LECTIO SEVEN

             § 87. Having argued in a general way against the view that movement pertains essentially to the soul, the Philosopher now brings forward arguments against particular philosophers whose theories of the movement of the soul seem to give rise to some special difficulty. These arguments fall into three groups. First, he opposes an opinion of Democritus; then, at 'In the same way', one of Plato; and thirdly, at 'There is another opinion', another theory.

             He begins, then, by stating the view of Democritus on the soul's movement; and then brings objections against it.

             § 88. This theory has already been referred to by Aristotle in his fourth objection to the view that the soul moves in itself and by this movement makes the body move. If the soul moves the body, he has said, it must do so in virtue of its own movement. This was admitted by those who said that each soul moved its own body in a manner corresponding to the movement in itself; among whom was Democritus who made use of the following illustration. There was a certain comic dramatist called Philip who tells somewhere of one Daedalus, that he made a wooden statue of the goddess Venus, and that this statue, being filled with quicksilver, was able to move. It moved as the quicksilver moved. And what Democritus said of the soul's movement was rather similar. The soul, he said, (as has been noted above) was composed of indivisible spheres or atoms which, being round in shape, were always moving about, and by their incessant movement made the whole body cohere and move accordingly.

             § 89. Then, at 'Now, what we, etc.', Aristotle puts two objections to this. First, it is agreed that in animals the soul is the cause of resting as well as the cause of movement. But according to Democritus the soul is never the cause of rest, though it is the cause of animal movements. For he could hardly maintain that those spherical atoms ever rested if they never cease to move.

             § 90. Again, at 'The soul seems', he puts a second objection. The movement caused by quicksilver in the statue is obviously not spontaneous; it is a compelled movement. On the contrary, that of the soul is spontaneous, proceeding from mind and will. Hence the view of Democritus seems worthless.

             § 91. Then at 'In the same way' he first states the opinion of Plato, which, at 'Now in the first place,' he will reject. But before explaining what Plato said about the soul he shows its similarity to the theory of Democritus. As Democritus had supposed that the soul's movements moved the body to which it was joined, so also did Timaeus, a speaker introduced by Plato. For he said that soul moves body in so far as soul itself moves; because the two are, as it were, bound up together.

             § 92. With 'Being compounded, etc.', Aristotle makes Plato's view explicit; first as to what constitutes the essence of the soul, and then, at 'God bent, etc.', as to how movement proceeds from it. Regarding the former question, note that the words quoted here are used by Plato in the Timaeus and refer to the Soul of the world which, according to him, is imitated by inferior souls. So when he touches, as here, on the nature of the World-Soul, he refers also, in a way, to any soul. Now Plato, for the reason already given, maintained that the essence of all things was numerical; and that in number the formal element, so to say, was one and the material element two--all numbers being made up of one and two. And as odd numbers retain something of the indivision of one, he laid down two elements of number, the even and the odd, attributing to the odd identity and finitude, but to the even difference and infinity.

             § 93. Some explanation of this theory may be found in the Physics, Book III. If odd numbers are added to unity in sequence the same type of number always results; e.g. if 3, the first odd number, is added to 1, you get the square number 4; if to 4 you add the second odd number, 5, you get 9, which is also a square number; and so on to infinity. But with even numbers the result is always a different type of number. Add 2, the first even number, to 1, the result is the 'triangular' number 3; to which if you add 4, the second even number, you get 7 which is 'septangular'; and so on to infinity. Hence Plato made Identity and Difference the first elements of all things, attributing the former to odd numbers, the latter to even.

             § 94. And because he placed the soul mid-way between the higher substances, which never change, and corporeal substances, which change and move, he thought that the soul was constituted of the elements of Identity and Difference, and so of odd and even numbers. For the mean must participate in both extremes. This is why Aristotle says that Plato held the soul to be constituted by these elements.

             § 95. Again, we should note that in numbers there are different proportions and infinities, of which some are harmonic, i.e. the cause of harmony. The double proportion causes the harmony called a whole octave; that of 3 to 2 causes the harmony called a fifth; (that of 4 to 3 causes the harmony called a fourth); that of 9 to 8 causes a tone; and the other harmonies are caused by other proportions: for example, the harmony composed of an octave and a fifth is caused by the triple proportion; that of the double octave is caused by the quadruple proportion which was discovered by Pythagoras, as Boethius relates, from the striking of four hammers which sounded in harmony according to the aforesaid proportions. Thus if one hammer weighed twelve ounces, one nine, one eight and one six, the one that weighed twelve ounces would be in the proportion of two to one to the one weighing six, and the two together would render the harmony of the octave. Again, the one weighing twelve ounces would be as three to two to the one that weighed eight, and the harmony produced would be that of a fifth; similarly in the case of those that weighed nine ounces and six ounces. Again, the one weighing twelve ounces is in the proportion of from four to three to the one weighing nine, and makes with it the harmony of a fourth; so also does the one that weighs eight with that weighing six; while the one weighing nine is proportioned to the one that weighs eight, and produces with it the harmony called a tone.

             § 96. But if Plato reduced everything to numbers, these were not harmonic numbers, except in the case of the soul. Hence Aristotle gives it as Plato's view that the soul was 'divided' or, as it were, weighed out, 'according to harmonic numbers', i.e. to numbers related to each other in musical proportions. He said that the soul was constituted of the numbers 1, 2, 3, 4, 8, 9 and 27; in which these harmonic proportions are found.

             § 97. And he had two reasons for thinking this. One was the fact that similarity and connaturality are always a cause of pleasure. We find the soul taking pleasure in all harmonies and disliking whatever is unharmonious in sounds and colours and indeed in any sensible quality. So harmony seems to be natural to the soul. This is what he means by saying that the soul has 'a connatural sense (i.e. knowledge) of harmony'.

             § 98. The second reason is that the Pythagoreans and Platonists thought that beautifully harmonious sounds resulted from the movements of the heavenly bodies; and since they supposed these movements to be caused by the World-Soul they naturally concluded that the soul was made up of harmonic numbers. Hence Aristotle says 'that the whole (i.e. Universe) be borne along with well-attuned motions'.

             § 99. Next, when he says 'God bent, etc.', Aristotle explains how the World-Soul is the cause of heavenly movements. Taking all numbers in their natural order, we must think of them as laid in a straight line, each one adding to the preceding one. Now the natural numerical series can give rise to several other series; for example, one might take the geometrical series whose common ratios are 2 or 3 or 4, and so on for other ratios. As then man, by thought, can manipulate numbers, so does God in building up the substances of things from numbers. In constructing the soul's substance out of the aforesaid numbers, namely all those placed in a straight line series according to their natural order, he divides them into two series: one, the geometrical series whose common ratio is 2; the other, the geometrical series whose common ratio is 3; because these two embrace all the harmonic proportions. For the double proportion is divided into the ratios 3:2 and 4:3; the triple into 2:1 and 3:2. Therefore the above-mentioned numbers are taken, in the geometrical series with common ratio 2, up to the first cube number, e.g. 1, 2, 4 up to 8; so also with the series with common ratio 3, e.g., 1, 3, 9, 27. These two series meet at unity like two straight lines containing an angle.

             § 100. Moreover, if the numbers in the series whose common ratio is three are joined to unity we get as a result the numbers of the series whose common ratio is 2; e.g. if to 1 is added 3 the result is 4. Conversely, if to 1 is added 2 the result is 3. Thus it is as if two lines were drawn intersecting each other like the Greek letter X.

             § 101. If we proceed further we return to the same numbers. For from 4 we go on to 8 and from 3 to 27; both series concluding with the same type of number, as though we were going round in a circle.

             § 102. We must realise that for Plato the more complex things found in nature are composed of simpler natures, just as the harmonies of sounds arise from the proportions between numbers. He put the essence of the soul mid-way between numbers, which are eminently abstract, and sensible substances; and so deduced the soul's properties from the said numbers. Thus in the soul we find, first, a direct knowing, in that it looks directly at its object; and then the circular return by which the intellect reflects upon itself. So too the intellectual soul moves in a sort of circle with respect to the even and the odd in knowing things both like and unlike itself And this principle is extended to the substance of the visible heavens moved by the World-Soul.

             § 103. For in the heavens we find two circular movements. One is simple and uniform by which the heavens move or revolve daily from east to west according to the equinoctial circle. The other is that of the planets, which is from west to east according to the circle of the zodiac, intersecting the equinoctial circle at the two points of solstice, i.e. at the beginning of Cancer and of Capricorn.

             § 104. And since the former motion is uniform, it is not divided into several motions; and in this it resembles the circle of the odd numbers; which is also why it is the greatest circle; for the odd numbers referred to are greater than the even.

             § 105. The second motion, however, is very much diversified, and seems therefore to answer to the circle of even numbers. It divides into seven circles according to the intervals between the numbers in the two series of multiples of 2 and of 3, as is said in the Timaeus. Where there are six points of division there must be seven parts divided off. Hence these circles are smaller and are contained by the highest circle which is that of the odd numbers. So the text is to be interpreted thus: 'As the whole', i.e. the Universe, is 'borne along with well-attuned motions', that is to say, as the harmonised movements of the heavens are due to the harmony of the World-Soul, God 'bent the straight line into a circle' in the manner described, according to the properties of number and of the soul; and dividing this one circle--one by the unity of the natural series of numbers, or by that of the intellectual power of the soul--into two, he forms the pair of numerical circles, the odd and the even, and the pair of circles in the soul, the understanding of moving and of motionless objects, and the pair of heavenly circles, the equinoctial and zodiacal motions.

             § 106. He adds, however, 'adjusted at two points', because any two intersecting circles touch each other at two points. And 'again one', i.e. the inferior one, 'he divided into seven circles', as if of the planets, 'as though the heavenly motions were the soul's motions', i.e. as if the heavens moved by the movement of the World-Soul.

407a 3-407b 25

SOUL AS A SPATIAL MAGNITUDE

CRITIQUE OF PLATO

             NOW IN THE FIRST PLACE IT IS NOT CORRECT TO say that the soul is a magnitude. For that of the Whole he (Plato) regards as of the same nature as what is sometimes called mind, not as the sensitive or the appetitive soul; for the movement of these is not circular. Now mind is one and continuous, as is the act of understanding, which in turn consists of thoughts. But these have unity by succession, like number, not like extension. Therefore neither is mind thus continuous; but it is either indivisible, or not continuous in the way that anything extended is.§§ 107-11

             How would it understand, if it were an extended quantity? As a whole, or by each of its parts? If by its parts, then by an extended part or by a point, if one may call a point a part. If by a point (of which there is an infinite number) it is evident that it will never complete the process. If by an extended part, it will understand the same thing many times over, even to infinity. Yet it seems to do so once for all. But if it is sufficient that it make contact with any one of its parts, why should it move in a circle or have any magnitude at all? But if it is necessary that it understand by contact with the whole of its circumference, what is the contact it makes by its parts?§§ 112-16

             Again, how can the divisible be understood by the  indivisible, or the indivisible by the divisible?§ 117

             It is necessary that intellect be this circle; for as the movement of the intellect is to understand, and that of the circle is to revolve, if, then, understanding is a revolving, the intellect must be a circle whose revolving is thinking. But then it will always think something--since revolving goes on for ever. Practical thoughts, however, have limits, each being for the sake of something else; while speculative thinking likewise is limited by ideas and every idea is either a definition or a demonstration. But demonstrations begin from principles, and have as their term a conclusion or an inference. Even if they do not reach a conclusion, they do not come round again to their starting-point; they always take a new middle term and conclusion, and proceed straight forward. But revolving returns again to the beginning. Definitions too are all finite.§§ 118-21

             Further, if the same revolving occurs many times over, there will be a multiple understanding of the same thing.§§ 122-4

             Moreover, intelligence is better compared with stillness and rest than with motion,--and the same holds of logical deduction.§§ 125-6

             Again, that will not be content which is not at ease but in a state of strain. But if movement is not of the essence of the soul, it will only move unnaturally.§ 127

             It must be burdensome for the soul to be entangled with the body without possibility of release; and indeed this should be shunned if it is better for the mind not to dwell in the body, as is commonly said, and as seems true to many.§ 128

             It is not clear why the Heavens move by circular movement; for the essence of the soul is not the cause of the soul moving in a circle, for such movement is only incidental to soul. Still less is the body the cause, but rather the soul a cause for the body. Nor is this alleged as for the best; yet the reason why God made the soul revolve must have been because it is more worthy for it to move than to remain stationary, and to move in this way rather than in any other. But this speculation is better suited to other contexts, so let us now dismiss it.§ 129

             Another absurdity arises in this argument and in many others dealing with the soul. They conjoin body and soul, placing the soul in the body without stating anything definite as to the cause of this, or how the body is disposed. Yet this explanation is surely necessary, for it is in virtue of something in common that one is an agent, the other acted upon, one moves and the other is moved. No such correlations are to be found at random. These thinkers only endeavour to state what the soul is, without determining anything about the body which receives it, as if it happened that any soul entered any body, as in the fables of the Pythagoreans. For each body seems to have its own proper form and species. It is like saying that carpentry enters into flutes; for each art must use its tools, and the soul its body.§§ 130-1