44 On Quantity Against the Moderns
44: On Quantity Against the Moderns Next we shall consider the category of quantity. It should be noted first that the common term quantity is an intention of the soul containing under it other intentions ordered according to greater and lesser universality. Recent writers frequently hold that every quantity is a being really and totally distinct from both substance and quality. They maintain that continuous quantity is an accident lying between a substance and its qualities, that it is subJectively in substance while being the subject of qualities. Likewise, they hold that discrete quantity is a thing really distinct from substance; they hold the same view as regards place and time. Their position ought to be examined closely.
I want to show first that this account runs counter to Aristotle; second, I want to present some arguments against the view; third, I shall outline an opposing view which seems to me Aristotelian, regardless of whether it is true or false, orthodox or heretical.
In the preceding chapter I showed that this account is incompatible with Aristotle. I showed that, for Aristotle, no accident really distinct from substance can admit contraries by itself undergoing a change; but if quantity were an accident and the subject of quality, it is clear that it would change in receiving qualities. By undergoing change, then, it would receive contraries.
But this is incompatible with Aristotle's account.
Again, as is clear in the fourth book of the Physics, Aristotle holds that air can be condensed without changing in either all or some of its qualities!
Thus, when air is condensed it is not necessary that it lose some of the qualities or at least not all of the qualities it had before. On the basis of this I argue: when air is condensed, either the whole quantity that was there before remains or it does not. If it does, then the same quantity is now less than before only in this—that the parts of the quantity lie closer to each other than they did before; but since the parts of substance, in exactly the same way, lie closer now than they did before, quantity seems to be a superfluous entity. But if the whole quantity which was first present does not remain, then some part is lost; but an accident is always corrupted when its immediate subject is corrupted. It follows then that not every quality remains, and that is incompatible with Aristotle's view.
Again, Aristotle holds that every accident is in some first subject in such a way that if the accident has parts, one part of the accident is in one part of the subject and another part of the accident is in another part of the subject. Thus, the whole whiteness is in the whole body and a part of the white217 27-34.
On Quantity Against the Moderns ness is in a part of the body. If on the other hand an accident is indivisible, then it is in some first indivisible subject. On the basis of this I argue that, for Aristotle, the point is not something different from the line; that the line is nothing ditferent from the surface; that the surface is not different from the solid and; finally, that the solid is not distinct from substance and quality.
That it follows from the preceding principle that the point is not something different from the line, I prove as follows: if the point is an absolute accident distinct from substance, then it is in some first subject. The point is either in a substance or in a line. It is not in a substance, for then it would be in a divisible or indivisible substance. It is impossible that it be in a divisible subject since a part of the point would be in a part of substance, and the point would be a divisible accident which everyone denies. It is also impossible that the point be in an indivisible substance; for according to Aristotle the genus of substance incorporates only matter, form, and the composite of these and Aristotle construes all of these as divisible. Thus, the point is not an indivisible accident existing subjectively and immediately in some substance as its first subject. Nor is its first subject the line or a part of the line; for the line and every part of the line are divisible and, consequently, cannot be the first subject of an indivisible accident. Thus, it is clear that in Aristotle's view a point is not an indivisible accident, but by the same line of reasoning the line is not an accident that is indivisible in breadth and really distinct from surface. Likewise, surface is not an accident indivisible as regards depth and really distinct from the solid. And Aristotle no more holds that the quantity known as the solid is really to be distinguished from substance than that the line and the surface are to be distinguished from the solid.
It seems that for Aristotle continuous quantity is not an absolute thing really and totally distinct from the solid. Therefore, I intend to present some arguments against the widespread view of recent writers. I also intend to indicate some theological difficulties in the view. Whether these theological considerations are decisive, they carry as much weight as such considerations can.
First, I argue as follows: God can conserve in existence any prior absolute thing without a change in its place while destroying that which is posterior to it. On the general view a piece of wood is a substance having parts one of which lies beneath a part of the quantity inhering in the whole and another of which lies beneath another part of that quantity. Further, on that view the substantial object is by nature prior to the quantity inhering in it; therefore, God could, without changing the location of the substance, conserve it in existence while destroying the quantity. If this is possible let us suppose it to happen. Either the substance has one part spatially separated from another or it does not. If it does it is quantified without quantity in which case quantity is superfluous. If it does not, then since its parts were previously
On Quantity Against the Moderns separated from each other spatially, the substance has undergone a change in place; but this is incompatible with the hypothesis.
Again, anything which by itself and its intrinsic parts is present to something quantified in such a way that the whole is present to the whole and the parts are present to the parts, is by itself and its intrinsic parts something whose parts lie at a distance from each other. But anything of that sort is by itself and its intrinsic parts a quantified object. Now material substance by itself and its parts is present to something quantified—the quantity which informs it (I am assuming here that there is such a thing). But by itself and its parts it really has one part spatially separated from another part; therefore, by itself and its parts it is quantified.
Again, that quantity is not an accident which lies between a substance and its qualities and which serves as the subject of those qualities can be proved by reference to the Sacrament of the Altar. For if it were such, the qualities remaining in the Sacrament of the Altar would be in quantity subjectively. The consequent seems false to many but likewise the antecedent.
I prove the falsity of the consequent as follows: if the supposition were true, the qualities would not subsist by themselves, which is incompatible with the view of the Master who, in the fourth Book of the Sentences speaking of color, taste, weight, and other such qualities, says that such accidents subsist by themselves in the Eucharist. Likewise, if quantity were the subject of such qualities, the quantity would really be heavy, white, and of this or that taste; the consequent, however, is incompatible with the gloss "On consecration" in the second distinction in the chapter beginning "If by negligence." The gloss says "Weight remains there with the other accidents; nevertheless, nothing there has weight."
These arguments prove that a long quantity, a wide quantity, and a deep quantity are not things distinct from substance and quality.
That the line is not distinct from surface I prove as follows: suppose a line were the sort of thing that unites surfaces with each other; then let some surface be divided. Once it has been divided either there is a new line or only the previous line remains. If there is a new line, there will be an infinite number of new lines, since when a body is divided, there will be an infinite number of surfaces all having new lines. In the same way oncea surface is divided, there will be infinite number of points terminating an infinity of lines. But if there is no new line, that line which was there before remains; but it is not more in one part of the surface than in the other. Therefore, either it will remain per se or it will remain in different places in the two surfaces, but both of these alternatives are absurd; therefore.
Again, if the line is something different from surface and the point, from the line, then God could conserve a line and destroy its points. But when this is done either the line is infinite or finite. Clearly it is not infinite; therefore,
On Quantity Against the Moderns it is finite, but it has nonetheless no points. There is no need then to posit the point for the purposes ofterminating the line.
Again, God could conserve a line in existence while destroying all points; but once that has been done the line remains a line, and consequently a quantity. It is not, however, a discrete quantity; therefore, it is a continuous quantity; but although it is a continuous quantity, there is nothing distinct from the line which connects the parts to each other. Thus, there is no need to postulate points as items distinct from lines. For the same reason it is pointless to posit lines as items distinct from surfaces, and for the same reaSon it is pointless to posit surfaces as objects different from bodies.
I want now to outline a different account of quantity. Whether or not it is an orthodox account, it seems to me to be the account Aristotle holds. I do not want to propound the account as my own. Thus, whenI set forth the account in commenting on the Philosopher, I did not write it as my own account, but only as Aristotle's view which I was expounding as I saw fit.
In the same way I shall now outline the account without committing myself to it. It is nonetheless a view that many theologians hold now and have held in the past—the view that no quantity is an object distinct from substance and quality; and they hold this view regardless of whether propositions like
'Substance is a quantity' and "Quality is a quantity' should be construed as true.
They say that a continuous quantity is merely one thing which has parts spatially separated from each other. Thus, the expressions 'continuous quantity' and 'one thing having parts spatially separated from each other' are equivalent in signification; the terms are convertible unless one of them incorporates some syncategorematic expression or equivalent determination which stands in the way ofconvertibility and mutual predication. Thus, since both substance and quality have parts lying at a distance from each other, some quantity is nothing different from substance and some quantity is nothing different from quality. These theologians do not think it appropriate to say that God could not make the parts of substance be spatially separated from each other without conjoining some additional absolute entity to them. But if He can do this, then substance really will have one part spatially separated from another without any absolute entity added so that substance will be quantified without any other absolute thing. The same argument holds as regards quality. Therefore, since both substance and quality can be quantified without the addition of quantity, in the form of a thing distinct from substance and quality, the notion of an entity standing between a substance and its qualities seems altogether superfluous. Thus they say that no quantity is a thing different from substance and quality, since nothing except substance and quality has parts spatially separated from: each other. Speaking of the Sacrament of the Altar, they say that one quantity was there before and On Quantity Against the Moderns was identical with the substance of the bread; but after the consecration of the body of Christ, the relevant quantity no longer remains; nonetheless, there remains a quantity which is identical with a quality. This quantity, they say, is not the subject of any quality, for all the accidents which remain after the consecration remain together with the Body of Christ but without any subject; they subsist, on the contrary, of and by themselves. That is the account of continuous substance which some theologians present.
As regards discrete quantity, they claim that number is nothing different from things enumerated. Thus they deny that the unity of a thing is some accident added to the thing which is one. Likewise, number is not some accident added to things enumerated. That unity is not an accident added to that which is one can be shown in the following way: if it were an accident, then according to everyone, it must either be a relative or an absolute thing.
It is not a relative term since it need not have a correlative term associated with it. Something can be one without being the one of something else or the one to something else and so on for the other cases in which something is related to something else. Likewise, it is not an absolute accident because then it would be a quality which clearly is false, or it would be quantity; but in that case it would be either continuous or discrete, both of which are clearly false. The only remaining possibility is that unity is not an accident which is really distinct from and added to the thing that is one. And for the same reason number is not an accident added to things enumerated.
Likewise, they claim that place and time are not objects distinct from substance and quality, but this view has already been examined in my book on the Physics.? They hold the same view about speech saying that it is simply uttered words.
Thus, the proponents of the outlined position must hold that the point, the line, surface, the solid, and number are not objects completely and really distinct either from each other or from substance and quality. Nevertheless, while they hold for the identity of the things designated by these terms, they want to claim that the terms themselves are different predicables constituting different species of quantity. For it sometimes happens that while different predicables signify the same things, it is impossible to predicate one of the other. Thus, while the terms 'man' and 'men' signify the same thing, the proposition 'Man is men' is absurd. Although all the terms listed above signify the same things, they are different predicables and different species of quantity.
2 Expositio super Octo Libros Physicorum, a work extant only in manuscript form.