1042aWe 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.² And 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.⁵ And 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, 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.⁸ As 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. 1042bSimilarly, 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); 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, 1043aand 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 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; 1043bbecause 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, 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; 1044aso 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.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.