Lecture 4 — Empedocles, Plato, and soul as self-moving number

All who have considered the soul as knowing and sensing things that exist identify it with the principles, some making it several, others one.

Empedocles, for instance, says that it is composed of all elements, and that each of these is a soul, saying:

As by earth we know earth, by ether, ether, / By water, water, but by fire, it is clear, fire / Concord by concord, discord by sad discord.

In the same way, Plato in the Timaeus constitutes the soul from the elements. For like is known by like, and things are made up of their principles.

In the things said about philosophy, he likewise determined that an animal itself is compounded of the very idea of the one, together with the primary length and depth and breadth, other things existing in the same manner.

Again, rather differently, he says that intellect is the one, knowledge is the two (for this proceeds as one to one), and the number of the plane is opinion, and that of the solid is sensation. For numbers were said to be the species and principles of beings and are themselves constituted from elements. Some things are discerned by understanding, some by science, some by opinion, some by sensation. But these same numbers are the species of things.

But since the soul seems to be both a moving and a knowing principle, some have joined the two aspects, stating that the soul is a self-moving number.

43. All who have considered the soul (404b8). Having shown how some have approached a knowledge of soul through movement, the Philosopher now turns to how some came to it by way of sensation or knowledge. He does this in two stages.

First, he shows where the philosophers who considered the soul by way of sensation were in agreement;

second, at Empedocles, for instance (404b11; [45]), where they disagreed.

He begins then by saying that all who came to knowledge of the soul through its knowing and sensing, that is, through knowledge and sensation, agreed in holding that the soul was composed of the principles of things; but some made, that is, posited, several principles, while others posited only one.

Even the earliest philosophers themselves were moved to constitute the soul from the principles, as though compelled by the truth itself; they dreamed, as it were, of the truth. The truth, in fact, is that knowledge arises from a likeness of the thing known being in the knower; for the reality known must be in the knower somehow.

The early philosophers, however, thought that the likeness of the thing known exists in the knower according to its own natural existence, and according to the existence that it has in its very self. For they said that like must be known by like. If, then, the soul is to know all things, it must contain a likeness of all things according to their natural existence, as they asserted. For they did not think to distinguish the mode whereby a thing exists in the intellect or the eye from that which the thing has in its very self. Therefore, since whatever is of a thing’s essence is a constituent principle of that thing, and to know such principles is to know the thing itself, these philosophers maintained that the reason why the soul can know all things is that it is made up of the principles of all things. This theory was common to them all.

44. But they diverged insofar as they disagreed about the principles that they posited. For they did not all admit the same principles: one admitted many, another only one, and one this, and another that. Hence they disagreed also about the constituents of the soul.

45. So, at Empedocles, for instance (404b11), Aristotle states these differences.

He gives first the opinion of Empedocles, saying that the early philosophers who contemplated the soul by way of sensation thought it was composed of the elements. Those who admitted only one principle said that this one thing is the soul; and those who admitted many said that the soul is made up of many; Empedocles, for instance, held that the soul was composed of all the elements, and that each of these is a soul. Note that Empedocles admitted six principles: four material, namely, earth, water, fire, and air; and two active and passive principles, namely, strife and friendship. And since he asserted that the soul is composed of principles, he said the soul and the senses are composed of such principles as he posits. Thus, as composed of earth, we know earth; as composed of ether (that is, of air), we know air; as composed of water, we know water; but as composed of fire, it is clear, we know fire; and through concord, we know concord, and from sad discord, we know discord. Sad comes in here because Empedocles wrote his books in verse.

46. Next, when he says, in the same way Plato (404b16), Aristotle states the opinion of Plato, who also, he says, constitutes the soul from the elements, that is, says the soul is made up of the principles. And that this is true, that is, that Plato says the soul is composed of the principles of things, he shows from three statements of Plato.

The first is from the Timaeus, where Plato says that there are two elements or principles of things: the same and the other. (Plato (ca. 427–348 BC), Timaeus, 35a.) For there is a certain nature that is simple and always remains the same, as are immaterial things; and this nature, he calls “the same.” And there is another nature that does not always remain the same but undergoes change and division, as do material things; and this nature, he calls “the other.” And it is of these two principles, of the same and the other, that the soul, he says, is composed; not that the two are in the soul as its parts, but rather, as it is a mean, insofar as the nature of the rational soul is lower and less noble than the higher and purely immaterial substances, but it is higher and nobler than material and lower things.

47. Now, this opinion rests on what was already mentioned, that like is known by like. For if the soul would know all things, and if the same and the other are the principles, he asserted that the soul must be constituted of these two in the way said, such that to the degree that it has the nature of sameness, it knew things that it asserts are the same, while to the degree that it has the nature of things that he calls “the other,” it knows the other, that is, material things. Hence also it uses this knowledge. For when it gathers things together under genera and species, then, said Plato, it manifests sameness or identity, but when it attends to accidents and differentiations, he finds in it difference. That is how Plato, in the Timaeus, understood the soul as made up of principles.

48. The second statement showing that this was Plato’s theory, Aristotle refers to when he says, in the things said about philosophy (404b18). Here the soul is represented as constituted from principles in the same way. Note, in this connection, that Plato took the objects known by the intellect to be things subsisting through themselves and separate, and that they were always in act, and that they were the cause of knowledge and of being for sensible things. (Aristotle, wanting to avoid this, as it was incongruous, was compelled to assert an agent intellect.) But from Plato’s position it followed that insofar as some things are abstract, so too, there are certain things that would be subsisting through themselves and actually. We have, however, abstractions in two ways: one is by proceeding from particulars to universals; and the other is that by which mathematical things are abstracted from sensible things. So Plato found himself obliged to posit three subsistent things: sensible things, mathematical things, and universals—these last being the cause, by participation, both of sensible realities and of mathematical ones.

49. Plato also held that numbers were causes of things—and he did this because he did not know to distinguish the one that is convertible with being and the one that is the principle of the number insofar as it is a species of quantity. Hence, he asserted that such universals were of the nature of number, for the separated universal is the cause of things, and numbers are the substance of things. For he said that the principles of all beings were species and specific number, which he called specific in the sense of being constituted from species. (Themistius, In De anima, f. 4rb15–16.) For he traced number itself back to unity and duality as to its principles and elements; for, as nothing can proceed from one alone, there must be some nature underlying the one itself, due to which multiplicity proceeds; and this nature he called “duality.”

50. Thus Plato ordered those three according to their order of materiality. As sensible things are more material than mathematical things are, and universals are more immaterial than mathematical things are, he placed sensible things first, and above them mathematicals, and above these the separate universals and ideas. Universals differ from mathematical objects in that the latter include numerical differences within the same species, whereas ideas and separated substances exhibit no numerical differences in the one species; there is but one idea for each species. These ideas, he said, are composed of numbers and are the accounts of sensible things according to the numbers within them, which accounts are composed of length, breadth and depth. (Themistius, In De anima, f. 4ra.) Hence, he said that the idea of length is the primary duality, for length is from unit to unit, that is, from point to point; and that of breadth is the first trinity, for the triangle is the first of plane figures; and that of depth, which includes both length and breadth, is the first quaternity, for the first solid figure is the pyramid which is constructed of four angles. So too, since Plato posited a sensitive soul, he also posited a separated soul as its cause, and this, like the other separate things and ideas, he said is composed from numbers, that is, from the unity and duality that he asserted are the principles of things.

51. Third, at again, rather differently (404b21), Aristotle alludes to the third statement of Plato to show that, for Plato, the soul was made up of the principles. For as we have said, it was Plato’s view that the species and principles of things are numbers; so when he came to treat of the soul, he based its knowledge of beings on its being composed of the principles (that is, of numbers), and all its activities come from them.

Take, for instance, the soul’s diverse powers for apprehending beings: understanding, science, opinion, and sensation. Plato says, then, that the soul has an intellect and its activity due to the idea of the one; (Themistius, In De anima, f. 4rb5.) for it has the nature of unity, for by one apprehension the intellect apprehends one thing. Again, science comes from the first duality since science proceeds from one thing to one thing, that is, from principles to conclusions. And opinion from the first trinity, for opinion goes from one thing to two, that is, from principles to a conclusion accompanied by the fear of a different conclusion, so a triad is formed out of one principle and one conclusion admitted and one feared. Finally, sensation derives from the first quaternity, that is, from the first idea of a body, constructed (as we have said) from four angles; for bodies are the object of sensation.

Since, then, all things are known by these four, that is, understanding, science, opinion, and sensation, all of which powers, said Plato, are in the soul insofar as it participates in the nature of unity, duality, trinity, and quaternity, it obviously follows that the separated soul, which he called the idea of this particular soul, was constituted from numbers, which are the elements and principles of things. So much to show that Plato regarded the soul as made up of principles.

52. Next, at but since the soul seems to be both (404b27), Aristotle observes that some philosophers came to know something about the soul through movement and sensation (that is, knowledge) together. He says that, as the soul seemed to them to be both self-moving and cognitive, some have joined the two aspects, that is, motion and knowledge, in their definition and called the soul a self-moving number. “Number” refers to the cognitive power because they thought, in accordance with what has been said already, that the soul was able to know realities in virtue of its participating in the nature of a specific number (which was Plato’s opinion). “Self-moving” refers to the soul’s motive power.