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One further feature of the theory of Forms must be mentioned here: the view that there is a supremely important Form, the Form of goodness, or of the Good, which somehow determines the contents of the world of Forms and brings order into it. In a celebrated but brief and tantalizing passage in Politeia, the Form of the Good is spoken of as being to the intelligible realm what the sun is to the visible realm; just as the sun makes living things grow and renders them visible, so the Good is responsible for the existence and intelligibility of Forms, though it is itself “on the other side of Being.” This passage had a tremendous historical influence on the Neoplatonists, who saw it as anticipating the ultimate ineffable reality—the One, from which everything describable was in some way an emanation—in which they came to believe. It seems possible, however, that Plato had no such mystical thoughts in mind but simply wanted to say that the world of Forms is ordered through and through, everything in it being there for a purpose. The Form of Good is, in fact, the counterpart of the nous (Mind) of Anaxagoras, another of Plato’s predecessors, which was supposed to arrange everything for the best. Categories and universals

The most famous critic of Plato’s theory of Forms was Aristotle, who devised his doctrine of categories largely to counter it. According to this doctrine, “being is spoken of in many ways”: one can say that there are such things as individual horses, but one can also say that there is such a thing as being a horse, or as being upside down. Expressions can be classified under various heads: predicates signify substances (e.g., “man” or “horse”), qualities (e.g., “white”), relations (e.g., “greater”), quantities (e.g., “three yards long”), time (e.g., “last year”), and so on—sometimes Aristotle listed ten categories, sometimes only eight. The kind of being that any predicate possesses, however, is derivative in comparison with the being of an individual substance, a particular man or a particular horse. It is such things that exist in the primary sense, and it is upon their existence that the existence of other types of being depends. Or, to put the point in not quite Aristotelian terms, primary substances are the only concrete existents; Socrates, the bearer of a proper name, exists in a way in which humanity or whiteness or being greater do not. The latter are really no more than abstractions, and nothing but confusion can arise from neglecting that fact.

Aristotle with a Bust of Homer, oil on canvas by Rembrandt van Rijn, 1653; in the collection of the Metropolitan Museum of Art, New York. 143.5 × 136.5 cm.Photos.com/Thinkstock

Mention has already been made of the difficulties into which this doctrine led when it came to describing primary substances; it appeared that these entities could not be characterized but only named or pointed to, a conclusion accepted much later by Ludwig Wittgenstein, a 20th-century philosopher, in his Tractatus Logico-Philosophicus and by Russell in his lectures on logical atomism. These difficulties, however, were not seen at the time the theory was promulgated, and it is more important here to emphasize the fact that it undermined any doctrine of the Platonic type. To argue that Forms, or numbers, alone are real is to argue for the reality of abstractions; to put the point succinctly, beauty exists only so long as something is beautiful, and that something must be a concrete individual. Or if this is not quite true (for, after all, it could be said that there is such a thing as having a million sides even if nothing in fact has a million sides), concrete existence must precede abstract existence in some cases at least: the “x” in “x is red” must sometimes be replaceable by an actual rather than a merely possible entity.

A prominent subject of philosophical discussion in the Middle Ages was what came to be known as the problem of universals, which concerned the ontological status, or type of existence, to be assigned to the referents of general words. One of Plato’s critics had said, “I see particular horses, but not horseness”; and Plato had answered, “That is because you have eyes but no intelligence.” There can be no doubt that Plato thought that horseness, the Form of horse, or Horse itself, to use his own expression, was something that existed separately; it could be discerned not by the bodily eyes but by the eye of the soul. The view that besides individual horses there also exists the Form of horse was known in the Middle Ages as Realism. Aristotle was also alleged to be a Realist, because he too thought that Forms were really there, although only as embodied in particular instances. More skeptical philosophers denied the reality of universals altogether, some identifying them with thoughts (conceptualists), others with mere names (nominalists).

The dispute about universals was in fact very confused. At least two quite separate issues were involved. First of all, there was the question about the status to be assigned to whatever it was that predicates referred to; this question seemed urgent just because, for example, geometricians were able to discuss the properties of the triangle or the circle. What and where were the triangle and the circle? In fact, the Aristotelian doctrine of categories had already indicated that the being of any predicate was necessarily different from that of primary substances; the circle did not and could not exist as this man or this horse did. When Aristotle is described as a Realist in the dispute about universals, the description is very misleading. In one sense he did not believe that universals are real at all; in another sense, however, he did, and this is where the second issue arose. Some people who denied the reality of universals wanted to say that all classification is artificial; the descriptions men give of things depend upon their interests as much as upon what is really there. Aristotle, by contrast, believed in a doctrine of natural kinds; he thought that every particular horse, for example, embodied the form or objective essence of horse, which was accordingly a genuine, if abstract, constituent of the world. The question of the extent to which classification is artificial is clearly quite different from that of the status of universals; it remains to be answered even if the latter problem is dismissed, as it is by modern philosophers who say that only proper names and individuating phrases have referents; general words do not. These differences, however, were not clearly seen either in the Middle Ages or during the 17th century, when the whole question was discussed at length by philosophers such as Thomas Hobbes and John Locke. Basic particulars

In discussions of the problem of universals, it was frequently claimed, especially by nominalists, that only particulars exist. The notion of a particular is in many respects unclear. Strictly speaking, the terms particular and universal are correlatives; a particular is an instance of universal (for example, this pain, that noise). It would seem from this that particulars and individuals should be the same, but there are writers who distinguish them. Bradley, in his Principles of Logic (1883), treated particulars as mere momentary instantiations of universals and contrasted them with individuals as continuants possessing internal diversity. An individual can be not merely identified but also re-identified; because it lasts through time, it may possess incompatible attributes at different periods of its history. A particular, on the other hand, is nothing but an instantiation of an attribute and as such must possess that attribute if it is to be anything. Similarly, a particular can be met with once, but not again; as time moves on, it passes out of existence and is replaced by another particular that may resemble it but is not literally identical with it.