LECTIO ELEVEN

             § 746. Having come to conclusions about the intellect the Philosopher now examines its activity; and this in two parts; first distinguishing two such activities, and then reaching conclusions about each of these. First, then, he says that the intellect, by one of its activities, understands things simply; understanding, for instance, man or ox, or any such thing, simply in itself. And this operation involves no falsehood, both because objects considered simply in themselves are neither true nor false, and also because, as we shall see later on, the mind is infallible with respect to what things are in themselves.

             § 747. On the other hand, where truth and falsehood are found in the intelligible objects themselves, there must have been already a certain composition of these objects, i.e. of the things understood, joining several such objects together. He gives as an example the theory of Empedocles that all things originated by chance, not design; by merely following a process of division and conjunction through strife and love respectively. Thus Empedocles said that in the beginning many heads 'grew' without necks; 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. Only afterwards did these parts, thus differentiated, come together in harmony and make up the single animal with its various parts--head, hands, feet and so on. And if all the parts necessary for the animal's existence were present it could go on living and would beget its own kind; but not if any were lacking. So then, just as love (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 simple 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 united in reality, e.g. the diagonal and incommensurability--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, e.g. that the diagonal of a square is commensurable with its sides.

             § 749. Now commensurability and the diagonal are sometimes understood separately, making two distinct intelligible objects; but when combined they make one object which the mind understands all together. But again, since the objects so combined are sometimes things past or future, not present, he adds that when the mind combines things 'done'--i.e. past--or things to come, it should include the notion of time past or future; 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, and that the falsehood is always in the combination itself. Again, there is falsehood if the not-white is combined with what is white, as when swans are said to be not white; or if white is combined with the not-white, as when crows are said to be 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 mind can always separate things, whether in the present, or past or future; and it can do this both truly and falsely. Clearly then, since combinations can be made with reference to time past and future as well as present, and since truth and falsehood are found precisely in combinations and separations (or divisions), it follows that not only are propositions about the present true or false--e.g. that Cleon is white--but also propositions about the past or future--e.g. that Cleon was or shall be white. Since, however, the combination that makes a proposition is a work of reason and understanding, not of nature, he subjoins that the agent of such propositions, composed of intelligible objects, is the mind. And since it is in combinations that truth and falsehood are found, he can say, in Book VI of the Metaphysics, that truth and falsehood are not in things but in the mind.

             § 752. Next, at 'As the indivisible is twofold', he comes to conclusions on both the aforesaid intellectual activities: (1) on the understanding of objects simply in themselves; (2) at 'Now every utterance', on the intellect's combinations and divisions; after which (3) he states something common to both. Section (1) divides into three parts according to three ways of considering indivisibility--that is to say, unity which consists in indivision.

             First of all, a thing may be one by continuity; hence the continuum is called an indivisible because it is actually undivided, though it is potentially divisible. So he says that, since anything may be divisible either potentially or actually, there is nothing to prevent the mind thinking of a continuum or length as indivisible actually. And, so doing, its thought will also occur in an undivided time.

             § 753. This is against the view of Plato, that the understanding of things in space involved a sort of continuous movement. In fact spatial things can be understood in two ways: either as potentially divisible--and thus the mind considers one section of a line after another, and so understands the whole in a period of time; or as actually indivisible--and thus the whole line is considered as a unity made up of parts and understood simultaneously. He adds therefore that, in the act of understanding, either both time and length are divided, or both are not divided.

             § 754. Consequently it cannot be said that the understanding involves dividing both by half, i.e. that half a line is understood in half the given time it takes to understand a whole one. This would be the case if the line were actually divided; but a line, as such, is only potentially divisible. If each of its halves, however, is understood separately, then the whole is actually divided mentally; and the time is divided also. But if the line is understood as a unity made up of two parts, the time also will be undivided or instantaneous--the instant being that which persists in every part of time. And if the mind's consideration is prolonged in time, the instants will not be separated with respect to distinct parts of the line understood one after another; but the whole line will be understood at every instant.

             § 755. Next, at 'But whatever', he mentions another kind of unity, namely that which comes of a thing being one in kind, though made up of discontinuous parts, e.g. the unity of a man, or a house, or even of an army. This is a specific, not a quantitative indivision; and the soul, he says, understands it by what is undivided in the soul and in an indivisible point of time--not, as Plato thought, by anything quantitative in the intellect. And though division may be contained in such unities, the divided parts are not understood--so far as the object and time of the understanding are concerned--as divided, but as united; for even though there be an actual division into parts, the species itself, as such, is indivisible; and this it is that is indivisibly understood. But if the parts are understood separately--e.g. the flesh and bones and so forth--the whole is not understood in an undivided time.

             § 756. Then he points out wherein this second kind of unity seems to resemble the former kind. For as the species is something indivisible unifying the parts of a whole, so perhaps there may be something indivisible in any period of time or spatial length,--the point perhaps or the instant, or perhaps the species itself of length and of time. But there is this difference that, while the indivisible in the continuum is one and the same in every continuum, whether temporal or spatial, the unity of species differs from one thing to another; for some things are made up of homogeneous and some of heterogeneous parts.

             § 757. Then at 'A point etc.', he goes on to show how the third sort of indivisibility, i.e. whatever seems to be entirely one, such as a point or unit, is understood. A point, he says, is a sort of sign of division between sections of a line, as an instant between periods of time; and all such--being, like the point, both actually and potentially indivisible,--are 'shown' to the mind 'as privation', i.e. as privations of the divisible continuum.

             § 758. The reason being that our mind has to start from sense-data. Sensibles therefore are the first things intellectually apprehended; and these all have some magnitude; hence the point and the unit can be only negatively defined. For the same reason whatever transcends the sensibles which we apprehend is known by us only negatively. Of 'separated' substances we only know that they are immaterial and incorporeal and so forth.

             § 759. It is the same with things known by opposition, such as evil or black, which are privations of their opposites; for of two contraries one is always a lack or privation of the other. So he adds that the mind somehow knows each of these by its contrary: evil by good and black by white. Now if our mind thus knows one contrary by means of another, it must do so by moving from potency into act, and also by receiving into itself the likeness of one contrary, e.g. of white, and only after and in virtue of this, the likeness of the other, e.g. of black. But if there exists a mind that does not have to move from one contrary to another, it must have itself for its primary and immediate object; and it must know all other things in knowing itself, and be always in act and entirely immaterial--even in its being; and such is the Divine Mind according to the teaching of Book XII of the Metaphysics.

             § 760. Then at 'Now every utterance', he states a conclusion about the mind's second activity of combining and distinguishing. He says that whenever a statement is made about anything--as when a mind affirms anything--the statement must be either true or false. Understanding as such, however, need not be true or false; its proper object is a simple one, and therefore, as bearing on this object, the act of understanding is neither true nor false. For truth and falsehood consist in a certain adequation or comparison of one thing to another, as when the mind combines or distinguishes; but not in the intelligible object taken by itself.

             § 761. Yet though this latter object as such is neither true nor false, the mind understanding it is true in so far as it is conformed to a reality understood. So he adds that just so far as the mind bears on an essence, i.e. understands what anything is, it is always true; but not just in so far as it relates one thing to another.

             § 762. The reason for this is that, as he says, essence is what the intellect first knows; hence, just as sight is infallible with respect to its proper object, so is the intellect with respect to essence. It cannot, for instance, be mistaken when it simply knows what man is; on the other hand, just as sight can be deceived in respect of what is joined with its proper object, e.g. in discerning that some white object is a man, so too the intellect sometimes goes astray in relating one object to another. But the totally immaterial substances understand in a manner corresponding to our human apprehension of essences; so that they are infallible.

             § 763. But note that even in knowing essences deception can occur indirectly, in two ways: (a) inasmuch as one thing's definition becomes false when applied to another thing; e.g. the definition of a circle applied to a triangle; and (b) inasmuch as the parts of a definition do not agree together, in which case the definition is simply false; e.g. if one were to include 'lacking sense-perception' in one's definition of 'animal'. Whence it follows that deception absolutely cannot occur where the definition involves no combining of parts; in this case one either understands truly or not at all (see Book IX of the Metaphysics).

             § 764. Finally, at 'Knowledge in act', he repeats what he has said of intellect in act, that actual knowledge is one with its actual object; and that in one and the same thing potential knowledge precedes actual knowledge in time; but that this is not true universally; for all actualities derive from one Actual Being, as was explained above.

431a 4-431b 19

SENSE AND INTELLECT COMPARED

THE PRACTICAL INTELLECT

ABSTRACTION AGAIN

             AND IT SEEMS THAT THE SENSE-OBJECT [SIMPLY] brings the sense-faculty from a state of potency to one of act; for [the latter] is not affected or altered. Hence it is a specifically distinct kind of movement. For movement is the actuality of the incomplete; whereas in its plain meaning act is different, as being of the thing completed.§§ 765-6

             Sensation therefore is like mere uttering and understanding; but, given a pleasant or painful object, the soul pursues or avoids with, so to say, affirmation or negation. To be 'pleased' or to feel pain is to act in the sensitive mean in relation to the good or the bad as such; and pursuit or avoidance are this operation in act. And the faculties of desire and avoidance are not distinct,--nor distinct from the sensitive faculty; though in essence they differ.§§ 767-9

             Imaginative phantasms are to the intellective soul as sense-objects. But when it affirms or denies good or evil it pursues or avoids. Hence the soul never understands apart from phantasms.§§ 770-2

             This is comparable to the way that air affects the pupil with such and such a quality, and this in turn affects another part with the same quality: and the hearing operates likewise. The ultimate is one, a single common mean whose essence, however, is various. With what it discerns how the sweet differs from the hot has been stated already and must be reaffirmed here.

             For it is a unity in the sense of a terminus; and this unity--according to analogy and number--is related to distinct objects as they to one another. (What difference indeed does it make whether the comparison be of qualities not homogeneous, or of contraries, like black and white?) Thus, as A (white) is to B (black) so is C to D; hence therefore, also, alternating the proportions. If then C and D pertain to one unifying principle, they are to each other as A and B: identical though distinct in essence; so too is the aforesaid [principle]. The same relation holds if A be the sweet and B the white.§§ 773-6

             The intellectual faculty therefore understands forms in phantasms. And as in these [forms] what is to be pursued by it, or avoided, is marked out for it, so too when these are in the imagination apart from sensation, is it moved. [For instance] when one sees something fearful [e.g. fire,] seeing the fire move one knows in general that someone is fighting. Sometimes, however, it is by means of the phantasms or concepts in the soul that one calculates as if seeing, and that one deliberates on future or present matters; and when one has said that the pleasing or the disagreeable is present, then one pursues or avoids.§§ 777-8

             And generally in practical affairs and apart from action, true and false are in the same category, whether good or evil. But they differ in being absolute and relative.§§ 779-80

             The mind understands by abstraction, so called, as one might understand a snub-nose: as snub-nose, not in separation; but as curved, then, if the understanding be actual, the mind thinks of the curve apart from the flesh in which it exists. Thus, understanding mathematical objects, the mind understands things not separated as separated. And in general, the mind in the act of understanding is the thing itself.§§ 781-4

             Whether it is possible for a mind that is not itself separated from extension to understand anything separated or no, is to be considered later.§§ 785-6