METAPHYSICS
BOOK I

ARISTOTLE’S INTRODUCTION
HISTORY OF METAPHYSICAL INQUIRY


CONTENTS

LESSON 1: The Dignity and Object of This Science
LESSON 2: Wisdom Considers Universal First Causes and First Principles
LESSON 3: The Nature and Goal of Metaphysics
LESSON 4: Opinions about the Material Cause
LESSON 5: Opinions about the Efficient Cause
LESSON 6: Love and Hate as Efficient Causes of Good and Evil
LESSON 7: The Views of the Atomists and the Pythagoreans
LESSON 8: The Pythagorean Doctrine about Contraries
LESSON 9: The Opinions of the Eleatics and Pythagoreans about the Causes of Things
LESSON 10: The Platonic Theory of Ideas
LESSON 11: A Summary of the Early Opinions about the Causes
LESSON 12: Criticism of the Views about the Number of Material Principles
LESSON 13: Criticism of the Pythagoreans' Opinions
LESSON 14: Arguments against the Platonic Ideas
LESSON 15: The Destruction of the Platonists' Arguments for Ideas
LESSON 16: Arguments against the View that Ideas Are Numbers
LESSON 17: Arguments against the View that the Ideas Are Principles of Being and Knowledge

LESSON 1

The Dignity and Object of This Science

ARISTOTLE’S TEXT Chapter 1: 980a 21-983a 3

1. All men naturally desire to know. A sign of this is the delight we take in the senses; for apart from their usefulness they are loved for themselves, and most of all the sense which operates through the eyes. For not only that we may act, but even when we intend to do nothing, we prefer sight, as we may say, to all the other senses. The reason is that of all the senses this most enables us to know and reveals many differences between things.

2. Animals by nature, then, are born with sensory power.

3. Now in some animals memory arises from the senses, but in others it does not; and for this reason the former are prudent and more capable of being taught than those which are unable to remember. Those which cannot hear sounds are prudent but unable to learn, as the bee and any other similar type of animal there may be. But any which have this sense together with memory are able to learn.

4. Thus other animals live by imagination and memory and share little in experience, whereas the human race lives by art and reasoning.

5. Now in men experience comes from memory, for many memories of the same thing produce the capacity of a single experience. And experience seems to be somewhat like science and art.

6. But in men science and art come from experience; for “Experience causes art, and inexperience, luck,” as Polus rightly states. Art comes into being when from many conceptions acquired by experience a Single universal judgment is formed about similar things. For to judge that this [medicine] has been beneficial to Callias and Socrates and many other individuals who suffer from this disease, is a matter of experience; but to judge that it has been beneficial to all individuals f a particular kind, as the phlegmatic, the bilious, or the feverish, taken as a lass, who suffer from this disease, is a matter of art.

7. In practical matters, then, experience seems to differ in no way from art. ut we see that men of experience are more proficient than those who have theory without experience. The reason is that experience is a knowledge of in singulars, whereas art is a knowledge of universals. But all actions and processes of generation are concerned with singulars. For the physician heals man only incidentally, but he heals Socrates or Callias, or some individual that can be named, to whom the nature man happens to belong. Therefore, if anyone has the theory without experience, and knows the universal but not the singulars contained in this, he will very often make mistakes; for it is rather the individual man who is able to be cured.

8. Yet we think that scientific knowledge and the ability to refute objections belong to art rather than to experience, and we are of the opinion that those who are proficient in art are wiser than men of experience, implying that it is more according to wisdom to know as one pursuing all things.

9. Now this is because the former know the cause whereas the latter do not. For those who have experience know that something is so but do not know why, whereas the others know the why and the cause. For this reason, too, we think that the master planners in each art are to be held in greater esteem, and that they know more and are wiser than the manual laborers, because they understand the reasons for the things which are done. Indeed, we think that the latter resemble certain inanimate things, which act but do not know what they do, as fire burns. Therefore inanimate things perform each of their actions as a result of a certain natural disposition, whereas manual laborers perform theirs through habit, implying that some men are wiser not insofar as they are practical but insofar as they themselves have the theories and know the causes.

10. In general a sign, of scientific knowledge is the ability to teach, and for this reason we think that art rather than experience is science. For those who have an art are able to teach, whereas the others are not.

11. Furthermore, we do not hold that any one of the senses is wisdom, since the cognition of singular things belongs especially to the senses. However, these do not tell us why a thing is so; for example, they do not tell us why fire is hot but only that it is so.

12 It is only fitting, then, that the one who discovered any art whatsoever that went beyond the common perceptions of men should be admired by men, not only because of some usefulness of his discoveries, but as one who is wise and as distinguishing [a thing] from others. And as more of the arts were discovered, some to supply the necessities of life, and others to introduce us [to the sciences], those who discovered the former were always considered to be wiser than those who discovered the former, because their sciences were not for the sake of utility. Hence, after all such arts had already been developed, those sciences were discovered which are pursued neither for the sake of pleasure nor necessity. This happened first in those places where men had leisure. Hence the mathematical arts originated in Egypt, for there the priestly class was permitted leisure. The difference between art and science and similar mental states has been stated in our work on morals.

13. Now the reason for undertaking this investigation is that all men think that the science which is called wisdom deals with the primary causes and principles of things. Hence, as we have said before (8, 9), the man of experience is considered to be wiser than one who has any of the senses; the artist wiser than the man of experience; the master planner wiser than the manual laborer and speculative knowledge wiser than practical knowledge. It is quite evident then, that wisdom is a science of certain causes and principles.

COMMENTARY

Three reasons why people naturally desire to know

1. Aristotle first sets down an introduction to this science, in which he treats of two things. First (2), he points out with what this science is concerned. Second (53), he explains what kind of science it is (“That this is not a practical science”).

In regard to the first he does two things. First, he shows that the office of this science, which is called wisdom, is to consider the causes of things. Second (36), he explains with what causes or kinds of causes it is concerned (“But since we are in search”).

In regard to the first he prefaces certain preliminary considerations form which he argues in support of his thesis. Second (35), he draws a conclusion from these considerations (“Now the reason for undertaking”).

In regard to the first he does two things. First, he makes clear the dignity of scientific knowledge in general. Second (9), he explains the hierarchy in knowing (“Animals by nature”).

Now he establishes the dignity of scientific knowledge from the fact that it is naturally desired as an end by all men. Hence, in regard to this he does two things. First, he states what he intends [to prove]. Second (1), he proves it (“A sign of this”).

Accordingly, he says, first, that the desire to know belongs by nature to all men.

2. Three reasons can be given for this:

The first is that each thing naturally desires its own perfection. Hence matter is also said to desire form as any imperfect thing desires its perfection. Therefore, since the intellect, by which man is what he is, considered in itself is all things potentially, and becomes them actually only through knowledge, because the intellect is none of the things that exist before it understands them, as is stated in Book III of The Soul, so each man naturally desires knowledge just as matter desires form.

3. The second reason is that each thing has a natural inclination to perform its proper operation, as something hot is naturally inclined to heat, and something heavy to be moved downwards. Now the proper operation of man as man is to understand, for by reason of this he differs from all other things. Hence the desire of man is naturally inclined to understand, and therefore to possess scientific knowledge.

4. The third reason is that it is desirable for each thing to be united to its source, since it is in this that the perfection of each thing consists. This is also the reason why circular motion is the most perfect motion, as is proved in Book VIII of the Physics, because its terminus is united to its starting-point. Now it is only by means of his intellect that man is united to the separate substances, which are the source of the human intellect and that to which the human intellect is related as something imperfect to something perfect. It is for this reason, too, that the ultimate happiness of man consists in this union. Therefore man naturally desires to know. The fact that some men do not devote any study to this science does not disprove this thesis; for those who desire some end are often prevented from pursuing it for some reason or other, either because of the difficulty of attaining it, or because of other occupations. And in this way, too, even though all men desire knowledge, still not all devote themselves to the pursuit of it because they are held back by other things, either by pleasures or the needs of the present life; or they may even avoid the effort that learning demands because they are lazy. Now Aristotle makes this statement in order to show that it is not pointless to search for a science that is not useful for anything else, as happens in the case of this science, since a natural desire cannot exist in vain.

5. Then he establishes his thesis by means of an example. Since our senses serve us in two respects: in knowing things and in meeting the needs of life, we love them for themselves inasmuch as they enable us to know and also assist us to live. This is evident from the fact that all men take the greatest delight in that sense which. is most knowing, i.e., the sense of sight, which we value not merely in order to do something, but even when we are not required to act at all. The reason is that this sense—that of sight—is the most knowing of all our senses and makes us aware of many differences between things.

6. In this part it is clear that he gives two reasons why sight is superior to the other senses in knowing. The first is that it knows in a more perfect way; and this belongs to it because it is the most spiritual of all the senses. For the more immaterial a power is, the more perfectly it knows. And evidently sight is a more immaterial sense, if we consider the modification produced in it by its object. For all other sensible objects change both the organ and medium of a sense by a material modification, for example, the object of touch by heating and cooling, the object of taste by affecting the organ of taste with some flavor through the medium of saliva, the object of hearing by means of motion in the body, and the object of smell by means of the evaporation of volatile elements. But the object of sight changes the organ and medium of sight only by a spiritual modification; because neither the pupil of the eye nor the air becomes colored, but these only receive the form of color in a spiritual mode of being. Therefore, because actual sensation consists in the actual modification of a sense by its object, it is evident that that sense which is changed in a more immaterial and spiritual way is more spiritual in its operation. Hence sight judges about sensible objects in a more certain and perfect way than the other senses do.

7. The other reason which he gives for the superiority of sight is that it gives us more information about things. This is attributable to the nature of its object, for touch and taste, and likewise smell and hearing, perceive those accidents by which lower bodies are distinguished from higher ones. But sight perceives those accidents which lower bodies have in common with higher ones. For a thing is actually visible by means of light, which is common both to lower and higher bodies, as is said in Book II of The Soul. Hence the celestial bodies are perceptible only by means of sight.

8. There is also another reason. Sight informs us of many differences between things, for we seem to know sensible things best by means of sight and touch, but especially by means of sight. The reason for this can be drawn from the fact that the other three senses perceive those accidents which in a way flow from a sensible body and do not remain in it. Thus sound comes from a sensible body inasmuch as it flows away from it and does not remain in it. The same thing is true of the evaporation of volatile elements, with which and by which odor is diffused. But sight and touch perceive those accidents which remain in sensible bodies, such as color, warmth and coldness. Hence the judgment of sight and touch is extended to things themselves, whereas the judgment of hearing and smell is extended to those accidents which flow from things and not to things themselves. It is for this reason that figure and size and the like, by which a sensible being itself is disposed, are perceived more by sight and touch than by the other senses. And they are perceived more by sight than by touch, both because sight knows more efficaciously, as has been pointed out (C 6), and also because quantity and those [accidents] which naturally follow from it, which are seen to be the common sensibles, are more closely related to the object of sight than to that of touch. This is clear from the fact that the object of sight belongs in some degree to every body having some quantity, whereas the object of touch does not.

9. Animals by nature, then (2).

Here he considers the hierarchy in knowledge. He does this, first (9), with respect to brute animals; and, then (14), with respect to men (“Thus other animals”).

With respect to brute animals he mentions first what all animals have in common; and second (10), that by which they differ and surpass one another (“Now in some animals”).

Now all animals are alike in the respect that they possess by nature the power of sensation. For an animal is an animal by reason of the fact that it has a sentient soul, which is the nature of an animal in the sense in which the distinctive form of each thing is its nature. But even though all animals are naturally endowed with sensory power, not all animals have all the senses, but only perfect animals. All have the sense of touch, for this sense in a way is the basis of all the other senses. However, not all have the sense of sight, because this sense knows in a more perfect way than all the other senses. But touch is more necessary; for it perceives the elements of which an animal is composed, namely, the hot, cold, moist and dry. Hence, just as sight knows in a more perfect way than the other senses, in a similar way touch is more necessary inasmuch as it is the first to exist in the process of generation. For those things which are more perfect according to this process come later in the development of the individual which is moved from a state of imperfection to one of perfection.

10. Now in some animals (3).

Here he indicates the different kinds and three levels of knowing found among brute animals. For there are certain animals which have sensation, although they do not have memory which comes from sensation. For memory accompanies imagination, which is a movement caused by the senses in their act of sensing, as we find in Book II of The Soul. But in some animals imagination does not accompany sensation, and therefore memory cannot exist in them. This is found verified in imperfect animals which are incapable of local motion, such as shellfish. For since sensory cognition enables animals to make provision for the necessities of life and to perform their characteristic operations, then those animals which move towards something at a distance by means of local motion must have memory. For if the anticipated goal by which they are induced to move did not remain in them through memory, they could not continue to move toward the intended goal which they pursue. But in the case of immobile animals the reception of a present sensible quality is sufficient for them to perform their characteristic operations, since they do not move toward anything at a distance. Hence these animals have an indefinite movement as a result of confused [or indeterminate] imagination alone, as he points out in Book III of The Soul.

11. Again, from the fact that some animals have memory and some do not, it follows that some are prudent and some not. For, since prudence makes provision for the future from memory of the past (and this is the reason why Tully in his Rhetoric, Book II, makes memory, understanding and foresight parts of prudence), prudence cannot be had by those animals which lack memory. Now those animals which have memory can have some prudence, although prudence has one meaning in the case of brute animals and another in the case of man. Men are prudent inasmuch as they deliberate rationally about what they ought to do. Hence it is saidin Book VI of the Ethics, that prudence is a rationally regulated plan of things to be done. But the judgment about things to be done which is not a result of any rational deliberation but of some natural instinct is called prudence in other animals. Hence in other animals prudence is a natural estimate about the pursuit of what is fitting and the avoidance of what is harmful, as a lamb follows its mother and runs away from a wolf.

12. But among those animals which have memory some have hearing and some do not. And all those which cannot hear (as the bee or any other similar type of animal that may exist), even though they have prudence, are still incapable of being taught, i.e., in the sense that they can be habituated to the doing or avoiding of something through someone else’s instruction, because such instruction is received chiefly by means of hearing. Hence in The Senses and Their Objects it is stated that hearing is the sense by which we receive instruction. Furthermore, the statement that bees do not have hearing is not opposed in any way to the observation that they are frightened by certain sounds. For just as a very loud sound kills an animal and splits wood, as is evident in the case of thunder, not because of the sound but because of the violent motion of the air in which the sound is present, in a similar fashion those animals which lack hearing can be frightened by the sounding air even though they have no perception of sound. However, those animals which have both memory and hearing can be both prudent and teachable.

13. It is evident, then, that there are three levels of knowing in animals. The first level is that had by animals which have neither hearing nor memory, and which are therefore neither capable of being taught nor of being prudent. The second level is that of animals which have memory but are unable to hear, and which are therefore prudent but incapable of being taught. The third level is that of animals which have both of these faculties, and which are therefore prudent and capable of being taught. Moreover, there cannot be a fourth level, so that there would be an animal which had hearing but lacked memory. For those senses which perceive their sensible objects by means of an external medium—and hearing is one of these—are found only in animals which have locomotion and which cannot do without memory, as has been pointed out (10).

14. Thus other animals (4).

Here he explains the levels of human knowing; and in regard to this he does two things. First (14), he explains how human knowing surpasses the knowing of the abovementioned animals. Second (17), he shows how human knowing is divided into different levels (“Now in men”).

Accordingly, in the first part (4) he says that the life of animals is ruled by imagination and memory: by imagination in the case of imperfect animals, and by memory in the case of perfect animals. For even though the latter also have imagination, still each thing is said to be ruled by that [power] which holds the highest place within it. Now in this discussion life does not mean the being of a living thing, as it is understood in Book II of The Soul, when he says that “for living things to live is to be”; for the life of an animal in this sense is not a result of memory or imagination but is prior to both of these. But life is taken to mean vital activity, just as we are also accustomed to speak of association as the life of men. But by the fact that he establishes the truth about the cognition of animals with reference to the management of life, we are given to understand that knowing belongs to these animals, not for the sake of knowing, but because of the need for action.

15. Now, as is stated below (18), in men the next thing above memory is experience, which some animals have only to a small degree. For an experience arises from the association of many singular [intentions] received in memory. And this kind of association is proper to man, and pertains to the cogitative power (also called particular reason), which associates particular intentions just as universal reason associates universal ones. Now since animals are accustomed to pursue or avoid certain things as a result of many sensations and memory, for this reason they seem to share something of experience, even though it be slight. But above experience, which belongs to particular reason, men have as their chief power a universal reason by means of which they live.

16. And just as experience is related to particular reason [in men], and customary activity to memory in animals, in a similar way art is related to universal reason. Therefore, just as the life of animals is ruled in a perfect way by memory together with activity that has become habitual through training, or in any other way whatsoever, in a similar way man is ruled perfectly by reason perfected by art. Some men, however, are ruled by reason without art; but this rule is imperfect.

17. Now in men (5).

Here he explains the different levels of human knowing; and in regard to this he does two things. First (17), he compares art with experience; and, second (31), he compares speculative art with practical art (“It is only fitting”).

He treats the first point in two ways. First, he explains how art and experience originate. Second (20), he explains how one is superior to the other (“In practical matters”).

In regard to the first he does two things. First, he explains how each of the above originates. Second (18), he makes this clear by means of an example (“For to judge”).

In regard to the first he does two things. First, he describes how experience originates, and second (18), how art originates (“But in men, science”).

He says first (5), then, that in men experience is caused by memory. The way in which it is caused is this: from several memories of a single thing a man acquires experience about some matter, and by means of this experience he is able to act easily and correctly. Therefore, because experience provides us with the ability to act easily and correctly, it seems to be almost the same as science and art. For they are alike inasmuch as in either case from many instances a single view of a thing is obtained. But they differ inasmuch as universals are grasped by art and singular things by experience, as is stated later (18).

18. But in men science and art (6). Here he describes the way in which art arises. He says that in men science and art come from experience, and he proves this on the authority of Polus, whp says that “Experience causes art and inexperience luck.” For when an inexperienced person acts correctly, this happens by chance. Furthermore, the way in which art arises from experience is the same as the way spoken of above in which experience arises from memory. For just as one experiential cognition comes from many memories of a thing, so does one universal judgment abour all similar things come from the apprehension of many experiences. Hence art has this [unified view] more than experience, because experience is concerned only with singulars, whereas art has to do with universals.

19. Thereupon he makes this clear by means of examples (“But in men”). For when a man has learned that this medicine has been beneficial to Socrates and Plato, and to many other individuals who were suffering from some particular disease, whatever it may be, this is a matter of experience; but when a man learns that this particular treatment is beneficial to A men who have some particular kind of disease and some particular kind of physical constitution, as it has benefited the feverish, both the phlegmatic and the bilious, this is now a matter of art.

20. In practical matters (7).

He compares art to experience from the viewpoint of pre-eminence; and in regard to this he does two things. First (20), he compares them from the viewpoint of action; and, second (23), from the viewpoint of knowledge (“Yet we think”).

He says then that in practical matters experience seems to differ in no way from art; for when it comes to acting, the difference between experience and art, which is a difference between the universal and the singular, disappears, because art operates with reference to singulars just as experience does. Therefore the aforesaid difference pertains only to the way in which they come to know. But even though art and experience do not differ in the way in which they act, because both act on singular things, nevertheless they differ in the effectiveness of their action. For men of experience act more effectively than those who have the universal knowledge of an art but lack experience.

21. The reason is that actions have to do with singular things, and all processes of generation belong to singular things. For universals are generated or moved only by reason of something else, inasmuch as this belongs to singular things. For man is generated when this man is generated. Hence a physician heals man only incidentally, but properly he heals Plato or Socrates, or some man that can be individually named, to whom the nature man belongs, or rather to whom it is accidental inasmuch as he is the one healed. For even though the nature man belongs essentially to Socrates, still it belongs only accidentally to the one healed or cured; for the proposition “Socrates is a man” is an essential one, because, if Socrates were defined, man would be given in his definition, as will be said below in Book IV.” But the proposition “What is healed or cured is man” is an accidental one.

22. Hence, since art has to do with universals and experience with singulars, if anyone has the theoretical knowledge of an art but lacks experience, he will be perfect insofar as he knows the universal; but since he does not know the singular, because he lacks experience, he will very often make mistakes in healing. For healing belongs to the realm of the singular rather than to that of the universal, because it belongs to the former essentially and to the latter accidentally.

23. Yet we think (8).

Here he compares art with experience from the viewpoint of knowing; and in regard to this he does two things. First (23), he states how art is superior to experience; and second (24), he proves this (“Now this is because”).

He claims that art and science are superior to experience in three respects. First, they are superior from the viewpoint of scientific knowledge, which we think is attained by art rather than by experience. Second, they are superior from the viewpoint of meeting objections, which occurs in disputes. For in a dispute the one who has an art is able to meet the objections raised against that art, but one who has experience [alone] cannot do this. Third, they are superior from this point of view, that those who have an art come nearer to the goal of wisdom than men of experience, “Implying that it is,” i.e., happens to be, “more truly to know if wisdom pursues all things,” i.e., insofar as it pursues universals. For one who has an art is judged wiser than one who has experience, by reason of the fact that he considers universals. Or in another version: “Implying that it is more according to wisdom to know as one pursuing all things,” i.e., universals. Another reading has: “As more conformable to knowing, since wisdom pursues all things,” as if to say: “As more dependent upon knowing” than upon doing, “since wisdom pursues all things,” i.e., it seeks to reach each single thing; so that those are rather called wise who are more knowing, not those who are more men of action. Hence another reading expresses this meaning more clearly, saying: “Implying that all pursue wisdom more with respect to knowing.”

24. Now this is (9).

Then he proves the superiority of art and science mentioned above, and he does this by means of three arguments. The first runs thus: those who know the cause and reason why a thing is so are more knowing and wiser than those who merely know that it is so but do not know why. Now men of experience know that something is so but do not know the reason, whereas men who have an art know not merely that something is so but also know its cause and reason. Hence those who have an art are wiser and more knowing than those who have experience.

25. For this reason too (9).

Here he proves the first aspect of superiority, and this runs as follows. Those who know the cause and reason why a thing is so are compared to those who merely know that it is so as the architectonic arts are to the arts of manual laborers. But the architectonic arts are nobler. In a similar way, then, those who know the causes and reasons of things are more knowing than those who merely know that things are so.

26. The first part of this proof becomes clear from the fact that architects, or master artists, know the causes of the things that are done. In order to understand this we must note that architect means chief artist, from αρχος meaning chief, and τεχνη meaning art. Now that art is said to be a chief art which performs a more important operation. Indeed, the operations of artists are distinguished in this way; for some operations are directed to disposing the material of the artifact. Carpenters, for example, by cutting and planing the wood, dispose matter for the form of a ship. Another operation is directed to introducing this form into the matter, for example, when someone builds a ship out of wood which has been disposed and prepared. A third operation is directed to the use of the finished product, and this is the highest operation. But the first operation is the lowest because it is directed to the second and the second to the third. Hence the shipbuilder is a superior artist compared with the one who prepares the wood; and the navigator, who uses the completed ship, is a superior artist comparedwith the shipbuilder.

27. Further, since matter exists for the sake of form, and ought to be such as to befit the form, the shipbuilder knows the rea son why the wood should be shaped in some particular way; but those who prepare the wood do not know this. And in a similar way, since the completed ship exists in order to be used, the one who uses the ship knows why it should have some particular form; for the form should be one that befits its use. Thus it is evident that the reason for the operations which dispose the matter is taken from the design of the product in the artist’s mind, and the reason for the operations which produce the form of the artifact is taken from the use [to which the artifact is put].

28. It is evident, then, that the master artists know the causes of the things which are done. In fact we judge and speak about the others, i.e., the manual laborers, as we do about certain inanimate things. This is not because they do not perform artful operations, but because the things which they do they do without knowing the cause; for they know that something is to be done but not why it is, just as fire burns without knowing why. Hence there is a likeness between inanimate things and manual laborers from this point of view, that, just as inanimate things act without knowing the causes, inasmuch as they are directed to their proper end by a superior intellect, so also do manual laborers. But they differ in this respect, that inanimate things perform each of their operations as a result of their nature, whereas manual laborers perform theirs through habit. And while habit is practically the same as nature inasmuch as it is inclined to one definite effect, still habit differs from nature inasmuch as it is open to opposites by reason of human knowledge. For we do not habituate natural bodies, as is stated in Book II of the Ethics; nor, indeed, is it possible to cause habits in things that lack knowledge. Now the statements that have been made, as is evident from the statements themselves, must be interpreted as meaning that some men are wiser, not insofar as they are “practical,” i.e., men of action, as befits men of experience, but insofar as they have a plan for things to be done and know their causes, which are the basis of such a plan; and this befits master artists.

29. In general a sign of scientific knowledge (10).

Here he gives the second argument, which is as follows: a sign of knowledge is the ability to teach, and this is so because each thing is perfect in its activity when it can produce another thing similar to itself, as is said in Book IV of Meteors. Therefore, just as the possession of heat is indicated by the fact that a thing can heat something else, in a similar way the possession of knowledge is indicated by the fact that one can teach, that is, cause knowledge in another. But men who have an art can teach, for since they know causes they can demonstrate from these; and demonstration is a syllogism which produces knowledge, as is said in Book I of the Posterior Analytics. But men who have experience [only] cannot teach; for since they do not know the causes, they cannot cause knowledge in someone else. And if they do teach others the things which they know by experience, these things are not learned after the manner of scientific knowledge but after that of opinion or belief. Hence, it is clear that men who have an art are wiser and more knowing than those who have experience.

30. Furthermore, we do not hold (11).

Here he gives the third argument, which is as follows: knowing singular things is proper to the senses rather than to any other type of knowing [power], since our entire knowledge of singular things originates with the senses. Yet we do not hold that “any one of these,” i.e., any one of the senses, is wisdom, because even though each sense knows that a thing is so, it does not know why it is so; for touch judges that fire is hot but does not know why it is hot. Therefore men of experience, who have a knowledge of singular things but do not know their causes, cannot be called wise men.

31. It is only fitting (12).

Here he compares practical art with speculative art; and in regard to this he does three things. First (20), he shows that a speculative art is wisdom to a greater degree than a practical art. Second (ibid.), he answers an objection (“The difference”).

He proves his first statement by this argument: in any of the sciences or arts we find that men with scientific knowledge are more admired and are held in higher esteem than all other men, because their knowledge is held to be nobler and more worthy of the name of wisdom. Now the discoverer of any art at all is admired because he perceives, judges and discerns a cause beyond the perceptions of other men, and not because of the usefulness of his discoveries. We admire him rather “as being wise, and as distinguishing [a thing] from others.” As being wise, indeed, in the subtle way in which he investigates the causes of his discoveries, and as distinguishing [a thing] from others insofar as he investigates the ways in which one thing differs from another. Or, according to another interpretation, “as being distinct from the others” is to be read passively, as being distinguished in this respect from others. Hence another text has “one who is different.” Some sciences, then, are more admirable and worthy of the name of wisdom because their observations are more outstanding, not because they are useful.

32. Therefore, since many useful arts have been discovered (some to provide the necessities of life, as the mechanical arts, and others to introduce us to the sciences, as the logical disciplines), those artists must be said to be wiser whose sciences were discovered not for the sake of utility but merely for the sake of knowing, that is to say, the speculative sciences.

33. That the speculative sciences were not discovered for the sake of utility is made clear by this fact, that after all sciences of this kind “had already been developed,” i.e., acquired or discovered, which can serve as introductions to the other sciences, or provide the necessities of life, or give pleasure (as those arts whose object is to delight man), the speculative sciences were discovered, not for this kind of end, but for their own sake. The fact that they were not discovered for the sake of utility becomes evident from the place in which they were discovered. For they originated in those places where men first applied themselves to such things. Another version reads, “And first in those places where men had leisure,” i.e., they had time for study because they were released from other occupations as a result of the abundance of things necessary [for life]. Hence the mathematical arts, which are speculative in the highest degree, were first discovered in Egypt by the priests, who were given time for study, and whose expenses were defrayed by the community, as we also read in Genesis (47:22)

34. But because the names “wisdom,” “science” and “art” have been used indifferently, lest someone should think that these terms are synonymous, he excludes this opinion and refers to his work on morals, i.e., to Book VI of the Ethics, where he has explained the difference between art, wisdom, science, prudence, and understanding. And to give the distinction briefly—wisdom, science and understanding pertain to the speculative part of the soul, which he speaks of in that work as the scientific part of the soul. But they differ in that understanding is the habit of the first principles of demonstration, whereas science has to do with conclusions drawn from subordinate causes, and wisdom with first causes. This is the reason it is spoken of there as the chief science. But prudence and art belong to the practical part of the soul, which reasons about our contingent courses of action. And these also differ; for prudence directs us in actions which do not pass over into some external matter but are perfections of the one acting (which is the reason why prudence is defined in that work as the reasoned plan of things to be done), but art directs us in those productive actions, such as building and cutting, which pass over into external matter (which is the reason why art is defined as the reasoned plan of things to be made).

Wisdom deals with causes.

35. From what has been said he proves his major thesis, that is to say, that wisdom deals with the causes of things. He says that the reason “for undertaking this investigation,” i.e., the above piece of reasoning, is that the science which is called wisdom seems to be about first causes and principles. This is evident from the foregoing; for the more a man attains to a knowledge of the cause, the wiser he is. This is also evident from the foregoing; because the man of experience is wiser than one who has sensation alone without experience; and the artist is wiser than any man of experience; and among artists the architect is wiser than the manual laborer. And similarly among the arts and sciences the speculative are more scientific than the practical. All these things are dear from the foregoing remarks. It follows, then, that that science which is wisdom in an absolute sense is concerned with the causes of things. The method of arguing would be similar if we were to say that that which is hotter is more afire, and therefore that that which is afire in an absolute sense is hot in an absolute sense.

LESSON 2

Wisdom Considers Universal First Causes and First Principles

ARISTOTLE’S TEXT Chapter 2: 982a 4-982b 11

14. But since we are in search of this science, it will therefore be necessary to consider with what kind of causes and principles wisdom or science deals. This will perhaps become evident if we take the opinions which we have about the wise man. First of all, then, we think that the wise man is one who knows all things in the highest degree, as becomes him, without having a knowledge of them individually.

15. Next, we say that that man is wise who is capable of knowing things that are difficult and not easy for man to understand. For sensory perception is common to all, and is therefore easy and not a matter of wisdom.

16. Again, [we consider him wise who is] more certain.

17. And in every branch of science we say that he is wiser who is more capable of teaching us about the causes of things.

18. Again, among the sciences we think that that science which exists for itself and is desirable for the sake of knowledge is wisdom to a greater degree than one which is desirable for the sake of contingent effects.

19. And we think that a superior science which is rather the more basic comes nearer to wisdom than a subordinate science. For a wise man must not be directed but must direct, and he must not obey another but must be obeyed by one who is less wise. Such then and so many are the opinions which we have about the wise and about wisdom.

20. Now of these attributes, that of knowing all things necessarily belongs to him who has universal knowledge in the highest degree, because he knows in which are subordinate.

21. But the things which are just about the most difficult for man to understand are also those which are most universal; for they are farthest removed from the senses.

22. Again, the most certain of the sciences are those which are most concerned with primary things. For sciences based on fewer principles are more certain than those which have additional principles, as arithmetic is more certain than geometry.

23. Moreover, that science which speculates about the causes of things is more instructive. For those who teach us are those who assign the causes of every single thing.

24. Again, understanding and scientific knowledge for their own sake are found in the highest degree in the science which has as its object what is most knowable. For one who desires scientific knowledge for itself will desire in the highest degree the science which is most truly science, and such a science has for its object what is most knowable. Now first principles and causes are most knowable; for it is by reason of these and from these that other things are known, and not these from things which are subordinate to them.

25. But that science is highest and superior to subordinate sciences which knows the reason why each single thing must be done. This is the good of every single thing, and viewed universally it is the greatest good in the whole of nature.

26. In view of everything that has been said, then, the term which we are investigating evidently falls to the same science. For this science must speculate about first principles and causes, because the good, or that for the sake of which something is done, is also one of the causes.

COMMENTARY

Six opinions about who is wise

36. Having shown that wisdom is a knowledge of causes, the Philosopher’s aim here is to establish with what kinds of causes and what kinds of principles it is concerned. He shows that it is concerned with the most universal and primary causes, and he argues this from the definition of wisdom.

In regard to this he does three things. First, he formulates a definition of wisdom from the different opinions which men have about the wise man and about wisdom. Second (44), he shows that all of these are proper to that universal science which considers first and universal causes (“Now of these”). Third (50), he draws the conclusion at which he aims (“In view of everything”). In regard to the first he gives six common opinions which men have entertained about wisdom.

He states the first where he says “But since we are in search”; and this opinion is this: in general we all consider those especially to be wise who know all things, as the case demands, without having a knowledge of every singular thing. For this is impossible, since singular things are infinite in number, and an infinite number of things cannot be comprehended by the intellect.

37. Next, we say that (15).

Here he gives the second opinion, which is this: we hold that man to be wise who is capable, by reason of his intellect, of knowing difficult things, and those which are not easy for ordinary men to understand. For sensory perception, i.e., the knowing of sensible things, is common to all men, and is therefore easy and so not a matter of wisdom. That is to say, it is neither a mark nor the office of a wise man. Thus it is clear that whatever pertains properly to wisdom is not easily known by all.

38. Again, [we consider] (16).

Here he gives the third opinion, namely, that we say that he is wise who, regarding what he knows, is more certain than other men generally are.

39. And in every branch (17). Here he gives the fourth opinion, namely, that that man is said to be wiser in every science who can give the causes of anything that is brought into question, and can teach by means of this.

40. Again, among the sciences (18).

Here he gives the fifth opinion, which is this: among the many sciences that science which is more desirable and willed for its own sake, i.e., chosen for the sake of knowledge and for knowledge itself alone, is more of the nature of wisdom than one which is for the sake of any of the other contingent effects which can be caused by knowledge, such as the necessities of life, pleasure, and so forth.

41. And we think (19). Here he gives the sixth opinion, namely, that this wisdom, of which mention has been made, must be or is said to be “rather the more basic,” i.e., nobler, than “a subordinate science.” This can be understood from the foregoing. For in the field of the mechanical arts, subordinate artists are those who execute by manual operations the commands of superior artists, whom he referred to above as master artists and wise men.

42. That the notion of wisdom belongs to sciences which give orders rather than to those which take them, he proves by two arguments. The first is that subordinate sciences are directed to superior sciences. For subordinate arts are directed to the end of a superior art, as the art of horsemanship to the end of the military art. But in the opinion of all it is not fitting that a wise man should be directed by someone else, but that he should direct others The second is that inferior artists are induced to act by superior artists inasmuch as they rely upon superior artists for the things which they must do or make. Thus the shipbuilder relies upon the instructions of the navigator for the kind of form which a ship ought to have. However, it does not befit a wise man that he should be induced to act by someone else, but that he should use his knowledge to induce others to act.

43. These, then, are the kind of opinions which men have of wisdom and the wise; and from all of these a description of wisdom can be formulated, so that the wise man is described as one who knows all, even difficult matters, with certitude and through their cause; who seeks this knowledge for its own sake; and who directs others and induces them to act. And in this way the major premise of the syllogism becomes evident. For every wise man must be such, and conversely whoever is such is wise.

These six attributes are found in the metaphysician.

44. Now of these (20). Here he shows that all of the above attributes come together in the man who knows the first and universal causes of things; and he follows the same order as he did above. Thus he held first that knowledge of all things in the highest degree belongs to him who has universal knowledge. This was the first opinion, and it is made clear in this way: Whoever knows universals knows in some respect the things which are subordinate to universals, because he knows the universal in them.’ But all things are subordinate to those which are most universal. Therefore the one who knows the most universal things, knows in a sense all things.

45. But the things (21).

Here he proves that the second attribute belongs to the same person, by the following argument. Those things which are farthest removed from the senses are difficult for men to know; for sensory perception is common to all men since all human knowledge originates with this. But those things which are most universal are farthest removed from sensible things, because the senses have to do with singular things. Hence universals are the most difficult for men to know. Thus it is clear that that science is the most difficult which is most concerned with universals.

46. But the statement which appears in Book I of the Physics seems to contradict this. For it is said there that more universal things are known first by us; and those things which are known first are those which are easier. Yet it must be said that those things which are more universal according to simple apprehension are known first; for being is the first thing that comes into the intellect, as Avicenna says, and animal comes into the intellect before man does. For just as in the order of nature, which proceeds from potentiality to actuality, animal is prior to man, so too in the genesis of knowledge the intellect conceives animal before it conceives man.

But with respect to the investigations of natural properties and causes, less universal things are known first, because we discover universal causes by means of the particular causes which belong to one genus or species. Now those things which are universal in causing are known subsequently by us (notwithstanding the fact that they are things which are primarily knowable according to their nature), although things which are universal by predication are known to us in some way before the less universal (notwithstanding the fact that they are not known prior to singular things). For in us sensory knowledge, which is cognitive of singular things, precedes intellective knowledge, which is about universals. And some importance must also be attached to the fact that he does not say that the most universal things are the most difficult absolutely, but “just about.” For those things which are entirely separate from matter in being, as immaterial substances, are more difficult for us to know than universals. Therefore, even though this science which is called wisdom is the first in dignity, it is still the last to be learned.

47. Again, the most certain (22).

Here he shows that the third attribute belongs to the same science, by this argument: the more any sciences are prior by nature, the more certain they are. This is clear from the fact that those sciences which are said to originate as a result of adding something to the other sciences are less certain than those which take fewer things into consideration; for example, arithmetic is more certain than geometry because the objects considered in geometry are a result of adding to those considered in arithmetic. This becomes evident if we consider what these two sciences take as their first principle, namely, the point and the unit. For the point adds to the unit the notion of position, because undivided being constitutes the intelligible structure of the unit; and insofar as this has the function of a measure it becomes the principle of number. And the point adds to this the notion of position. However, particular sciences are subsequent in nature to universal sciences, because their subjects add something to the subjects of universal sciences. For example, it is evident that mobile being, with which the philosophy of nature deals, adds to being pure and simple, with which metaphysics is concerned, and to quantified being, with which mathematics is concerned. Hence that science which treats of being and the most universal things is the most certain. Moreover, the statement here that this science deals with fewer principles is not opposed to the one made above, that it knows all things; for the universal takes in fewer inferiors actually, but many potentially. And the more certain a science is, the fewer actual things it has to consider in investigating its subject-matter. Hence the practical sciences are the least certain, because they must consider the many circumstances attending individual effects.

48. Moreover, that science (23).

Here he proves that the fourth attribute belongs to the same science, by this argument: that science is more instructive, or better able to teach, which is concerned to a greater degree with causes. For only those teach who assign the causes of every single thing, because scientific knowledge comes about through some cause, and to teach is to cause knowledge in another. But that science which considers universals considers the first of all the causes. Hence it is evidently the best fitted to teach.

49. Again, understanding (24).

Here he proves that the fifth attribute belongs to the same science, by this argument: it is the office of those sciences which deal with things that are most knowable, most properly to know and understand for their own sake, i.e., for the sake of those sciences themselves and not for something else. But it is the sciences that deal with first causes which consider the most knowable things. Therefore those sciences are desired most for their own sake. He proves the first premise thus: One who most desires knowledge for the sake of knowledge most desires scientific knowledge. But the highest kind of knowledge is concerned with things that are most knowable. Therefore those sciences are desired most for their own sake which have to do with things that are most knowable. He proves the second premise thus: Those things from which and by reason of which other things are known are more knowable than the things which are known by means of them. But these other things are known through causes and principles, and not vice versa, etc.

50. But that science (25).

Here he proves that the sixth attribute belongs to the same science, by the following argument: that science which considers the final cause, or that for the sake of which particular things are done, is related to the other sciences as a chief or master science is to a subordinate or ancillary one, as is evident from the foregoing remarks. For the navigator, to whom the use, or end, of the ship belongs, is a kind of master artist in relation to the shipbuilder who serves him. But the aforesaid science is concerned most with the final cause of all things. This is dear from the fact that that for the sake of which all particular things are done is the good of each, i.e., a particular good. But the end in any class of things is a good; and that which is the end of all things, i.e., of the universe itself, is the greatest good in the whole of nature. Now this belongs to the consideration of the science in question, and therefore it is the chief or architectonic science with reference to all the others.

51. In view of everything (26). Here he draws from the foregoing arguments his intended conclusion, saying that it is clear from everything that has been said that the name wisdom which we are investigating belongs to the same science which considers or speculates about first principles and causes. This is evident from the six primary conditions which clearly pertain to the science that considers universal causes. But because the sixth condition touched on the consideration of the end, which was not clearly held to be a cause among the ancient philosophers, as will be said below (1177), he therefore shows in a special way that this condition belongs to the same science, namely, the one which considers first causes. For the end, which is a good and that for the sake of which other things are done, is one of the many causes. Hence the science which considers first and universal causes must also be the one which considers the universal end of all things, which is the greatest good in the whole of nature.

LESSON 3

The Nature and Goal of Metaphysics

ARISTOTLE’S TEXT Chapter 2: 982b 11-983a 23

27. That this is not a practical science is evident from those who first philosophized. For it is because of wonder that men both now and formerly began to philosophize, about less important matters, and then progressing little by little, they raised questions about more important ones, such as the phases of the moon and the courses of the sun and the stars and the generation of the universe. But one who raises questions and wonders seems to be ignorant. Hence the philosopher is also to some extent a lover of myth, for myths are composed of wonders. If they philosophized, then, in order to escape from ignorance, they evidently pursued their studies for the sake of knowledge and not for any utility.

28. And what has happened bears witness to this; for when nearly all the things necessary for life, leisure and learning were acquired, this kind of prudence began to be sought. It is evident, then, that we do not seek this knowledge for the sake of any other necessity.

29. But just as we say that a man is free who exists for himself and not for another, in a similar fashion this is the only free, science, because it alone exists for itself.

30. For this reason, too, it might rightly be thought that this science is not a human possession, since in many respects human nature is servile.

31. Hence, according, to Simonides, “Only God has this honor,” I and it is unfitting that a man should not seek a knowledge which befits him. Some poets accordingly say that the deity is naturally envious; and it is most likely that it should happen in this case, and that all those who are imperfect are unfortunate. But it is not fitting that the deity should be envious, for as the proverb says: “The poets tell many lies.”

32. Nor must we think that any other science is more honorable than this. For what is most divine is most honorable. But then it alone will be such, and in two ways. For of all knowledge that which God most properly has is divine; and if there is any such knowledge, it is concerned with divine matters. But this science alone has both of these characteristics; for God seems to be a cause and in some sense a principle according to all men; and such [knowledge as this] God either alone has, or has in the highest degree. Therefore, all the other sciences are more necessary, but none is more excellent.

33. But it is necessary in a sense to bring to a halt the progression of this science at the contrary of our original questions. Indeed, as we have said, all men begin by wondering whether things are as strange as chance occurrences appear to those who do not yet know the cause; or by wondering about the changes in the course of the sun, or about the incommensurability of the diagonal [of a square]. For it would seem an object of wonder to all it something having the nature of number were immeasurable. But it is necessary to advance to the contrary view and, as the proverb says, the worthier one, as also happens in a sense in these matters when men have learned them. For nothing would surprise a geometrician more than if the diagonal [of a square] should become commensurable [with a side]. It has been stated, then, what the nature is of the science which we are seeking, and what its goal is for which our search and whole method must be undertaken.

COMMENTARY

Why this science is called speculative

53. First, he gives this argument. No science in which knowledge itself is sought for its own sake is a practical science, but a speculative one. Bot that science which is wisdom, or philosophy as it is called, exists for the sake of knowledge itself. Hence it is speculative and not practical. He proves the minor premise in this way. Whoever seeks as an end to escape from ignorance tends toward knowledge for itself. But those who philosophize seek as an end to escape from ignorance. Therefore they tend towards knowledge for itself.

54. That they seek to escape from ignorance is made clear from the fact that those who first philosophized and who now philosophize did so from wonder about some cause, although they did this at first differently than now. For at first they wondered about less important problems, which were more obvious, in order that they might know their cause; but later on, progressing little by little from the knowledge of more evident matters to the investigation of obscure ones, they began to raise questions about more important and hidden matters, such as the changes undergone by the moon, namely, its eclipse, and its change of shape, which seems to vary inasmuch as it stands in different relations to the sun. And similarly they raised questions about the phenomena of the sun, such as its eclipse, its movement and size; and about the phenomena of the stars, such as their size, arrangement, and so forth; and about the origin of the whole universe, which some said was produced by chance, others by an intelligence, and others by love.

55. Further, he points out that perplexity and wonder arise from ignorance. For when we see certain obvious effects whose cause we do not know, we wonder about their cause. And since wonder was the motive which led men to philosophy, it is evident that the philosopher is, in a sense, a philo-myth, i.e., a lover of myth, as is characteristic of the poets. Hence the first men to deal with the principles of things in a mythical way, such as Perseus and certain others who were the seven sages, were called the theologizing poets. Now the reason why the philosopher is compared to the poet is that both are concerned with wonders. For the myths with which the poets deal are composed of wonders, and the philosophers themselves were moved to philosophize as a result of wonder. And since wonder stems from ignorance, they were obviously moved to philosophize in order to escape from ignorance. It is accordingly evident from this that “they pursued” knowledge, or diligently sought it, only for itself and not for any utility or usefulness.

56. Now we must note that, while this science was first designated by the name wisdom, this was later changed to the name philosophy, since they mean the same thing. For while the ancients who pursued the study of wisdom were called sophists, i.e., wise men, Pythagoras, when asked what he professed himself to be, refused to call himself a wise man as his predecessors had done, because he thought this was presumptuous, but called himself a philosopher, i.e., a lover of wisdom. And from that time the name “wise man” was changed to “philosopher,” and “wisdom” to “philosophy.” This name also contributes something to the point under discussion, for that man seems to be a lover of wisdom who seeks wisdom, not for some other reason, but for itself alone. For he who seeks one thing on account of something else, has greater love for that on whose account he seeks than for that which he seeks.

57. And what has happened (28).

Here he proves the same point by means of an example. The statement (he says) that wisdom or philosophy is not sought for any utility but for knowledge itself is proved by “what has happened,” i.e., by what has occurred in the case of those who have pursued philosophy. For when nearly all those [arts] were discovered which are necessary for life, “leisure” (i.e., for the sort of pleasure which consists in a life of ease), and learning, such as the logical sciences, which are not sought for themselves but as introductions to the other arts, then man began for the first time to seek this kind of prudence, namely, wisdom. And from this it is clear that wisdom is not sought because of any necessity other than itself but for itself a one; for no one seeks something which he already possesses. Hence, because wisdom was sought after all other knowledge had been discovered, it is evident that it was not sought for some reason other than itself but for itself.

Why this science is liberal

58. But just as (29).

Here he proves the second attribute, namely, that wisdom is free; and he uses the following argument: that man is properly said to be free who does not exist for someone else but for himself. For slaves exist for their masters, work for them, and acquire for them whatever they acquire. But free men exist for themselves inasmuch as they acquire things for themselves and work for themselves. But only this science exists for itself; and therefore among all the sciences only this science is free.

59. Now we must note that this can be understood in two ways. In one way, the expression “only this” may indicate every speculative science as a class. And then it is true that only this class of science is sought for itself. Hence, only those arts which are directed to knowing are called free [or liberal] arts, whereas those which are directed to some useful end attained by action are called mechanical or servile arts.

Understood in another way, the expression may specifically indicate this philosophy or wisdom which deals with the highest causes; for the final cause is also one of the highest causes, as was stated above (51). Therefore this science must consider the highest and universal end of all things. And in this way all the other sciences are subordinated to it as an end. Hence only this science exists in the highest degree for itself.

Why this science is super-human

60. For this reason (30).

Here he proves the third attribute, namely, that this science is not a human [possession]. In regard to this he does two things. First, he proves his thesis. Second (61), he criticizes an erroneous view held by certain men (“Hence, according to Simonides”).

He proves his thesis by the following argument. A science which is free in the highest degree cannot be a possession of that nature which is servile and subordinate in many respects. But human nature is servile “in many respects,” i.e., in many ways. Therefore this science is not a human possession. Now human nature is said to be servile insofar as it stands in need of many things. And on this account it happens that man sometimes neglects what should be sought for its own sake because of the things necessary for life. Thus it is said in Book III of the Topics that it is better to philosophize than to become wealthy, although sometimes becoming wealthy is more desirable, that is, to one lacking life’s necessities. From this it is clear that that wisdom is sought for itself alone which does not belong to man as his proper possession. For man has as his possession what he can have at his command and use freely. But that science which is sought for itself alone, man cannot use freely, since he is often kept from it because of the necessities of life. Nor again is it subject to man’s command, because man cannot acquire it perfectly. Yet that very small part of it which he does have outweighs all the things known through the other sciences.

61. Hence, according to Simonides (31).

Here he rejects the error of a certain poet, Simonides, who said that it is proper to God alone to have the honor of desiring that knowledge which ought to be sought for its own sake and not for the sake of something else. But it is not fitting that man should not seek that knowledge which is in keeping with his own condition, namely, that which is directed to the necessities of life required by man.

62. Now Simonides’ error came from that of certain poets who said that the Deity is envious, and that since He is envious He does not desire that the things which pertain to His honor should be shared by all. And if God is envious of men in other things, He is rightly more so in this case, i.e., in the case of the science which is sought for its own sake, which is the most honorable of all the sciences. And according to the opinion of these men it follows that all who are imperfect are unfortunate’ for they said that men are fortunate as a result of the providence of the gods, who communicate their goods to men. Hence as a result of the envy of the gods, who are unwilling to communicate their goods, it follows that men, who remain outside the perfection of this science, are unfortunate.

63. But the basis of this opinion is most false, because it is not fitting that any divine being should be envious. This is evident from the fact that envy is sadness at someone else’s prosperity. But this can occur only because the one who is envious thinks that someone else’s good diminishes his own. Now it is impossible that God’ should be sad, because He is not subject to evil of any kind. Nor can His goodness be diminished by someone else’s goodness, since every good flows from His goodness as from an unfailing spring. Hence Plato also said that there is no envy of any kind in God.’ But the poets have lied not only in this matter but in many others, as is stated in the common proverb.

Why this science is most honorable

64. Nor must we think (32).

Here he proves the fourth attribute, namely, that this is the most honorable science, by the following argument. That science which is most divine is most honorable, just as God Himself is also the most honorable of all things. But this science is the most divine, and is therefore the most honorable. The minor premise is proved in this way: a science is said to be divine in two ways, and only this science is said to be divine in both ways. First, the science which God has is said to be divine; and second, the science which is about divine matters is said to be divine. But it is evident that only this science meets both of these requirements, because, since this science is about first causes and principles, it must be about God; for God is understood in this way by all inasmuch as He is one of the causes and a principle of things. Again, such a science which is about God and first causes, either God alone has or, if not He alone, at least He has it in the highest degree. Indeed, He alone has it in a perfectly comprehensive way. And He has it in the highest degree inasmuch as it is also had by men in their own way, although it is not had by them as a human possession, but as something borrowed from Him.

65. From these considerations he draws the further conclusion that all other sciences are more necessary than this science for use in practical life, for these sciences are sought least of all for themselves. But none of the other sciences can be more excellent than this one.

The relation between wonder and wisdom

66. But it is necessary (33).

He now gives the goal toward which this science moves. He says that its progression comes to rest, or is terminated, in the contrary of what was previously found in those who first sought this science, as also happens in the case of natural generations and motions. For each motion is terminated in the contrary of that from which the motion begins. Hence, since investigation is a kind of movement towards knowledge, it must be terminated in the contrary of that from which it begins. But, as was stated above (53), the investigation of this science began with man’s wonder about all things, because the first philosophers wondered about less important matters and subsequent philosophers about more hidden ones. And the object of their wonder was whether the case was like that of strange chance occurrences, i.e., things which seem to happen mysteriously by chance. For things which happen as if by themselves are called chance occurrences. For men wonder most of all when things happen by chance in this way, supposing that they were foreseen or determined by some cause. For chance occurrences are not determined by a cause, and wonder results from ignorance of a cause. Therefore when men were not yet able to recognize the causes of things, they wondered about all things as if they were chance occurrences; just as they wondered about changes in the course of the sun, which are two in number, namely, the solstices, that of winter and that of summer. For at the summer solstice the sun begins to decline toward the south, after previously declining toward the north. But at the winter solstice the opposite occurs. And they wondered also that the diagonal of a square is not commensurable with a side. For since to be immeasurable seems to belong to the indivisible alone (just as unity alone is what is not measured by number but itself measures all numbers), it seems to be a matter of wonder that something which is not indivisible is immeasurable, and consequently that what is not a smallest part is immeasurable. Now it is evident that the diagonal of a square and its side are neither indivisible nor smallest parts. Hence it seems a matter of wonder if they are not commensurable.

67. Therefore, since philosophical investigation began with wonder, it must end in or arrive at the contrary of this, and this is to advance to the worthier view, as the common proverb agrees, which states that one must always advance to the better. For what that opposite and worthier view is, is evident in the case of the above wonders, because when men have already learned the causes of these things they do not wonder. Thus the geometrician does not wonder if the diagonal is incommensurable with a side. For he knows the reason for this, namely, that the proportion of the square of the diagonal to the square of a side is not as the proportion of the square of a number to the square of a number, but as the proportion of two to one. Hence it follows that the proportion of a side to the diagonal is not as the proportion of number to number. And from this it is evident that they cannot be made commensurable. For only those lines are commensurable which are proportioned to each other as number to number. Hence the goal of this science to which we should advance will be that in knowing the causes of things we do not wonder about their effects.

68. From what has been said, then, it is evident what the nature of this science is, namely, that it is speculative and free, and that it is not a human possession but a divine one; and also what its aim is, for which the whole inquiry, method, and art must be conducted. For its goal is the first and universal causes of things, about which it also makes investigations and establishes the truth. And by reason of the knowledge of these it reaches this goal, namely, that there should be no wonder because the causes of things are known.

LESSON 4

Opinions about the Material Cause

ARISTOTLE’S TEXT Chapter 3: 983a 24-984a 16

34. It is evident, then, that one must acquire scientific knowledge of those causes which stand at the beginning, for we say that we have scientific knowledge of each thing when we think we comprehend its first cause. Now causes are spoken of in four ways. Of these we say that one is the substance or quiddity of a thing, for the first “why” of a thing is reduced to its ultimate intelligible structure, and the first why of a thing is a cause or principle; another is the matter or subject; a third is the source of motion; and a fourth is the cause which is opposite to this, namely, that for the sake of which, or the good; for this is the goal of every generation and motion. There has been sufficient consideration of these in our works on nature.

35. However, let us examine those who have undertaken an investigation of existing things and have philosophized about the truth before us. For evidently they too speak of certain principles and causes. Therefore, to us who come later [their views] will serve as an introduction to the study which we are now making; for we shall either discover some other class of cause, or be more convinced of those which have just been expounded.

36. Most of those who first philosophized thought that only the things which belong to the class of matter are the principles of all things. For that of which all things are composed, from which they first come to be, and into which they are finally dissolved, while their substance remains although it is changed in its attributes—this they call the element and principle of existing things.

37. And for this reason they thought that nothing is either generated or corrupted, as if such a reality always remained in existence. And just as we do not say that Socrates comes to be in an unqualified sense when he becomes good or musical, or is corrupted when he loses these states, because the subject Socrates himself remains, in the same way they say that nothing else is generated or corrupted. For there must be some matter, either one or more than one, from which other things come to be, and which itself remains in existence. However, they do not all speak in the same way about the number and nature of such a principle.

38. Thales, the originator of this kind of philosophy, says that this principle is water; and this is why he also claimed that the earth rests upon water.

39. For presumably he took this position because he saw that the nutriment of all things is moist, that heat itself is generated from this, and that animal life comes from this. But that from which each thing comes to be is a principle of all things. He bases his opinion on this, then, and on the fact that the seeds of all things have a moist nature, whereas water is by nature the principle of moist things.

40. Moreover, there are some who think that the ancients who lived long before the present generation and were the first to speculate about the gods held this view about the nature of things. For they made Oceanus and Tethys the parents of generation, and held the oath of the gods to be by a body of water, to which the poets gave the name Styx. For what is oldest is most honorable, and what is most honorable is that by which one swears. Whether this view of nature is in fact the ancient and primary one is perhaps uncertain. Thales is said to have expressed himself in this way about the first cause, but no one could say that Hippo is to be included in this group, because of the weakness of his understanding.

41. Anaximenes and Diogenes hold that air is prior to water and is the most fundamental of the simple bodies.

42. Hippasus of Metopontium and Heraclitus of Ephesus hold that fire [is the primary principle].

43. Empedocles holds that there are four [simple bodies], since he adds a fourth—earth—to those already mentioned. For he says that these always remain and only become many or few in number by being combined into a unity and separated out of a unity.

44. Anaxagoras of Clazomenae, who was prior to Empedocles in years but later in his speculations, says that the principles of things are infinite in number. For he says that nearly all bodies which are made up of parts like themselves, such as fire or water, are generated or corrupted in this way, merely by combining and separating; but that otherwise they are neither generated nor corrupted but always remain in existence. From these views, then, one might think that the only cause is the one which is said to belong to the class of matter.

COMMENTARY

69. Having set f orth a preface in which he indicates the aim of this science, its dignity and goal, Aristotle begins to deal with this science; and this is divided into two parts. In the first (70), he explains what the first philosophers had to say about the causes of things. In the second (274), he begins to pursue the truth of this science. He does this in Book II (“Theoretical, i.e., speculative, knowledge”).

The first part is divided into two members. First, he gives the opinions of the philosophers about the causes of things. Second (181), he criticizes them insofar as their statements are unsatisfactory (“Therefore all those”).

In regard to the firsthe does two things. First, he takes up again the enumeration of causes which was treated in greater detail in Book II of the Physics. Second (72), he presents the opinions of the philosophers (“However, let us examine”).

The four causes, & three characteristics of final cause

70. Accordingly, he says, first, that since it is evident that wisdom speculates about causes, we ought to begin by acquiring knowledge from the causes of things. This also seems to be in keeping with the intelligible structure of science, because we say that we know each thing scientifically when we think we are not ignorant of its cause. Now causes are spoken of in four ways. (1) One of these is the formal cause, which is the very substance of a thing by which we know what each thing is. For it is well known, as is stated in Book II of the Physics, that we do not say that anything has a nature before it has received a form. Now it is clear that a form is a cause, because the question “Why is something so?” we reduce to its formal cause as its ultimate explanation, beginning with proximate forms and proceeding to the ultimate form. But evidently the “why?” asks about a cause and principle. Hence it is evident that a form is a cause. (2) A second cause is the material cause. (3) A third is the efficient cause, which is the source of motion. (4) A fourth is the final cause, which is opposite to the efficient cause as a goal is to a starting-point; for motion begins with the efficient cause and terminates with the final cause. This [latter] cause is also that for the sake of which a thing comes to be, and the good of each nature.

71. He makes the final cause known by three considerations: (1) It is the goal of motion, and thus is opposite to the source of motion, which is the efficient cause. (2) It is first in intention, and for this reason is said to be that for the sake of which [something is done]. (3) It is desirable of itself, and for this reason is called a good; for the good is what all desire.

Hence, in explaining how the final cause is opposite to the efficient cause, he says that it is the goal [or end] of every process of generation and motion, whose starting-point is the efficient cause. By these two types of change he seems to imply that there is a twofold goal: (1) For the goal of a process of generation is the form itself, which is a part of a thing. (2) But the goal of motion is something sought for outside the thing moved. He says that he has treated these causes at sufficient length in the Physics, lest he should be asked to make a more extensive treatment of them.

72. However, let us examine (35).

Here he states what the philosophers had to say about the causes; and in regard to this he does two things. First, he gives the reasons why this must be done; and, second (36:C 73), he begins to carry out his plan ("Most of those").

Accordingly, he says that even though there is a treatise on the causes in the Physics it is still necessary to consider the opinions of the philosophers who first undertook an investigation of the natures of existing things, and have philosophized about the truth before him; because they too set down causes and principles. Therefore, for us who have come later, a consideration of their opinions will be "a first [step]," or preamble, "to the investigation," i.e., to the art which we are now seeking. Hence the text of Boethius also says: "Therefore as we enter upon the task of this science, their opinions will constitute a prearn ble to the road that is now to be travelled." Another text has: "Therefore to us who are beginning this inquiry it will be a certain vital work in the investigation that now confronts us, " and it must be read in this way: "Therefore, as we enter upon our present course," i.e., upon the present study and art, it will be necessary to consider the opinion of these men "as a work of life," that is to say, as necessary, like works which are done for the preservation of life, so that this reading is interpreted as a metaphorical way of speaking, meaning by "work of life" anything necessary. Now this is useful, because from the opinions of these men we will either discover another class of causes over and above those already enumerated, or be more convinced of the things that have just been stated about the causes, namely, that there are four classes of them.

73. Most of those (36).

Here he begins to deal with the opinions of the ancient philosophers; and in regard to this he does two things. First (36), he states their opinions; and, second (86:C 181) he finds fault with them ("Therefore all those").

In regard to the first he does two things. First, he states the opinions which each one of the philosophers held about the causes. Second (79:C 170, he summarizes the discussion ("We have examined").

The first part is divided into two members. In the first (36:C 74), he gives the opinions of those who omitted the formal cause. In the second (69:C 151), he gives the opinion of Plato, who was the first to posit a formal cause ("After the philosophies").

In regard to the first he does two things. First, he gives the opinion of those who claimed that certain evident things are principles. Second (55:C, 12), he gives the opinions of those who devised extrinsic principles ("Leucippus").

In regard to the first he does two things. First, he touches on the opinions which the ancient philosophers held about the material cause; and, second (45:C 93), on their opinions about the efficient cause ("But as men").

In regard to the first he does two things. First, he states in a general way the views of those who posited a material cause. Second (38:C 77), he examines their views in detail ("Thales, the originator").

In regard to the first he does two things. First, he states their opinions about the material cause. Second (37:C 75), he states their opinions about the generation of things, which follow from the first ("And for this reason").

OPINIONS OF THOSE WHO GAVE ONLY MATERIAL CAUSE

Four characteristics of matter

74. Accordingly he says, first (36), that most of those who first philosophized about the natural world held that the principles of all things are merely those which are referred to the class of material cause. In regard to this it must be said that they took the four conditions of matter which seem to belong to the notion of a principle. For, (1) that of which a thing is composed seems to be a principle of that thing. But matter is such a thing; for we say that a thing that has matter is of its matter, as a knife is of iron. (2) That from which a thing comes to be, being also a principle of the process of generation of that thing, seems to be one of its causes, because a thing comes into being by way of generation. But a thing first comes to be from matter, because the matter of things precedes their production. And a thing does not come from matter in an accidental way; for a thing is generated in an accidental way from its contrary or privation, as when we say that white comes from black. (3) Third, that into which all things are ultimately dissolved by corruption seems to be a principle of things. For just as principles are first in the process of generation, in a similar way they are last in the process of dissolution; and obviously this too pertains to matter. (4) Fourth, since a principle must remain in existence, then that which remains throughout the process of generation and corruption seems to be a principle. Now the matter which they said is the substance of a thing remains throughout every transmutation, although its attributes, such as its form and everything that accrues to it over and above its material substance, are changed. From all these considerations they concluded that matter is the element and principle of all beings.

Without material cause, no generation or corruption

75. And for this reason (37).

Then he gives, as a secondary point, what they held as following from the above, namely, that in the world nothing is generated or corrupted in an absolute sense. For when some change occurs with regard to a thing’s attributes, and its substance remains unchanged, we do not say that it is generated or corrupted in an absolute sense, but only in a qualified one; for example, when Socrates becomes good or musical, we do not say that he simply comes to be, but comes to be this. And similarly when he loses a state of this kind, we do not say that he is corrupted in an absolute sense, but only in a qualified one. But matter, which is the substance of things according to them, always remains; and every change affects some of a thing’s accidents, such as its attributes. From this they concluded that nothing is generated or corrupted in an absolute sense, but only in a qualified one.

76. Yet even though they all agreed on this point, in positing a material cause, nevertheless they differed in their position in two respects: first, with respect to the number of material causes, because some held that there is one, and others many; and second, with respect to its nature, because some held that it is fire, others water, and so on. Similarly, among those who posited many material causes, some assigned certain ones as the material principles of things, and some the others.

77. Thales, the originator (38).

Here he begins to give the opinions of each of the philosophers about the material cause. First, he gives the opinions of those who posited one material cause; and second (88), the opinions of those who posited many (“Empedocles”).

In regard to the first he does three things. First, he gives the opinions of those who claimed that water is the principle of all things; second (86), he gives the opinion of those who made air the principle of things (“Anaximenes”); and third (87), the opinion of those who claimed that fire is the principle of things (“Hippasus”).

In regard to the first he does two things. First, he gives the opinion of Thales, who said that water is the principle of things; and second (79), the reason for this opinion (“For presumably”).

He says then that Thales, the originator of this kind of philosophy, i.e., speculative philosophy, said that water is the first principle of all things. Thales is said to have been the originator of speculative philosophy because he was the only one of the seven wise men, who came after the theological poets, to make an investigation into the causes of things, the other sages being concerned with moral matters. The names of the seven wise men are as follows. The first was Thales of Miletus, who lived during the time of Romulus and when Achaz, King of Israel, was reigning over the Hebrews. The second was Pittacus of Mitylene, who lived when Sedecias was reigning over the Hebrews and when Tarquinius Priscus was reigning over the Romans. The other five sages were Solon of Athens, Chilo of Lacedaemon, Periander of Corinth, Cleobulus of Lydia, and Bias of Prienne, all of whom lived during the period of the Babylonian captivity. Hence, since Thales alone among these men investigated the natures of things and distinguished himself by committing his arguments to writing, he is described here as the originator of this science.

78. Nor should it be thought unfitting if he touches here on the opinions of those who have treated only the philosophy of nature; because according to the ancients, who knew no other substance except the corporeal and mobile, it was necessary that first philosophy be the philosophy of nature, as is stated in Book IV. And from this position Thales next adopted this one, that the earth rests upon water, as anything having a principle is based on its principle.

79. For presumably he took (39).

Here he gives the reasons by which Thales could be led to the above position. First, he shows how he was led to this position by his own reasoning; and second (82), by the authority of his predecessors (“Moreover, there are some”).

Now he was led by two lines of reasoning; one is taken from the cause itself of a thing, and the other from a consideration of the generation of things (“And on the fact”). Therefore these premises are related. For the second follows from the first, because that which is a principle of being of other things is also the first principle from which things are generated. The third follows from the second, because by corruption each thing is dissolved into that from which it was generated. The fourth follows from the second and the third; for that which precedes the generation of things and remains after they have been corrupted must always remain in being.

80. In the first line of reasoning he uses three indications to show that water is the principle of being of things. The first of these is that the nutriment of living things must be moist. But living things derive nourishment and being from the same principle; and thus moisture appears to be the principle of being of things. The second indication is that the being of any physical thing, and especially of a living one, is conserved by its proper and natural heat. But heat seems to be generated from moisture, since moisture itself is in a sense the matter of heat. Hence from this it appears that moisture is a principle of being of things. The third indication is that animal life depends on moisture. Hence an animal dies as a result of its natural moisture being dried up and is kept in existence as a result of its moisture being preserved. But in living things to live is to be. Hence it is also evident from this that moisture is a principle of being of things. These three indications also have a natural connection with one another. For an animal is nourished by moisture, because its natural heat is sustained by moisture. And from these two it follows that animal life is always due to moisture. But that from which a thing comes to be, i.e., from which a thing gets its being, is a principle of everything that derives being from it. And for this reason he adopted this opinion that moisture is the principle of all things.

81. In a similar way he also draws an indication of this from the generation of things, because the processes of generation of living things, which are the noblest of [natural] beings, come from seed. But the seed or spermata of all living things have a moist nature. Hence from this it also appears that moisture is a principle of generation of things. Again, if we add to all of the above points the fact that water is the principle of moisture, it follows that water is the first principle of things.

82. Moreover, there are (40).

Here he shows how Thales was led to the above position by the authority of the ancients. He says that prior to Thales and many years before the men of Aristotle’s time there were some men, the first to speculate about the gods, who seem to have held this opinion about nature, namely, that water is the principle of all things.

83. With a view to making this clear, we must bear in mind that among the Greeks the first who were famous for their learning were certain theological poets, so called because of the songs which they wrote about the gods. These poets, who were three in number, Orpheus, Museus and Linus, of whom Orpheus was the more famous, lived during the time when the judges ruled over the Jewish people. Hence it is dear that they lived long before Thales and much longer before Aristotle, who lived during the time of Alexander. These poets dealt to some extent with the nature of things by means of certain figurative representations in myths. For they said that Oceanus [i.e., the ocean], where the greatest aggregation of waters is found, and Tethys, which is the name they gave to the goddess of the waters, are the parents of generation, implying by this, under the form of a myth, that water is the principle of generation.

84. They cloaked this view in another fabulous story, saying that the oath or vow of the gods was by a certain body of water, which the poets call Styx and describe as an underground swamp. And when they said that the gods swore by water, they implied that water was nobler than the gods themselves, because an oath or vow is taken on what is most honorable. Now that which is prior is more honorable; for the perfect is prior absolutely to the imperfect, both in nature and in time, although in a particular being imperfection is prior temporally to perfection. Hence, from this it is evident that they thought that water is prior to the gods themselves, whom they thought to be celestial bodies. And since these earliest thinkers said that water is the principle of things, if there was any opinion about natural bodies prior to theirs, we do not know what it was. Thus what Thales is said to have thought about the first cause of things is now clear.

85. A certain philosopher named Hippo was not credited with adding anything to those mentioned because of the imperfection of his knowledge or understanding. Hence, in The Soul, Hippo is placed among the ruder [thinkers]; for in that work it is stated that Hippo, basing his argument on the seeds of things, as was said here of Thales, held water to be the soul and principle of things. Hence it is clear that he adds nothing to Thales’ view. Or the statement can mean that, since he spoke imperfectly, he did not make himself worthy to have his doctrine included here with the others.

86. Anaxinienes and Diogenes (41).

Here he gives the opinions of those who held that air is the principle of things, namely, Diogenes and Anaximenes, who held that air is naturally prior to water and is the principle of all simple bodies, i.e., of the four elements, and thus of all other things. Anaximenes is the third philosopher after Thales and the disciple of Anaximander, who was the disciple of Thales; and Diogenes is said to have been the disciple of Anaximenes. Yet there is this difference between the opinion of Diogenes and that of Anaximenes: Artaximenes held that air is the principle of things in an absolute sense, whereas Diogenes said that air could be the principle of things only if it possessed a divine nature. From this comes the opinion which is touched on in The Soul, Book I. Now the reason why he held that air is the principle of things could be taken from the process of respiration, by which the life of animals is conserved, and because the processes whereby things are generated and corrupted seem to be modified as a result of changes in the air.

87. Hippasus of Metopontium (42).

Here he states that the two philosophers, Hippasus and Heraclitus, held that fire is the material principle of things. And they could have been influenced by its subtileness, as is said below.

88. Empedocles (43).

Here he gives the opinions of those who posited many material principles. First, he gives the opinion of Empedocles, who held that there are a limited number of such principles; and second 90), that of Anaxagoras, who held that there are an infinite number (“Anaxagoras”).

First (43), he gives Empedocles’ opinion regarding the three elements mentioned above, water, air, and fire, which he says are the principles of things, adding to them a fourth, earth.

89. Second, he gives Empedocles’ opinion about the permanence of these elements; for, like those who hold that there is one material cause, he holds that these elements always remain and are neither generated nor corrupted. However, he said that other things are generated from and dissolved into these elements according as a greater or smaller number of them are combined or separated out, i.e., inasmuch as these four are united by the process of combination and lose their unity by the process of separation.

90. Anaxagoras (44).

Here he gives the opinion of Anaxagoras, who was the other disciple of Anaximenes and the classmate of Diogenes. A native of Clazomenae, he was prior to Empedocles in years but later in his activity or work, either because he began to philosophize later, or because his explanation of the number of principles is less satisfactory than that of Empedocles. For he said that there are an infinite number of material principles, whereas it is better to take a limited and smaller number, as Empedocles did, as is stated in Book I of the Physics. For Anaxagoras not only said that fire, water, and the other elements are the principles of things, as Empedocles did, but also claimed that all things having like parts, such as flesh, bones, marrow and so forth, whose smallest parts are infinite in number, are the principles of things. For he claimed that in each being there are an infinite number of parts of each type of thing, because he found that in the case of inferior things one of these can be generated from another. He said, in fact, that things could be generated only by being separated out from a mixture, as Aristotle has explained more fully in the Physics, Book I.

91. Second, Anaxagoras also agrees with Empedocles on this point, namely, that things are generated and corrupted only insofar as the parts of these infinite principles are combined or separated out, and that if this were not the case nothing would be generated or corrupted. But he said that the infinite number of principles of this kind, from which the substances of things are produced, always remain in being.

92. From the opinions of these philosophers, then, Aristotle concludes that the only cause which these men recognized was the one which belongs to the class of material cause.

LESSON 5

Opinions about the Efficient Cause

ARISTOTLE’S TEXT Chapters 3 & 4: 984a 16-984b 32

45. But as men proceeded in this way, reality itself again opened up a path and forced them to make investigations. For if every process of generation and corruption is from some one thing or more than one, why does this occur, and what is the cause? For certainly the subject itself does not cause itself to change. I mean, for example, that neither wood nor bronze is the cause of the change undergone by either one of them; for wood does not produce a bed, or bronze a statue, but something else is the cause of the change. But to seek this is to seek another principle, as if one were to say that from which the beginning of motion comes.

46. Now in general those who have taken such a course from the very beginning, and who said that the subject is one, created no difficulty for themselves when they said that everything is one. [But some of those who say that it is one ], being baffled, so to speak, by this question, say that this [one subject] and the whole of nature is immobile not only with respect to generation and

corruption (for this is an ancient opinion and one which all men confess to be true), but also with respect to every other change. This opinion is peculiar to them. Hence, of those who said that the [universe] itself is one, it occurred to none of them to conceive of such a cause, except perhaps Parmenides, and to him only insofar as he claims that there is not one cause but also in a sense two causes. But for those who make the elements of things many, such as the hot and cold, or fire and earth, a better explanation is possible, because they use fire as if it were a material principle which is active in nature, but water and earth and the like they use in the opposite way.

47. After these men and such principles, as if they were insufficient to generate the natures of existing things, men were again compelled (as we said [45]) by the truth itself to seek for the next principle. For perhaps it is unlikely that either fire or earth or anything else of this kind should be the cause of the good dispositions of things which are or come to be; nor was it consistent that they should think this to be the case. Nor again would it be right to attribute so important a matter to chance occurrence and fortune.

48. And when someone said that there is one intellect present in nature as in animals, and that this is the cause of the world and the arrangement of the whole, he seemed to atone for the untenable statements made by his predecessors.

We know that Anaxagoras expressed these views, although Hermotimus of Clazomenae was the first to speak of such a cause. Those, therefore, who held these opinions likewise posited a principle in existing things which is the cause of their goodness, and that sort of cause which is the source of motion in the world.

Chapter 4

49. Now someone might have suspected that Hesiod was the first to have investigated this sort of cause, or anyone else who held that love or desire is a principle in existing things, as Parmenides did. For in the place where he attempts to explain the generation of the universe, he says that “Love, the first of all the gods, was made.” And Hesiod says that “The first of all things to be made was chaos, then broad earth, and love, who is pre-eminent among the immortals”—as though there must be in the world some cause which moves things and brings them together. How one must arrange these thinkers in sequence will be decided later on.

COMMENTARY

93. Having given the philosophers opinions about the material cause, Aristotle now gives their opinions about the efficient cause, which is the source of motion. This is divided into two parts. First, he gives the opinion of those who assigned without qualification a cause of motion and generation. Second (97), he examines the opinion of those who posited an efficient cause, which is also the principle of good and evil in the world (“After these men”).

In regard to the first he does two things. First, he gives the reasoning which compelled them to posit an efficient cause. Second (94), he shows the different positions which different men have held regarding this (“Now in general”).

He says (45), then, that some philosophers have proceeded in this way in positing a material cause, but that the very nature of reality clearly provided them with a course for understanding or discovering the truth, and compelled them to investigate a problem which led them to the efficient cause. This problem is as follows: no thing or subject changes itself; for example, wood does not change itself so that a bed comes from it, nor does bronze cause itself to be changed in such a way that a statue comes from it; but there must be some other principle which causes the change they undergo, and this is the artist. But those who posited a material cause, whether one or more than one, said that the generation and corruption of things come from this cause as a subject. Therefore there must be some other cause of change, and to seek this is to seek another class of principle and cause, which is called the source of motion.

94. Now in general (46).

He shows here that the philosophers have adopted three positions with respect to the foregoing issue. For those who adopted this course from the very beginning, and said that there is one material cause, were not greatly concerned with the solution of this problem. For they were content with their view of matter and neglected the cause of motion altogether.

95. But others, who said that all things are one, being defeated as it were by this issue, as they were unable to go so far as to assign a cause of motion, denied motion altogether. Hence they said that the whole universe is one immobile being. In this respect they differed from the first philosophers of nature, who said that one cause is the substance of all things although it is moved by rarefaction and condensation, so that in this way many things come to be in some measure from one principle. However, they did not say that this principle is subject to generation and corruption in an absolute sense. For the view that nothing was generated or corrupted without qualification is an ancient one admitted by all of them, as is clear from what was said above (75). But it was peculiar to these later thinkers to say that the whole of reality is one immobile being, devoid of every kind of motion. These men were Parmenides and Melissus, as will be explained below (138). Hence it is evident that it was impossible for those who said that the whole is one immobile being to conceive of “such a cause,” i.e., a cause of motion. For, by the very fact that they did away with motion, they sought in vain for a cause of motion. An exception was Parmenides; for even though he held that there is only one thing according to reason, he held that there are many things according to the senses, as will be stated below (101). Hence, inasmuch as Parmenides held that there are many things, it was in keeping with his position to hold that there are many causes, one of which would be a mover and the others something moved. For just as he held that there are many things according to the senses, in a similar way it was necessary for him to hold that there is motion according to the senses, because a plurality of things can be understood to be produced from one subject only by some kind of motion.

96. Third, there were those who, in making the substances of things many, assented to the aforesaid reasoning by positing a cause of motion. For they maintained that the hot or the cold, i.e., fire or earth, are causes; and of these they used fire as having a mobile, i.e., an active, nature, but water, earth and air they used in the opposite way, i.e., as having a passive nature. Thus fire was a sort of efficient cause, but the others a sort of material cause.

97. After these men (47).

Here he gives the opinion of those who posited an efficient cause, not only as a principle of motion, but also as a principle of good and evil in things. In regard to this he does two things. First, he expounds their views. Second (107), he shows in what respect they failed in assigning the causes of things (“These thinkers”).

In regard to the first he does two things. First, he gives the reasons for their position by which they were induced to posit another cause besides the foregoing one. Second (100), he shows how they posited this kind of cause in different ways (“And when someone”).

He says first, then, that after the foregoing philosophers who held that there is only one material cause, or many bodies, one of which was active and the others passive, and after the other first principles given by them, men were again compelled by the truth itself ‘ “as we have said,” i.e., as was stated above (93), to seek the “next” principle, i.e., the one which naturally follows the foregoing one, namely, the cause of good, which is really the final cause, although it was held by them only incidentally, as will be see below (177). For they held that there is a cause of goodness in things only after the manner of an efficient cause. They were compelled to do this because the foregoing principles were not sufficient to account for the generation of the natural world, in which some things are found to be well disposed. The fact that bodies are conserved in their proper places and are corrupted outside of them proves this; and so do the benefits resulting from the parts of animals, which are found to be disposed in this manner according as this is in keeping with an animal’s good state of being.

98. But neither fire nor earth nor any such bodies were held to be adequate causes of this kind of good disposition or state of being which some things already have but others acquire by some kind of production. For these bodies act in one definite way according to the necessity of their proper forms, as fire heats things and tends upward, and water cools things and tends downward. But the aforesaid benefits and good states of being of things must have a cause which is not limited to one effect only, since the parts of different animals are found to be disposed in different ways, and in each one insofar as it is in keeping with its nature.

99. Hence, it is not reasonable that fire or earth or the like should be the cause of the aforesaid good state of being which things have, nor was it reasonable that these men should have thought this to be the case. Nor again would it be reasonable to say that these things are chance occurrences, i.e., that they are accidental or come about by chance, and that their causality is changed only fortuitously; although some of these thinkers had said this, as Empedocles and all those who posited a material cause, as is evident in Book II of the Physics. However, this is also seen to be false by reason of the fact that good dispositions of this kind are found either always or for the most part, whereas things that come about by chance or fortune do not occur always or for the most part but seldom. For this reason, then, it was necessary to discover besides the four elements some other principle which would account for the good dispositions of things. Another text has “Nor would it be right that these should be attributed to chance occurrence and fortune,” but this means the same as the above.

OPINIONS ON EFFICIENT CAUSE: intellect or love

100. And when someone said (48).

Here he gives in detail the opinions about the aforesaid principle. First, he gives the opinions of those who held that there is one [efficient] cause; and second (104), the opinions of those who held that there are two such causes (“But since there would seem”).

In regard to the first he does two things. First, he gives the views of those who held that the first efficient cause is an intellect; and second (101), the opinions of those who held that it is love (“Now someone might”).

He says, then, that after the foregoing doctrine someone appeared who said that there is an intellect present in nature at large, just as there is in animals, and that this is the cause of the world and the order of the whole, i.e., of the universe, in which order the good of the entire universe and that of every single part consists. And this man atoned for the first philosophers by reducing to pure truth those who said unreasonable things and did not mention this kind of cause. Now Anaxagoras clearly stated this doctrine, although another philosopher —Hermotimus of Clazomenae—first gave him the idea of proposing this opinion. Hence it is evident that those who held this opinion claimed at the same time that the principle by which things are well disposed and the one which is the source of motion in things, are one and the same.

101. Now someone might (49).

Here he gives the opinion of those who claimed that love is the first principle, although they did not hold this very explicitly or clearly. Accordingly, he says that some suspected that Hesiod had sought for such a principle to account for the good disposition of things, or anyone else who posited love or desire in nature. For when Parmenides attempted to explain the generation of the universe, he said that in the establishing of the universe “Love, the first of all the gods, was made.” Nor is this opposed to his doctrine that there is one immobile being, of which Aristotle speaks here; because this man held that there are many things according to the senses, although there is only one thing according to reason, as was stated above and will be stated below. Moreover, he called the celestial bodies, or perhaps certain separate substances, gods.

102. But Hesiod said that first of all there was chaos, and then broad earth was made, to be the receptacle of everything else; for it is evident that the receptacle [or void] and place are principles, as is stated in Book IV of the Physics. And he also held that love, which instructs all the immortals, is a principle of things. He did this because the communication of goodness seems to spring from love, for a good deed is a sign and effect of love. Hence, since corruptible things derive their being and every good disposition from immortal beings of this kind, this must be attributed to the love of the immortals. Furthermore, he held that the immortals are either the celestial bodies themselves, or material principles themselves. Thus he posited chaos and love as though there had to be in existing things not only a material cause of their motions, but also an efficient cause which moves and unites them, which seems to be the office of love. For love moves us to act, because it is the source of all the emotions, since fear, sadness and hope proceed only from love. That love unites things is clear from this, that love itself is a certain union between the lover and the thing loved, seeing that the lover regards the beloved as himself. This man Hesiod is to be numbered among the poets who lived before the time of the philosophers.

103. Now, as to which one of these thinkers is prior, i.e., more competent in knowledge, whether the one who said that love is the first principle, or the one who said hat intellect is, can be decided later on, that is, where God is discussed. He calls this decision an arrangement, because the degree of excellence belonging to each man is allotted to him in this way. Another translation states this more clearly: “Therefore, in what order it is fitting to go over these thinkers, and who in this order is prior, can be decided later on.”

LESSON 6

Love and Hate as Efficient Causes of Good and Evil

ARISTOTLE’S TEXT Chapter 4: 984b 32-985b 4

50. But since there would seem to be in nature things which are contrary to those that are good, and not only order and good but also disorder and what is base, and evil things more numerous than good ones, and base things more numerous than noble ones, for this reason another thinker introduced love and strife as causes, each of its own type of effects. For if anyone grasps what Empedocles said, taking it according to its meaning rather than according to its faltering expression, he will find that love is the cause of things which come to be by aggregation, and strife the cause of evil things. Hence, if anyone were to say that Empedocles, in a sense, both said and was the first to say that good and evil are princip es, he would perhaps speak correctly, i.e., if the cause of all good things is good and that of all evil things is evil.

51. These thinkers, then, as we have said, to this extent have touched on two of the causes which we established in the Physics,—matter and the source of motion—though only obscurely and with no clarity, much as untrained men conduct themselves in battle. For the latter, though encircled, often deal telling blows, but without science. In the same way these thinkers do not seem to be aware of what they are saying. For it seems that they almost never make use of the causes except to a small degree.

52. Anaxagoras uses “intellect” in an artificial way in generating the world. For when he is in difficulty as to what is necessarily the cause of something, he drags in this intellect; but in other cases he makes everything but intellect the cause of what comes to be.

53. Empedocles, it is true, makes greater use of causes than Anaxagoras, though not sufficiently; nor does one find in his use of them what he professed. In many places he argues that love separates things, and that strife brings them together. For when being itself is separated into its elements by strife, then fire and each of the other elements are brought together into a unity. But when they are united by love, the particles must again be separated out from each element.

54. In contrast to the first philosophers, then, Empedocles was the first to introduce this cause, dividing it in such a way as to make the source of motion not a single principle but different and contrary ones. Moreover, he was the first to claim that the elements, which are said to belong to the class of matter, are four in number, although he does not use them as four but as two, taking fire by itself alone, and its opposites—earth, air, and water—as a single nature (46).

But anyone may see this by studying his basic sayings. This philosopher, then, as we have said, has spoken in this way about the principles of things and their number.

COMMENTARY

104. Here Aristotle gives the opinion of those who posited contrariety in beings of this kind, and the reason which moved them, which is as follows. There would seem to be in nature things which are contrary to those that are good, because in nature one finds not only things which are ordered and good, but sometimes things which are disordered and base. Now it cannot be said that evil things have no cause but happen by chance, because evil things are more numerous than good ones, and base things more numerous than those which are unqualifiedly noble. But those things which come to be by chance without a definite cause do not occur for the most part but in the smaller number of cases. Hence, since contrary effects have contrary causes, it was necessary to hold as a cause of things not only love, from which the order and good in things originate, but also hate, which is the source of disorder and baseness or evil in things, so that in this way particular instances of evil and good have their own type of causes.

105. That this was the reason which moved Empedocles is evident if anyone grasps what he says, taking his statement according to its meaning rather than according to the words which he used imperfectly and, as it were, in a faltering way. For he said that it is the office of love to bring the elements together, and of hate to separate them. But since the generation of things is a result of the coming together [of the elements], by reason of which there is being and good in things, and their corruption a result of the separation [of the elements], which is the way to non-being and evil, it is now evident that he wanted love to be the cause of things which come to be by aggregation, i.e., of good things, and hate the cause of evil things. Thus if one were to say that Empedocles was the first to maintain that good and evil are principles, he would perhaps speak correctly.

106. That is to say, this would follow if Empedocles did hold that good is the cause of all good things, and evil the cause of all evil things. For it is evident that he posited evil as the cause of some evil things, namely, of corruption, and good as the cause of some good things, namely, of generation. But because it would not follow that all good things would be caused by friendship or all evil things by hate, since the parts of the world would be differentiated by hate and fused together by friendship, therefore he did not always hold that good is the cause of good things, and evil the cause of evil things.

107. These thinkers (51).

Here he shows that in giving these causes the philosophers treated them inadequately. First, he mentions them in a general way. Second (108), he treats each one individually (“Anaxagoras”).

He says first, then, that these philosophers—Anaxagoras and Empedocles—arrived at a doctrine of two of the causes which have been established in the Physics, namely, matter and the cause of motion, although they treated these obscurely and with no clarity, because they did not explain that those principles which they held to be the causes of things could be reduced to these classes of causes. But insofar as they posited two of these causes, they may be likened to untrained warriors who, ttiough encircled by the enemy, sometimes strike good blows, not by art but by chance. This is evident from the fact that, even though they happen to do this sometimes, this does not occur always or for the most part. In like manner, too, these philosophers were not accustomed to express themselves accurately, nor was it their custom to speak with awareness, i.e., as men who know. Hence another translation has, “But these men neither have science, nor are they to be compared with men who realize what they are saying.” This is shown by the fact that, although they had proposed these causes, they hardly ever used them, because they employed them in few instances. Hence it seems that they introduced them not as a result of art but by accident, because they were moved to, do so by necessity.

108. Anaxagoras (52).

Here he shows in what particular respect the view of each is unsatisfactory. First, he speaks of Anaxagoras; and second (109), of Empedocles (“Empedocles”).

He says first, then, that Anaxagoras uses “intellect” to generate the world, and in so doing he seems to speak of it in an artificial way. For when he inquires about the causes of the world’s generation, he drags it in of necessity, i.e., he invents this intelligence only because he is unable to attribute the generation of the world to any other cause which would differentiate things except to one which is essentially distinct and unmixed, and intellect is a thing of this kind. But in all other cases he draws his causes from any other source rather than intellect, for example, in the case of the particular natures of things.

109. Empedocles (53).

Here he shows in what respect Empedocles’ doctrine is inadequate; and in regard to this he does two things. First, he shows in what respect Empedocles’ doctrine is inadequate. Second (111), he explains what Empedocles himself held in contrast to the other philosophers (“In contrast”)

He says, first (53), that Empedocles, in dealing with the particular natures of things, “makes greater use of the causes” posited by him (the four elements, and love and hate) than Anaxagoras did, because he reduced the generation and corruption of particular things to these causes, and not to intelligence as Anaxagoras did. But Empedocles failed in two ways.

First, he failed because he does not treat causes of this kind adequately enough; for he uses things which are not self-evident as though they were self-evident axioms, as is stated in the Physics, Book W that is, insofar as he assumed that they are self-evident, because at one definite time strife has dominion over the elements and at another, love.

110. Second, he failed because in the matters which he investigates, one does not find what he has professed, i.e., what he held as a principle, namely, that love combines things and that strife separates them, because in many places love must on the contrary “separate” or divide things, and strife “bring them together,” i.e., unite them. For when the universe itself “is separated out,” i.e., divided into its parts, by hate, as occurs when the world is generated, all particles of fire are then combined into one whole, and so also are the individual particles of the other elements “brought together,” i.e., joined to each other. Hence, strife not only separates the particles of fire from those of air, but also brings together the particles of fire. But, on the other hand, when the elements come together through love, which occurs when the universe is destroyed the particles of fire must then be separated from each other, and so also must the particles of the other elements. For fire can be mixed with air only if the particles of fire are separated from each other; and the same is true of the particles of air only if these elements penetrate one another, so that love not only unites unlike things but also separates like things, according to what follows from his position.

111. In contrast (54).

Here he shows in what respect Empedocles’ own doctrine differs from that of the other philosophers. He says that Empedocles maintained two things in contrast to the others. First, he divided the cause which is the source of motion into two contrary parts. Second, he held the material cause to be constituted of four elements—not that he uses the four elements as four, but rather as two, because he contrasts fire with the other three, saying that fire is active in nature and the others passive in nature. Anyone can gather this from the elements of things treated by him, or from his “basic sayings” in the sense of the rudiments of the doctrine which he propounded. Another version reads “from his verses,” because he is said to have written his philosophy in meters. And still another version, which says “from his statements,” agrees with this. As has been stated, then, this philosopher was the first to stipulate in this way that the principles of things are so many in number, namely, four, and to speak of those which have been mentioned.

LESSON 7

The Views of the Atomists and the Pythagoreans

ARISTOTLE’S TEXT Chapters 4 & 5: 985b 4-986a 13

55. Leucippus and his colleague Democritus say that the elements of things are the full and the void, calling the one being and the other non-being. For this reason they say that the full or solid is being, and the void, non-being. For this reason too they say that being no more is than non-being, because the void no more is than body; and they hold that these are the material causes of things.

56. And just as those who make the underlying substance one generate other things from this by means of its attributes, holding that rarity and density are the principles of these attributes, in the same way these men say that the differences [of the atoms] are the causes of other things. These differences, they say, are three: shape, arrangement, and position. For they claim that what exists differs only by rhythm, inter-contact, and turning; and of these rhythm means shape, inter-contact arrangement, and turning position. For A differs from N in shape, and Z from N in position. But with regard to motion, from whence it comes or how it is present in things, these men carelessly dismissed this question as the other thinkers did. As we have said before, then, these two types of causes seem to have been investigated to this extent by the first thinkers.

Chapter 5

57. But during the time of these and prior to them, lived the group called the Pythagoreans who dealt with mathematics and were the first to develop it; and having been brought up in these sciences, they thought that their principles were the principles of all things. But since among these principles numbers are naturally first, they thought they saw in numbers, more than in fire and earth, many resemblances to things which are and come to be, because [according to them] this attribute of numbers is justice, another is soul and mind, and still another is opportunity. The case is the same, so to speak, with every other thing.

58. Moreover, since they considered the attributes and ratios of harmonies in terms of numbers, and since other things in their whole nature seemed to be likened to numbers, and since numbers are the first things in the whole of nature, they thought that the elements of numbers are the elements of all things, and that the whole heaven is a harmony and number. And whatever they had revealed in the case of numbers and harmonies [which they could] show [to be in agreement] with the motions and parts of the heavens, and its whole arrangement, they collected and adapted to these. And if anything was lacking anywhere, they called it in in order that their undertaking might be complete. I mean that since the number ten seems to be the perfect number and to comprise the whole nature of numbers, they said that the bodies which move in the heavens are ten in number; but as only nine are observable they therefore invented a tenth, the counter-earth. These things have been dealt with more exactly in another work [ De Coelo, II, 13].

COMMENTARY

112. Here he begins to give the positions of those who held strange and obscure views about the principles of things. First, he gives the position of those who held that there are many principles of things; and second (134) the position of those who held that there is only one being (“But there are some”).

In regard to the first he does two things. First, he gives the opinion of Leucippus and Democritus, who held that the principles of things are corporeal. Second (119), he gives the opinion of the Pythagoreans, who held that the principles of things are incorporeal entities (“But during the time”).

In regard to the first he does two things. First, he gives the opinion of Democritus and Leucippus about the material cause of things; and second (115), their opinion about the cause of diversity, that is, how matter is differentiated into many things. In this discussion the cause of the generation and corruption of things also becomes evident; and this is a point on which these men agreed with the ancient philosophers (“And just as those who”). He says, then, that two philosophers, Democritus and Leucippus, who are called friends because they followed each other in all things, held that the principles of things are the full and the void or empty, of which the full is being, and the void or empty, non-being.

113. Now in order to clarify this opinion we must recall what the Philosopher says in Book I of Generation, where he treats it more fully. For certain philosophers had held that everything is one continuous immobile being, because it seems that there cannot be motion without a void, or any distinction between things, as they said. And though they could not comprehend the privation of continuity, by reason of which bodies must be understood to be differentiated, except by means of a void, they claimed that the void existed in no way. Democritus, who came after them, and who agreed with their reasoning but was unable to exclude diversity and motion from things, held that the void existed, and that all bodies are composed of certain indivisible bodies [i.e., the atoms]. He did this because it seemed to him that no reason could be given why the whole of being should be divided in one part rather than another. And lest he should hold that the whole of being is continuous, he therefore chose to maintain that this whole is divided everywhere and in its entirety; and this could not be the case if anything divisible remained undivided. And according to him indivisible bodies of this kind can neither exist nor be joined together except by means of the void. For if the void did not come between any two of them, one continuous whole would result from the two; which he did not hold for the above reason. Hence he said that the continuous quantity of each body is constituted both of those indivisible bodies filling indivisible spaces and of certain empty spaces, which he called pores, coming between these indivisible bodies.

114. And since the void is non-being and the full is being, it is evident from this that he did not hold that a thing was constituted by being rather than non-being, because the [indivisible] bodies did not constitute things more than the void, or the void more than bodies; but he said that a body is composed at once of these two things, as is clear in the text. Hence he held that these two things are the causes of beings as their matter.

115. And just as those (56).

Here he shows in what respect these philosophers agreed with the ancients who claimed that there is only one matter. He indicates agreement in two respects.

First, just as the ancient philosophers held that there is one matter, and from that one matter generated something else according to the different attributes of matter (i.e., the rare and dense, which they accepted as the principles of all other attributes), in a similar way these philosophers—Democritus and Leucippus—said that there were different causes of different things (namely, of the bodies composed of these indivisible bodies), i.e., that different beings were produced as a result of certain differences of these indivisible bodies and their pores.

116. Now they said that these differences are, first, differences in shape, which is noted from this that things are angular, circular or square; second, differences in arrangement, i.e., insofar as the indivisible bodies are prior or subsequent; and, third, differences in position, i.e., insofar as these bodies are in front or behind, right or left, or above and below. Hence they said that one being differs from another “either by rhythm,” which is shape, “or by inter-contact,” which is arrangement, “or by turning,” which is position.

117. He illustrates this by using the letters of the Greek alphabet, which differ from each other in shape just as in our alphabet one letter also differs from another; for A differs from N in shape. Again, AN differs from NA in arrangement, because one letter is placed before the other. And one letter also differs from another in position, as Z from IN, just as in our language we also see that semivowels cannot stand after liquids preceded by mutes in the same syllable. Therefore, just as tragedy and comedy come from the same letters as a result of the letters being disposed in different ways because of this threefold difference, in a similar fashion different species of things are produced from the same indivisible bodies as a result of the latter being disposed in different ways.

118. The second respect in which these philosophers agreed with the ancients is this: just as the ancient philosophers neglected to posit a cause which accounts for motion in things, so also did these men, although they would say that these indivisible bodies are capable of self-motion. Thus it is evident that these philosophers mentioned only two of the causes, i.e., all of them spoke of the material cause) and some of the efficient cause.

119. But during the time of these (57).

Here he gives the opinions of the Pythagoreans, who held that numbers are the substances of things. In regard to this he does two things. First, he gives their opinions about the substance of things; and second (124), their opinions about the principles of things (“But the reason”).

In regard to the first he gives two reasons by which they were led to assert that numbers are the substances of things. He gives the second reason (121) where he says “Moreover, since they considered.”

He says that the Pythagoreans were philosophers who lived “during the time of these,” i.e., they were contemporaries of some of the foregoing philosophers; “and prior to them,” because they preceded some of them. Now it must be understood that there were two groups of philosophers. One group was called the Ionians, who inhabited the land which is now called Greece. This group originated with Thales, as was pointed out above (77). The other group of philosophers were the Italians, who lived in that part of Italy which was once called Greater Greece and is now called Apulia and Calabria. The leader of these philosophers was Pythagoras, a native of Samos, so called from a certain city of Calabria. These two groups of philosophers lived at the same time, and this is why he says that they lived “During the time of these and prior to them.”

120. These Italian philosophers, also called Pythagoreans, were the first to develop certain mathematical entities, so that they said that these are the substances and principles of sensible things. He says that they were “the first” because the Platonists were their successors. They were moved to bring in mathematics because they were brought up in the study of these sciences, and therefore they thought that the principles of mathematics are the principles of all existing things. For men are wont to judge about things in terms of what they already know. And since among mathematical entities numbers are first, these men therefore tried to see resemblances of natural things, both as regards their being and generation, in numbers rather than in the sensible elements—earth, water and the like. For just as the foregoing philosophers adapted the attributes of sensible things to those of natural things because of a certain resemblance which they bear to the properties of fire, water, and bodies of this kind, in a similar fashion these mathematicians adapted the properties of natural things to the attributes of numbers when they said that some one attribute of number is the cause of justice, another the cause of soul and intellect, and still another the cause of opportunity, and so on for other things. And in this way the attributes of numbers are understood to be the intelligible structures and principles of all things appearing in the sensible world, both in the realm of voluntary matters, signified by justice, and in that of the substantial forms of natural things, signified by soul and intellect, and in that of accidents, signified by opportunity.

STRANGE AND OBSCURE VIEWS ABOUT THE PRINCIPLES OF THINGS

Hidden principles: numbers

121. Moreover, since they (58).

Here he gives the second reason which motivated them. For they thought of the attributes of harmonies, musical consonants and their ratios, i.e., proportions, in terms of the nature of numbers. Hence, since harmonious sounds are certain sensible things, they attempted by the same reasoning to liken all other sensible things, both in their intelligible structure and in their whole nature, to numbers, so that numbers are the first things in the whole of nature.

122. For this reason too they thought that the principles of numbers are the principles of all existing things, and they said that the whole heaven is merely a kind of nature and harmony of numbers, i.e., a kind of numerical proportion similar to the proportion found in harmonies. Hence, whatever they had “revealed,” i.e., had shown, which they could adapt to numbers and harmonies, they also adapted both to the changes undergone by the heavens, as its motion, eclipses and the like; and to its parts, as the different orbs; and to the whole arrangement of the heavens, as the different stars and different figures in the constellations.

LESSON 8

The Pythagorean Doctrine about Contraries

ARISTOTLE’S TEXT Chapter 5: 986a 13-986b 10

59. But the reason we have come [to examine these philosophers] is that we may also learn from them what they hold the principles of things to be, and how these principles fall under the causes already described. Now these men also seem to think that number is the principle of existing things both as their matter and as their attributes and states. According to them the elements of number are the even and odd, and of these the latter is limited and the former, unlimited. The unit is composed of both of these, since it is both even and odd, and number is derived from the unit. And number, as has been stated (58), constitutes the whole heaven.

60. But other members of the same school say that the principles of things are ten in number, which they give as co-elements: the limited and unlimited, even and odd, one and many, right and left, masculine and feminine, rest and motion, straight and curved, light and darkness, good and evil, square and oblong.

61. Alcmaeon of Croton seems to have formed his opinion in the same way, and either he derived the theory from them or they from him; for Alcmaeon (who had reached maturity when Pythagoras was an old man) expressed views similar to those of the Pythagoreans. For he says that many things in the realm of human affairs are in twos [i.e., pairs], calling them contrarieties, not distinguished as these men had distinguished them, but such as are taken at random, for example, white and black, sweet and bitter, good and evil, small and great. It is true that this philosopher threw out vague remarks about the other contrarieties, but the Pythagoreans have declared both what the contrarieties are and how many there are.

62. From both of these, then, we can gather this much, that contraries are the principles of existing things; but how many they are and that they are these [determinate ones must be learned] from other thinkers. The way in which many principles can be brought together under the causes described is not clearly expressed by them, although they seem to allot their elements to the class of matter; for they say that substance is composed and moulded out of these as something inherent. From these remarks, then, it is possible to get an adequate understanding of the meaning of the ancient philosophers who said that the elements of things are many.

COMMENTARY

124. Here he states what the Pythagoreans had to say about the principles of things. In regard to this he does two things. First, he expounds their opinions about the principles of things; and second (132), he indicates to what class of cause the principles laid down by them are reduced (“From both of these”).

In regard to the first he gives three opinions. The second (127) begins at the words “But other members”; and the third (131), where he says “Alcmaeon of Croton.”

He says first (59), then, that the reason he came to examine the opinions of the Pythagoreans is that he might show from their opinions what the principles of things are and how the principles laid down by them fall under the causes given above. For the Pythagoreans seem to hold that number is the principle of existing things as matter,1 and that the attributes of number are the attributes and states of existing things. By “attributes” we mean transient accidents, and by “states,” permanent accidents. They also held that the attribute of any number according to which any number is said to be even is justice, because of the equality of division, since such a number is evenly divided into two parts right down to the unit. For example, the number eight is divided into two fours, the number four into two twos, and the number two into two units. And in a similar way they likened the other accidents of things to the accidents of numbers.

125. in fact, they said that the even and odd, which are the first differences of numbers, are the principles of num hers. And they said that even number is the principle of unlimitedness and odd number the principle of limitation, as is shown in the Physics, Book III, because in reality the unlimited seems to result chiefly from the division of the continuous. But an even number is capable of division; for an odd number includes within itself an even number plus a unit, and this makes it indivisible. He also proves this as followswhen odd numbers are added to each other successively, they always retain the figure of a square, whereas even numbers change their figure. For when the number three is added to the unit, which is the principle of numbers, the number four results, which is the first square [number], because 2 x 2 = 4. Again, when the number five, which is an odd number, is added to the number four, the number nine results, which is also a square number; and so on with the others. But if the number two, which is the first even number, is added to the number one, a triangular number results, i.e., the number three. And if the number four, which is the second even number, is added to the number three, there results a septangular number, i.e., the number seven. And when even numbers are added to each other successively in this way, they do not retain the same figure. This is why they attributed the unlimited to the even and the limited to the odd. And since limitedness pertains to form, to which active power belongs, they therefore said that even numbers are feminine, and odd numbers, masculine.

126. From these two, namely, the even and odd, the limited and unlimited, they produced not only number but also the unit itself, i.e., unity. For unity is virtually both even and odd; because all differences of number are virtually contained in the unit; for all differences of number are reduced to the unit. Hence, in the list of odd numbers the unit is found to be the first. And the same is true in the list of even numbers, square numbers, and perfect numbers. This is also the case with the other differences of number, because even though the unit is not actually a number, it is still virtually all numbers. And just as the unit is said to be composed of the even and odd, in a similar way number is composed of units. In fact, [according to them], the heavens and all sensible things are composed of numbers. This was the sequence of principles which they gave.

127. But other members (60).

Here he gives another opinion which the Pythagoreans held about the principles of things. He says that among these same Pythagoreans there were some who claimed that there is not just one contrariety in principles, as the foregoing did, but ten principles, which are presented as co-elements, that is, by taking each of these principles with its co-principle, or contrary. The reason for this position was that they took not only the first principles but also the proximate principles attributed to each class of things. Hence, they posited first the limited and the unlimited, as did those who have just been mentioned; and subsequently the even and the odd, to which the limited and unlimited are attributed. And because the even and odd are the first principles of things, and numbers are first produced from them, they posited, third, a difference of numbers, namely, the one and the many, both of which are produced from the even and the odd. Again, because continuous quantities are composed of numbers, inasmuch as they understood numbers to have position (for according to them the point was merely the unit having position, and the line the number two having position), they therefore claimed next that the principles of positions are the right and left; for the right is found to be perfect and the left imperfect. Therefore the right is determined from the aspect of oddness, and the left from the aspect of evenness. But because natural bodies have both active and passive powers in addition to mathematical extensions, they therefore next maintained that masculine and feminine are principles. For masculine pertains to active power, and feminine to passive power; and of these masculine pertains to odd number and feminine to even number, as has been stated (125).

128. Now it is from active and passive power that motion and rest originate in the world; and of these motion is placed in the class of the unlimited and even, because it partakes of irregularity and otherness, and rest in the class of the unlimited and odd. Furthermore, the first differences of motions are the circular and straight, so that as a consequence of this the straight pertains to even number. Hence they said that the straight line is the number two; but that the curved or circular line, by reason of its uniformity, pertains to odd number, which retains its undividedness because of the form of unity.

129. And they not only posited principles to account for the natural operations and motions of things, but also to account for the operations of living things. In fact, they held that light and darkness are principles of knowing, but that good and evil are principles of appetite. For light is a principle of knowing, whereas darkness is ascribed to ignorance; and good is that to which appetite tends, whereas evil is that from which it turns away.

130. Again, [according to them] the difference of perfection and imperfection is found not only in natural things and in voluntary powers and motions, but also in continuous quantities and figures. These figures are understood to be something over and above the substances of continuous quantities, just as the powers responsible for motions and operations are something over and above the substances of natural bodies. Therefore with reference to this they held that what is quadrangular, i.e., the square and oblong, is a principle. Now a square is said to be a figure of four equal sides, whose four angles are right angles; and such a figure is produced by multiplying a line by itself. Therefore, since it is produced from the unit itself, it belongs to the class of odd number. But an oblong is defined as a figure whose angles are all right angles and whose opposite sides alone, not all sides, are equal to each other. Hence it is clear that, just as a square is produced by multiplying one line by itself, in a similar way an oblong is produced by multiplying one line by another. Hence it pertains to the class of even number, of which the first is the number two.

131. Akmaeon of Croton (61).

Here he gives the third opinion of the Pythagoreans, saying that Alcmaeon of Croton, so named from the city in which he was raised, seems to maintain somewhat the same view as that expressed by these Pythagoreans, namely, that many contraries are the principles of things. For either he derives the theory from the Pythagoreans, or they from him. That either of these might be true is clear from the fact that he was a contemporary of the Pythagoreans, granted that he began to philosophize when Pythagoras was an old man. But whichever happens to be true, he expressed views similar to those of the Pythagoreans. For he said that many of the things “in the realm of human affairs,” i.e., many of the attributes of sensible things are arranged in pairs, understanding by pairs opposites which are contrary. Yet in this matter he differs from the foregoing philosophers, because the Pythagoreans said that determinate contraries are the principles of things. But he throws them in, as it were, without any order, holding that any of the contraries which he happened to think of are the principles of things, such as white and black, sweet and bitter, and so on.

132. From both of these (62).

Here he gathers together from the above remarks what the Pythagoreans thought about the principles of things, and how the principles which they posited are reduced to some class of cause.

He says, then, that from both of those mentioned above, namely, Alcmaeon and the Pythagoreans, it is possible to draw one common opinion, namely, that the principles of existing things are contraries; which was not expressed by the other thinkers. This must be understood with reference to the material cause. For Empedocles posited contrariety in the case of the efficient cause; and the ancient philosophers of nature posited contrary principles, such as rarity and density, although they attributed contrariety to form. But even though Empedocles held that the four elements are material principles, he still did not claim that they are the first material principles by reason of contrariety but because of their natures and substance. These men, however, attributed contrariety to matter.

133. The nature of the contraries posited by these men is evident from the foregoing discussion. But how the aforesaid contrary principles posited by them can be “brought together under,” i.e., reduced to, the types of causes described, is not clearly “expressed,” i.e., distinctly stated, by them. Yet it seems that such principles are allotted to the class of material cause; for they say that the substance of things is composed and moulded out of these principles as something inherent, and this is the notion of a material cause. For matter is that from which a thing comes to be as something inherent. This is added to distinguish it from privation, from which something also comes to be but which is not inherent, as the musical is said to come from the non-musical.

LESSON 9

The Opinions of the Eleatics and Pythagoreans about the Causes of Things

ARISTOTLE’S TEXT Chapter 5: 986b 10-987a 28

63. But there are some [the Eleatics] who spoke of the whole as if it were a single nature, although the statements which they made are not all alike either with regard to their acceptableness or their conformity with nature.

64. Therefore a consideration of these men pertains in no way to the present investigation of causes. For they do not, like certain of the philosophers [the early physicists] who supposed being to be one, still generate it from the one as matter; but they speak of this in another way. For the others assume motion when they generate this whole, whereas these thinkers say it is immobile.

65. Yet their opinion is relevant to the present investigation to some extent; for Parmenides seems to touch on unity according to intelligible structure and Melissus on unity according to matter. This is why the former says that it is limited, and the latter that it is unlimited. Xenophanes, the first of those to speak of the one (for Parmenides is said to have been his disciple), made nothing clear, nor does he seem to have touched on either of these. But with regard to the whole heaven he says that the one is God.

66. As we have stated, then, these men must be dismissed for the purposes of the present inquiry. In fact, two of them—Xenophanes and Melissus—are to be disregarded altogether as being a little too rustic. Parmenides, however, seems to speak with more insight; for he thought that besides being there is only non-being, and this is nothing. This is why he thinks that being is necessarily one and nothing else. We have discussed this point more clearly in the Physics. But being compelled to follow the observed facts, and having assumed that what is one from the viewpoint of reason is many from the viewpoint of the senses, he postulates in turn two principles, i.e., two causes, the hot and cold, calling the one fire and the other earth; and of these he ranks the hot with being and the cold with non-being.

67. From what has been said, then, and from the wise men who have already agreed with this reasoning, we have acquired these things. From the first philosophers we have learned that the principle of things is corporeal, because water and fire and the like are bodies; and from some we have learned that there is one corporeal principle, and from others, many; although both suppose that these belong to the class of matter. And from others we have learned that in addition to this cause there is the source from which motion begins, which some claim to be one and others two. Down to the Italian philosophers, then, and independent of them, others have spoken of these things in a more trivial way, except that, as we have said, they have used two kinds of causes, and one of these—the source of motion—some thinkers consider as one and others as two.

68. Now the Pythagoreans have spoken of these two principles in the same way, but added this much, which is peculiar to them, that they did not think that the limited, unlimited and one are different natures, like fire or earth or anything else of this kind, but that the unlimited itself and the one itself are the substance of the things of which they are predicated. And this is why they considered number as the substance of all things. These thinkers, then have expres emselves thus with regard to these things, and they began to discuss and define the “what” itself of things, although they treated it far too simply. For they defined things superficially and thought that the substance of a thing is that to which a given definition first applies; just as if one supposed that double and two are the same because that to which the double first belongs is the number two. But perhaps “to be double” is not the same as “to be two”; and if they are not, then the one itself will be many. This, indeed, is the conclusion which they reached. From the first philosophers and others, then, this much can be learned.

COMMENTARY

Unitarians

134. Here he gives the opinions of those philosophers who spoke of the whole universe as one being; and in regard to this he does two things. First, he gives the opinion which they held in common; and second (135), he shows how a consideration of this opinion is relevant to the present treatise, and how it is not (“Therefore a consideration”).

He says, then, that there were certain philosophers, other than those just mentioned, who spoke “of the whole,” i.e,, of the universe, as if it were of one nature, i.e., as if the whole universe were a single being or a single nature. However, not all maintained this position in the same way, as he will make clear below (138-49). Yet in the way in which they differ their statements are neither acceptable nor in conformity with nature. None of their statements are in conformity with nature, because they did away with motion in things. And none of them are acceptable, because they held an impossible position and used sophistical arguments, as is clear in Book I of the Physics.

135. Therefore a consideration (64).

Here he shows how a consideration of this position pertains to the present investigation and how it does not. He shows, first, that it has no bearing on this investigation if we consider their position itself; and, second (137), that it does have a bearing on this investigation if the reasoning or method behind their position is considered (“Yet their opinion”).

He says, then, that since these philosophers held that there is only one being, and a single thing cannot be its own cause, it is clear that they could not discover the causes. For the position that there is a plurality of things demands a diversity of causes in the world. Hence, a consideration of their statements is of no value for the purposes of the present study, which deals with causes. But the situation is different in the case of the ancient philosophers of nature, who held that there is only one being, and whose statements must be considered here. For they generated many things from that one principle as matter, and thus posited both cause and effect. But these men with whom we are now dealing speak of this in a different way. For they do not say that all things are one materially, so that all things are generated from one matter, but that all things are one in an absolute sense.

136. The reason for this difference is that the ancient philosophers of nature added motion to the view of those who posited one being and one principle, and said that this one being is mobile; and therefore different things could be generated from that one principle by a certain kind of motion, i.e., by rarefaction and condensation. And they said that the whole universe with respect to the diversity found in its parts is generated in this way. Yet since they held that the only change affecting substance is accidental, as was stated above (75), the conclusion then followed that the whole universe is one thing substantially but many things accidentally. But these thinkers [i.e., the Eleatics], said that the one being which they posited is immobile in an absolute sense; and therefore a diversity of things could not be produced from that one being. For since this being is immobile they could not posit any plurality in the world, either substantial or accidental.

137. Yet their opinion (65).

Here he shows how their opinion is relevant to the present inquiry. First, he deals with all of these thinkers in general; and second (142), with Parmenides in particular.

He says, first, that although they did away with diversity in the world, and consequently with causality, nevertheless their opinion is relevant to the present study to this extent, let us say: as regards the method by which they establish their position and the reason for their position.

138. Parmenides, who was a member of this group, seems to touch on unity according to intelligible structure) i.e., according to form; for he argued as follows: besides being there is only non-being, and non-being is nothing. Therefore besides being there is nothing. But being is one. Therefore, besides the one there is nothing.

In this argument he clearly considered the intelligible structure itself of being, which seems to be one, because nothing can be understood to be added to the concept of being by which it might be diversified. For whatever is added to being must be other than being. But anything such as this is nothing. Hence it does not seem that this can diversify being; just as we also see that differences added to a genus diversify it, even though these differences are outside the substance of that genus. For differences do not participate in a genus, as is stated in the Topics, Book IV, otherwise a genus would have the substance of a difference. And definitions would be nonsense if when a genus is given the difference were added, granted that the genus were the substance of the difference, just as it would be nonsense if the species were added. Moreover a difference would not differ in any way from a species. But those things which are outside the substance of being must be non-being, and thus cannot diversify being.

139. But they were mistaken in this matter, because they used being as if it were one in intelligible structure and in nature, like the nature of any genus. But this is impossible. For being is not a genus but is predicated of different things in many ways. Therefore in Book I of the Physics it is said that the statement “Being is one” is false. For being does not have one nature like one genus or one species.

140. But Melissus considered being in terms of matter. For he argued that being is one by reason of the fact that being is not generated from something prior, and this characteristic pertains properly to matter, which is ungenerated. For he argued in this way: whatever is generated has a starting-point. But being is not generated and therefore does not have a starting-point. But whatever lacks a starting-point lacks an end and therefore is unlimited. And if it is unlimited, it is immobile, because what is unlimited has nothing outside itself by which it is moved.

That being is not generated he proves thus. If being were generated, it would be generated either from being or from non-being. But it is not generated from non-being, because non-being is nothing and from nothing nothing comes. Nor is it generated from being, because then a thing would be before it came to be. Therefore it is not generated in any way.

In this argument he obviously treats being as matter, because it is of the very nature of matter not to be generated from something prior. And since limitation pertains to form, and unlimitedness to matter, Melissus, who considered being under the aspect of matter, said that there is one unlimited being. But Parmenides, who considered being under the aspect of form, said that being is limited. Hence, insofar as being is considered under the aspect of form and matter, a study of these men is relevant to the present investigation; because matter and form are included among the causes.

141. But Xenophanes, who was the first of those to say that everything is one (and therefore Parmenides was his disciple), did not explain by what reasoning he maintained that all things are one, either by arguing from the viewpoint of matter, or from that of form. Hence, with respect to neither nature, i.e., neither matter nor form, does he seem “to come up to these men,” that is, to reach and equal them in their irrational manner of arguing.

But concerning the whole heaven he says that the one is God. For the ancients said that the world itself is God. Hence, seeing that all parts of the universe are alike insofar as they are bodies, he came to think of them as if they were all one. And just as the foregoing philosophers held that beings are one by considering those things which pertain either to matter or to form, in a similar way these philosophers maintained this position regarding the composite itself.

142. As we have stated (66).

His aim here is to explain in a special way how the opinion of Parmenides pertains to the present investigation. He concludes from the foregoing that, since these men did away with (~) diversity in the world and therefore with (~) causality, all of them must be disregarded so far as the present study is concerned. Two of them—Xenophanes and Melissus—must be disregarded altogether, because they are a little too “rustic,” i.e., they proceeded with less accuracy. But Parmenides seems to have expressed his views “with more insight,” i.e., with greater understanding. For he employs the following argument: besides being there is only non-being, and whatever is non-being “is thought to be nothing”; i.e., he considers it worthy to be nothing. Hence he thought that it necessarily followed that being is one, and that whatever is other than being is nothing. This argument has been treated more clearly in the Physics, Book I.

143. But even though Parmenides was compelled by this argument to hold that all things are one, yet, because there appeared to the senses to be many things in reality, and because he was compelled to accept what appeared to the senses, it was his aim to make his position conform to both of these, i.e., to what is apprehended both by the senses and by reason. Hence he said that all things are one according to reason but many according to the senses.

And inasmuch as he held that there is a plurality of things according to the senses, he was able to hold that there is in the world both cause and effect. Hence he posited two causes, namely, the hot and the cold, one of which he ascribed to fire, and the other to earth. And one of these—the hot or fire—seemed to pertain to the efficient cause, and the other—cold or earth—to the material cause. And lest his position should seem to contradict the conclusion of his own argument that whatever is besides being is nothing, he said that one of these causes—the hot—is being, and that the other cause—the one besides being, or the cold—is non-being, according to. both reason and the truth of the thing itself, and is a being only according to sensory perception.

144. Now in this matter he comes very close to the truth; for the material principle, which he held to be earth, is not an actual being.

And in a similar way, too, one of two contraries is a privation, as is said in Book I of the Physics. But privation does not belong to the intelligible constitution of being. Hence in a sense cold is the privation of heat, and thus is non-being.

145. From what has been said (67). Here he summarizes the remarks which have been made about the doctrines of the ancient philosophers; and in regard to this he does two things. First, he summarizes the remarks made about the doctrines of the ancient philosophers of nature; and second (147), those made about the doctrines of the Pythagoreans, who introduced mathematics.

Therefore from the above remarks he concludes, first, that from the foregoing philosophers, who adopted the same opinion, namely, that the material cause is the substance of things, and who were already beginning by the use of reason to know the causes of things by investigating them, we learn the causes which have been mentioned. For from the first philosophers it was learned that the principle of all things is corporeal. This is evident from the fact that water and the like, which are given as the principles of things, are bodies. However, they differed in this respect, that some, such as Thales, Diogenes and similar thinkers, claimed that there is only one corporeal principle, whereas others, such as Anaxagoras, Democritus and Leucippus, held that there are several corporeal principles. Yet both groups, i.e., both those who posited one principle and those who posited many, placed such corporeal principles in the class of material cause. And some of them not only posited a material cause but added to this the cause from which motion begins: some holding it to be one, as Anaxagoras did in positing intellect, and Parmenides, love, and others to be two, as Empedocles did in positing love and hate.

146. Hence, it is clear that these philosophers who lived down to the time of the Italians, or Pythagoreans, “and [were] independent of them,” i.e., who had their own opinions about reality and were unaware of those of the Pythagoreans, spoke obscurely about the principles of things; for they did not designate to what class of cause such principles might be reduced. Yet they made use of two causes, i.e., the source from which motion begins and matter: some saying that the former—the source from which motion begins—is one, and others two; as has been pointed out (145).

147. Now the Pythagoreans (68).

Here he summarizes the opinions expressed by the Pythagoreans, both what they held in common with the foregoing philosophers, and what was peculiar to themselves. Now the opinion common to some of the foregoing philosophers and to the Pythagoreans was this that they posited, in a sense, two principles in the same way as the foregoing philosophers did. For Empedocles held that there are two contrary principles, one being the principle of good things, and the other the principle of evil things, and the Pythagoreans did the same thing, as is clear from the co-ordination of contrary principles which they posited.

148. However, they did not do this in the same way; because Empedocles placed these contrary principles in the class of material cause, as was stated above (111), whereas the Pythagoreans added their own opinion to that of the other thinkers. The first thing that they added is this: they said that what I call the one, the limited and the unlimited are not (~) accidents of any other natures, such as fire or earth or the like, but claimed that what I call the one, the limited and the unlimited constitute the (+) substance of the same things of which they are predicated. From this they concluded that number, which is constituted of units, is the substance of all things. But while the other philosophers of nature posited the one, the limited and the unlimited, they nevertheless attributed these to another nature, as accidents are attributed to a subject, for example, to fire or water or something of this kind.

149. The second addition which they made to the views of the other philosophers is this: they began to discuss and to define “the whatness itself,” i.e., the substance and quiddity of things, although they treated this far too simply by defining things superficially. For in giving definitions they paid attention only to one thing; because they said that, if any given definition were to apply primarily to some thing, this would be the substance of that thing; just as if one were to suppose that the ratio “double” is the substance of the number two, because such a ratio is found first in the number two. And since being was found first in the one rather than in the many (for the many is composed of ones), they therefore said that being is the substance itself of the one.

But this conclusion of theirs is not acceptable; for although the number two is double, the essence of twoness is not the same as that of the double in such a way that they are the same conceptually, as the definition and the thing defined. But even if their statements were true, it would follow that the many would be one. For some plurality can belong primarily to something one; for example, evenness and the ratio double belong first to the number two. Hence [according to them] it would follow that the even and the double are the same. And it would likewise follow that that to which the double belongs is the same as the number two, so long as the double is the substance of the number two. This, indeed, is also the conclusion which the Pythagoreans drew; for they attributed plurality and diversity to things as if they were one, just as they said that the properties of numbers are the same as the properties of natural beings.

150. Hence, Aristotle concludes that it is possible to learn this much from the early philosophers, who posited only one material principle, and from the later philosophers, who posited many principles.

LESSON 10

The Platonic Theory of Ideas

ARISTOTLE’S TEXT Chapter 6: 987a 29-988a 17

69. After the philosophies described came the system of Plato, which followed them in many respects, but also had other [theses] of its own in addition to the philosophy of the Italians. For Plato agreeing at the very beginning with the opinions of Cratylus (362) and Heraclitus that all sensible things are always in a state of flux, and that there is no scientific knowledge of them, also accepted this doctrine in later years. However, when Socrates, concerning himself with moral matters and neglecting nature as a whole, sought for the universal in these matters and fixed his thought on definition, Plato accepted him because of this kind of investigation, and assumed that this consideration refers to other entities and not to sensible ones. For [according to him] it is impossible that there should be a common definition of any one of these sensible things which are always changing. Such entities, then, he called Ideas or Forms (species); and he said that all sensible things exist because of them and in conformity with them; for there are many individuals of the same name because of participation in these Forms. With regard to participation, he [merely] changed the name; for while the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation, changing the name. Yet what this participation or imitation of Forms is they commonly neglected to investigate.

70. Further, he says that besides sensible things and Ideas there are the objects of mathematics, which constitute an intermediate class. These differ from sensible things in being eternal and immobile; and from the Ideas in that there are many alike, whereas each Idea is itself only one.

71. And since the Forms [or Ideas] are the causes of other things, he thought that the elements of these are the elements of all existing things. Hence, according to him, the great and small are principles as matter, and the one as substance [or form]; for it is from these by participation in the one that the Ideas are numbers.

72. Yet Plato said that the one is substance and that no other being is to be called one, just as the Pythagoreans did; and like them too he said that numbers are the causes of real substance.

73. But to posit a dyad in place of the indeterminate one, and to produce the unlimited out of the great and small, is peculiar to him. Moreover, he says that numbers exist apart from sensible things, whereas they say that things themselves are numbers. Further, they do not maintain that the objects of mathematics are an intermediate class.

74. Therefore, his making the one and numbers to exist apart from things and not in things, as Pythagoreans did, and his introducing the separate Forms, were due to his investigation into the intelligible structures of things; for the earlier philosophers were ignorant of dialectic.

75. But his making the dyad [or duality] to be a different nature was due to the fact that all numbers, with the exception of prime numbers, are naturally generated from the number two as a matrix.

76. Yet what happens is the contrary of this. For this view is not a reasonable one; because the Platonists produce many things from matter but their form generates only once.

77. And from one matter one measure seems to be produced, whereas he who induces the form, even though he is one, produces many measures. The male is also related to the female in a similar way; for the latter is impregnated by one act, but the male impregnates many females. And such are the changes in these principles. Concerning the causes under investigation, then, Plato defines them thus.

78. From the foregoing account it is evident that Plato used only two causes: one being the the whatness of a thing, and the other, matter; for the Forms are the cause of the quiddity in other things, and the one is the cause of the quiddity in the Forms. What the underlying matter is of which the Forms are predicated in the case of sensible things, and the one in the case of the Forms, is also evident, namely, that it is this duality, the great and small. Moreover, he assigned the cause of good and evil to these two elements, one to each of them; which is rather a problem, as we say (48), that some of the first philosophers, such as Empedocles and Anaxagoras, [have attempted] to investigate.

COMMENTARY

Plato and form

151. Having given the opinion of the ancient philosophers about the material and efficient cause, he gives a third opinion, that of Plato, who was the first to clearly introduce the formal cause. This is divided into two parts. First, he gives Plato’s opinion. Second (171), from all of the foregoing remarks he makes a summary of the opinions which the other philosophers expressed about the four classes of causes (“We have examined”).

In regard to the first he does two things. First, he gives Plato’s opinion about the substances of things; and second (159), his opinion about the principles of things (“And since the Forms”).

In regard to the first he does two things. First, he gives Plato’s opinion insofar as he posited Ideas; and second (157), insofar as he posited intermediate substances, namely, the separate mathematical entities (“Further, he says”).

He says, first, that after all the foregoing philosophers came the system of Plato, who immediately preceded Aristotle; for Aristotle is considered to have been his disciple. And even if Plato followed in many respects the natural philosophers who preceded him, such as Empedocles, Anaxagoras and the like, he nevertheless had certain other doctrines of his own in addition to those of the preceding philosophers, because of the philosophy of the Italians, or Pythagoreans. For insofar as he was devoted to the study of truth he sought out the philosophers of all lands in order to learn their teachings. Hence he came to Tarenturn in Italy, and was instructed in the teachings of the Pythagoreans by Archytas of Tarenturn, a disciple of Pythagoras.

152. Now Plato would seem to follow the natural philosophers who lived in Greece; and of this group some of the later members held that all sensible things are always in a state of flux, and that there can be no scientific knowledge of them (which was the position of Heraclitus and Cratylus). And since Plato became accustomed to positions of this kind from the very beginning, and agreed with these men in this position, which he acknowledged to be true in later years, he therefore said that scientific knowledge of particular sensible things must be abandoned. And Socrates (who was Plato’s master and the disciple of Archelaus, a pupil of Anaxagoras), because of this position, which arose in his time, that there can be no science of sensible things, was unwilling to make any investigation into the nature of physical things, but only busied himself with moral matters. And in this field he first began to investigate what the universal is, and to insist upon the need for definition.

153. Hence, Plato, being Socrates’ pupil, “accepted Socrates,” i.e., followed him, and adopted this method for the purpose of investigating natural beings. He did so believing that in their case the universal in them could successfully be grasped and a definition be assigned to it, with no definition being given for any sensible thing; because, since sensible things are always “changing,” i.e., being changed, no common intelligible structure can be assigned to any of them. For every definition must conform to each thing defined and must always do so, and thus requires some kind of immutability. Hence universal entities of this kind, which are separate from sensible things and that to which definitions are assigned, he called the Ideas or Forms of sensible things. He called them Ideas, or exemplars, inasmuch as sensible things are made in likeness to them; and he called them Forms inasmuch as [sensible things] have substantial being by participating in them. Or he called them Ideas inasmuch as they are principles of being, and Forms inasmuch as they are principles of knowledge. Hence all sensible things have being because of them and in conformity with them. They have being because of the Ideas insofar as the Ideas are the causes of the being of sensible things, and “in conformity with them” insofar as they are the exemplars of sensible things.

154. The truth of this is clear from the fact that “many individuals of the same name” are attributed to one Form alone, i.e., there are many individuals which have the same Form predicated of them, and predicated by participation. For the Form or Idea [of man] is the specific nature itself by which there exists man essentially. But an individual is man by participation inasmuch as the specific nature [man] is participated in by this designated matter. For that which is something in its entirety does not participate in it but is essentially identical with it, whereas that which is not something in its entirety but has this other thing joined to it, is said properly to participate in that thing. Thus, if heat were a self-subsistent heat, it would not be said to participate in heat, because it would contain nothing but heat. But since fire is something other than heat, it is said to participate in heat.

155. In a similar way, since the separate Idea of man contains nothing but the specific nature itself, it is man essentially; and for this reason it was called by him man-in-itself. But since Socrates and Plato have in addition to their specific nature an individuating principle, which is designated matter, they are therefore said to participate in a Form, according to Plato.

156. Now Plato took this term participation from Pythagoras, although [in doing so] he made a change in the term. For the Pythagoreans said that numbers are the causes of things, just as the Platonists said that the Ideas are, and claimed that sensible things of this kind exist as certain imitations of numbers. For inasmuch as numbers, which have no position of themselves, received positions, they caused bodies. But because Plato held that the Ideas are unchangeable in order that there might be scientific knowledge of them, he did not agree that the term imitation could be used of the Ideas, but in place of it he used the term participation. However, it must be noted that, even though the Pythagoreans posited participation or imitation, they still did not investigate the way in which a common Form is participated in by individual sensible things or imitated by them. But the Platonists have treated this.

157. Further, he says (70).

Here he gives Plato’s opinion about the mathematical substances. He says that Plato posited other substances—the objects of mathematics—in addition to the Forms and sensible things. Moreover, he said that beings of this kind were an intermediate class among the three kinds of substances; or that they were above sensible substances and below the Forms, and differed from both. The mathematical substances differed from sensible substances, because sensible substances are corruptible and changeable, whereas the mathematical substances are eternal and immobile. The PIatonists got this idea from the way in which mathematical science conceives its objects; for mathematical science abstracts from motion. The mathematical substances also differed from the Forms, because the objects of mathematics are found to be numerically different and specifically the same, otherwise the demonstrations of mathematics would prove nothing. For unless two triangles belonged to the same class, geometry would attempt in vain to demonstrate that some triangles are alike; and the same thing is true of other figures. But this does not happen in the case of the Forms. For, since a Form is just the specific nature itself of a thing, each Form can only be unique. For even though the Form of man is one thing, and the Form of ass another thing, nevertheless the Form of man is unique, and so is the Form of ass; and the same thing is true of other things.

158. Now to one who carefully examines Plato’s arguments it is evident that Plato’s opinion was false, because he believed that the mode of being which the thing known has in reality is the same as the one which it has in the act of being known. Therefore, since he found that our intellect understands abstractions in two ways: in one way as we understand universals abstracted from singulars, and in another way as we understand the objects of mathematics abstracted from sensible things, he claimed that for each abstraction of the intellect there is a corresponding abstraction in the essences of things. Hence he held that both the objects of mathematics and the Forms are separate.

But this is not necessary. For even though the intellect understands things insofar as it becomes assimilated to them through the intelligible form by which it is put into act, it still is not necessary that a form should have the same mode of being in the intellect that it has in the thing known; for everything that exists in something else exists there according to the mode of the recipient. Therefore, considering the nature of the intellect, which is other than the nature of the thing known, the mode of understanding, by which the intellect understands, must be one kind of mode, and the mode of being, by which things exist, must be another. For although the object which the intellect understands must exist in reality, it does not exist there according to the same mode [which it has in the intellect]. Hence, even though the intellect understands mathematical entities without simultaneously understanding sensible substances, and understands universals without understanding particulars, it is not therefore necessary that the objects of mathematics should exist apart from sensible things, or that universals should exist apart from particulars. For we also see that sight perceives color apart from flavor, even though flavor and color are found together in sensible substances.

159. And since the Forms (159).

Here he gives Plato’s opinion concerning the principles of things; and in regard to this he does two things. First, he states the principles which Plato assigned to things; and second (169), the class of cause to which they are reduced (“From the foregoing”).

In regard to the first he does two things. First, he tells us what kind of principles Plato had assigned to things. Second (160), he shows in what respect Plato agreed with the Pythagoreans, and in what respect he differed from them (“Yet Plato”).

He says, first, that, since the Forms are the causes of all other beings according to Plato, the Platonists therefore thought that the elements of the Forms are the elements of all beings. Hence, they assigned as the material principle of things the great and small, and said that “the substance of things,” i.e., their form, is the one. They did this because they held these to be the principles of the Forms. For they said that just as the Forms are the formal principles of sensible things, in a similar way the one is the formal principle of the Forms. Therefore, just as sensible things are constituted of universal principles by participation in the Forms, in a similar way the Forms, which he said are numbers, are constituted “of these,” i.e., of the great and small. For the unit constitutes different species of numbers by addition and subtraction, in which the notion of the great and small consists. Hence, since the one was thought to be the substance of being (because he did not distinguish between the one which is the principle of number, and the one which is convertible with being), it seemed to him that a plurality of different Forms might be produced from the one, which is their common substance, in the same way that a plurality of different species of numbers is produced from the unit.

160. Yet Plato (72).

Here he compares the position of Plato with that of Pythagoras. First, he shows in what respect they agreed; and second (160), in what respect they differed (“But to posit”).

Now they agreed in two positions; (1) and the first is that the one is the substance of things. For the Platonists, like the Pythagoreans, said that what I call the one is not predicated’ of some other being as an accident is of a subject, but signifies a thing’s substance. They said this, as we have pointed out (159), because they did not distinguish between the one which is convertible with being and the one which is the principle of number.

161. (2) The second position follows from the first; for the Platonists, like the Pythagoreans, said that numbers are the causes of the substance of all beings; and they held this because [in their opinion] number is just a collection of units. Hence if the one is substance, number must also be such.

162. But to posit (73).

Here he shows in what respect they differed; and in regard to this he does two things. First, he states how they differed. Second (164), he gives the reason for this difference (“Therefore, his making”).

Now this difference involves two things. First, the Pythagoreans, as has already been stated, posited two principles of which things are constituted, namely, the limited and the unlimited, of which one, i.e., the unlimited, has the character of matter. But in place of this one principle—the unlimited— which the Pythagoreans posited, Plato created a dyad, holding that the great and small have the character of matter. Hence the unlimited, which Pythagoras claimed to be one principle, Plato claimed to consist of the great and small. This is his own opinion in contrast with that of Pythagoras.

163. The second difference is that Plato held that numbers are separate from sensible things, and this in two ways. For he said that the Forms themselves are numbers, as was pointed out above (159); and he also held, as was stated above (157), that the objects of mathematics are an intermediate class between the Forms and sensible things, and that they are numbers by their very essence. But the Pythagoreans said that sensible things themselves are numbers, and did not make the objects of mathematics an intermediate class between the Forms and sensible things; nor again did they hold that the Forms are separate from things.

164. Therefore, his making (74).

Here he gives the reason for the difference. First, he gives the reason for the second difference; and then (165), the reason for the first difference.

He says, then, that the Platonists adopted the position that both the one and numbers exist apart from sensible things and not in sensible things, as the Pythagoreans claimed; and they also introduced separate Forms because of the investigation “which was made into the intelligible structures of things,” i.e., because of their investigation of the definitions of things, which they thought could not be attributed to sensible substances, as has been stated (150). This is the reason they were compelled to hold that there are certain things to which definitions are assigned. But the Pythagoreans, who came before Plato, were ignorant of dialectic, whose office it is to investigate definitions and universals of this kind, the study of which led to the introduction of the Ideas.

165. But his making (75).

Here he gives the reason for the other difference, that is, the one concerning matter. First, he gives the reason for such a difference. Second (166), he shows that Plato was not reasonably motivated.

He accordingly says that the Platonists made the dyad [or duality] to be a number of a different nature than the Forms, because all numbers with the exception of prime numbers are produced from it. They called prime numbers those which are not measured by any other number, such as three, five, seven, eleven, and so on; for these are produced immediately from unity alone. But numbers which are measured by some other number are not called prime numbers but composite ones, for example, the number four, which is measured by the number two; and in general every even number is measured by the number two. Hence even numbers are attributed to matter, since unlimitedness, which belongs to matter, is attributed to them, as has been stated above (125). This is why he posited the dyad, from which as “a matrix,” or exemplar, all other even numbers are produced.

166. Yet what happens (76).

Here he proves that Plato made unreasonable assumptions; and in regard to this he does two things. For, first, he proves this by an argument from nature. Second (167), he gives the argument based on the nature of things, which led Plato to adopt this position (“And from one matter”).

He says that, although Plato posited a dyad on the part of matter, still what happens is the contrary of this, as the opinions of all the other natural philosophers testify; for they claimed that contrariety pertains to form and unity to matter, as is clear in Book I of the Physics. For they held that the material principle of things is air or water or something of this kind, from which the diversity of things is produced by rarefaction and condensation, which they regarded as formal principles; for Plato’s position is not a reasonable one. Now the natural philosophers adopted this position because they saw that many things are generated from matter as a result of a succession of forms in matter. For that matter which now supports one form may afterwards support rnany forms as a result of one form being corrupted and another being generated. But one specifying principle or form “generates only once,” i.e., constitutes the thing which is generated. For when something is generated it receives a form, and the same form numerically cannot become the form of another thing that is generated, but ceases to be when that which was generated undergoes corruption. In this argument it is clearly apparent that one matter is related to many forms, and not the reverse, i.e., one form to many matters. Thus it seems more reasonable to hold that unity pertains to matter but duality or contrariety to form, as the philosophers of nature claimed. This is the opposite of what Plato held.

167. And from one matter (77).

Here he gives an opposite argument taken from sensible things according to the opinion of Plato. For Plato saw that each thing is received in something else according to the measure of the recipient. Hence receptions seem to differ according as the capacities of recipients differ. But one matter is one capacity for reception. And Plato also saw that the agent who induces the form, although he is one, causes many things to have this form; and this comes about because of diversity on the part of matter. An example of this is evident in the case of male and female; for a male is related to a female as an agent and one who impresses a form on matter. But a female is impregnated by one act of a male, whereas one male can impregnate many females. This is why he held that unity pertains to form and duality to matter.

168. Now we must note that this difference between Plato and the philosophers of nature is a result of the fact that they considered things from different points of view. For the philosophers of nature considered sensible things only insofar as they are subject to change, in which one subject successively acquires contrary qualities.

Hence they attributed unity to matter and contrariety to form. But Plato, because of his investigation of universals, went on to give the principles of sensible things. Therefore, since the cause of the diversity of the many singular things which come under one universal is the division of matter, he held that diversity pertains to matter and unity to form. “And such are the changes of those principles” which Plato posited, i.e., participations, or, as I may say, influences in the things generated. For Pythagoras understands the word change in this way. Or Aristotle says “changes” inasmuch as Plato changed the opinion which the first philosophers of nature had about principles, as is evident from the foregoing. Hence it is evident from the foregoing that Plato dealt thus with the causes which we are investigating.

169. From the foregoing (78).

Here he shows to what class of cause the principles given by Plato are referred. He says that it is evident from the foregoing that Plato used only two kinds of causes. For he used as “one” cause of a thing the cause of its “whatness,” i.e., its quiddity, or its formal cause, which determines its quiddity; and he also used matter itself. This is also evident from the fact that the Forms which he posited “are the causes of other things,” i.e., the causes of the whatness of sensible things, namely, their formal causes, whereas the formal cause of the Forms themselves is what I call the one, which seems to be the substance of which the Forms are composed. And just as he holds that the one is the formal cause of the Forms, in a similar fashion he holds that the great and small are their material cause, as was stated above (159). And these causes—the formal and the material cause—are referred not only to the Forms but also to sensible substances, because [there is some subject of which] the one is predicated in the case of the Forms. That is to say, that which is related to sensible substances in the same way as the one is to the Forms is itself a Form, because that duality which relates to sensible things as their matter is the great and small.

170. Furthermore, Plato indicated the cause of good and evil in the world, and he did this with reference to each of the elements which he posited. For he made Form the cause of good and matter the cause of evil.

However, some of the first philosophers attempted to investigate the cause of good and evil, namely, Anaxagoras and Empedocles, who established certain causes in the world with this special end in view that by means of these causes they might be able to give the principles of good and evil. And in touching upon these causes of good and evil they came very close to positing the final cause, although they did not posit this cause directly but only indirectly, as is stated below (177).

LESSON 11

A Summary of the Early Opinions about the Causes

ARISTOTLE’S TEXT Chapter 7: 988a 18-988b 21

79. We have examined, then, in a brief and summary way those philosophers who’ have spoken about the principles of things and about the truth, and the way in which they did this. Yet we have learned from them this much: that none of those who have discussed principle and cause have said anything beyond the points established by us in the Physics.

80. Yet all have approached these causes obscurely.

81. For some speak of the [first] principle as matter, whether they suppose it to be one or many, and whether they assume it to be a body or something incorporeal, as Plato speaks of the great and small; the Italians of the unlimited; Empedocles of fire, earth, water and air; and Anaxagoras of an infinite number of like parts. All these have touched on this kind of cause, and so also have those who make the first principle air or fire or water or something denser than fire or rarer than air. For they have said that some such body is the primary element. These thinkers, then, have touched only on this cause.

82. But others [have introduced] the source of motion, for example, those who make friendship and strife, or intellect, or love, or something besides these, a principle of things.

83. But the quiddity or substance no one has presented clearly. Those who express it best are those wbo posit the Ideas and the intelligible natures inherent in the Ideas. For they do not think of the Ideas and the things inherent in them as the matter of sensible things; nor do they think of them as the source from which motion originates, for they say that these things are the causes rather of immobility and of that which is at rest. But [according to them] the Forms are responsible for the quiddity of all other things, and the one for the quiddity of the Forms.

84. That for the sake of which there are actions and changes and motions they affirm in some way to be a cause, but not in the way we are determining causes, or in the way in which it is truly a cause. For while those who speak of intellect or love posit these causes as good, they do not say that anything exists or comes to be because of them, but claim that the motion of things stems from them. In like manner those who say that the one or being is such a reality, say that it is the cause of substance, but not that things either are or come to be for the sake of this. Hence, it happens to them that in a way they both say and do not say that the good is a cause; for they do not speak of it in its principal aspect but in a secondary one.

85. Therefore all these philosophers, being unable to touch on any other cause, seem to bear witness to the fact that we have dealt correctly with the causes, both as to their number and their kinds. Moreover, it is evident that all principles must be sought in this way or in some similar one. As to the way in which each of these philosophers has spoken, and how they have raised possible problems about the principles of things, let us discuss these points next.

COMMENTARY

171. Here he makes a summary of everything that the early philosophers have said about causes* and in regard to this he does three' things. First (79:C 171), he shows that the early philosophers were unable to add artother kind of cause to the four classes of causes given above (34:C 70). Second (80:C 172), he indicates the way in which they touched upon these causes ("Yet all"). Third (85:C 180) he draws the conclusion at which he chiefly aims ("Therefore all these").

He says, first (79), that in giving this brief and summary account he has stated who the philosophers are, and how they have spoken of the principles of things and of what is true of the substance itself of things. And from their statements this much can be learned: that none of those who have spoken about causes and principles were able to mention any causes other than those distinguished in Book II of the Physics.

172. Yet all (80).

Here he gives the way in which they dealt with each of the causes. He does this, first (80), in a general way: and, second (81:C 172), in a special Way ("For some speak").

Accordingly be says, first, that they not only have not added anything, but in the way in which they approached these causes they proceeded obscurely and not clearly. For they have not stated to what class of cause the principles posited by them would belong; but they gave as principles things that can be adapted to some class of cause.

173. For some speak (81).

Here he shows in a special way how they touched on each of these causes. He shows, first (81), how they touched on the material cause; second (82:C 174), On the efficient cause ("But others"); third (83:C 175), on the formal cause ("But the quiddity"); and fourth (84:C 177), on the final cause ("That for the sake of which").

He says, first (81), then, that those philosophers, i.e., the early ones, all agree insofar as they assign some material cause to things. Yet they differ in two respects. First, they differ in that some, such as Thales, Diogenes and the like, held that the material principle is one, whereas others, such as Empedocles, claimed that it is many; and second, they differ in that some, such as the first group above, held that the material principle of things is a body, whereas others, such as Plato, who posited a dyad, claimed that it is something incorporeal. For Plato posited the great and small, which the Platonists do not speak of as a body. The Italians, or Pythagoreans, posited the unlimited; but neither is this a body. Empedocles, on the other hand, posited the four elements, which are bodies; and Anaxagoras also posited "an infinite number of like parts," i.e.) [he claimed] that the principles of things are an infinite number of like parts. All of these thinkers have touched on "this kind of cause," i.e., the material cause, and so also have those who said that the principle of things is air or water or fire or something midway between these elements, i.e., what is denser than fire and rarer than air. For all philosophers such as those just mentioned have claimed that some kind of body is the first element of things. Thus Aristotle's statement is evident, namely, that in the light of the foregoing remarks these philosophers have posited only the material cause.

174. But others (82).

Here he gives their opinions about the efficient cause. He says that some of the foregoing philosophers have posited, in addition to the material cause, a cause from which motion begins, for example, those who made love or hate or intellect a cause of things, or those who introduced some other active principle distinct from these, as Parmenides, who made fire an efficient cause.

175. But the quiddity (83)

Here he gives their opinions about the formal cause. He says that the cause through which a thing's substance is known, i.e., the formal cause, no one attributed to things with any clarity. And if the ancient philosophers touched on something that might pertain to the formal cause, as Empedocles did when he claimed that bone and flesh contain some proportion [of the elements], by which they are things of this kind, nevertheless they did not treat what belongs to the formal cause after the manner of a cause.

176. But among the other philosophers, those who posited the Forms and those intelligible aspects which belong to the Forms, such as unity, number and the like, came closest to positing the formal cause. For the Forms and everything that belongs to the Forms in the aforesaid way, such as unity and number, are not acknowledged or assumed by them to be the matter of sensible things, since they place matter rather on the side of sensible things; nor do they claim that the Forms are the causes from which motion originates in the world, but rather that they are the cause of immobility in things. For they said that whatever is found to be necessary in sensible things is caused by the Forms, and that these, i.e., the Forms, are immobile. For they claimed that the Forms, because immobile, are uniform in being, as has been said (69:C 156), so that definitions can be given of them and demonstrations made about them. But according to the opinion of these men the Forms are responsible for the quiddity of pparticular things after the manner of a formal cause, and the one is responsible for the quiddity of the Forms.

All the foregoing weak on FINAL cause

177. That for the sake of which (84). Here he gives the opinions of certain thinkers about the final cause. He says that in one sense the philosophers say that the goal for the sake of which motions, changes and activities occur is a cause, and in another sense they do not. And they neither speak of it in the same way, nor in the way in which it is a true cause. For those who affirm that intellect or love is a cause, posit these causes as good. For they said that things of this kind are the causes of things being well disposed, since the cause of good can only be good. Hence it follows that they could make intellect and love to be causes, just as the good is a cause. But good can be understood in two ways: (1) in one way as a final cause, in the sense that something comes to be for the sake of some good; and (2) in another way as an efficient cause, as we say that the good man does good.

Now these philosophers did not say that the foregoing causes are good in the sense that they are the reason for the existence or coming to be of some beings, which pertains to the intelligibility of the final cause, but in the sense that there proceeds from these causes—intellect and will—a kind of motion toward the being and coming-to-be of things; and this pertains to the intelligibility of the efficient cause.

178. In a similar way the Pythagoreans and Platonists, who said that the substance of things is the one itself or being, also attributed goodness to the one or being. Thus they said that such a reality, i.e., the good, is the cause of the substance of sensible things, either in the manner of a formal cause, as the Platonists maintained, or in the manner of a material cause, as the Pythagoreans claimed.

However, they did not say that the being and coming-to-be of things exists for the sake of this, i.e., the one or being; and this is something that pertains to the intelligibility of the final cause.

Hence, just as the philosophers of nature claimed that the good is a cause in the manner of an (+) efficient cause and not in that of a (~) formal cause, in a similar way the Platonists claimed that the good is a cause in the manner of a (+) formal cause, and not in that of a (~) final cause. The Pythagoreans, on the other hand, considered it to be a cause in the manner of a (+) material cause.

179. It is evident, then, that in one sense they happened to speak of the good as a cause and in another not. For they did not speak of it as a cause in its principal aspect but in a secondary one; because according to its proper intelligible structure the good is a cause in the manner of a final cause. This is clear from the fact that the good is what all desire. Now that to which an appetite tends is a goal. Therefore according to its proper intelligible structure the good is a cause in the manner of a goal.

Hence those who make the good a cause in its principal aspect claim that it is a final cause. But those who attribute a different mode of causality to the good claim that the good is a cause but only in a secondary way; because they do not hold that it is such by reason of being good, but by reason of that to which good happens to belong by reason of its being active or perfective.

Hence it is clear that those philosophers posited a final cause only incidentally, because they posited as a cause something that is fitting to be an end, namely, the good. However, they did not claim that it is a cause in the manner of a final cause, as has been stated.

Conclusion

180. Therefore all these (85).

Here he draws the conclusion at which he chiefly aims: that the things established about the causes, both as to their number and their kinds, are correct. For the foregoing philosophers seem to bear witness to this in being unable to add another class of cause to those discussed above. This is one of the useful pieces of information resulting from the account of the foregoing views.

Another is that evidently the principles of things must be investigated in this science, either all those which the ancient philosophers posited, and which have been established above, or some of them. For this science considers chiefly the formal and final cause, and also in a sense the efficient cause.

Now it is not only necessary that the above views be discussed, but after this examination it is also necessary to describe the way in which each of these men has spoken (both in what sense their statements are acceptable and in what sense not), and how the statements which have been made about the principles of things contain a problem.

LESSON 12

Criticism of the Views about the Number of Material Principles

ARISTOTLE’S TEXT Chapter 8: 988b 22-989b 24

86. Therefore all those who hold that the whole is one and say that there is a certain single nature as matter, and that this is corporeal and has measure, are clearly at fault in many ways. For they give only the elements of bodies and not those of incorporeal things, as if incorporeal things did not exist.

87. And in attempting to state the cause of generation and corruption, and in treating all things according to the method of natural philosophy, they do away with the cause of motion.

88. Furthermore, they did not claim that the substance or whatness of a thing is a cause of anything.

89. And they were wrong in holding that any of the simple bodies except earth is a principle, without considering how they are generated from each other.

90. I mean fire, earth, water and air; for some of these are generated from each other by combination and others by separation. Now it makes the greatest difference as to which of these is prior and which subsequent.

91. For in one way it would seem that the most basic element of all is that from which a thing first comes to be by combination. But such an element will be one which has the smallest parts and is the subtlest of bodies. Hence all those who posit fire as the first principle make statements that conform most closely to this theory. But each of the other thinkers admits that the primary element of bodies is something of this kind.

92. For none of the later thinkers, and none of those who spoke about the one, wanted earth to be an element, evidently because of the size of its particles. But each of the other three elements finds some supporter, for some say that this primary element is fire, others water, and others air. But why do they not say that it is earth, as in a sense most men do? For they say that everything is earth. And Hesiod says that earth is the first of bodies to be generated; for this happens to be the ancient and common view. Therefore, according to this theory, if anyone says that any of these bodies with the exception of fire is the primary element of things, or if anyone holds that it is something denser than air but rarer than water, he will not speak the truth.

93. However, if that which is later in generation is prior in nature, and if that which is condensed and compounded is later in generation, then the reverse will be true—water will be prior to air, and earth to water. Let these points suffice, then, regarding those who posit one cause such as we have described.

94. The same consequence will also be true if anyone posits many elements, as Empedocles says that the four [elemental] bodies are the matter of things. For these same consequences must befall this man, as well as some which are peculiar to himself. For we see things being generated from each other in such a way that the same body does not always remain fire or earth. But we have spoken of these matters in our physical treatises.

95. And concerning the cause of things in motion, whether one or more than one must be posited, it must not be thought that what has been said is either entirely correct or reasonable.

96. And in general those who speak thus must do away with alteration, because the cold will not come from the hot, nor the hot from the cold. For what is it that undergoes these contraries and what is the one nature which becomes fire and water? Such a thing Empedocles does not admit.

97. But if anyone were to maintain that Anaxagoras speaks of two elements, they would acknowledge something fully in accord with a theory which he himself has not stated articulately, although he would have been forced to follow those who express this view. For to say, as he did, that in the beginning all things are mixed together is absurd, both because it would be necessary to understand that things previously existed in an unmixed state, and because it is not fitting that anything should be mixed with just anything; and also because properties and accidents could be separated from substances (for there is both mixture and separation of the same things). Yet, if anyone were to follow him up and articulate what he means, his statement would perhaps appear more astonishing. For when nothing was distinct from anything else, evidently nothing would be truly predicated of that substance. I mean that it would neither be white nor black nor tawny, nor have any color, but would necessarily be colorless; for otherwise it would have one of these colors. And, similarly, it would be without humors. And for the same reason it would have no other similar attribute. For it could not have any quality or quantity or whatness, because, if it had, some of the attributes described as formal principles would inhere in it. But this is obviously impossible, since all things are mixed together; for they would already be distinct from each other. But he said that all things are mixed together except intellect, and that this alone is unmixed and pure.’ Now from these statements it follows for him that there are two principles, one being the intellect itself (for this is unmixed in an absolute sense), and the other being the kind of thing we suppose the indeterminate to be before it is limited and participates in a form. Hence, what he says is neither correct nor clear, although he intends something similar to what later thinkers said and what is now more apparent. But these thinkers are concerned only with theories proper to generation, corruption and motion; for usually it is only of this kind of substance that these men seek the principles and causes.

COMMENTARY

181. Having stated the opinions which the philosophers held about the principles of things, Aristotle begins here to criticize them; and this is divided into two parts. First, he criticizes each opinion. Second (272), he summarizes his discussion and links it up with what follows (“From the foregoing”).

The first is divided into two parts. First, he criticizes the opinions of those who have treated things according to the method of natural philosophy. Second (201), he criticizes the opinions of those who have not treated things according to the method of natural philosophy, i.e., Pythagoras and Plato, because they posited higher principles than the natural philosophers did (“But all those”).

In regard to the first part he does two things. First, he criticizes the opinions of those who posited one material cause; and second (190), the opinions of those who posited many (“The same consequence”).

In regard to the first he does two things. First, he criticizes the foregoing opinions in a general way; and second (183), in a special way (“And they were wrong”).

He criticizes these opinions in a general way by means of three arguments. The first (86) is this: in the world there are not only bodies but also certain incorporeal things, as is clear from The Soul. But these men posited only corporeal principles, which is clear from the fact that they maintained that “the whole is one,” i.e., that the universe is one thing substantially, and that there is a single nature as matter, and that this is corporeal and has “measure,” i.e., dimension. But a body cannot be the cause of an incorporeal thing. Therefore it is evident that they were at fault in this respect that they treated the principles of things inadequately. And they were at fault not only in this respect but in many others, as is clear from the following arguments.

182. And in attempting (87).

Here he gives the second argument, which runs thus: whoever feels obliged to establish the truth about motion must posit a cause of motion. But these philosophers felt obliged to treat motion, which is clear for two reasons: first, because they tried to state the causes of generation and corruption in the world, which do not occur without motion; and second, because they wanted to treat things according to the method of natural philosophy. But since a treatment of things according to this method involves motion (because nature is a principle of motion and rest, as is clear in Book II of the Physics), they should therefore have dealt with that cause which is the source of motion. And since they did away with the cause of motion by saying nothing about it, obviously they were also at fault in this respect.

183. Furthermore, they did not (88).

Here he gives the third argument: every natural being has “a substance,” i.e., a form of the part, “and whatness,” i.e., quiddity, which is the form of the whole.3 He says form inasmuch as it is a principle of subsistence, and whatness inasmuch as it is a principle of knowing, because what a thing is is known by means of this. But the foregoing philosophers did not claim that form is a cause of anything. They treated things inadequately, then, and were also at fault in neglecting the formal cause.

184. For none of the later (92).

Here he criticizes their opinions in a special way; and he does this with respect to two things. First, he criticizes them for maintaining that all the elements with the exception of fire are the principles of things. Second (187), he criticizes them for omitting earth (“However, if”).

First (92), he takes up once more the position of those who claimed that each of the simple bodies except earth is the [primary] element of things. The reason which he gives for this position is that these men saw that the simple bodies are generated from each other in such a way that some come from others by combination or compacting, as grosser things come from more refined ones.

185. He also explains how to proceed against their opinions from their own arguments. For they claimed that one of these elements is the principle of things by arguing that other things are generated from it either by combination or by separation. Now it makes the greatest difference as to which of these two ways is prior and which subsequent, for on this depends the priority or posteriority of that from which something is generated. For, on the one hand, that seems to be prior from which something is produced by combination; and he gives this argument first. Yet, on the other hand, that seems to be prior from which something is produced by rarefaction; and he bases his second argument on this.

186. For the fact that the primary element is that from which something is produced by combination supports the opinion which is now held that the most basic element is that from which other things are produced by combination. This in fact is evident both from reason and from the things that they held. It is evident from reason, because that from which other things are produced by combination is the most refined type of body, and the one having the smallest parts; and this seems to be the simpler body. Hence, if the simple is prior to the composite, this body seems to be first. It is also evident from the things that they held, because all those who posited fire as the principle of things asserted that it is the first principle. Similarly, others have been seen to follow this argument, for they thought that the primary element of bodies is the one having the finest parts. This is evident from the fact that none of the later philosophers followed the theological poets, who said that earth is the primary element of things. Evidently they refused to do this “because of the size of its parts,” i.e., because of the coarseness of its parts. However, it is a fact that each of the other three elements finds some philosopher who judges it to be the principle of things. But their refusal to make earth a principle is not to be explained by a refusal to reject a common opinion; for many men thought that earth is the substance of things. Hesiod, who was one of the theological poets, also said that earth is the first of all bodies to come into

being. Thus the opinion that earth is the principle of things is evidently an ancient one, because it was maintained by the theological poets, who preceded the philosophers of nature. It was also the common opinion, because many men accepted it. It follows, then, that the later philosophers

avoided the position that earth is a principle only because of the coarseness of its parts. But it is certain that earth has coarser parts than water, and water than air, and air than fire; and if there is any intermediate element, it is evident that it is grosser than fire. Hence by following this argument it is clear that none of them spoke correctly, except him who held that fire is the first principle. For as soon as some element is held to be a principle by reason of its minuteness, the most minute element must be held to be the first principle of things.

187. However, if that which (93).

Here he gives another argument, and according to it the opposite seems to be true, namely, that earth is the most basic element of things. For it is evident that whatever is subsequent in generation is prior in nature, because nature tends to the goal of generation as the first thing in its intention. But the denser and more composite something is, the later it appears in the process of generation; for the process of generation proceeds from simple things to composite ones, Just as mixed bodies come from the elements, and the humors and members [of a living body] from mixed bodies. Hence, whatever is more composite and condensed is prior in nature. In this way a conclusion is reached which is the opposite of that following from the first argument; i.e., water is now prior to air and earth to water as the first principle of things.

188. It should be noted, however, that it is a different thing to look for what is prior in one and the same entity and for what is prior without qualification. For if one seeks what is prior without qualification, the perfect must be prior to the imperfect, just as actuality is prior to potentiality; because a thing is brought from a state of imperfection to one of perfection, or from potentiality to actuality, only by something completely actual. Therefore, if we speak of what is first in the whole universe, it must be the most perfect thing. But in the case of one particular thing which goes from potentiality to. complete actuality, potentiality is prior to actuality in time, although it is subsequent in nature. It is also clear that the first of all things must be one that is simplest; for the composite depends on the simple, and not the reverse. It was necessary, then, that the ancient philosophers should attribute both of these properties (the greatest perfection along with the greatest simplicity) to the first principle of the whole universe. However, these two properties cannot be attributed simultaneously to any corporeal principle, for in bodies subject to generation and corruption the simplest entities are imperfect. They were Compelled, then, as by contrary arguments, to posit different principles. Yet they preferred the argument of simplicity, because they considered things only insofar as something passes from potentiality to actuality, and in this order it is not necessary that anything which is a principle should be more perfect. But this kind of opposition can be resolved only by maintaining that the first principle of things is incorporeal, because this principle will be the simplest one, as Aristotle will prove below (2548).

189. Last of all he concludes that for the purpose of the present discussion enough has been said about the positions of those who affirm one material cause.

190. The same consequence (94).

Here he gives the arguments against those who posited many material causes. First, he argues against Empedocles; and second (194), against Anaxagoras (“But if anyone”).

First (94), he says that the same consequence faces Empedocles, who held that the four [elemental] bodies are the matter of things, because he experienced the same difficulty with regard to the above contrariety. For according to the argument of simplicity fire would seem to be the most basic principle of bodies; and according to the other argument earth would seem to be such, as has been stated (187). And while Empedocles faced some of the same absurd conclusions as the preceding philosophers (i.e., he did not posit either a formal cause or

the aforesaid contrariety of simplicity and perfection in corporeal things), there is no argument against him for doing away with the cause of motion. But he did face certain other absurd conclusions besides those that confronted the philosophers who posited one material cause.

191. This is shown by three arguments, of which the first is as follows.

First principles are not generated from each other, because a principle must always remain in existence, as is pointed out in Book I of the Physics. But we perceive that the four elements are

generated from each other, and for this reason their generation is dealt with in natural philosophy. Hence his position that the four elements are the first principles of things is untenable.

192. And concerning the cause (95).

Here he gives the second absurdity, which has to do with the cause of motion. For to posit many and contrary causes of motion is not at all correct or reasonable; because if the causes of motion are understood to be proximate ones, they must be contraries, since their effects seem to be contraries. But if the first cause is understood, then it must be unique, as is apparent in Book XII (2492) of this work, and in Book VIII of the Physics. Therefore, since he intends to posit the first causes of motion, his position that they are contraries is untenable.

193. And in general (96).

Here he gives the third argument which leads to an absurdity: in every process of alteration it must be the same subject which undergoes contraries. This is true because one contrary does not come from another in such a way that one is converted into the other; for example, the cold does not come from the hot in such a way that heat itself becomes cold or the reverse, although the cold does come from the hot when the underlying subject is one only inasmuch as the single subject which is now the subject of heat is afterwards the subject of cold. But Empedocles did not hold that contraries have one subject. In fact he held that they are found in different subjects, as heat in fire and cold in water. Nor again did he hold that there is one nature underlying these two. Therefore he could not posit alteration in any way. Yet it is absurd that alteration should be done away with altogether.

194. But if anyone (97).

Here he deals with Anaxagoras’ opinion; and in regard to this he does two things. First, he shows in general in what respect Anaxagoras’ opinion should be accepted as true, and in what respect not. Second (97), he explains each of these in particular (“For to say”).

He says, first, that if anyone wishes to maintain that Anaxagoras’ opinion is true insofar as he posited two principles, i.e., matter and efficient cause, let him understand this according to the reasoning which Anaxagoras himself seems to have followed, as if compelled by some need for truth, inasmuch as he would have followed those who expressed this theory. But “he himself has not stated it articulately”; i.e., he has not expressed it distinctly. Therefore, with reference to what he has not expressly stated his opinion is true; but with reference to what he has expressly stated his opinion is false.

195. This is made clear in particular as follows. If his opinion is taken in its entirety according to a superficial understanding of his statements, a greater absurdity will appear for four reasons. First, his opinion that all things were mixed together at the beginning of the world is absurd; for in Aristotle’s opinion the distinction between the parts of the world is thought to be eternal. The second reason is this: what is unmixed is related to what is mixed as the simple to the composite. But simple bodies are prior to composite ones, and not the reverse. Therefore what is unmixed must be prior to what is mixed. This is the opposite of what Anaxagoras said. The third reason is this: in the case of bodies not anything at all is naturally disposed to be mixed with anything else, but only those things are naturally disposed to be mixed which are naturally inclined to pass over into each other by some kind of alteration; for a mixture is a union of the altered things which are capable of being mixed. But Anaxagoras held that anything is mixed with just anything. The fourth reason is this: there is both mixture and separation of the same things; for only those things are said to be mixed which are naturally disposed to exist apart. But properties and accidents are mixed with substances, as Anaxagoras said. Therefore it follows that properties and accidents can exist apart from substances. This is evidently false. These absurdities appear then, if Anaxagoras’ opinion is considered in a superficial way.

196. Yet if anyone were to follow him up “and articulate,” i.e., investigate clearly and distinctly, the things which Anaxagoras “means,” i.e., what he intended, although he did not know how to express this, his statement would appear to be more astonishing and subtler than those of the preceding philosophers. This will be so for two reasons. First, he came closer to a true understanding of matter. This is clear from the fact that in that mixture of things, when nothing was distinguished from anything else but all things were mixed together, nothing could be truly predicated of that substance which is so mixed, which he held to be the matter of things. This is clear in the case of colors; for no special color could be predicated of it so that it might be said to be white or black or have some other color; because, according to this, that color would necessarily be unmixed with other things. Nor, similarly, could color in general be predicated of it so that it might be said to be colored; because everything of which a generic term is predicated must also have a specific term predicated of it, whether the predication be univocal or denominative. Hence, if that substance were colored, it would necessarily have some special color. But this is opposed to the foregoing statement. And the argument is similar with respect to “humors,” i.e., savors, and to all other things of this kind. Hence the primary genera themselves could not be predicated of it in such a way that it would have quality or quantity or some attribute of this kind. For if these genera were predicated of it, some particular species would necessarily belong to it. But this is impossible, if all things are held to be mixed together. For this species which would be predicated of that substance would already be distinguished from the others. And this is the true nature of matter, namely, that it does not have any form actually but is in potentiality to all forms. For the mixed body itself does not have actually any of the things which combine in its mixture, but has them only potentially. And it is because of this likeness between prime matter and what is mixed that he seems to have posited the above mixture; although there is some difference between the potentiality of matter and that of a mixture. For even though the elements which constitute a mixture are present in the mixture potentially, they are still not present in a state of pure passive potency; for they remain virtually in the mixture. This can be shown from the fact that a mixture has motion and operations as a result of the bodies of which the Mixture is composed. But this cannot be said of the things which are present potentially in prime matter. And there is also another difference, namely, that even though a mixture is not actually any of the mixed bodies which it contains, yet it is something actual. This cannot be said of prime matter. But Anaxagoras seems to do away with this difference, because he has not posited any particular mixture but the universal mixture of all things.

197. The second reason is this: he spoke more subtly than the others, because he came closer to a true understanding of the first active principle. For he said that all things are mixed together except intellect, and that this alone is unmixed and pure.

198. From these things it is clear that he posited two principles: one of these he claimed to be the intellect itself, insofar as it is simple and unmixed with other things; and the other is prime matter, which we claim is like the indeterminate before it is limited and participates in a form. For since [prime] matter is [the subject] of an infinite number of forms, it is limited by a form and acquires some species by means of it.

199. It is clear, then, that, in regard to the things which he stated expressly, Anaxagoras neither spoke correctly nor clearly. Yet he would seem to say something directly which comes closer to the opinions of the later philosophers, which are truer (namely, to those of Plato and Aristotle, whose judgments about prime matter were correct) and which were then more apparent.

200. In concluding Aristotle excuses himself from a more diligent investigation of these opinions, because the statements of these philosophers belong to the realm of physical discussions, which treat of generation and corruption. For these men usually posited principles and causes of this

kind of substance, i.e., of material and corruptible substance. He says “usually,” because, while they did not treat other substances, certain of the principles laid down by them can also be extended to other substances. This is most evident in the case of intellect. Therefore, since they have not posited principles common to all substances, which pertains to this science, but only principles of corruptible substances, which pertains to the philosophy of nature, a diligent study of the foregoing opinions belongs rather to the philosophy of nature than to this science.

LESSON 13

Criticism of the Pythagoreans’ Opinions

ARISTOTLE’S TEXT Chapters 8 & 9: 989b 24-99oa 34

98. But all those who make a study of all existing things, and who claim that some are sensible and others not, evidently make a study of both classes. And for this reason one should dwell at greater length on the statements they have made, whether they be acceptable or not, for the purposes of the present study which we now propose to make.

99. Therefore, those who are called Pythagoreans used principles and elements which are foreign to the physicists; and the reason is that they did not take them from sensible things. For the objects of mathematics, with the exception of those that pertain to astronomy, are devoid of motion. Nevertheless they discuss and treat everything that has to do with the physical world; for they generate the heavens and observe what happens in regard to its parts, affections and operations. And in doing this they use up their principles and causes, as though they agreed with the others, i.e., the physicists, that whatever exists is sensible and is contained by the so-called heavens. But, as we have stated, the causes and principles [of which they speak] are sufficient to extend even to a higher class of beings, and are better suited to these than to their theories about the physical world.

100. Yet how there will be motion if only the limited and unlimited and even and odd are posited as principles, they do not say. But how can there be generation or corruption, or the activities of those bodies which traverse the heavens, if there is no motion or change?

101. And further, whether one grants them that continuous quantities come from these things, or whether this is demonstrated, how is it that some bodies are light and others heavy? For from what they suppose and state, they say nothing more about mathematical bodies than they do about sensible ones. Hence they have said nothing about fire, earth and other bodies of this kind, since they have nothing to say that is proper to sensible things.

102. Further, how are we to understand that the attributes of number and number itself are [the causes] of what exists and comes to pass in the heavens, both from the beginning and now? And how are we to understand that there is no other number except that of which the world is composed? For when they [place] opportunity and opinion in one part of the heavens, and a little above or below them injustice and separation or mixture, and when they state as proof of this that each of these is a number, and claim that there already happens to be in this place a plurality of quantities constituted [of numbers], because these attributes of number correspond to each of these places, [we may ask] whether this number which is in the heavens is the same as that which we understand each [sensible] thing to be, or whether there is another kind of number in addition to this? For Plato says there is another. In fact, lie also thinks that both these things and their causes are numbers, but that some are intellectual causes and others sensible ones.

Chapter 9

Regarding the Pythagoreans, then, let us dismiss them for the present; for it is enough to have touched upon them to the extent that we have.

COMMENTARY

201. Here he argues dialectically against the opinions of Pythagoras and Plato, who posited different principles than those which pertain to the philosophy of nature. In regard to this he does two things. First, he shows that a study of these opinions rather than those mentioned above belongs to the present science. Second (202), he begins to argue dialectically against these opinions (“Therefore those who”).

He says, first (98), then, that those who “make a study,” i.e., an investigation, of all existing things, and hold that some are sensible and others non-sensible, make a study of both classes of beings. Hence an investigation of the opinions of those who spoke either correctly or incorrectly, belongs rather to the study which we now propose to make in this science. For this science deals with all beings and not with some particular class of being. Hence, the things which pertain to every class of being are to be considered here rather than those which pertain to some particular class of being.

202. Therefore those who (99).

Here he argues against the opinions of the foregoing philosophers. First (99), he argues against Pythagoras; and second (208), against Plato (“But those who posited Ideas”).

In regard to the first he does two things. First, he shows in what way Pythagoras agreed with the philosophers of nature, and in what way he differed from them. Second (204), he argues against Pythagoras’ position (“Yet how”).

We must understand (99), then, that in one respect the Pythagoreans agreed with the philosophers of nature, and in another respect they differed from them. They differed from them in their position regarding principles, because they employed principles of things in a way foreign to the philosophers of nature. The reason is that they did not take the principles of things from sensible beings, as the natural philosophers did, but from the objects of mathematics, which are devoid of motion, and are therefore not physical. And the statement that the objects of mathematics are devoid of motion must be referred to those sciences which are purely mathematical, such as arithmetic and geometry. Astronomy considers motion’ because astronomy is a science midway between mathematics and natural philosophy. For astronomy and the other intermediate sciences apply their principles to natural things, as is clear in Book II of the Physics.

203. Now Pythagoras agreed with the philosophers of nature concerning the things whose principles he sought; for he discussed and treated all natural beings. He dealt with the generation of the heavens, and observed everything that happens to the parts of the heavens, by which are meant the different spheres, or also the different stars. He also considered what happens to its affections, or to the eclipses of the luminous bodies; and what happens to the operations and motions of the heavenly bodies, and their effects on lower bodies. And he used up causes on particular things of this kind by applying to each one its proper cause. He also seemed to agree with’ the other philosophers of nature in thinking that that alone has being which is sensible and is contained by the heavens which we see. For he did not posit an infinite sensible body as the other philosophers of nature did. Nor again did he hold that there are many worlds, as Democritus did. He therefore seemed to think that there are no beings except sensible ones, because he assigned principles and causes only for such substances. However, the causes and principles which he laid down are not proper or limited to sensible things, but are sufficient for ascending to higher beings, i.e., intellectual ones. And they were better fitted to these than the theories of the natural philosophers which could not be extended beyond sensible things, because these philosophers claimed that principles are corporeal. But since Pythagoras posited incorporeal principles, i.e., numbers, although he only posited principles of sensible bodies, he came very close to positing principles of intelligible beings, which are not bodies, as Plato did later on.

204. Yet how (100).

Here he gives three arguments against the opinion of Pythagoras. The first is this: Pythagoras could not explain how motion originates in the world, because he posited as principles only the limited and unlimited and the even and odd, which he held to be principles as substance, or material principles. But he had to admit that there is motion in the world. For how could there be generation and corruption in bodies, and how could there be any activities of the heavenly bodies, which occur as a result of certain kinds of motion, unless motion and change existed? Evidently they could not exist in any way. Hence, since Pythagoras considered generation and corruption and the operations of the heavenly bodies without assigning any principle of motion, his position is clearly unsatisfactory.

205. And further (101).

Here he gives the second argument. For Pythagoras claimed that continuous quantities are composed of numbers. But whether he proves this or takes it for granted, he could not give any reason on the part of numbers as to why some things are heavy and others light. This is clear from the fact that his theories about numbers are no more adapted to sensible bodies than they are to the objects of mathematics, which are neither heavy nor light. Hence they obviously said nothing more about sensible bodies than they did about the objects of mathematics. Therefore, since sensible bodies, such as earth and fire and the like, considered in themselves, add something over and above the objects of mathematics, it is evident that they said nothing proper in any true sense about these sensible bodies. Thus it is also evident that the principles which they laid down are not sufficient, since they neglected to give the causes of those [attributes] which are proper to sensible bodies.

206. Further, how are we (102).

Here he gives the third argument, which is based on the fact that Pythagoras seemed to hold two contrary [positions]. For, on the one hand, he held that number and the attributes of number arc the cause both of those events which occur in the heavens and of all generable and corruptible things from the beginning of the world. Yet, on the other hand, he held that there is no other number besides that of which the substance of things is composed; for he held that number is the substance of things. But how is this to be understood, since one and the same thing is not the cause of itself? For Pythagoras says that the former position may be demonstrated from the fact that each one of these sensible things is numerical in substance; because in this part of the universe there are contingent beings, about which there is opinion, and which are subject to time inasmuch as they sometimes are and sometimes are not. But if generable and corruptible things were partly above or partly below, there would be disorder in the order of the universe: either after the manner of injustice, i.e., insofar as some being would receive a nobler or less noble place than it ought to have; or after the manner of separation, i.e., in the sense that, if a body were located outside its own place, it would be separated from bodies of a like nature; or after the manner of mixture and mingling, provided that a body located outside its proper place must be mixed with some other body, for example, if some part of water occupied a place belonging to air or to earth. In this discussion he seems to touch on two ways in which a natural body conforms to its proper place: one pertains to the order of position, according to which nobler bodies receive a higher place, in which there seems to be a kind of justice; and the other pertains to the similarity or dissimilarity between bodies in place, to which separation and mingling may be opposed. Therefore, insofar as things have a definite position, they are fittingly situated in the universe. For if their position were fitting would result, inasmuch as it has been stated and shown that all parts of the universe are arranged in a definite proportion; for every definite proportion is numerical. And it was from this that Pythagoras showed that all things would be numbers. But, on the other hand, we see that the continuous quantities established in different places are many and different, because the particular places in the universe correspond to the proper attributes by which bodies are differentiated. For the attributes of bodies which are above differ from those which are below. Hence, since Pythagoras by means of the above argument affirms that all sensible things are numbers, and we see that the difference in sensible bodies is attributable to difference in place, the question arises whether the number which exists “in the heavens” i.e., in the whole visible body which comprises the heavens, is merely the same as that which must be understood to be the substance of each sensible thing, or whether besides this number which constitutes the substance of sensible things there is another number which is their cause. Now Plato said that there is one kind of number which is the substance of sensible things, and another which is their cause. And while both Plato himself and Pythagoras thought that numbers are both sensible bodies themselves and their causes, Plato alone considered intellectual numbers to be the causes of things that are not sensible, and sensible numbers to be the causes and forms of sensible things. And since Pythagoras did not do this, his position is unsatisfactory.

207. In concluding Aristotle says that these remarks about the Pythagoreans’ opinions will suffice; for it is enough to have touched upon them to this extent.

LESSON 14

Arguments against the Platonic Ideas

ARISTOTLE’S TEXT Chapter 9: 990a 34-991a 8

103. But those who posited Ideas, and were the first to seek an understanding of the causes of sensible things, introduced other principles equal in number to these—as though one who wishes to count things thinks that this cannot be done when they are few, but believes that he can count them after he has increased their number. For the separate Forms are almost equal to, or not fewer than, these sensible things in the search for whose causes these thinkers have proceeded from sensible things to the Forms. For to each thing there corresponds some homogeneous entity bearing the same name; and with regard to the substances of other things there is a one-in-many, both in the case of these sensible things and in those which are eternal.

104. Furthermore, with regard to the ways in which we Prove that there are Forms, according to none of these do they become evident. For from some no syllogism necessarily follows, whereas from others there does; and [according to these] there are Forms of things of which we do not think there are Forms.

105. For according to those arguments from [the existence of] the sciences there will be Forms of all things of which there are sciences; and according to the argument of the one-in-many there will also be Forms of negations.

106. Again, according to the argument that there is some understanding of corruption, there will be Forms of corruptible things; for of these there is some sensible image.

107. Again, according to the most certain arguments [for the Forms] some establish Forms of relations, of which they deny there is any essential class; whereas others lead to “the third man.”

108. And in general the arguments for the Forms do away with the existence of the things which those who speak of the Forms are more anxious to retain than the Forms themselves. For it happens that the dyad [or duality] is not first, but that number is; and that the relative is prior to that which exists of itself. And all the other [conclusions] which some [reach] by following up the opinions about the Ideas are opposed to the principles [of the theory].

109. Again, according to the opinion whereby we claim that there are Ideas [or Forms], there will be Forms not only of substances but also of many other things. For there is one concept not only in the case of substances but also in that of other things; and there are sciences not only of substance itself but also of other things. And a thousand other such [difficulties] face them.

110. But according to logical necessity and the opinions about the Ideas, if the Forms are participated in, there must be Ideas only of substances. For they are not participated in according to what is accidental. But things must participate in each Form in this respect: insofar as each Form is not predicated of a subject. I mean that if anything participates in doubleness itself, it also participates in the eternal, but only accidentally; for it is an accident of doubleness to be eternal. Hence the Forms will be substances.

111. But these things signify substance both here and in the ideal world; [otherwise] why is it necessary that a one-in-many appear in addition to these sensible things? Indeed, if the form of the Ideas and that of the things which participate in them are the same, there will be something in common. For why should duality be one and the same in the case of corruptible twos and in those which are many but eternal, rather than in the case of this [Idea of duality] and a particular two? But if the form is not the same, there will be pure equivocation; just as if one were to call both Callias and a piece of wood man, without observing any common attribute which they might have.

COMMENTARY

208. Here he argues disputatively against Plato’s opinion. This is divided into two parts. First (208), he argues against Plato’s opinion with reference to his position about the substances of things; and second (259), with reference to his position about the principles of things (“And in general”).

The first is divided into two parts. First, he argues against Plato’s position that the Forms are substances; and second (122:C 239), against the things that he posited about the objects of mathematics (“Further, if the Forms”).

In regard to the first he does two thinks. First, he argues against this position of Plato; and second (210), against the reasoning behind it (“Furthermore, with regard to”).

He says, first (103), that the Platonists, in holding that the Ideas are certain separate substances, seemed to be at fault in that, when they sought for the causes of these sensible beings, they neglected sensible beings and invented certain other new entities equal in number to sensible beings. This seems to be absurd, because one who seeks the causes of certain things ought to make these evident and not add other things, the premising of which only adds to the number of points which have to be investigated. For it would be similar if a man who wished to count certain things which he did not think he was able to count because they are few, believed that he could count them by increasing their number through the addition of certain other things. But it is evident that such a man has a foolish motive, because the path is clearer when there are fewer things; for it is better and easier to make certain of fewer things than of many. And the smaller a number is, the more certain it is to us, inasmuch as it is nearer to the unit, which is the most accurate measure. And just as the process of counting things is the measure we use to make certain of their number, in a similar fashion an investigation of the causes of things is the accurate measure for making certain of their natures. Therefore, just as the number of fewer numerable things is made certain of more easily, n a similar way the nature of fewer things is made certain of more easily. Hence, when Plato increased the classes of beings to the extent that he did with a view to explaining sensible things, he added to the number of difficulties by taking what is more difficult in order to explain what is less difficult. This is absurd.

209. That the Ideas are equal in number to, or not fewer than, sensible things, whose causes the Platonists seek (and Aristotle includes himself among their number because he was Plato’s disciple), and which they established by going from sensible things to the aforesaid Forms, becomes evident if one considers by what reasoning the Platonists introduced the Ideas. Now they reasoned thus: they saw that there is a one-in-many for all things having the same name. Hence they claimed that this one-in-many is a Form. Yet with respect to all substances of things other than the Ideas we see that there is found to be a one-in-many which is predicated of them univocally inasmuch as there are found to be many things which are specifically one. This occurs not only in the case of sensible things but also in that of the objects of mathematics, which are eternal; because among these there are also many things which are specifically one, as was stated above (157). Hence it follows that some Idea corresponds to each species of sensible things; and therefore each Idea is something having the same name as these sensible things, because the Ideas agree with them in name. For just as Socrates is called man, so also is the Idea of man. Yet they differ conceptually; for the intelligible structure of Socrates contains matter, whereas that of the ideal man is devoid of matter. or, according to another reading, each Form is said to be something having the same name [as these sensible things] inasmuch as it is a one-in-many and agrees with the things of which it is predicated so far as the intelligible structure of the species is concerned. Hence he says that they are equal to, or not fewer than, these things. For either there are held to be Ideas only of species, and then they would. be equal in number to these sensible things (granted that things are counted here insofar as they differ specifically and not individually, for the latter difference is infinite); or there are held to be ideas not only of species but also of genera, and then there would be more ideas than there are species of sensible things, because all species would be Ideas and in addition to these each and every genus [would be an Idea]. This is why he says that they are either not fewer than or more. Or, in another way, they are said to be equal inasmuch as he claimed that they are the Forms of sensible things. And he says not fewer than but more inasmuch as he held that they are the Forms not only of sensible things but also of the objects of mathematics.

210. Furthermore, with regard to (104).

Here he argues dialectically against the reasoning behind Plato’s position; and in regard to this he does two things. First, he gives a general account of the ways in which Plato’s arguments fail. Second (211), he explains them in detail (“For according to those”).

He says, first, that with regard to the ways in which we Platonists prove the existence of the Forms, according to none of these are the Forms seen to exist. The reason is that “no syllogism follows” necessarily from some of these ways, i.e., from certain arguments of Plato, because they cannot demonstrate with necessity the existence of the Ideas. However, from other arguments a syllogism does follow, although it does not support Plato’s thesis; for by certain of his arguments there are proved to be Forms of certain things of which the Platonists did not think there are Forms, just as there are proved to be Forms of those things of which they think there are Forms.

211. For according to (105).

Here he examines in detail the arguments by which the Platonists establish Ideas. First, he examines the second argument; and he does this by showing that from Plato’s argument it follows that there are Forms of some things for which the Platonists did not posit Forms. Second (225), he examines the first argument; and he does this by showing that Plato’s arguments are not sufficient to prove that Ideas exist (“But the most”).

In regard to the first member of this division he gives seven arguments. The first is this: one of the arguments that induced Plato to posit Ideas is taken from scientific knowledge; for since science is concerned with necessary things, it cannot be concerned with sensible things, which are corruptible, but must be concerned with separate entities which are incorruptible. According to the argument taken from the sciences, then, it follows that there are Forms of every sort of thing of which there are sciences. Now there are sciences not only of that which is one-in-many, which is affirmative, but also of negations; for just as there are some demonstrations which conclude with an affirmative proposition, in a similar way there are demonstrations which conclude with a negative proposition. Hence it is also necessary to posit Ideas of negations.

212. Again, according to the argument (106).

Here he gives the second argument. For in the sciences it is not only understood that some things always exist in the same way, but also that some things are destroyed; otherwise the philosophy of nature, which deals with motion, would be destroyed. Therefore, if there must be ideas of all the things which are comprehended in the sciences, there must be Ideas of corruptible things as such, i.e., insofar as these are singular sensible things; for thus are things corruptible. But according to Plato’s theory it cannot be said that those sciences by which we understand the processes of corruption in the world attain any understanding of the processes of corruption in sensible things; for there is no comprehension of these sensible things, but only imagination or phantasy, which is a motion produced by the senses in their act of sensing, as is pointed out in The Soul, Book II.

213. Again, according to the most (107).

Here he gives the third argument, which contains two conclusions that he says are drawn from the most certain arguments of Plato. One conclusion is this: if there are Ideas of all things of which there are sciences, and there are sciences not only of absolutes but also of things predicated relatively, then in giving this argument it follows that there are also Ideas of relations. This is opposed to Plato’s view. For, since the separate Ideas are things which exist of themselves, which is opposed to the intelligibility of a relation, Plato did not hold that there is a class of Ideas of relations, because the Ideas are said to exist of themselves.

214. The second conclusion is one which follows from other most certain arguments, namely, that there is “a third man.” This phrase can be understood in three ways. First, it can mean that the ideal man is a third man distinct from two men perceived by the senses, who have the common name man predicated of both of them. But this does not seem to be what he has in mind, even though it is not mentioned in the Sophistical Refutations, Book II; for this is the position against which he argues. Hence according to this it would not lead to an absurdity.

215. The second way in which this expression can be understood is this: the third man means one that is common to the ideal man and to one perceived by the senses. For since both a man perceived by the senses and the ideal man have a common intelligible structure, like two men perceived by the senses, then just as the ideal man is held to be a third man in addition to two men perceived by the senses, in a similar way there should be held to be another third man in addition to the ideal man and one perceived by the senses. But neither does this seem to be what he has in mind here, because he leads us immediately to this absurdity by means of another argument. Hence it would be pointless to lead us to the same absurdity here.

216. The third way in which this expression can be understood is this: Plato posited three kinds of entities in certain classes of things, namely, sensible substances, the objects of mathematics and the Forms. He does this, for example, in the case of numbers, lines and the like. But there is no reason why intermediate things should be held to exist in certain classes rather than in others. Hence in the class of man it was also necessary to posit an intermediate man, who will be a third man midway between the man perceived by the senses and the ideal man. Aristotle also gives this argument in the later books of this work (2160).

217. And in general (108).

Here he gives the fourth argument, which runs as follows. Whoever by his own reason he does away with certain [principles] which are better known to him than the ones which he posits, adopts an absurd position. But these theories about the Forms which Plato held do away with certain principles whose reality the Platonists (when they said that there are Ideas) were more convinced of than the existence of the Ideas. Therefore Plato’s position is absurd. The minor premise is proved in this way. According to Plato the Ideas are prior both to sensible things and to the objects of mathematics. But according to him the Ideas themselves are numbers; and they are odd numbers rather than even ones, because he attributed odd number to form and even number to matter. Hence he also said that the dyad [or duality] is matter. Therefore it follows that other numbers are prior to the dyad, which he held to be the matter of sensible things, and identified with the great and small. Yet the Platonists asserted the very opposite of this, that is to say, that the dyad is first in the class of number.

218. Again, if, as has been proved by the above argument (213), there must be Ideas of relations, which are self-subsistent relations, and if the Idea itself is prior to whatever participates in the Idea, it follows that the relative is prior to the absolute, which is said to exist of itself. For sensible substances of this kind, which participate in Ideas, are said to be in an unqualified sense. And in like manner whatever those who follow the opinion about the Ideas say of all things is opposed to self-evident principles which even they themselves are most ready to acknowledge.

219. Again, according to the opinion (109).

Here he gives the fifth argument, which is as follows: Ideas were posited by Plato in order that the intelligible structures and definitions of things given in the sciences might correspond to them, and in order that there could be sciences of them. But there is “one concept,” i.e., a simple and indivisible concept, by which the quiddity of each thing is known, i.e., not only the quiddity of substances “but also of other things,” namely, of accidents. And in a similar way there are sciences not only of substance and about substance, but there are also found to be sciences “of other things,” i.e., of accidents. Hence according to the opinion by which you Platonists acknowledge the existence of Ideas, it evidently follows that there will be Forms not only of substances but also of other things, i.e., of accidents. This same conclusion follows not only because of definitions and the sciences, but there also happen to be many “other such” [reasons], i.e., very many.reasons why it is necessary to posit Ideas of accidents according to Plato’s arguments. For example, he held that the Ideas are the principles of being and of becoming in the world, and of many such aspects which apply to accidents.

220. But, on the other hand, according to Plato’s opinion about the Ideas and according to logical necessity, insofar as the Ideas are indispensable to sensible things, i.e., “insofar” s as they are capable of being participated in by sensible things, it is necessary to posit Ideas only of substances. This is proved thus: things which are accidental are not participated in. But an Idea must be participated in by each thing insofar as it is not predicated of a subject. This becomes clear as follows: if any sensible thing participates in “doubleness itself,” i.e., in a separate doubleness (for Plato spoke of all separated things in this way, namely, as self-subsisting things), it must participate in the eternal. But it does not do this essentially (because then it would follow that any double perceived by the senses would be eternal), but accidentally, i.e., insofar as doubleness itself, which is participated in, is eternal. And from this it is evident that there is no participation in things which are accidental, but only in substances. Hence according to Plato’s position a separate Form was not an accident but only a substance. Yet according to the argument taken from the sciences there must also be Forms of accidents, as was stated above (219).

221. But these things (111).

Then he gives the sixth argument, which runs thus: these sensible things signify substance both in the case of things perceived by the senses and in that of those in the ideal world, i.e., in the case of intelligible things, which signify substance; because they held that both intelligible things and sensible ones are substance. Therefore it is necessary to posit in addition to both of these substances—intelligible and sensible ones—some common entity which is a one-in-many. For the Platonists maintained that the Ideas exist on the grounds that they found a one-in-many which they believed to be separate from the many.

222. The need for positing a one apart from both sensible substances and the Forms he proves thus: the Ideas and the sensible things which participate in them either belong to one class or not. If they belong to one class, and it is necessary to posit, according to Plato’s position, one common separate Form for all things having a common nature, then it will be necessary to Posit some entity common to both sensible things and the Ideas themselves) which exists apart from both. Now one cannot answer this argument by saying that the Ideas, which are incorporeal and immaterial, do not stand in need of any higher Forms; because the objects of mathematics, which Plato places midway between sensible substances and the Forms, are similarly incorporeal and immaterial. Yet since many of them are found to belong to one species, Plato held that there is a common Form for these things, in which not only the objects of mathematics participate but also sensible substances. Therefore, if the twoness [or duality] which is the Form or Idea of twoness is identical with that found in sensible twos, which are corruptible (just as a pattern is found in the things fashioned after it), and with that found in mathematical twos, which are many in one class (but are nevertheless eternal) ‘ then for the same reason in the case of the same twoness, i.e., the Idea two, and in that of the other twoness, which is either mathematical or sensible, there will be another separate twoness. For no reason can be given why the former should exist and the latter should not.

223. But if the other alternative is admitted—that sensible things, which participate in the Ideas, do not have the same form as the Ideas—it follows that the name which is predicated of both the Ideas and sensible substances is predicated in a purely equivocal way. For those things are said to be equivocal which have only a common name and differ in their intelligible structure. And it follows that they are not only equivocal in every way but equivocal in an absolute sense, like those things on which one name is imposed without regard for any common attribute, which are said to be equivocal by chance; for example, if one were to call both Callias and a piece of wood man.

224. Now Aristotle added this because someone might say that a name is not predicated of an Idea and of a sensible substance in a purely equivocal way, since a name is predicated of an Idea essentially and of a sensible substance by participation. For, according to Plato, the Idea of man is called “man in himself,” whereas this man whom we apprehend by the senses is said to be a man by participation. However, such an equivocation is not pure equivocation. But a name which is predicated by participation is predicated with reference to something that is predicated essentially; and this is not pure equivocation but the multiplicity of analogy. However, if an Idea and a sensible substance were altogether equivocal by chance, it would follow that one could not be known through the other, as one equivocal thing cannot be known through another.

LESSON 15

The Destruction of the Platonists’ Arguments for Ideas

ARISTOTLE’S TEXT Chapter 9: 991a 8-991b 9

112. But the most important problem of all that one might raise is what the Forms contribute to sensible things, either to those which are eternal or to those which are generated and corrupted.

113. For they are not the cause of motion or of any change whatever in these things.

114. Nor are they of any assistance in knowing other things; for they are not the substance of other things, because if they were they would exist in them. Nor do they contribute anything to the being of other things; for they are not present in the things which participate in them. For if they were they would perhaps seem to be causes, as whiteness mixed with some white thing. But this theory, which was first stated by Anaxagoras and later by Hesiod and certain other thinkers, is easily disposed of. For it is easy to bring many absurd conclusions against such a view. In fact other things are not derived from the Forms in any of the customary senses.

115. Again, to say that they are exemplars, and that other things participate in them, is to speak with empty talk and to utter poetic metaphors.

116. For what is the work which looks towards the Ideas [as an exemplar]? For one thing may both be and become similar to another thing and not be made in likeness to it. So whether Socrates exists or not, a man such as Socrates might come to be.

117. Similarly, it is evident that this will be the case even if Socrates is eternal. And there will be many exemplars of the same thing, and for this reason many Forms, as animal and two-footed and man-in-himself will be the Form of man.

118. Further, the Forms will be the exemplars not only of sensible things but also of the Forms themselves, as the genus of the species. Hence the same thing will be both an exemplar and a copy.

19. Again, it is thought to be impossible that the substance of a thing and that of which it is the substance should exist apart. Hence, if the Forms are the substances of things, how will they exist apart from them?

120. But in the Phaedo it is stated that the Forms are the causes both of being and of coming to be. Yet even if the Forms do exist, still the things which participate in them will not come to be unless there is something which produces motion.

121. And many other things come to be, such as a house and a ring, of which we do not say that there are any Forms. It is evident, then, that other things can exist and come to be because of such causes as those [responsible for the things] just mentioned.

COMMENTARY

225. Here Aristotle attacks the opinion of Plato insofar as he did not draw the conclusion which he intended to draw. For Plato intended to conclude that there are Ideas by this argument that they are necessary in some way for sensible things. Hence, Aristotle, by showing that the Ideas cannot contribute anything to sensible things, destroys the arguments by which Plato posits Ideas. Thus he says (112) that of all the objections which may be raised against Plato the foremost is that the Forms which Plato posited do not seem to contribute anything to sensible things, either to those which are eternal, as the celestial bodies, or to those which are generated and corrupted, as the elemental bodies. He shows (113) that this criticism applies to each of the arguments by which Plato posited Ideas (“For they are not”).

226. At this point in the text (113) he begins to present his five objections [against the Platonic arguments for Ideas].

He argues, first (226), that they are useless in explaining motion; second (227), that they are use

less in explaining our knowledge of sensible things (“Nor are they”); third (231), that they are of no value as exemplars (“Again, to say”); fourth (236), that they are of no value as the substances of things (“Again, it is thought”); and fifth (237) that they are of no value as causes of generation (“But in the Phaedo ”).

Accordingly, he says, first (113), that the Forms cannot contribute anything to sensible things in such a way as to be the cause of motion or of any kind of change in them. He does not give the reason for this here but mentioned it above (237), because it is clear that the Ideas were not introduced to explain motion but rather to explain immutability. For since it seemed to Plato that all sensible things are always in motion, he wanted to posit something separate from sensible things that is fixed and immobile, of which there can be certain knowledge. Hence, according to him, the Forms could not be held to be sensible principles of motion, but rather to be immutable things and principles of immutability; so that, undoubtedly, whatever is found to be fixed and constant in sensible things will be due to participation in the Ideas, which are immutable in themselves.

227. Nor are they of any assistance (114).

Second, he shows that the Forms do not contribute anything to the knowledge of sensible things, by the following argument: knowledge of each thing is acquired by knowing its own substance, and not by knowing certain substances which are separate from it. But these separate substances, which they call Forms, are altogether othef than sensible substances. Therefore a knowledge of them is of no assistance in knowing other sensible things.

228. Nor can it be said that the Forms are the substances of these sensible things; for the substance of each thing is present in the thing whom substance it is. Therefore, if then Forms were the substances of sensible things, they would be present in sensible things. This is opposed to Plato’s opinion.

229. Nor again can it be said that the Forms are present in these sensible substances as in things which participate in them; for Plato thought that some Forms are the causes of sensible things in this way. For just as we might understand whiteness itself existing of itself as a certain separate whiteness to be mingled with the whiteness in a subject, and to participate in whiteness, in a similar way we. might say that man [in himself], who is separate, is mingled with this man who is composed of matter and the specific nature in which he participates. But this argument is easily “disposed of, ‘ i.e., destroyed; for Anaxagoras, who also held that forms and accidents are mingled with things, was the first to state it. Hesiod and certain other thinkers were the second to mention it. Therefore I say that it is easily disposed of, because it is easy to bring many absurd conclusions against such an opinion. For it would follow as he pointed out above (194) against Anaxagoras, that accidents and forms could exist without substances. For only those things can exist separately which are naturally disposed to be mixed with other things.

230. It cannot be said, then, that the Forms contribute in any way to our knowledge of sensible things as their substances. Nor can it be said that they are the principles of being in these substances by way of participation. Nor again can it be said that from these Forms as principles other things—sensible ones—come to be in any of the ways in which we are accustomed to

speak. Therefore, if principles of being and principles of knowledge are the same, the Forms cannot possibly make any contribution to scientific knowledge, since they cannot be principles of 1wing. Hence he says “in any of the customary ways” of speaking, because Plato invented many new ways of deriving knowledge of one thing from something else.

231. Again, to say (115).

Here he gives the third objection against the arguments for separate Forms. He says that the Forms are of no value to sensible things as their exemplars. First (115), he states his thesis; and, second (232), he proves it (“For what is the work”).

Accordingly he says, first (115), that to say that the Forms are the exemplars both of sensible things and the objects of mathematics (because the latter participate in causes of this kind), is untenable for two reasons. First, because it is vain and useless to posit exemplars of this kind, as he will show; and second, because this manner of speaking is similar to the metaphors which the poets introduce, which do not pertain to the philosopher. For the philosopher ought to teach by using proper causes. Hence he says that this manner of speaking is metaphorical, because Plato likened the generation of natural substances to the making of works of art, in which the artisan, by looking at some exemplar, produces something similar to his artistic idea.

232. For what is the work (116).

Here he proves his thesis by three arguments. For the work, i.e., the use, of an exemplar, seems to be this, that the artisan by looking at an exemplar induces a likeness of the form in his own artifact. But in the operations of natural beings we see that like things are generated by like, as man is generated by man. Therefore this likeness arises in things which are generated, either because some agent looks toward an exemplar or not. If not, then what is “the work,” or utility, of the agent’s so looking toward the Ideas as exemplars?—as if to say, none. But if the likeness results from looking at a separate exemplar, then it cannot be said that the cause of this likeness in the thing generated is the form of an inferior agent. For something similar would come into being with reference to this separate exemplar and not with reference to this sensible agent. And this is what he means when he says “and not be like it,” i.e., like the sensible agent. From this the following absurdity results: someone similar to Socrates will be generated whether Socrates is held to exist or not. This we see is false; for unless Socrates plays an active part in the process of generation, no one similar to Socrates will ever be generated. Therefore, if it is false that the likeness of things which are generated does not depend on proximate agents, it is pointless and superfluous to posit separate exemplars of any kind.

233. However, it should be noted that, even though this argument does away with the separate exemplars postulated by Plato, it still does not do away with the fact that God’s knowledge is the exemplar of all things. For since things in the physical world are naturally inclined to induce their likeness in things which are generated, this inclination must be traced back to some directing principle which ordains each thing to its end. This can only be the intellect of that being who knows the end and the relationship of things to the end. Therefore this likeness of effects to their natural causes is traced back to an intellect as their first principle. But it is not necessary that this likeness should be traced back to any other separate forms; because in order to have the above-mentioned likeness this direction of things to their end, according to which natural powers are directed by the first intellect, is sufficient.

234. Similarly, it is evident (117).

Here he gives the second argument, which runs as follows: just as Socrates because he is Socrates adds something to man, in a similar way man adds something to animal. And just as Socrates participates in man, so does man participate in animal. But if besides this Socrates whom we perceive there is held to be another Socrates who is eternal, as his exemplar, it will follow that there are several exemplars of this Socrates whom we perceive, i.e., the eternal Socrates and the Form man. And by the same reasoning the Form man will have several exemplars; for its exemplar will be both animal and two-footed and also “man-in-himself,” i.e., the Idea of man. But that there should be several exemplars of a single thing made in likeness to an exemplar is untenable. Therefore it is absurd to hold that things of this kind are the exemplars of sensible things.

235. Further (118).

Here he gives the third argument, which runs thus: just as a Form is related to an individual, so also is a genus related to a species. Therefore, if the Forms are the exemplars of individual sensible things, as Plato held, there will be also certain exemplars of these Forms, that is to say, their genus. But this is absurd, because then it would follow that one and the same thing, i.e., Form, would be an exemplar of one thing, namely, of the individual whom we perceive by the senses, and a copy made in likeness to something else, namely, a genus. This seems to be absurd.

236. Again, it is thought (119).

Here he proves his fourth objection, namely, that the Forms contribute nothing to sensible things as their substances or formal causes; because “It is thought by him,” that is to say, it is a matter of opinion (to put this impersonally), that it is impossible for a thing’s substance to exist apart from the thing whose substance it is. But the Forms exist apart from the things of which they are the Forms, i.e., apart, from sensible things. Therefore they are not the substances of sensible things.

237. But in the “Phaedo” (120).

Here he shows that the Forms are of no value in accounting for the coming to be of sensible things, although Plato said “in the Phaedo,” i.e., in one of his works, that the Forms are the causes both of the being and of the coming to be of sensible things.

But Aristotle disproves this by two arguments. The first is as follows: to posit the cause is to posit the effect. However, even if the Forms exist, the particular or individual things which participate in the Forms will come into being only if there is some agent which moves them to acquire form. This is evident from Plato’s opinion that the Forms are always in the same state. Therefore, assuming that these Forms exist, if individuals were to exist or come into being by participating in them, it would follow that individual substances of this kind would always be. This is clearly false. Therefore it cannot be said that the Forms are the causes of both the coming to be and the being of sensible things. The chief reason is that Plato did not hold that the Forms are efficient causes, as was stated above (226). For Aristotle holds that the being and coming to be of lower substances proceeds from immobile separate substances, inasmuch as these substances are the movers of the celestial bodies, by means of which generation and corruption are produced in these lower substances.

238. And many other (121).

Here he gives the second argument, which runs thus: just as artifacts are related to artificial causes, so are natural bodies to natural causes. But we see that many other things besides natural bodies come into being in the realm of these lower bodies, as a house and a ring, for which the Platonists did not posit any Forms. Therefore “other things,” namely, natural things, can both be and come to be because of such proximate causes as those just mentioned, i.e., artificial ones; so that, just as artificial things come to be as a result of proximate agents, so also do natural things.

LESSON 16

Arguments against the View that Ideas Are Numbers

ARISTOTLE’S TEXT Chapter 9: 991b 9-992a 24

122. Further, if the Forms are numbers, in what way will they be causes? Will it be because existing things are other numbers, so that this number is man, another Socrates, and still another Callias? In what respect, then, are the former the cause of the latter? For it will make no difference if the former are eternal and the latter are not. But if it is because the things here are ratios of numbers, like a harmony, then clearly there will be one kind of thing of which they are the ratios. And if this is matter, evidently the numbers themselves will be certain ratios of one thing to something else. I mean that, if Callias is a numerical ratio of fire, water, earth and air, [his Idea will also be a ratio of certain things], and man-in-himself, whether it be a number or not, will still be a numerical ratio of certain things and not just a number; nor will it be any number because of these.

123. Again, one number will come from many numbers, but how or in what way can one Form come from [many] Forms?

124. But if one number is not produced from them but from the units which they contain, as the units in the number ten thousand, how are the units related? For if they are specifically the same, many absurdities will follow; and if they are not, neither will they be the same as one another nor all the others the same as all.

125. For in what way Will they differ, if they have no attributes? For these statements are neither reasonable nor in accord with our understanding.

126. Further, [if the Forms are numbers], it is necessary to set up some other class of number: that with which arithmetic deals. And all the things which an said to be intermediate, from what things or what principles in an absolute sense will they come, or why will they be [an intermediate class] between a the things at hand and those [in the ideal world]?

127. Again, each of the units which are contained in the number two will come from a prior two. But this is impossible.

128. Further, why is a number something composed of these?

129. And, again, in addition to what has been said, if the units are different, it will be necessary to speak of them in the same way as do those who say that the elements are four or two. For none of them designate as an element what is common, namely, body, but fire and earth, whether body is something in common or not. But now we are speaking of the one as if it were one thing made up of like parts, as fire or water. But if this is the case, numbers will not be substances. Yet it is evident that, if the one itself is something common and a principle, then the one is used in different senses; otherwise this will be impossible.

130. Now when we wish to reduce substances to their principles, we claim that lengths come from the long and short, i.e., from a kind of great and small; and the plane from the wide and narrow; and body from the deep and shallow.

131. Yet how will a surface contain a line, or a solid a line or surface? For the wide and narrow is a different class from the deep and shallow. Hence, just as number is not present in these, because the many and few differ from these, it is evident that no one of the other higher classes will be present in the lower. And the broad is not in the class of the deep, for then the solid would be a kind of surface.

132. Further, from what will points derive being? Plato was opposed to this class of objects as a geometrical fiction, but he called them the principle of a line. And he often holds that there are indivisible lines. Yet these must have some [limit]. Therefore any argument that proves the existence of the line also proves the existence of the point.

COMMENTARY

239. Here he destroys Plato’s opinion about the Forms inasmuch as Plato claimed that they are numbers. In regard to this he does two things. First, he argues dialectically against Plato’s opinion about numbers, and second (254), against his opinion about the other objects of mathematics (“Now when we wish”).

In regard to the first part he gives six arguments. The first (122) is this: in the case of things which are substantially the same, one thing is not the cause of another. But sensible things are substantially numbers according to the Platonists and Pythagoreans. Therefore, if the Forms themselves are numbers, they cannot be the cause of sensible things.

240. But if it is said that some numbers are Forms and others are sensible filings, as Plato literally held (as though We were to say that this number is man and another is Socrates and still another is Callias), even this would not seem to be sufficient; for according to this view the intelligible structure of number will be common both to sensible things and the Forms. But in the case of things which have the same intelligible structure, one does not seem to be the cause of another. Therefore the Forms will not be the causes of sensible things.

241. Nor again can it be said that they are causes for the reason that, if those numbers are Forms, they are eternal. For this difference, namely, that some things differ from others in virtue of being eternal and non-eternal in their own being considered absolutely, is not sufficient to explain why some things are held to be the causes of others. Indeed, things differ from each other as cause and effect rather because of the relationship which one has to the other. Therefore things that differ numerically do not differ from each other as cause and effect because some are eternal and some are not.

242. Again, it is said that sensible things are certain “ratios” or proportions of numbers, and that numbers are the causes of these sensible things, as we also observe to be the case “in harmonies,” i.e., in the combinations of musical notes. For numbers are said to be the causes of harmonies insofar as the numerical proportions applied to sounds yield harmonies. Now if the above is true, then just as in harmonies there are found to be sounds in addition to numerical proportions, in a similar way it was obviously necessary to posit in addition to the numbers in sensible things something generically one to which the numerical proportions are applied, so that the proportions of those things which belong to that one genus would constitute sensible things. However, if that to which the numerical proportion in sensible things is applied is matter, evidently those separate numbers, which are Forms, had to be termed proportions of some one thing to something else. For this particular man, called Callias or Socrates, must be said to be similar to the ideal man, called “man-in-himself,” or humanity. Hence, if Callias is not merely a number, but is rather a kind of ratio or numerical proportion of the elements, i.e., of fire, earth, water and air, and if the ideal man-in-himself is a kind of ratio or numerical proportion of certain things, the ideal man will not be a number by reason of its own substance. From this it follows that there will be no number “apart from these,” i.e., apart from the things numbered. For if the number which constitutes the Forms is separate in the highest degree, and if it is not separate from things but is a kind of proportion of numbered things, no other number will now be separate. This is opposed to Plato’s view.

243. It also follows that the ideal man is a proportion of certain numbered things, whether it is held to be a number or not. For according to those who held that substances are numbers, and according to the philosophers of nature, who denied that numbers are substances, some numerical proportions must be found in the substances of things. This is most evident in the case of the opinion of Empedocles, who held that each one of these sensible things is composed of a certain harmony or proportion [of the elements].

244. Again, one number (123).

Here he gives the second argument which runs thus: one number is produced from many numbers. Therefore, if the Forms are numbers, one Form is produced from many Forms. But this is impossible. For if from many things which differ specifically something specifically one is produced, this comes about by mixture, in which the natures of the things mixed are not preserved; just as a stone is produced from the four elements. Again, from things of this kind which differ specifically one thing is not produced by reason of the Forms, because the Forms themselves are combined in such a way as to constitute a single thing only in accordance with the intelligible structure of individual things, which are altered in such a way that they can be mixed together. And when the Forms themselves of the numbers two and three are combined, they give rise to the number five, so that each number remains and is retained in the number five.

245. But since someone could answer this argument, in support of Plato, by saying that one number does not come from many numbers, but each number is immediately constituted of units, Aristotle is therefore logical in rejecting this answer (124) (“But if one number”).

For if it is said that some greater number, such as ten thousand, is not produced “from them,” namely, from twos or many smaller numbers, but from “units,” i.e., ones, this question will follow: How are the units of which numbers are composed related to each other? For all units must either conform with each other or not.

246. But many absurd conclusions follow from the first alternative, especially for those who claim that the Forms are numbers. For it will follow that different Forms do not differ substantially but only insofar as one Form surpasses another. It also seems absurd that units should differ in no way and yet be many, since difference is a result of multiplicity.

247. But if they do not conform, this can happen in two ways. First, they can lack conformity because the units of one number differ from those of another number, as the units of the number two differ from those of the number three, although the units of one and the same number will conform with each other. Second, they can lack conformity insofar as the units of one and the same number do not conform with each other or with the units of another number. He indicates this distinction when he says, “For neither will they be the same as one another (125),” i.e., the units which comprise the same number, “nor all the others the same as all,” i.e., those which belong to different numbers. Indeed, in whatever way there is held to be lack of conformity between units an absurdity is apparent. For every instance of non-conformity involves some form or attribute, just as we see that bodies which lack conformity differ insofar as they are hot and cold, white and black, or in terms of similar attributes. Now units lack qualities of this kind, because they have no qualities, according to Plato. Hence it will be impossible to hold that there is any non-conformity or difference between them of the kind caused by a quality. Thus it is evident that Plato’s opinions about the Forms and numbers are neither “reasonable” (for example, those proved by an apodictic argument), nor “in accord with our understanding” (for example, those things which are self-evident and verified by [the habit of] intellect alone, as the first principles of demonstration).

248. Further, [if the Forms] (126).

Here he gives the third argument against Plato, which runs thus: all objects of mathematics, which Plato affirmed to be midway between the Forms and sensible substances, are derived unqualifiedly from numbers, either as proper principles, or as first principles. He says this because in one sense numbers seem to be the immediate principles of the other objects of mathematics; for the Platonists said that the number one constitutes the point, the number two the line, the number three surface, and the number four the solid. But in another sense the objects of mathematics seem to be reduced to numbers as first principles and not as proximate ones. For the Platonists said that solids are composed of surfaces, surfaces of lines, lines of points, and points of units, which constitute numbers. But in either way it followed that numbers are the principles of the other objects of mathematics.

249. Therefore, just as the other objects of mathematics constituted an intermediate class between sensible substances and the Forms, in a similar way it was necessary to devise some class of number which is other than the numbers that constitute the Forms and other than those that constitute the substance of sensible things. And arithmetic, which is one of the mathematical sciences, evidently deals with this kind of number as its proper subject, just as geometry deals with mathematical extensions. However, this position seems to be superfluous; for no reason can be given why number should be midway “between the things at hand,” or sensible things, and “those in the ideal world,” or the Forms, since both sensible things and the Forms are numbers.

250. Again, each of the units (127).

Here he gives the fourth argument, which runs thus: those things which exist in the sensible world and those which exist in the realm of mathematical entities are caused by the Forms. Therefore, if some number two is found both in the sensible world and in the realm of the objects of mathematics, each unit of this subsequent two must be caused by a prior two, which is the Form of twoness. But it is “impossible” that unity should be caused by duality. For it would be most necessary to say this if the units of one number were of a different species than those of another number, because then these units would acquire their species from a Form which is prior to the units of that number. And thus the units of a subsequent two would have to be produced from a prior two.

251. Further, why is (128).

Here he gives the fifth argument, which runs thus: many things combine so as to constitute one thing only by reason of some cause, which can be considered to be either extrinsic, as some agent which unites them, or intrinsic, as some unifying bond. Or if some things are united of themselves, one of them must be potential and another actual. However, in the case of units none of these reasons can be said to be the one “why a number,” i.e., the cause by which a number, will be a certain “combination,” ‘ i.e., collection of many units; as if to say, it will be impossible to give any reason for this.

252. And, again, in addition (129).

Here he gives the sixth argument, which runs thus: if numbers are the Forms and substances of things, it will be necessary to say, as has been stated before (245), either that units are different, or that they conform. But if they are different, it follows that unity as unity will not be a principle.

This is clarified by a similar case drawn from the position of the natural philosophers. For some of these thinkers held that the four [elemental] bodies are principles. But even though being a body is common to these elements, these philosophers did not maintain that a common body is a principle, but rather fire, earth, water and air, which are different bodies. Therefore, if units are different, even though all have in common the intelligible constitution of unity, it will not be said that unity itself as such is a principle. This is contrary to the Platonists’ position; for they now say that the unit is the principle of things, just as the natural philosophers say that fire or water or some body with like parts is the principle of things. But if our conclusion against the Platonists’ theory is true-that unity as such is not the principle and substance of things-it will follow that numbers are not the substances of things. For number is held to be the substance of things only insofar as it is constituted of units, which are said to be the substances of things. This is also contrary to the Platonists’ position which is now being examined, i.e., that numbers are Forms.

253. But if you say that all units are undifferentiated, it follows that “the whole,” i.e., the entire universe, is a single entity, since the substance of each thing is the one itself, and this is something common and undifferentiated. Further, it follows that the same entity is the principle of all things. But this is impossible by reason of the notion involved, which is inconceivable in itself, namely, that all things should be one according to the aspect of substance. For this view contains a contradiction, since it claims that the one is the substance of all things, yet maintains that the one is a principle. For one and the same thing is not its own principle, unless, perhaps, it is said that “the one” is used in different senses, so that when the senses of the one are differentiated all things are said to be generically one and not numerically or specifically one.

254. Now when we wish (130).

Here he argues against Plato’s position with reference to his views about mathematical extensions. First (130), he gives Plato’s position; and second (255), he advances an argument against it (“Yet how will”).

He says, first, that the Platonists, wishing to reduce the substances of things to their first principles, when they say that continuous quantities themselves are the substances of sensible things, thought they had discovered the principles of things when they assigned line, surface and solid as the principles of sensible things. But in giving the principles of continuous quantities they said that “lengths,” i.e., lines, are composed of the long and short, because they held that contraries are the principles of all things. And since the line is the first of continuous quantities, they first attributed to it the great and small; for inasmuch as these two are the principles of the line, they are also the principles of other continuous quantities. He says “from the great and small” because the great and small are also placed among the Forms, as has been stated (217). But insofar as they are limited by position, and are thus particularized in the class of continuous quantities, they constitute first the line and then other continuous quantities. And for the same reason they said that surface is composed of the wide and narrow, and body of the deep and shallow.

255. Yet how will a surface (130).

Here he argues against the foregoing position, by means of two arguments. The first is as follows. Things whose principles are different are themselves different. But the principles of continuous quantities mentioned above are different, according to the foregoing position, for the wide and narrow, which are posited as the principles of surface, belong to a different class than the deep and shallow, which are held to be the principles of body. The same thing can be said of the long and short, which differ from each of the above. Therefore, line, surface and body all differ from each other. How then will one be able to say that a surface contains a line, and a body a line and a surface? In confirmation of this argument he introduces a similar case involving number. For the many and few, which are held to be principles of things for a similar reason, belong to a different class than the long and short, the wide and narrow, and the deep and shallow. Therefore number is not contained in these continuous quantities but is essentially separate. Hence, for the same reason, the higher of the above mentioned things will not be contained in the lower; for example, a line will not be contained in a surface or a surface in a body.

256. But because it could be said that certain of the foregoing contraries are the genera of the others, for example, that the long is the genus of the broad, and the broad the genus of the deep, he destroys this [objection] by the following argument: things composed of principles are related to each other in the same way as their principles are. Therefore, if the broad is the genus of the deep, surface will also be the genus of body. Hence a solid will be a kind of plane, i.e., a species of surface. This is clearly false.

257. Further, from what will (132).

Here he gives the second argument, which involves points; and in regard to this Plato seems to have made two errors. First, Plato claimed that a point is the limit of a line, just as a line is the limit of a surface and a surface the limit of a body. Therefore, just as he posited certain principles of, which the latter are composed, so too he should have posited some principle from which points derive their being. But he seems to have omitted this.

258. The second error is this: Plato seems to have held different opinions about points. For sometimes he maintained that the whole science of geometry treats this class of things, namely, points, inasmuch as he held that points are the principles and substance of all continuous quantities. And he not only implied this but even explicitly stated that a point is the principle of a line, defining it in this way. But many times he said that indivisible lines are the principles of lines and other continuous quantities, and that this is the class of things with which geometry deals, namely, indivisible lines. Yet by reason of the fact that he held that all continuous (quantities are composed of indivisible lines, he did not avoid the consequence that continuous quantities are composed of points, and that points are the principles of continuous quantities. For indivisible lines must have some limits, and these can only be points. Hence, by whatever argument indivisible lines are held to be the principles of continuous quantities, by the same argument too the point is held to be the principle of continuous quantity.

LESSON 17

Arguments against the View that the Ideas Are Principles of Being and Knowledge

ARISTOTLE’S TEXT Chapters 9 & 10: 992a 24-993a 27

133. And, in general, even though wisdom investigates the causes of apparent things, we have neglected this study. For we say nothing about the cause from which motion originates. And while we think that we are stating the substance of these sensible things, we introduce other substances. But the way in which we explain how the latter are the substances of the former is empty talk; for to participate, as we have said before (115), signifies nothing. Moreover, that which we see to be the cause in the sciences, that by reason of which all intellect and all nature operates, on that cause which we say is one of the principles the Forms do not touch in any way. But mathematics has been turned into philosophy by present-day thinkers (566), although they say that mathematics must be treated for the sake of other things.

134. Further, one might suppose that the underlying substance [which they consider] as matter is too mathematical, and that it is rather a predicate and difference of substance and matter, like the great and small; just as the philosophers of nature speak of the rare and dense (56), which they say are the primary differences of the underlying subject; for “ these are a kind of excess and defect.

135. And with regard to motion, if these entities [the great and small] are motion, evidently the Forms are moved; but if they are not, from what does motion come? For [if it has no cause], the whole study of nature is destroyed.

136. And what seems easy to show is that all things are not one; for from their position all things do not become one. But if someone should assert that all things are some one thing, not even this is true unless one grants that the universal is a class; and in certain other cases this is impossible.

137. For they do not have any theory about the lengths, widths, and solids which come after the numbers: either as to how they now exist or will exist, or what importance they have. For it is impossible that they should be Forms (since they are not numbers), or intermediate things (for those are the objects of mathematics), or corruptible things; but, on the contrary, it seems that they form a fourth class.

138. And, in general, to look for the elements of existing things without distinguishing the different senses in which things are said to be, makes it impossible to discover them. And [their view is unsatisfactory] in another way, i.e., in the way in which they seek for the elements of which things are composed. For it is impossible to understand of what things action or passion or straightness is composed. But if this is possible only in the case of substances, then to look for the elements of all existing things, or to think that we have found them, is a mistake.

139. But how will one acquire knowledge of the elements of all things? For it is clearly impossible to have prior knowledge of anything. For just as one acquiring knowledge of geometry must have a prior knowledge of other things, but not of the things which this science [investigates], and which he is to learn, so it is in the case of the other sciences. Hence, if there is a science of all things (and there must be a science of these), as some say, the one learning this science does not have any prior knowledge of it. But all learning proceeds from things previously known, either all or some of them, whether the learning be by demonstration or by definitions. For [the parts] of which definitions are composed must already be known beforehand and be evident. The same thing is true in the case of things discovered by induction.

140. But if this science were connatural, it is a wonder how we could be unconscious of having the most important of the sciences.

141. Again, how is anyone to know the elements of which things are composed, and how is this to be made evident? For this also presents a difficulty; because one might argue in the same way as one does about certain syllables. For some say that sma is made up of s, m and a, whereas others say that it is a totally different sound and not any of those which are known to us.

142. Again, how could one know the things of which a sense is cognizant without having that sense? Yet this will be necessary if they [i.e., sensible things] are the elements of which all things are composed, just as spoken words are composed of their proper elements.

Chapter 10

143. From the foregoing, then, it is evident that all [the early philosophers] seem to seek the causes mentioned in the Physics, and that we cannot state any other in addition to these. But they understood these obscurely; and while in one sense all causes have been mentioned before, in another sense they have not been mentioned at all. Indeed, the earliest philosophy seems to speak in a faltering way about all subjects inasmuch as it was new as regards principles and the first of its kind. For even Empedocles says that ratios are present in bone, and that this is the quiddity or substance of a thing. But [if this is true], there must likewise be a ratio of flesh and of every other thing or of nothing. For it is because of this that flesh and bone and every other thing exists, and not because of their matter, which he says is fire, earth, air and water. But if someone else had said this, he would have been forced to agree to the same thing. But he has not said this. Such things as these, then, have been explained before. So let us return again to whatever problems one might raise about the same subject; for perhaps in the light of these we shall be able to make some investigation into subsequent problems.

COMMENTARY

259. Here Aristotle destroys Plato’s opinion about the principles of things. First, he destroys Plato’s opinion about principles of being; and second (268), his opinion about principles of knowledge (“But how will one”).

In regard to the first part he gives six arguments. The first is based on the fact that Plato neglected to deal with the classes of causes. Thus he says that, “in general, wisdom,” or philosophy, has as its aim to investigate the causes “of apparent things,” i.e., things apparent to the senses. For men began to philosophize because they sought for the causes of things, as was stated in the prologue (53). But the Platonists, among whom he includes himself, neglected the principles of things, because they said nothing about the efficient cause, which is the source of change. And by positing the Ideas they thought they had given the formal cause of things. But while they thought that they were speaking of the substance of these things, i.e., sensible ones, they posited the existence of certain other separate substances which differ from these. However, the way in which they assigned these separate substances as the substances of sensible things “is empty talk,” i.e., it proves nothing and is not true. For they said that the Forms are the substances of sensible things inasmuch as they are participated in by sensible things. But what they said about participation is meaningless, as is clear from what was said above (225). Furthermore, the Forms which they posited have no connection with the final cause, although we see that this is a cause in certain sciences which demonstrate by means of the final cause, and that it is by reason of this cause that every intellectual agent and every natural one operates, as has been shown in the Physics, Book II. And just as they do not touch on that cause which is called an end [or goal], when they postulate the existence of the Forms (169), neither do they treat of that cause which is called the source of motion, namely, the efficient cause, which is the opposite, so to speak, of the final cause. But the Platonists by omitting causes of this kind (since they did omit a starting-point and end of motion), have dealt with natural things as if they were objects of mathematics, which lack motion. Hence they said that the objects of mathematics should be studied not only for themselves but for the sake of other things, i.e., natural bodies; inasmuch as they attributed the properties of the objects of mathematics to sensible bodies.

260. Further, one might (134).

Here he gives the second argument, which runs thus: that which is posited as the matter of a thing is the substance of a thing, and is predicable of a thing to a greater degree than something which exists apart from it. But a Form exists apart from sensible things. Therefore, according to the opinion of the Platonists, one might suppose that the underlying substance as matter is the substance of the objects of mathematics rather than a separate Form. Furthermore, he admits that it is predicated of a sensible thing rather than the above Form. For the Platonists held that the great and small is a difference of substance or matter; for they referred these two principles to matter, just as the philosophers of nature (115) held that rarity and density are the primary differences of the “underlying subject,” or matter, by which matter is changed, and spoke of them in a sense as the great and small. This is clear from the fact that rarity and density are a kind of excess and defect. For the dense is what contains a great deal of matter under the same dimensions, and the rare is what contains very little matter. Yet the Platonists said that the Forms are the substance of sensible things rather than the objects of mathematics, and that they are predicable of them to a greater degree.

261. And with regard (135).

Here he gives the third argument, which runs thus: if those attributes which exist in sensible things are caused by separate Forms, it is necessary to say either that there is an Idea of “motion” among the Forms or there is not. If there is a Form or Idea of motion among the Forms, and there cannot be motion without something that is moved, it also follows that the Forms must be moved. But this is opposed to the Platonists’ opinion, for they claimed that the Forms are immobile. On the other hand, if there is no Idea of motion, and these attributes which exist in sensible things are caused by the Ideas, it will be impossible to assign a cause for the motion which occurs in sensible things; and thus the entire investigation of natural philosophy, which studies mobile things, will be destroyed.

262. And what seems easy (136).

Then he gives the fourth argument, which runs thus: if unity were the substance of all things, as the Platonists assumed, it would be necessary to say that all things are one, just as the philosophers of nature also did in claiming that the substance of all things is water, and so on for the other elements. But it is easy to show that all things are not one. Hence the position that unity is the substance of all things is not held in high repute.

263. But let us assume that someone might say that it does not follow, from Plato’s position, that all things are one in an unqualified sense but in a qualified sense, just as we say that some things are one generically or specifically. And if someone wished to say that all things are one in this way, even this could be held only if what I call the one were a genus or universal predicate of all things. For then we could say that all things are one specifically, just as we say that both a man and an ass are animal substantially. But in certain cases it seems impossible that there should be one class of all things, because the difference dividing this class would necessarily not be one, as will be said in Book III (432). Therefore, in no way can it be held that the substance of all things is one.

264. For they do not have (137).

Here he gives the fifth argument, which runs thus: Plato placed lengths, widths and solids after numbers as the substances of sensible things, i.e., that of which they are composed. But according to Plato’s position there seems to be no reason why they should be held to exist either now or in the future. Nor does this notion seem to have any efficacy to establish them as the causes of sensible things. For things which exist “now” must mean immobile things (because these always exist in the same way), whereas things which “will exist” must mean those which are capable of generation and corruption, which acquire being after non-being. This becomes clear thus: Plato posited three classes of things—sensible things, the Forms and the objects of mathematics, which are an intermediate class. But such lines and surfaces as those of which sensible bodies are composed cannot be Forms; for the Forms are essentially numbers, whereas such things [i.e., the lines and surfaces composing bodies] come after numbers. Nor can such lines and surfaces be said to be an intermediate class between the Forms and sensible things; for the things in this intermediate class are the objects of mathematics, and exist apart from sensible things; but this cannot be said of the lines and surfaces of which sensible bodies are composed. Nor again can such lines and surfaces be sensible things; for the latter are corruptible, whereas these lines and surfaces are incorruptible, as will be proved below in Book III (466). Therefore these things are either nothing at all or they constitute a fourth class of things, which Plato omitted.

265. And, in general (138).

Here he gives the sixth argument, which runs thus: it is impossible to discover the principles of anything that is spoken of in many senses, unless these many senses are distinguished. Now those things which agree in name only and differ in their intelligible structure cannot have common principles; otherwise they would have the same intelligible structure, since the intelligible structure of a thing is derived from its own principles. But it is impossible to assign distinct principles for those things which have only the name in common, unless it be those whose principles must be indicated to differ from each other. Therefore, since being is predicated both of substance and the other genera in different senses and not in the same sense, Plato assigned inadequate principles for things by failing to distinguish beings from each other.

266. But since someone could assign principles to things which differ in their intelligible structure and have a common name, by adjusting proper principles to each without distinguishing the many senses of the common name, and since the Platonists have not done this, then “in another way,” i.e., by another argument, they assigned inadequate principles to things when they looked for the elements of which things are made, i.e., in the way in which they sought for them, inasmuch as they did not assign principles which are sufficient for all things. For from their statements it is impossible to understand the principles of which either action and passion, curvature and straightness, or other such accidents, are composed. For they only indicated the principles of substances and neglected accidents.

267. But if in defense of Plato someone wished to say that it is possible for the elements of all things to have been acquired or discovered at the moment when the principles of substances alone happen to have been acquired or discovered, this opinion would not be true. For even if the principles of substances are also in a sense the principles of accidents, nevertheless accidents have their own principles. Nor are the principles of all genera the same in all respects, as will be shown below in Book XI (2173) and Book XII (2455) of this work.

268. But how will one (139).

Here he argues dialectically against Plato’s position that the Ideas are the principles of our scientific knowledge. He gives four arguments, of which the first is this: if our scientific knowledge is caused by the Ideas themselves, it is impossible for us to acquire knowledge of the principles of things. But it is evident that we do acquire knowledge. Therefore our knowledge is not caused by the Ideas themselves. That it would be impossible to acquire knowledge of anything, he proves thus: no one has any prior knowledge of that object of which he ought to acquire knowledge; for example, even though in the case of geometry one has prior knowledge of other things which are necessary for demonstration, nevertheless the objects of which he ought to acquire knowledge he must not know beforehand. The same thing is also true in the case of the other sciences. But if the Ideas are the cause of our knowledge, men must have knowledge of all things, because the Ideas are the intelligible structures of all knowable things. Therefore we cannot acquire knowledge of anything) unless one might be said to acquire knowledge of something, which he already knew. if it is held, then, that someone acquires knowledge, he must not have any prior knowledge of the thing which he comes to know, but only of certain other things through which he becomes instructed; i.e., one acquires knowledge through things previously known, [either] “all,” i.e., universals, “or some of them,” i.e.,:singular things. One learns through universals in the case of those things which are discovered by demonstration and definition, for in the case of demonstrations and definitions the things of which definitions or universals are composed must be known first. And in the case of things which are discovered by induction singular things must be known first.

269. But if this, science (140).

Here he gives the second argument, which runs thus: if the Ideas are the cause of our knowledge, it must be connatural to us; for men grasp sensible things through this proper nature, because sensible things participate in Ideas according to the Platonists. But the most important knowledge or science is one that is connatural to us and which we cannot forget, as is evident of our knowledge of the first principles of demonstration, of which no one is ignorant. Hence there is no way in which we can forget the knowledge of all things caused in us by the Ideas. But this is contrary to the Platonists’ opinion, who said that the soul as a result of its union with the body forgets the knowledge which it has of all things by nature, and that by teaching a man acquires knowledge of something that he previously knew, as though the process of acquiring knowledge were merely one of remembering.

270. Again, how is anyone (141).

Here he gives the third argument, which runs thus: in order to know things a man must acquire knowledge not only of the forms of things but also of the material principles of which they are composed. This is evident from the fact that occasionally questions arise regarding these; for example, with regard to this syllable sma, some raise the question whether it is composed of the three letters s, m and a, or whether it is one letter which is distinct from these and has its own sound. But only the formal principles of things can be known through the Ideas, because the Ideas are the forms of things. Hence the Ideas are not a sufficient cause of our knowledge of things when material principles remain unknown.

271. Again, how could (142).

Here he gives the fourth argument, which runs thus: in order to know reality we must know sensible things, because sensible things are the apparent material element of which all things are composed, just as complex sounds (such as syllables and words) are composed of their proper elements. If, then, knowledge is caused in us by the Ideas, our knowledge of sensible things must be caused by the Ideas. But the knowledge which is caused in us by the Ideas is grasped without the senses, because we have no connection with the Ideas through the senses. Therefore in the act of perception it follows that anyone who does not have a sense can apprehend the object of that sense. This is clearly false; for a man born blind cannot have any knowledge of colors.

272. From the foregoing (143).

Here he summarizes the statements made by the ancient philosophers. He says that from what has been said above it is evident that the ancient philosophers attempted to investigate the cause which he [Aristotle] dealt with in the Physics, and that in their statements we find no cause in addition to those established in that work. However, these men discussed these causes obscurely; and while in a sense they have mentioned all of these causes, in another sense they have not mentioned any of them. For just as young children at first speak imperfectly and in a stammering way, in a similar fashion this philosophy, since it was new, seems to speak imperfectly and in a stammering way about the principles of all things. This is borne out by the fact that Empedocles was the first to say that bones have a certain ratio, or proportional mixture [of the elements], and that this is a thing’s quiddity or substance. But the same thing must also be true of flesh and of every other single thing or of none of them, for all of these things are mixtures of the elements. And for this reason it is evident that flesh and bone and all things of this kind are not what they are because of their matter, which he identified with the four elements, but because of this principle-their form. However, Empedocles, compelled as it were by the need for truth, would have maintained this view if it had been expressed more clearly by someone else, but he did not express it clearly. And just as the ancient philosophers have not clearly expressed the nature of form, neither have they clearly expressed the nature of matter, as was said above about Anaxagoras (90). Nor have they clearly expressed the nature of any other principles. Therefore, concerning such thing, as have been stated imperfectly, we have spoken of this before (190). And with regard to these matters we will restate again in Book III (423) whatever difficulties can be raised on both sides of the question. For perhaps from such difficulties we will discover some useful information for dealing with the problems which must be examined and solved later on throughout this whole science.