LESSON 3

The Nature of Form as Part of a Thing's Essence. The Resemblance

between Numbers and Forms

  Chapter 3: 1043a 29-1044a 14

             708. And we must not disregard the fact that sometimes it is not apparent whether a name signifies the composite substance or the actuality or form; for example, whether house signifies both the form and the matter together, i.e., a shelter composed of bricks, timbers and stones arranged in such and such a way, or whether it signifies the actuality or form--a shelter; and whether line signifies twoness in length or twoness; and whether animal signifies a soul in a body or a soul, for the latter is the substance or actuality of some body.

             709. Now animal will also apply to both, not in the sense that both are expressed by one meaning, but insofar as they are related to some one thing.

             710. These distinctions make a difference with regard to something else, but not to the investigation of sensible substances, because the essence of this other thing consists of form or actuality. For a soul and the essence of a soul are the same, but a man and the essence of a man are not the same, unless a man is also called a soul. And in some things essence and thing are identical and in others not.

             711. Accordingly, to those who make investigations it does not seem that a syllable consists of letters and their combination, nor does a house consist of bricks and their combination. And this is true, because a combination or mixture does not consist of the things of which it is the combination or mixture. Nor likewise do any of the other differences. If a threshold, for example, is constituted by its position, the position is not constituted by the threshold, but rather the latter by the former. Nor is man animal and two-footed, but there must be something else in addition to these, if these are matter. Now this is neither an element nor a combination of the elements, but the substance; but omitting this they speak only of matter. Therefore, if this is the cause of a thing's being, and this is its substance, they will not be stating its substance.

             712. Now this must be either eternal or corruptible without being in the process of corruption, and generated without being in the process of generation. But it has been demonstrated and made clear elsewhere (611) that no one produces a form, nor is it generated; but it is this particular thing which is produced and comes to be from these principles.

             713. But whether the substances of corruptible things are separable or not is not yet clear.

             714. It is evident, however, that this may not occur in the case of some things, i.e., in the case of all those that are incapable of existing apart from particular things, for example, a house or a vessel.

             715. Indeed, perhaps neither these particular things nor any of the others which are not produced by nature are substances. For at least one might hold that only the nature of corruptible things is substance.

             716. For this reason the problem which confronted Antisthenes and other uninstructed people is applicable here, i.e., that one cannot define what a thing is (for according to them the definition is a lengthy statement), but one can say what it is like; for example, one cannot say what silver is, but one can say that it is like tin. Hence, of one kind of substance there can be a limit or definition, i.e., of the composite, whether it be sensible or intelligible. But this cannot be true of the primary parts of which it is composed, since the definitive concept designates something as determining something else, and one of these must have the character of matter and the other that of form.

             717. Further, it is also clear that if numbers are in any sense substances, they are such in this way and not [as groups] of units, as some claim. For a definition is like a number and is divisible into indivisible parts, because definitions are not made up of an unlimited number of parts; and this is also true of numbers.

             718. And just as when any part constituting a number is subtracted or added it is no longer the same number that remains but a different one, even though the minimum is subtracted or added, so too neither the definition nor the essence will any longer be the same when anything is subtracted or added.

             719. And there must be something by reason of which a number is one thing, although they cannot say what makes it to be one thing; i.e., if it is one thing. For either it is not one thing but like a heap, or if it is one thing it is necessary to state what makes it to be one thing out of many. And a definition is one thing; but they are also unable to say what makes it to be one thing; and this follows as a natural consequence. For by the same argument substance is also one thing in the way we have explained, but not, as some claim, as being a kind of unit or point, but as an actuality and a kind of nature.

             720. And just as number does not admit of more or less, neither does substance in the sense of form; but if this were the case [it would be that substance which is joined] to matter.

             721. In regard to the generation and corruption of the foregoing substances, in what way this is possible and in what way it is impossible, and in regard to the likeness which they have to numbers, we have established these things this far.

COMMENTARY

             1703. Having investigated the principles of sensible substances, and having shown that sensible substances are composed of matter and form, the Philosopher's aim here is to establish the truth about the formal and material principles of things by investigating the points which must be considered about each.

             This is divided into two parts. In the first (708:C 1705), he investigates the things which must be considered about the formal principle. In the second (722:C 1729), he investigates the things which must be considered about the material principle ("Concerning material substances").

             1704. And since Plato was the one who devoted special treatment to the formal principle, therefore Aristotle deals with the formal principle in reference to those things which Plato posited. Now Plato claimed that species [i.e., separate Forms or Ideas] and numbers are the forms of things. Hence the first part is divided into two sections. In the first (708:C 1705), he deals with the formal principle in relation to the species [or Ideas]; and in the second (717:C 1722), in relation to numbers ("Further, it is also clear").

             Now Plato held four things about forms in relation to the species [or Ideas]. The first of these is that specific names signify form alone and not form with matter. The second is that form is something besides the material parts. The third is that form can neither be generated nor corrupted. The fourth is that forms are separate from sensible things.

             The first part is divided into four sections inasmuch as Aristotle investigates the four points just mentioned. The second (711:C 1712) begins where he says "Accordingly, to those." The third (712:C 1715) begins where he says "Now this must." The fourth (713:C 1717) begins where he says "But whether."

             1705. In regard to the first he does three things. First (708) he raises a question. We must understand, he says, that for some men there is the problem whether a specific name signifies the composite substance or only the form or something having the status of actuality; for example, whether the word house signifies both matter and form together so that a house means a shelter made of bricks and stones properly arranged (for shelter is as form, and bricks and stones as matter), or whether this word signifies only the actuality or form, a shelter.

             1706. Similarly, there is the problem whether the word line signifies twoness and length or twoness alone. He mentions this because the Platonists claimed that numbers are the forms of continuous quantities; for they said that a point is merely the number one having position, so that position is a sort of material principle, and the number one a formal principle. They likewise claimed that the number two is the form of a line, so that a line is merely twoness in length. Therefore the Philosopher asks whether the word line signifies twoness alone as form, or twoness grounded in length as form in matter. And again, there is the problem whether the word animal signifies a soul in a body as a form in matter, or only a soul, which is the form of an organic body.

             1707. Now animal will also apply (709).

             He shows what follows if one says that specific names are used in both senses, so that they sometimes signify form alone and sometimes form in matter. And the result is that animal will be taken of either in either meaning, not univocally, as though it were predicated with one meaning, but analogically, as happens in the case of those things which have one name because they are related to one thing. For the specific name will be predicated of the composite only by reason of relationship to that which is predicated according to form alone, as the Platonists held. For they maintained that man, who is a composite of matter and form, is so named because he participates in the Idea man, which is only a form.

             1708. These distinctions (710).

             Then the Philosopher shows the result to which the aforesaid search leads. He says that, while the question whether a specific name signifies the composite substance or only the form, makes a difference in regard to something else, it makes no difference to the investigation of sensible substance. For it is evident that a sensible substance is composed of matter and form.

             1709. Now to what kind of thing it makes a difference, whether to those in this state or in another, he makes clear next. For it is obvious that if there is something which is only form or actuality, its essence "consists of this," i.e., the thing and its essence will be identical, as a soul is identical with its essence, or is its own quiddity. But if a thing is composed of matter and form, then in this case the thing itself and its essence will not be the same; for example, a man and the essence of a man are not the same, unless perhaps a man is said to be only a soul, as was held by those who say that specific names signify only the form. Thus it is evident that something does exist whose essence is the same as itself, namely, whatever is not composed of matter and form but is only a form.

             1710. The reason for this position is that essence is what the definition signifies, and the definition signifies the nature of the species. But if there is something which is composed of matter and form, then in that thing there must be some other principle besides the nature of the species. For since matter is the principle of individuation, then in anything composed of matter and form there must be certain individuating principles distinct from the nature of the species. Hence such a thing is not just its own essence but is something in addition to this. But if such a thing exists which is only a form, it will have no individuating principles in addition to the nature of its species. For a form that exists of itself is individuated of itself. Therefore this thing is nothing else than its own essence.

             1711. It is clear, then, that if the specific name signifies only the form, the essence of anything will be the same as its being, as a man will be his essence, and a horse its essence, and so also will all other things of this kind. But if specific names signify things composed of matter and form, then such things will not be the same as their essence.

             1712. Accordingly, to those who (711).

             Here he deals with the second point mentioned above, namely, that the form is something in addition to the material parts. He says that for the Platonists, in raising this question, it does not seem that a syllable consists of its elements and their combination, as if combination, which is the form of a syllable, were a material part of a syllable like its elements or letters. Nor does it seem to them that a house consists of stones and their combination, as if a house were constituted of these as material parts.

             1713. And on this point their remarks are true, because, if the form were one of the material parts, it would depend on matter. But we see that this is false; for combination or mixture, which are formal principles, are not constituted of those things which are combined or mixed; nor is any other formal principle constituted of its matter, but the reverse. For a threshold is constituted by position, which is its form, and not the reverse.

             1714. Therefore, if one holds that animal and two-footed are the matter of man, man will not be animal and two-footed but will be something else in addition to these. And this will not be an element or anything composed of the elements but will be only a form as the Platonists claim, who omit matter from definitions. But it seems that we must hold, in opposition to this position, that, if form alone apart from matter is the substance or principle of being of a thing, they will not be able to say that this particular thing is that separate substance; i.e., they will not be able to say that this man as a sensible entity is composed of matter and form, but that man is only a form.

             1715. Now this must (712).

             He considers the third point mentioned above, namely, the Platonists' position that forms are eternal and incorruptible. Hence he concludes, from what has been said, that either a form must be eternal, as the Platonists held when they claimed that the Ideas, which they called the forms of things, are eternal; or a form must be corruptible by reason of something else without being corrupted in itself, and similarly it must come to be by reason of something else without coming to be in itself. This is in agreement with the position of Aristotle, who does not hold that forms are separate but that they exist in matter.

             1716. Further, the statement that forms can neither be corrupted nor generated in themselves (710-12:C 1708-15), on which each of the aforesaid points depends, Aristotle proceeds to demonstrate by reason of what was shown above, namely, that no one makes or produces a form, nor is a form generated or produced in itself; but it is this particular thing which comes to be or is generated in itself. And the reason is that everything which comes to be comes to be from matter. Hence, since this particular thing is composed of matter and form, it comes to be or is generated "from these principles," i.e., from its material and individuating principles. But it was stated above (711:C 1714) that a form is not an element or anything composed of the elements. Therefore it follows that a form neither comes to be nor is generated in itself.

             1717. But whether the substances (713).

             He examines the fourth point given above, namely, Plato's position that forms are separate from matter. In regard to this he does three things. First, he exposes what the problem is in this position, saying that it is not clear whether "the substances," i.e., the forms, of corruptible things are separable as the Platonists claimed.

             1718. It is evident, however (714).

             Second, he indicates what seems to be evident on this point. He says that it is evident that the forms of some corruptible things are not separate, namely, "all those" which are incapable of existing apart from their matters, as house or vessel, because neither the form of a house nor that of a vessel can exist apart from its proper matter.

             1719. Indeed, perhaps (715).

             Third, he precludes an objection, saying that perhaps the forms of artifacts are not substances or anything in their own right, and so cannot have separate existence. Nor similarly can other artificial forms, which have no natural existence, because in artifacts the matter alone is held to be substance, whereas the forms of artifacts are accidents. Natural forms, however, belong to the class of substance; and this is why Plato did not hold that the forms of artifacts exist apart from matter but only substantial forms.

             1720. For this reason (716).

             He advances arguments that are clearly opposed to Plato's position. He says that if one holds that there are separate forms, as the Platonists maintained, the problem which the followers of Antisthenes raised, even though they seem to be uninstructed, may be used against the Platonists. For they argued that it is impossible to define a thing by means of a definition which signifies its quiddity, since a thing's quiddity is simple and is not fittingly expressed by a statement composed of many parts. For we see that "the limit," or definition, which is given to a thing, is a lengthy statement made up of many words. Therefore it does not signify what a thing is but "what it is like," i.e., something to which it is similar; as if one were to say that the definition of silver does not signify silver but signifies something like lead or tin.

             1721. Hence in order to solve this problem we must say that the substance which is defined, whether it be intellectual or sensible, must be one that is composite. But since the primary parts of which a definition is composed are simple, they are incapable of definition. For it was stated above (706:C 1700) that the definitive statement joins one part to another, one of which is as form and the other as matter, because genus is derived from matter and difference from form, as was pointed out above (704:C 1696-8). Hence, if the species of things were forms only, as the Platonists held, they would be indefinable.

             1722. Further, it is also clear (717).

             Having determined what is true of forms in relation to the Ideas introduced by Plato, Aristotle now determines what is true of forms in relation to numbers. For Plato held that numbers are the forms and substances of things by establishing a kind of likeness between forms and numbers. This is divided into four parts inasmuch as there are four ways in which he likens forms to numbers.

             First, he says that, if numbers are in any sense the substances or forms of things, it is evident that they are such in this way, as can be understood from the foregoing, but not as numbers of units as the Platonists said. Now a number of units is called a simple and absolute number [i.e., an abstract number], but the number applied to things is called a concrete number, as four dogs or four men; and in this way the substances of things, which are signified by a definition, can be called numbers. For a definition is divisible into two parts, one of which is as form and the other as matter, as was pointed out above (706:C 1700). And it is divisible into indivisible parts; for since definitions cannot proceed to infinity, the division of a definition must terminate in certain indivisible parts. For example, if the definition of man is divided into animal and rational, and the definition of animal into animated and sensible, this will not go on to infinity. For it is impossible to have an infinite regress in material and formal causes, as was shown in Book II (152:C 299). Hence he explains that the division of a definition is not like the division of a continuous quantity, which is divisible to infinity, but is like the division of a number, which is divisible into indivisible parts.

             1723. And just as when (718).

             He gives the second way in which the substance that the definition signifies is like number. He says that, if anything is added to or subtracted from any number, even if it is a bare minimum, the resulting number will not be specifically the same. For in the case of numbers the minimum is the number one, which, when added to the number three, gives rise to the number four, which is a specifically different number; but if it is subtracted from the same number, the number two remains, which is also a specifically different number. And this is true because the ultimate difference gives to a number its species.

             1724. And it is similar in the case of definitions and of the essence, which the definition signifies; because, howsoever small a part has been added or subtracted, there results another definition and another specific nature. For animated sensible substance alone is the definition of animal, but if you also add rational to this, you establish the species man. And in a similar way if you subtract sensible, you establish the species plant, because the ultimate difference also determines the species.

             1725. And there must be (719).

             He gives the third way in which forms are like numbers. He says that a number is one thing. For a number is an essential unity inasmuch as the ultimate unity gives to a number its species and unity, just as in things composed of matter and form a thing is one and derives its unity and species from its form. And for this reason those who speak about the unity of a number as though a number were not essentially one cannot say what makes it to be one thing, i.e., if it is one. For since a number is composed of many units, either it is not one thing in an absolute sense but its units are joined together in the manner of a heap, which does not constitute a unity in an absolute sense, and therefore not a being in any class of things (and thus number would not be a class of being); or if it is one thing in an absolute sense and a being in itself, it is still necessary to explain what makes it one thing out of a plurality of units. But they are unable to assign a reason for this.

             1726. Similarly, a definition is one thing essentially, and thus they do not have to assign anything which makes it one. This is understandable, because the substance which the definition signifies is one thing for the very same reason that a number is, i.e., essentially, because one part of it is related to the other as form [to matter]. And it is one, not as being something indivisible such as a unit and a point, as some men claimed, but because each of them is one form and a kind of nature.

             1727. And just as number (720).

             He gives the fourth way in which forms are like numbers. He says that just as a number does not admit of more or less, neither does substance in the sense of form, although perhaps substance in the sense of matter does admit of such difference. For just as the concept of number consists in some limit to which neither addition nor subtraction may be made, as has been pointed out (718:C 1723), so also does the concept of form. But things admit of more or less because of the fact that matter participates in a form in a more or less perfect way. Hence too whiteness does not differ in terms of more or less, but a white thing does.

             1728. In regard to the generation (721).

             He summarizes the points discussed. He says that he has dealt with "the generation and corruption of such substances," or forms, both as to the way in which this is possible, namely, by reason of something else; and as to the way in which this is impossible, i.e., essentially; and also with the likeness which forms have to numbers, i.e., by reducing them to numbers by way of a likeness.