Chapter 2

Quantity

But there seems to be a kind or level of limitation that probably deserves the name of another mode of finiteness: that sort of limitation by which we can apply numbers to acts and objects.

Quantity is the mode of finiteness by which numbers apply to activities.

It is obviously a mode of finiteness, because any number always implies "no more than this," since the number system is such that for any number there is always a greater number. Hence, whatever the form of consciousness that "reports" a number refers to in the object, it has to be a limit of "muchness," whatever that is.

It is obvious, I think (and we are about to explore the implications of this), that at least in most cases, quantity applies to a form of existence; we measure heat, light, motion, weight, size, and so on, rather than "existence"; and on the face of it it would sound peculiar, to say the least, to claim that one object has "twelve degrees of existence," while some other object is "twenty units of existence."

So the first question to ask is whether quantity can be a direct limitation of existence, or whether the mode of finiteness called the "form of existence" is what the limitation called "quantity" applies to--which sounds strange, because it makes quantity a kind of limitation of a limitation, or a nothingness of a nothingness of something. Of course, if this is the case, the solution to the problem is that the quantity would not really be the limit of the limit itself, but of the formed existence as formed.

In any case, if quantity could be a direct limitation of existence, then this would mean that there was an existence which was similar to other existences in being "two" or "three" or "six" or "one," or whatever the number its quantity as perceived "pointed to." It would be analogous to all forms of existence which also had this number; but it itself would be something like an "absolute two" (or an "absolute three," or whatever).

But how could such a thing be perceived? First of all, it couldn't be a countable two, because this would imply two distinct existences--or at least distinct parts of some object, each of which could be considered as a distinct existence. That is, the kind of "two" that describes "being conscious" and "being conscious of being conscious" is, as we have so often said, a description of one and the same reality, because each "part" is contained within the other and contains the other within it, so that there is no distinction between "them"; but that means that the number two does not really describe this sort of thing (because it "means" the same thing as the number One in this case).

Further, "two" would not really describe the same idea as shared by two people, say. If both of us are thinking, "Being is analogous," then how many ideas "Being is analogous" are there? In one sense two, because each of us is thinking of it; but in another sense, it is (to the extent that we agree) identically the same idea that each of us "has." It would be silly to count the number of people in a class and find out that ten of them understood a given proposition, and then say that there were "ten" of that idea in the classroom.

This seems to indicate that something like an "absolute two" really doesn't make any sense, at least when discussing countability. We can recognize "red" when we see it, but we can recognize the "countable two" if we recognize many objects. That is, if there are two in this countable sense, "it" is not a Two, but there are two. Hence, this is a sense of quantity which relates (many) objects, and so it is nonsense to talk of existence as directly limited by quantity in this sense.(1)

But that leaves us with what might be called a "measurable two" as opposed to a "countable two": such as two degrees rather than two things. The point here is that 72 degrees of heat is not a "piling up" of little units of heat, each of which is distinct from the others, as if they were in a stack; it is a limit to--shall we call it the "strength"?--of the heat; or a speed of 50 miles an hour is not a summation of 50 single miles an hour, but a limit on how fast you are traveling. Here it is obvious that the quantity applies to a single act, and is a limit of it, rather than a relation between acts.

But with quantities of this sort, the only way numbers can actually be put on them is in fact by comparing them to some measuring instrument on which numbers have been arbitrarily marked. The number itself is objectively meaningless, as can be seen from the fact that 32 degrees of heat (Fahrenheit) is zero degrees (Celsius), or that 50 miles per hour is 73 feet per second. Where the zero is put on the measuring scale and how big the measuring units are determines what the actual number of the measured act will be. But more than this, if the act to be measured has to be compared with an instrument, then the instrument has to be comparable to it, implying that it has to be the same form of activity. You can't measure heat in miles per hour or speed in calories; or as the saying is, "you can't compare apples and oranges"--to which I would add "except as desirable objects," in which case they are assumed to have (at least to you) some common form of existence.(2)

But the point here is that measurable quantity also implies a common form of existence between the measured and the instrument, and so an "absolute two" here also is meaningless.

Hence, we may take it that

Conclusion 4: Quantity is a limitation of a form of existence.

That is, when something is measurable, it is limited on two levels: it is limited qualitatively to being some kind of activity; and the kind of activity in question has differences between different instances of it; and these differences are what allows us to attach a number to each of the forms of activity in relation to the "degrees" of the other forms of activity. The assumption is that differences in quantity imply differences within the same form of activity.

Just as existences differ from each other in form, meaning that each is limited to being this kind of existence and no other, so a given form of existence (heat, say) is limited to being in one case 72 degrees of heat, and in another case 55 degrees of heat, and so on. The different temperatures are differences in the heat, not something that is "attached" to it; they are the fact that in each case there is no more of it than there is.

Note this: it is a very important point: In the case of a given form of existence various instances of which have different quantities, the form of existence is not the same in each case; it is different, but in quantity.

That is, the different quantities indicate that the forms of existence in question are analogous; it does not indicate that they are identical, and "have" different degrees; the quantity, as a finiteness of the form of existence, is precisely a difference in the form, not a "something" that it has tacked on to it; it is the fact that the form of existence in question is limited to being not all of what it could be, and hence it is an "impotence" of the form to be itself, just as the form is an "impotence" of the existence to be itself.

This needs stressing, because in Scholastic philosophy, it is assumed that forms of existence are "univocal," not analogous: that is, that the form of existence in each case is identically the same as the form in all other cases, and the difference in the various objects comes from what the form is "received in": either the body as a whole (as in the case of the "accidental forms") or the matter (as in the case of the "substantial form"). So a Scholastic would argue that as humans we are all the same; and what I am saying here is that as humans we are all similar, but "to be human" in my case means something different (though not wholly different) from what it means in your case; and the difference is precisely the "degree" of humanity that each of us "possesses." (Can we actually have "degrees of humanity"? Yes indeed, as we will see in the next section.)

What I am saying is that just as the form of existence is precisely the difference in the existence from what it would otherwise be; because the existence, after all, all there is to the object; so the quantity of the form of existence is the difference in the form from what it would otherwise be.

I gave a model to picture existence with its form: a ball of wood, where the spherical surface is the difference in the wood making it a ball of wood and not, for example, an egg. To picture the level of existence called "quantity," imagine a cube of wood. Now the surface itself has edges. That is, if you go along the surface and come to the edge, you have to change direction or you will move off the cube altogether. Now of course, the edge doesn't have any more reality than the surface does; all there really is in the cube is wood. But a cube is a different sort of surface from a continuous type of surface like a sphere, which has no "special places" on it where you would have to do something different to stay on the surface. So the edge is the surface of the wood at that point; but it is also the fact that the surface leaves off in this direction--in a sense analogous to the way the wood leaves off at the surface; and of course, as a "leaving off," the surface and its edge are nothing but the wood itself.

Similarly, any form of activity that is limited quantitatively is only just activity; but it is activity that is simultaneously only this kind of activity and only this much of this kind of activity.

There is no law, of course, that says that a form of activity has to have this "extra" limitation on it; and in fact, later on we will conclude that there are forms of activity (consciousness is one) which cannot be limited quantitatively.

Let me say just a word about what in Thomism is called "quantity." In ancient and medieval times, about all you could measure was size or weight; and so quantity was not looked on by Aristotle or St. Thomas as the limit of a form, but as a form, which was called the "extension"--and St. Thomas tacked on the other quantity of "weight," which he didn't do much of anything with. They thought that this particular "accidental form" was intimately related to the "matter" of the body as a whole, and became a kind of intermediary between the body as such and the other "accidental forms" which somehow "inhered" in the body (the "substance") by way of the quantity or extension.

Some contemporary Thomists, such as Fr. Hoenen, have tried to reduce all the quantities we have now in physics and chemistry to variations on extension; but I think they have produced a tour de force of reasoning which ultimately fails. What they missed, I think, is that "accidental forms" can have a limit, just as the "substantial form" can; and in fact the sum total of the quantities of the "accidental forms" is a kind of manifestation of the limit of the "substantial form," which is the "matter" of the body. There are just too many ways to measure too many things to say that every degree of everything is just a way of describing the size of the body.

Actually, as we will see later, extension or size is a form of activity, but one which has a quantitative limit; it isn't quantity itself.

But to return to where we were, since quantity is a limitation, then it follows that

Conclusion 5: God has no quantity.

To see what I am driving at here, God's infinite activity is to quantified (measurable) activity as colorlessness is to color. If you say that air is colorless, you do not mean it is black (the color that an object is when it re-radiates none of the light falling on it), or white (the color it is when it re-radiates all of the light falling on it); you mean that it doesn't "do" what color "does" at all. It isn't no color (black) and it isn't all colors (white) and it isn't any color in between. "Colorless" means that color-terms cannot be used to describe the object.

Similarly, God's infinite activity is not an activity that has the quantity that is expressed by (the sideways figure eight--"infinity"), which means "a quantity greater than any one you can name." Why? Because a quantity is a limit, and God simply is not limited.

Nor, of course, is God's activity zero in quantity, any more than glass is black because it has no color. God's activity is infinite in the sense that to ask "How much of it is there?" is to ask a question that is as meaningless as "How heavy is blue?".

When I was defining "energy" I also defined "spiritual activity." The reason for using this term is that what is "spiritual" is in ordinary speech opposed to what is "material"; and it turns out (as we will see) that what makes a body a body is that the activity uniting its parts has a quantity (which in fact was what was "pointed to" by the old philosophical use of "matter"). Hence, the "spiritual" really is the "unquantified" or "unmeasurable."

If this is what "spiritual" means, then, of course, as I said, there is at least one spiritual act: God. I said that we would conclude that there are also spiritual forms of activity; but whether there are or not is not really at issue at the moment. The way they could be discovered, however, would be to show that if you tried to describe the act in terms of a quantity (i.e. as "this much and no more") it would contradict itself. For example, you would have to show that, no matter what quantity it had, it would have to have a quantity greater than that one. And this is the way we will in fact argue in the next Part of this treatise when discussing the implications of "knowing that you know" as being a "reduplication" of the act of knowing.

But suffice it here to say that if there is such a thing as a finite spiritual act, it is an act which is describable qualitatively but not (in any meaningful sense) quantitatively; numbers do not apply to it in principle.

I am stressing this here because it is a kind of dogma of contemporary science that anything real is measurable; that is, in order for something to be objectively knowable as factually existing, it has to be measurable; any unmeasurable "reality" is actually only a projection of fantasy onto the world by way of a version of the "ontological argument."

This dogma came about, as I have already said so often, by the mistake of Galileo and Descartes in calling "truth" the matching of the perception with the object, and their assumption that the two matched when measurable forms as measurable were in question. But as I have also said, it is known in science now that the quantity cannot in fact be measured "as it is out there," so that the quantity as known exactly matches the objective quantity--and in quantum physics, this discrepancy is a discrepancy in principle, not something due to the crudity of the measuring instrument; and something similar can be said in General Relativity.

The dogma is also reinforced by Kant's "refutation" of the "out thereness" of any aspect of perception; and I tried to show how his explanation was inadequate in the preceding Part.

So it is enough for our purposes here to reiterate that the dogma of science that whatever is real is at least in principle measurable is a dogma that is based on faulty philosophy, and has nothing to do with science itself. And so let us pursue the even tenor of our ways and let the scientists sneer at us because we dare to talk about the spiritual as objective. At least we know what we are talking about now.

Before going on to define energy, let me point out something that is suggested by the assumption that a given act could have many forms and by the model of the cube, whose edges themselves have corners, which seem to be limitations of the edges: It may be possible for an act to be limited quantitatively in more than one way also.

This is a very mysterious area of things. But it does seem that, for example, light is limited in wave length (which is perceived as hue) and the amplitude of the wave (which is perceived as brightness); motion is limited in distance and speed; heat can be measured by temperature and calories, etc.

One might explain the apparent double quantification of an act as being a measure, in the one case, of the limit of the act in itself, and in the other case of the limit the act has as the act of some body; but this does not always seem to be the case. For instance, in talking of motion, the velocity of the motion (which is its limitation "in itself," so to speak) can be further limited to being a degree of acceleration, in which the velocity itself is increasing or decreasing. Acceleration would sound like a description of an activity very much along the lines of the corner of the edge of the surface of a cube. And, of course, acceleration doesn't need to be constant either; and if it varies in a regular fashion, then it would also have a speed of variation, and so there would be a further level of "meta-acceleration" that would have its own number.

The point, I suppose, is that once you admit that existence is limited, and that the limited existence can be further limited, there is in principle no limit to the number of limitations of limitations there could be.

Next

Notes

1. This, of course, means that Plato's notion that forms and quantities are "the realities themselves" and it is the individual which "shares" in them is false. Aristotle properly saw that it is the individual which is "really real," and these aspects are things that are true of it.

2. But that "form of existence," unfortunately is "value," by which they lead to a more or less important goal--which is your evaluative idea of the "real you" and is your expectations for your future. Actually, this opens up the whole field of economics, in which qualitatively distinct things are compared quantitatively; but the comparison is subjective, not objective, and varies even with a given person a different times. We will get into this subject much later; but in point of fact, it makes "mathematical economics" a farce. Market economics is much more mob psychology than it is something measurable. There is simply no such thing as the "objective degree of desirability" that an object "has." .