Talk:Analogy of the divided line

External Link (Psychology, Philosophy, and Plato's Divided Line)
I previously added a link to this paper, which seems clearly relevant, and all-the-more helpful to users because it supplies (1) the complete text of the Divided Line (including the often-neglected section in Book 7 of the Republic), and (2) perhaps the most extensive bibliography available (with hyperlinks!).

User BlueMist removed the link, giving as the sole reason, and without explanation, that it was, in his or her opinion, "unphilosophical." How this person could have arrived at this opinion (unless perhaps they didn't look at the article at all, but only its title) is beyond me.

In any case, I contest the removal of the link for the following reasons:

1. On what basis do you (BlueMist) call it "unphilosophical?" It cites all the major papers, and pursues a well-known and extremely important theme (the distinction between dianoia and noesis). It follows in large part Annas and Murdoch. Evidently what you mean is that it doesn't agree with your interpretation of the Divided Line.

2. The interpretation of the Divided Line is controversial. It is not your place to limit points of view, as long as they are reasonable, plausible, logically presented, and adequately referenced.

3. What are your qualifications to call it unphilosophical? Are you a professional philosopher?

4. Most importantly: Where is rule that says that philosophers alone own Plato, and that the only valid way to read Plato is philosophically? Wouldn't Plato have considered himself a psychologist (a scientist of the mind or soul) as well as a philosopher? Would you please tell me the name of a single professional philosopher who would say that psychology is not a proper perspective to take on Plato? (I know dozens of professional philosophers who would assert the contrary. Richard Kraut, for starters.)

5. In any case, the citation does nothing but give users more information. It supplies the entire text (including Rep. 7.533d-534b, which the Wikipedia article doesn't even mention), and a solid, professional-caliber bibliography. Any academic researcher interested in this topic would find this bibliography most helpful indeed.

I am putting the link back in pending any logical and explicit reason being given as to why it shouldn't be. If anyone thinks it shouldn't be there, please raise your concerns here, before acting like a 'Wiktator' and arbitrarily deleting it!

Practical321 (talk) 23:52, 2 December 2014 (UTC)

Practical, I resent your personal attacks and insinuations about my being this or that. I am not on trial here, and you are not the prosecution.

What is at issue is whether an online blog, you insist on linking, does or does not belong in this Wiki article. http://www.john-uebersax.com/plato/plato1.htm is a personal blog by a non-professional, unqualified writer. The blog is a stew of philosophy, psychology, and religion. All of which are poorly thought out. Re-read the blog entry with attention to key philosophical terms, and you can judge for yourself. BlueMist (talk) 02:56, 3 December 2014 (UTC)

messed up
When I try to view this article (only this article), it's all messed up, for want of a better phrase. It looks like it starts displaying the page, and then when it gets to the table, it starts again from the top of the screen and writes everything over the top of what ws there before. Previous versions of the article are the same. This is in Opera 6 on Windows XP (I'm not proud of running Windows XP, but there it is). I can provide a screengrab if needed. --Camembert

I'm going to rewrite that table entirely, don't worry. --LMS


 * Thanks, looks great now. Just out of interest, and for future reference: do you know what it was exactly that was causing the problem? --Camembert

Don't know! I suspect the caption tag isn't supported by Opera. If the table looked good after I removed it, that's probably why. --LMS

I'm willing to debate this, but I think the following (the original article) basically omits a lot of essential information about the divided line, and is actually misleading in places. The table really strikes me as unhelpful. It's a nice graphic and it's better than nothing, but simply having English words arranged in boxes like this really doesn't convey anything important that Plato's own metaphor (the divided line itself) wasn't supposed to convey.

'''I agree that most of what was written previously was at best misleading and at worst utter shit. In keeping with Socratic style I have exposed the truth by pointing out how wrong you lot's previous beliefs were. If anyone wants to re-write this in a more conventional style, I think that would be a good idea. Probably best to ditch the article and begin again from scratch.'''

As for the rest (explanations of "Conjecture," "Belief," "Understanding," and "Reason"), without the context of the rest of the discussion of the metaphor, this is just confusing and less than helpful. With the context, it becomes redundant. --Larry Sanger

Conjecture (Imagining) This knowledge is the lowest degree of truth; it is all mere reflections or dreams, and only shadows of the real object itself. Plato is thus saying that a still-life painting of an apple points less to the truth of the apple than the apple itself.

'''Knowledge???????? this is very loose and misleading language, conjecture is not knowledge at all according to Plato. This is a state of ignorence, or at very most, 'opinon' (doxa)'''

Belief (Perception) This knowledge is higher and helps explain (or make more intelligible) the Conjecture level; this level is the physical apple itself. However, this level is still very limited in that its knowledge of the physical apple cannot grasp the botanist's knowledge of an apple. The botanist's knowledge, what defines an apple, is in the above levels, past the "divided line" between knowledge and opinion.

'''again, this is not knowledge, and this is not 'intelligable'. Only the objects in CE are 'intelligable'. you very incorrectly classed an empirical science such as botony in the CD division. the botanist most certainly belongs in this catagory'''

Botany is perhaps a very good example of something in this division. Note the discussion in book 7 about how concideration of our relative predicates (e.g. heavy, light) lead us, because our mind cannot aquiese in the contradiction that all is heavy and light, lead us to ask questions like "what is heaviness" and "what is lightness". From this we are lead to ask also about the particulars of our world, what is a unified thing (e.g. an apple)? we see that the apple qua apple is a single apple. but then we concider that it may have many parts (the concideration of the botanist, looking at the composition of a physical thing that we generally class as a unitary item).

Now THIS type of concideration, still firmly in the realm of belief, is what leads us to concider the idea of unity and numbers of things as things in themselves, abstracted from any particular instance. I.e it leads us to concider mathematics, which falls in the CD part of the line.

there is a really important reason why mathematics and not empirical science occupy the CD part. the objects of mathematics are accecible only by the intellect, but the objects of the emprical sciences are accecible only by perception.

I can understand how this confusion of yours arose: the way of thinking about objects in empirical sceinces and mathematical thought is similar in many ways, and that is why the sections BC and CD are equivalent in length, but the SUBJECT MATTER of those thoughts is very different.

Understanding (Science, Mathematics) This level puts us into knowledge instead of belief or opinion; at this level the apple is understood by the botanist's definition of it. Here, all is abstract and universal and unchanging; below, all is concrete and in flux. The limitation, however, is that science and mathematics depend on particulars and physical (the level below, Belief) representations.

'''for my point about science see the note above. For God's sake if you really wanted to put science in this catagory you really would have been better off with something like a priori theoretical physics, but even this is questionable. Are you a botanist by any chance?'''

all is abstract here, that is true. Everything other than the forms depends upon particulars. a representation is also a kind of particular. mathematics is not 'universal' really, at least not in the sense that forms are universal. the study of mathematics for the guardians say is not an end in itself but to train to mind to concider the idea of abstract particulars not physical particulars. mathematics is not exactly unchanging and eternal. But it is indeed truer and of higher metaphysical and epistemological status than botany etc. As this is the intelligable realm, mathematical 'knowledge' is possible.

[N.b. This argument is an illustration of mine and not one used by Plato] To see the difference between empircal science and the abstract pursuit of mathematics concider the difference in certainty one can have about even something like the laws of physics vs the fact that 1+1=2. We only arrive at these scientfic beliefs through inductive reasoning based on our past observations, which are inherently less certain than the fact that 1+1=2, because the truth of the former is inherently fallible and the truth of the latter is inherently infallible, and thus certain. Even if we were brains in vats and there were no apples really, 1+1 would still equal 2.

The kind of reasoning that a scientist performs with respect to various empircally driven postulates, an instance of this logical reasoning being the if... then... conditionals themselves (IF gravity exists THEN objects fall the ground, for instance), is of the same kind as in mathematics (IF 1+1=2 THEN 1+2=3) but the key difference is the subject matter and hence certainty of the postulates in the two cases. We can only gain infallible knowledge therefore through not just reasoning to conclusions from any old postulates but from CERTAIN, intelligable, ones. According to Plato all knoweldge must be infallible, and hence scientfic 'knowledge' is not knowledge. this may seem to be an unrealistically high standard of knowledge but this is what Plato said.

Reason (Dialectic) Finally, we reach pure reason itself. At this level all of the Forms developed in the Understanding level are brought together into unity and into a single Form, the Idea of the Good. Through dialectic reasoning, one can analyze all forms and see their relation to one another.

'''WHAT??? We were able to apply reason to the objects at every level of the line, what we concider here is the form of reason itself. to say 'we reach pure reason' is very very misleading. Dialectic is indeed the method through which Plato says the forms will be revealed, in that any true account of any of the forms, including the form of the good, will stand up the the dialectic method of destroying false hypotheses. The key thing about DE is that we are concidering the forms themselves as our subject matter, and that the only way Plato believes we can be doing this is via dialectic. eventually after concidering the multiplicity of forms we realise that they all really reduce to the form of the good'''

To complete the example of the apple:
 * Conjecture: a mirror image, a painting, or a reflection off the water
 * Belief: seeing and feeling
 * Understanding: the definition or concept
 * Reason: the form of the apple is brought together with all other forms and melded into the supreme and complete Idea of the Good

I think this summary is beyond repair, here's an alternative but with justice, not apples


 * Ignorence: concideration of justice in a play or novel
 * Opinion: concideration of instances in the world that are just and unjust, and seeing patterns
 * [not easy to classify]: concideration of abstract objects, like mathematical ones
 * Knowledge: concideration of the form of justice itself, and then the form of the good

the third catagory is known to be rather difficult to interpret in a similar way to the others. It is a kind of transitional phase, higher than opinion as it doesn't feature concrete particulars like  the instances of justice that we might draw patterns or empirical ethical formulations from, but lower than the true knowledge of forms. I didn't mention the word justice here for good reason. one could in theory move straight from seeing patterns in justice to concidering the form of justice itself, BUT Plato reackons that in actual fact we will need to concider mathematical objects, which are well known abstract objects with physical embodiments, to prepare ourselves mentally for concidering that there is some abstract form of justice such that all conrete instances of it are mere shadows and approximations of it, which is the forth part.

(Source: From Socrates to Sartre: the Philosophic Quest, by T.Z. Lavine)

'''I've not read this book, but either you've horribly misunderstood what it said or T.Z. Lavine has horribly misunderstood what Plato said. Try reading J.Annas - an introduction to the Republic, or N.Pappas - an introduction to the Republic (not sure if those are the exact titles off hand'''

"Imagine a line divided" Formatting Problems
I tried to fix the formatting so that frist quotation wasn't compressed into a tiny side bar. But the formatting appears differently on my phone and it even appears differently in the preview. This needs someone to fix it properly. Pulu (talk) 18:49, 10 October 2012 (UTC)

Ratios of the divided line.
I can't help but note that the line is divided and subdivided by thirds, rather than by the golden mean. Is this intentional? Did Plato ever explicitly state a proportion, or just that it shouldn't be half? Seems to me that it should be the golden mean, since both Socrates and Plato drew from Pythagoras.

answer: I think you've been reading too much of the da vinci code... the goldern ratio is totally unessential to this and is not at all relevant to this allegory. Plato doesn't state a specific ratio by which the line must be divided, and then further subdivided, except that one part in each subdivision must be longer than the other (i.e. 1:1 is excluded). The exact ratio is not important whatsoever, but what, given any ratio, a line divided in this way, will reduce to. suppose the length AC = x, CE = y and x + y = z. Then it follows that the lengths are:

AB = x*x/z = x^2/z

BC = x*y/z = xy/z

CD = y*x/z = xy/z

DE = y*y/z = y^2/z

so that a line divided in this way by any ratio x:y and then the divided parts being divided again, reduces to a line divided in the ratio:

x^2:xy:xy:y^2  =    AB:BC:CD:DE

i.e. the two middle sections are identical in length, which is important as far as length implies clarity/understanding or however we interpret the allegory. which is important as we are supposed to move without any major increase in clarity from the concideration of objects to the concideration of mathematics say. I'm shocked that the diagram of the line on this page doesn't seem to show this eqauality. Also, the ratio of AB:DE, the difference between ignorence and knowledge of the form of the good, is greater than the mere difference between the empirical and intelligable parts of the line by a squaring of the ratio. This emphasises how great the episomological significance is between the knowledge of the form of the good and ignorence (Akrasia).

reply to above: The line should be divided at the golden point. The use of the word proportion is the giveaway for this. The golden point is the only single point where proportion is granted rather than just a ratio created. Continuous Geometric Proportion, such as 3:9:27, entails (at least) 3 entities wherein the initial term is reflected in the last. A simple ratio, such as 1:1, entails 2 entities wherein the terms have no anchor. Plato, by specifying not to divide the line in half, implied by proxy not to introduce ratio. The golden point is the only one "cut" wherein 3 entities are created: the Lesser, Unity & the Greater, such that the Lesser (defect) is to Unity as Unity is to the Greater (excess). —Preceding unsigned comment added by 207.38.194.89 (talk) 07:38, 4 January 2009 (UTC)

Fundamental misunderstanding of Idealism: Proposed Rewrite
Before I launch this crtique, let me say thet this article, is well wriiten, and accurately reflects most contemporary understanding of Plato's divided line. The problem is that it does refect contemporary understanding which means it is almost by definition biased toward empericism, materialism, Aristotelianism. An accurate explanation of the divided line without that bias means basically everything in the current article gets shifted down one step: The world of sense objects IS the world of shadows; and does not differ substantially from what we call shadows, images, etc. What we call science is NOT a form af higher knowing, but a system of beliefs, albeit a pretty effective system, still just "a likely story." The two forms of higher knowing are "dianoetic" and "noetic" fr. Grk. nous, noesis, dianoesis Reason is dianoetic, "divided knowing" (hence rational, ratio), intermediate between the World of pure ideas and our everyday experience and is the souls mediation of how universal meaning appears in our concepts and perceptions. This definition is thus very different from the common definition of reason as scientific judgement (ie logical rasoning). Noesis is pure contemplation of the divine Ideas, knowledge without any intermediary relationship, a knowledge by pure "being", a state of "void" consciousness, a kind of knowing that has just begun to dawn on the horizon of contemporary understanding. Daffdaemon 2/20/2006 --12.31.6.104 20:59, 20 February 2006 (UTC)

The analogy of the line is a reflection of Dualism, then. Segment AC represents the "Mind", or the Platonic; segment CE represents the empirical world. The BC and CD segments being the same length represents simply where the non-empirical Mind and the Empirical World intersect. This is why they are the same length. "Higher" forms of mind-content have no representation in the physical world. "Shadow" or "Reflection" parts of the physical world have no direct confluence to the mind. The same-sized segments can be seen as overlapping. Parallelism later re-identified this overlap in the 1600's during the Protestant reformation, and placed it under the control of God, but was narrow-minded enough (still coming out of the dark ages, after all) to skip the parts in segments AB and DE. maxnort8.14.172.48 (talk) 13:03, 26 June 2009 (UTC)

Divided Line - Image ?
I agree in that the article is well written however i think that the page would benefit most from an image or diagram with the information bellow. The reason is that most students learn the divided line and the Allegory of the cave in introduction classes and these are very difficult to grasp without the use of an aide. If someone has an image i think it would be timeworthy to critique it and then post something that is agreeable to the majority. -alexderbez 3/4/2007

Divided Line Translation
The current translation used for the final segment of the divided line by Paul Shorey, is notoriously bad.

The Greek reads: "hôsper eph' hois estin alètheias metechei" which means "as they partake in truth." Shorey's translation is "partake in truth and reality." Obviously this is a very significant and dubious addition. There is only one predicate term in that part of the sentence, and it is aletheias, which means truth.

I would use Allan Bloom's translation of the whole passage: "Take these four affections arising in the soul in relation to the four segments: intellection (noesis) in relation to the highest one, and thought (dianoia) in relation to the second; to the third assign trust (pistis), and to the last imagination(eikasia). Arrange them in a proportion, and believe that as the segments to which they correspond participate in truth, so they participate in clarity."

Also, I would recommend a whole section on eikasia and its role in Platonic philosophy, especially in Republic. —Preceding unsigned comment added by 69.209.223.74 (talk) 19:17, 27 September 2007 (UTC)

Factual accuracy tag
I tagged the article based on this edit summary by an anonymous user:
 * The whole basis of this article is incorrect. The divided line is broken into sections opposite the representation that they are portrayed in here. (Republic, 509c-511e)

and removed these comments from the article:
 * The Proceeding passage is so filled with error that I do not with to try and edit it. [...] I don't have time to elaborate on this, but I hope some scholar does and will check over the rest of what was written about this subject.

&mdash; Miles 05:54, 2 November 2007 (UTC)

Actually, it is debatable which way the four parts can be assigned to the divided line, considering the fact that Plato is ambiguous with his explanation. The important part of the line is that the two middle sections are the same size, indicating a deeper relationship between the two. If anything, I would like to see the page present both interpretations of the orientation of the line and the explanation of each interpretations importance, focusing on the middle two segments and their special relationship. —Preceding unsigned comment added by 130.49.17.252 (talk) 23:12, 3 April 2009 (UTC)


 * I've rewritten the article with some quotes and referenced statements. It still needs work. -- Radagast3 (talk) 11:34, 15 January 2010 (UTC)

____________________________________________________________________

"This article has been rated as low-importance on the importance scale."

I am so pleased. I have no idea what this is all about. I was looking for the article on broken eggs.

Chuck. 3 Nov 2007

____________________________________________________________________ —Preceding unsigned comment added by 203.164.154.198 (talk) 23:19, 2 November 2007 (UTC)

I'm just registering my shock that the proportions should be worng (it's true!). I regret that I'm not qualified to fix it, but please somebody do something! —Preceding unsigned comment added by 172.200.200.73 (talk) 18:29, 9 November 2007 (UTC)

Imagine a line divided into two parts -> a matter of misspelling, right?
The (AC) segment should be the intelligible world and (CE) the visible one.

leonard.pistol 04:22, 9 November 2009 (UTC)


 * The labels A-E are different from those in my Penguin Plato, but that hardly matters. -- Radagast3 (talk) 11:13, 15 January 2010 (UTC)

Category: Articles containing proofs (Re-revert)
The article has a proof contained in a footnote. There is active debate as to whether and how proofs should be included in Wikipedia and it is important to have an accurate listing of which articles have proofs (even when they are hidden in footnotes) so that they can be used in the development of forthcoming guidelines and so that, once developed, the guidelines will be applied consistently. I am therefore re-reverting the earlier addition of this article to the Articles containing proofs category.--RDBury (talk) 18:51, 13 December 2009 (UTC)

This article makes almost no sense
That quote from Plato is opaque to the point of illegibility. What on earth is he saying?? Surely there is a translation that actually makes sense in English.  Matt Yeager   ♫  (Talk?)  20:30, 12 September 2010 (UTC)
 * It's a standard translation, though an older one. However, the article explains what he means. -- Radagast 3 (talk) 22:49, 12 September 2010 (UTC)

My 2 cents
It seems to me that the Divided Line analogy corresponds to the Cave analogy in that it describes the kinds of people that are in society. The philosopher has the most wisdom and know what Good and the Forms are, but there are few philosophers. There are more people who can understand abstract ideas, but like the Guardian class, they are an elite group and the philosophers are chosen from this group. Note that both of these groups are distinguished by their ability to understand abstract ideas, and these are the things outside the Cave which can only be imagined. Many people, but certainly not all, understand the next lower knowledge group, physical objects which produce the shadows in the Cave, the things of natural science. The lowest level of understanding is those who see the shadows on the Cave walls and think those shadows are real. This is by far the largest group in the population, and they talk as if they "know" things, but because their knowledge is so limited they are actually espousing opinions, without knowing it.

Now we draw the line which divides humanity's intellect. The first unequally divided line, let's say it is 1 unit long for ease of calculation, and let's divide it so that AC is 0.1 unit and CE is 0.9 unit. Then we subdivide each of those sections proportionally. First, AB is (0.1)AC=0.01 unit, which leaves 0.09 units for BC. Second, CD is 0.1(CE)=0.09 unit, leaving 0.81 unit for DE. AB is the shortest, which corresponds to the smallest group, the philosophers. BC is the next smallest, thus it represents the Guardians/mathematicians. CD corresponds to those who comprehend physical objects and DE represents the people who see only shadows. — Preceding unsigned comment added by Misha1204 (talk • contribs) 00:20, 10 December 2010 (UTC) Misha1204 (talk) 00:29, 10 December 2010 (UTC)

Ratio of Segments
Let me temporarily call the individual segments (1),(2),(3),(4); with (1)=AB, (2)=BC, (3)=CD, (4)=DE.

The ratio of (1):(2) is the same as that of (3):(4). This much is clearly stated by Plato. However, no other ratio is!

The present article insists that the ratio of the first half to the second half (1+2):(3+4) is also the same, so that (2) and (3) must then be of the same length. This wishful Pythagorean interpretation is based on a copying and translation ambiguity from older Greek texts that do not in fact differentiate unequal from equal (ανίσα, αν ίσα). Since Plato did not clarify further, you can accept whichever as you wish. Either way, this ratio makes no difference from the point of view of the framework of Plato's metaphysics or his epistemology. BlueMist (talk) 16:08, 2 August 2011 (UTC)

Socrates as author of the Divided Line (This is an inappropriate title as our edits did not assert this to be the case
Hi Mercer.philosophy,

Most, but not all of your changes to the [Analogy of the Divided Line] considerably degrade the contents. In particular, 1) English Wikipedia uses English titles, i.e. Timaeus, not the Greek title. 2) Your changing of 'Plato' to 'Socrates' is very wrong in the context of the article. The name of the puppet character is quite irrelevant when it comes to Plato's epistemology of the Republic.

Will you please reverse all your latest changes, with the exception of the Upper-lower case for the titles, which is great. BlueMist (talk) 23:02, 15 January 2014 (UTC)


 * Who is this "we" who decides to credit the philosophy of the greatest philosopher in history to his primary literary character?


 * I see no evidence that you are familiar with the prevailing secondary literature, according to which, only the 'Socratic' dialogues mirror the views of the historical philosopher Socrates.


 * The 'middle' and 'late' dialogues are deemed as Plato's original philosophy, with the literary character Socrates as the primary protagonist. The Republic belongs to the middle group.


 * Do you have any peer-reviewed evidence or reference that supports your personal, unorthodox views?


 * I am transferring this conversation to talk:Analogy of the Divided Line for public comments. BlueMist (talk) 00:58, 17 January 2014 (UTC)

The Need for an Improved Table in the Intelligible Section
Edits were made to improve this table as it omits very important things mentioned in the Analogy. The product can be viewed at this old version.

The edits have not been accepted as of yet but this does not remove the necessity to improve the table. Here are some suggestions:
 * 'Soul' is a Germanic word. The word used in the Analogy is ψυχή from which we directly derive 'psyche.' The use of this word therefore is more honest to the ancient Greek.
 * Socrates mentions four 'affections'(παθήματα) of the psyche. These four are currently listed as types of knowledge, which is incorrect on several accounts. The most basic is that the lower two affections of the soul cannot be said to have knowledge, according to the Analogy, but rather opinion.
 * The current version does not indicate the difference of method between the two sections of the intelligible. The Analogy specifically mentions that they are different in the psyche's use of likenesses and hypotheses.
 * The length of the line is itself a measure of relative truth and reality, according to the Analogy. These relative degrees are not indicated in the current version.

Note that all these suggestions we attempted to resolve by the newer version. Yet, all things can be improved, so please do suggest how the newer table can be made even more so.

--Mercer.philosophy (talk) 02:28, 17 January 2014 (UTC)

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The problem of Socrates in Plato
This article proceeds as if the various theories Socrates propounds are Plato's own views on topics X or Y (e.g. "Plato's metaphysics." This is a very, very contested area in Platonic scholarship. Simply put, Plato did not write treatises from which his doctrines can be straightforwardly read. So, essentially, the article passes off a contested interpretation as if it is simply the case. The division of the dialogues into three periods is also disputed and increasingly under question. See the main article on Plato, and the Problem of Socrates, which reflect these fundamental interpretive problems in Plato. 209.2.47.17 (talk) 01:50, 11 May 2023 (UTC)

Table menu
I used "Correlation" (to avoid the need for citation), though it could just as well be titled "Facet(s)" [of Plato's concept]. Stjohn1970 (talk) 13:17, 5 August 2023 (UTC)