LESSON 7

The Views of the Atomists and the Pythagoreans

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. Of these 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, AN from NA in arrangement, 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 particular 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.

COMMENTARY

             112. Here he begins to give the positions of those who held strange and obscure views about the principles of things. First (55:C 112), he gives the position of those who held that there are many principles of things; and second (63:C 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 (57:C 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 (56:C 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 (55), 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 N, 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 (57:C 119), he gives their opinions about the substance of things; and second (59:C 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 (58:C 121) where he says "Moreover, since they considered."

             He says (57) 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 (38:C 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.

             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.

             123. And if anything was lacking in the observable order of things which did not seem to be adapted to numbers, "they called it in," i.e., they invented something new "in order that their whole undertaking might be complete," i.e., in order that their whole undertaking, which was to adapt sensible things to numbers, might be made complete, until they had adapted all sensible things to numbers, as is evident in one example. For the number ten seems to be the perfect number, because it constitutes the first limit and contains within itself the nature of all numbers; for all other numbers are merely a kind of repetition of the number ten. This is why Plato counted up to ten, as Aristotle says in the Physics, Book IV. Hence Pythagoras also said that the spheres which move in the heavens are ten in number, although only nine of these are observable; because we observe seven in the motions of the planets, an eighth in the motion of the fixed stars, and a ninth in the daily motion, which is the first motion. But Pythagoras adds a tenth sphere, which was that of the "counter-earth," i.e., which is moved in the opposite direction to the motion in the lower spheres and therefore produces a contrary sound. For he said that a kind of harmony results from the motion of the celestial bodies, so that just as a harmony is produced from a proportion of contrary sounds, i.e., of low and high notes, in a similar way he claimed that in the heavens there was a single motion in the opposite direction to that of the other motions in order that a harmony might result. According to this position the daily motion belonged to the tenth sphere, which moves from east to west, the other spheres being revolved in the opposite direction from west to east. In fact, according to him, it could have been the ninth sphere which first revolved all the lower spheres in the opposite direction to the first motion. The things that pertain to this opinion of Pythagoras are considered more extensively and more definitely in the last books of this science.