Unity

The Error of Parmenides

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Parmenides entirely identified “what can be” and “what can be thought”:

Come now, I will tell thee—and do thou hearken to my saying and carry it away— the only two ways of search that can be thought of. The first, namely, that It is, and that it is impossible for it not to be, is the way of belief, for truth is its companion. The other, namely, that It is not, and that it must needs not be,— that, I tell thee, is a path that none can learn of at all. For thou canst not know what is not—that is impossible— nor utter it; . . . . . . for it is the same thing that can be thought and that can be.

As I pointed out here, the error here comes from an excessive identification of the way a thing is known and the way a thing is. But he does this only in a certain respect. We evidently think that some things are not other things, and that there are many things. So it would be easy enough to argue, “It is the same thing that can be thought and that can be. But we can think that one thing is not another, and that there are many things. So one thing can fail to be another, and there can be many things.” And this argument would be valid, and pretty reasonable for that matter. But Parmenides does not draw this conclusion and does not accept this argument. So his claim that what can be thought and what can be are the same must be taken in a more particular sense.

His position seems to be that “to be” has one and only one real meaning, in such a way that there is only one way for a thing to be. Either it is, or it isn’t. If it is, it is in the only way a thing can be; and if it is not, it is not in the only way a thing can be. But this means that if it is not, it is not at all, in any way, since there is only one way. And in this case it is not “something” which is not, but nothing. Thus, given this premise, that there is only one way to be, Parmenides’s position would be logical.

In reality, in contrast, there is more than one way to be. Since there is more than one way to be, there can be many things, where one thing is in one way, and another  thing is in another way.

Even granting that there is more than one way to be, Parmenides would object at this point. Suppose there is a first being, existing in a first way, and a second being, existing in a second way. Then the first being does not exist in the second way, and the second being does not exist in the first way. So if we say that “two beings exist,” how do they exist? The two do not exist in the first way, but only the first one does. Nor do the two exist in the second way, but only the second one does. And thus, even if Parmenides grants for the sake of argument that there is more than one way to be, he can still argue that this leads to something impossible.

But this happens only because Parmenides has not sufficiently granted the premise that there is more than one way to be. As I pointed out in the discussion of being and unity, when two things exist, the two are a pair, which is being in some way, and therefore also one in some way; thus the two are “a pair” and not “two pairs.” So the first being is in one way, and the second being is in a second way, but the two exist in still a third way.

The existence of whole and part results from this, along with still more ways of being. “The two” are in a certain respect the first, and in a certain respect the second, since otherwise they would not be the two.

Thus we could summarize the error of Parmenides as the position that being is, and can be thought and said, in only one way, while the truth is that being is, and can be thought and said, in many ways.

Defining Order

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Earlier I discussed Aristotle’s senses of before and after. Using yesterday’s discussion of one and many, we can now find a more exact definition of the same terms.

We can define “second” as the formal part of something two, namely the part by which the two is two.

Thus “first” is the part of something two which is not the second. This way of defining first and second may seem backwards, but it is analogous with how we defined the unity of a thing by negating division.

Something first, as such, implies the existence of something second, and likewise something second implies the existence of something first. However, the existence of two implies the existence of one (as a part), while the existence of one does not imply the existence of two. This corresponds to the difference in the definitions of first and second given above. The second is the part by which two is two, while the first is a part, but not the part by which two is two. If first and second are considered only with respect to what is formal in them, then, as “not that by which two is two”, and “by which two is two”, then according to this consideration the first does not imply a second, but the second implies a first.

From this we can see that being before by nature, or as Aristotle says, “what does not reciprocate according to consequence of being,” if not the first thing to which the words before and after are applied, is nonetheless first in the nature of things to possess the before and after.

We can also see that this sense of before and after must be found in some way in all other senses, for every case of before and after will involve something first and something second.

This can be illustrated with the order of time, the first thing to which the words before and after are actually applied. At first it might seem that such a before and after are completely separate from the idea of reciprocation according to consequence of being, since one day can exist without another, nor is it evident that the existence of one day implies that another day existed or that another will exist.

If we consider our actual experience of the past and present (since we have no experience of the future), however, we find something different. Our experience of the present includes our memory of the past, and in this respect implies the past existence of the past. But our experience of the past, namely not the present experience of remembering the past, but the remembered experience of the past that was once present, does not include anything of the present. In this way the present implies the past, but the past does not imply the present, and thus according to these considerations the past is before the present even according to consequence of being.

This is not to deny that according to other considerations the present might be before the past. Rather, these considerations show why the past is considered to be before the present, namely because the present seems to build on the past, as though the past were one block of wood, with the present being a second block of wood stacked on top of the first block. We will find that something similar is the case in every way in which we can say that one thing is before or after another thing.

One and Many

entirelyuseless Logic, Metaphysics

“Many” has two meanings:

  1. That which is divided, namely something and something else such that the something is not the something else. Taken in this way, the idea of many comes before the idea of one, because many in this sense is simply defined by distinction.
  2. A whole composed of ones as parts. In this sense many comes after one.

Using the second definition, we can define numbers according to what sort of parts they have. Thus for example two is something many in the second way, such that it does not have any part which is itself many. Similarly, three is something many such that it has a part which is two, but does not have any part which has a part which is two. One can define other numbers in a similar way. Of course such definitions will quickly become nearly unintelligible as one increases the value of the number. This is not so much a problem with this kind of definition, as a sign of the fact that numbers are not very intelligible to us in themselves, and that we grasp them in practice mainly by the use of the imagination.

Being and Unity

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The unity of a being is simply a certain negation of distinction or division. As was said in the last post, distinction consists in the fact that this thing is not that thing. To say that a thing is one is to say that it is “this thing” rather than “this thing which is not that thing, and that thing which is not this thing”. Thus saying that the thing is one does not deny all distinction, since “this thing” remains “not that thing.” But it denies the distinction within “this thing and that thing,” since this is not one thing.

Or with a concrete example, if I am talking about an apple and an orange, the apple is not the orange, and the orange is not the apple. By reason of this mutual distinction, “the apple and the orange” does not constitute something one. But the apple is one precisely because it is not something like this; “apple” does not name a distinct something and something else. Likewise the orange is one, for the same reason, despite the fact that the apple is not the orange.

St. Thomas explains that it follows that one and being are in some way the same:

“One” does not add any reality to “being”; but is only a negation of division; for “one” means undivided “being.” This is the very reason why “one” is the same as “being.” Now every being is either simple or compound. But what is simple is undivided, both actually and potentially. Whereas what is compound, has not being whilst its parts are divided, but after they make up and compose it. Hence it is manifest that the being of anything consists in undivision; and hence it is that everything guards its unity as it guards its being.

In other words, if you cut the apple into two halves, there is no longer an apple, but one half and another half. And just as you no longer have an apple, you no longer have the being that you had, since that being was an apple. The apple is always one apple; and one apple is always an apple. In this way being and unity are convertible.

On the other hand, just as there are many ways of being, there are many ways to be one. Thus although the two halves are not an apple, and consequently not one apple, they are a pair of apple halves. And being a pair of something is being something at least in some way; and consequently they are also one pair.