(4th tetralogy : The Soul - 2nd dialogue of trilogy)

Foreword (April 8, 2026): At this point in time, this page, aside from the translation from the Greek of the analogy, includes only a translation in English of the Introduction, which is common to both the analogy of the line and the allegory of the cave, an shows how both "images" should be read in parallel, each one shedding light on the other. The translation of the notes available in the French version is in progress and will come later.
Another page of this site, titled "The Vocabulary of the Line", that can be accessed by clicking on this link, provides a table listing all the occurrences of a number of important words of this analogy, and also of Republic VII, 533e7-534a8, which recalls the analogy, along with their translation in English in the various editions of the Repuplic I had access to. This table, along with the commentaries that accompany it, including the list of the 9 English words used by the 7 quoted translators to translate the 7 occurrences of the Greek word eidos in the analogy of the line, gives an idea of how difficult it is to translate such a text without betraying it, showing that the same Greek word may be translated by different English words, not only from a translator to another, but also by the same translator within a few lines' interval, and that the same English word may be used to translate several Greek words, here again sometimes by the same translator.

(direct access to translation)

Introduction and setting

This section of the Republic is one of the most difficult to properly understand, insofar as it describes in a static way through a geometric analogy the four increasingly rich and faithful modes of apprehension of reality, first through sight (the "seen", the first two modes), then through intelligence (the "perceived by intelligence", the last two modes), which are accessible to human beings (anthrôpoi) because of their nature and that, obviously, to understand it completely, one must have reached the fourth mode, the richest, which is not given to everyone. In doing so, it tries to make us understand the power, but also the limits, of logos*, which specifies us as human beings, by means of logoi, that is, to free ourselves from the grip of words by means of words, using images for this purpose. It is complemented by another image, the allegory of the cave, which follows it and sheds light on it by illustrating the progression over time through these different modes of apprehension for each human being through "education" (paideia, 514a2) in a broad sense not limited to "scholastic" education, but considered as potentially continuing throughout life (as Socrates examplifies throughout the dialogues). But the allegory in turn must be understood against the backdrop of the analogy of the line, since it presents in a dynamic perspective the progression through the different modes of apprehension of reality that the analogy of the line presents to us in a static perspective, up to the ultimate mode of apprehension, culminating in the allegory in the contemplation at leisure of the sun itself, which everyone, starting with Socrates himself, knows to be almost impossible in this life without blinding oneself, a mode of apprehension that is problematic because it is beyond words. And these two images must be understood in the light of what immediately preceded them, the parallel between the good and the sun, which makes the idea of the good (hè tou agathou idea) the analogue for intelligence of the sun for sight, and in a more distant way, the discussion on knowledge and opinion that opened the long discussion that responds to what Socrates called the "third wave" of objections (cf. 472a1-7), the one that the principle of the "philosopher king" that he stated at 473c11-e2 cannot fail to arouse, and also from what follows, with the reminder of these two images towards the end of Book VII in reverse order in the discussion on dialektikè as the ultimate knowledge that the philosopher must master, which is not a mere summary but offers important clarifications, and finally the discussion on the different kinds of beds at the beginning of Book X, which sheds light on the meaning of the terms eidos and idea and the differences Plato makes between both.
So rather than artificially maintaining in my notes and comments a suspense of no great value, I prefer to take into account in the notes both what preceded and what follows the analogy to avoid the reader getting lost in false leads which will complicate one's understanding of this text, all the more so since there are many false leads in the secondary literature on this analogy, which most commentators have misunderstood, among other things because they did not try to reconcile the second part of this analogy, the one dealing with the perceived by intelligence, with the detailed description of what happens outside the cave in the allegory that follows, preferring to read these two images in the light of a supposed "theory of forms / ideas" accepted a prioiri even if it does not fit with what they suggest, and by giving too much importance to the geometric dressing of the analogy.

 * For the multiplicity of meanings of the Greek word logos (logoi in the plural), which I prefer to leave untranslated, please refer to the page of this site where I have reproduced the entry in the LSJ Greek-English Lexicon dedicated to it. Let it be said in short that the range of meaning of this word is organized around two main registers: on the one hand, everything that has to do with human speech and the various uses that can be made of it (speech, conversation, discourse, report, narrative, etc.), and on the other hand, everything that revolves around the notion of reason, the faculty to which speech gives us access and what it allows us to do (reason, reasoning, justification, relationship, proportion, etc.). The link between the two registers of meaning is made through the idea that logos designates speech as bearing meaning, that is to say, as reasonable speech. Plato's dialogues as a whole can be seen as a long exploration of what it means and implies to be an anthrôpos ("human being"), i.e. an animal endowed with logos, in the line of the gnôthi sauton ("learn to know thyself", not only as an individual, but as a member of the species anthrôpos ("human being")).
In the translation of the analogy, I do not translate the word logos, only specifying in a footnote, on occasion, in what more specific sense it is used in this instance, especially when it participates in ready-made expressions. In the introduction and notes, I use the Greek word, as here, without specifying the relevant translation(s) in each case.(<==)

Summary of the analogy of the line

To make what following understandable to someone who has not yet read the analogy of the line, it is therefore necessary to give a brief summary of it (those who prefer to read the text to get a first feel of it by themselves before reading this commentary can go directly to the translation and come back here later, keeping in mind that any translation, mine included, is necessarily biased by the translator's choices). This analogy, as I just said, immediately follows the parallel between the good and the sun, and uses another imagery to complement it. Socrates, in the continuity of what was said before, begins by equating the good and the sun with two sovereigns reigning (basileuein, 509d2) each on what he calls by various names so as not to freeze a "technical" vocabulary to speak with necessarily unsuitable words of "ensembles" which have at least as many differences as resemblances and to which one would not spontaneously associate the same words: he begins by speaking simultaneously of genos ("birth, origin, family, nation, people, genus, species...") and topos ("place, position, region, district... "), which he qualifies respectively as "intelligible" (noèton), i.e. open to understanding by the intellect (noûs), for what the good "reigns" over, and "visible" (horaton) for what the sun "reigns" over, before introducing the term eidos ("appearance (for sight), form, shape, figure, kind, sort, class, species", a word derived from a root meaning "to see"), also associated with the same qualifiers, "visible" (horaton) and "intelligible" (noèton), but repeated in reverse order.
Socrates then asked Glaucon to imagine a line segmented into two unequal segments, which he described in 509d8 as "that of the seen family and that of the though / perceived by intelligence one" (to te tou horômenou genous kai to tou nooumenou), returning to the word genos ("birth, origin, family, nation, people, genus, species...") but this time using new qualifiers, horômenon ("seen") and nooumenon ("perceived by the noûs" ("mind / intelligence"). Then he asks him to segment each of these two segments into two subsegments "according to the same logos" (ana ton auton logon), a key expression to which I will return later in this presentation and in which, because of this geometric dressing which implies the lengths of segments, logon is naturally understood as meaning "(numerical) ratio", one of the possible meanings of this word rich in multiple meanings in Greek. He then describes the division of the segment of the seen, saying that it is done "based on the [relative] clearness (saphèneia) and lack of clearness (asaphèia) of the ones compared to the others, contrasting images (eikones), of which he gives as examples shadows and reflections, that is to say, moving images that occur spontaneously, without the intervention of man, unlike paintings or sculptures, which are otherwise objects in their own right, with the "originals" of these images, that is to say the living beings, the plants and everything that is produced by human craftsmanship (including statues and painted images), designated by the expression to skeuaston holon genos. By way of transition between the description of the division of the segment of the seen and the description of the division of the segment of the perceived by intelligence, he suggests that "it is divided with regard to truth (alètheia) and its absence [according to the following ratio(nale)]: as the opined [is] to the known, so what is made similar (to homoiôthèn) [to something is] to what it has been made similar to (to hôi hômoiôthè)". Socrates then comes to the division of the segment of the perceived by intelligence made "according to the same logos" and, while, in the realm of the seen, he characterized each of the two sub-segments by the "objects" that are perceived by sight, in the realm of the perceived by intelligence, he characterizes each of the two sub-segments by approaches (methodoi, 510b8) that are used there. He thus opposes:
- an approach that could be described as "problem-solving oriented" in that it is the one used by people who seek to solve specific problems, practical or theoretical, starting from "bases / starting-points" (hupotheseis, a word that should not be understood in the modern sense of "hypotheses", but in the etymological sense of "what is laid under", that is, "basis, foundation, support (of reasoning), starting point") chosen according to the problem to be solved (the examples he gives when he illustrates it with the example of geometers are the even, the odd, angles, figures) and admitted without asking questions about them, designated by words whose meaning is supposed to be obvious, and using as "images" of what they are talking about with these words "objects" (for example, drawings of geometric figures) that are part of what populates the second sub-segment of the seen and that have been discussed before, even though they admit that what they reason upon are "things" "that cannot be seen otherwise than by thought (dianoia)" (511a1), and satisfied as soon as, the problem being delt with having been solved, they have reached the end (teleutè, 510b6) of their specific reasoning and found the solution they were looking for;
- to an approach, which could be described as "comprehensive" (both in the sense of "showing extensive understanding" and in that of "encompassing everything") in that it is the one used by people who, before rushing in search of solutions, question the "bases / starting points" (hupotheseis) which they might have to rely upon to do so, one by one, in order to test their "solidity / stability", that is to say, they seek to understand what is hidden behind the words they use, trying to go back to a unifying principle (archè) that "enlightens" everything and gives meaning and coherence to all these "bases / starting points" without being itself the "starting point" toward something else (anupotheton, 510b7) of greater "value" (which is none other than the idea of the good, the good being that which everyone seeks for oneself and not for the sake of something else (cf. 505d5-506a2), even if Socrates leaves it to us to understand it), no longer relying on "images" (eikones) (visible "things"), but on what Socrates calls eidè, and which designates for him what we suppose to be common to everything to which we attribute the same name, as he will specify in the prelude to the discussion on the different kinds of seats( / beds) at the beginning of Book X, at 596a6-7, and which refers to what is described in the first approach as what "cannot be seen otherwise than by thought (dianoia)" but is apprehended through the "images" that visible / material realities are supposed to give of them, which makes them horômena eidè (horômenois eidesi, "seen appearances", 510d5), but which must now become a noeton ("intelligible", in the sense of "percetible by intelligence") eidos and must be apprehended by abstracting from all the "images" (eikones) that one would be tempted to associate with them and above all as distinct both from the words that are associated with them and from what they are only "appearances" of for a human mind.
In both cases, the tool used is the logos, but only the second approach fully implements the power of the dialegesthai (hè tou dialegesthai dunamis, 511b4), that is to say, assumes that we master the power and limits of logos by having understood how it can give us access to something other than the words that compose it, provided that one relies on the sharing of experiences in the practice of dialogue (to dialegesthai), that is to say, by having become dialektikos by mastering dialektikè ("dialectic", but in a sense that has yet to be specified), which Socrates will describe as the ultimate knowledge that the philosopher must possess and in which we must see, not a particular technique, but the ability to properly use logos (which, as the allegory of the cave will show, is available at all stages of the progression through the segments since this is what distinguishes the anthrôpoi from other animals), to access what is beyond words without letting oneself be trapped by them and of which the eidè that we associate with these words are still only "reflections". A good example of the conflict between these two approaches, in a non-geometric register (but where geometry also plays an exemplary role that resonates with what Socrates is saying here), is given by the Meno, who opposes an interlocutor who wants us to answer his question (can excellence (aretè) for a human being be taught?) to a Socrates who refuses to answer it until he and Meno have agreed on what they mean by "excellence" (aretè) in the case of human beings.
At the end of the analogy, Socrates asks Glaucon to associate each of the four segments with an "affection / state of mind" (pathèma, a noun derived from the verb paschein ("to suffer / have sometning done to oneself / be affected by"), which is opposed to pragma ("fact / thing"), derived from prattein ("to do / act / accomplish"), as paschein is opposed to prattein), proposing the following names for them, which should not be considered as perfectly adequate, exclusive and definitive insofar as Socrates introduces a new analysis for which he does not have pre-existing names, names which would anyhow not convey the full import of what he has in mind, and the names he proposes highlight only an aspect of what he is talking about without exhausting all its richness, as shown by the fact that, when he returns to the analogy in the discussion on dialektikè towards the end of Book VII (533e7-534a3), he changes one of these names, and not the least, since it is that of the pathèma ("affection / state of mind") associated with the second sub-segment of the perceived by intelligence, the one corresponding to the final stage of the progression toward knowledge: to the first sub-segment of the seen, that of "images", he associates eikasia, a word having the same root as eikôn, the word he used to speak of images; to the second sub-segment of the seen, that of material realities, he associates pistis, a word that may be translated as "trust, faith" and which puts forward the idea that at this point, we have become aware of the fact that our knowledge of the world around us is based more on the trust we have in the people around us and their words about things that we have never seen for ourselves and perhaps never will be able to see (including everything that belongs to the past before our birth, such as Achilles and Ulysses) than on direct view with our own eyes of these things, what we see for ourselves representing only a very small part of what we admit as "existing"; to the first sub-segment of the perceived by intelligence, he associates dianoia, a word derived from noûs ("mind / intelligence") via the verb dianoeisthai ("to think"), which can therefore be translated as "thought", or, to be precise, as "discursive thought" to highlight the fact that it manifests itself through discourse, speech, logoi, or else by "wandering thought" by privileging one of the possible meanings of the prefix dia, which may mean in composition "here and there", to emphasize the fact that it is a thought that does not have the compass that the idea of the good constitutes, precisely because it has not taken the time to examine the hupotheseis ("bases / starting points") that it uses in the light of this principle; to the second sub-segment of the perceived by intelligence, he associates noèsis, a word having a meaning close to that of dianoia but from which the prefix dia- ("through / to the end", or, as we have just seen, "here and there") is absent), which is replaced by epistèmè ("knowledge") in the recalling of the analogy toward the end of Book VII. And he asks Glaucon to order them "according to this ratio(nale) (ana logon), thinking that as that upon which it is (eph' hois estin) partakes of truth (aletheia), so these partake of clearness (saphèneia)", suggesting that the degree of "clearness / evidence" (saphèneia) of these different affections / states of mind depends on the level of participation in the truth (aletheia) of that upon which it is (eph' hois estin), an expression that opens the door to all sorts of misunderstandings, which must be unnderstood in the light of the previous discussion on knowledge and opinion at the end of Book V (provided it too has properly been understood) and to which I will return in the notes. Let us say here only for the sake of brevity that the "that upon which it is" of sight is not the object we see, which could then just as well be the "that upon which it is" of hearing if it produces sounds, the "that upon which it is" of smell if it produces odors, or the "that upon which it is" of opinion if we form an opinion about it, but that which is specifically produced in our mind by sight, and which the mind interprets as patches of colour to which it will give one meaning or another, and that the "that upon which it is" of opinion is not the "object" or the event about which one forms an opinion, which might as well be an object of knowledge for another, or for the same person at another time in his life, but that which is formed in the mind about it and expresses by means of thought or uttered words the apprehension of it by the one whose opinion it is, a formulation which, in the case of opinion, is only a sequence of words which the one who thinks or says them is not able to justify.

Summary of the allegory of the cave

After this summary of the analogy of the line, let us proceed with a summary of the allegory of the cave, which, as Socrates tells us in the opening, illustrates "our nature regarding education (paideia) and the fact of not being educated (apaideusia)". He depicts human beings (anthrôpoi) who have been chained in a cave since birth, caught in bonds that prevent them from any kind of movement, including simply moving their heads, so that they can only see the wall of the cave in front of them. Behind them, and therefore invisible to them, there is a road, hidden by a wall, on which human beings (anthrôpoi) walk, bearing at arm's length all kinds of implements as well as statues of men (andriantai, a word formed on the root anèr, andros which means "man" as opposed to "woman", and therefore implies the difference between sexes, unlike anthrôpos) and other animals, which are the only things that protrude from the wall (the anthrôpoi that carry them are completely hidden by the wall). Farther away behind the wall, the road and the bearers, and high up, there is a fire whose light casts on the wall of the cave facing the prisoners the shadows of the utensils and statues protruding from the wall. These shadows (one of the examples of images used by Socrates in the analogy of the line about the first subsegment of the seen) are therefore the only things they can see as long as they remain caught in the bonds that prevent them from moving. But, if they cannot move, they can talk with one another (dialegesthai) and, in order to do this, must give names to the shadows they see by grouping them into families on the basis of similarities of appearance and by assigning these names to the families thus identified (the allegory merely says that, "the same [things] being around [again], they would take the habit of giving names to those [things] they see", 515b4-5), and they hear the echo (sound reflection, reflections being the other example of images used by Socrates in the analogy of the line) of the words spoken by the bearers behind the wall when they happen to produce sounds (phtheggesthai), which makes them believe that these sounds come from the shadows (let us not forget that they can neither move, nor turn their heads and therefore see each other as long as they remain in bonds). In such a situation, when dialoguing with one another, they "would hold as the true (to alethes) nothing but the shadows of the implements (515c1-2). Socrates then imagines that one of these prisoners is freed "naturally" (phusei) from one's bonds and forced to turn the head towards the fire, the wall and the objects that protrude from it and of which so far, he has only seen the shadows. At this point, he imagines a dialogue between the prisoner freed from his bonds and still dazzled by the light of the fire and therefore having difficulty distinguishing the objects of which he could only see the shadows until now and an interlocutor about whom Socrates says nothing but who is obviously not another prisoner immobilized in bonds, in which, when asked about what he sees now as compared to what he was seeing before, the prisoner who was released from his bonds shortly before (but who is still in the cave), "would deem the [things] he formerly used to see (the shadows) truer (alethestera) than those now pointed at (the objects protruding from the wall)" (515d6-7) and turns back toward what he used to see, considering it "clearer" (saphestera) than what he is now forced to look at. Later, he is pulled out of the cave through a side opening (not behind the fire) toward the outside, without having to walk toward the fire and pass the wall (Socrates does not specify this explicitly, but his silence on this point is a "proof" of it: considering the time he spent describing the turning around and reactions of the prisoner freed from his bonds when looking towards the fire, if he had had to go to the other side of the wall and discover the porters, he would not have failed to describe the prisoner's reactions to this new stage of progression.) Once out, the prisonner is at first dazzled by the light of the sun and therefore "unable to see a single one of the [things] now called true" (tôn nun legomenôn alèthôn, 516a2-3) and a period of habituation is required to become able to see what is outside in the bright light of the sun. In the course of this habituation, the freed prisoner at first sees only the shadows and reflections (again the two examples of images used by Socrates in the analogy of the line) of human beings (anthrôpoi) and everything else (of what was visible in the cave) before being able to see them "themselves" (auta) and finally to discover the heavens and the stars, including the moon, first at night, and of course the sun, first through its reflections (another reference to the images of the analogy of the line), then by looking directly at it. Socrates then describes the reasoning (sullogizein) that the prisoner who has finally been able to see the sun at leisure (at least this is what the allegory suggests) holds to oneself: "he would by this time conclude by way of reasoning (sullogizoito) about it that it is the one providing the seasons and the years and supervising all the [things] in the seen place and, of those [things] they themselves used to see, responsible (aitios) in some way of all [of them]" (516b9-c2). Then, he remembers his former life as a prisoner in the cave and the way in which those who live there form opinions (doxazein) and "the privileges for the one most sharply observing the [things] passing by and best at remembering which ones among them used to be carried before or after or simultaneously, and as a result of this, most capable indeed of foretelling what would come" (516c9-d2) and he pities his former comrades in captivity, preferring everything rather than living such a life based exclusively on opinion. And yet, he has to go back and the allegory ends with the return of the freed prisoner to the cave, where, at first, he has difficulty seeing the shadows (a symmetrical vision problem of the one caused by the passage from darkness to light, caused this time by the passage from light to darkness), and where he is the object of ridicule by the other prisoners who have remained in their bonds when he pretends to share his discoveries with them when he is no longer even able to see clearly what, for them, is the only "reality", so much so that, tired of his dissenting speeches, they would no doubt end up killing him if given the opportunity (a transparent allusion to the trial and death sentence of Socrates).

The reminder

In the discussion on dialektikè as the ultimate skill that the philosopher must master, towards the end of Book VII, Socrates returns to the allegory of the cave and the analogy of the line, recalling them in reverse order, and he uses this reminder to add important information along the way. Concerning the allegory of the cave, he twice clarifies what was meant by the expression "the shadows and after that the images on waters of men and those of the other [***]" (tas skias... kai meta touto en tois hudasi ta te tôn anthrôpôn kai ta tôn allôn eidôla) used at 516a6-7 to describe what the prisoner who has just exited the cave can see: first in 532a1-5, when he speaks of "the song / law (nomos) itself that the dialegesthai executes / fulfills, the one which, despite its being intelligible (noèton), the power of sight would mimic, which we described as attempting to look first toward the living [creatures] themselves (auta ta zôia), then toward the stars themselves (auta) and in the very end toward the sun itself (auton)", where it is obvious that the reference to sight which would imitate a "song / law" in the intelligible realm refers to the allegory where sight is indeed meant to represents analogically intellectual activity outside the cave, which means that what is evoked here is the aim of the freed prisoner's progress out of the cave, the "*** themselves" (ta auta) visible only outside the cave, which now includes, before he turns toward the stars and the sun, "the living [creatures]" (ta zôia), and not only the anthrôpoi; then a few lines later, when he evokes the previous stages of this progress and in particular the exiting from the cave, speaking of "the ascent out of the subterranean [place] toward the sun, and there, regarding the living [creatures] and plants (ta zôia te kai phuta) and the light of the sun, inability to yet look [at them]" (532b7-c1). As can be seen, each new mention is an opportunity to expand the whole of what he has in mind, which confirms that it is ultimately everything that is visible in the cave that also has an intelligible dimension outside the cave. And the discussion about tables and beds at the beginning of Book X will show that this includes even the artefacts produced by human activity, the skeuè of 514c1. Concerning the analogy of the line, he begins by providing some clarifications on what he means by dianoia, the affection he associated with the first sub-segment of the perceived by intelligence when he speaks of the subject-matters that are parts of the training program of the future philosopher kings that he has just described (arithmetic, geometry (plane), geometry in space, which he calls stereometry, astronomy, harmony), describing them as "the arts (technai) we have been reviewing, which we often called “sciences” (epistèmas) out of habit, but would require another name, connoting more clearness than 'opinion' (doxa), but more obscurity than 'science / knowledge' (epistèmè); '(discursive / wandering) thought' (dianoia), I think, [is how] we defined it earlier" (533d4-7), then he resumes, again in reverse order, the list of the four affections / states of mind (pathèmata), which he now calls moirai, "parts / lots", with an idea of destiny / fate which suggests that not all are necessarily destined to reach all these "lots", by changing his vocabulary, introducing new notions and adding some decisive details on the different relationships between all these elements, saying that "it is satisfactory then, as before, to call 'science / knowledge' (epistèmè, which here takes the place of what was called noesis in the analogy) the first part, the second one '(discursive / wandering) thought' (dianoia), the third one 'trust / faith' (pistis) and 'imagery' (eikasia) the fourth one, and those two together 'opinion' (doxa) and the two other together 'intellection' (noèsis, which, in the analogy, designated only the second sub-segment of the perceived by intelligence); and opinion (doxa) on the one hand [is] about becoming (genesis), intellection (noèsis) on the other hand about beingness (ousia); and what beingness (ousia) [is] with regard to becoming (genesis), intellection (noèsis) [is] with regard to opinion (doxa), and what intellection (noèsis) [is] with regard to opinion (doxa), science / knowledge (epistèmè) [is] with regard to trust / faith (pistis) and (discursive / wandering) thought (dianoia) with regard to imagery (eikasia)" and immediately adding "but the relation of analogy (analogian) between what those [are] about (eph' hois), and the division into two parts of each one of these two, opinable (doxaston) and intelligible (noèton), let us drop [that], so that it doesn’t fill us full with discussions many times longer than those having preceded" (533d7-534a8), confirming in particular by these last words that he intends to say nothing more about the relation (logos) used to divide in two "according to the same ratio(nale)" (ana ton auton logon) each of the two segments that he no longer calls that of the seen (horômenon) and that of the perceived by intelligence (nooumenon), but opinable (doxaston) and intelligible (noèton). It should be noted at this point that all these fluctuations in vocabulary are not due to inaccuracies on Plato's part manifesting a lack of mastery of his subject, but on the contrary result of a deliberate choice on his part not to freeze in each case on a single word, which would thus become a "technical" term, to invite us to look for what he is talking about beyond the words he uses to talk about them, which, for him, is precisely the mark of one being dialektikos.

The limits of the use of images (analogy and allegory)

Before undertaking the "decoding" of these two "images", one should be conscious of the limits imposed on an author by the use of images. Plato is perfectly aware of the fact that an image is never identical in all respects to what it is only an image of, as shown by the words he puts in the mouth of his Socrates speaking to Cratylus in Cratylus, 432b1-d10 about names envisioned as "images" (eikones) of what they designate: "images are far from possessing the same [things / attributes / properties / characteristics...] as what they are images of" (endeousin hai eikones ta auta echein ekeinois hôn eikones eisin, Cratylus, 432d2-3). Thus, for instance, when he chooses to represent, in the allegory of the cave, the idea of the good (hè tou agathou idea) by the sun, in keeping with the choice already made earlier in the parallel between the good and the sun, he is more or less "constrained", to be consistent with this choice, to represent all the other ideas (ideai) by the stars, but then, if this choice is fitting for suggesting that ideas, like the stars in heaven, can only be distinguished from one another by their relative position in relation to one another, that is to say, by the relations they maintain with one another in a whole (heaven for the stars) which has meaning only as a whole, the implied consequence of this choice is that, in the allegory, he cannot describe a situation where one sees at the same time, directly or through reflections, both the sun and the other stars (that is to say, all the ideas, including the idea of the good), and he has to make do with the alternation of day and night, thus suggesting an excessive difference between the idea of the good and all the other ideas (even if this primacy of the idea of the good is emphasized by Socrates just before the analogy of the line, at 509b8-10, when he says that "the good is not beingness (ousia), but still beyond beingness (ousia), standing above them (the [fact of] being (intelligible) and the beingness (to einai te kai tèn ousian)) owing to its seniority and power"), which will not prevent him from using this day / night alternation to represent another aspect of the separation between the two sub-segments of the perceived by intelligence, thought (dianoia) without the compass of the sun / idea of the good for the night and the apprehension of the world around us in the full light of this sun / idea of the good for the day. Nor can he speak of shadows in relation to the stars, including the sun, but only of reflections, when he proposes to take up outside the cave the reference to the shadows and reflections evoked in connection with the first sub-segment of the line, as he did inside the cave by mentioning the shadows on the wall of the cave and the echo / reflection of the words of the bearers, to suggest a correspondence between the two images (line and cave) and to try to illustrate in the allegory the similarity of the relationship (logos) which serves to divide the two segments of the line. Similarly, by choosing to represent the whole of the "real", visible as well as intelligible, by a line, while it emphasizes the continuity between the two realms, he also directs the reader's mind towards an arithmetical understanding of the word logos that he uses in connection with the division of the two segments resulting from the first segmentation (logos in the sense of "numerical ratio "), and thus towards a "population" of the different segments by countable elements / "units" supposed different for each segment (each such "unit" can be in one segment only), which ended up polluting the understanding of the analogy until today.
If it is almost certain that Plato chose these "images" with the greatest care and composed his text in such a way as to make the best use of their potentialities in order to make clear what he was trying to have his readers understand, we must never, in interpreting them, seek perfect concordism, nor want at all costs to give too precise a meaning to the slightest detail of the text, nor, above all, expect that a single one of these images would say everything he tries to make readers understand about the "real", forgetting that, if he proposed several "images", it is precisely because none could alone represent everything he was trying to make readers understand. It is therefore recomended to read in parallel both the analogy of the line and the allegory of the cave, in order to interpret them in the light of one another, and in the light of other sections of the Republic and other dialogues on the same themes, and to move back and forth between them in order to progressively reach an overall view of their common model, which will have to be clarified and refined over the course of these comings and goings until arriving at an understanding of the "original" that allows to understand how each of the proposed images is a relevant, though partial, image of it, not only roughly, but up to a certain level of detail, so long as as one doesn't want it to say everything.
What Plato seeks to describe are the different ways in which our senses, and mainly sight, and our mind / intelligence (noûs), apprehend a "real" that acts on them (the pragmata, a word derived, let us remember, from prattein, "to do / act / accomplish"), and of which we are a part. In this quest, three terms / expressions play a major role: (to) auto / (ta) auta ("(the) *** itself / themselves"), eidos ("appearance", étymologically "for sight", evolving toward "sort, kind") and idea ("idea"), not so much in the images, since this is precisely what he seeks to "image" analogically, but in the explanation that is given of these images. The main issue here is to figure out if, as Socrates asks at the beginning of the Sophist with regard to the three words sophistès ("sophist"), politikos ("politician") and philosophos ("philosopher"), "[we] deem all these to be one [and the same thing] or two or, as is the case for the names, three and, distinguishing the families / classes (genè) exactly as a single name, [we] attach a family / class (genos) to each" (Sophist, 217a7-9), in short, if these three terms / expressions refer to the same thing, to two distinct things (and in this case which are the two that are synonymous), or to three distinct things. Neither of these two images alone can answer this question since:
- the analogy of the line speaks of eidè ("appearances / kinds"), never of ideai ("ideas") and evokes auta ("the *** themselves") when Socrates mentions, in an allusion to the conversation with Meno's slave in the eponymous dialogue, "the square itself" (tou tetragônou autou, genitive singular) and "the diagonal itself" (diametrou autès, genitive singular) at 510d7-8, specifying that it is on this that geometers conduct their reasoning by "attempting to see (idein) what cannot be seen otherwise than by thought (dianoia)" (510e3-511a1) even if they make images of it to help themselves in their reasoning.
- the allegory of the cave suggests viewing the stars as images of ideai ("ideas") rather than eidè ("appearances / kinds") by clearly implying that the sun represents the idea (and not the eidos) of the good (Plato never uses the words to tou agathou eidos ("the eidos of the good")), and refers to the auta ("the *** themselves") in a way that clearly distinguishes them from the stars / ideai ("ideas") since at 516a8 he talks about finally seeing, once out of the cave ( therefore in the intelligible), men (anthrôpoi, in the plural) and all the rest auta ("themselves"), and no longer only their shadows and reflections ("the images on waters of men and those of the other [***]" (en tois hudasi ta te tôn anthrôpôn kai ta tôn allôn eidôla, 516a7), the only things visible at first, when exiting the cave, due to lack of habituation to the light of the sun.
From this standpoint, what any serious interpretation of the allegory of the cave must take into account and explain concerning what takes place outside the cave, that is, in the intelligible, is:
- that we can see two categories of "objects", on the one hand men (in the plural, which excludes that it is the unique "form / idea of Man") and all the rest of what was also visible inside the cave (each "object" in its individuality, as is hinted at by the fact that, for men, Socrates uses the plural), and on the other hand the heaven and the stars, invisible from inside the cave, which can be called respectively "terrestrial objects" and "celestial objects";
- that the "objects" of these two categories are perceived first through their shadows (for "terrestrial objects" only) and their reflections (for both categories of "objects"), then in themselves (if reflections only is mentioned about the stars, it is indeed, as I said above, because of one of the limits imposed by the choice of the image since the stars do not produce shadows of themselves);
- that the "earthly objects", men and all the rest, are only listed one after another, while the "celestial objects", the stars, are apprehended as a whole, heaven (ouranos), explicitly mentioned in the words "the [***] in heaven and heaven itself" (ta en tôi ouranôi kai auton ton ouranon, 516a8-9), for which the succession of shadows and reflections / originals is replaced by the succession of night and day, the reflections being mentioned only in relation to the sun (even if it is quite possible to see reflections of stars in waters);
- that the prisoner, at the moment he exits the cave, can at first only see shadows and reflections of the "earthly objects", those that he already saw and heard inside the cave, and that therefore, what he sees in this first of four stages outside (two for the "earthly objects", two for "celestial objects", where, moreover, the case of the sun is treated separately from that of the other stars, but, here again, in two distinct stages) cannot be the ultimate "reality", but he cannot know it since he is precisely not able to see the originals of what he sees only images and reflections of and is therefore in the same situation in relation to these new "objects" of apprehension as he was inside the cave when he could only see the shadows of objects protruding from the wall and "would hold as the true nothing but the shadows of the implements" (515c1-2);
- that even with regard to the sun, image in the allegory of the idea of the good (or, to be more specific, image of the good itself, what plays in the allegory the role of the idea of the good being the image of the sun perceived by sight, itself image of the intelligence in the allegory once outside the cave, by human beings remaining on earth and thus unable to see it as it is in itself in it's own place), there are, outside the cave, therefore, two levels of apprehension, first through reflections, then directly, which implies that what can be seen outside the cave is not limited to "forms / ideas" (a reflection of the sun is not the analogue in the allegory of the "idea of the good", since it is the image of the sun directly formed in the eyes that plays this role), or that these "forms / ideas" come in two flavors, ideai (the sun and stars, or rather the light they emit perceived directly by human beings) and eidè (their "reflections" in the minds of human beings).
To refuse to seek an analogical meaning for these elements is to suppose that Plato, carried away in a poetic delirium by the enthusiasm induced in him by the image he had chosen, would have diluted it at pleasure by stuffing it with useless details (insofar as they had no analogical meaning), at the risk of compromising its understanding, which is contrary to everything that a careful reading of the dialogues leads us to suppose about Plato as a writer, philosopher all the time before being poet on occasion. Why in particular, if this were the case, would he have taken care to create resonances between the allegory of the cave and the analogy of the line, and in the allegory between the descriptions of the interior and exterior of the cave with references to shadows and reflections in each case? We cannot therefore claim to have understood Plato if we limit ourselves to saying that what "populates" the outside of the cave, that is to say "the intelligible place" (to noèton topos, cf. 509d2 and 517b5), are the "forms / ideas", without specifying whether we are talking about eidè or ideai, and most often by considering these two terms as synonymous in this context, and designating the auta ("the *** themselves"), i.e. the ultimate "realities", and without saying which of the four families of "objects" mentioned by Socrates in his description of the exterior of the cave (shadows and reflections of "terrestrial objects", the "earthly objects" themselves, reflections of "celestial objects", the "celestial objects" themselves) corresponds to these "forms / ideas / *** themselves".
Similarly, concerning the analogy of the line, it is necessary to explain:
- what Socrates means when he asks to divide the two segments "according to the same ratio(nale)" (ana ton auton logon) and which logos he has in mind;
- why he speaks only of eidè ("appearances / sorts"), never of ideai ("ideas");
- why he describes "objects" in the division of the segment of the seen and intellectual processes in the division of the segment of the perceived by intelligence;
- what he means by "eidè vus" (horômenois eidesi, plural dative) at 510d5 and by "eidos intelligible" (noèton eidos, singular) at 511a3;
- what are the "images" (eikones) that he mentions at 510b8 and opposes to the eidè ("appearances / kinds"), the only kind of "things" the approach (methodos) that characterizes the second segment of the perceived by intelligence must deal with;
- What is meant by an approach that relies only on eidè ("appearances / kinds").

Additional insights

As I have already suggested, the decoding of the two images provided by the analogy of the line and the allegory of the cave, must take into account other passages of the dialogues dealing with the same subjects, both in the Republic and in other dialogues that precede or follow them in the order that I claim to be that of the dialogues organized in tetralogies. Particularly relevant from this point of view, on top of the "decoding" of the allegory by Socrates who immediately follows it (517a8-c5) and the recalling of the two images in the discussion on dialektikè already mentioned, are:
- the experience with Meno's slave in the eponymous dialogue (to which the mentions of the square and the diagonal in the analogy of the line refer) which shows how, on the same subject, the same person can move from an opinion (doxa), in this case false, to knowledge, and, at the end of the dialogue, the discussion on the difference between right / true opinion (orthè / alèthès doxa) and knowledge (epistèmè) (Meno, 97a9-98b6), where, with regard to the same thing, in this case the road to Larissa, that is to say, something that concerns the sensible world, one person may have knowledge and another may have a mere opinion;
- the myth of the soul compared to a winged chariot in the Phaedrus (Phaedrus, 246a3, ff.) and more specifically the section that describes the procession of human souls following those of the gods who pass to the other side of the vault of heaven where "they contemplate the [realities that are] beyond heaven" (theôrousi ta exô tou ouranou, 247c1-2) while human souls can only glimpse at them from a distance without being able to access the "supracelestial place" (huperouranion topon, 247c3) where are "the colorless and formless and intangible beingness really being, that can be contemplated only by the intelligence, pilot of the soul, around which [takes place] the birth of true knowledge" (hè gar achrômatos te kai aschèmatistos kai anaphès ousia ontôs ousa, psuchès kubernètèi monèi theatè nôi, peri hèn to tès alèthous epistèmès genos, 247c6-8) and where the auta ("the *** themselves"", cf. autèn dikaiosunèn, "justice itself", at 247d6) are visible, which only a few, privileged, can no more than glimpse at from afar;
- later, in the "dialogical" part of the same dialogue, the description, at Phaedrus, 265d3-e4, of the two processes favored by Socrates that characterize the one he qualifies as dialektikos ("skilled in the art of dialogue", 266c1): on the one hand, a process of synthesis aimed at leading what is initially dispersed in multiple ways "towards a single idea" (eis mian te idean), on the other hand, a process of analysis aimed at "carving according to the eidè (kat' eidè) while respecting the natural joints (kat' arthra hèi pephuken, word for word "according to the joints where it is disposed by nature"), and taking care not to break any part by dealing [with them] in the manner of a bad butcher" (265e1-3), formulas in which it should be noted that idea is used to speak of what is a target (eis) towards which one tends without being sure of reaching it, as one can look at the stars to find one's way, and eidè is used to speak of carving with the risk of making a mistake if one does not do it according to (kata) the natural joints (arthra hèi pephuken), which suggests a certain distance from the ideai that one is not certain to reach and an uncertainty about the eidè, which are the result of our activity of analysis of a "real" which is not these ideai and in relation to which we can be mistaken;
- the discussion on knowledge (epistèmè) and opinion (doxa) at the end of Book V of the Republic, where Socrates seeks the "about / upon what it is" (eph' hôi esti) of both and finds it, not in the "objects" on which knowledge or opinion is formed, which, as the Meno has shown and as everybody knows, can be the same, but, regarding knowledge, in "the being / what is" (to on, 477a9), and regarding opinion, in the "received ideas" (nomima, 479d4) of the many, that is to say, regarding knowledge, in something that is external to the logos and serves as a regulator by implying the notion of true and false, and for opinion, in the words and logoi borrowed from others by people who do not seek to test their relevance themselves and are content to accept them based on the greater or lesser trust they have in those they borrow them from, or more precisely in what is induced in the minds of the people whose opinion it is by the logoi of other people whose (true or false) opinion it is also or who have knowledge about the subject (which loses its status as knowledge for anyone who accepts it without verification and without really "understanding" it and being able to justify it);
- the discussion on the different kinds of beds in Book X of the Republic, which clearly marks the difference between eidè, human constructs that vary from one person to another and evolve for each person over the course of one's life due to growing experience, answering a problem of naming and intended to give meaning to the words one uses, and ideai, non-human constructs, principles of intelligibility, the same for all, distant targets of the eidè having an "objectivity" which is "proven" by the fact that we can more or less understand one another, which are, in the example chosen by Socrates among the creations of human craftsmanship of which we all have daily experience to facilitate our understanding, what craftsmen look toward (with the "eyes" of the mind) to make what they want to make (a table or a bed in the example), and which are not "models" for their instantiations, as he tries to make us understand, on the one hand by never presenting, in this discussion on imitation in the most general sense, the craftsman as an "imitator" (of the idea that inspires him), contrary to what he does for the painter, who is indeed an imitator of what he takes as a model, and on the other hand by attributing their authorship to a "creator" whom he successively qualifies as "a god" (theos, 597b6), to make it clear that the ideai are not human creations, but are the creations of a being endowed with intelligence, and even with an intelligence superior to that of men; as a "gardener / planter" (phutourgos, 597d5) sowing his creations "in nature" (en tèi phusei), to make it clear that the ideai do not constitute a separate "world" but are an integral part of our world that they make intelligible to us and that they have more to do with "seeds" from which multitudes of "shoots" can germinate, all different from one another from the same seed (all the leaves of the same oak tree are different from one another and have nothing to do in their appearance with the acorn from which they grew, but are nevertheless all oak leaves, not willow leaves or pine needles, and even less horses or men) than with a "model" that would have to be reproduced as accurately as possible; and finally as "king" (basileus, 597e7), to make it clear that these ideai that he "sows" are akin to laws, the works par excellence of a king, for the nature in which he sows them, thus complementing each image with other images highlighting other aspects of this divine creator of whom we can only speak in myths (the Timaeus) or images;
-Phaedo, 99d4-100c8, where Socrates on the one hand warns against the risk of blindness if we try to look at the sun in direct view rather than through reflections in water, even and especially during an eclipse, which should lead us to be wary of what he proposes as the final stage of the progression of the prisoner freed from his bonds and out of the cave in words that their redundancy and emphasis should suffice to invite us to question the idea that anybody might "see clearly and contemplate the sun itself by itself in its own place as it is" (ton helion... auton kath' hauton en tèi autou chôrai ... katidein kai theasasthai hoios estin, 516b4-7), and on the other hand, after explaining that, fearing that his soul would suffer the same blindness by looking at facts / things (pragmata) with the eyes and the other senses, he had decided to seek "the truth of beings" (tôn ontôn tèn alètheian, 99e6) in the logoi, adding that he did not consider "that one who examines in logoi the beings (ta onta), examines them more in images (en eikosi) than the one [who examines them] in acts / facts (en ergois)" (100a1-3), thereby suggesting that apprehension by the senses is just as much an apprehension through images as apprehension by logoi, simply though images that are of a different kind in each case, speaks of auta ("the *** themselves") by saying that he reasons "taking as a base / starting point that beautiful itself as such is something, as well as good and great and all the others" (hupotemenos einai ti kalon auto kath' hauto kai agathon kai mega kai talla panta, 100b5-7), which he makes "the kind of cause" (tès aitias to eidos, 100b3-4) which satisfies him to explain that something is beautiful or good or great, etc., these qualifiers resulting for him from the fact that what is thus qualified "partakes" (metechei, 100c5) in the auton ("the *** itself") from which it receives a qualification, beautiful, good, great... "itself as such" (auto kath' hauto), and not in any eidos or idea of that (the word eidè ("appearances / sorts") is used a little later, but it is by Phaedo retelling to Pythagoreans in Phlius years after the event the death of Socrates, not in the words he attributes to Socrates himself, and more precisely in a summary of which he is the author, not in a restitution of the verbatim of the discussion with Socrates, when he summarizes his story after an interruption by Echecrates by saying "after... it had been agreed that each of the eidè is something... (epei... hômologeito einai ti hekaston tôn eidôn...,102a11-b1), so that it is Phaedo, far from Athens and outside the control of Socrates, who has been dead for some time, who equates the auta ("the *** themselves") that he believes Socate spoke of with the eidè ("appearances"), not Plato's Socrates);
- Sophist, 259e4-6, where the Elean Stranger who leads the dialogue with Theaetetus, at the moment when he is about to investigate "what logos can be" (logon... ti pot' estin, 260a7-8), preludes to this investigation by saying that ""[it is] by means of the intertwining of eidè with one another [that] logos happens for us" (dia tèn allèlôn tôn eidôn sumplokèn ho logos gegonen hèmin), a key statement that makes logos an intertwining, and not a mere juxtaposition, not of words, but of eidè with one another, and which can help us to understand why, in the second process of the perceived by intelligence, the one that must use the logos by making use of the power of dialegesthai, one must find one's way through the eidè and the eidè alone, since they, and they alone, are what carry the meaning we give to words, which are in themselves no more than modulations of sounds with no relation with what they purport to designate other than through mere convention, and can change from one language to another without the meaning of the words changing.

The limits of logos

But in this decoding, we must also take into account the limits of logos, the only tool we have for this work, and understand that, if Plato had recourse to images, analogy and allegory, and in other places such as the Phaedrus, myth, it is because he was perfectly aware of the fact that these things cannot be explained in a totally satisfactory way by reasoning, rational discourses, purely explanatory logoi that do not have recourse to analogies and other forms of spoken images. To attempt to put back into purely explanatory discourse what Plato has wittingly chosen to present through images is to believe that we are smarter than him and simply not to have understood what he is trying to make us understand about the power, and the limits, of logos, and more specifically of the dialegesthai, which is the use of it through dialogue (hè tou dialegesthai dunamis, 511b4), which precisely conditions access to the second sub-segment of the perceived by intelligence. If, as he implies in the passage from the Phaedo quoted above, the logoi only give us images of beings, any apprehension of beings that would go beyond the stage of the "images" provided by the words that constitute the logos, or rather by the eidè that we associate with them to give them meaning, whatever form it takes, reasoning, as well as myth or allegory, would be incommunicable by nature, since communicating it would bring us back to the level of words and logoi. As a matter of fact, logoi are not the prerogative of the segment of the perceived by intelligence, and the allegory of the cave is clear on the fact that prisoners who remain immobilized in bonds since childhood are capable of dialegesthai ("practice dialogue") and, to do so, give names to the shadows they see on the basis of similarities and differences in their visual appearance (cf. 515b4-5). This suggests that a form of logoi is present in all four sub-segments of the line, potentially different in each case, but it is precisely these differences that distinguish the segments from one another. If we accept the relation mentioned by Socrates at the beginning of the discussion on the different kinds of beds between names and eidè, if there is logos, there are eidè, and eidè in a collective, not individual sense, referring to something common to several "beings" sharing the same name or attribute. The whole question is then to know what these eidè are based upon in each case. In the first sub-segment of the seen, corresponding to the initial state of the men (anthrôpoi) staged in the allegory when they are still prisoners immobilized in bonds, they are based exclusively on the visual appearance, represented by the shadows on the wall of the cave, the only things that the prisoners can see at this initial stage. In the second sub-segment of the seen, represented in the allegory by the turning around towards the objects projecting these shadows, they are based on the whole three-dimensional material dimension of the "beings" and the data of the five senses that can be taken into consideration to enrich the eidè associated with the names, whether inherited from the first stage or new, given to these "beings", not only those that we have been able to collect ourselves on what we have personally experienced, but also those that we have been able to gather from logoi of people we trust on what we have not personally witnessed. The move to the first sub-segment of the perceived by intelligence, that is to say the exit from the cave, presupposes that we have become aware of the fact that these "beings" are not only material, but also have a part of intelligibility resulting from the fact that they are the work of a craftsman (dèmiourgos), divine or human, endowed with intelligence and who had a purpose in creating them, and that the names by which they are designated no longer refer only to a simple visual appearance or to material properties, but to something "that cannot be seen otherwise than by thought (dianoia)" (511a1), and moreover that certain "beings" that were not visible in the cave (because they were immaterial) are visible outside the cave (the stars in heaven). The eidè associated with the names of all these "beings", material and immaterial, are then made explicit by relations between "beings" (translated into logoi, thus in an "intertwinning of eidè" which, according to the Elean Stranger at Sophist, 259e4-6, constitutes logos) which can take, in their most rudimentary form, the form of "definitions" and in a more elaborate form, the form of "Socratic" dialogues) rather than by references to visual and more generally sensible properties. The last stage is the one where we have understood that words, no more than the eidè that are associated with them and which change as each one progresses towards the stars / ideai that constitute the target for each one of them and the sun / idea of the good that "enlightens" them all and gives them meaning, are the "beings" themselves (auta) and that the best we can hope for is to "map" as closely as possible the starry heaven that is offered to us, that is to say, to master the relations that exist between all the stars / ideai, and above all between each of them and the sun / idea of the good, by expressing them in logoi / "intertwinning of eidè" whose strongness will be tested through dialegesthai, that is to say, the confrontation of points of view in interpersonal dialogue. In short, the ideai are the distant target towards which the eidè tend, which evolve for each one as he progresses in and out of the cave, but they are not yet the auta, who, as the myth of the Phaedrus mentioned above says, are on the other side of heaven and are accessible only to the gods, and perhaps to a few privileged humans who will not be able to benefit others directly since it would require to fall back to the level of words and logoi.

Keys to understanding the allegory of the cave

A few keys now to understand the allegory of the cave: the anthrôpoi ("men" in the sense of human beings regardless of sex) are human souls, in accordance with what Socrates says to Alcibiades at Alcibiades, 130c1-6, that, "since (as the preceding discussion has shown) neither the body, nor the whole of the two (body and soul) is man (anthrôpos), there remains that either it is nothing, or, if it is something, the [word] 'man' (anthrôpos) can be attributed to nothing else but the soul" (mèden allo ton anthrôpon sumbainein è psuchèn), and therefore that "the soul is man" (hè psuchè estin anthrôpos). These anthrôpoi ("human beings") as prisoners before and after being freed from their bonds are these human souls as capable of education and knowledge that will indeed free them form those bonds; as bearers hidden by the wall, they are these same human souls as objects of knowledge for one another as "animators" of their bodies perceptible by the senses, but invisible so long as one remains inside the cave since they are immaterial (which is depicted by the fact that they are hidden by the wall), but becoming "visible", that is to say, in the imagery used by the allegory, intelligible, when one leaves the cave, like all the rest of what was visible in the cave.
The bonds (desmoi) that have prevented these anthrôpoi from moving and turning their heads since childhood, allowing them to see only the shadows on the wall of the cave facing them, i.e. the images provided by sight, and thus make them prisoners (desmôtai), represent the prejudices inherited from their environment and the prevailing opinion that it is sight and sight alone that reveals the world around us and that it gives us an adequate and exhaustive apprehension of everything that "exists", leading us to admit without prior reflection on the way sight and human beings as a whole function that things are as we see them ("they [the prisoners caught in these bonds] would hold as the true nothing but the shadows of the implements, 515c1-2). All the spontaneous and unconscious work that takes place naturally in each person from the first moments of one's life and allows one to learn little by little to interpret the data from sight with the help of movement and the data from the other senses, in particular touch and hearing, leading one to individualize the patches of color that sight provides in a two-dimensional space, to associate "forms" (eidè) with them and to become aware of the three-dimensional character of the space in which one evolves, and to realize that the world is made up of a multitude of "things" that are more or less autonomous from one another and are not limited to what one sees at a given moment, that the "things" that one sees do not cease to "exist" because one closes one's eyes or they disappear from one's field of vision, that they do not change size depending on the distance at which they are from us, contrary to what the images of them that form in our eyes might lead us to believe, in short, everything that allows one to give meaning to the raw data provided by the eyes which are limited to patches of color, all this work, precisely because it was done unconsciously before we began to think and became automatic and remained unconscious, does not induces a specific reflection in most people that would make them aware of the fact that all this work of interpretation is done by the mind (noûs) and not by the eyes, and which could challenge the received idea that things are as we see them and that only the things that can be seen "exist". In other words, the word "bonds" (desmoi) used in the allegory refers, in the real world of which it is an image, to something that can still be described as "bonds", provided that this word is understood in a figurative sense that it can have in Greek (as in English), close to that which it has at Laws, VII, 793b4, in the mention of the "bonds of every constitution" (desmoi pasès politeias) constituted by the "unwritten customs" (agrapha nomima), described with the help of a word, nomima, which is found in the mouth of Socrates at Republic, V, 479d4, towards the end of the discussion on knowledge and opinion, where he makes them the "about / upon what it is" (eph' hôi esti) of opinion and where I have translated it as "received ideas". This understanding implies that the liberation from these bonds / prejudices cannot be the work of a third party but is purely internal to those who free themselves from them: it is the personal awareness of the fact that sight can be deceptive and above all that there are a multitude of things whose "existence" we admit without ever having seen them ourselves, such as the inside of our own body, or animals that do not live in the region we inhabit. The allegory limits itself to illustrating this by contrasting two-dimensional shadows and three-dimensional objects of which they are shadows, statues of men and animals representing their material bodies and manufactured objects, whose interior these shadows do not reveal to us, but we could broaden the issue by introducing the dimension of time and speak of everything that we admit without having been eyewitnesses, persons as well as events. In other words, our apprehension of the world is based more on "belief" than on actual sight. It is mainly the result of the "trust" (pistis, the affection (pathèma) that Socrates associates with the second sub-segment of the seen) that we have in the people around us and in their words and in those who have preceded us and have transmitted to us oral histories or writings on things and facts from elsewhere or from the past. It is therefore, at least initially and forever for some of them (those that belong to the past in particular), in the range of opinion, not of knowledge, and reaches us through logoi more than through the senses and opportunities to see for ourselves what we believe "exists" (whatever this word means) or "has existed". And, as a matter of fact, opinion is based on the trust (pistis) we place in those who transmit to us information about the world by means of logoi, and not on a personal experience and even less on the result of a personal search for knowledge by means of reason. The liberation of the prisoner that Socrates evokes is therefore indeed a turning around that compels ("he would be compelled", anagkazoito, 515c6) from the inside those who realize that sight is at the origin of only a small part of what one claims to know and is not always reliable, and we understand, with this way of understanding the "bonds" that bind prisoners, why he can say that this liberation takes place "naturally" (phusei). It is only the result of an inner work of the mind / intelligence (noûs) with which each human being (anthrôpos) is endowed, which other people can arouse by their words, but which they cannot do in the place of those who want to be freed from their "blinders". The prisoner thus freed moves from the illusion that it is sight that guarantees the existence of things for him and reveals them to him as they are to a state in which he is obliged to trust others to apprehend the world in its complexity (and in its duration). And it is not difficult to understand that this awareness does not take place without hesitation, without going back and forth (the "sparklings" (marmarugas) mentioned by Socrates at 515c9) and that whoever frees oneself in this way "deems the [things] he formerly used to see (ta tote horômena) truer than those now pointed at (deiknumena) (515d6-7) since the former (the shadows), one could see them, and the others, one does not see them with one's eyes but they are "shown / depicted" by means of words and logoi: thus, for instance, it is by trusting people who have examined disembowelled corpses on a battlefield or decaying bodies showing the skeleton, or doctors who have dissected cadavers, and supposing that all men are constituted in more or less the same way, that one can admit without seeing it that there are inside one's own bodies, made invisible by the skin that surrounds them, a heart, lungs, brain, bones, etc., which one will never see as long as one remain alive (X-rays, ultrasounds and other MRIs did not exist in Plato's time, and even this still provides only images whose interpretation is based on reasoning and scientific theories that are not within everyone's reach), and will at most be able to palpate (the bones) or hear (the heart). But this "turning around" does not yet take us out of the cave and, as long as it remains in the register of trust and not of the personal practice of reasoning validating the opinions that we have initially accepted without proof, leaves us in the material world of the objects protruding from the wall, and the path is still long and difficult toward admitting that there can also "exist" "beings" that are not accessible to any of our senses, but only to our mind / intelligence (noûs), that is to say, are "visible" (figuratively speaking) only outside the cave, as is the case for the "souls" that move the bodies / statues of which we see, in the literal sense, only the shadows (the bearers hidden by the wall).
The stars, which are only visible outside the cave, are, as I have already said, the immaterial ideai ("ideas") associated not only with abstract notions such as "beautiful", "just", "good" (the sun, which, by Socrates' own admission in his "decoding" of the allegory in 517b8-c1, represents the idea of the good, hè tou agathou idea), but also with everything that is sensible / visible and has a name, as "man" (the moon?), or even "table" or "bed" (cf. the discussion on the different kinds of beds in Republic X, 596a10, ff.). They represent the "objective" target, the same for all, in our search for knowledge (gnôsis in the sense of "inquiry"), that which is accessible to human reason about what they are the ideai of, the auta ("the *** themselves") which are on the other side of heaven, as the myth of the Phaedrus says, and therefore out of reach by human logos. On the other hand, what is not pictured in the allegory are the eidè, which exist at all stages of the prisoner's progress, accompanying the words one uses and evolving as one progresses from a simple visual appearance associated with the shadows that are the only thing one sees when one is still caught in bonds to logoi locating the star / idea corresponding in relation to the neighboring stars and to heaven as a whole, leaving aside any reference to the sensible "images" associated with the specific instances of this idea, accessible as sensible in the cave and as intelligible outside the cave thanks to these ideai, and especially thanks to the light projected on them by the sun / idea of the good.
What must be deduced from all this is that there are two categories of "things" in this allegory, those that can be apprehended both in the cave through the senses (as visible, and more generally sensible) and outside the cave through intelligence and reasoning (as intelligible), the example of which is detailed by Socrates in the case of the anthrôpoi ("human beings"), and those that can only be apprehended outside the cave (as intelligible) because they do not activate any of our senses, the stars in heaven and the brightest of them, the sun. But in each case (the sensible in the cave, the intelligible part outside the cave of the sensible which are only visible in the cave, the purely intelligible), there are always two stages: that of shadows and reflections and that of the "originals" of these shadows and reflections. Thus, if we go into detail in the case of humans, their bodies are represented in the allegory by the andriantai ("statues of men" with a reference to sex) carried by the bearers who circulate hidden by the wall (their souls in their role as invisible animators of these bodies); their shadows that prisoners see while immobilized in bonds are the visual appearance of their bodies (the statues of men protruding from the wall), and more precisely the image of them formed in the eyes; the sound reflections that constitute the echo of the words spoken by the bearers and that seem to come from the shadows, are their words, considered at this point as exclusively sensible phenomena, sounds (hence the use to describe them of the verb phtheggesthai, whose general meaning is "to produce sounds", whether for humans or animals or anything else); outside the cave, this time it is the anthrôpoi themselves, that is to say their immaterial souls, which can end up being apprehended, but at first, as long as one is not yet accustomed to the light of the sun / idea of the good, it is still only possible to "see", in this intelligible register that manifests itself through logos, their shadows (the words they say) and their reflections (the words said by others about them), before possibly being able, after habituation, to see them "themselves" (auta), in a vision that can only be individual and of which nothing can be said, since to speak of them supposes falling back to the level of words and logoi. And in all this, what is perceived, whether by the senses or by intelligence, is always anthrôpoi (in the plural) considered and understood individually, individual souls understood each as principle of intelligibility of a particular human being. If we wish to find in the allegory an "idea of man," we must look for it in heaven, which can only be understood as a whole of which the individual elements, the stars, spots of light all more or less identical with one another, images in the allegory of intelligible ideai, as I have already said, are only understood and can be identified by their position in relation to each others on the basis of a "cartography" that it is our responsibility to establish as precisely as possible (just as intelligible ideai have meaning only through the relationships they have with each others and that we seek to represent through logoi), probably in the moon, the one that takes up the most space there and the only heavenly body aside from the sun that is explicitly mentioned by name, just as anthrôpoi are the only "objects" in the cave that are explicitly mentioned by name (at 516a7) in what is to be seen by the freed prisoner just out of the cave.
What is true of humans is also true of all natural material creatures and all human creations as intelligible, for which these four stages are depicted. But the fact is that their names (such as for instance "anthrôpos") were given by the prisoners immobilized in bonds on the basis of eidè limited to only the visual appearances that the shadows constitute, and that these names do not change for those who are freed from their bonds and may eventually exit the cave, so much so that the same names are used in the real world, associated with eidè that evolve as they progress, to talk about what the allegory represents by things that it distinguishes by different names: in the case of the word anthrôpos, shadows (skiai) of statues of men, statues of men (andriantai), "shadows" (skiai) and "reflections" (eidôla) in waters outside the cave of these men invisible in the cave, but present outside, and finally these men (anthrôpoi) themselves (auta) and the idea that corresponds to them in heaven (the moon?), and that it is very difficult not to spontaneously associate with them the "shadows", the visual images from which they originated, and that it is difficult not to try to establish relations between the original and the image between these different levels of apprehension, a particularly risky practice as long as one has not reached the end of the progression and undertakes it in the progression from the interior to the exterior of the cave before having mastered the apprehension of what is outside as a whole, where it leads to mistaking mere reflections, the eidè that we associate at this point with the words we use and that we naively think are the same for everyone, for the ultimate reality and the statues seen inside the cave for "images" of these eidè: this is what happens with the supposed "theory of forms / ideas" attributed to Plato even though he warns us against such an understanding by means of the images completely understood of the analogy of the line and allegory of the cave; but to completely understand them, one must have reached the end of the progress he describes in them, have understood that these eidè, different for each one according to one's degree of progression towards the stars / ideai which are their "objective" but distant target, inaccessible to most, if not all, are not yet these stars and even less the auta ("the *** themselves") which, as the myth of the Phaedrus tells us, are in the supercelestial place, which is not given to everybody*. The last step is therefore to have become aware of the fact that any "cartography" of the stars / ideai that does not take into account the preeminent role played in relation to them by the sun / idea of the good as the "(leading) principle not set to serve as a base / starting-point [in view of something else]" (archèn anupotheton, 510b7) leaves us in the night, where it does not matter whether we see the stars themselves or their reflections (the logoi held on them) (which explains why Socrates doesn't mention reflections of the stars, but only of the sun) since we do not see the one who "illuminates" them all and whose light during the day allows us to see / understand everything, including what is inside the cave made "visible" / understandable by it outside the cave. And here, contrary to what is the case for the stars of the night, which can only become comprehensible in the light of the sun, even if it makes them "invisible" in broad daylight, it is important to determine whether the representation we have of the sun / idea of the good is still only a reflection of it more or less resembling and more or less fluctuating (the logoi held over it by the city) or an image of itself in direct sight. But at the same time, we must not presume our strength and believe that we can, in this life, "see distinctly and contemplate the sun itself by itself in its own place as it is." The teleutaion that introduces the line from which these words are taken means "in the end / finally" without specifying what "end" is meant and teleutè ("end, accomplishment, completion"), from which it derives, may mean "death", which leaves open the possibility that the "end" that Socrates is thinking of here is death, which is probably the only means, if there is one for us, to be able to see the god sun "in its own place". The real conclusion of this whole process of education is not the enduring contemplation of the sun / idea of the good itself, which everyone knows is practically impossible, and which Socrates does not present in an assertoric way, but qualified by an oimai ("I suppose"), and which moreover would teach us nothing about anything (it is not by looking at the sun that we can see the world around us, but by taking advantage of its light to look at the world around us), but the sullogizesthai that follows in the allegory (516b9-c2), the reasoning that leads to the understanding of the role of the sun / idea of the good as the "light" of intelligence, as Socrates explained just before the two images in the paralleling of the good and the sun, introduced by the expression kai meta tauta, which everybody understands as meaning "and after that", i.e. in the sense of a temporal succession (which the preposition meta can indeed have), but can also be understood from the primary meaning of meta, which is "among, in the midst of", in the sense of "and in the midst of these [reflections]", that is, as suggesting that the conclusions it presents can be reached in the context of attempts to better see the sun / idea of the good and its light illuminating everything else, without this implying having seen it "itself by itself in its own place as it is".

* To temper the presumptuous character that such an assertion can have, I will simply add that my first serious work on Plato dates back to the end of the 70s, that the first version of my annotated translation of the analogy of the line dates from 2001 and that it is only during a fourth update of it in 2022, at the age of 78, that I really understood everything I present here about this analogy, in particular about the interpretation of the division of the segment of the perceived by the intelligence, even if I had found most of the keys to reading the allegory of the cave about ten years earlier. Plato does not give himself up without effort and the education of the man he describes in the allegory of the cave is never finished... (<==)

Keys to reading the analogy of the line

The first mistake that must be avoided about the analogy of the line is that of believing that Socrates opposes two kinds of "realities", those that are "visible", qualified by a property that refers only to the sense of sight, but in fact includes everything that is accessible to the senses (aistheton, a word used later in the analogy, at 511c1), that is to say, all material "realities" that are sensible and subject to becoming, and those that are "intelligible", and only intelligible, therefore immaterial, inaccessible to the senses and not subject to becoming, which leads in fact to consider that all "reality" is either one or the other, but not both at the same time, and that therefore the material world is unintelligible and cannot be an object of knowledge, whereas precisely the allegory of the cave, properly understood, shows us that visible (and by extension sensible) "realities" can also be intelligible ("visible", in the analogical sense relating to the "sight" of the mind, outside the cave). What Socrates opposes here are, not two categories of "realities", but two modes of apprehension of the "realities" that surround us and are accessible to us by the senses and / or intelligence (noûs), apprehension by sight (and only sight at this point) and apprehension by intelligence. If sight is thus emphasized, it is because it is the sense to which we attach the most importance and trust most for our apprehension of the world around us, to the extent that, as I said above, for the Greeks of the time, one of the verbs meaning "to know" (eidenai) is none other than the perfect of the verb meaning "to see" (idein, which replaces certain tenses of the verb horan, another verb meaning "to see", from which horaton ("visible") comes), as if to better confirm that to have seen is to know. And so we should not immediately generalize the term "visible" to assume that it is used instead of "sensible" to refer to the material world as a whole (as I myself have sometimes done in other pages of this site and in previous versions of this page in French) in a synecdoche that would designate the whole by a part, effectively inviting the reader to think more about the "objects" that can be apprehended by the senses than about the modes of apprehension of these "objects" compared to the mode of apprehension by intelligence. Once we have understood this, there is no longer any reason to suppose a priori that these two modes of apprehension are exclusive of each other for the same "object" of apprehension, even though we have no difficulty in admitting that the same "object" can be at the same time visible, audible, tangible..., in short, apprehensible also by other senses, and that therefore visible "objects" can be intelligible as well as they can be tangible and / or audible and / or fragrant and / or sapient.
If we take a closer look at the text with these remarks in mind, we see that Socrates distinguishes three levels for which he uses a different vocabulary:
- the level of "objective realities", of the pragmata, which act (prattein) on our eyes and our mind / intelligence (noûs) and which are therefore qualified as "visible" (horaton) when they have the power to activate sight and "intelligible" (noèton, in the sense of "perceivable by intelligence") when they are capable of activating the mind / intelligence (noûs) without necessarily passing through the mediation of the senses, the one being no more exclusive of the other than the fact of being visible is exclusive of the fact of being tangible, or audible, or perceptible by other senses (in other words, a "reality" qualified as "visible" can also be "intelligible", and a "reality" qualified as "intelligible" may or may not be "visible", and may even not be perceptible by any of the senses): At this level, he uses verbal adjectives ending in -tos (-ton in the neuter) which indicate in this case a simple possibility, equivalent in Greek to the adjectives ending in -able or -ible in English, as precisely visible, intelligible, thinkable which serve to translate them;
- the level of the "affections / states of mind", of the pathèmata (cf. 511d7), produced in us by these "objective realities" (pragmata) visible or only accessible to intelligence but not to sight: he uses the terms "seen" (horômenon) and "perceived by intelligence" (nooumenon) in connection with them, passive present participles that refer, not to what activates sight or intelligence, but to what is produced in our mind, which "is born" (the primary meaning of genos), under the effect of these activators of sight or intelligence during effective occurrences of what is implied by the verbs used, "to see" (horan) and "to think" (noein);
- the level of the different kinds of logoi, expressed or simply thought, that these "affections" (pathèmata) arouse in us: he speaks of them as "opined" (doxaston), i.e. expressed as a mere opinion, and as "known" (gnôston), i.e. being the end result of a personal search for knowledge (gnôsis in the sense of "inquiry").
By qualifying at 509d8 the two segments of the first division of the line as "that (the segment) of the genos seen and that (the genos) of the perceived by intelligence" (to te tou horômenou genous kai to tou nooumenou), he shows that he locates the line at the level of the second of these three levels, the intermediate level of the "affections / states of mind" (pathèmata) produced in us by the "objective realities", the pragmata ("facts / things") that act (prattein, from which pragma derives, which is the opposite of paschein "to suffer / be affected by", from which pathèma derives) on our eyes and our mind / intelligence, and not at the level of these pragmata, these "objective realities". This is suggested by the use of the word genos, which must be taken here in a sense that evokes "origin" ("that which originates in sight / perception by intelligence") with an idea of filiation that my translation by "family" seeks to preserve. And this is confirmed by the preference for the words "seen" (horômenou) and "perceived by intelligence" (nooumenou) rather than "visible" (horaton) and "intelligible" (noèton) which emphasize the intrinsic properties of the "activators" (pragmata) of sight and intelligence and thus orient the mind towards a classification of "objects" rather than of the "affections" produced by these "objects". Talking about "visible" (horaton) and "intelligible" (noèton) makes it easier to suppose that they are disjoint subsets (a "thing" is either visible or intelligible, not both), while talking about "seen" and "perceived by intelligence" facilitates the acceptance of the fact that the same "thing" can be both seen and perceived by intelligence, which is what Plato's Socrates has in mind, as confirmed by the allegory of the cave. This should therefore avoid an almost general error in the understanding of the analogy, the one that suggests that the division proposed by the analogy of the line is a division of the "real" in which each element of this whole is in one and only one of the four sub-segments described by Socrates, with in the background the idea of opposing what is visible (and by extension sensible / material) and, as such, supposedly unintelligible because it is in perpetual becoming and therefore can only be the object of opinions, with what is only intelligible and therefore escapes becoming and can only be the object of knowledge. Exit then, for instance, the thesis that the "proper objects" of the first segment of the perceived by intelligence (that of the dianoia) are who knows what "mathematical objects", not that such "objects" do not exist (between the square itself (to tetragonon auton, cf. 510d7), which has neither dimensions nor spatial position and can be represented by the logos "a closed plane figure which has four equal rectilinear sides forming between them four right angles", and a square drawing made by a surveyor on a material support, which will never be strictly a "real" square, there is the square of two feet on each side, to which Socrates refers in his discussion with Meno's slave, the square of ninety feet on each side drawn on all baseball fields, and all those which have a specific dimension, considered in the abstract and not in a particular material figure, and which are immaterial and in infinite number), but because they are not the exclusive "population" of the first sub-segment of the perceived by intelligence, the proper object of dianoia, which can consider with its own modes of reasoning, which, alone, characterize it, any "object" that is sensible / material or only intelligible. A symptom of this error of interpretation is to speak of the segment of the visible (horaton) and of the segment of the intelligible (noèton) and not of the segment of the seen (horômenon) and of the segment of the perceived by intelligence (nooumenon), ignoring the change of vocabulary that takes place at 509d8 compared to 509d2-3, a change in vocabulary that the vast majority of translators indeed ignore, translating the two series of words (horaton and horômenon on the one hand, noeton and nooumenon on the other) by the same words ("visible" and "intelligible" respectively) Now, as I have already said, the allegory of the cave confirms that this is not the case and that the analogy does not seek to classify in distinct "boxes" with no possibility of moving from one to another the "things" (pragmata) with which we are confronted in our lives, depending on whether they affect our sight or our mind / intelligence (noûs), but to highlight the different ways in which we react to the "affections" (pathèmata) that they cause on them, and that it is in fact the same "things" that are apprehended in the four (if they are visible) or only two (if they are purely intelligible) sub-segments, simply under different "appearances" (eidè) conditioned by what gives us access to them, sight or mind / intelligence (noûs). But, by the second division of each segment, Socrates shows us that the "affections" (pathèmata) that he has in mind are not limited to the "gross" production resulting from the action of the pragmata on the "organs" that they can act upon (eyes for sight, ears as receptors of logoi for intellingence or thought as merely capable of producting inner logoi), that is to say, to the image produced in the eyes (no matter where exactly and by what physical process) for the seen, or to the words heard or simply thought for the perceived by intelligence, but include the way in which intelligence interprets them, either straightforwardly without becoming aware that they are only images (in the seen) or words (in the perceived by intelligence), or by becoming aware that they are only "representations" that do not show us what they represent as it is. It is indeed when we are not aware of the fact that sight gives us only "images" (eikones) of what it allows us to see, that is, in the terms of the allegory of the cave, that we "hold as the true nothing but the shadows of the implements" (515c1-2), that we live in a world of images, of "shadows" (the first segment of the seen), and only when we become aware of that that we can begin to gain access to what sight gives us only an image of, as indeed distinct from the image we perceive of it (the second segment of the seen). And in the same way, we cannot consider what we speak of and think about with words as having an autonomous "reality", and therefore know it (the second segment of the perceived by intelligence), so long as we do not think of that as distinct from the words we associate with it, as do those for whom "beautiful", "just", "good" for instance, are only words (the first segment of the perceived by intelligence).
But there is more. Once we have understood that the divisions that Socrates invites us to make on the line do not seek to define "boxes" in which to locate distinct "beings", each one in one and only one of these "boxes", but to distinguish different ways of apprehending the same "beings", we can finally understand why, if the division of the segment of the seen inventories indeed perceptible "things" (images and originals), the division of the segment of the perceived by intelligence inventories, not "things", but intellectual processes, modes of reasoning, and, only as "objects" of these approaches, "beings" distinct from those of the segment of the seen (words and eidè). Sight, with the help of a first stage of interpretation by the mind (Plato would say "by the soul (psuchè)") of the raw data it provides, can only identify and distinguish individual "objects" from one another, whereas intelligence as such can only function through reasoning that establishes relations between these "objects", or rather between the "abstractions" that it associates with them. precisely to make them intelligible, the eidè gradually rid of their references to the sensible. In the visible, the defining criterion is the "status" that the soul grants to what sight allows it to apprehend, that of adequate and exhaustive representation of what activates it (which amounts to taking a simple image for reality) or that of a simple partial image of it; in the intelligible, the defining criterion is the "status" intelligence grants to that by means of which it reasons, words and the logoi it constructs with them, that is, whether or not it is aware of the fact that the eidè that it associates, unconsciously or consciously, with these words, are the very things to which these words claim to refer (the auta) or simple "images" of them adapted to the human mind and its limits. In both cases, therefore, the division is indeed made "according to the same logos": in each case, the difference is made according to whether or not one is aware that what the involved organ, the eyes in one case, the intelligence in the other, is working on is only an "image / representation" of what activates this organ and not the "thing" itself.
The second mistake that must be avoided is that of misunderstanding the expression ana ton auton logon ("according to the same logos") used by Socrates to tell Glaucon how to divide the two segments, that of the seen and that of the perceived by intelligence, resulting from the first division of the line, about which he said only one thing, which is that it had to be segmented into two unequal (anisa) segments without giving any reason for this request and, what's more, without specifying a proportion (one of the meanings of logos) between these two segments. Concerning the first division of the line into two segments, the anisa ("unequal") reading has been disputed since antiquity, but no one to my knowledge has ever found an acceptable reason to justify them being unequal or on the contrary equal (isa), while the explanation is implicitely provided by the allegory of the cave that follows: if one finds outside the cave, that is to say, in the segment of the perceived by intelligence, all that is visible / sensible in the cave, that is to say, in the segment of the seen, plus the stars of heaven invisible from within the cave, that is to say the purely intelligible beings with no action on our senses, it is therefore that the segment of the perceived by intelligence must be greater than that of the seen, and Socrates can say this without knowing what the size of the one and the other are (which would require first having said what they represent that is measurable and having defined an appropriate unit of measurement) and without even knowing what is the numerical ratio between the two, since he does not specify how to measure them. If, then, Socrates knows that he does not know the ratio (logos) between the two segments, at least not as a numerical ratio, how could he ask Glaucon to segment each of the two segments according to that same ratio?! ... But what the commentators have not noticed is that the "same" (auton) of "according to the same logos" (ana ton auton logon) can be understood in two ways: (1) according to the same logos as the one used to divide the line into two segments (the way the vast majority, if not all, of translators and commentators understanding it), or (2) both according to the same logos as the other, without reference to the first division. Now, if (1) implies (2) (the two ratios which serve to divide each of the two segments being both equal to a same third, the one which served to divide the line into two segments, are equal to each other), the converse is not true. Now, nothing in the analogy (except the weight of tradition) invites us to think that the division of each of the two segments, that of the seen and that of the perceived by intelligence, must be done according to the logos (numerical ratio or logical reason) which served to divide the segment the first time around, logos about which, as I have already said, Socrates says nothing except that the two segments must be unequal. And when he returns to these divisions in the discussion on dialektikè, towards the end of Book VII, using a vocabulary that takes us from the level of "affections / states of mind" (pathèmata), which is the one where he had initially located the line, to the level of logoi, the vocabulary of opinion (doxa) and intelligence (noèsis), by proposing to call "these two together ("trust  / faith" (pistis) and "imagery" (eikasia), the two "affections / states of mind" (pathèmata) associated with the segment of the seen), 'opinion' (doxa), and the other two ("knowledge" (epistèmè, which here replaces what was called noèsis in the analogy) and "(discursive / wandering) thought" (dianoia), the two "affections / states of mind" (pathèmata) associated with the segment of the perceived by intelligence), 'intelligence' (noèsis, which, in the analogy, designated only the second sub-segment of the perceived by intelligence)", it is, after associating "opinion" (doxa) with "becoming" (genesis) and "intelligence" (noèsis) with "beingness" (ousia), to propose a number of equivalences of relations between these different notions: " what beingness (ousia) [is] with regard to becoming (genesis), intellection (noèsis) [is] with regard to opinion (doxa), and what intellection (noèsis) [is] with regard to opinion (doxa), science / knowledge (epistèmè) [is] with regard to trust / faith (pistis) and (discursive / wandering) thought (dianoia) with regard to imagery (eikasia). However, none of these parallels concerns the relationship between "knowledge" (epistèmè) and "discursive / wandering thought" (dianoia), the "affections / states of mind" (pathèmata) associated with the two sub-segments of the perceived by intelligence, and that between "trust / faith" (pistis) and "imagery" (eikasia), the "affections / states of mind" (pathèmata) associated with the two sub-segments of the seen, which he said at the outset should be equal (division "according to the same logos"). The relationships he evokes here are those between the homologous sub-segments of the two segments: the relationship between "knowledge" (epistèmè) and "trust / faith" (pistis) (the second sub-segment of each segment) and the relationship between "discursive / wandering thought" (dianoia) and "imagery" (eikasia) (the first sub-segment of each segment), to say that they are analogous to the relationship between "intelligence" (noèsis) and "opinion" (doxa), which is itself analogous to the relationship between "beingness" (ousia) and "becoming" (genesis). Now, it should be noted that this equality of relations (the ratio of the first sub-segment of the seen to the first sub-segment of the perceived by the intelligence is equal to the ratio of the second sub-segment of the seen to the second sub-segment of the perceived by intelligence, and they are both equal to the ratio of the segment of the seen as a whole to the segment of the perceived by intelligence as a whole) is mathematically true whatever the ratio that has been used to segment the two segments so long as it is the same, even if it is not the one that was used to segment the line into two segments, in other words, is true in the understanding (1) as well as in the understanding (2) of ana ton auton logon, since its truth depends only on the equality of the relations used for the second division, which holds both in understanding (1) and in understanding (2). So, if Socrates had also wanted the ratio between "knowledge" (epistèmè) and "discursive / wandering thought" (dianoia) on the one hand, and between "trust / faith" (pistis) and "imagery" (eikasia) on the other hand, equal by hypothesis since the division must be made "according to the same logos" (ana ton auton logon), to be also equal to the ratio between "intelligence" (noèsis) and "opinion" (doxa), designating here the segment of the perceived by intelligence and that of the seen, he would not have failed to say so. One may also wonder whether the clarifications he gives on the relations of homologous sub-segments, which only complicates his already dense sentence without adding much to what he has said before, have not been added by him to make us understand that, if he goes into such detail and does not add the equality of the ratio between the two sub-segments of each segment and that between the two segments as a whole, it's indeed because this equality is not true. And this is confirmed by what he says immediately afterwards, precisely of these two relations, when he adds: '"but the relation of analogy between what those [are] about, and the division into two parts of each one of these two, opinable (doxaston) and intelligible (noèton), let us drop [that], Glaucon, so that it doesn’t fill us full with discussions many times longer than those having preceded" (533d7-534a8), that is to say that he does not want to say more about the identical ratio that served to divide the two initial segments "according to the same logos" (ana ton auton logon), which implies that it is equal to none of those he has already mentioned, including the ratio between "intelligence" (noèsis) and "opinion" (doxa), the new names by which he refers to the two segments of the fisrt segmentation. We must therefore understand ana ton auton logon ("according to the same logos") in sense (2) (the two segments are segmented both according to the same logos as the other, which is not the logos that was used to segment the line into two segments).

Clearness (saphèneia) and truth (alètheia)

Concerning the division of each segment, that of the seen and that of the perceived by intelligence, "according to the same logos" (ana ton auton logon), even if, as we have just seen, Socrates ends up saying that he does not want to discuss it, we can nonetheless try to understand the scattered indications he gives about it. In the course of the analogy, Socrates evokes two "criteria" that could be relevant: the notion of "clearness" (saphèneiai) and its opposite (asapheia), which he mentions at 509d9 at the beginning of his description of the division of the segment of the seen, and that of "truth" (aletheia) and its absence, which appears at the transition between the description of the division of the segment of the seen and that of the division of the segment of the perceived by intelligence, at 510a9. If these two notions are so close that saphes, the adjective from which sapheneia is derived, from the primary meaning of "clear, manifest, obvious", also has the derived meaning of "sure, true", it is necessary to make a clear distinction between the two and above all to see what role truth plays in the analogy.
Saphenia, "clearness", only makes sense in relation to an observer and the perception of what one observes. It is therefore a relevant property for affections (pathèmata) and everyone would agree that, in most cases at least, an image is less clear, or if not less clear, less exhaustive, than its original, since it does not reveal everything. But it should also be noted that, as the allegory of the cave highlights, "clearness" being a partly subjective notion in that it depends on the generic specificities and the individual quality of the observer's organs, the lack of clearness can be caused by a lack as well as by an excess of light, as it happens to the prisoner when he turns around in the cave and, dazzled by the fire when he tries to see the objects protruding from the wall, considers the shadows to which he was accustomed "clearer" (saphestera, 515e4) than the objects protruding from the wall seen in the full light of the fire, the same phenomenon being reproduced when he exits the cave with regard to the objects present outside ("men and the other [***]"), 516a7), and, again, the other way around, when he returns to the cave and can no longer distinguish the shadows after becoming accustomed to the brightness of the sun outside the cave. And since the allegory makes us understand that the "objects" that are found in the different segments under different "appearances" are the same, we must conclude that this notion of saphèneiai ("clearness") is not what permits to sort and classify different "objects" into different segments, but a property of the perception we have of the same "object", whatever it is, in the different segments. The perception to which the second segment of the seen gives access (the statues of men, in the case of the anthrôpoi, i.e. their material body) will always, once one has become accustomed to this mode of perception, be clearer than that to which the first segment of the seen gives access (the shadows, i.e. the mere two-dimensional visual appearance), and so on until the fourth segment, the second segment of the perceived by intelligence, which gives access to a perception which, complemented by those obtained in the other three segments put in their appropriate place, will give the clearest, because it is the most complete, apprehension of what is submitted to examination, whatever it may be.
Alètheia ("truth"), designated by a noun derived from the adjective alèthès whose primary meaning is "not hidden", concerns the greater or lesser accuracy in the relationship that exists between the perception by an observer of something, fact or "thing", which acts on that observer (a pragma) and what it is the perception of. It therefore also presupposes an observer, but where saphenia ("clearness") had a partly subjective character depending on the observer and his organs of observation, aletheia ("truth") has an "objective" character in that it is assessed by comparison to what is observed and more or less "revealed". And since an observer alone cannot appraise this accuracy, being unable to apprehend the observed "object" otherwise than by means of one's organs of perception (senses and intelligence), whose accuracy is precisely what must be appraised, and since no one can read in the thoughts of someone else, this appraisal can only take place between observers confronting their perceptions expressed in the form of logoi by means of dialogues. And indeed, in the analogy of the line, aletheia ("truth") is mentioned in a context (510a8-10) dealing with opined (doxaston) and known (gnôston), terms that refer to logoi expressing opinions or manifesting knowledge, and in the allegory of the cave, reference is made to aletheia ("truth") only in contexts of logoi or dialegesthai: at 515c1-2 when Socrates says that prisoners immobilized in bonds " holds as the true nothing but the shadows of the implements" shortly after having said that "if they were able to dialogue (dialegesthai) with one another... the same [things] being around [again], they would take the habit of giving names to those [things] they see" (515b4-5); at 515d1-7, in the context of a dialogue between the prisoner who has just been freed from his bonds and an unidentified character ("if someone told him...", "ei tis autôi legoi, 515d1-2) but who is clearly not one of the prisoners immobilized in bonds, where Socrates suggests that the freed prisoner would come to "deem the [things] he formerly used to see (the shadows) truer (alèthestera) than those now pointed at (the objects protruding from the wall)" (515d6-7); at 515e6-516a3, when Socrates says about the prisoner exiting the cave that, dazzled by the light of the sun, he would be "unable to see a single one of the [things] now called true" (tôn nun legomenôn alèthôn, 516a2-3).
To properly understand the role that Socrates attributes to the criterion of "truth" in the division of the line, one must be very attentive to the formulation he uses and not let oneself be fouled by preconceived ideas or influenced by words from him that will only come later and in another context (what he says about the relationship between opinion and knowledge in the discussion on dialektikè towards the end of Book VII): at the transition between the description of the division of the segment of the seen in images and originals of these images and that of the division of the segment of the perceived by intelligence, he asks Glaucon if he agrees that "it (the segment of the seen, whose mode of division he has just described) is divided with regard to truth (alètheia) and its absence [according to the following ratio(nale):] as the opined [is] to the known, so what is made similar (to homoiôthèn) [to something is] to what it has been made similar to (to hôi hômoiôthè)" (510a8-10). What Socrates proposes here is to extend to the relationship between image and model, generalized here, in the perspective of its imminent extension to the segment of the perceived by intelligence, by the use of the expressions "what has been made similar" (to homôiothen) and "what it has been made similar to" (to hôi hômoiôthè), a distinction supposedly accepted between opined and known with regard to truth. Thus, the question is to figure out what is this distinction between opined and known that can be extended to the case of the relationship between an image / resemblance and its model / original and, since it is supposed to have been accepted, to look for it in a distinction which has been discussed earlier. And what is suggested here cannot be to consider opinion as an "image" of knowledge, since that would amount to making the parallel suggested by Socrates work the other way around and, moreover, ignores the problem of "truth" that is at the start of this parallel. The distinction between opined and known from the standpoint of truth supposedly accepted that Socrates proposes to Glaucon to extend to the image / resemblance with respect to its model / original, is the one that Glaucon himself stated at Republic, V, 477e6-7, in the discussion on the difference between knowledge and opinion, when he described knowledge as "infallible" (anamartèton) and opinion as the opposite ("that which is not infallible"), which, reformulated in terms of "truth", amounts to saying that knowledge is always true, whereas opinion, as we have known since the Meno, can be either true or false. Transposed to the image in relation to the original, what Socrates wants us to admit here is that an original, as an original, is always "true", whereas an image / reproduction / similarity of this original can be true or false in relation to it, that is to say, give a more or less accurate and more or less exhaustive image / reproduction / similarity of it. In other words, the problem of "truth" arises only for "images / reproductions / similarities" with regard to their "original / model". And, from this point of view, the "truth" is not appraised in terms of all or nothing, but in the perspective of a progressive "unveiling" that can admit of multiple stages when we are confronted with multiple "images / reproductions / similarities" of the same "original / model", some in the form of images provided by sight, others in the form of logoi, which is precisely the case for us in our apprehension of what surrounds us, as the allegory of the cave makes clear. Socrates therefore does not invoke truth to help us sort out things that, as images / reproductions, would be false in relation to others that would be their originals / models and, as such, would be true, such as visible / material objects in relation to who knows what immaterial "ideas", but to draw our attention to the fact that everything that has the status of "image / reproduction" in relation to something else poses a problem of "truth" / accuracy when compared to its "model / original" which cannot be reduced to the dilemma "true / false", true for the original, false for the reproduction / image, and it is indeed the case for opinion in relation to knowledge, which can be totally or partially true, or completely false.

Knowledge and opinion

It is only when the analogy is reminded in the discussion on dialektikè towards the end of Book VII that Socrates evokes, not the distinction between opined (doxaston) and known (gnôston), but that between opinion (doxa) and intelligence (noèsis), by grouping together the two affections / states of mind (pathèmata) associated with the segment of the seen under the name of opinion (doxa) and the two of the perceived by intelligence (noûs, as an "organ") under the name of intellection (noesis, as an activity), and will clarify his thought on these subjects in terms that I have already quoted in the discussion on the meaning of "according to the same logos" (ana ton auton logon), but which should be examined here from another standpoint: "It is satisfactory then, said I, as before, to call “science / knowledge” (epistèmè) the first part, the second one “(discursive / wandering) thought” (dianoia), the third one “trust / faith” (pistis) and “imagery” (eikasia) the fourth one, and those two together “opinion” (doxa) and the two other together “intellection” (noèsis); and opinion (doxa) on the one hand [is] about becoming (genesis), intellection (noèsis) on the other hand about beingness (ousia); and what beingness (ousia) [is] with regard to becoming (genesis), intellection (noèsis) [is] with regard to opinion (doxa)". But here again, it is necessary to understand what Socrates is saying, in the light of a proper understanding of the two images of the analogy of the line and the allegory of the cave. When he says that "opinion (doxa) [is] about becoming (genesis)" and that "intellection (noesis) [is] about beingness (ousia)", he does not mean that everything that is of the visible / sensible / material order and therefore subject to becoming can only be the object of opinion and that only that which is of an exclusively intelligible order can be attributed a "beingness" (ousia), since the allegory of the cave has shown us that everything that is in the cave as visible is found outside the cave as intelligible. It simply means that as long as we remain in the affections / states of mind associated with the segment of the seen, eikasia and pistis, that is to say, that we remain inside the cave, we can only arrive at opinions and that it is only when we agree to leave the cave and therefore to reach at least dianoia, that we can begin to have an understanding of what we are interested in, whether it is sensible or purely intelligible, and that we may hope to reach some day knowledge (epistèmè) by gaining access to the last sub-segment. In other words, it is each one of us who, by accepting or refusing to admit that even those things that partake of becoming can have a share of intelligibility and that there can be "beings" that do not affect any of our senses (the stars of the allegory of the cave), that is to say, to leave the cave, either forces oneself to remain at the level of opinions or opens the door to intelligence, including intelligence of "realities" subject to becoming. If we do not accept that things subject to becoming can nonetheless, through the power of logos, be assigned "attributes" by means of words saying that "it is" this or that and thus describing their "beingness" (ousia), it is we ourselves who condemn ourselves to remain in the realm of mere opinions. And it is also the case if we refuse to admit that these "attributes" are more than mere words.

The same logos

If one wants to maintain at all costs that the logos used to segment each segment of the line in two is the same as the one used to segment the line the first time around (as I have said that all commentators do), supposing in a simplistic way that this relationship is that of image to original, even though, as we have seen above, Socrates refuses to discuss this relationship for fear of endless discussions (which shows that it is not as simple as that), arguing that, in the discussion on dialektikè, he associates the first segment with opinion (doxa) and the second with intelligence (noèsis), we may try to liken the relationship between opinion and knowledge to that between image and original. And indeed, we may consider a particular opinion, something "opined" (doxaston), that is to say, an opinion expressed by specific words spoken or thought, as an "image" of knowledge, of something "known" (gnôston), when it is a true opinion, insofar as it can reproduce exactly the words that would be used by someone who possesses knowledge about what this opinion is about, and as the difference between the two is not in the wording used, the words which express it, but in the ability or lack of ability of the person who uses these combinations of words to account for them and to justify their relevance, in the fact that for one of them these words are justified only by the fact of having heard them, or words with a similar meaning, used by others, while for the other they are the result of a personal work of investigation (one of the meanings of gnôsis) whose unfolding he is able to reproduce, but Socrates never says this explicitly and, as we have seen above, this is not what he says in the analogy at 510a8-10 when he draws a parallel between "opined" (doxaston) and "known" (gnôston) on the one hand, "image / reproduction / similitude" ("that which has been made similar" (to homôiothen)) and "original / model" ("that to which it has been made similar" (to hôi hômoiôthè)) on the other hand. And, in any case, opinion as an abstraction (doxa), which encompasses both true and false opinions, is not the same as a particular opinion present in the thought of a particular person (a doxaston), just as intelligence (in the sense of understanding) as abstraction (noesis) is not the same thing as a particular knowledge (a gnôston) present in the mind of a particular person, and it is not because certain particular opinions constituted by sequences of words may, when they are true, be "images / reproductions / similarities" of knowledge on the same subject, capable of being expressed by the same sequence of words, that opinion as such, an abstraction which is no particular sequence of words, can be considered as an "image / reproduction / similarity" of knowledge as such, an abstraction which is also no particular sequence of words. It cannot therefore be deduced from the fact that Socrates associates "opinion" with the two sub-segments of the seen and "knowledge" with the two sub-segments of the perceived by intelligence that the relationship between the segment of the seen as a whole and that of the perceived by intelligence as a whole is a relation of image to original and is therefore the same as that which presided over the division of each of these two segments into two sub-segments "according to the the same logos" (ana ton auton logon), which, by the way, is not itself a mere relationship between image and original. In fact, the difference between the affection / state of mind (pathèma) incured by prisoners who have only ever seen shadows (the first sub-segment of the seen), eikasia, and that incured by the prisoners who have been released but remain in the cave (the second sub-segment of the seen), pistis, is not so much the fact that, in one case, they see images and in the other their originals, since, among the originals, there may be fabricated objects (skeuè) that are themselves images (paintings and statues, for instance), but the fact that if, in the first case, they do indeed see images (the shadows), they are not aware of that and take these images for "reality", that, as Socrates says in the allegory, "[they] hold as the true (to alethes) nothing but the shadows of the implements" (515c1-2), whereas in the second case, when they have become able to "see" both shadows ("see" in the literal sense) and manufactured objects of which they are shadows ("see" in the figurative sense), they can no longer ignore that shadows are only shadows, that is to say, some kind of images of something else that they also "see", but this time with the eyes of the mind, through the words (logoi) of people they trust (pistis).
And just as, in the seen, the notion of "image" (eikôn) used to distinguish the second sub-segment from the first is a "false lead" that should lead us to generalize the notion of "image" to everything that is perceived by sight, so, in the perceived by intelligence, the notion of "image" (eikôn) used to distinguish the second sub-segment from the first, the one according to which some of the words we use would serve to designate "things" which are "images" of who knows what "realities" accessible only by "thought" (dianoia) and which will end up being called eidè when Socrates comes to speak of the second sub-segment, is a "false lead" that should lead us to generalize this notion of "image" to everything that is expressed by logoi, that is, to understand, so as to be able to make the best possible use of the whole power of dialegesthai (hè tou dialegesthai dunamis, 515b4), that it is all the logoi that give access only to "images" of "beings" (ta onta) through the mediation of the eidè the words refer to, provided we stop associating them with visual images (eikones in the primary sense) in order to try to reach the ideai they point toward, that is to say, the principles of intelligibility that allow them to be understood in the light of the good (thus, for instance, one will not understand what a bed is by looking for what is shared, from a visual, or even material, standpoint, between all the beds one has seen before, that is to say, by limiting oneself to the horômenon eidos ("seen appearance"), but only when one understands that a bed (klinè) is a piece of furniture intended to allow one or more people (in general no more than two) to lie down (klinein) on it to sleep (noèton eidos ("intelligible appearance") which points toward the idea of bed); or, to give another example, in order to become a philosopher, it is not enough to physically resemble Socrates, as is the case for Theaetetus (cf. Theaetetus, 143e8-9), who may well be a brilliant mathematician, but is unable to give birth to a meaningful logos on what "knowledge" means, because he has not started with an inquiry on logos, through which this "knowledge" is manifested (to use the wording of the analogy, he posits logos as a hupothesis for which he does not feel the need to give an explanation), an inquiry he ends up starting, but will leave unfinished and unsuccessful, only at the end of the dialogue when all his previous attempts to define knowledge have failed, ending with a definition of knowledge as true opinion accompanied with logos, even though shortly before, Socrates had him admit that opinion is a kind of logos, which means that his definition can be reformulated as true logos accompanied with logos, one must resemble him at the level of the logos, as is symbolically the case for the young Socrates, who bears the same name, and who takes the place of Theaetetus to dialogue in the Politics with the Elean Stranger, who took Socrates' place in the Sophist to make Theaetetus understand what logos is and how it can be true or false, on a subject of much greater importance for a future philosopher ideally destined to become "king", the proper function of the one who should govern the city).
In both cases, it is the allegory of the cave that makes it possible to set things right: for the seen, by presenting as the "proper object" of the first sub-segment the shadows of everything that protrudes from the wall, whether they are "originals" (the "statues of men" (andriantai) that are part of it are not there as statues, but as representing the bodies animated by the anthrôpoi / souls hidden by the wall) or "images" in the usual sense ( which are part, as manufactured objects, of the skeuè of 514c1), to lead us to understand that it is all that sight reveals us that is only "images" of what activates it; for the perceived by intelligence, by evoking the logoi uttered in the cave by the bearers hidden by the wall, considered at this point as purely physical phenomena, through their echo, which makes them sound "reflections", to prepare us to understand that outside the cave, it is all the logoi uttered by the anthrôpoi that constitute intelligible "shadows" and "reflections" of those who utter them and what they speak of, that is to say, of the "beings" (ta onta), of the "*** themselves" (ta auta) that act on our senses and our mind / intelligence (noûs) and are only perceptible to us through eidè, visible / sensible or intelligible. More specifically, logoi are made with words that only take on meaning for us through the eidè that we associate with them, consciously or unconsciously, and these eidè, even when they are purely intelligible and freed from the sensible images that gave rise to them, are still only "images", indeed intelligible, but nevertheless always "images", of "beings" that we seek to understand but cannot apprehend as they are in themselves (the auta). In other words, what is at stakes there is the way we understand the role of words in relation to what is not them and of which we claim to speak, and moreover, to speak as "knowing", that is to say as possessing knowledge (epistèmè) about them. These words are what serve as a "support" for the logos, for the reasoning that we carry out to try to reach knowledge, and it is these words that Socrates has in mind when, in the description of the division of the perceived by intelligence, he uses the word hupothesis, whose etymological meaning is "placing (thesis) under (hupo)",. And the difference between the two sub-segments is that between the reasoning of those who accept the words of the language they speak and give them the meaning(s) resulting from usage without asking questions about them (to know the name is to know what it is the name of, just as, in the cave, to see the shadow is to see what it is the shadow of) and about something else, distinct from them, to which they would refer, and who therefore construct reasoning possibly exhibiting perfect logical rigour on "foundations" (one of the meanings of hupothesis) which are ultimately only opinions inherited from usage (the meaning of the words they use), which prohibits the result of their reasoning, no matter how rigorous they are, from being "knowledge" since it is built on opinions, and the reasoning of those who seek to know what is hidden behind the words before embarking on reasoning with them and who have become aware of the fact that what matters is not the words, but the intelligible eidè that we associate with them in our minds, free of any reference to specific visual images and capable of being associated with several different words, which are still only the "appearance" that can be taken for our intelligence (noûs) by the auta, the pragmata ("facts / things") themselves, which we seek to know, which play in the perceived by intelligence the role of objects protruding from the wall in the cave.
So, the two divisions were indeed made "according to the same logos", according to a similar justification / rationale (possible meaning of logos), which is not the one that was used to segment the line the first time around, but, as Socrates himself suggests at the end, this logos is not easy to formulate in a succinct way and is not simply the relationship between image and original, of "what has been made similar in relation to what it has been made similar to", but is more a difference than a relationship, the difference between perceiving something that, as a mere perception (by sight and the other senses or by the mind), is only an "image / resemblance" without being aware that it is only that, an "image / resemblance", and the fact of having become aware of it. In short, the goal is ultimately to understand that, in the perceived by intelligence as well as in the seen, we only have access to "images / resemblances / likenesses" of the "*** themselves" (auta) that act upon our senses and intelligence, not to the "*** " themselves (or only in a way that cannot be shared since any sharing passes through words).

Conclusion: Is Theaetetus sitting?

Let us try to summarize all that has just been said in order to bring out the main lines of what Plato seeks to make us understand through the analogy of the line and the allegory of the cave illuminating each other and illuminated by other sections of the Republic and other dialogues. Our senses and our intelligence (noûs) are subjected to "affections" (pathèmata) under the effect of "things" (pragmata) that may or may not affect one or more of our senses, but always affect our intelligence (noûs), either through the mediation of the senses, or directly, the one not being exclusive of the other (for instance, we can both see something with the eyes and conceive it by thought). Each of these "organs" (sense organs and intelligence insofar as it apprehends what affects it) has its own specifications and constraints and apprehends a different "aspect" (eidos in its original meaning in the case of sight, also used by analogy in the case of intelligence) of what may affect it (colors, sounds, smells, etc., for the senses, criteria of intelligibility for intelligence directly affected without the mediation of the senses). In the analogy of the line and the allegory of the cave, Socrates limits himself, as far as the senses are concerned, to that of sight, because it is the most pregnant, the richest in "practical" information to allow us to find our way in the world and the one that, for this reason, we have the most trust (pistis) in, in short, the one that most "binds / chains" us, and therefore he distinguishes between "seen appearances" (horômena eidè) and "intelligible appearances" (noèta eidè), but wants us to understand that everything that reveals itself to us under a "seen appearance" (horômenon eidos), that is to say, that is visible (horaton) as capable of affecting the organs of sight, also has an "intelligible appearance" (noèton eidos), but that certain "things" can have only an "intelligible appearance" (noeton eidos) and therefore not be "visible" (nor perceivable by the other senses). On the basis of resemblances ("same", tauton) and differences ("other", thateron) and disregarding the location in time and space in the case of sensible perceptions, each person associates names (most often pre-existing) with these eidè, and uses them to produce logoi, simply thought or audible. But Socrates does not stop there and is mainly interested in the different ways in which we interpret these "affections" and conceive what is at their origin, since we cannot know the "things" (pragmata) that affect us as they are "in and by themselves" (auta), but only through the "affections" (pathèmata) that they induce in us "filtered" by the "organs" that they affect, intelligence (noûs) included. From this perspective, he differentiates "affections" (pathèmata) not so much based on what is at their origin, but by the different manners in which the person who is affected envisions the "thing" (pragma) that is at the origin of this affection and expresses it, explicitly or implicitly, into logoi, in short, by the "state of mind" (one of the possible meanings of pathèma) of that person with regard to what affects him / her. And he distinguishes four ways in which a person can apprehend what affects him / her. Either the person considers that "things" (pragmata) are only what (s)he (or others) can see (segment of the seen / inside the cave), or one admits that there are also "things" "that cannot be seen otherwise than by thought (dianoia)" (511a1), such as for instance the square about which geometers demonstrate theorems, and that the role of intelligence (noûs, from which dianoia derives) is not so much to inventory the "things" (pragmata) that we see (with our eyes) in order to give them names as to bring to light the relationships between "things" (pragmata), whether seen or not, which allow us to progress toward understanding them (segment of the perceived by intelligence / outside the cave). For those who are in the first case, inside the cave, the words are of two kinds, those which refer to "things" (pragmata) seen, or at least visible, that is to say, that others have seen and that one could see by oneself if the circumstances allowed it, and those which refer to nothing that can be seen, therefore for them to no "thing" (pragma), and which therefore, for them, have meaning only through the various uses that are made of them, what Socrates calls nomima at Republic, V, 479d4, towards the end of the discussion on the distinction between knowledge (epistèmè) and opinion (doxa) and which he considers the proper object (in the Aristotelean sense) of opinion. Thus, if such a person hears the sentence "Theaetetus sits" (Theaitetos kathètai, Sophist, 263a2) which the Elean Stranger uses in the Sophist as an example of a minimal sentence carrying meaning whose truth or falsity can be put to the test among the people who witness the scene in which it is supposed to be spoken, for such a person, the word "Theaetetus" refers to a "thing" (pragma) that one can see, while the word "sits" does not refer to any "thing" (pragma) that one can see independently of the person to whom this qualifier is applied. This word therefore has for this person only the meaning(s) learned from others when learning to speak or, in later life, though discussions, but in all cases resulting from usage. And since some of the words one uses have meaning for that person only through the way they are used by others in their logoi or by logoi defining them in a dictionary, one cannot reach knowledge (epistèmè) when using them, but only express opinions (doxa) that might be called into question if usage were to change, since they refer only to logoi, not to "facts" (the primary meaning of the word pragma), to "beings" (onta), and this not because of the intrinsic nature of the "things" (pragmata) he speaks about as being subject to becoming, but because of that person's attitude towards them, one's refusal to consider as "things" (pragmata) what one cannot see. Such a person therefore does not see in the logos "Theaetetus sits" the connection between two distinct "things" (pragmata), "Theaetetus" and "sit", but the mention of a single "fact / thing" (pragma) "Theaetussitting", so that in the end he never sees "Theaetetus", but only "Theetetetussitting" or "Theaetetusstanding" or "Theaetetuslying" or "Theaetetusasleep" or..., and therefore cannot "know" what "sitting" is, but cannot "know" either what "Theaetetus" is apart from everything that participates in the sight of him at a given moment when seeing him, whether it is a permanent feature of him, such as the color of his eyes or hair (which can change with age), or an "accident" (in the Aristotelean sense), such as sitting or standing, or wearing a white or red garment that replaces the color of his skin in some places and hides his nakedness. In this first category of people, Socrates distinguishes two subgroups (sub-segments on the line / situations in the cave) depending on whether they consider that sight gives them a perfectly adequate apprehension of what they see and that therefore what they consider to be "things" (pragmata) is exactly as what sight reveals to them, without realizing that sight only gives them an "image" of it (first sub-segment of the seen, that of eikasia ("imagery") / prisoners immobilized in bonds "that [can] hold for the true nothing but the shadows of the implements" (515c1-2)), or that they admit that sight gives them only a partial and potentially misleading "image" of what they see in certain situations, reveals to them only the outer envelope, and above all that they cannot see with their own eyes everything they admit as "existing" and have to trust (pistis) other people to give them a more complete idea of the world around them (second sub-segment of the seen, that of pistis / prisoner freed from one's bonds but remaining in the cave).Among those who admit that there are also "things" (pragmata) "which cannot be seen otherwise than by reflection (dianoia)" (511a1) (segment of the perceived by intelligence / outside the cave), the distinction into two groups is made on the basis of their attitude toward words. To highlight these two possible attitudes, let us return to our minimal sentence "Theaetetus sits": for all these people, "sitting" refers to a pragma ("fact / thing") regardless of whether it is applied to Theaetetus or to anyone else, but to a pragma ("fact / thing") that is accessible only to intelligence (noûs). When we read these words in the Sophist, we imagine the scene: Socrates and his young namesake, Theodore, Theaetetus and the Elean Stranger are in a gymnasium, sitting on one or more benches and discussing. But let's imagine a different setting where this small group is in a modern hospital room where four of them have come to visit Theaetetus who is being treated there and that Theaetetus is in a hospital bed with a reclineable upper part. Does "Theaetetus sit" mean that Theaetetus has raised the reclining part of his bed to be in a position closer to sitting than lying? But from what degree of inclination should we say "sitting" rather than "lying"? In other words, what exactly does "sitting" mean? From there, two attitudes are possible: either we will try to define "sitting" more precisely by asking ourselves questions about the feet (can they still touch the ground when we are "sitting"?), the angle that the legs make with the thighs (are we still sitting when the legs are horizontal in the extension of the thighs, for instance, on an articulated hospital bed, or on a beach chair that can be reclined to the horizontal?), the angle that the thighs make with the trunk (at what angle are we no longer standing, but sitting, thinking for example of a sit-stand stool?), the part of the body weight that may still rest on the legs, the minimum surface area of the buttocks which must be supported on a load-bearing support, etc. (and it is easy to imagine a "Socratic dialogue" on this important question ending in aporia!), or we will try to get around the difficulty by reformulating the statement in a less problematic way that will allow us to obtain everyone's agreement on the de facto situation (pragma) of Theaetetus, for instance "Theaetetus is in his hospital bed". The first approach (to look for a more precise definition of "sitting"), which would be that of an Aristotle, is an approach that focuses on words and thinks that to understand is to make a rigorous reasoning on the right words, so that the word ends up taking the place of the "thing" (pragma) with which it is associated in the thought of a person having this approach (first sub-segment of the perceived by intelligence, that of dianoia / first stage of the prisoner exiting the cave, where one still cares only for the shadows and reflections that logoi are). The second approach, which is that of Plato's Socrates, takes note of the imprecision of language by understanding that it is made up of words that are not the "things" (pragmata) that they designate, but simple "labels" more or less arbitrarily chosen to which we give meaning by attaching them to fluctuating eidè that each person constructs and adjusts for this purpose in one's head and which are not even yet the "things" (pragmata) of which one seeks to speak and that it is therefore better not to obsess over words but always focus on the "facts" (pragmata), admitting that in many cases the "boundaries" between words, in fact between eidè, are blurred rather than seeking an inaccessible rigor in the fixing of these "boundaries" and forcing the "facts" (pragmata), in fact to freeze the eidè that we associate with the words with which we try to describe them, under labels that do not quite suit them, the "truth" not being in the words and logoi, but in the pragmata (facts / things) (the second segment of the perceived by intelligence, that of noesis / epistèmè / the prisoner looking toward the *** themselves (ta auta) of the "things" seen in the cave and found in their intelligible dimension outside along with the stars in heaven). But above all, the person who is in the second approach knows that the logos was not given to humans simply to make an inventory of the shadows in the cave and stick labels (names) on them, nor even to reason outside the cave according to the specific problems we are faced with, but to find a path toward the good and that it is this idea of the good that must serve as a compass in all one's reasoning. Thus, in the case of the words "Theaetetus sits" used by the Elean Strange, his purpose in employing them was not to provide circumstantial information on the position of Theaetetus during the discussion, which is perfectly neutral with regard to the good and has no bearing whatsoever on the discussion itself, but to give a minimal example of logos whose truth could be acknowledged by all the participants in the discussion, as opposed to another example, "Theaetetus flies", the falsity of which could also be acknowledged by all present, in order to show that it is possible to hold a false speech (pseudo logos), a fundamental demonstration to make good use of logos, an essential requirement to be a good human being since it is precisely the fact of being endowed with logos that specifies one as a human being. And under these conditions, in the modern setting of a hospital that I proposed for the discussion, in any case imaginary, invented by Plato for his dialogue, if the sentence "Theaetetus sits" had raised objections on the part of one or more of the participants preferring to consider it as lying, he would have circumvented the difficulty by changing his example rather than embarking into a long discussion on the precise meaning of "sitting" and the "boundary" between "sitting" and "lying" which would not have brought anything good to the ongoing discussion on false speech, for instance by replacing it with "Theaetetus is hospitalized" which, in the supposed context, would have been considered true by all present.
We are therefore far from the simplistic image that opposes a visible / sensible world in perpetual becoming, not object of knowledge but only of opinion, to an intelligible world of pure ideas escaping becoming, which would be the only object of knowledge and of which the visible "world" would be only a pale "image". It is within the intelligible realm, that is to say, outside the cave, that the distinction between what is subject to becoming and what is not and the thought process that allows the intelligibility of both is made by intelligence. And the question of whether the sensible "world" is an "image" of an intelligible "world" can no longer be posed in these terms. To put it in the imagery of the allegory of the cave, do we mean that the statues of men (andriantai) that represent human bodies in the allegory are "images" of the moon or the star that represents in the heaven of the allegory the "idea of Man" (as suggested by the "simplistic" understanding conveyed by the supposed "theory of ideas"), or that they are each the "image" of the bearer / soul that animates it, represented in the allegory by the anthrôpos hidden by the wall that carries it, invisible in the cave and which becomes "visible", i.e., intelligible, only outside the cave, or that it is these human souls, only "visible" outside the cave, that is to say, in the intelligible, who are an "image" of the moon or the star which represents in the heaven of the allegory the "idea of Man", in which case the relationship between image and original, if there is one, is no longer between the visible and the intelligible, but within the intelligible itself?...
With these preliminaries in mind, it is now time to grapple with the text of the analogy.

(to previous section: The Good and the Sun)

[509c]...
And no way indeed, he said, you shall stop here but at least, this likeness concerning the sun, expound it again, in case you omit [something] one way or another.
But of course, I said, I’m certainly omitting many [things]!
Well then, he said, don’t leave aside the smallest bit of it.
I think, said I, [it will] still [be] a lot. Nevertheless, in so far as [it is] presently possible, I won’t willingly omit anything.
Don’t indeed, he said.
[509d] Then conceive them, said I, as we were saying, as being two and reigning, the one over the intelligible (noèton) family (genos) and place (topos), the other in turn over the visible (horaton) [family and place] – [I say “visible" (horatou)] so that I don’t seem to you, in saying“heaven (ouranou)”, to behave like a sophist about the word. But then, do you grasp those two appearances (eidè), visible, intelligible?
I grasp.
Well then, taking for instance a line segmented into two unequal segments, segment anew each one of the two segments according to the same ratio(nale) (ana ton auton logon), that of the seen (horômenon) family (genous) and that of the though / perceived by intelligence (nooumenon) one, and you will have, based on the [relative] clearness and lack of clearness of the ones compared to the others, on the one hand in the seen, [509e] on the one hand one of the two segments: images (eikones) –I call indeed images, first [510a] shadows, then reflections (phantasmata) on waters and on [other things] insofar as they are by design at the same time compact, smooth and bright, and everything of that kind, if you understand [what I mean].
But [of course] I understand.
Then place the other one, to which this one is similar: the living creatures around us, and all that is planted and the whole family of what is fabricated.
I place it, he said.
Would you then be willing to say about it, said I, that it is divided with regard to truth (alètheia) and its absence [according to the following ratio(nale):] as the opined [is] to the known, so what is made similar (to homoiôthèn) [to something is] to what it has been made similar to (to hôi hômoiôthè)?
[510b] Yes indeed, he said, absolutely.
Consider then also in turn the segmentation of the intelligible, how it is segmented.
How?
The [first segment] of it [is] where, using the [things] formerly imitated as images, a soul is constrained / constrains itself to investigate from bases / starting-points (ex hupotheseôn), driven / advancing, not toward a (leading) principle (archè), but toward an end (teleutè), while the other on the contrary [is] the [one where it is] by going toward a (leading) principle not set to serve as a base / starting-point [in view of something else] (archè anupothetos) from a base / starting-point (ex hupotheseôs) and without the images [revolving] around that, building with the appearances (eidè) themselves its own approach (methodos) through them.
Those [things] you say, he said, I don’t quite understand.
[510c] One more time, then! Said I. This way, you’ll understand more easily what was said before. I think indeed that you know that those who busy themselves in geometry and computation and the like, setting as bases / starting-points (hupothemenoi) the odd and the even and the [various] figures and three appearances (eidè) of angles and other [things] akin to these according to each one’s approach (methodos), those [things] on the one hand, [behaving] as knowledgeable [persons], using them as bases / starting-points (hupotheseis), they don’t think fit to give any further explanation (logon didonai) about them either to themselves or to others, [510d] as if [it were] completely evident, starting from these on the other hand, going through all the rest in great details, they end up in a consistent way on what they had set their investigation in motion upon.
Of course indeed, he said, that at least I know!
Thus also that besides, they also make use of the seen appearances (horômena eidè) and develop their reasoning (logous poiountai) on them thinking not about them but about those they resemble, developing their reasoning for the sake of the square itself, of the diagonal itself, and not [510e] of the one they draw, and same [thing] in the other cases, those very [things] they draw and mold, of which there are shadows and reflections in waters, using them in turn as images, but attempting [511a] to see (idein) what cannot be seen otherwise than by thought (dianoia).
You tell the truth, he said.
So I indeed said intelligible this appearance (noèton to eidos), but the soul constrained / constraining itself to make use of bases / starting-points (hupothesesi) in its investigation about it, not going toward a (leading) principle (archè), as if unable to rise higher than the bases / starting points, but using as images the very [things] that are copied by those below, and the former in comparison with the latter because, [being] dazzling, [they are] held in esteem and honored.
[511b] I get it, he said, that you are talking about that [which falls] under the scope of geometry and the arts akin to it.
Get it then about the other segment of the intelligible, when I talk about what logos itself can reach through the power of dialoguing (hè tou dialegesthai dunamis), using bases / starting-points not as (first) principles, but really as [mere] bases / starting points (hupotheseis), like stepping stones and springboards, so that, going all the way to what [is] not [itself] set to serve as a base / starting-point [in view of something else] (to anupotheton), toward the (leading) principle of the whole (hè tou pantos archè), having grasped it, deriving in return from it all that can be derived, it thus follows a downward path toward an end [511c] without making also use in any way of anything sensible, but with appearances (eidè) themselves, through them, into them, it ends also into appearances (eidè).
I get it, he said, though definitely not sufficiently, for you seem to me to be talking about a long-term work, but at least that you want to distinguish as being clearer what, among what is and [is] intelligible, is examined under the guidance of the science of dialoguing (hè tou dialegesthai epistèmè) from what [is examined] under that of what is called “arts / techniques” (technai), where bases/starting-points [are] (first) principles and those who examine are indeed constrained / indeed constrain themselves to examine these through thought (dianoia) rather than through senses, but because they don’t investigate by going back up to a (guiding) principle [511d] but from bases (hupotheseis), they seem to you not to have intelligence (noun ischein) about those [things], despite their being intelligible with the help of a (guiding) principle. And it seems to me that you are calling“thought" (dianoia) the state of mind of those dealing with geometry and that of those dealing with similar [things] rather than “intelligence” (noûs), considering thought as intermediate between opinion (doxa) and intelligence (noûs).
You have most sufficiently followed, said I. And now, receive from me over the four segments, those four affections / states of mind(pathèmata) produced in the soul, intellection (noèsis) first over the highest, (discursive / wandering) thought (dianoia) [511e] then over the second, to the third one then assign trust / faith (pistis) and to the last imagery (eikasia), and order them according to this ratio(nale) (ana logon), thinking that as that upon which it is partakes of truth, so these partake of clearness.
I get it, he said, and I concur and order them as you say.

(to next section : The Allegory of the Cave)

(1) This page is an adapted translation of the French version dated April 17, 2023 (V4.1). The translation of Plato's Greek has been reworked directly from the Greek. For the translation of the introduction (completed April 8, 2026) and notes (work in progress) in French, I worked with the help of Microsoft Word "Translate" function, but only as a starting point to be reworked and adjusted to the English. When the French version quoted other translations in French of the Republic, they have been replaced by quotations of translations in English and the comments had to be adjusted accordingly.
For a few comments of what I am attempting to achieve in my translations, see the page listing the translated excerpts of the Republic. There are certain words, such as logos, eidos, idea, that I prefer not to translate because they may have different meanings in different contexts, and thus warrant different English words to translate them in each case, but, when translating them, the reader no longer sees that they are the same word in Greek, a fact that Plato often plays with. (<==)