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

man:woman::poet:world

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.

 

 

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:

 

THE CAVE ALLEGORY
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 GENESIS OF THE CITIES
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)

 

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

 

THE TRIPARTITE PSYCHOLOGY (See Republic, 436a-b)
eikasia — desiring-part/epithymia
pistis — spirited-part/thumoeides
dianoia — calculating-part/logistikon
noesis — not included. Thus, Socrates calls the threefold scheme, “deficient.” (504b)

 

THE MAJOR CHARACTERS
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.

On specific ignorance

Quisquis ubique habitat, Maxime, nusquam habitat.
[“He who lives everywhere, lives nowhere.”  — Martial, vii]

General ignorance is a bad thing, perhaps the worst thing. Let us never accept our ignorance placidly. Just as life is greater than death — infinitely greater — so too is knowledge greater than ignorance. We should strive for knowledge as we strive for life, for both types grow toward the same source.

But I want to argue that specific ignorance is a good thing. What do I mean by “specific ignorance”? Specific ignorance is not mere absence but absence of something definite. The form of general ignorance is “I don’t know anything,” whereas specific ignorance is “I don’t know this thing”. Such ignorance is essentially dynamic and oriented toward the reality of the specific. Perhaps the first rule of good teaching is to transform a general ignorance into a specific ignorance, so that the striving that ought to accompany ignorance can flower into actuality. Here are a few leftover thoughts to get you thinking:

1. The vehicle of specific ignorance is the questionable opinion, not the blank page.

2. Try replacing periods with question marks.

3. There is no consummation without a prior animation.

4. Real knowledge is the fruit of specific ignorance; no plant, no fruit.

 

What Socrates claimed to know

There are only a few places in the entire Platonic corpus in which Socrates claimed to know anything, at least as far as I have been able to discover:

1. “I claim to know nothing aside from erotic matters…” — Symposium, 177d. (Ta erotika could also be rendered variously, “erotic things,” “the erotic,” “erotic matters”)

2. “It is certainly not conjecture to say that right opinion and knowledge are different. There are few things I would claim to know, but that is among them at least…” — Meno, 98b

3. “Come then, tell me this, [Euthydemus] said: Do you know anything? Certainly, [Socrates] replied, many things, though trifling.” — Euthydemus, 293b.  (The relevant objects of knowledge are qualified as polla, i.e. “many,” and as smikra, which is “small” or “unimportant” or, as I have rendered it in my translation, “trifling.”)

4. “I am wiser than this man, for neither of us seems to know anything great and good; but he imagines that he knows something, even though he knows nothing; whereas I, not knowing anything, do not believe that I do. In this trifling thing (smikron) then, I seem to be wiser than he is, because I do not believe that I know what I do not know.” — Apology, 21; (It must be said that this is the closest as Plato’s Socrates ever gets to saying, “I know that I do not know.” Literally, this is not what is said, although it is not clear how recognizing one’s lack of knowledge could ever be doubtful if recognized at all. Notice that this recognition of a difference between himself and the one claiming wisdom is also called a “trifling thing.”)

Is there some way in which Socrates’ few admitted objects of knowledge — (i) the difference between opinion & knowledge, (ii) erotic matters, (iii) many trifling things, and (iv) one’s own ignorance — are related in some way?

 

Whom to believe?

I recently listened to a debate/conversation between atmospheric scientists on both sides of the climate change debate. The conversation was unusually civil and I learned a lot from it. Now, I’m not here to tell you about whom to believe concerning climate change. I admit to my ignorance of the facts and science (although I am fully aware of the headline facts and the headline science.)  I simply don’t know enough to be much of a partisan for either side, and I am just not able to devote the time to attain a PhD level in atmospheric science. I fully admit that the question matters, but we can only do what we can do. Better to admit ignorance when the knowledge is out of reach. This post is about thinking how we might generally justify assuming any belief at all. Here are a few ideas:

1. We are stuck with beliefs; there is no getting around our practical need for them. We believe a host of things we cannot prove but which have proven reliable for the purpose of governing our lives. Our minds would be terribly impoverished, our worlds much more circumscribed, without the treasury of beliefs that we learned from teachers (who learned them from their teachers.) I can confidently assert that holding belief can be quite reasonable and that to refuse belief altogether is unreasonable.

2. I believe quite confidently that the earth traces an elliptical orbit around the sun. I haven’t taken made the careful observations or done the math necessary to ground that belief. I just trust the scientists on this one. More than that, I trust the self-correcting process among the community of astronomers. I understand the scientific method and how it operates and I grasp why trusting its results is better than merely speculating on matters of physical fact.

3. The self-criticism is an essential feature of the process. I want to see that the purveyor of belief is appropriately critical of his/her methods and sources. If any supposed knower dismisses a legitimate doubt or qualm out of hand, then I would recommend not trusting him/her.

4. I trust no one who is not transparent about how he/she came to believe what he/she knows. Every belief comes with a genealogy that shouldn’t be suppressed.

5. An authority ought to be frank about the caveats and boundaries of their knowing. All empirical knowledge reaches a limit beyond which certainty breaks down. All empirical knowledge has a range of reasonable confidence, outside of which it must confess its ignorance. Knowledge must be self-aware of these limits/caveats.

6. I tend not to trust people who grow shrill or angry in response to critical questioning.

7. I trust no one who’s best defense is an ad hominem attack on the other side.

8. The public advocates of politically-charged scientific positions had better be humble in the face of questioning, willing to accept their critics as potentially reasonable people, or I pay them no mind.

9. Some situations are critical in the sense that refusing to believe in such situations is practically to take a side. In a crisis, not deciding is as consequential as deciding. (Perhaps the global warming debate is of this type. I am still trying to decide.)

10. Beware of mood affiliation in which we trust/distrust a line of argument based on how we feel about its conclusion.

11. Similarly, we must try to work around our own confirmation bias and seek out the most reasonable advocates for the position we are biased to disbelieve. An abundance of “proof” is not our friend when we are in the grip of this bias.

12. We, and by extension our preferred authorities, ought to be open about our susceptibility to bias and be able to demonstrate the steps we have taken in our own learning process to overcome it.

On political opining

How much do you know about Ukraine? Or better, how much did you know before the recent political turmoil there? For my own part, I must confess I knew pitifully little. I have of course never been there. I knew bits of trivia, like the fact that its capital is Kiev. I knew about the Crimean War (vaguely) and that Florence Nightingale made her reputation there. I have read just two books that are located (at least partially) in Ukraine: one is Tolstoy’s Sevastopol Sketches, the other is Bloodlands by Timothy Snyder, which has a horrific description of the Stalinist manufactured famine of 1932-3. I remember somewhat Ukraine breaking away from the Soviet Union in the early 90’s. And I knew that it was a fertile agricultural land, the “bread-basket” of the USSR. That’s pretty much it.

Since the recent crisis, my treasury of facts has increased quite a bit. I have a nice little wikipedia education on aspects of Ukrainian history. I have read a couple of decent essays on Ukrainian/Russian relations. I went from knowing next-to-nothing to knowing next-to-next-to-nothing. Good for me.

Yet, I know more than enough to offer a strong opinion on the Ukraine. I can sound really learned in an argument with other poorly-informed opinionated persons. (I am pretty good at sounding smart about something I know little of.) We opiners can really go at it, getting angrier in turns, at each other if we disagree or someone else (Putin or Obama or the opposition party perhaps) if we agree. Of course, we will think the person who disagrees with us is ignorant or poorly informed without noticing that we are as well. And in a representative democracy, this rhetoric has an effect as our representatives fall all over themselves to ally themselves to the majority opinion, to voice strongly the pundit-manufactured opinions of the poorly informed, and they are armed with confident-sounding phrases decorated with a few decontextualized facts. The result can be utterly tragic. Let’s hope it is not in this case.

Do we understand what we are doing when we do this? One of the aims of the Platonic dialogues is to make the strong case about the dangers of assertive, immoderate doxa/opinion. When talk is cheap we forget that it is also consequential. Countering doxa with a louder, contradicting version of the same type of doxa leads to an ever increasing scandal. We must be critical of punditry as such, not just the pundits with whom we disagree. (Nate Silver recently tweeted: “Never would have guessed how many political pundits also happen to be experts on Crimea.”) Let’s remember that pundits get paid to be opiners, not knowers.  Making clear to ourselves and others the ignorance inherent in opinion is the only antidote that I know for the chief political disease.  But that requires a kind of self-critical thinking that is much less fun in a world that celebrates rhetorically effective opinion. In all the hubbub about this crisis or that, what has really escaped notice is that philosophy is always the proper response.

Here are a few of my former posts on the nature of opinion: here, here, and here.

Ignorance and Pedagogy

This post is something of a coda to my previous slow reading assignment of Book 2 of the Republic. There, two young brothers of Plato, Glaucon and Adeimantus, revisit the Thrasymachus argument that a just life is worse than an unjust one, despite (i) having just witnessed Thrasymachus “losing” the argument to Socrates, and (ii) expressing the firm belief that the just life is better. They do not waver in the belief and yet are willing and ready to put that belief at peril by making Thrasymachus’ argument even stronger. Belief as such always includes a residuum of doubt, and the brothers voice this doubt as a way of encouraging further thinking with Socrates’ help. Socrates is amazed at his students. (So am I when the same thing happens to me among my own.) This has encouraged me to think again about belief and thinking. I hope this isn’t too repetitive, but here goes:
(more…)

What is tyranny?

The original meaning of tyrannos is not bad/oppressive rule, although it did come to mean that, but rather rule by someone foreign to the jurisdiction in which he governs. Not coincidentally, the word itself seems to be a foreign term ingested into the Greek language, perhaps during some epoch of occupation by a foreign power. To cite one well-known example of this relation between tyranny and foreignness: Oedipus Tyrannos isn’t given that epithet for being evil but for being raised outside of Thebes — Oedipus for the most part seems to have been considered a good ruler. So how does the word “tyrant” come to mean what we now take it to mean? (more…)

What grounds opinion?

The short answer is that nothing grounds an opinion. If it were grounded, it would constitute knowledge and would no longer be opinion. OK, what settles opinion then? Obviously, there are many opinions and to hold a particular opinion is to settle on one rather than moving on to another. To answer this question, I will rely on the schema of the tripartite soul in Book IV of the Republic. The tripartite psychology articulated there results from Socrates pointing out that the soul is often in conflict with itself, which he takes as evidence that the soul has parts. The city/soul analogy leads (more…)

Upcoming posts

Here are a few posts that you can look forward to over the coming weeks/months:

1. A continuation of my introduction to Mimetic Theory, including the following topics: the gospel unmasking of sacrificial myths, the apocalyptic situation that results from this unmasking, the notion of “structural innocence”, the “interdividual” status of human beings, the mimetic origins of occult phenomena, hominization and the birth of meaning, and (more…)