stat. and referred to in Plat. Theaet. 147c, Plat. Soph.
218b. 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 any 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 Aristot. Met. 7.10.17. —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 this soul and this 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. In Books 13 and 14. 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. Aristot. Met. 8.6. 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. Chapters. 10-11; and cf. Aristot. Met. 7.4. 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 Aristot. An.
Post. 92a 29. 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 The other type of definition, that which states the constituent parts of a thing, is not discussed here. 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 Chs.
4-5.,10-12. and the substrate Ch. 3.; 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 The Platonists. 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 i.e., the argument in ch. 3 will apply to this case also.; 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." See note on Aristot. Met.
1.9.3. 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. Cf. Aristot. De Caelo 303a 6, Aristot. De Gen. et Corr. 325a 35. 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 actually 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, Aristot. Met. 7.5.5-7. 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. Aristot. Met. 7.15, Aristot. Met.
8.6. 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 being destroyed, since neither does it so admit of generation (for the essence of house is not generated, but only the essence of this house); formulae are, and are not, independently of generation and destruction; for it has been shown Cf. Aristot. Met.
7.8.3. 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 statement has only been implied in the preceding arguments. 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 sc. in the night. 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 thing —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 e.g. wasps, bees, tortoises ( P. Nat. 467a 18, 468a 25 ). 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. i.e., it is only when they do