Show Me the Numbers

Misshapes the beauteous forms of things,

we murder to dissect

William Wordsworth

To understand Plato's Doctrine of Ideals, or the Forms, I had to think back. I clearly remembered early attempts to draw a horse. Not just a horse, but the horse. The picture that came to mind wasn't a horse like those I saw outside, but a black-and-white image of the ultimate horse: grace and strength embodied in bold, unfailing lines: it wasn't a literal horse, but something better because it was perfect. As a phenomonologist, I hesitate to think that what I saw was actually a memory from the time I spent drifting as undifferentiated vapor through some vast hall of Forms. Yet that is exactly the explanation given by Plato for what I experienced. He took the best of what was known and followed it to his best logical conclusion. W.T. Stace, in his Critical History of Greek Philosophy, explains: "From Socrates he took the doctrine of concepts, and proceeded to identify the Eleatic Being with the Socratic concepts. This gives him his theory of ideas" (193). Understanding how he got there, by reconciling Parmenedian physics with Socratic ethics, we are in a position to respect what he did in formulating the doctrine, but, like Aristotle, we have leisure to remark on some glaring flaws.

If, in Platonic terms, "All we can know of the mountain is the Ideas in which it participates" (Stace 193), we may not actually know the mountain, since we are not allowed to trust in sensory observation of it--and haven't been since Parmenides. However that begs the question, what exactly are we observing when our senses claim we are before a mountain? An Aristotelian answer might be along the lines of "...the word substance has three meanings--form, matter, and the complex of both--and of these matter is potentiality, form actuality" (Baird 366). So the mountain does contain the Idea--potentiality--but that is nothing without matter, without which no "actuality" is possible.

One can think of the perfect horse, the one animal after which all others are modeled. The same can go for dogs or outlaws: a perfect Form can be imagined, perhaps even remembered from the eternal verities, as Plato surmised. But they fall short when it's necessary to find the model for grace or power, or anything not of concrete form on earth--nouns fit the scheme more readily, and believably, than adjectives. According to Plato, this is because what we see and experience on earth is but a shadow of the way things really are. "That is to say, they [we] must recover the knowledge of the perfect Idea of which all the goodness in this world is but a pale, unsteady reflection' (Guthrie 100). Such things cannot even really be imagined, though they may be universal. Even in the case of love, the most important virtue of them all, we can think of the body and mind of the beloved and exalt them: the person at least, but at some point, if love succeeds, that person must be fed, clothed, and washed. They are not an ideal but a human being. Thus the Platonic concept of the Forms, while noble, is insufficient. We exist in a world of pain and pleasure, hunger and plenty, order and disorder: we not only can but must act, and our acts take place in a world of experience. In the end, even if the Forms themselves are out there, guiding us, we take our chances and accept the consequences here, not in some ethereal stage where Ideas recline, perhaps dreaming themselves into ever newer and more spectacular manifestations. Moreover, the Forms of Plato's day were limited to the actualities of Plato's day: they cannot predict or anticipate what might be created in the future. To venture along those lines leads to conceiving of divinity as a novelist who writes the ending first, and only then considers plot and character. As though we exist only to fulfill a pattern set and waiting at an unspecified date and time, but toward which we are inevitably drawn, as though in a vacuum. In other words, if the Forms do contain perfect models of everything, and not models, but originals, they can only have been created at the end of time, when all that happens during time is already known.

Parmenides had insisted on the existence of something eternal and permanent, perceptible not to sense, but to reason. Plato followed by reasoning out the realm of the Forms, proceeding from Socratic proofs of immortality which considered as self-evident the existence of a kind of intelligence apart from living human consciousnesses. If we (as disembodied souls) did not exist in another realm, there would be no souls to animate bodies in this realm. It's not a perfect cosmology because it fails dramatically at establishing cause--we have no way of knowing where the Forms themselves come from, or even where they are. However it was sufficient for Plato to arrive at the Doctrine of Ideas.

Plato's most severe limitation was, as he understood, that things change. Thus there could be no certain knowledge, except, "...if its subject stands fixed before the mind, is permanent and changeless. The only knowledge is the knowledge of the Ideas" (Stace 192). To a Greek mind, these ideai were not, as the English meaning suggests, the ephemeral product of daydreaming minds, but full and complete, independent entities. Plato saw that it was necessary to define abstract terms such as good, to discover what about "good" was universal. If one understands that "good" has a meaning apart from describing an apple or a night on the town, it follows that there ought to be a being called "Good" who embodies the characteristics of goodness. And this being ought to be able to stand 'before the mind.' That he does not stand before the eyes is at once Plato's great weakness and his great strength. Even if it takes a leap of faith, or deduction, to "see" the Forms, the reasoning Plato supplied for their existence can be convincing. The syllogistic force of his argument resonates through time, so that William Barrett could write, in The Irrational Man, "It has been said that every man is born either a Platonist or an Aristotelian" (141). That is to say, some of us are more willing to make that leap than others.

Barrett compares Jonathan Swift's kingdom of Laputa--"an island that floats in the air" (120), to Plato's place of the forms. "Laputa might thus be called the kingdom of the pure Platonists" (121). The Laputans live with one eye turned toward the stars and the other focused inward, an impractical arrangement. Much of their world is similarly awkward: they wear clothes measured with nautical instruments rather than tailor's implements, and eat food cut into geometric shapes. They cannot even manage to walk in public without a servant, more observant, signaling to them what to do next, so lost are they in contemplation of abstractions. Barrett sees in the incident of a Laputan wife taking up with a drunken footman a sharp criticism of the distance Plato infers

between our actual lives and their ethereal mirror-images. "Women as creatures of nature

Swift surely saw in Plato a fatal reliance on faux-intellectual speculation. Myth created the ligature holding his doctrine together, and linking the world we see to the world that it suggests must exist elsewhere. The more rational Aristotle admits that what we know cannot be accounted for by what we see, and relies on "divinity" as a source: reason "enters from outside and is divine" (Guthrie 145). Modern physics and biology has articulated the substrate; we can reliably say what we're composed of, contemplating the cell and the microbe as well as the peculiar qualities of light, but we have yet to take a step past where Aristotle leaves us. Something bigger, wiser, must be behind things, whether in the remote past or as a constant influence on events, though we are fairly certain it's not Zeus and his court of jealous, mischievous, super-humans.

Appetites are not ideas, they are imperatives driven by instinct, deep memory, biology; they are required for surival, like the Laputan servants reminding their contemplative masters to eat and drink from time to time. While Plato establishes our participation in, and relation to, the forms as an eternal measure of virtues--something grail-like and ultimately irretrievable--Aristotle presents the case for defining phenomena on their own, verifiable, terms. For all the needs the forms do satisfy, in terms of supplying useful models or blueprints, what they lack, as Aristotle saw, was the ultimate Form, the one that caused the others. Forms are static, and life that remains static ceases to be life. When movement is encouraged: room to grow, room to maneuver, life floods in and increases.

"Aristotle, with his belief in real and substantive form--as real as form was to Plato, but in the creature, not above and outside it--can for the first time draw a distinction on the level of sensation between physical and psychical events." (Guthrie 148)

So it's to Aristotle we owe the great leap out of mysticism, and reason caulked with mysticism, to the hard, evidence-based science of observation and testing. His reluctance to accept the relevance of Plato's stories of arduous journeys followed by draughts of magical waters, in an underworld not subject to the orderly laws of nature, marks an important step in the development of the mind. The ability to think beyond gods, (even if only to imagine different kinds of gods) or at least the possibility of it, has ultimately led out of the Cave toward a more complete, but still imperfect knowledge of the world.

"Clearly then wisdom," says Aristotle, 'is knowledge about certain causes and principles" (Baird 982a). It is not just knowing how things work, but why they work. "Thus we view them as being wise not in virtue of being able to act, but of having the theory for themselves and knowing the causes" (Baird 981b). He explains that the common worker, the producer who can make things work without being able to explain how they work, is bound by nature, "the divine power," to follow those who do understand. And those who understand most, of the principles and causes, have the task and responsibility of defining for others what actions mean. When Aristotle writes, "The human race lives also by art and reasonings" (Baird 980b), he is telling us that, once the struggle for animal survival has been mastered, and we have leisure to consider our place in things, we are fulfilling the role of the human by drawing conclusions based on evidence, and extrapolating from the visible what is most likely. "Progress is from the potential to the actual" (Guthrie 145). We infuse the raw materials: leather, onions, our own lives, with knowledge originating somewhere else, to arrive at the combinations: shoes, soup, a good life. Thus, Aristotle could conclude, "So with the soul: it's highest and only perfect manifestation--pure mind--exists eternally (Guthrie 145), which assumes, with both Plato and Socrates, that our intellectual life belongs to an eternal realm, while our bodies, constructed of components certain to change and eventually decay, belong to a lesser, dependent kind of manifestation.

There is a strong temptation to propose answers to eternal riddles. Plato took logic as far as it could go and filled in the blanks with folktales, but his enduring popularity testifies to the power of his synthesis of ideas with myths. Aristotle, as many today might, writes, "the theory is not a reasonable one' (Baird 988a), primarily because it fails to account for the uniqueness of the physical forms, but also because of a paradoxical relationship to numbers, which Plato believed "could be neatly produced out of the dyad as out of a plastic material" (988a), a position hard to support except through magical thinking. Evolutionary science, which can only define species according to their position in a vast timeline, during which one observable form transforms gradually to another, offers a firm roadblock to Platonic Idealism. The Forms must then contain an infinite supply of minutely variegated originals; there can literally never be a point in time where a single phenotype (out of millions) can be said to have reached its "final" expression," (except in cases of extinction), which means any Form would have to reflect the continuous, overlapping spectrum of appearances. "...but positing a dyad and constructing the infinite out of great and small, instead of treating the infinite as one, is peculiar to him; and so is his view that the numbers exist apart from sensible things" (Baird 988a).

As Aristotle admits,"It was a good idea to call the soul 'the place of forms,' though this description holds only of the thinking soul, and even this is the forms only potentially, not actually" (Baird 368). Finally, it is the gulf between potentiality, which is infinite, and actuality, which can't be, that dooms Plato. Composition is also an issue, as Aristotle shows us, "...for they [Platonists] do not suppose either that the Forms are the matter of sensible things, and the One the matter of the Forms, or that they are the source of movement" (988a), and of course movement itself is utterly inexplicable in terms of the Forms. Even in exploiting the weaknesses of Plato's argument, though, we are impressed by its strengths. We do aspire to both physical and moral ideals which must originate somewhere. In fact, 2,000 years of inquiry have offered mostly rhetoric, and little in the way of conclusive proof, against him.

Works Cited

Barrett, William, Irrational Man, Random House, New York, 1958

Baird and Kaufmann eds, Ancient Philosophy, Pearson, Upper Saddle River, NJ, 2008

Guthrie, W.K.C., The Greek Philosophers, Harper, New York,1950-1975

Stace, W.T. Critical History of Greek Philosophy, MacMillan & co., New York, 1965