Plato's Theory of Forms and the World's Diversity

This paper dates from a fall 2010 Introduction to Philosophy course.

Everyone, it seems, has a concept of justice. We can therefore say that this concept is universal. However, everyone’s definition of justice is different. We can see this as we compare Thrasymachus with Polemarchus in Book 1 of Plato’s The Republic, wherein these two characters approach Socrates’s challenge of defining justice quite differently. Thrasymachus puts forward the claim that justice is “the advantage of the stronger” while Polemarchus is much more circumspect in his definition; in the end Socrates succeeds in dismissing Thrasymachus’s idea. This universality of the concept ‘justice’ can lead us to believe that there is a prototype of ‘justice’ which gets manifested in the minds of most people; this is what Plato would call the Form of Justice. But what occurs in the instantiation of the Form to produce such different definitions of justice wherever it shows up? A similar question might be asked for the ideal Form of a Table; why do tables look so different in their myriad instantiations? Judging from concepts set out in The Republic, the differences between instantiations of forms is due to the mechanism by which the forms become manifest in the human mind, and to the interactions between the instantiations themselves. This investigation will begin with a discussion of the ways in which we can come to know of the forms, and will from there move on to an argument for interactions between the forms based on several examples.

Before delving into the question at issue, it would be helpful to first give a basic overview of the theory of forms as understood by modern scholars. Most agree that the theory of forms is pieced together from various passages and hints in Plato’s dialogues. Some of the most instructive of these are Phaedo, The Republic, and Parmenides.1 These hints usually come to light within Socrates’s efforts to define various general concepts, such as justice or knowledge. Since the character of the theory of forms changes over the course of Plato’s opus, for the purposes of this paper, the theory of forms will be defined solely on the basis of evidence contained within The Republic. In his introduction to Plato’s Forms: Varieties of Interpretation, William Welton writes that, “The doctrine seemed to be that there exist incorporeal, eternal entities which constitute the ultimate reality, and the ordinary things of the changing physical world around us are in some sense mere imitations of these ultimate realities. These eternal realities, beyond space, and time, seem to have something like the nature of what we would call abstractions or concepts, except that the forms are objective entities that do not depend at all upon the human mind for their being…[and which] have a radically different mode of existence from the kinds of things—physical individuals or ‘particulars’—that we habitually take as most real” (3). A form is a kind of universal upon which all derivations depend for their existence; for example, all justice in the material world depends on the unchanging Form of Justice.

Perhaps the most captivating information on the forms comes from the end of Book 6 of The Republic and the beginning of Book 7, what are known as the allegories of the sun, the line, and the cave. In these passages, Socrates explains that “What the good itself is in the intelligible realm, in relation to understanding and intelligible things, the sun is in the visible realm, in relation to sight and visible things” (508b, c). In this way, he is putting forth the idea that the form of the good is what causes the other forms to be knowable, just as the sun causes everything in the material world to be visible. As Glaucon, Socrates’s interlocutor, says, “Not only do the objects of knowledge owe their being known to the good, but their being is also due to it, although the good is not being, but superior to it in rank and power” (509b). Thus when examining how the forms come to be projected into the material world to give being to the things which participate in them, it seems that the good is what is responsible for this projection. This language of ‘projecting’ the forms is in keeping with the allegory of the cave, in which the good is visualized as a giant fire beyond the cave opening, the forms as objects being carried in front of the fire, and the instantiations of the forms as shadows of the forms themselves projected onto the cave wall.2 If this vague notion of ‘projecting’ suffices for how the forms come to be instantiated in the material world, how can humans come to know the forms themselves?

Knowledge of the forms in the human mind is what causes many of the forms to exist as particulars. Knowing what justice is allows us to act justly or to be just, just as knowing about tables allows us to make tables if we so desire. In this way, humans become a means of the ‘projection’ of the forms. Many forms, of course, are independent of the human mind, namely those of things in the natural world. However, they can still be objects of knowledge and of projection by humans; we can say that someone is ‘a star’ or that in anger one becomes ‘like a tiger.’ For the forms of the natural world, our mode of projection is solely through metaphor and allegory. After close inspection, it seems that there are four main modes by which we can come to know the forms: education, divine action, necessity and recollection.

Education is perhaps the most plausible way by which we can come to recognize the forms. Plato spends much of The Republic explaining the proper education for citizens of the kallipolis, the most perfect city. In these discussions, he puts forth the idea that the most educated will know the most about the forms and that knowledge of the forms causes the form to become instantiated in the knower. “Because rhythm and harmony permeate the inner part of the soul more than anything else, affecting it most strongly and bringing it grace, so that if someone is properly educated in music and poetry, it makes him graceful, but if not, then the opposite” (401e). This example makes clear the power of education in music to effect the instantiation of the form of Grace. Another excerpt makes this concept clearer: “Then the philosopher, by consorting with what is ordered and divine, himself becomes as divine and ordered as a human being can” (500c). The philosopher, who according to the structure of the kallipolis, spends most of his life in school, is able to see the forms more clearly than anyone else and, by having this ability, personifies the forms more perfectly than anyone else and is able to bring them into instantiation more perfectly than anyone else.

The next method is that of divine action, whereby some force or actor plants knowledge of the forms into minds at will. This would make all knowledge of the forms a priori as one would not need empirical knowledge of the world to know the forms by their instantiations. This method, while plausible, is not supported by The Republic, and in fact runs dangerously close to the Third Man argument, where for any interaction between a form and its instantiation, there needs to be a form for that interaction, and so on into an infinite regression. In this case, there is a third party in the world of forms that puts knowledge of the forms into our minds but in order for us to know this there would have to be something that puts knowledge of this third party giving us knowledge into our minds, and so on.

Another method that is not mentioned in The Republic is that of knowledge of the forms through necessity. This means that the forms become known to us as we have a need to know them. One day we need to have a place elevated above the ground to write on; the rocks are too uneven and the pen punctures the paper when we write on softer surfaces. Thus we invent a table. Once there are enough tables, we begin to notice a commonality between all of them which we might call ‘tableness.’ This then leads us to knowledge of a form of the Table. Similarly, if our community is experiencing a high homicide rate, we might need to find a means to deter more of them from occurring, thus inventing a concept of justice. One might find a contradiction here in that we enact the instantiation of the form before knowing the form. A response to this objection is that before enacting the instantiation we already have a concept of the form (we have to in order to want to instantiate it) but have no experience of it, thus we don’t know that we know the form.

Finally, there is the theory that Plato himself puts forward—the theory of recollection as explained in Meno. Here Plato posits through Socrates that we already know everything there is to know before we’re born due to reincarnation. Once one dies, one travels to the world of forms and there gains knowledge of all of them.3 Once we are reborn we forget all this knowledge until we remember it, either by necessity or education.

Again, the method-by-education is the most plausible of these, even though it does not explain how the first person came to know the forms without someone else to teach him or her. But it does provide intimations regarding the problem at hand: accounting for the differences between instantiations of the same form. Most importantly, it shows that, according to The Republic, one can participate in the forms by degrees and that knowing a form is participating in that form.

This exercise in figuring out by what means we come to know the forms was not in vain. Indeed, it will become of the utmost importance later on, for now we turn to the main topic of discussion.

In accounting for the differences in instantiations of the same form, it might be instructive to form a visualization or allegory for the process. The best way to do this is probably to borrow from and add to an allegory that Plato has already put forth, namely that of light. If one lets a beam of light stand in for a form, then when a beam of light hits a glass prism, it diffracts into its component hues. This spectrum is analogous to the spectrum of different instantiations of the same form. When the immaterial form interacts with the material world, it gets diffracted into instantiations, just as the immaterial form of light diffracts when it meets the matter of the prism. This is hinted at in the Allegory of the Cave as the shadows of the objects being carried in front of the fire need to be cast upon the wall of the cave in order to become manifest. How then to account for which instantiation ends up where?

To extend the allegory, white light hits an object such as a rose. Most of the wavelengths of light are absorbed into the rose, but one wavelength is reflected, that of the color red. This makes the rose red rather than green or blue. The rose has a natural disposition to appear red due to the molecules which make up its pigments. In a similar vein, certain parts of the world of matter might have properties which make them more accepting of certain types of instantiation rather than others. Therefore, an object would have a natural disposition to be a writing table rather than a table for cutting vegetables on.

This explanation, however, seems to be too simplistic to explain the enormous variation in the particulars of the forms as it cannot explain change in the form’s instantiation over time, nor does it explain degrees of participation in forms, something that needs to be accounted for after the discussion of how people come to know the forms. It seems clear that the forms must interact with something else in order to change how they become manifest in the material world, and if that something is not the material world itself, it must be that forms interact with other forms. Indeed, this is supported by numerous examples, as well as by evidence from the discussions in The Republic.

It might be prudent to begin this discussion with examining all of the conditions that would have to be met in order for the forms to be able to modify each other and from there it should be simple to prove that this occurs and explains diversity in instantiation. First, a form must be able to instantiate in the same location as other forms. Second, the forms would have to be able to instantiate in degree rather than as complete imitations of the universal, otherwise there could be no diversity in instantiation which is contrary to what we experience in the world. Finally, a form must be able to exist in the same location as its opposite, for this is the primary way in which a form could instantiate in degree.

Socrates says much in The Republic concerning the ability of forms to instantiate in the same location, and tends to support the idea that this is almost always the case. When discussing universal forms versus their particulars, Socrates says, “Knowledge itself is knowledge of what can be learned itself (or whatever it is that knowledge is of), while a particular sort of knowledge is of a particular sort of thing. For example, when knowledge of building houses came to be, didn’t it differ from the other kinds of knowledge, and so was called knowledge of building?” (438c, d). In this case, the form of knowledge and the form of building came to be instantiated in the same location to produce a hybrid, knowledge of building. In his discussion with Glaucon on thirst, Socrates says, “Therefore a particular sort of thirst is for a particular sort of drink. But thirst itself isn’t for much or little, good or bad, or, in a word, for drink of a particular sort. Rather, thirst itself is in its nature only for drink itself” (439a). Here, Socrates is saying that the form of thirst is the opposite of the form of drink, but when the instantiation of the form of thirst coincides with the instantiation of another form, that of drink does as well. In this way, if we are thirsty and it is hot outside, we might wish for the form of drink to become instantiated with the form of coldness. If we are very thirsty, we might wish for it to become instantiated with the form of largeness.

The Republic also supports the idea that a form can be instantiated in degrees. After their discussion of the sharing of mates and children, Socrates and Glaucon return to their discussion of justice and injustice. “’But if we discover what justice is like, will we also maintain that the just man is in no way different from the just itself, so that he is like justice in every respect? Or will we be satisfied if he comes as close to it as possible and participates in it far more than anyone else?’ -‘We’ll be satisfied with that’” (472b, c). Here, by acknowledging that someone can come as close to being like justice in every respect as possible, Socrates is really saying that one can move along a scale in terms of participation in the form of justice. In “Middle-Dialogue Forms are Universals,” a chapter within his Plato on the Self-Predication of the Forms, John Malcolm puts forth this example: “Suppose we have a series of increasingly imperfect circles. At some point they become so oblate, say, that they no longer count as circles. Yet, of those which do so qualify, some may sensibly said to be more circular than others. While each degree of imperfection is unquestionably an instance of that degree of imperfection, this is irrelevant to the point under consideration which is the instantiation of ‘circle,’ not that of ‘figure at 98 percent of absolute circularity.’ There is no reason in principle why instances of a universal, F-ness, cannot be those which are F to a degree or within certain specified limits. Although the instances all possess F-ness, some possess F-ness more than do others” (8, 9). In other words, something can participate in the form of circle to a certain degree without participating fully. Indeed, if we look at the material world, nothing participates in the form of circle perfectly—there are always slight imperfections. Even circles in computer aided drawing programs, software which is marketed mainly on the basis of its precision, are composed of a large number of segments of tangents, rather than as perfect circles.

Finally, instances of forms can coincide with instances of their opposites. In discussing lovers of beauty, Socrates and Glaucon have this back-and-forth:

“The lover of sights who wouldn’t allow anyone to say that the beautiful itself is one or that the just is one or any of the rest: ‘My dear fellow,’ we’ll say, ‘of all the many beautiful things, is there one that will not also appear ugly? Or is there one of those just things that will not also appear unjust? Or one of those pious things that will not also appear impious?’
-There isn’t one, for it is necessary that they appear to be beautiful in a way and also to be ugly in a way, and the same with the other things you asked about.
-What about the many doubles? Do they appear any the less halves than doubles?
-Not one.
-So, with the many bigs and smalls and lights and heavies, is any one of them any more the thing someone says it is than its opposite?
-No, each of them always participates in both opposites” (Republic 479a, b).
This is solid evidence that according to The Republic, instances of forms not only coincide with instances of their opposites but, in fact, always do so.

So with these three conditions satisfied, we must now prove that the forms modify each other in their instantiations. A good way to start is to move back to the discussion of thirst mentioned earlier. Eventually, Socrates starts to wonder about why people who are thirsty can hold themselves back from drinking. He says, “Hence the soul of the thirsty person, insofar as he’s thirsty, doesn’t wish anything else but to drink, and it wants this and is impelled towards it…Therefore, if something draws it back when it is thirsting, wouldn’t that be something different in it from whatever thirsts and drives it like a beast to drink?” (439a, b). Socrates uses the existence of this ‘something’ to advance a notion of a tripartite soul in which the thirsting animalistic part is held back by the moderating rational part. What if this was not the case, or at least not the complete explanation? Since we see that instances of different forms may exist in the same location, and that forms can occur in degrees, might it be that the form of thirst is being tempered by another form, that of moderation? Indeed, Socrates is open to this sort of interaction between forms in another part of The Republic. “And the same account is true of the just and the unjust, the good and the bad, and all the forms. Each of them is itself one, but because they manifest themselves everywhere in association with actions, bodies, and one another, each of them appears to be many” (476a). It seems probable that in this excerpt the association of forms with actions and bodies produces ‘manyness’ while association with each other produces differences between instances of the same form.

Indeed, going back to John Malcolm’s example of the circle, we could say that the imperfection in the instances of this form is due to the influence of other forms. When the form of circle interacts with the form of line, an ellipse results. When Circle interacts with Incomplete, an arc results. This sort of analysis holds for many other examples as well.

To continue with the example of a table, when the form of Table interacts with other forms, this results in a variation in the shape of its instance. When Tableness interacts with Longness and Woodness, the result is a long, wooden table. When it interacts with Squareness and Plasticness, it results in a square, plastic table.

This is most clearly seen with colors. When we say something is blue, we could be talking of any one of a number of shades such as navy blue, sky blue, or cerulean. The form of Blueness interacts with the forms of other colors, as well as the forms of darkness and lightness to produce all of these shades. The ability of degrees of forms to occur in their instances is an obvious enabler of this as a color which is part green and part blue can be said to be blue-green. Which one it is depends on our ability to discern which form is instantiated more strongly.

It is interesting to note that an artist manipulates this mixing of forms consciously and with a high degree of intentionality. This brings us back to the discussion of the effects of knowing the forms. If, as shown before, knowing the forms results in being able to instantiate the forms, then knowing how the forms interact can result in greater control of the eventual outcome of this interaction. This is why the philosopher king is most suited to rule the kallipolis—he or she knows best how to manipulate the interactions between forms to create and maintain it. Socrates might even say that the philosopher king becomes god-like for this reason. As humans come to know more and more of the forms, not only those that occur in our souls but those of the natural world as well, we come to be able to affect the manner of their instantiation to a greater degree, giving us the power to maintain or destroy the world. If to know a form is to participate in it, then perhaps to know that one participates in it is to be able to change the degree of participation.

1. Welton, William A. Introduction. Plato’s Forms: Varieties of Interpretation. Lanham: Lexington Books, 2002. 8.
2. The Republic. 514a, b.
3. Plato. Meno.

Other works cited:
Malcolm, John. Plato on the Self-Predication of Forms: Early and Middle Dialogues. Oxford: Clarendon Press, 1991.
Plato. The Republic. G.M.A. Grube, trans. Indianapolis: Hackett Publishing Company, 1992.
Welton, William A., ed. Introduction. Plato’s Forms: Varieties of Interpretation. Lanham: Lexington Books, 2002.


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