Why your big toe is a Platonic form...

“Anyone who is acquainted with the works of Plato is aware that in spite of the precision and consistency of his thinking he is not at all careful about what we may call terminology.”1

H.J. Paton’s remark says a lot about what philosophers think the written word is capable of, but Plato was far more skeptical. For him, carefulness meant avoiding fixed terminology. Meaning lives in souls, not in marks on a page. Perhaps this is what the divided line analogy is meant to teach us: Static signs, no matter how mathematically precise, are but shadowy images that only appear to pin down the truth. Because the soul’s shapeshifting process cannot be captured by word math, Plato wrote holistically, with an eye to the living organism as his model.2

Of course, this makes Plato especially hard to write about in the usual way. He didn’t make arguments. He made cunning creatures that play dead while planning their escape. As one scholar puts it:

“…in the past I found it impossible to comment in a satisfying way on any single part of the Republic—say the divided-line passage of book 6—without factoring in, and then losing myself in, the surrounding whole in which it is embedded. This was a sobering, even frustrating experience, and it caused me to write little on the work that I believe is the most philosophically rich of them all.”3

Boy, can I relate. Consider the Greek word, pistis, for example, which refers to the least controversial segment of the line. It has been called belief, faith, confidence, trust, common sense, sense-belief, conviction, sensory inspection, empirical observation, to name a few. Unfortunately, none of these terms come close to capturing Plato’s meaning, not even the Greek pistis comes close. But who can resist a clearly-labeled stairway to heaven?

Still, however cartoonish they may be, images can be useful. We just have to be careful not to take them as definitive. We’ll keep in mind that these diagrams distort the liquid reality by presenting it as a frozen declaration. Here’s my take, for now, on What Plato Meant:

1. D: FORMS, noesis : SOCRATES

2. C: PERFECT PARTICULARS, dianoia : GLAUCON (Adeimantus below)

3. B: SENSIBLE PARTICULARS, pistis : THRASYMACHUS (Polymarchus below)

4. A: ?, eikasia : CEPHALUS, the old man who values religious tradition

I’ll start at the top and work my way down, saving the last and the most difficult section for next time.

Nobody can say for sure what forms are, but I suspect at the highest level they’re functions defined by their relationships to each other and to the whole.

CONSIDER A CAR ENGINE. Pistons produce the power to make the car move, but the pistons rely on spark plugs which ignite gas to keep the pistons moving. Spark plugs rely on the distributor to distribute spark at the right time. Each part relies on something else—the engine won’t work if any of its parts is missing. But to know how any part functions, we need to know what an engine does, which means knowing what a car is good for.

Maybe the Good is like a functioning car and the forms are its engine parts. Each form has a function that relies on all the others such that they’re completely interconnected in organic unity, and no part can be removed without destroying the whole.

If this interpretation is correct, each form comes to light only after grasping the Good—the purpose of the whole.

THERE ARE CERTAIN ASSUMPTIONS AND AXIOMS that mathematicians and scientists take for granted, without questioning their foundations. Throwing these into question marks a conversion to philosophy, one that stands in direct opposition to scientific-mathematical certainty. It might even be thought of as the birth of metaphysics. We’re told the dialectician “destroys hypotheses” (533c), but not by discarding them. Instead a transformation takes place that allows the philosopher to see unfounded assumptions for what they are. The attempt to delineate each form’s relationship to all other forms then begins in earnest, but this time with the awareness that no knowledge is possible without knowledge of the whole.

Now it’s one thing to talk about the purpose of a car and quite another to talk about the purpose of the universe. If we’re basically in the position of ants trying to comprehend a spark plug, then knowledge of our own ignorance starts to look like real wisdom, the possession of which Socrates would have had every right to boast about.

Which is why the dialectic must, above all, begin in humility…

“…by treating its assumptions not as absolute beginnings but literally as hypotheses, underpinnings, footings, and springboards so to speak, to enable it to rise to that which requires no assumption and is the starting point of all.”

Humility may be called the starting point of philosophy, but that word fails us in some respect, since the philosopher’s humility is nothing like pious incuriosity or smug stagnation. On the contrary, having a flaming big ego is a prerequisite to becoming a philosopher, so for the philosophical type, humility has got to hurt like hell.4 This humility, let’s not forget, must come from being intellectually humiliated—the philosopher’s worst nightmare. One must have a great deal of self-respect to feel its loss so acutely.5 Some people can suffer a blow to the ego and just shrug it off, but for the philosophical soul, the pain must be intolerable if it is to fuel the quest to find the cure for not knowing.

Having attained insight into the first principle, the Good, the now-wise philosopher is presumably equipped to answer everything that came before, but purely through forms. Assuming insight into the Good is possible.

WHO KNOWS IF THIS SECTION EVEN HAS OBJECTS. Some think not. Others think these objects are mathematical intermediates, but WTF is a mathematical intermediate? It’s hard to get a clear account. It sounds like what we call math: triangles and numbers and stuff like that. But in that case, mathematical objects must be somehow mixed up in the defective world of becoming.6 But wouldn’t that make Plato not a Mathematical Platonist!?

Whatever. I think the mathematical intermediates interpretation makes some sense, especially when we compare our understanding of numbers as units to the quasi-qualitative mathematical entities the Pythagoreans are said to have believed in, like oneness, twoness, triangle-ness, and so on, which seem more like quintessential Platonic forms. And let’s not forget how the Pythagoreans lost their shit when they discovered the diagonal and side of a square can’t be measured by a common whole number—revealing this incommensurability to the public could get you drowned at sea, or so the legend goes. Perhaps Plato drew something more positive from their observations when he took there to be something deeply screwy embedded in the universe, even at the level of mathematics. (He gives a very interesting account in the Timaeus, though there are indications of this in the Republic as well.)

Still, I think there’s more than math going on here, which is why I’m going with the more general Abstract Particulars or Perfect Particulars. In this section I would include all the standard examples of Platonic forms that you hear about in Intro to Philosophy—tree-ness, chair-ness, etc. But these aren’t pure or eternal; they’re as mixed up with the sensible world as a form can be. To see why, consider the process by which we comprehend them as forms. We begin by picking some particular thing and we ask of it, “What is the general idea behind all such things that makes this thing what it is?” Maybe your professor even spoke of “abstract ideas”. But if this is Plato’s theory of forms, it’s no wonder people think its stupid.

I remember the first time I encountered an e-cigarette; a “cigalike” fooled me into thinking someone just lit one up inside a shopping mall. Recalling lessons from Philosophy 101, we might question the tenability of a theory that would have these and all such nicotine-delivery devices, which popped into the sensible world at some point during the mid-2000s, derive their existence from an eternal form. We might even wonder whether there exists a Platonic idea of a cigalike and another of a vape pen and another of…whatever you call those ginormous tank-like monster-cloud producing devices, and so on.

Something doesn’t sit right.

And it gets worse. Is there a form of me? An eternal Tina Form or Tina-ness hanging out invisibly in some parallel Platonic universe? Does that make me-me a defective copy of some blandly generic version of me? And if so, doesn’t that mean there needs to be an even more boring form of both me-me and virtual-me that unites both of us? And so on to infinity?7

Fishy stuff going on here. But maybe we’re looking at this all wrong.

BRIGHT-EYED GLAUCON8, whom Socrates addresses in the divided line section, is an upward-looking scientific-mathematical thinker. When he summarizes this section, he “most adequately” echoes what Socrates says and understands it as being between opinion and knowledge. But he must realize the implications for him. It’s as if Socrates had said: You, Glaucon, are in the halfway house. Yet unlike Thrasymachus, Glaucon’s pride doesn’t appear to be in the least bit injured, and it’s not because he’s dense. He does an admirable job of rescuing Thrasymachus’ definition of justice, which did, after all, launch the The Lord of the Rings multimedia franchise.9 On the other hand, he only props up anti-justice because he wants to see Socrates demolish it; he knows better than to think he can do so himself. Which is to say the second-best critical thinker in the dialogue exhibits humility, and precisely the kind we’d expect at this level. Throughout their conversation Socrates inundates him with battle imagery and seemingly irrelevant remarks about bravery and courage, all of which is meant to evoke the thumos-ego part of the tripartite soul and to clue us in to Glaucon’s placement on the divided line: he’s teetering on the precipice of conversion, though not quite ready for it.10 Recognizing this, Socrates shies away from disclosing the full splendor of the dialectic, humbly apologizing that he would if he could, but he hasn’t got it all worked out just yet. He nevertheless continues to play the role of Glaucon’s luring, daimonic force until the training wheels can come off and his student can become his own daimon, a philosopher. Until then, Socrates coaxes him on:

“Those who pursue geometry and the allied arts apprehend reality to some degree, as we have seen. But mostly they dream.” (533b)

While the dialectic may not deliver the Good right away, if ever, there’s always something of the form in every particular, always a reason to hope the dream will end with an awakening.

FINALLY, WE’RE ON FIRMER GROUND:

‘The second section you must regard as what the first section is an image of, the animals we see every day, the entire plant world, and the whole class of human artefacts.’

We can (for now) take this section to refer to sensible particulars—this computer or this phone in front of you. Common sense takes these to be as real as it gets.

THRASYMACHUS ONLY BELIEVES IN WHAT HE SEES. Since justice is not instantiated, he takes it to be the “interest of the stronger”. Notice, he doesn’t pull this shocking conclusion from thin air; his definition of justice comes suspiciously close to being the opposite of justice. Clearly he arrives at it by reducing a conventional image of justice to what he takes to be really real—the concrete world of sensible particulars. “I’ll believe it when I see it.” To this worldview, justice looks as fluffy as the Easter bunny, a human-invented epic lie to keep the masses in their place.

But why should we believe our knowledge is no better than an ant’s? Thrasymachus might say today. Look at all that we have achieved! Look at your iPhone, you’ve got the world at your fingertips! We’ve been to the moon and back! Who’s to say we’re so ignorant of The Way Things Really Are?

There can be no impetus to seek higher knowledge without destroying the materialistic assumptions of this nothing-but worldview, and yet the cave allegory reveals how difficult this conversion will be. Turning the entire soul away from what it takes to be the whole of reality will be extraordinarily painful, almost impossible—like trying to see behind your eyes. Of course, the search for the first principle will require conversions at each “level”, but the hardest conversion seems to be here at the first cut in the divided line separating the visible from the intelligible. And if we were somehow able to climb through the mirrored ceiling of pistis to the epistemic regions beyond, we might glance over our shoulder and realize we haven’t really left the region we came from, it’s just that everything looks different. That’s why the two middle sections of the divided line are equal.

(Tomorrow I may change my mind.)

FORMS OF SOME SORT OR OTHER MUST EXIST at all “levels” along the divided line if we are to have a passageway out of the cave. If we think reality only exists at the very top, then the objects below it aren’t even pseudo-realities, but nothing at all. The whole is not at the top, but consists of the entire line. So the Good must exist everywhere, at least to some degree.

It may be that everyone’s life (or lives) passes through all levels of the line at various times—how else could we make sense of the Republic’s ending with an elaborate near-death experience containing a reincarnation myth?—so that what we experience at one “level” transforms into a new meaning or theme at other stages.

“Education is not what some professors say it is. They claim they can transplant the power of knowledge into a soul that has none, as if they were engrafting vision into blind eyes…but our reasoning goes quite to the contrary. We assert that this power is already in the soul of everyone.” (518b-c)

Just as there’s a latent philosopher king in all of us, and an infinite regress of many-headed beastly tyrants too, the Good must not turn its back on the incoherent, otherwise there would be no ladder, no desire, no motion or self-motion anywhere whatsoever. The inward journey begins in humility and ends, if it ends, in discovery, in bringing to light what has been forgotten, but intuited, all along—even in some way by downward-looking Thrasymachus. And so the cosmic must take a cosmic journey as well, one in which the darkest shadows and recesses of the cave are lured into sunlight.

I’ll suggest, ever so tentatively, that the middle sections point not to two different objects, but to two different attitudes toward the same object—all objects turn out to be forms in the end, after all. Those who think they see sensible particulars with their eyes are really seeing forms, they just don’t realize it.

Both Thrasymachus and Glaucon refer to the same object in the flux of becoming, but the latter recognizes the form as real whereas the former refuses to acknowledge the form, even though he must implicitly recognize it too, otherwise he would not be so quick to identify its opposite.11

“Supposing, I say, he [the downward-looking philosophical type] were freed from all these kinds of things that draw the soul’s vision downward. If he were then turned and converted to the contemplation of real things, he would be using the very same faculties of vision and be seeing them just as keenly as he now sees their opposites.” 519a-b

What we think we see with our eyes are actually forms seen by the mind’s eye. It’s not clear we ever see solely with our eyes. Isn’t this, after all, the takeaway of the sun analogy? By itself, the eye sees nothing at all. The eye’s vision is a relationship with sunlight as well as the light of intelligibility. Ditto for all sense perception.12

This would suggest the artist is capable of reproducing the mind’s image, not some thing in-itself out there in the so-called real world. How can the artist turn our private mental objects into public images we all recognize? If that’s what the artist does, where does this skill come from? The artist can’t give a clear account, so Socrates declares them touched by the divine. The rest of us are just plain ignorant.

On the other hand, perhaps we’re all artists in some sense, given that we all possess the skill of “seeing” forms, as Edmund Husserl’s eidetic (“seeing”) phenomenology makes clear. For example, your big toe—the left one, if you really want to get specific—can be thought of as a Platonic form, though perhaps not an eternal form. Even so, your left toe does nevertheless achieve some form-like status, and we might even say it “participates” in some higher, more generic toe-ness. Or some other category. If we want to go there.

Why is your left toe a form at all? Simply because it exhibits a salient unity, a selfsameness we can all mysteriously identify, even if its selfsameness is relatively momentary. Whatever it is, it is capable of rising into the foreground of our awareness against the blurry background we call the world. When we direct our attention to an object like a toe, in one sense we see it partially and from our own limited perspective; this is what we call (perhaps erroneously) “seeing with our eyes”. Yet in that very act of perspectival eye-like seeing, we simultaneously see with the mind all of the toe’s other sides, an infinite number of possible perspectives, all joined together in one object. This unification is what makes the object an object. Somehow unified wholes transcend our ever-incomplete streams of experience, and they do so on a regular basis. How is this possible? Mystery lurks even in the mundane. And the magic trick doesn’t end there, since the unified wholes we each individually experience on a daily basis are for the most part the same unified wholes others experience. Somehow our transcendental objects are largely the same, as is evidenced in our coherent communications about them with each other. Transcendence within immanence mirrors itself on a social scale…and perhaps on the grand scale as well.

On the other hand, someone might object, do we really experience infinity? This is a fair point. Personally, I can’t wrap my mind around it. To me infinity is just an uncountably high or unthinkably long something or other, though Husserl probably had a firmer grasp of it than I. In any case, if we’re gonna have terms, I think the Pythagoreans were more experientially accurate in calling the stream-flux13 the Indefinite Dyad. Plato is said to have renamed this cosmic generative principle The Great and The Small. But we’ll forgive him for that. Everyone makes mistakes.

THE MOVEMENT UP the divided line is a progression towards the first principle, the Good. This movement takes place when the philosopher recasts the assumptions and axioms of the sciences into humble hypotheses and uses them as trampolines in an upward-bouncing dialectical inquiry into the nature of the Good. Then, after attaining some extra-rational insight into the first principle, we’re told that the wise (which is basically no one, not even Socrates) must come back down through the continuum of epistemic “realms”, enlightening each form with a form with a form...

All knowledge is shaped like a pyramid. We begin our journey at the indefinite bottom and move our way up the continuum of becoming to the unity of everything. Then back down. And so on.

The Good turns out to be the transcendent unity of the best of all possible worlds, which is ours. Even if it’s but a dream.

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A MORE BECOMING DIVIDED LINE DIAGRAM

There’s no sound.

• Is the universe intelligent? A Platonic response to the indeterminacy of interpretation.

• Mechanism vs. Teleology Is reconciliation possible?

• No one knows what they want, yet everyone wants the same thing... is the object of our desire within reach?

• Constructing the divided line in the Republic with simple geometry…if you teach Plato, this one’s for you.

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—Tina Lee Forsee