Authors: William H Gass
Gradually, the idea that everything was alive became modified, and life withdrawn from some things like savings from a bank; but as the withdrawal occurred, the questions of just what the elixir was, and where the difference between the living and the lifeless lay, went unanswered. When the élan vital was universal it scarcely needed to be explained—everything lived, and lived in its own way—but the bodies that littered the battlefield, unlike the same ones that had, shouting, swung a vigorous sword before, had ceased breathing (was that it?), were motionless and soon stiff, became pale and cold (did life dwell in the heart like a hearth with its heat?); and blood in drying puddles could be regularly found near the wounds the fallen warriors had sustained (surely that was it); because life was clearly something that came and went, danced away, maybe, like motes in the air do (so some maintained); it was as physical as a muscle and might live in one place rather than another, or perhaps had parts, for flowers were alive as well as bees, as well as the women who valued both blooms and honey (perhaps reason resided in the head, the passionate part had a room in the heart, while desire—all our vegetable loves—had to make do with the gut); yet was it not soon a rule that whatever died did so because it came apart? So if the soul (as life stuff got called) were to be indestructible it would have to be indivisible; however, blood (a likely candidate for what it was) infused each so called part with its warmth, and went out of lifeless limbs like a light.
Within this swirl of issues, and the first movement toward some system of classification, the notion of form began to acquire meaning. Its development depended upon other ideas, of course, which were equally inchoate. How was one to understand where a living thing’s living began, and where its edges ended? Two kinds of definition emerged. One was dynamic and understood form to refer to territorial rights, like those demanded by birds or hunting animals (it has been said that wolves marked these limits by peeing on rocks and trees), or by tribes that posted warning signs, including the skulls of enemies, on the borders of their lands. The form of a thing was that
area whose touch or intrusion drew a response. The other definition was static and seemed to have been based on the silhouette; hence the importance of the shadow something cast, and the visual outline of an entity—in short, its shape, for the origin of
eidos
(that which is seen) lies in
idein
(to see). The early draftsmen’s renderings of men and animals were probably outlines of life, while, for the dynamic definition of the term, the drawings they did were like maps. The suggestion of the dynamic was that the life force moved around and the pattern of its movements—its responses and its sallies—were its form. The experiences men had of instantaneous travel while drunk, in dreams or hallucinations, when mad or merely vividly imagining, were convincing. Meanwhile, the static sense of form said, in effect, that what had been an aggregate of elements—arms, elbows, eyelids, hair, and ears
—soma
—was now understood to belong to a single purposive whole.
Change, then—these inexplicable alterations of habit and routine—could be understood in terms of a change of form or shape or even residence: a
meta morphosis
.
When the Greeks began to study change (which was almost right away), their model was metamorphosis, or change of form, but what was form or shape? Something so rigid it didn’t change, or something so malleable it was a part of the problem? Some of the pre-Socratic philosophers had differed over which of the famous four elements was the one real substance of which all things were made—fire, water, or air (slighting earth somewhat, although, especially for them,
matter
was the right choice); but it was Parmenides who provided the first rationalist argument, since Thales had offered only the realist’s commonsense observation that water frozen became a solid, and when heated turned to air.
The argument is classic. One has to admire it. When anything changes, there has to be some part of the changing thing that does not change; otherwise we would not recognize it as having altered, but, at best, as having been replaced. In sentences like, “Wow, Achilles, how you’ve grown, once so small and now so tall,” the subject
remains as steady as nouns in that position always do, only the predicate
small
has shifted its spelling slightly so that Achilles can don the toga of a stripling. Even when the gas station on the corner is demolished and its buried tanks dug up, the lot stays put. Otherwise we should not know that anything had happened to it. We do not say, “Why, Fred, you’re Ned now, what a change!” unless Fred has married his boyfriend and taken his name. Not only is there something unchanging in change
it
self,
it
underlies
it
, and even makes
it
possible, whatever
it
is. These days (from Aristotle on) we might say that form was the unchanging substance—the skeleton, the DNA, the fingerprint, the eyeshade; and indeed one’s identity—for others—may rest just there; however, for Parmenides the visible provided only adjectives and adverbs, borne to their nouns by verbs like Trojans proffering their dubious gifts. As Frankfort puts it concerning Egypt, “only the changeless is truly significant.” For Parmenides multiplicity was equally suspect. And his attitude prepared Plato also to deny ultimate reality to it. Many sheep are grazing on the hillside. But each is a sheep, and the class of sheep is one class, though its members may be a multitude. The class, moreover, is without flesh, bone, or blood, and therefore cannot decay, did not come to be, and cannot pass away. Sheep and goats belong to two different groups, but both are included in
animal
, which is one and pure and perfect.
Und so weiter
. Till we reach the form of the good, or Hegel’s absolute—whichever comes first.
Why is the class so separate from its members? Because the members vary indefinitely and inexplicably (there are black sheep and skinny sheep, dumb sheep and dumber sheep), while the definition that determines which ones shall be called
sheep
defines only the nature of the class. As far as their species is concerned all members are identical. Sheep are sheep the way business is business. And if all the sheep in the world were eaten, the class would still be as real and thinkable as ever because an idea has a quite different ontology. To reach such refinements of objectivity and abstraction—to see the Form Forest rather than a forest, the Form Tree not a tree—Parmenides,
Plato, and Aristotle had to take steps no other culture to that time had taken. And if Socrates and Plato did not discover the human mind, as Bruno Snell maintains, they invented it. The psyche, as they conceived it, may have never existed—certainly the soul was given little chance of being a reasonable conjecture after it left Aristotle’s hands for those of the Romans and the Christians—but it was the first abstract idea, which is like the invention for the mind of the wheel.
If it was Socrates who first began to sense that the soul was everywhere structurally the same and strangely immaterial, it was Plato who transformed our understanding of language and meaning, because he began to see words as altogether abstract, and as designating universals. A possible exception to this might be proper nouns like
Achilles
or
Socrates, Fido
or
Bill’s book
, each of which refers to a specific empirical thing. Slowly, one of philosophy’s most distinguished arguments fell into place: the argument for the Forms, an argument I should like to perform for you now, not as it was born, through piecemeal appearances in the
Dialogues
, but as it can be recovered, like a pot, from its shards. Aristotle refers to five arguments for the existence of the Forms, but his references to them are so brief and almost by-the-way that many commentators are inclined to think the Forms had to be entities with which his audience could be assumed to be familiar. Plato does not develop a technical philosophical terminology like Aristotle. He had to cope with the wayward language of daily life, and in that sphere
eidos
most usually meant the outline of something “sensible” or “visible,” so by students of Pythagoras it could confidently designate the shape of numbers. The shapes of the numbers were geometrical figures. At that moment the move toward abstraction was on its way. And the building of the proof began.
We do have knowledge of some things, most reliably of geometrical figures, expressed as definitions of circles, squares, triangles, and the like.
Plato assumes that knowledge is a matter of definition—What is X? What is Y?—and maintains that we know everything in the same way—knowing Greek and knowing Homer, knowing what and knowing why—and that there is one and only one definition that legitimately belongs to each term. This is a common rationalist desire, but no language will satisfy it, because words have always been as slippery as the convictions of a politician, and their ambiguities convenient for human exchange.
Moreover, to anticipate a principal objection to the proof, an animistic thinglike character is still a part of Plato’s conception of the Forms, as is a standard of “perfection” which tends to conflate immateriality with superiority.
The definition of
triangle
(to pick a handy figure) includes the fact that it must have three enclosing sides which are straight lines meeting at three points, with the sum of the interior angles equal to 180 degrees.
In the
Phaedo
, Plato uses the example of two sticks and wonders whether they are of equal length. The issue is not the sticks, of course, but the idea of equality and its representation.
The argument asks us to draw a triangle (on a blackboard if in a modern classroom; on a piece of paper, since you may try this at home; or in your mind’s eye). The argument then asks whether you
really believe that you can make a triangle that truly fits the definition, because no triangle you might try to construct will have perfectly straight lines, actually meet at points, or have angles equaling
180
degrees. Even with the best instruments you would fail, if only by a molecule.
Nor could we find a triangle in nature anywhere, because nothing we should find could possibly conform to the definition. And if there were one that we’d found or somehow made, we wouldn’t recognize it, because our instruments could not measure the properties it would be required to have.
Our problem is that we started out designating points with pebbles. Greeks assumed that points had dimensions and that a straight line took the shortest route between two of them. This materialism seemed far more sensible than supposing points had no dimensions and that a straight line (one dimension) went from nowhere A to nowhere B without the wherewithal to do it. Or was a compacted row of no-dimensional spots. Or was the path of a point like the trail of a plane. Without dimensions you simply cannot be: you cannot be located; you cannot line up for inspection; you cannot travel from Nowhere to Noplace.
Zeno’s paradoxes make a fundamental contribution to the argument. Zeno points out that between any two points A and B, a line can be imagined that is capable of being divided in half (at C), and that segment (AC) further divided in half (at D), while that part (AD) also can be cut in two (at E). This can go on longer than anyone has the energy for it. Yet if points have dimensions, and any line is divisible into countless numbers of them, every line is—we hate to say the word—infinitely long. Moving from A to B would be equivalent to picking up an infinite number of points and putting them, like pebbles, into a sack—namely as impossible as undesirable. If, however, points are without dimensions (heretofore unimaginable),
picking them up will be only a figurative exercise that will get you nowhere. To pass through an infinite number of points in a finite time is as impossible as doing so in an infinite time, for one amount cannot be picked and the other cannot be passed.
One of the outcomes of this famous, and justly admired, argument is that geometrical figures cannot be figures found in our space, a consequence of which Zeno does not appear to have been aware. But Plato is. Space with its extentions—those fundamental properties of early Greek materialism, and every materialism since—is not geometry’s subject. A mathematical defense of this would have to wait for Descartes, who was able to transform geometry into algebra.
Our knowledge of
triangle
(which we admitted we had at the opening of this proof) did not emerge from an observation of triangles, either found or formed. The definition is neither empirically derived nor empirically verified; nor does it have as its subject anything empirical.
The things we call triangles, since they are not triangles, but nevertheless are recognized as “triangles” in contrast, say, to “circles,” must be copies of triangles, or imitations of triangles, or representations of triangles, rather than mere words for triangles, inasmuch as words do not mimic, in any sense, their referents.
Indeed, the same may be said of Galileo’s renowned principles of motion. None of these laws are empirical either, and the Leaning Tower of Pisa trick was just that—to fool the eye into believing something only the mind knew was true; for, of course, in nature bodies always fall at different rates, and nothing in motion will ever move at a uniform speed for very long. Galileo, as Galileo avers, was an ardent Platonist.
Maybe we could derive our idea of
triangle
from observations of them by simply choosing one, either found or constructed, to serve as the standard (as some imagine the meter bar in Paris does). When we do that we always cheat, because we begin with our knowledge of
triangle
intact; we are only pretending to be ignorant. Suppose we tried to define
hiccobite
. We probably would have no idea how to collect our candidates, though the shrewder among us might begin by canvassing bars. Moreover, in order that any one thing serve as a standard, either the whole of that thing serves (down to the zerkin they commonly wore) or, if a zerkin is chosen to provide the norm, the same thing can be said of it, as was said of the hiccobites—who, for all we know, although members of a joyous monastic order, are almost perfectly peevish when questioned.