[1042a] [3]

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 said1 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.2And arguments show that there are yet other substances: the essence and the substrate.3 Again, from another point of view, the genus is more nearly substance than the species, and the universal than the particulars4; 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.5And since the essence is substance, and definition is the formula of the essence, we have therefore systematically examined definition and essential predication.6 And since the definition is a formula, and the formula has parts, [20] 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.7 Further, then, neither the universal nor the genus is substance.8As for the Ideas and the objects of mathematics (for some say that these exist apart from sensible substances) we must consider them later.9 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,10 and is separable in an unqualified sense—for of substances in the sense of formula some are separable11 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 place , that which is now in one place and subsequently in another; and if the change is of magnitude , that which is now of such-and-such a size, and subsequently smaller or greater; and if the change is of quality , that which is now healthy and subsequently diseased. [1042b] [1] Similarly, if the change is in respect of being , there is something which is now in course of generation, and subsequently in course of destruction, and which is the underlying substrate, now as this individual thing, and subsequently as deprived of its individuality. In this last process of change the others are involved, but in either one or two12 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.13 The difference between absolute and qualified generation has been explained in the Physics.14

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 Democritus15 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); [20] and others by place <or direction>, 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, [1043a] [1] 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, [20] while that which involves the constituent parts is rather that of the matter. The same is true of the kind of definitions which Archytas16 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”17; 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; [1043b] [1] 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,18 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” plus “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 elsewhere19 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 clear20; only it is clear that this is impossible in some cases, [20] i.e. in the case of all things which cannot exist apart from the particular instances; e.g. house or implement.21 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 Antisthenes22 and others similarly unlearned has a certain application; I mean the difficulty that it is impossible to define what a thing is (for the definition, they say, is a lengthy formula), but it is possible actually to teach others what a thing is like; e.g., we cannot say what 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 some23 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; [1044a] [1] so neither the definition nor the essence will continue to exist if something is subtracted from or added to it. And © 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.24

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 causes25; 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— [20] 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. [1044b] [1] (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.26Moreover, 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 <efficient> 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? [20] 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 destruction27—e.g. points,28 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 contraries29 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, [1045a] [1] 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 described30 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 cause ; 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 one 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”? [20] 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 X31 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 is no other cause of the potential sphere's being an actual sphere; this was the essence of each.32

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.33 But such thing34 as have no matter, neither intelligible nor sensible, are ipso facto each one of them essentially something one; [1045b] [1] 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 thinkers35 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., Lycophron36 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,37 the proximate matter and the shape are one and the same; the one existing potentially, and the other actually. [20] 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.

1 Cf. Aristot. Met. 7.1.

2 Cf. Aristot. Met. 7.2.

3 Cf. Aristot. Met. 7.3-4.

4 Cf. Aristot. Met. 7.13.

5 Cf. Aristot. Met. 7.14.

6 Cf. Aristot. Met. 7.4-6, 12, 15.

7 Cf. Aristot. Met. 7.10, 11.

8 Cf. Aristot. Met. 7.13, 16.

9 Books 13 and 14.

10 Cf. Aristot. Met. 7.8.

11 In point of fact the only form which is absolutely separable is Mind or Reason. Cf. Aristot. Met. 12.7, 9.

12 i.e., locomotion does not involve substantial change; alteration may or may not involve it (in Aristot. Met. 9.8.17 we find that it does not); increase or decrease does involve it.

13 e.g., the heavenly bodies, though imperishable, can move in space (Aristot. Met. 8.4.7, Aristot. Met. 12.2.4).

14 Aristot. Phys. 225a 12-20; cf. Aristot. De Gen. et Corr. 317a 17-31.

15 Cf. Aristot. Met. 1.4.11.

16 A celebrated Pythagorean, contemporary with Plato.

17 Cf. Aristot. Met. 7.11.6.

18 Cf. Plat. Theaet. 204aff.

19 Cf. Aristot. Met. 7.8.

20 Cf. Aristot. Met. 8.1.6. n..

21 Cf. Aristot. Met. 7.8.6.

22 Cf. Aristot. Met. 5.29.4.

23 Aristotle is referring to the Pythagoreans and Platonists, but seems as usual to misrepresent their views. His object in this section is to show that the relation of number to substance is only one of analogy. Cf. Aristot. Met. 13.6, 7, and see Introduction.

24 In Aristot. Categories 3b 33-4a 9 Aristotle does not allow this exception.

25 i.e. from prime matter or the four elements.

26 Cf. Aristot. Met. 8.1.8 n.

27 Cf. Aristot. Met. 6.3.1, Aristot. Met. 7.8.3.

28 Cf. Aristot. Met. 3.5.8, 9.

29 i.e., we must distinguish “contraries” in the sense of “contrary qualities” from “contraries” in the sense of “things characterized by contrary qualities.”

30 Aristot. Met. 7.12, Aristot. Met. 8.3.10, 11.

31 Literally “cloak”; cf. Aristot. Met. 7.4.7 n.

32 i.e., it was the essence of the potential sphere to become the actual sphere, and of the actual sphere to be generated from the potential sphere.

33 Even formulae contain matter in a sense (“intelligible matter”); i.e. the generic element in the species. “Plane figure” is the generic element of “circle.”

34 The highest genera, or categories.

35 The Platonists.

36 A sophist, disciple of Gorgias.

37 Cf. sects. 4, 5.