Lecture 14 — Whether sensible objects are infinitely divisible

But someone will raise an objection: if every body is infinitely divisible, are sensible affections also? For instance, color and flavor and odor and sound, and heaviness and coldness, and hot and light, and hard and soft.

But this is impossible. For each of these is something that activates a sense power. For all are named from the fact that they are able to move a sense power. Necessarily, then, sense is infinitely divisible, and every magnitude is sensible. For it is impossible to see something that is white but not a quantity.

For if this is not so, then there can be a body that has no color, or heaviness, or other such affection, and so is not sensible at all: for these are the sensible objects. Therefore, there will be something sensible composed of what is not sensible. But it necessarily is, for it is not composed of mathematical objects.

Moreover, what will we assign them to other than intellect, or how will we know them? But they are not intelligible, for intellect does not understand what is outside except with sensation.

But if this is so, it seems to support those who make indivisible magnitudes: thus the discussion is resolved. But this is impossible, as was said before in the discussions of motion.

With the resolution of this, it will at the same time also be made clear why the species of color and flavor and sounds and other sensible objects are limited. For what is inside the extremes is necessarily determinate, and extremes are contraries. But every kind of sensible object has contrariety, for instance, black and white in color, sweet and bitter in flavor. And so in all the others there are extremes that are contraries.

A continuum, then, is divisible into an infinite number of unequal parts, but into a finite number of equal ones. And what is not of itself continuous is divisible into finite species.

We must speak of the affections as “species,” although they exist in a continuity and in these parts. Therefore, we must take it that what is in potentiality and what is in actuality are different.

For this reason a tenth of a thousandth of a grain of millet escapes the notice of sight, although sight goes over it. And the sound in a diesis escapes notice, although all of the singing, which is continuous, is heard. The distance between the extremes escapes notice. It is similar with the extremely small in other sensible objects. They themselves are visible in potentiality, but not in actuality when they are not separated. Thus a one-foot length exists in potentiality in something two feet long, and exists in actuality when it is divided off.

But it is reasonable that separated parts of such extremely small size are dissolved into the surroundings, like a tiny amount of flavor poured into the sea.

But there is no extremity of the sense power to correspond to that of the sensible object itself, even if it is separated. The extreme smallness is in potentiality to a surer sense power. And a separated sensible object of such a size will not be sensed in actuality. Still, it will be a sensible object, for there is already the power, and it will be in actuality when a sense power comes to it. Thus it has been said that some magnitudes and affections escape notice; and for what cause; and the way in which they are sensible objects, and the way in which they are not.

But since there are quantities existing within so as to be sensible in actuality, and not only as in the whole, but also separately, they—colors and flavors and sounds—are necessarily finite according to some number.

208. But someone will raise an objection (445b3). After the Philosopher has determined about sense-organs and sensible objects, here he determines some questions about the sense power and sensible objects.

First, he raises a question about sensible objects themselves.

Second, he raises another about alteration of the sense power by a sensible object, where he says but someone will raise an objection (446a20; [225]).

Third, he raises a third about the sense power itself, where he says but there is also another such objection (447a12; [253]).

On the first point, he does three things.

First, he raises the question.

Second, he introduces arguments about it, where he says but this is impossible (445b6; [209]).

Third, he solves it, where he says with the resolution of this (445b20; [215]).

Accordingly, he first says that every body is infinitely divisible: for this is of the nature of a continuum, as is clear in the book, The Physics. (Aristotle, Physics 1.2, 185b10–11; 3.1, 200b18–20; 3.7, 207b16–17; 6.8, 239a22; cf. Aquinas, Commentary on Physics, bk. 3, lect. 12; bk. 6, lect. 9.) But sensible qualities—which are called affections, as is said in the Categories (Aristotle, Categories 8, 9a28–b27.)—are in a body as in their subject. Therefore there is a question someone can raise in objection: whether sensible qualities themselves, such as color and flavor and so on, are infinitely divisible also.

209. Then, when he says but this is impossible (445b6), he raises objections concerning the question posed.

First, he raises objections to show that sensible qualities are not infinitely divisible.

Second, he raises objections on the other side, where he says for if this is not so (445b11; [211]).

Third, he eliminates a false solution, where he says but if this is so (445b17; [214]).

Accordingly, he first says that it seems impossible for sensible qualities to be divided infinitely, because each of the above-mentioned sensible qualities naturally acts on a sense power. For the proper nature of each of them consists in this: it is able to move a sense power; for example, it belongs to the nature of color to be able to move the sense of sight. If, then, the above-mentioned qualities are infinitely divisible, the consequence will be that sense—that is, the act of sensing itself—is infinitely divisible. Now an instance of being moved is infinitely divisible according to division of the magnitude through which a thing is moved; and so it would follow that, as something moved goes through every part of the magnitude, so one who senses would sense any magnitude, however small, and so every magnitude would be sensible.

210. But he adds a reason why he does not conclude that even points are perceptible to sense: because it is impossible to see something white that is not a quantity; and the argument is the same with respect to other sensible objects. The reason for this is that a sense power is a power in a magnitude, since it is the actuality of a bodily organ, and so it can be affected only by what has magnitude: for what is active must be proportioned to what is passive.

There remains the problem that every magnitude is perceptible; how this is to be understood will be made clear below. (1.7, 449a20–31; cf. ch. 18, nn. 294–96.)

Hence it can be concluded that sensible qualities are not infinitely divisible.

211. Then, when he says for if this is not so (445b11), he raises objections on the opposite side with two arguments.

The first is this. If sensible qualities are not infinitely divisible, then there can be a minimal body that transcends division of sensible qualities and has no sensible quality, i.e., neither color nor heaviness nor any other such quality. And so such a body will not be sensible, because only the qualities mentioned are sensible objects. Therefore, since these tiny bodies are parts of a whole body that is sensible, it will follow that a sensible body is composed of what is not sensible. But a sensible body is necessarily composed of what is sensible, for it cannot be said that a sensible body is composed of mathematical bodies, in which quantity is considered without sensible qualities. Therefore it remains that sensible qualities must be infinitely divisible.

212. He presents the second argument where he says moreover, what will we assign them to (445b15). His argument proceeds from the point that the soul by nature knows all things, whether by sense or intellect, as was established in On the Soul 3. (Aristotle, On the Soul 3.8, 431b20–28; cf. Aquinas, Commentary on Aristotle’s On the Soul, bk. 3, lect. 7, nn. 787–90.)

Accordingly, if the above-mentioned minimal bodies that transcend division of sensible qualities are not sensible because they lack sensible qualities, they can be assigned only to intellect as the power that knows them. But it cannot be said that they are intelligible: for intellect understands none of the things outside the soul except with sensation of them—that is, by simultaneously sensing them. If, therefore, these minimal bodies are not sensed, they will not be able to be understood.

213. He says this to eliminate an opinion of Plato, who held that the forms understood exist outside the soul. But according to Aristotle the things understood are the very natures of things in singulars, which, inasmuch as they are in singulars, fall under the apprehension of the sense power. But the intellect apprehends these natures in an absolute way and assigns to them certain intelligible intentions, namely that of being a genus or species. These intentions exist only in the intellect, not outside it: hence only the intellect knows them.

214. Then, when he says but if this is so (445b17), he eliminates a false response. One might argue as follows. A problem follows from positing the infinite divisibility of magnitude, whatever may be said about sensible qualities, whether that they are infinitely divisible or not. This, then, seems to support the opinion of those who posit indivisible magnitudes, because the difficulty is solved in this way: for if a body is not infinitely divisible, then, since sensible quality is not infinitely divisible, it will not follow that there are bodies that cannot be sensed. But this opinion that some magnitudes are indivisible is impossible, as is evident from what was said in the discussions of motion, that is, in Physics 6. (Aristotle, Physics 6.1–2, 231a21–233b31; cf. Aquinas, Commentary on Physics, bk. 6, lect. 1–4.)

215. Then, when he says with the resolution of this (445b20), he solves the question he raised above about division of sensible qualities.

And first, he treats their formal division, that is, of genus into species.

Second, their quantitative division, where he says a continuum, then (445b27; [216]).

Accordingly, he first says that, together with the solution of the above-mentioned difficulties, at the same time it will have to be made clear why the species of color and flavor and other such things are finite: for he promised above that this would be determined. (1.3, 440b23–25; cf. ch. 7, n. 116.)

He gives the following reason for this. If it is possible to reach the furthest point starting from either extreme, what is in the middle is necessarily finite, as was proved in Posterior Analytics 1. (Aristotle, Posterior Analytics 1.20, 82a21–35; 1.22, 84a29; cf. Aquinas, Commentary on Posterior Analytics, bk. 1, lect. 32.) Now it is clear that in any genus of sensible objects there is a contrariety that is the greatest distance, and so the contraries must be the extremes, for instance black and white in color, sweet and bitter in flavor, and likewise in the others. Hence it remains that intermediate species are finite.

216. Then, when he says a continuum, then (445b27), he solves the question raised earlier about quantitative division of sensible qualities.

First, he makes some presuppositions.

Second, he proceeds to solve the question where he says we must speak of the affections (445b29; [217]).

On the first point, he makes two presuppositions.

The first is that a continuum is in a way divisible into an infinite number of parts, and in another way into a finite number. For if a division into equal parts is made, it will not be able to proceed to infinity as long as the continuum is finite, because if one repeatedly removes something the size of a palm from anything finite, it will be completely taken away. But if a division into unequal parts is made, it will proceed to infinity: for instance, if a whole is divided in half, and again the half in half, which is a quarter of the whole, the division will proceed to infinity.

The second supposition is that what is continuous not of itself, but accidentally, for example color and other such things, is of itself formally divided into finite species, as was said a little before (445b20–27).

217. Then, when he says we must speak of the affections (445b29), he proceeds to solve the principal question, which was about division of sensible qualities.

Because he had taken his argument on this question from what appears in sensation, first, he inquires about division to infinity with respect to the act of sensing itself.

Second, he concludes to his proposal with respect to sensible things themselves, where he says but since there are quantities (446a16; [223]).

On the first point, he does two things.

First, he inquires whether sensing proceeds to infinity with respect to parts existing in a whole.

Second, whether it does so with respect to separated parts, where he says but it is reasonable (446a7; [220]).

Accordingly, he first says that because we must speak of the affections—that is, the sensible qualities—as “species” and forms that are not, considered in themselves, infinite, as was said; and nevertheless they exist in a continuum as their subject, by division of which they are accidentally divided; it follows that, as in a continuum there is something in actuality—namely a separated part—and something else in potentiality—namely a part existing in the continuum unseparated—so also in these qualities that are divisible accidentally a separated part exists in actuality, and hence can be sensed in actuality, but a part not divided off exists in potentiality, and so is not sensed in actuality.

218. And thus, although sight goes over a grain of millet, nevertheless some tiny part of the latter—say a tenth of a thousandth—escapes the notice of sight. Likewise, although a whole continuous singing is heard, nevertheless some small part of the singing—such as a diesis, which is the smallest unit in melody, being a distance between a tone and a semitone—escapes the notice of hearing. For this kind of intermediate distance between the extremes escapes notice. And so in the case of other sensible objects what is extremely small altogether escapes the notice of the sense power. For it is visible in potentiality, but not in actuality, except when it is separated. Similarly we see in magnitudes that a one-foot line exists in potentiality in a two-foot line, but exists in actuality when it is divided from the whole.

219. It is clear from the foregoing that what some mathematicians say is false: that nothing is seen whole all at once, but rather sight runs over the parts of a visible object as if seeing were a continuum, like being moved. They are mistaken in this, because the parts of a continuum are visible not in actuality, but only in potentiality. Hence sight takes a visible whole as an indivisible unit belonging to a genus of its own—unless it takes parts that are not divided off as if they were, as when it looks at each, one by one. Nevertheless, even this does not reach as far as every minimal part, because then sensing would be infinitely divisible, which was dismissed above as inconsistent.

220. Then, when he says but it is reasonable (446a7), he shows that not even parts separated off are infinitely perceptible by sense.

First, from the point of view of the parts themselves.

Second, from the point of view of the sense power itself, where he says but there is no extremity (446a10; [221]).

Accordingly, he first says that if extremely small parts are separated from a whole, it seems reasonable, because of the smallness of their power of self-preservation, that they cannot continue to last; for bodily power is divided according to division of magnitude, as is clear from Physics 7. (Aristotle, Physics 7.5, 249b27–250b6; cf. Aquinas, Commentary on Physics, bk. 7, lect. 5–6.) And so those separated minimal parts are immediately converted into the surrounding body, for instance air or water, as is clear in the case of flavored drink poured into the sea.

From this it is clear why a mathematical body—in which only the nature of quantity, which has nothing to oppose infinite division, is considered—is infinitely divisible. But a natural body, which is considered under a whole form, cannot be infinitely divided, because once it is reduced to its smallest part, it is immediately, because of the weakness of its power, changed into something else. Hence one can find a smallest part of flesh, as is said in Physics 1. (Aristotle, Physics 1.4, 187b37–188a1; cf. Aquinas, Commentary on Physics, bk. 1, lect. 9.) But a natural body is not, as was said in objection, composed out of mathematical ones.

221. Then, when he says but there is no extremity (446a10), he shows the proposal from the point of view of the sense power itself. For evidence on this point it must be known that the more excellent a sensitive power is, the more it can perceive a smaller alteration of the organ by a sensible object. But it is clear that the smaller a sensible object is, the smaller the alteration it causes of the organ, and so the more excellent power of sense it needs in order to be sensed in actuality. But it is clear that sensitive power cannot be increased infinitely, any more than can other natural powers.

Hence even if sensible bodies were infinitely divisible, nevertheless there would not always be extremity of the sense power in superiority of power to correspond to the extremity of the sensible object in smallness—not even if the extreme smallness of the sensible object continued to last when separated. For the extreme smallness of the sensible object exists in potentiality, to be perceived by a surer and more perfect sense power, and if the latter is not present, it will not be able to be sensed in actuality. Still, it will be a sensible object in itself, for already, by being separated, it has active power to alter a sense, and when a sense comes to it, it will be perceived in actuality. Therefore it is clear that what he said above is true, that no magnitude is invisible—that is, in itself, although a magnitude may be invisible because of imperfection of sight.

222. Therefore he concludes that it has been said that some magnitudes and affective qualities escape the notice of the sense power; and for what cause; and the way in which they are sensible objects, and the way in which they are not.

223. Then, when he says but since there are quantities (446a16), he concludes from the foregoing that since some parts of sensible bodies have quantity in this way—so as to be sensible in actuality not only when existing in a whole, but also when divided off—parts of this kind are necessarily finite according to some number, whether in the case of colors or flavors or sounds. And thus, according as they are perceptible in actuality, they are not infinitely divisible.