Lecture 5 — Intellectual activities with simple and complex intelligibles

The intellectual grasping of indivisible things is, therefore, about things where there is no falsehood. But in things where there is immediately falsehood and truth, there is also immediately some composition of things understood, as of many brought to a unity.

As Empedocles said, the heads of many grew with no neck, but concord afterwards brought them together. So in the same way, these separate things are combined, like the diagonal and the incommensurate or the diagonal and the commensurate.

If the composition be of things done, or of future events, time also is taken into the reckoning with the composition. For falsity always occurs in a composition, for instance, if one has combined the white and the not-white, or not-white with the white. All these statements can also be divisions. It is not only, then, false or true that Cleon is white, but that he was or will be. But it is the intellect that makes each of these one.

As the indivisible, however, is twofold, either potentially or actually, there is nothing to prevent the understanding of an indivisible when one understands a length.

For it is actually indivisible, and in an indivisible time; for time is divisible and indivisible the way length is. It is not right, then, to say that the intellect understands both by halving both; for there is no half, save potentially, unless it were to be divided.

However, in understanding separately each of the halves, it divides the time also, which is then divided like the length. But if it is as made up of both, then there is something corresponding to each in the time also.

But that which is indivisible not in quantity but in species, the intellect understands in an indivisible time and in an indivisible act of the soul. What is understood is understood accidentally, however, and not insofar as they are divisible and in that time; rather, it understands them insofar as they are indivisible; there is indeed in these things something indivisible. In this way perhaps what makes the time one and the length one is not separable; but this holds of all that is continuous, whether by time or extension.

A point, however, and every division and what is thus indivisible is shown as a privation. A similar account holds in other matters, as how one knows evil or black; for in some way the knowledge is by contrariety. But the knowing power must be in potency, and it must be in it. But if there is something to which there is no contrary, it is self-knowing, and in act, and separate.

Now, every utterance, e.g., an affirmation, something said about something else, is either true or false. Yet not all understanding is thus; understanding that is of what a thing is, according to the what-it-was-to-be is true, and not something belonging to something else; rather, as sight of the proper object is true, but as whether the white thing is a man or not, it is not always true. So it stands with whatever things exist without matter.

Knowledge in act is the same as the thing itself. But what is potential is prior in time in the individual, though universally it is not prior even in time; for all things that are in act come to be from a being in act.

746. The intellectual grasping of indivisible things (430a26). Having come to conclusions about the intellect, the Philosopher now examines its activity; and this is divided into two parts.

In the first, he distinguishes two such activities;

in the second, he reaches conclusions about each of these, at as the indivisible, however, is twofold (430b6; [752]).

First, then, he says that the intellect, by one of its activities, understands indivisible things, for instance, when it understands man or ox, or any such non-composed thing, simply in itself. And this is about things where there is no falsehood, both because non-composed things are neither true nor false, and also because, as we shall see later on, the intellect is not deceived about what a thing is. (Lect. 5, nn. 761–63.)

747. On the other hand, in things where there is falsehood and truth, there is immediately some composition of things understood, that is, of the realities understood, as when many become something one. He gives, as an example, the theory of Empedocles that all things originated by chance, not for the sake of any end, but by merely following the division of things, through strife, and the conjunction of things through friendship. Thus Empedocles said that in the beginning many heads grew with no neck, and similarly, that many other parts of animals grew up in separation from other parts; and he says, “grew,” as though these things sprang from the elements, not from the seed of animals, as grass grows from the earth. (Cf. Aristotle, On the Generation of Animals 1.11, 722b17–20.) Only afterwards did these parts, thus divided, come together in harmony and make up the single animal with its various parts—head, hands, feet, and so on. And where all the parts necessary for the animal’s preservation were present, it was preserved and would beget its own kind, but if any were lacking, it could not be preserved and did not remain through its generation of a like. So then, just as friendship, according to Empedocles, brought together the different parts of animals and formed of them one animal, so too, the intellect is able to combine many non-composed and separate objects and make one intelligible object of them. And such combinations are sometimes true and sometimes false.

748. They are true when they put together what are combined and one in reality, for example, the diagonal and incommensurability (that is, lacking a common measure, for the diagonal of a square is incommensurable with its sides). And they are false when they put together what are not combined in reality, saying, for example, that the diagonal of a square is commensurable with its sides.

749. Therefore, commensurability and the diagonal are sometimes understood separately, and then they are two intelligible objects; but when one combines them, they make one intelligible object, and it is understood by the intellect at once. But since the intellect does not always combine things that are in the present, but sometimes things that were or will be, he adds that if the intellect makes a combination of things done—that is, past—or future events, it must include as well in its composition the past or future time; and in this way its combination will refer to past or future.

750. And he proves this by saying that combinations concerning past or future may be false, but that falsity always occurs in a composition.

As for instance, there is falsehood if the not-white is combined with what is white, as if I were to say, “swans are not white”; or, if white is combined with the not-white, as if I were to say, “crows are white.” And because all that can be affirmed can also be denied, he adds that all these combinations might also have been divisions.

751. For the soul can divide things both according to the present time, and according to the past and future, and it can do this both truly and falsely. Not only, then, is it clear that, since combination and division can be made not only with reference to the present time, but also the past and future, whereas truth and falsehood consist in combination and division, it is necessary that not only are propositions about the present true or false—for example, that Cleon is white—but also propositions about the past or future—for example, that Cleon will be or was white.

However, one should consider that the combination of a proposition is not a work of nature, but a work of reason and understanding; and therefore he adds that what makes each of the intelligible things into one thing, by composing propositions from intelligible things, is the intellect. And since the true and the false exist in combinations, he can say, in Metaphysics 6, that truth and falsehood are not in the realities but in the mind. (Aristotle, Metaphysics 6.4, 1027b25–27; cf. Aquinas, Commentary on Metaphysics, bk. 6, lect. 4, nn. 1230–40.)

752. Next, at as the indivisible, however (430b6), he comes to conclusions on both the aforesaid intellectual activities:

first, on the intellectual grasping of indivisible objects;

second, at now, every utterance (430b26; [760]), on the intellect’s combinations and divisions;

third, he states something common to both, at knowledge in act (431a1; [764]).

The first divides into three parts according to three ways in which one speaks of the “indivisible”—that is to say, the three ways of speaking of unity, the account of which comes from non-division.

First of all, something is said to be one by continuity; hence, a continuum is called “indivisible” because it is not actually divided, though it is potentially divisible. So he says that, since the indivisible is spoken of as twofold, either potentially or actually, there is nothing to prevent the intellect’s understanding of an indivisible when one understands something continuous, like a length, which is actually indivisible, although potentially divisible. And because of this, the intellect understands it in an indivisible time, because it understands it as indivisible.

753. This is against the view of Plato, who posited the understanding as occurring through a certain continuous movement of magnitude. (Bk. 1, lect. 8.) In fact, the intellect can understand a magnitude in two ways: either as potentially divisible—and thus the intellect understands a line by numbering one part after another, and thereby understands it in a period of time; or as actually undivided—and thus it understands it as one thing made up of many parts, and thereby it is understood simultaneously. He adds, therefore, that, in the act of understanding, a time and a length are divided or not divided in the same way.

754. Consequently, it cannot be said that the understanding involves dividing both by half, that is, that half a line is understood in half the given time. For this would not be so unless the line were to be actually divided, but it is divisible only potentially. If each of the line’s halves, however, is understood separately, then the whole is actually divided in the intellect; this is why it divides the time also, the way the length is. But if the line is understood as one thing made up of two parts, it will be understood in an undivided time—but as something that is in both parts of the time, that is, in the instant, and if the intellect’s consideration is prolonged in time, the time will not be divided such that it understands one thing in one part of time and something else in another, but rather the same thing in both.

755. Next, at but that which is indivisible in quantity (430b14), he mentions another mode of indivisibility; for what has one species is called “one” in a different way, even if it is made up of discontinuous parts, for example, a man, or a house, or even of an army; this corresponds to the indivisible according to species. And of this he says that what is indivisible not in quantity, but in its species, the soul understands in an indivisible time and through an indivisible part of the soul—not, as Plato thought, that the intellect when understanding is some magnitude. And even if what is specifically indivisible has a certain division in its parts, still the intellect understands those divided parts accidentally, and not insofar as they are divisible, whether on the side of what is understood and on the side of time, but rather, insofar as they are indivisible; for even in the actually divided parts, there is something indivisible, and this is the species itself, which the intellect understands in an indivisible way. But if the parts are understood as divided—for example, the flesh in itself and bones in itself and so forth—then it will understand in a divisible time.

756. But the Philosopher wishes then to show a likeness to the first mode of unity. For just as in this way there is something indivisible, that is, the species, which makes all the parts of the whole be one thing, so perhaps in continuous things there is something not separable, that is, indivisible, that makes the time one and the length one—whether this is said to be the point, in length, and in time, the instant, or the very species of length or time. But there is this difference, that it is indivisible in all that is continuous, whether by time or extension, but the indivisible that is a species is not similarly in all things that have species, since some are composed of homogeneous parts, and some of heterogeneous parts, and of the latter in different ways.

757. Then, at a point (430b20), he shows how the third sort of indivisibility is understood, for that is also called “one” which is entirely indivisible, such as a point or unit. And he now shows how this is understood, when he says that a point, which is a sort of sign of division between the parts of a line, and every division between the parts of a continuum, like an instant between the parts of time and so on, and everything that is thus indivisible, both actually and potentially, like a point, is shown, that is, is made manifest, to the intellect as a privation, that is, through a privation of the continuous and divisible.

758. The reason for this is that our intellect receives from the senses, and therefore, sensibles are the first things intellectually apprehended. And these all have some magnitude; hence, the point and the unit are only negatively defined. For the same reason, whatever transcends the sensibles which we apprehend is known by us only negatively. For example, of separated substances we only know that they are immaterial and incorporeal and so forth.

759. A similar account holds in other matters that are known by opposition, as in how the intellect knows evil or black, which stand to their opposites as privations; for of two contraries one is always incomplete or a privation relative to the other. So he adds, in response, that the intellect knows both of them in some way by its contrariety: evil through good and black through white.

But our intellect, which in this way knows one contrary through another, must be knowing in potency, and what is in it, through which it knows the opposite, must be the species of the other opposite; in this way, at one time the species of white is in it, and at another time the species of black, and thereby it can know the latter through the former. But if there exists an intellect to which there is no knowing one contrary from the other, such an intellect must know its very self primarily and know other things through itself, and it must be always in act and entirely separate from matter and in its being, as is shown of the divine intellect in Metaphysics 12. (Aristotle, Metaphysics 12.7, 1072b26–30, 1073a4–5; 12.9, 1074b33–35; 12.10, 1075b21–24; cf. Aquinas, Commentary on Metaphysics, bk. 12, lect. 8, nn. 1536ff.; lect. 11, nn. 2600ff.)

760. Then, at now, every utterance (430b26), he states a conclusion about the intellect’s second activity, which is combination and division. He says that an utterance, that whereby the intellect says something about something else—as happens in affirmation—is always either true or false. But not all understanding, however, is always true or false, since there is the understanding of non-composed objects which is neither true nor false in regard to what is being understood. For truth and falsehood consist in a certain comparison of one thing to another, as when the intellect combines or distinguishes; but they are not in the non-composed intelligible object.

761. Yet though this non-composed intelligible object is neither true nor false, the intellect understanding it is true insofar as it is conformed to the reality understood. So he adds that understanding of what a thing is, according to the what-it-was-to-be, that is, insofar as it understands what the thing is, is always true; but not insofar as it understands something belonging to something else.

762. The reason for this is that, as he says, what a thing is, is the proper object of the intellect; hence, just as sight is never mistaken with respect to its proper object, so neither is the intellect in knowing what a thing is. This is why it is never deceived in knowing what a man is; rather, just as sight is not always true in the judgment of things that are joined with its proper object, for example, in that some white thing is a man, so, too, the intellect is not always true in combining something with something else. So it stands in the understanding of a separated substance, which substances wholly exist without matter, the way it is when we understand what a thing is; and this is why there is no falsity in their intellects.

763. But note that even in knowing what a thing is, a deception can occur accidentally, in two ways, on account of intervening composition: in one way, inasmuch as one thing’s definition becomes false when applied to another thing (for example, the definition of a circle applied to a triangle); and in another way, inasmuch as the parts of a definition do not agree with each other, in which case, the definition is false simply speaking (for example, if one were to include “lacking sense-perception” in the definition of some animal). Whence it follows that deception cannot occur where the definition involves no combining; in this case, one either understands truly or not at all, as is said in Metaphysics 9. (Aristotle, Metaphysics 9.10, 1051b31–32; cf. Aquinas, Commentary on Metaphysics, bk. 9, lect. 11, nn. 1904ff.)

764. Finally, at knowledge in act (431a1), he takes up again something he has said earlier of the intellect in act, because then he has also spoken of the thing actually understood. And he says that actual knowledge is the same as the reality actually known, and that the knowledge that is potential is prior in time in the same individual; but universally speaking, it is not prior even in time; for all things that are in act come to be from a being in act, as was explained above. (Lect. 4, nn. 740–41.)