Sophist [1] - Plato's View On being and non-being

Abstract
The Theory of Form, as proposed in Republic, is the hallmark of Plato's metaphysics. However Plato did not view it as a final answer to the quest of being. In this essay, I gave an outline to a revised theory on being described in Sophist, with comparison to other philosophical thoughts.

Introduction
The Sophists are often viewed as rivals of Socrates, because of their contrasting characters in attitude and theory. In the Dialog Sophist, Plato gave a complete refutation to the universalism and relativism of the Sophist school, therefore declaring that they have nothing to do with true statesmans and philosophers. At the same time, by making use of the words of a countryman of Parmenides (simply called "Stranger" in the Dialog), Plato brought his response to contemporary thoughts of his time, and built a new theory on being and non-being.

In this Dialog, the argument was delivered by Stranger instead of Socrates, when discussing with Theaetetus, a student of Socrates. Similar to other Dialogs, the discussions do not focus on any single theme, and the arguments are not straight forward and are lack of focus.

First, Stranger located the nature of Sophists' work as "imitation — making of semblance" after lengthy dichotomous division on the concept of "work" (218d - 230e). Here, the term "imitation" has the same meaning as in Republic, book X, when Plato criticized arts as imitations of appearance (597b), though in this Dialog the imitation under criticism is different. The semblance Sophists make, is "a person who understand everything", as it is not possible to be such a person (233a - 236e).

The discussion reached a turning point when Stranger pointed out the difficulties on describing such semblance. Since it is not possible for "a person who understand everything"  to exist, it seems contradictory to talk about him at all (239e - c). So they started analysing the concept of non-being (256e - 264b), after equally detailed analysis on what being is (242c - 256d). Finally they concluded that the Sophistic imitation of knowledge is just opinions, instead of divine truth. So the Sophists' claim of universalism is refuted (264c - 268d).

In this essay,  I will only concentrate on the analysis of being and non-being, while skipping all the sections on classification of work of Sophist, and the discussions on form and object at the end, which are not relevant to our major concern.

Being — what is
It is important to identify what being is, before talking about non-being. Without such a reference, it is not possible to make any comparison between the two opposing sides.

Talking about being is to talk about the criteria of what is meant to exist, and how such entities interact with each other. Therefore Stranger first presented several prevailing theories of reality, which refers to different versions of Ionian and Eleatic teachings, arguing for a changing whole against an eternal one, respectively (242c - 243b). Stranger viewed all such doctrines not being convincing, because they failed to distinguish the relation between reality and other factors, such as number and motion.

Arguing against the naturalistic view (246e - 247e), which held that everything having a body is real (therefore everything in the "visible realm"), otherwise not, Stranger pointed out that soul and virtues are bodiless. Since the naturalists admitted whatever can come to be present or absent from a thing is real, they are then self defeating. He suggested to use "the power to affect or to be affected" as the criteria of judging whether something is real, which accepts both body and bodiless entities as existence.

On the other hand, when arguing against the theory of Form (248a - 249c), Stranger found that it is impossible for Forms to be unchangeable, if they are to be known, or are to be projected to form the "becomings". It is because Forms are not supposed to be acted on or act, since such actions belong to the visible realm which Forms are separated from; and acting itself represents changes, which is contradictory to eternity. It also sounds strange to imagine the Form of a living organism to be stationary. Therefore unchanging must not be the sole criteria of reality. Equally speaking, changing cannot stand alone, because no intelligence is possible when there is an absence of stationary reference point.

It is remarkable that Plato now pointed out the weaknesses of his theory of Form by stating the difficulties of eternal Forms. But it does not mean a complete abandonment of his partition of intelligible and visible realm, as shown at the end of this Dialog. Instead, he is now trying to revise his view on being to be a more down-to-earth version.

From the refutation of stationary form, we see that both movement and rest are fundamental. Each of them cannot stand alone, but both of them are real. As a result, Stranger introduced existence (or reality), which serve as a "vehicle" of either movement or rest, to be another fundamental (250b - c). Stranger maintained that some of these three must "blend", otherwise we cannot explain why things happen in the way we see, i.e. keep changing. By using an analogy of grammar which regulate the possible combination of words, Stranger suggested that some blending are allowed while some others are not. So it is obvious that existence can blend with each of the other two, with no other possibilities (252d - 253c).

By Law of Identity — A ≡ A, each of these three must be the same as itself. It is no doubt that they are also different from one another. Therefore we have to add two new members (255d).

The impermeability between movement — rest and sameness — difference is obvious. Their relation with existence is more subtle. Since movement and rest exists, if existence is equal to sameness, then movement and rest, when blending with existence, become the same, which is not possible. Similarly, if existence is difference, then actually we cannot tell what the difference is, without any common ground for comparison.

Therefore, we can briefly conclude that "a thing" "possesses" five "characteristics" [2], namely existence, movement, rest, difference, and sameness. They blend with one another, following the rules stated above.

Some may found such a theory resembling Aristotle's Category because of several similarities. It is possible to treat existence as similar to substance, which are substratum for other accidentals to occur upon. While movement and rest hold similar meaning to kinesis, with less detail on the nature of change. And finally difference and sameness refers to the overall comparison in all aspects. Maybe we can view Plato's theory as a preliminary version of Category, but we should also notice how much more exact details were told in Category, and the fundamental difference between Plato's existence in heaven and Aristotle's individual based substance.

Non-being — what is not
Stranger introduced the trouble of non-being when discussing how difference and existence blend (256d - 257a). It is to say that, something which is completely different from existence, is of course "non-existence" (that which is not). But it is self defeating to say that non-existence exists.

Plato did not view the problem like this, as Stranger claimed that that which is not is not in contrary to what is, but simply different from what is. Similar to other cases of absence of certain properties such as "not tall" is just the same as "short"; while "not short" just means "tall". Any thing which are "not tall" does not undermine the existence of other things that are "tall" (257b). This sort of analysis was accepted by Aristotle in his analysis on change in book XI of Metaphysics, which stated that changes must either be from the positive side to negative side, or the reverse. Therefore the so-called "not something" is just a privation of that something, and can be regarded as contrary. We can therefore view "not something" and something as two extremes of a certain quantity on a thing, which can change arbitrarily without affecting the existence of the thing.

Plato described this explanation as a victory over Parmenides's prohibition of talking in the direction of "not something", by which the verbal puzzle of non-existence is solved. However I do not find this explanation satisfactory, because Plato just solved a lower level of non-being which is the absence of accidentals, without tackling the problem of nothingness.

In the previous discussion of being, Plato shown that existence, movement, rest, difference, and sameness are the fundamentals. Within these five, movement and rest, difference and sameness form two pairs. In each pair, the two are opposing and impermeable, which is not the same as the privation of other external properties, because each of them cannot stand alone, as shown before. However existence stands on its own. But we can still imagine an exact opposition to existence, which is also different from the other four.

Plato did mentioned about this kind of non-existence (257b), but he did not go into details, and claim that non-existence is just privation. These are entirely different matters in two different levels, but Plato did not fixed the former one. Some may regard this concern simply as horror vacui, or some kind of verbal tricks. However I believe it is important to answer on the status of this kind of logical impossibilities. Even if "void" is accepted as being, as suggested by Democritus, the status of non-being is still suspended, because one can form an infinite regression of non-being, no matter what else are accepted as being. Therefore it is probably a defect which is unavoidable in the studies of being.

The last trouble lies on the way to talk about non-being. As we have seen, Plato viewed non-being as a privation. A privation of truth is of course falsity. So the present difficulty is whether non-being blends with discourse. Otherwise there would be no ground talking about falsity and therefore refuting the Sophists' relativism on lack of falsity (260b - d).

From the basic sentence structure, Stranger point out that there must be both subject and verb to make a statement. The statement must be about something instead of nothing. On other words it must be a denoting phrase (262a - e). Each statement has a character of either true or false. A true statement states the things that are as they are; while a false statement states the things different from the things that are (263b).  As a result, by using a rather empirical criteria of being correspondence to what is, Stranger described how discourse is related to falsity.

In modern view, Plato's analysis on statement is insufficient, because he just considered some very simple statements such as "Theatetus sits", and therefore did not see any complications concerning the subject. Though a statement must be about something, the something in the statement may 1) exist e.g. "Theatetus" in "Theatetus talks"; 2) not exist e.g. "a disciple of Socrates" in "A disciple of Socrates is talking to Stranger now"; or 3) exist, but is denoted ambiguously e.g.  "Someone" in "Theatetus is now talking with someone" [3]. Case 1) and 3) can be handled easily. But when dealing with case 2), it will be more difficult to judge the truth value. For the sake of completeness on the discussion of statement, I will introduce a modern view to cope with case 2), though it may not be an important problem in Plato's time.

Considering the statement A: "A disciple of Socrates is talking to Stranger now". "A disciple of Socrates" surely does not exist nowadays, so is the statement false? Then what does B: "A disciple of Socrates is not talking to Stranger now" mean? Since we cannot find "a disciple of Socrates" in the set of people of either talking or not talking now, what is the truth value of this statement [4]?

In On Denoting, Russell suggested a distinction of two different kinds of occurrence of the denoting phrase. A proposition contains a denoting phrase, e.g. A contains the denoting phrase "a disciple of Socrates". We can interpret this proposition as A1: "There is a man who is talking to Stranger now, and that man is a disciple of Socrates". In this case, the situation of the denoting phrase affects the whole proposition, thus called a  primary occurrence. Another possible interpretation is A2: "It is true that there is a man who is talking to Stranger now, and that man is a disciple of Socrates", in which the denoting phrase is a mere constituent which is to be considered alone, instead of affecting the whole proposition. Therefore it is called a secondary occurrence [5]. There are practical difficulties in determining whether a denoting phrase is in primary or secondary occurrence. But such a distinction does help to determine the truth value in principle.

When the denoting phrase is denoting a non-existing entity, all propositions in which there is primary existence of such a phrase are false, because the non-existence of that entity decided the proposition to be false. However it is more complicated for secondary occurrence.

Obviously the proposition A2 is also false, as no one is now talking to Stranger. Then let us consider B: "A disciple of Socrates is not talking to Stranger now". Its primary occurrence B1: "There is a man who is not talking to Stranger now, and that man is a disciple of Socrates" is false for sure; while the secondary occurrence B2: "It is false that there is a man who is talking to Stranger now, and that man is a disciple of Socrates" is true! It is then clear that such a distinction, though looks redundant, is crucial when we are dealing with non-existing terms. Otherwise we may get totally opposite meanings.

This analysis is applicable to many different kinds of non-existing entities, including those which is logically possible but does not occur; the logically impossible once; as well as fictitious names (such as Apollo, Venus, etc.). As a result, by checking whether the subject is in primary or secondary occurrence, we can go further to talk about the truth value of statements denoting such non-existing entities, which is a step forward on the discussion of non-being, and avoid all possible sophistry on this issue.

Conclusion
In the beginning of this Dialog, Plato intended to refute the universalism and relativism to of the Sophist School. He did so in such an exhaustive manner which turned out to be a detailed investigation on the concept of being and non-being. In the discussion of being, Plato refuted his contemporaries on the debate of whether the reality is changing or unchanging; many or one, as well as his own theory of Form. He them established a more generalized and experience based theory of reality, accepting both movement and rest, difference and sameness as reality.

At the side of non-existence, Plato suggested that it is just a privation of properties, instead of being contradictory to existence. As a result, one can speak about false arguments without contradictions, which spared no place for sophistry to hide. However this analysis on non-existence is not completed in two ways. First, Plato did not give a satisfactory account on the case which non-existence is contradictory to existence. Second, he did not articulate how one should talk about false arguments, which was left until 20th century to be solved.

Bibliography and Notes
1. Plato. Sophist. Trans. F. M. Cornford. In Plato: The Collected Dialogues, ed. E. Hamilton and H. Cairns (Princeton University Press, 1961), 957 - 1017.
2. The use of words in quotation is obviously inappropriate, concerning the subject in discussion. But I cannot think of better substitutions.
3. Bertrand Russell. On Denoting. In Logicism and the philosophy of language: selections from Frege and Russell, ed. A. Sullivan (Broadview Press, 2003), 235.
4. Same article as 3. 240.
5. Same article as 3. 245.