The Republic’s cast of characters and the Divided Line, Part II

This in the continuation of an earlier attempt to assign the major characters of the Republic places on the Divided Line:

Thrasymachus (dianoia as skeptical apistia)Dianoia is the power of grasping the insufficiency of opinion as such. Opinion must be ultimately grounded in a higher order reality or it will wither under skeptical dianoia. Thrasymachus takes the cynical point of view that justice is an arbitrary invention of those in power. In doing so, he grasps the conventional/contingent/malleable nature of opinion as such, which is a defining feature of dianoia. Mapping him on the Cave Allegory, Thrasymachus sees that the puppets are not the realities the credulous masses believe them to be and wants to be a puppeteer. He even thinks Socrates’ “method” is exactly that, and consists of tricks to mold and generate self-serving beliefs in his interlocutors. (338d) Thrasymachus is faithless, i.e. suffers from apistia, and does not see the beliefs as defective images of some higher level reality. His dianoia is downward looking, a means of critiquing (others’) beliefs in order to undermine them and replace them with self-serving substitutes. Yet, his notion of “advantage” must be based on a criterion other than mere opinion in order to provide the infallibility his notion of justice seems to demand (341a). Advantage cannot itself be a product of arbitrary will, if will is to be well-guided by appeal to advantage.

Both Adeimantus (Dianoia trying to secure a better pistis) and Glaucon (Dianoia leading upward to noesis), brothers of Plato, accept that Thrasymachus’ cynical account of justice has some sort of force. They understand and raise questions about the contingent genesis of belief, even their own beliefs. But, unlike Thrasymachus, neither is willing to abandon their belief about justice. The two essentially beg Socrates to help them secure their belief on a securer basis against Thrasymachus’ threat. Both trust that justice must be more than an arbitrary product for the self-service of those in power. Their willingness to expose their own beliefs to testing is evidence of the dianoietic virtue in them. But there is an important difference between the two brothers. At one point in the dialogue while discoursing about The Good, Adeimantus essentially gives up looking up toward noesis and requests an adequate opinion from Socrates:

Adeimantus: But, Socrates, you must tell us whether you consider the good to be knowledge or pleasure or something else altogether.
Socrates: What a man! It’s been clear for some time that other people’s opinions about these matters won’t satisfy you.
Adeimantus: Well, Socrates, it doesn’t seem right to for you to be willing to state other people’s convictions and not your own, especially when you’ve spent so much time occupied with these matters.
Socrates: What? Do you think it’s right to talk about things one doesn’t know as if one does know them?
Adeimantus: Not as if one knows them…but one ought to be willing to state one’s opinions as such.
Socrates: What? Haven’t you noticed that opinions without knowledge are shameful and ugly things? The best of them are blind — or do you not think that those who express a true opinion without understanding are any different from blind people who happen to travel the right road?
Adeimantus: They’re no different. (Grube/Reeve, 506b-d — I have added the character names before each line.)

At this point Adeimantus drops out of active participation until Book VIII, while it is Glaucon who participates in the very heights of the dialogue: the Sun Allegory, the Divided Line and Cave Allegory. Adeimantus is ultimately downward-looking, using dianoia to hone and sharpen belief but never advancing beyond this honing. Glaucon, on the other hand, is upward-looking and never abandons the upward quest towards noetic truth.

Socrates (Noesis) — I am the least confident here, since Socrates continually refuses to own any claim to knowledge and knowledge is located at the noetic stage. But Socrates continually maintains noetic openness to his lack of other knowledge. He is never satisfied with mere opinion as such and never confuses opinion with knowledge. I think that Socrates, in denying any claim to knowledge is really denying any ability to adequately express his knowledge in a way understandable to others. Any logos of knowledge will be only a ready-to-hand opinion, however true. But I am unsure whether Socrates is just the highest stage of dianoia or a full participant in noesis. The Republic, after all, never advances beyond the dianoietic level. It’s claims are all hypothetical, defectively pointing toward realities that it is unable to express directly.

The Republic’s cast of characters and the Divided Line, Part I

This is a continuation of a series arguing for the importance of the Divided Line in understanding the Republic. In an earlier post, I gave some indication of the mapping of the Divided Line quarternity (eikasia, pistis, dianoia, noesis) onto features of the larger dialogue. One of those mappings was of the speaking characters in the dialogue, which can be expanded in the following manner:

eikasia — Cephalus


pistis (right opinion) — Polemarchus
pistis (wrong opinion) — Cleitophon


dianoia (downward-looking, undermining belief, cynical) — Thrasymachus,
dianoia (downward-looking, establishing belief) — Adeimantus
dianoia (upward looking toward noesis) — Glaucon


noesis — Socrates


Let me begin to point out the grounds of these homologies:

Cephalus (Eikasia) — The segment corresponding to eikasia on the Line is the region of images and shadows. Cephalus has been freed from the tyranny of desires (a type of shadow) but is afraid of the shadows of injustices that he may have committed in life:

[When] someone thinks his end is near, he becomes frightened and concerned about things he didn’t fear before. It’s then that the stories we’re told about Hades, about how people who’ve been unjust here must pay the penalty there — stories he used to make fun of — twist his soul this way and that for fear they’re true. (Grube/Reeve, 330d)

His fears take shape in the theater of his dreams:

If he finds many injustices in his life, he awakes from sleep in terror, as children do, and lives in anticipation of bad things to come. (Grube/Reeve, 330e – 331a)

His obsession is with overcoming injustice (which can only be a shadow of some unspoken working notion of justice) but he never gives voice to justice as such. Socrates tries to turn him toward some belief in justice, even puts words in his mouth, but Cephalus departs the scene without pursuing justice. In the Cave Allegory, Cephalus would be like one who is turned from the shadows toward the fire, but finds the light too confusing and dazzling and so turns back to his fears and dreams. His concern is thus fully for images, not the higher reality of which they are the images. He is aware that his fears are shadows of realities, but the realities he pursues are his prior acts of injustice toward which he attempt to make recompense to gods and offended persons.


Polemarchus and Cleitophon (Pistis)Pistis means dedication to, and defense of, belief. Polemarchus begins by defending his father and the traditional belief about justice that is implicit in his father’s fears. He is characterized as loyal and courageous. The traditional version is that justice is a matter of “giving back what is owed” (331e); that what is owed are “benefit to friends and harm to enemies” (332d); that “friends” are those who are actually just and “enemies” are those who are actually unjust (334d). But Polemarchus is converted by Socrates to a truer belief about justice: that justice is always a benefit, that “it is never just to harm anyone” (335e). (Note that this amounts to a true belief about justice and not a true belief of justice — there is a difference.) Polemarchus commits to defending this modified opinion of justice. He becomes a loyal ally (i.e. “auxiliary”) of Socrates, and he commits to serve as his “partner in battle” (335e) against any version of justice that has been shown by the argument to be defective. Polemarchus later in fact comes to Socrates’ aid against Thrasymachus and his follower Cleitophon at 340a-b. The brief appearance of Cleitophon as a “believer” in the teachings of Thrasymachus show that pistis is also capable of defending a false belief (that it is “just to obey the orders of the rulers” — even presumably orders that harm the ruled (340a)) to the one unfortunate enough to follow the wrong teacher. In the Cave Allegory, both Polemarchus and Cleitophon are like those who measure the various shadows of justice in accordance with the puppets that produce them i.e. belief in a trusted authority such as tradition, family or teacher. Belief, at this level, is the highest standard of measure. Courage, spirit, steadfastness and loyalty are the virtues of this stage; Polemarchus is the paradigm.



The darkness is light enough

Let me begin with four examples of a curious phenomenon:

1. In Aristotle’s Rhetoric, the chief instrument of persuasion is the enthymeme, which is a defective syllogism. The defect is that one of the premises is withheld, so that the listener must provide or assume the missing premise. Aristotle:

The enthymeme must consist of few propositions, fewer often than those which make up the normal syllogism. For if any of these propositions is a familiar fact, there is no need even to mention it; the hearer adds it himself. (Rhetoric, Book I, Chapter 2, 1356a)

Why is a defective syllogism more persuasive than a complete syllogism? Why wouldn’t supplying the missing premise have more force?


2. Heraclitus claims in one of his fragments that:

ἁρμονίη ἀφανὴς φανερῆς κρείττων
(A unapparent harmony is more potent that an apparent one.)

Why isn’t an apparent harmony better?


3. In the John 20:29, Jesus tells Thomas: “You believe because you have seen; blessed are those who have not seen and yet believe.” Is this a similar phenomenon to the previous examples — that the potent harmony not-seen is greater than the one seen?


4. To use another verse from John 1: “The light shines in the darkness, but the darkness has not comprehended it.” Could “light shining in darkness” point to the same phenomenon: the greater power of the implicit over the explicit?


The core principle of Defective Reading is that defects/imperfections can only be experienced as such if there is operative within the soul a prior sense of wholeness/completion. We experience the defect first and yet can grasp on reflection that the immanent criterion must somehow be prior. Platonic philosophy is the struggle to direct our attention on this light that somehow always shines behind us.

This metaphorical light has two chief effects: shadows and reflections. Experiencing defect is the shadow of occluded light, whereas the seeming-true of opinion is the reflection. Shadow is an unapparent effect of light whereas reflection is an apparent effect, but both are effects. But beholding the reflected light is passive, whereas inferring the light behind the shadow requires an active and fuller understanding of the light’s power. We can allow ourselves to be satisfied with the dim light of reflection, but the felt absence of light can shake us from such small satisfactions. The understanding that grasps a defect, a shadow, a hidden harmony as deficient is one that is energetic (in Aristotle’s sense). Reflected light is more evident, but the inferred light is more potent. A fault-finding power also seems to be a protreptic power, guiding us to greater perfection.

Let me end with some lines from Wallace Stephens that should make perfect sense in the light of my theory of Defective Reading:

The exceeding brightness of this early sun
Makes me conceive how dark I have become,


And re-illumines things that used to turn
To gold in broadest blue, and be a part


Of a turning spirit in an earlier self.


Happy (belated) Easter, everyone!

The Divided Line as “Protreptic Analogy”

This post is continuing a discussion of the Divided Line analogy. Earlier contributions were here and here.

The Greek word analogia divides into two roots: the prefix  ana, meaning “upward”, and logos, meaning “ratio”.  An analogia is the application of a ratio derived from something well-known in order to point toward some feature of a less known pair. A analogy has four terms and two ratios. The missing feature may be (1) a unexpected similarity of relation or a (2) undefined term. Let me explain them in turn:

(1) An example of analogy revealing a ratio is Wallace Stevens’ claim that “A poet looks at the world the way a man looks at a woman.” Put in analogy form, the analogy is


All four terms are known, but the surprising point seems to be in the equivalence of ratio, that the relation between poet and world should take the same form as the well known man-toward-woman relation. The analogy communicates Wallace Stevens’ experience of being a poet, which is otherwise invisible to untutored eyes. We can point to features of external experience, but must rely on ratio — which is invariant to perspective (*see below) — and analogy to communicate inner experience. The philosophical importance of analogy should be obvious, since philosophy wants to point out features that are subjective but non-arbitrary. The form of Stevens’ philosophical vocation is an inner-something to which he conforms (subjective) but which he lives into without being its creator (non-arbitrary.) This protreptic pointing can really only happen through analogy.

(*Let me give an example of the perspectival invariance of ratio. Imagine looking a person from a distance of 50′ and then again at 100′.  From the former perspective, the person will look taller and the latter shorter. Now imagine that the person is holding the same 12″ ruler in both cases. Although visually the two perspective differ in size, the ratio of length of ruler (e.g. 12″) to height of person (e.g. 72″) will be invariant in both cases. This is how measurement works, to allow the invariance made possible by ratio (logos).)

(2) Every analogy has four terms. If three are known and the ratios asserted to be equivalent, we can use an analogy to solve for the fourth term. The Divided Line is an analogy that guides the search for the fourth segment, e.g. noesis. The first two segments establish its guiding invariant ratio the difference between an image and that of which it is an image. We are then to apply this ratio to the third segment in order to find the fourth term. The Divided Line communicates a beginning point (the third segment, doxa-as-hypothesis) and a direction of search (an image calling forth its original, defined both by the first two segments and by the large division of the line as a whole) as a guide to understand noetic reality. It is protreptic, “forward-reaching”, since it frames an aspiration more than giving an answer. Noesis is what would be known if we are successful in following the guidance of the Divided Line analogy. The communication of noetic truth (immanent subjective criteria that are non-arbitrary) for someone who does not yet recognize it can happen no other way. Let me summarize my point with an analogy:

pointing : objects-in-the-world  : :  analogy : objects-of-inner-experience

The Divided Line is an invitation to look where Plato is pointing. It is less a conclusion than a task. It’s goal is the illumination of noetic experience for the willing seeker.



Update on the Book Project

I began this blog for the purpose of airing out some of my ideas on Plato in anticipation of writing a book on the subject. My life is busy and my attention span short. Unless I want to sacrifice other parts of my life to writing (I don’t), the project will likely take me a very long time. That’s OK. My personal motto is from Ovid:

Gutta cavat lapidem, non vi, sed saepe cadendo.

(Dripping hollows rock, not by force, but by always dripping.)

I think it is helpful to reflect periodically on what I think I am doing and how I am doing it in order to guide my deliberations about what to do next. Here are a rough plan of my project, not of the contents, but of the process:

1. Last Summer, when I began to entertain such my book project, I set myself the modest goal of writing five sentences per day on Plato. That’s it — just five sentences a day. Sometimes I wrote more than five and sometimes sentences flowed into paragraphs, but everyday I wrote five.
2. Some time around December, I could see that my sentences were starting to coalesce around certain themes. I began sorting my scraps into rough categories. I organized them in a notebook, which has about 130 pages of these sentences and fragments.
3. I decided then that I need to move on to paragraphs and so here I am writing a blog. I really didn’t set myself any goal for posting other than regular progress. I have for the most part kept moving forward, although I have allowed myself the liberty of pursuing any topic that begs to be written.
4. I gave up standards of fluency and perfection. I tried to practice the economist James Buchanan’s advice to his students working on dissertations: “Don’t get it right; get it written!” This was hard for me, to release something into the world that I hadn’t massaged over a couple dozen times, but I know that “good enough” will yield a better harvest than “just right.” The stalk must come before before the flower.
5. I have purposefully shunned reading secondary works on Plato since beginning my project. (This has taken quite a bit of discipline — books are piling up that I am eager to read.) I will maintain this resolution unit I can produce a synoptic draft of the work “out of my head” as it were.
6. I wrote a rough program of topics to cover in my very first blog post, based on my arranging, and have been referring to that occasionally to fill in lacunae in the work. By the beginning of the summer, I hope to have aired all of the themes.
7. This summer I plan to collect those blog posts into a text editing program, play around with the order of exposition and figure out how to create a single synoptic narrative.
8. No post is finished as written, nowhere close. Each needs more examples, more extended development, more textual support. But my immediate goal is not to polish them in any sort of detailed way, but to expand them enough to provide stitching between sections. My next goal for now is a synopsis, not even a draft.
9. Finally, my work and methods should be an enactment of the ideas that they are trying to communicate. I am overcoming my fear of exposing my defects and have learned at Plato’s knee that the defective places are exactly where the real discoveries will eventually happen.

Thanks to all of you who have contributed to this work by commenting and asking probing questions. That has been a genuine help to me and I am humbly grateful to all of you.

The Divided Line as organizational key to Plato’s Republic

In my last post, I gave a very compressed explanation of the four segments of the Divided Line Analogy. (Republic, 509d-511e) But the Divided Line can be best understood by using it as an overlay for different parts of the Republic — then the parts and whole of the dialogue are mutually illuminating. The Divided Line Analogy is the representative of the whole; it give the logos or ratio of the parts in relation both to each other and to the whole itself. ( It took me about a decade of reading and rereading to figure all this out.) Here is a schematic version of some of those overlays, each of which I hope to unpack in future posts:


First, we need to distinguish the three main levels, each with its own type of object:

1. bottom level — where the prisoners sit shackled. The only “objects” are the shadows and echoes.
2. middle level — the level of the puppets, puppeteers and fire. A partition divides this level in two: (a) a front side in which only puppets are seen; (b) a back side, where one can see the puppets, the puppeteers and the fire.
3. top level — the ground outside the cave opening. The objects of attention here are the animals-themselves, the plants-themselves, and the light of the sun.

Given those three levels, one of which is divided by a partition, we get the following four “stations”:

1. eikasia — (Level 1) — turning from the shadows on the cave wall;
2. pistis — (Level 2a) — seeing the puppets on the front side of the partition wall;
3. dianoia — (Level 2b) — seeing the puppets, puppeteers and illumining fire behind the partition wall;
4. noesis — (Level 3) — emerging from the cave.


The parts of the Divided Line map to the four gradations of city in Books 2 through 5. (These divisions come from Eric Voegelin’s Order and History, Volume III: Plato and Aristotle.)

eikasia — Primitive City (369b – 372c)
pistis — Luxurious City (372c – 375c)
dianoia — Purified City (376e – 448e)
noesis — Philosopher’s City (449a – 541b)


eikasia — justice/dikaiosyne
pistis — courage/andreia
dianoia — moderation/sophrosyne
noesis — wisdom/sophia


eikasia — desiring-part/epithymia
pistis — spirited-part/thumoeides
dianoia — calculating-part/logistikon
noesis — not included. Thus, Socrates calls the threefold scheme, “deficient.” (504b)


eikasia — Cephalus
pistis — Polemarchus
dianoia — Thrasymachus, Adeimantus, Glaucon
noesis — Socrates


IGNORANCE – OPINION – KNOWLEDGE (See Republic, 477a – 478e)
eikasia — ignorance/agnoia/aporia
pistis — opinion/doxa (as belief)
dianoia — opinion/doxa (as hypothesis)
noesis — knowledge/episteme


FOUR “DRAFTS” OF THE REPUBLIC (discussed here)
eikasia — A first aporetic (i.e. unsatisfying) draft, i.e. Book I alone.
pistis — A second poretic (i.e. satisfying) draft comprised of Books I – IV and Books VIII – X
dianoia — The final written draft, i.e. the Republic as we have it.
noesis — The *real* final draft — the teaching of the Republic realized in the soul of its reader.

The four segments of the Divided Line

This is the beginning of a series of posts on the Divided Line Analogy, which can be found at the end of Republic, Book VI (509d-511e). I maintain that the Divided Line Analogy is is the hermeneutic key to understanding the purpose of the Republic as a whole, and the proper proportions of everything else in the Republic are revealed by it. The Analogy is so compact that it will take some development to convey its structure and meaning. Perhaps the best way to begin is not with the geometrical construction of the line (as the dialogue does) but to begin where Plato ends, by labeling its four segments: