Classics and the Western Canon discussion

There's still plenty of good discussion to go in the earlier books, but for those who may be up to the schedule, it's only fair to open the Book 6 discussion.

Here we get the irresolvable, to me, dilemma that in the ideal state we are creating philosophers would be the best rulers, but in "real life" philosophers who try to enter politics inevitably fail.

So does this mean that philosophers really wouldn't make the best rulers? Or does it mean that the people are too ignorant of their own best interests to choose the best rulers?

Keep in mind that while monarchies, theocracies, and dictatorships were the norm in governance in the ancient world, Athens prided itself on being a democracy (whatever Socrates may have thought about democracy), and so in the Athenian real world the people really did get the chance to choose their own rulers.

(In his Apology, those who have read it will recall, Socrates also says that a just man cannot lead a public life.)

Another important aspect of this book, it seems to me, is Socrates's refusal (or inability?) to define the Good. He is very good at demanding that other people answer the "what is" question so he can then refute their definitions, but when Glaucon demands that he define the Good, he refuses.

Everyman wrote: "So does this mean that philosophers really wouldn't make the best rulers? Or does it mean that the people are too ignorant of their own best interests to choose the best rulers? "

For Socrates there seems to be an unbridgeable divide between the wisdom of the philosopher and the practical business of running the state. The main problem seems to be the philosopher's lack of interest, or maybe even disgust toward human affairs. The people see the philosopher as a stargazer and a babbler, and the philosopher is oblivious to practical matters.

The Ship of State metaphor is fascinating -- the ship commander is near-sighted and a bit deaf, and his understanding of navigation is imperfect. Shouldn't the first question be why he is allowed to captain a ship, considering his disabilities? And when Socrates says that the philosopher thinks that human life is of little importance (486a) shouldn't we then ask if this disqualifies him as unfit to rule human cities?

And if they are to be what we were describing, is there not another quality which they should also possess?

What quality?
Truthfulness: they will never intentionally receive into their mind falsehood, which is their detestation, and they will love the truth.

Yes, that may be safely affirmed of them.
'May be,' my friend, I replied, is not the word; say rather 'must be affirmed:' for he whose nature is amorous of anything cannot help loving all that belongs or is akin to the object of his affections.

Right, he said.
And is there anything more akin to wisdom than truth?
How can there be?
Can the same nature be a lover of wisdom and a lover of falsehood?
Never.
The true lover of learning then must from his earliest youth, as far as in him lies, desire all truth?

Socrates's "noble lie" has been much mentioned. Is he trying to say here that "regular" guardians are expected to use the noble lie, but there is a different standard for philosophers? I feel like I am missing something.

Thomas wrote: "And when Socrates says that the philosopher thinks that human life is of little importance (486a) shouldn't we then ask if this disqualifies him as unfit to rule human cities? "

For me, this was a weird statement for him to make. Since he follows it by asking "Won't such a man also believe that death is not something terrible?", do you think he means that life is not great in comparison to what comes after death rather than that life is not "anything great" (Bloom's translation) , in general?

I thought this book was straightforward and interesting in that S/P has stepped out of his ideal city and into the real world to make his point that finding a philosopher respected by the people and willing to serve is an almost impossible task. Do we see an admission here that his ideal city is not practical because it ignores human behavior?

The Ship of State metaphor is indeed fascinating and a direct attack on the demos, which S/P considers to be an uninformed mob ruled by passions rather than knowledge and wisdom. There are people to this day who believe that. S/P's constitution would not be a democracy, and if forced to create one he would have more qualifications than citizenship, age, and, gender to participate. So would some people today.

Genni wrote: "Socrates's "noble lie" has been much mentioned. Is he trying to say here that "regular" guardians are expected to use the noble lie, but there is a different standard for philosophers? I feel like I am missing something. "

I think he's saying that philosophers are essentially different than guardians in their love of the truth. Earlier he argued that wine lovers love every kind of wine, lovers of honor love every kind of honor, and boy lovers love all boys (even the ugly snub-nosed ones like Socrates ...) Someone who loves these sorts of things will accept the best he can get, even if it isn't the best there is. But the truth does not admit degrees -- something is either true, or it isn't. The truth is by definition the best; there is no lesser form of truth, no "sort of true." Which means the philosopher, who loves the truth, loves only what is absolutely perfect, what is unchanging and eternally true.

The guardians can make use of the noble lie as an explanation for the different classes of the city, but as far as I can tell, the philosopher would have no use for the lie, except as a way of controlling the citizens.

Genni wrote: "For me, this was a weird statement for him to make. Since he follows it by asking "Won't such a man also believe that death is not something terrible?", do you think he means that life is not great in comparison to what comes after death rather than that life is not "anything great" (Bloom's translation) , in general? "

I think that's exactly right, and it seems to present a serious problem when it comes to ruling the city. How does absolute truth translate to practical everyday life? Can it help me load the dishwasher? (Which, according to my wife, is completely beyond my grasp.)

Xan Shadowflutter wrote: "The Ship of State metaphor is indeed fascinating and a direct attack on the demos, which S/P considers to be an uninformed mob ruled by passions rather than knowledge and wisdom. There are people to this day who believe that. S/P's constitution would not be a democracy..."

It seems that the philosopher is alone on a pinnacle high above the demos. If the philosopher communes with a Good which cannot be communicated, since it cannot be defined, and which cannot be translated into the practical business of everyday life, then he is what Greeks would call an "idiotes," a private person. (The pejorative "idiot" is related to this word.) The philosopher might be a supremely honorable person, but I'm not sure that he can serve any political function.

It also strikes me as odd that Socrates was not this sort of person at all. He was social in every way, not at all a private person. Exile from the city was a fate worse than death for him.

Thomas wrote: "It also strikes me as odd that Socrates was not this sort of person at all. He was social in every way, not at all a private person. Exile from the city was a fate worse than death for him ..."

Which raises the question, how much of this is Socrates and how much of this is Plato putting words in his mouth? By all accounts Socrates was affable yet strange. What would we think of someone who walked around the mall (while they still exist) attempting to engage strangers in philosophical debate? Were Athenians all that different from us? Meanwhile Plato seems to have been more reserved and withdrawn, spending most of his time writing and teaching, although he did travel.

I sometimes wonder how differently we might view Plato if only one of his lectures had survived on a subject covered in his dialogs. Would it be different in structure and depth? Would it clearly state what he thought the Good or Justice was? Would it be more religious? I have not read Aristotle, and perhaps he provides a partial answer, but I don't think so.

Thomas wrote: "How does absolute truth translate to practical everyday life? Can it help me load the dishwasher?"

This made me chuckle. Maybe there is actually a fixed eternal form of the ideally stacked dishwasher, with the cutlery facing the right way and the space perfectly maximized, but my wife would also contend that my mind hasn't been able to elevate itself above the dividing line to the sunlit uplands of this perfect form.

You make a serious point though. I'm yet to comprehend how the philosophical appreciation of all these perfect forms translates into our everyday lives. I can see its application in mathematics and science, especially physics, but I'm less certain about how it applies to the messiness of people and cities.

Xan Shadowflutter wrote: "Which raises the question, how much of this is Socrates and how much of this is Plato putting words in his mouth?"

Yes, I thought this too after reading Thomas' comment. Many of us have opted for S/P so far, as we're not sure if it's Socrates or Plato talking, but this passage does seem out of character with what little I know of Socrates' life.

I'm reading Simon Blackburn's book on Plato's Republic, which Everyman mentioned at the start of this group read, and he outlined how two major philosophers have responded to this section in the book (Theory of Forms):

"For Nietzsche, Plato is here the sick, sadistic ascetic who plunged Europe into the darkness of his extraterrestrial nightmares. For Kant, he has made a slightly more pardonable blunder, believing that in the name of real understanding he can simply jettison the connection with sense experience which alone makes understanding possible."

Thomas wrote: " Can it help me load the dishwasher? (Which, according to my wife, is completely beyond my grasp.) ."

Lol! There is only one correct way to load the dishwasher, and that one way varies from person to person. :-)

And when Socrates says that the philosopher thinks that human life is of little importance (486a) shouldn't we then ask if this disqualifies him as unfit to rule human cities?

The first time I read your question, I thought you were saying he thinks human life is not great, as in "of no intrinsic value" which, to me, is a little different from thinking it not-so-great in comparison to what is to come. If I remember correctly, in other works Socrates seems to believe in something like reincarnation. If I am remembering correctly, the life you live on earth has a direct bearing on the kind of after-life you will have (please correct me if I'm getting all of this confused). So if the philosopher is looking forward to the after-life, but doing so in a way that he is concerned about life down here (but again, in a comparative way), then I would not think this would disqualify him from ruling??

Genni wrote: "Thomas wrote: " Can it help me load the dishwasher? (Which, according to my wife, is completely beyond my grasp.) ."

Lol! There is only one correct way to load the dishwasher, and that one way var..."

Isn't the "correct way" really a question of one's methodology for UNLOADING the dishwasher?

The future matters??? In ruling, in making decisions, in choosing justice or not, ...

Genni wrote: "Thomas wrote: " Can it help me load the dishwasher? (Which, according to my wife, is completely beyond my grasp.) ."

Lol! There is only one correct way to load the dishwasher, and that one way varies from person to person. :-)"

I am imagining there is a "form" of a perfectly loaded dishwasher floating out there in space somewhere.

Which brings me to a real question. Forms by their nature appear to be static perfections of a thing in one state. Jokingly I asked myself if Plato would think there was a form of a perfectly loaded dishwasher full of plates and cups, and a separate perfectly loaded dishwasher full of bowls and utensils or just one form of one perfectly loaded dishwasher that covered anything it could be loaded with? In more general terms, what is the form of something that needs to exist in different states?

We often use chairs as the example for explaining forms, but I never understood how there could be one perfect one that everybody would be comfortable sitting in. If there is, could someone please inform the airlines and movie theaters of its measurements.

Dave wrote: "Thomas wrote: "How does absolute truth translate to practical everyday life? Can it help me load the dishwasher?"

This made me chuckle. Maybe there is actually a fixed eternal form of the ideally stacked dishwasher, with the cutlery facing the right way and the space perfectly maximized, but my wife would also contend that my mind hasn't been able to elevate itself above the dividing line to the sunlit uplands of this perfect form..."

Clearly this is a flaw that pervades husband-hood... teaching my husband the correct way of stacking the dishwasher is a lost cause.

Janice(JG) wrote: "Clearly this is a flaw that pervades husband-hood... teaching my husband the correct way of stacking the dishwasher is a lost cause. ..."

The solution is easy -- allow him to both load and unload it. Certainly that is a specialization of work that would not be inconsistent with S/P and allow the development of skills. (My bug-a-boo after my son visits is not getting stuck with fork tines. Clearly I didn't train him properly. But his dad did teach him it was no crime to do the chore entirely himself. He could stack it better than I, but we did share the task--preferably not at the same time [g].) (view spoiler)[Yes, for the record, I am a widow. I still miss having someone with whom to share household duties, regardless of differences in methods.) (hide spoiler)]

Genni wrote: "The first time I read your question, I thought you were saying he thinks human life is not great, as in "of no intrinsic value" which, to me, is a little different from thinking it not-so-great in comparison to what is to come."

In the Phaedo Socrates is agnostic on the subject of the afterlife, and he hasn't spoken about it yet in the Republic, so I don't think that's what he's talking about here. (He will get to something like that later, though.)

For now, I think what makes human life of little importance is its transience. I think it's probable that the story of Gyges early in the Republic comes from Herodotus because transience is a major theme in the Histories:

...since many of those that were great long ago have become inferior, and some that are great in my own time were inferior before.... human prosperity never remains constant... Histories, 1.5

Human existence is in constant flux, always becoming one thing or another. We prosper, and we decline. We do well for a while, we get sick, we suffer, and we get well again, on both an individual and a national scale. Truth, wisdom, the Good -- all the "Ideas" are things that for Plato cannot be in flux. They must always be one perfect thing that never changes. I'm not sure if this is what the afterlife is for Plato, but if it is, it reminds me of the Talking Heads song "Heaven." "Heaven is a place where nothing ever happens." Socrates seems to long for such a place.

David wrote: "In more general terms, what is the form of something that needs to exist in different states?."

"Forms," as I understand them, do not really exist. Sometimes the Greek word (eidos) is translated "genus," if that helps. Things that exist can belong to a genus if they have all of the characteristics of the genus, but things within the genus are not identical to each other because they exist in different states, as all things in the real world do. Even chairs made by the same carpenter with the same materials in the same pattern will have some variation because that is the nature of material existence. No member of a genus is exactly the same, but we still group them in our minds as "forms" or "ideas" or "patterns" and give the genus and its members one name.

Plato makes a huge jump though when he goes from genus as a taxonomical hierarchy to the idea of The Good. What does everything that we think of as Good have in common? Or is the Good not an idea at all, but more akin to light from the Sun, as Socrates argues at the end of Book 6? The Good is that by which we are able to understand what is beneficial to us, what makes things understandable to us as useful things. If Justice is a useful thing, is it the Good that allows us to know it as useful?

Thomas wrote: "For now, I think what makes human life of little importance is its transience. I think it's probable that the story of Gyges early in the Republic comes from Herodotus because transience is a major theme in the Histories:

...since many of those that were great long ago have become inferior, and some that are great in my own time were inferior before.... human prosperity never remains constant... Histories, 1.5

Human existence is in constant flux, always becoming one thing or another. We prosper, and we decline. We do well for a while, we get sick, we suffer, and we get well again, on both an individual and a national scale. Truth, wisdom, the Good -- all the "Ideas" are things that for Plato cannot be in flux. They must always be one perfect thing that never changes. I'm not sure if this is what the afterlife is for Plato, but if it is, it reminds me of the Talking Heads song "Heaven." "Heaven is a place where nothing ever happens." Socrates seems to long for such a place.
"

Thanks, Thomas. This is helpful.

This book (so far, I haven't finished it yet) reminds me of your comment a few books back that Plato is making an honest attempt at the impossible. The idea that Plato is exploring ideas here that people intuitively dismiss jives with me a little more.

David wrote: "Which brings me to a real question. Forms by their nature appear to be static perfections of a thing in one state. Jokingly I asked myself if Plato would think there was a form of a perfectly loaded dishwasher full of plates and cups, and a separate perfectly loaded dishwasher full of bowls and utensils or just one form of one perfectly loaded dishwasher that covered anything it could be loaded with?"

I have thought (maybe incorrectly) that Socrates thinks those static ideas exist, but only pertain to things metaphysical. He seems to intuitively think they exist but can never find them in his search. But Thomas points out that "forms" do not really exist, only slight variants under "genus" that all have something in common. I wondered if this can be applied to justice. If the answer to the question about giving keys to a drunk person varies according to circumstance, then maybe it can be applied?

Thomas wrote: ""Forms," as I understand them, do not really exist. Sometimes the Greek word (eidos) is translated "genus," if that helps."

I am with you on Forms not existing as were many later philosophers. However, it seems S/P took a different view that the forms actually existed and the particulars were mere shadows. The upcoming explanation of the divided line may make more sense of this, and this passage from Wikpedia's theory of universals page:

Plato believed there to be a sharp distinction between the world of perceivable objects and the world of universals or forms: one can only have mere opinions about the former, but one can have knowledge about the latter. For Plato it was not possible to have knowledge of anything that could change or was particular, since knowledge had to be forever unfailing and general. For that reason, the world of the forms is the real world, like sunlight, while the sensible world is only imperfectly or partially real, like shadows.
https://en.wikipedia.org/wiki/Problem...

Additinmally, εἶδος (eidos) is translated on the Tuffs site as, "that which is seen: form, shape" http://www.perseus.tufts.edu/hopper/m...
although I can see it taken as "Genus" (or even Species) but most often think "Idea", or "Ideal" to myself as an opening into nominalist critical opinion of Forms, which we seem to share.

David wrote: "I am with you on Forms not existing as were many later philosophers. However, it seems S/P took a different view that the forms actually existed and the particulars were mere shadows."

Very true. Sometimes philosophers use the term "Being" to refer to transcendent reality -- what really exists for Plato -- and "beings" to refer to immanent reality, the sensible world. I should be more careful in my terminology.

Anything that changes can not be for Plato because it is never one thing, which rules out the sensible world entirely. The sensible world in that way does not exist. (Aristotle "fixes" this problem by explaining how things can change in a material way and stay the same in an essential way. Very helpful, that.)

εἶδος (eidos) is translated on the Tuffs site as, "that which is seen: form, shape"

Eidos literally means "the look of a thing". It originally comes from the verb "eido", to see (in Latin, video) but is used more commonly in its perfect form, "oida", to know. It's probably not accidental that seeing is an everyday metaphor for knowing or understanding. It doesn't really work in translation though -- the look of Justice? Or maybe it works just as well as "form," which is fairly obscure as well.

Genni wrote: "I have thought (maybe incorrectly) that Socrates thinks those static ideas exist, but only pertain to things metaphysical. He seems to intuitively think they exist but can never find them in his search."

No, you're right. I should not have said that the static ideas don't exist, because for Socrates they are actually the only things that exist. It's the sensible world that doesn't exist. Sorry for the confusion. :/

Socrates says that material things "participate" in the static ideas. A barstool and a recliner are chairs because they participate in the idea (or form or eidos) of chairness. He never explains how "participation" works exactly, but there is some connection between the metaphysical idea and the sensible thing that participates in the idea. (He sort of explains this with the myth of the cave in the next book of the Republic. I'll be interested to see what you think.)

Thomas wrote: "I should not have said that the static ideas don't exist, because for Socrates they are actually the only things that exist. It's the sensible world that doesn't exist. Sorry for the confusion. :/."

Thanks for clarifying!

While we are on the subject of confusion, in message 17 you said that Socrates was agnostic on the subject of the afterlife in Phaedo. (By agnostic, I understood that to mean that he didn't have a definite belief.) I was under the impression that he DID definitely believe in the afterlife (since he was attempting to prove the immortality of the soul), and sought to prove it but never could through argumentation. His belief was one reason he was able to meet death so calmly? (And I am not trying to get off topic here, but I do keep thinking about previous dialogues and bringing them to this reading, what little I understood from them!)

Genni wrote: "I was under the impression that he DID definitely believe in the afterlife (since he was attempting to prove the immortality of the soul), and sought to prove it but never could through argumentation."

He does believe in the immortality of the soul, but is that the same as an "afterlife"? When he speaks of an afterlife it is always in the form of a myth, and knowing what he thinks about myths I have to wonder if he thought such an afterlife was really possible or if it was just a comforting story. The passage I was thinking of is at the end of the Apology, from 40c to the end.

Let us consider in another way also how good reason there is to hope that it is a good thing. For the state of death is one of two things: either it is virtually nothingness, so that the dead has no consciousness of anything, or it is, as people say, a change and migration of the soul from this to another place. And if it is unconsciousness, like a sleep in which the sleeper does not even dream, death would be a wonderful gain. ...But on the other hand, if death is, as it were, a change of habitation from here to some other place, and if what we are told is true, that all the dead are there, what greater blessing could there be, judges? For if a man when he reaches the other world, after leaving behind these who claim to be judges, shall find those who are really judges who are said to sit in judgment there, Minos and Rhadamanthus, and Aeacus and Triptolemus, and all the other demigods who were just men in their lives, would the change of habitation be undesirable? Or again, what would any of you give to meet with Orpheus and Musaeus and Hesiod and Homer? I am willing to die many times over, if these things are true; for I personally should find the life there wonderful...

The question that all this raises for me is what does Plato mean by the "soul"? Is it any different from the way you think of it?

(And this is definitely not off topic. :)

I spent the last hour or so working out the geometry of the Divided Line (509-511), and I want to share the result in case some of us have not seen it before.

Socrates posits a line divided into two unequal parts, and each of the two parts divided in the same proportion. As he explains, the smaller part of the smaller part (let's call it D) corresponds to shadows, reflections, and such images. The larger part of the smaller part (C) corresponds to the physical world. The smaller part of the larger part (B) corresponds to the world of mathematics, which we apprehend with the mind but only "by hypothesis" (as in "let there be a line"). Finally, the larger part of the larger part (A) corresponds to pure ideas apprehended by reason.

Let's call the ratio of division R. Then we have:
(1) A/B = R (the division of the larger part)
(2) C/D = R (the division of the smaller part)
(3) (A+B)/(C+D) = R (the division of the whole)
From (1), we have A = BR.
From (2), we have C = DR.
Putting these into (3), (BR+B)/(DR+D) =R.
Factoring out B and D, we get [B(R+1)]/[D(R+1)] = R.
We can simplify that to B/D = R.
But from (3), we also know C/D = R.
So B = C. In other words, the mathematical realm and the real physical world are exactly the same size.

I always thought this identity had deep spiritual significance for Plato, and justified the notion (now almost universal) that mathematics can give a complete account of the physical world.

Thomas wrote: "He does believe in the immortality of the soul, but is that the same as an "afterlife"? When he speaks of an afterlife it is always in the form of a myth, and knowing what he thinks about myths I have to wonder if he thought such an afterlife was really possible or if it was just a comforting story. "

I do think believing in the immortality of the soul is to believe in the afterlife, if only in the most simple sense of the word. IOW, if the soul is immortal and obviously departs after physical death then there must be something "after" for the soul to go to if it does not die. ??

I like your observation that he engages in a rather waffling treatment of myths and then uses them to illustrate his point. But I also wonder, what other options did he have to reach those around him who believed in myths? (If his goal was to convince?) I keep thinking he did not have Scriptures to refer to as Jews/Christians do, or the Quran as Muslims do. If argumentation fails, where else could he turn? But it seems to me that he was much too sincere in Phaedo, and strove too hard to prove the immortality of the soul, to not believe in the existence of an afterlife. (Or rather should I say that Socrates believed in it, not Plato? It's like running a marathon trying to keep them separated.)

The question that all this raises for me is what does Plato mean by the "soul"? Is it any different from the way you think of it?

Largely, he seems to believe that the soul is a spiritual part of man. A part that you cannot see that fully separates from the body. More specifically, I don't know. I was hoping someone here would! If this is how he views it, then it is not different from how I see it. But obviously, if Socrates couldn't prove it, I certainly can't.

Roger wrote: "I spent the last hour or so working out the geometry of the Divided Line (509-511), and I want to share the result in case some of us have not seen it before.

Socrates posits a line divided into t..."

Wow, Roger, kudos.

I am in no way a mathematician but I wonder whether this correspondence is what Plato intended, since he places the mathematical world above the visible in his diagram. Is this an oversight or mistake on his part? Or perhaps a very clever trick?

Genni wrote: "Largely, he seems to believe that the soul is a spiritual part of man. A part that you cannot see that fully separates from the body."

From Book 4 we might conclude that there are three parts of the soul: the calculating or "intellectual" part (logistikos), the emotional part (thumoeides), and the appetitive part (epithumetikos). Are all three immortal -- or is it only the first part, the intellectual part? Is that what you think of as "spiritual"?

I would like to think that all three parts are immortal so there will be ice cream in heaven, but I suspect for Plato that's not the case. The ancient Greeks thought of the soul as a self-animating principle -- things are alive due to the presence of soul -- plants, animals, and humans alike all have some animating soul that causes them to live and grow. We have Plato to thank for the idea that the soul is separate from the body, a truly revolutionary idea with enormous repercussions. But I suspect that for him it's just the most sophisticated part of the soul that is immortal -- the intellectual part. There will be math in heaven, but no ice cream.

When you have math, who needs ice cream?

Thomas wrote: "From Book 4 we might conclude that there are three parts of the soul: the calculating or "intellectual" part (logistikos), the emotional part (thumoeides), and the appetitive part (epithumetikos). Are all three immortal -- or is it only the first part, the intellectual part? Is that what you think of as "spiritual"? "

I was actually traveling around books 4 and 5. I'd like to go back and see what you are referring to. Can you give some references numbers from Book 4? Sorry!

Thomas wrote: "The ancient Greeks thought of the soul as a self-animating principle -- things are alive due to the presence of soul -- plants, animals, and humans alike all have some animating soul that causes them to live and grow. ."

Last year, I read Aristotle's On the Soul because I was curious about what he said about the soul. When I got to the end, I thought, "This wasn't about the soul at all!". After I started looking around, I discovered that the word "Soul" in the title is rather misleading and something of an unfortunate translation that has kind of hung around?

But I didn't know that all ancient Greeks thought of it this way. You have read them more widely than I have so I defer to you. From Phaedo, I actually thought Socrates differed from Aristotle in his thoughts on the soul? The self-animating force from Aristotle bears little resemblance to Socrates's immortal counterpart? Or maybe they are the same but Aristotle just wasn't concerned with the soul before/after life on earth? Does Plato use the same Greek word that Aristotle uses?

Roger wrote: "When you have math, who needs ice cream?"

[g] Especially when it is recognized how to divvy up proportions to get the desired result. Little room left for William James's "authentic" mystics?

Kathy wrote: "I am in no way a mathematician but I wonder whether this correspondence is what Plato intended, since he places the mathematical world above the visible in his diagram. Is this an oversight or mist..."

I'm not sure if this addresses your concern exactly, or at all, but the correspondence that I think he is making is between vision and understanding ("intellection" or noesis). It's very difficult to articulate what happens in the top section of the divided line, but the suggestion is that we know this top-level "noetic" world with more certainty than the mathematical one.

The mathematical world stands in the same relation to the "noetic" world in the top section as images stand to the physical, material world. We can express mathematical things with the help of hypotheses, axioms that can't be proven, which makes them similar to images. Plato suggests that we can understand noetic things -- pure "Ideas" -- in the way we see real things, as opposed to images. We grasp them in an immediate way, but in a way we cannot easily articulate. We need poetry, analogies, and metaphors to express them, but these are verbal "images," things Socrates distrusts. They can't express the real thing, which is why ideas like virtue, justice, etc. are so hard to express in words, and yet... we understand them without presuppositions or hypotheses...

I'm not sure if I buy this, personally, but it does get a little clearer in Book 7.

Genni wrote: "I'd like to go back and see what you are referring to. Can you give some references numbers from Book 4? Sorry! "

No worries. It's around 436 and on, where he is discussing how it's possible to want something and not want it at the same time. (Cue Don Giovanni... https://www.youtube.com/watch?v=GATj9... )

Genni wrote: "Last year, I read Aristotle's On the Soul because I was curious about what he said about the soul. When I got to the end, I thought, "This wasn't about the soul at all!"."

It's been a while since I looked at On the Soul, but they do use the same term. Aristotle takes a more systematic approach, but when he starts to examine the human soul specifically, he examines many of the same attributes that Plato does. Not in the same way, of course, but despite their disagreements they would say that they were examining the same thing. If only we had Aristotle's dialogues...

Thomas wrote: "I'm not sure if this addresses your concern exactly, or at all, but the correspondence that I think he is making is between vision and understanding ("intellection" or noesis)..."

Thanks, Thomas. I think I understand the proportional nature of the diagram (images:visible things as mathematical objects:forms), but I was reacting more to Roger's B=C, which crosses over the line from lower world to upper world. Maybe it's "just" a clever bit of math and we should leave it at that! But if not, I was wondering whether Plato might have intended that congruence, which seems unlikely since the structure of the diagram puts mathematics above visible things (to use all of the terminology from Cornford's translation).

It seems to me that P/S is setting a very high bar for the Rulers: they must not just believe in what is good and true, they must have actual knowledge of it. An ideal. It strikes me that theory actually poses a danger if the theoretical is understood to be possible. The attempts to enact it then become dystopian, as we've mentioned in other threads: getting rid of the "bad" children, manipulating relationships through lies, etc. Whereas, if we were to treat theory as theory, we might live striving for that ideal but knowing we will never attain it (a lot like my yoga class!), and therefore pass over extreme actions intended to force it into reality.

Perhaps the identity -- nice work Roger -- points out that the territory B & C cover in our conceptual landscape are equal in size but says nothing about the concepts being alike or of equal importance.

If one of the rulers were mistaken in his apprehension of the Good, how could he ever be set right?

Whether it is correct or not I cannot say, but the congruence in length on the divided line between the mathematical/hypothetical realm and the visible/sensible things makes sense if you think each real and visible object is a corresponding shadow of some mathematical model that describes it. Since it would seem that you should not have an object that is without a mathematical representative, and you should not have a mathematical representation without a corresponding visible object, the resulting one to one correspondence would entail the lines representing each should be of equal length.

Furthermore, I think it is important to visualize this line not as a horizontal line, but as a vertical one with the good at the top and images at the bottom. Now I have not as yet determined how S/P intended this line to be divided, but it seems to work best for me with the shortest division representing good at the top, and the largest division representing images at the bottom. This make sense to me because there never seems any end to the vast sea of mere opinions that would take up the bulk of the line in generated by all the speculation of a singular good. {edited to add: also forms being the single defining instance of many particulars seems to imply the good as the shortest segment with the rest being longer.]

If you want to visualize this line to scale for yourself, you may draw a line 16 units long with segments of 1, 3, 3, and 9 top to bottom or bottom to top). this is the shortest one I could derive in which the math works out with all the lengths in simple whole numbers. A 25 unit long line segmented into 1, 4, 4, and 16 also works.

1, x, x, x^2 works for any positive x.

Roger wrote: "1, x, x, x^2 works for any positive x."

Except X cannot equal 1 because you would be dividing the line equally. Nice formula! I was lazy and just plugged things into a spreadsheet. Your formula does make it easier to spot a shorter over overall line using whole numbers at 9 units, composed of segments 1, 2, 2, and 4 units long.

I was lazier still and just went with Cornford's diagram, which I can't figure out how to reproduce here, but which is incorrect according to Roger's math anyway ("visible things" is larger than "mathematical objects").
David's explanation that "if you think each real and visible object is a corresponding shadow of some mathematical model that describes it" doesn't work for me, though, if we are to think of "shadows" as lesser than the "real" objects to which they correspond. Unless "shadows" and "models" are really part of the same realm. Maybe the "intelligible world" section picks up where the "world of appearances" leaves off, and the lowest section of one overlaps directly with the highest section of the other--a three-dimensional model in that case!

Roger wrote: "If one of the rulers were mistaken in his apprehension of the Good, how could he ever be set right?"

Exactly!

Kathy wrote: "David's explanation that "if you think each real and visible object is a corresponding shadow of some mathematical model that describes it" doesn't work for me. . ."

I was thinking volume, as in number of objects. Somehow ranking things as greater to lesser makes sense too and was escaping me, thanks. But then I am back to wondering how the middle segments are ranked equally. . .hmm. . .my thinking cap is starting to short out! :)

I couldn't get the image to appear here but the drawing of the divided line on this page is credited to Cornford:
https://kenschles.wordpress.com/2011/...

LOL, mine too!

Roger wrote: "If one of the rulers were mistaken in his apprehension of the Good, how could he ever be set right?"

A true Scotsman philosopher is never wrong.

David wrote: "Roger wrote: "If one of the rulers were mistaken in his apprehension of the Good, how could he ever be set right?"

A true Scotsman philosopher is never wrong."

And how do you determine which ones are true?