Commentary Aristotle Metaphysics
Lecture 14
Are there separate forms which are the essences of sensible things?
But in general one will wonder why, in addition to sensible things and those which are intermediate, it is necessary to look for certain other things that we posit as the specific essences (or forms) of sensible things.
For if it is because the objects of mathematics differ in one respect from the things that are at hand, they do not differ in being from many things that are specifically the same. Hence the principles of sensible things will not be limited in number but only in species; unless one were to consider the principles of this particular syllable or word, for these are limited in number. And this is likewise true of the intermediate entities, for in their case too there are an infinite number of things that are specifically the same.
Hence, if in addition to sensible substances and the objects of mathematics there are not certain other things, such as some call the forms, there will be no substance which is one both numerically and specifically. Nor will the principles of beings be limited in number, but only in species. Therefore, if this is necessary, it will also be necessary on this account that there should be forms. And even if those who speak of the forms do not express themselves clearly, although this is what they wanted to say, they must affirm that each of the forms is a substance, and that nothing accidental pertains to them.
But if we hold that the forms exist, and that principles are one numerically but not specifically, we have stated the untenable conclusions that follow from this view.
Are forms substances or principles of things?
515. Having inquired whether the objects of mathematics are the principles of sensible substances, the Philosopher now inquires whether in addition to the objects of mathematics there are certain other principles, such as those which we call forms, which are the substances and principles of sensible things. In regard to this, he does three things.
First, he presents the question.
Second, he argues one side of the question, at for if it is because.
Third, he argues the other side, at but if we hold.
Accordingly, he first says that, if one assumes that the objects of mathematics are not the principles of sensible things and their substances, one will next have the problem of why, in addition to both sensible things and the objects of mathematics (which are an intermediate genus between sensible things and the forms), it is necessary to posit a third genus of entities, namely, the specific essences, that is, the ideas or separate forms.
516. For if it is because. Here he argues one side of the question. The reason why it is necessary to posit separate forms over and above sensible substances and the objects of mathematics seems to be that the objects of mathematics differ in one respect from the things that are at hand, that is, from sensible things, which exist in the universe. For the objects of mathematics abstract from sensible matter.
Yet in another respect they do not differ, but rather agree. For just as we find many sensible things that are specifically the same but numerically different, as many men or many horses, in a similar way we find many objects of mathematics which are specifically the same but numerically different, such as many equilateral triangles and many equal lines. And if this is true, it follows that, just as the principles of sensible things are not limited in number, but in species, the same thing is true of the intermediate entities—the objects of mathematics.
For, since in the case of sensible things there are many individuals of one sensible species, it is evident that the principles of sensible things are not limited in number, but in species—unless, of course, we can consider the proper principles of a particular individual thing, which are also limited in number and are individual.
He gives words as an example, for in the case of a word expressed in letters it is clear that the letters are its principles, yet there are not a limited number of individual letters taken numerically, but only a limited number taken specifically, some of which are vowels and some consonants. But this limitation is according to species and not according to number. For A is not only one, but many, and the same applies to other letters. But if we take those letters which are the principles of a particular syllable, whether written or spoken, then they are limited in number.
And for the same reason, since there are many objects of mathematics which are numerically different in one species, the mathematical principles of mathematical science could not be limited in number, but only in species. We might say, for example, that the principles of triangles are three sides and three angles, but this limitation is according to species, for any of them can be multiplied to infinity.
Therefore, if there were nothing besides sensible things and the objects of mathematics, it would follow that the substance of a form would be numerically one, and that the principles of beings would not be limited in number, but only in species. Therefore, if it is necessary that they be limited in number (otherwise it would happen that the principles of things are infinite in number), it follows that there must be forms in addition to the objects of mathematics and sensible things.
517. This is what the Platonists wanted to say, because it necessarily follows from the things that they held that, in the case of the substance of sensible things, there is a single form to which nothing accidental belongs. For something accidental, such as whiteness or blackness, pertains to an individual man; but to this separate man, who is a form according to the Platonists, there pertains nothing accidental, but only what belongs to the definition of the species. And although they wanted to say this, they did not express themselves clearly; that is, they did not clearly distinguish things.
518. But if we hold that. Then he counters with an argument for the other side of the question. He says that, if we hold that there are separate forms and that the principles of things are limited not only in species but also in number, certain impossible consequences will follow, which are touched on above in one of the questions. But the Philosopher will deal with this problem in book 12 and book 14 of this work. And the truth of the matter is that, just as the objects of mathematics do not exist apart from sensible things, neither do forms exist apart from the objects of mathematics and from sensible substances. And while the efficient and moving principles of things are limited in number, the formal principles of things (of which there are many individuals in one species) are not limited in number, but only in species.
Lecture 15
Do first principles exist actually or potentially, and are they universal or singular?
And connected with these problems there is the question of whether the elements of things exist potentially or in some other way.
If they exist in some other way, then there will be something else prior to first principles. For potency is prior to that cause, but the potential need not exist in that way.
But if the elements exist potentially, it is possible for nothing to exist, for even that which does not yet exist is capable of existing, because that which does not exist may come to be. But nothing that is incapable of existing may come to be. It is necessary, then, to investigate these problems.
And there is also the problem of whether principles are universals or singular things, as we maintain.
For if they are universals, they will not be substances, because a common term signifies not a particular thing, but what sort of thing, and a substance is a particular thing.
But if it is a particular thing, and is held to be the common whatness which is predicated of things, Socrates himself will be many animals: himself and man and animal. (That is, if each of these signifies a particular thing and a one.) If, then, the first principles of things are universals, these consequences will follow.
However, if they are not universals but have the nature of singular things, they will not be knowable, for all scientific knowledge is universal. Hence, if there is to be any scientific knowledge of first principles, there will have to be different principles which are predicated universally and are prior to first principles.
Are principles of substances actual or potential?
519. Having inquired what the principles are, the Philosopher now asks how they exist.
First, he asks whether they exist potentially or actually;
second, whether they are universals or singulars, at and there is also the problem.
First, he raises the question.
Second, he argues one side, at if they exist.
Third, he argues the opposite side, at but if the elements.
His first question, then, is whether first principles exist potentially or in some other way, that is, actually. This problem is introduced because of the ancient philosophers of nature, who held that there are only material principles, which are in potency. But the Platonists, who posited separate forms as formal principles, claimed that they exist actually.
520. If they exist. He proves that principles exist potentially. For if they were to exist in some other way, that is, actually, it would follow that there would be something prior to principles, for potency is prior to act. This is clear from the fact that one thing is prior to another when the sequence of their being cannot be reversed. For if a thing exists, it follows that it can be, but it does not necessarily follow that, if a thing is possible, it will exist actually. But it is impossible for anything to be prior to a first principle. Therefore, it is impossible for a first principle to exist in any other way than potentially.
521. But if the elements. Here he argues the other side of the question. If the principles of things exist potentially, it follows that no beings exist actually, for that which exists potentially does not yet exist actually. He proves this on the grounds that that which is coming to be is not a being. For that which exists is not coming to be, but only that comes to be which exists potentially. Therefore, everything that exists potentially is non-being. Hence if principles exist only potentially, beings will not exist. But if principles do not exist, neither will their effects. It follows, then, that it is possible for nothing to exist in the order of being. And in summing this up he concludes that according to what has been said it is necessary to inquire about the principles of things for the reasons given.
522. This question will be answered in book 9 of this work, where it is shown that act is prior to potency in an unqualified sense, but that in anything moved from potency to act, potency is prior to act in time. Hence it is necessary that the first principles exist actually and not potentially, as is shown in book 12 of this work.
Are principles of substances universal or singular?
523. And there is also the problem. Here he asks whether the principles of things exist as universals or as singular things, and in regard to this he does three things.
First, he presents the question.
Second, he argues one side, at for if they are universals.
Third, he argues the other side, at however, if they are not universals.
The problem, then, is whether principles are universals or exist in the manner of singular things.
524. For if they are. Then he proves that principles are not universals, by the following argument. No predicate common to many things signifies a particular thing, but rather signifies such and such a thing or of what sort a thing is. It does this not according to accidental quality, but according to substantial quality, as is stated below in book 5 of this work. The reason for this is that a particular thing is said to be such insofar as it subsists of itself. But that which subsists of itself cannot be something that exists in many, as belongs to the notion of common. For that which exists in many will not subsist of itself unless it is itself many. But this is contrary to the notion of common, because what is common is what is one-in-many. Hence it is clear that a particular thing does not signify anything common, but rather signifies a form existing in many things.
525. Further, he adds the minor premise, namely, that substance signifies a particular thing. And this is true of first substances, which are said to be substances in the full and proper sense, as is stated in the Categories. For substances of this kind are things that subsist of themselves. Thus it follows that, if principles are universals, they are not substances. Hence either there will be no principles of substances, or it will be necessary to say that the principles of substances are not substances.
526. But since it is possible for someone to affirm that some common predicate might signify this particular thing, he therefore criticizes this when he says, but if it is.
He explains the untenable consequence resulting from this. For if a common predicate were a particular thing, it would follow that everything to which that common predicate is applied would be this particular thing which is common. But it is clear that both animal and man are predicated of Socrates, and that each of these—animal and man—is a common predicate. Hence, if every common predicate were a particular thing, it would follow that Socrates would be three particular things. For Socrates is Socrates, which is a particular thing, and he is also a man, which is a particular thing according to the above, and he is also an animal, which is similarly a particular thing. Hence he would be three particular things. Further, it would follow that there would be three animals; for animal is predicated of itself, of man, and of Socrates.
Therefore, since this is impossible, it is also impossible for a common predicate to be a particular thing. These, then, will be the impossible consequences which follow if principles are universals.
527. However, if they are not. He argues the other side of the question. Since all sciences are universal, they are not concerned with singulars, but with universals. Therefore, if some principles were not universals, but were singular things, they would not be knowable in themselves. Hence, if any science were to be had of them, there would have to be certain prior principles, which would be universals. It is necessary, then, that first principles be universals in order that science may be had of things, because if principles remain unknown, other things must remain unknown.
528. This question will be answered in book 7 of this work, where it is shown that universals are neither substances nor the principles of things. However, it does not follow for this reason that, if the principles and substances of things were singulars, there could be no science of them: both because immaterial things, even though they subsist as singulars, are nevertheless also intelligible, and also because there is science of singulars according to their universal concepts which are apprehended by the intellect.