Republic Books 6-7: Plato’s Theory of Forms (The Sun, The Divided Line, and the Allegory of the Cave).

Republic Books 6-7: Plato’s Theory of Forms (The Sun, The Divided Line, and the Allegory of the Cave).

This essay explores Books 6-7 of The Republic and explains Plato’s theory of the forms through his famous analogies of the sun, the divided line, and the cave.

Plato’s theory of forms is an extension of the older Pythagorean view that the visible world is grounded in an unseen world of number. One villager, for example, might have one tree in his garden, and another might have two. In such a scenario, we could thus perceive that the one villager has more trees than the other, since two trees is more than one. But note that the numerical fact that two is greater than one would still hold true even if barbarians were to invade the village and burn down all its trees. Indeed, the fact that two is greater than one was true before there were any trees on earth and will be true even after the end of all physical life on the planet. Facts about the realm of numbers thus hold true independently of their sensible manifestations. Plato’s theory of the forms can be thought of as an elaboration of this basic insight.

Plato elaborates this basic notion of the invisible grounding of the visible in two key ways. First, the theory of forms is meant to explain why visible objects are what they are. For example, the reason a tree is a tree and not a dog is that it participates in the form of <treeness>. Particular things have essences that make them what they are, and these essences are distinct from the particulars that participate in them. For, while we can predicate essences such <treeness>  to many things, but we cannot do this for particulars themselves. Consider, for instance, two particular Linden trees. Let’s call them Tristan and Isolde. Note that they both share the common essence of “being a linden tree”. We can predicate “is a linden tree” to both Tristan and Isolde. But when we consider the particular trees themselves, we cannot predicate them to other particulars. We can’t for example, predicate Tristan to Isolde or Isolde to Tristan. There is thus a difference between concrete sensible particulars, and the universal essences that make them what they are.

A second key feature of Plato’s theory of forms is the idea that universals are arranged hierarchically. Consider, again, our example of Tristan and Isolde. These particular trees are what they are in virtue of participating in the form <Linden Tree>, but this form itself is what it is by participating in the form of <Tree>, which itself participates in the form <Plant>, which itself participates in the form <Living Thing>, etc. We thus have an ascending hierarchy in which lower forms are determined by and emanate from the higher forms in which they participate.

With these basic features of Plato’s account in view, we can now see how he further explains his theory through the analogies of the sun, the divided line, and the cave.

The Form of the Good

Socrates comes to the theory of forms through a discussion of the education of the guardians. For, he observes that we have yet to grasp the true aim of such an education, “the most important subject and the most appropriate for” the guardians “to learn” (504d). For, though he has sketched the basic nature of the cardinal virtues of wisdom, courage, moderation, and justice, he has not yet set them forth in detail or grasped the higher knowledge that lies beyond them. He observes:

“There is something even more important. However, even for the virtues themselves, it isn’t enough to look at a mere sketch, as we did before, while neglecting the most complete account. It’s ridiculous, isn’t it, to strain every nerve to attain the utmost exactness and clarity about other things of little value and not to consider the most important things worthy of the greatest exactness” (504d).

Knowledge of the forms, then, proves necessary for a full understanding of the virtues. Specifically, Socrates contends that the highest form of all, and thus the ultimate object of contemplation and devotion, is the Form of the Good. It stands at the apex of the hierarchy of forms as the ground and source of all the rest. This conceptualization, in which the forms are ordered according to their relation to the Good is suggested by his account of nature and craft at the beginning of the Republic. Humans engage in various crafts, each of which aims at a particular goal or telos encoded in the nature of the subject matter in its care. Shepherding, for example, aims at the good of sheep; medicine at human health; and farming at the fructification of crops. Because each nature aims at its own good, this suggests that they all strive for The Good. And just as crafts are subordinated to one another through the various goods towards which they strive, so too are the forms ordered by their relation to the form of The Good.

Socrates explains the importance of the form of the Good as follows:

“For you’ve often heard that the form of the good is the most important thing to learn about and that it’s by their relation to it that just things and the others become useful and beneficial…. [yet] we have no adequate knowledge of it. [And] if we don’t know it, even the fullest possible knowledge of other things is of no benefit to us, any more than if we acquire any possession without the good of it. Or do you think that it is any advantage to have every kind of possession without the good of it? Or to know everything except the good, thereby knowing nothing fine or good?” (505a-b).

It is the form of the good that makes all other objects and activities good. Without it, nothing would be desirable, and all other knowledge would be rendered worthless, because, cut off from the Good, we would know only the evil and base.

Yet, despite its importance, people don’t know what the Good is. Most are content to opine and equate it with either knowledge or pleasure, but Socrates argues against both identifications. If the Good is to be equated with knowledge, one needs to explain what kind of knowledge it is. Is it, for example, knowledge of fishing or farming? To this, people respond that it is knowledge of the Good. But such an answer presupposes that we already understand what the Good is. Hence, identifying it with knowledge does not actually elucidate its nature. Similarly, Socrates argues that it cannot be identified with pleasure. For, some pleasures are bad, such as those of a sadistic tyrant who takes pleasure in torturing the innocent. If pleasure were the highest good, then the tyrant’s pleasure would be good. But it isn’t. Hence, the position is contradictory, since it predicates both goodness and badness to pleasure.

1. The Sun as the Offspring of the Good

Socrates interlocutors ask him to define the nature of the Good. He remarks that this task is beyond his powers, but he will attempt to clarify it as best he can through an analogy to the sun, the Good’s offspring. Socrates observes:

“That [i.e. an account of the Good], my friend… would satisfy me too, but I’m afraid that I won’t be up to it and that I’ll disgrace myself and look ridiculous by trying. So let’s abandon the quest for what the good itself is for the time being, for even to arrive at my own view about it is too big a topic for the discussion we are now started on. But I am willing to tell you about what is apparently an offspring of the good and most like it” (506d).

Though defining the form of the good is too demanding a task at the moment, Socrates will try to adumbrate its nature by drawing an analogy to its offspring. Socrates identifies this offspring with the sun (508a), noting that sensible perception requires not only the power of vision and the existence of sensible objects, but also light, a mediating third. For example, a man might have functioning eyes and the power of sight, and an eagle fly before him, but, without light, he would fail to see it. To see, for example, that the eagle is golden and majestic, light must mediate between the man’s eyes (and perceptual faculties) and eagle’s body. For us on earth, the sun is the primary source of light. Without it, we could perceive nothing. Thus, Socrates suggests that sight, “the most sunlike of the senses”, receives its power from the sun, “just like an influx from an overflowing treasury” (508b). Socrates then to goes on to note that the sun not only allows us to see, but is also the source of earthly life, growth, and nourishment (509b). Seeds grow into life giving trees by the sun’s power. Without it, the earth would be barren.

Socrates then speculates that the form of the Good, the parent of the sun, plays a similar role in the invisible world. It is the mediating third between the understanding (nous) and indelible objects (nooumena). For our minds perceive the forms only through its intellectual light. Socrates maintains that the soul:

“When it focuses on something illuminated by the truth and what is, it understands, knows, and apparently possesses understanding, but when it focuses on what is mixed with obscurity, on what comes to be and passes away, it opines and is dimmed, changes its opinions this way and that, and seems bereft of understanding…. So that what gives truth to the things known and the power to know to the knower is the form of the good. And though it is the cause of knowledge and truth, it is also an object of knowledge. Both knowledge and truth are beautiful things, but the good is other and more beautiful than they. In the visible realm, light and sight are rightly considered sunlike, but it is wrong to think that they are the sun, so here it is right to think of knowledge and truth as goodlike but wrong to think that either of them is the good–for the good is yet more prized” (508d-509a).

The form of the good thus gives the power of knowing to the soul and truth to the objects of knowledge. And, as the source of both, it stands above them to them, superior and more beautiful than either truth or knowledge.

Likewise, just as the sun is the source of earthly fructification, so too is the form of the Good responsible for the Being of that which is. For, “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, for Plato, the form of the Good stands above even Being. This conception of a Goodness in absolute excess of Being played a central role in Neoplatonism and the medieval mystical tradition. We see it, for example, John Scottus Eriugena’s meditations on the Prologue of the Gospel of John when he notes:

“The voice of the spiritual eagle strikes in the hearing of the church. May our outer senses grasp its transient sounds and our inner spirit penetrate its enduring meaning.

This is the voice of the bird of high flight–not of the bird who soars above the material air or over the aether, orbiting the entire sensible world–but the voice of that spiritual bird who, on swiftest wings of innermost theology and intuitions most brilliant and high contemplation, transcends all vision and flies beyond all things that are and are not. […]

The blessed theologian John therefore flies beyond not only what may be thought and spoken, but also beyond all mind and meaning. Exalted by the ineffable flight of his spirit beyond all things, he enters into the very arcanum of the one principle of all” (Trans. Bamford).

For Neoplatonic mystics such as Eriugena, the mind must soar beyond itself to its source, the ultimate object of yearning and ground of all Being.

2. The Divided Line

Socrates then goes on to further elaborate his theory through the analogy of the divided line. He tells us to draw a line and divide it into two unequal parts, the one standing for the intelligible realm, and the other for the visible (509d). Then divide each of those halves by the same ratio, so that there are four sections. At the bottom lies the lowest section of the visible. It “consists of images”, such as “shadows… reflections in water, and… close packed, smooth, and shiny materials” (510a). Above that are the visible things responsible for those reflections, “the originals of these images”, e.g. “the animals around us, all the plants, and the whole class of manufactured things” (510a).  Note that, in this illustration, what is above has more reality than what is below. For example, we would say a tree has more reality than its shadow. The shadow exists only derivatively as a mere epiphenomenal relation between the tree and a light source. For Plato, the same holds for the whole of the visible world in relation to the intelligible realm. The unseen world is thus more real than seen. Indeed, the entirety of the empirical world can be thought of as a mere shadow of the more substantial world of the forms.

Immediately above the visible world are the mathematical and geometrical objects through which we hypothesize about the world of the forms. We might, for example, draw a particular triangle, and use it to prove geometrical facts about triangularity as such. (510e).

And finally, at the top of the line, stands the pure world of the forms, and, ultimately, the form of the Good which is grasped as a first principle from which everything below it can be deduced. Here one grasps “the unhypothetical first principle of everything” (513b). And “having grasped this principle”, the mind “keeping hold of what follows from it, comes down to a conclusion without making use of anything visible at all, but only of forms themselves, moving on from forms to forms, and ending in forms” (513b-c).

To these four metaphysical realms, Socrates then correlates four epistemic powers of the soul. The soul grasps reflections through imaging (εἰκασία), empirical objects through belief (πίστις), hypothetical mathematical and geometrical objects through thought (διάνοια), and pure forms through the understanding (νόησις).

3. Allegory of the Cave

Finally, Socrates attempts to further explain this theory through the famous allegory of the cave. He asks us to imagine a pitiful tribe of prisoners who have been raised deep in a cave. They are chained so that they can only look at the wall directly in front of them. Above them is a little screen, and behind that a fire. At this upper level of the cave, people carry objects over their heads, so that these objects protrude above screen and cast shadows into the cave wall below like in a puppet show. (514a-b). So, for example, when someone walks by with a little statue of an elephant, an elephant shaped shadow is projected into the cave below, and when someone carries an image of a tree, a tree shadow is cast below, etc. (514c).

Since this shadow theater is the only reality these prisoners know, they take it for the real world. They fail to grasp the true nature of reality, but only the shadows on their dingy cave wall. (515b-c).

Socrates then asks us to consider what would happen if one of these prisoners were freed from his chains and led up to the fire behind him. He would be confused, “pained, and dazzled”, being wrenched from one reality and taken into another (515d). Socrates inquires:

“What do you think he’d say, if we told him that what he’d seen before was inconsequential, but that now–because he is a bit closer to the things that are and is turned toward things that are more–he sees more correctly? Or to put it another way, if we pointed to each of the things passing by, asked him what each of them is, and compelled him to answer, don’t you think he’d be at a loss and that he’d believe that the things he saw earlier were truer than the ones he was now being shown?” (515d).

The position would be so disorienting that he would initially prefer the shadow world to the real one. And a similar situation would occur would if he were to be progressively dragged out of the cave entirely and behold the world above ground (516a). He would need time to get his bearings. First, he would most easily bear to seeing shadows, then the objects which cast them, then the heavenly bodies, and, finally, the sun itself, understanding it to be the cause and source of earthly life (516c). After understanding the true nature of the world above ground, he would care nothing for his prior life in the shadows. Socrates inquires:

“And if there had been any honors, praises, or prizes among them for the one who was sharpest at identifying the shadows as they passed by and who best remembered which usually came earlier, which later, and which simultaneously, and who could thus best divine the future, do you think that our man would desire these rewards or envy those among the prisoners who were honored and held power? Instead, wouldn’t he feel with Homer, that he’d much prefer to ‘work the earth as a serf to another, one without possessions’ and go through any sufferings, rather than share their opinions and live as they do?” (516d).

Furthermore, if he were to go back down and try to rescue his friends and family below, he would again become disoriented–this time not from the light but from the darkness. He would be unable to recognize the shadows, and, as a result, would be ridiculed by the prisoners in the cave. They’d say that “he’d returned from his upward journey with his eyesight ruined and that it isn’t worthwhile even to try to travel upward” (517a). And, if he were to try to lead them upward, they would attempt to kill him if they could (517a).

Socrates takes this parable of the cave to be an analogy to the soul’s ascent to the intelligible world. He explains:

“The visible realm should be likened to the prison dwelling, and the light of the fire inside it to the power of the sun. And if you interpret the upward journey and the study of things above as the upward journey of the soul to the intelligible realm, you’ll grasp what I hope to convey…. In the knowable realm, the form of the good is the last thing to be seen, and it is reached only with difficulty. Once one has seen it, however, one must conclude that it is the cause of all that is correct and beautiful in anything, that it produces both light and its source in the visible realm, and that in the intelligible realm it controls and provides truth and understanding, so that anyone who is to act sensibly in private or public must see it” (517b-c).

Just as the prisoner made his ascent from the cave, so too must the soul make its ascent from the visible world to the intelligible, coming, with difficulty, to finally grasp the form of the Good from which all Being emanates. Once one grasps the true reality of the forms, he will not be content with life among the shadows. Socrates observes, “the ones who get to this point are unwilling to occupy themselves with human affairs and…their souls are always pressing upwards, eager to spend their time above” (517c). And, if one were compelled to do so, he would be like the man who returned to the cave, no longer accustomed to life there and an object of mockery. Socrates asks:

“What about what happens when someone turns from divine study to the evils of human life? Do you think it’s surprising, since his sight is still dim, and he hasn’t yet become accustomed to the darkness around him, that he behaves awkwardly and appears completely ridiculous if he’s compelled, either in the courts or elsewhere, to contend about the shadows of justice or the statues of which they are the shadows and to dispute about the way these things are understood by people who have never seen justice itself?” (517d).

As noted previously, such philosophers would be considered useless in such a society.

Additionally, Socrates takes this allegory to have an important consequence about the nature of education. He observes:

“Education isn’t what some people declare it to be, namely, putting knowledge into souls that lack it, like putting sight into blind eyes” (518b-c).

The human soul is not a blank slate to be written upon by the instructor. It is not an impotent receptacle for party dogma, but intrinsically possesses the power of intellectual sight. It needs an education not because it is empty and needs to be filled, but because it is focused in the wrong direction (towards the shadows), and needs to turn its gaze to the light. Socrates explains:

“The power to learn is present in everyone’s soul and… the instrument with which each learns is like an eye that cannot be turned around from darkness to light without turning the whole body. This instrument cannot be turned around from that which is coming into being without turning the whole soul until it is able to study that which is the brightest thing that is, namely, the one we call the good.” (518c-d).

And, as a result,

“Then education is the craft concerned with doing this very thing, this turning around, and with how the soul can most easily and effectively be able to do it. It isn’t the craft of putting sight into the soul. Education takes for granted that sight is there but that it isn’t turned the right way or looking where it ought to look, and it tries to redirect it appropriately.” (518d).

Education, for Plato, is not about downloading information into brains, but about turning the whole soul towards the Good. In the language of religion, education is a matter of repentance (μετάνοια), a changing of one’s mind and a turning from one way of life to another, from the realm of shadows, to the light of the true intellectual sun. This is view of education remains important today, when tribal dogma threatens to tear our society apart. What if, instead of trying to inject our own ideology into the minds of our children and neighbors–as if they were empty heads to be filled with #trusted sources and protected from #misinformation–we encouraged them to turn away from their screens and the shadowy forces that direct the world within them, and to instead direct their gaze upward to the true intellectual light, that supernal Good in whom we live and move and have our being?

[The image used in the thumbnail of this essay is Psyche et l’Amour by William Bougouereau and is in the public domain. It can be found here:]

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