Commentary Aristotle Physics
Lecture 11. There are only three principles of natural things
The next question is whether the principles are two or three or more in number.
One they cannot be, for there cannot be one contrary.
Nor can they be innumerable, for if so, being will not be knowable;
and, in any one genus, there is only one contrariety, and substance is one genus.
Also, a finite number is sufficient, and a finite number, such as the principles of Empedocles, is better than an infinite multitude. For Empedocles professes to obtain from his principles all that Anaxagoras obtains from his innumerable principles.
Finally, some contraries are more primary than others, and some arise from others—for example, sweet and bitter, white and black—but the principles must always remain principles. This will suffice to show that the principles are neither one nor innumerable.
Granted, then, that they are a limited number, it is plausible to suppose them more than two. For it is difficult to see how either density should be of such a nature as to act in any way on rarity, or rarity on density. The same is true of any other pair of contraries, for love does not gather strife together and make things out of it, nor does strife make anything out of love, but both act on a third thing different from both. Some indeed assume more than one such thing from which they construct the world of nature.
But someone would have still more difficulties if he did not assume some other nature besides the contraries. For we do not find that the contraries constitute the substance of any thing.
But what is a first principle ought not to be the predicate of any subject. If it were, there would be a principle of the supposed principle: for the subject is a principle, and prior presumably to what is predicated of it.
Again we hold that a substance is not contrary to another substance. How, then, can substance be derived from what are not substances? Or how can non-substances be prior to substance?
If, then, we accept both the former argument and this one, we must, to preserve both, assume a third somewhat as the substratum of the contraries, such as is spoken of by those who describe the all as one nature—water or fire or what is intermediate between them. What is intermediate seems preferable; for fire, earth, air, and water are already involved with pairs of contraries. There is, therefore, much to be said for those who make the underlying substance different from these four; of the rest, the next best choice is air, as presenting sensible differences in a less degree than the others; and after air, water.
All agree in this, however, that they differentiate their one by means of the contraries, such as density and rarity and more and less, which may of course be taken universally as excess and defect, as has already been said.
Indeed, this doctrine too (that the one and excess and defect are the principles of things) would appear to be of old standing, though in different forms, for the early thinkers made the two the active and the one the passive principle, whereas some of the more recent maintain the reverse. Thus, to suppose that the elements are three in number would seem, from these and similar considerations, a plausible view, as I said before.
On the other hand, the view that they are more than three in number would seem to be untenable. For the one substratum is sufficient to be acted on; but if we have four contraries, there will be two contrarieties, and we shall have to suppose an intermediate nature for each pair separately.
If, on the other hand, the contrarieties, being two, can generate from each other, the second contrariety will be superfluous.
Moreover, it is impossible that there should be more than one primary contrariety. For substance is a single genus of being, such that the principles can differ only as prior and posterior, not in genus; in a single genus, there is always a single contrariety, all the other contrarieties in it being held to be reducible to one. It is clear, then, that the number of elements is neither one nor more than two or three; but whether two or three is, as I said, a question of considerable difficulty.
82. After the Philosopher has investigated the contrariety of the principles, he here begins to inquire about their number.
Concerning this, he makes three points.
First, he raises the question.
Second, at “one they cannot be” (189a12; [83]), he excludes certain things that are not pertinent to this question.
Third, he takes up the question at “granted, then, that” (189a20; [89]).
Therefore, he first says that, after an investigation into the contrariety of the principles, an inquiry about their number should follow, namely, whether they are two, or three, or more.
83. Next, at “one they cannot be” (189a12), he excludes those things that are not pertinent to this question.
He shows first that there is not just one principle, and second, at “nor can they be” (189a12; [84]), he shows that the principles are not infinite.
He says first that it is impossible for there to be only one principle. For it has been shown (188a19; [75]) that the principles are contraries. But contraries are not just one, for nothing is the contrary of itself; therefore, there is not just one principle.
84. Next, at “nor can they be” (189a12), he gives four arguments to show that the principles are not infinite.
The first of these is as follows. The infinite as such is unknown. If, therefore, the principles are infinite, they must be unknown. But, if the principles are unknown, then those things that are from the principles are unknown. It follows, therefore, that nothing in the world could be known.
85. He gives the second argument at “and in any one genus” (189a13). The argument is as follows. The principles must be primary contraries, as was shown above. But the primary contraries belong to the primary genus, which is substance. But substance, since it is one genus, has one primary contrariety. For the first contrariety of any genus is that of the primary differentiae by which the genus is divided. Therefore, the principles are not infinite.
86. He gives the third argument at “also, a finite number” (189a14). The argument is as follows. It is better to say that what can be brought about by finite principles comes from finite principles rather than from infinite principles.
But all things that come to be according to nature are explained by Empedocles through finite principles, just as they are explained by Anaxagoras through infinite principles. Hence, an infinite number of principles should not be posited.
87. He gives the fourth argument at “finally, some contraries” (189a17). The argument is as follows. Principles are contraries. If, therefore, the principles are infinite, it is necessary that all the contraries be principles. But not all of the contraries are principles. This is clear for two reasons. First, the principles must be primary contraries, but not all contraries are primary, since some are prior to others. Second, the principles ought not to be from each other, as was said above. But some contraries are from each other, as the sweet and the bitter, and the white and the black. Therefore, the principles are not infinite. Thus he finally concludes that the principles are neither one nor infinite.
88. However, we must note that the Philosopher proceeds here by way of disputation from probable arguments. Hence he assumes certain things that are seen in many instances and that cannot be false all the time, but are true in particular instances. Therefore, it is true that, in a certain respect, contraries do come to be from each other, as was said above, if the subject is taken along with the contraries.
For that which is white later becomes black. However, whiteness itself is never changed into blackness. But some of the ancients, without including the subject, held that the primary contraries come to be from each other. Hence, Empedocles denied that the elements come to be from each other.
And thus Aristotle significantly does not say in this place that the hot comes to be from the cold, but the sweet from the bitter and the white from the black.
89. Next, at “granted, then” (189a20), he takes up the question under discussion, namely, the number of the principles.
Concerning this, he makes two points.
First, he shows that there are not just two principles, but three.
Second, at “on the other hand” (189b16; [95]), he shows that there are no more than three principles.
Concerning the first part, he makes two points.
First, he shows through arguments that there are not just two principles, but that a third must be added.
Second, at “if, then, we accept” (189a34; [93]), he shows that even the ancient philosophers agreed on this point.
90. Concerning the first part (189a20), he gives three arguments.
He says first that, since it was shown that the principles are contraries, and so could not be just one, but are at least two, and further since the principles are not infinite, then it remains for us to consider whether there are only two principles or more than two.
Since it was shown above that the principles are contraries, it seems that there are only two principles, because contrariety exists between two extremes. But it is difficult to see how this is, that is, one might question this. For it is necessary that other things come to be from the principles, as was said above.
If, however, there are only two contrary principles, it is not apparent how all things can come to be from these two. For it cannot be said that one of them makes something from the other one. For density is not by nature such that it can convert rarity into something, nor can rarity convert density into something.
And the same is true of any other contrariety. For peace does not move strife and make something out of it, nor does the converse happen.
Rather, each of the contraries changes some third thing that is the subject of both of the contraries. For heat does not make coldness itself to be hot, but makes the subject of coldness to be hot. And conversely, coldness does not make heat itself to be cold, but makes the subject of heat to be cold.
Therefore, in order that other things can come to be from the contraries, it seems that it is necessary to posit some third thing that will be the subject of the contraries. It does not matter for the present whether that subject is one or many. For some have posited many material principles from which they prepare the nature of beings. For they said that the nature of things is matter, as will be said later in book 2.
91. He gives the second argument at “but someone would have still more difficulties” (189a27). He says that, unless there is something other than the contraries that are given as principles, then there arises an even greater difficulty. For a first principle cannot be an accident that is predicated of a subject. For since a subject is a principle of the accident that is predicated of it and is naturally prior to the accident, then, if the first principle were an accident predicated of a subject, it would follow that there would be a principle of the principle, and there would be something prior to the first. But, if we hold that only the contraries are principles, it is necessary that the principles be an accident predicated of a subject. For no substance is the contrary of another. Rather, contrariety is found only between accidents. It follows, therefore, that the contraries cannot be the only principles. Moreover, it must be noted that, in this argument he uses predicate for accident, since a predicate designates a form of the subject. The ancients, however, believed that all forms are accidents. Hence he proceeds here by way of disputation from probable propositions that were well known among the ancients.
92. He gives the third argument at “again we hold” (189a32). The argument is as follows. Everything that is not a principle must be from principles. Therefore, if only the contraries are principles, then, since substance is not the contrary of substance, it follows that substance would be from non-substance. And, thus, what is not substance is prior to substance, because what is from something is posterior to it. But this is impossible. For substance, which is being per se, is the first genus of being. Therefore, it cannot be that only the contraries are principles; rather, it is necessary to posit some other third thing.
93. Next, at “if, then, we accept” (189a34), he shows how the position of the philosophers also agrees with this.
Concerning this, he makes two points.
First, he shows how they posited one material principle.
Second, at “all agree in this, however” (189b8; [94]), he shows how they posited two contrary principles besides this one material principle.
However, we must first note that the Philosopher seemed in the preceding arguments to be opposed, in the manner of those who dispute, to both sides of the question.
For he first proved that the principles are contraries, and now he brings forth arguments to prove that the contraries are not sufficient for the generation of things. And, since disputatious arguments do come to a partially true conclusion, though it is not the whole truth, he concludes one truth from each argument.
He says that, if someone thinks that the first argument (which proves that the principles are contraries) is true, and that the argument just given (which proves that contrary principles are not sufficient) is also true, then to maintain both conclusions he must say that some third thing lies beneath the contraries, as was said by those who held that the whole universe is some one nature—understanding nature to mean matter, such as water, or fire, or air, or some intermediate state between these, such as vapor, or some other thing of this sort.
This seems especially true in regard to an intermediate. For this third thing is taken as the subject of the contraries and as distinct from them in some way.
Hence, that which has less of the nature of a contrary about it is more conveniently posited as the third principle beyond the contraries. For fire and earth and air and water have contrariety attached to them, such as the hot and the cold and the wet and the dry. Hence, it is not unreasonable that they make the subject something other than these and something in which the contraries are less prominent.
After these philosophers, however, those who held that air was the principle spoke more wisely, for the contrary qualities found in air are less sensible. After these philosophers are those who held that water was the principle. But those who held that fire was the principle spoke most poorly, because fire has a contrary quality that is most sensible and that is very active. For in fire, there is an excellence of heat. But if the elements are compared with reference to their subtlety, those who made fire the principle seem to have spoken better, as is said elsewhere, for what is more subtle seems to be more simple and prior. Hence, no one held that earth was the principle because of its density.
94. Next, at “all agree in this, however” (189b8), he shows how they posited contrary principles with the one material principle. He says that all who posited one material principle said that it is figured or formed by certain contraries, such as rarity and density, which are reducible to the great and the small and to excess and defect.
And, thus, the position of Plato—that the one and the great and the small are the principles of things—was also the opinion of the ancient natural philosophers, but in a different way. For the ancient philosophers, thinking that one matter was differentiated by diverse forms, held two principles on the part of form, which is the principle of action, and one on the part of matter, which is the principle of passion. But the Platonists, thinking that many individuals in one species are distinguished by a division of matter, posited one principle on the part of the form, which is the active principle, and two on the part of the matter, which is the passive principle.
And thus he draws the conclusion that he had principally intended, namely, that, by considering the above and similar positions, it seems reasonable that there are three principles of nature. And he points out that he has proceeded from probable arguments.
95. Next, at “on the other hand” (189b16), he shows that there are no more than three principles.
He uses two arguments.
The first is as follows. It is superfluous for that which can come to be through fewer principles to come to be through many. But the whole generation of natural things can be achieved by positing one material principle and two formal principles. For one material principle is sufficient to account for passion. But, if there were four contrary principles, and two primary contrarieties, it would be necessary that each contrariety have a different subject. For it seems that there is one primary subject for any one contrariety. And so, if, by positing two contraries and one subject, things can come to be from each other, it seems superfluous to posit another contrariety. Therefore, we must not posit more than three principles.
96. He gives the second argument at “moreover, it is impossible” (189b22). If there are more than three principles, it is necessary that there be many primary contrarieties. But this is impossible, because the first contrariety seems to belong to the first genus, which is one, namely, substance. Hence, all contraries that are in the genus of substance do not differ in genus, but are related as prior and posterior. For in one genus, there is only one contrariety, the first, because all other contrarieties seem to be reduced to the first one. For there are certain first contrary differentiae by which a genus is divided. Therefore, it seems that there are no more than three principles.
It must be noted, however, that each of the following statements is probable: that there is no contrariety in substances and that, in substances, there is only one primary contrariety. For if we take “substance” to mean that which is, it has no contrary. If, however, we take “substance” to mean formal differentiae in the genus of substance, then contrariety is found in them.
97. Finally, by way of summary, he concludes that there is not just one principle, nor are there more than two or three. But deciding which of these is true—that is, whether there are only two principles or three—involves much difficulty, as is clear from the foregoing.