1. Socrates yields to Glaucon. He will speak, though not of the Good itself but rather of its “offspring,” which is most like it (506e). Socrates reminds Glaucon of the “oft-told” story of the one and the many (cf. 476). Those many good and beautiful things are seen but not known, while the thing itself, by which what was many comes “under one idea,” is “known” but not “seen” (507b9). Now the artificer of the senses has made sight the most costly of the senses since it needs a “third kind of thing” (e1), light, to work. The sun is he of all the gods in heaven who gives us this light, and so the “sense” (aisthesis) of sight and the “power” of being seen (e6) depend upon. The eye is, of all “the organs of sense,” “most like the sun” (508b3). This sun is the child of the Good, a child begotten “analogous to itself” (b13). For the Good is “in the place of thought” in relation both “to thought and to things thought” (nous, noumena, c1) what the sun is “in the place of visibility” (c2) in relation to sight and things seen. Socrates completes the analogy by likening “that in the soul which knows in this way” to the eye; as the eye sees things “clearly” (d1) when lit up by the sun, so the soul knows, or merely opines, things in the measure that the idea of the Good gives or fails to give “truth” (aletheia, d5). Glaucon is amazed. Adeimantus’s question is now certainly answered: The Good cannot be either knowledge or pleasure (509a6). Socrates says that there is yet more to be seen in the image (a9), for the sun provides not only visibility but also growth and “becoming,” genesis (b3), though it is not itself Becoming. Analogously, the Good is the source of being, though not itself Being (b7, 9). This “image” or eikon, which we shall call the “sun image” for short, is best seen in a schematic sentence:
This image is now explicated in the “Divided Line.” Glaucon is to take the “double kinds” (509d4), the “visible” (horaton) and the “intelligible” (noeton), and to cut them, as he would a line, into two unequal parts. Then he is to cut each section again in the same ratio (d7). Thus, he will have, in the lower part, one subsection related to the other “in respect to clarity and lack of clarity” (d9) in the same way that images such as shadows and reflections are related to that of which they are images; namely, natural objects and manufactured things (510a). To this whole lower part belongs “the opinable” (doxaston, a9). Next, the lower subsection of the upper part is considered. Here, “the soul, using those things before imitated as images” (510b4), proceeds “from hypotheses” not “to the beginning” (ep’archen) but “to the end,” while in the uppermost section she makes “her way” (methodon) without any use of images but by the “ideas” or eide themselves and through them alone, up to the un-hypothetical beginning (b6). Socrates explains the lower of these subsections in terms of the work of the mathematicians, who assume certain hypotheses without giving an account of them and who reach consistent conclusions on the basis of these. In doing this, they may use the “visible looks” of things, but these are not what they are really thinking about. The true object of their thinking is the intelligible eidos (511a3), the “look” that “one may see in no other way than by means of the thinking faculty” (dianoia, a1); thus, Socrates indicates that his use of the term eidos is fundamentally ironic. In the top section, this paradoxically named “intelligible look” itself, the eidos noeton, is attained by “the power of dialectic” (b4), which uses the hypotheses as “hypotheses in effect”—or “in being.” This is a double entendre which means both that the soul is now aware of the hypotheses as being so far nothing but hypotheses and that it will now treat them as hypotheses underlying being. And having risen by means of these “up to the unhypothesized, unto the beginning of the whole,” it descends, using nothing sensible, but only the hypotheses which are now no longer “suppositious;” these are the eide themselves (b-c). Book VI closes as Socrates assigns four “affections” or receptive powers (d7) of the soul to the four sections: thought or noesis to the highest, thinking or dianoia to the second, trust or pistis to the third, and to the lowest image-recognition or eikasia; these are to be “ordered analogously” to their objects (e2). (Noesis, usually “intellection,” and nous, usually “intellect,” are here both rendered by “thought” to contrast their perfect and direct mode with the progressive and intermediary mode of dianoetic “thinking.”) This table relating the line to the sun image will make the correlation clearer:
2a. In presenting the sun image to Glaucon. Socrates is requiring him to exercise his doxa.
Of the two “doxastic” powers, the lower, whose pregnant name is eikasia, and which is thrown in at the very end with conscious nonchalance, will prove to be the most pervasive of the four “affections.”
Ordinarily the verb eikazein means to “imagine,” both in the sense of making an image and likeness, and of discovering a likeness or likelihood; so it means to compare or conjecture. The noun eikasia means both the ability to make or see images, likelihoods, and conjectures, and the image, likelihood, or conjecture itself. For Glaucon, the word would probably call to mind a witty and malicious amusement with which clever people spice their symposia, called “likenesses” or eikasiai. The game consisted of representing someone in an image, whereupon the victim might retaliate by making a “counter-image”—or by refusing to play. So Meno tells Socrates that he appears to be “most like” (80a5) a torpedo fish (while Socrates ostensibly declines to make a counter-image—of course, the whole dialogue is an unflattering portrait of Meno); and Alcibiades, in the one true triumph of his life, appearing in the Symposium as the god Dionysus himself, speaks of Socrates “through images” and compares him to one of the Sileni in his train, except that, in his image, which is “for the sake of truth” (215a6), this Silenus is more sober and far more divine than the god himself. And in Xenophon’s Symposium (VI, 8; cf. also VIII, 43) Socrates curtly forbids the game when the eikasiai threaten to become injurious and false. Now Socrates is in the habit of introducing great matters under the image of a game or riddle (cf. 479b11, 521c5), and Glaucon will soon see that the “game of images” is an image—and an example—of the most distinctive of human faculties.
In the meantime, it must startle him to hear “conjecturing” elevated into a power of the soul along with thought itself. But as the meaning of Socrates’ central image penetrates, he must notice that this image itself required a peculiar application of his ability to see images. For he is, on the one hand, intended to imagine by means of the image what the Good is “like,” but he is also, on the other hand, required to recognize simultaneously that the sun’s world is but a likeness, that his own visible world is a counterfeit of being. Socrates had, in fact, prepared Glaucon for the fundamental importance of this power to recognize an image as an image when he had intimated earlier that to fail to possess it is to be permanently asleep to being: “Look, isn’t that just what dreaming is: when someone either in his sleep or while awake regards that which is like to something not as like but as the same as that to which it is like?” (476c4). In taking in the sun image, Glaucon then learns to use his eikasia in both of the fundamental senses that Socrates, as the savior of the true and original meaning of words, has restored to it.
2b. Similarly the next power, pistis or trust, comes into play. For just as in seeing the sun’s world as an image Glaucon has been forced to lose trust in the visible world, so in seeing the sun as an image of the Good and “most like it” (506e3) he acquires a better doxa of this world, a trust that life and government in the image of the Good are possible here. This trust is the “eikastic” counterpart of that persuasion to virtue which is the purpose of Socratic myth-telling (cf. 621c1, 3). The question “whatever is the Good itself?” is bidden goodbye for now” (506e1), and no explicit dialectical account of the Good is given at all. The Good appears here only as an object for belief, namely as the motive for study, the end and incentive to learning and doing. It is “that which every soul pursues and on account of which it does everything, having a pre-sentiment that there is some such thing” (505d11). It is the one same, single, thing which all human action, be it for show or genuine, intends not in seeming but in being, that which makes anything, including the virtues, good for us, namely “useful and profitable” (504a4). What makes the difference between attaining this true desire or missing it is precisely knowledge, or lack of knowledge, of the Good (e2). In that sense only is it the “greatest study,” for, as we shall see, in another sense it is no “learning matter” at all. Nevertheless, the explicit consideration of the relation that human excellence and the human good have to the agathon, the good, was dropped as soon as Glaucon reentered the conversation (506e); clearly, it is a question to be discussed either very superficially or only after long preparation (cf. Aristotle, Magna Moralia 1182a27, who refers to the discussion of this question in Concerning the Good).
2c. Perhaps the absence of any direct reflection on the nature of the Good seems to be in want of some further explanation.
An Aristotelian anecdote about the audience’s reaction to Plato’s “Lecture on the Good,” that half-mythical event when he spoke to the public of the “Unwritten Teachings” of his school, is related by Aristoxenus in his Harmonic Elements (II, 30), and is pertinent here: “They came, every one of them, expecting to get some one of the goods considered human…but when his reasonings appeared to be of mathematical studies and numbers and geometry and astronomy and [when he said], at last, that the Good is the One, I think it seemed to them very strange indeed; and then some sneered at it and others criticized it. Now what was the reason for this? That they knew nothing beforehand, but just like intellectuals (eristikol) were present to lap it up on the strength of the mere name.” Now Socrates himself has several such argumentative types, such “eristics,” on his hands—one of them Adeimantus, to whom he is careful to mention the “idea of the Good” as something Adeimantus has often heard of before, as something which is a cause of usefulness and profit and without which a man “cannot have the sentiments of a gentlemen” (505b3). Adeimantus reacts with a pat, eristic question worthy of the obtuse cleverness of a Meno: “But you, Socrates, do you think the Good is knowledge or pleasure or some other thing besides these?” (506b2; cf. Meno 70a); clearly, this is a standard, routine question about the Good (cf. Philebus 19c). Here, Plato, as is his wont, nobly shows a Socrates wiser in practice than Plato himself was, for, in the two dialogues dealing with the Good, the Republic and the Philebus, Socrates finds tactful ways to choose his interlocutor and to bring him along. In the present dialogue, he silences Adeimantus by suggesting to him that he has heard it all before—the ritual-like use of the term “idea of the Good” (505a, 505e, 517b, 526e, 534b), although it is made clear enough that the Good is not an eidos at all, sounds like a soothing allusion to current discussions (cf. Epicharmus in Diogenes Laertius III, 14, 27). Meanwhile, he gently brings Glaucon to face, without taking refuge in clowning, the “awe-inspiring enormity” (509c1) of this Socratic Good.
But Socrates’ indirection is not only a matter of avoiding public misunderstanding; it also has a positive pedagogic purpose, which is precisely to prevent Glaucon from pouncing precipitously on some bare truths that might turn his high spirits (c1) into bored sneers. In providing Glaucon with images to reflect upon, Socrates instills in him a kind of artificial “recollection” (cf. Meno 81c), which will enable him to “recognize” the logos whenever he himself should come upon it. This is, after all, what the effect of any artfully wrought image ought to be—a slow or a sudden dawning of its logos. Therefore, in some way, a dialectical account of the Good, formulable in terms not unlike those of the “Unwritten Teachings,” must be latent here. We shall try to work it out.
3a. When Socrates has delivered his sun image, Glaucon asks him to go once more through the “likeness of the sun” (509c5) in order to fill in whatever had been omitted before. Socrates’ answer to this request is the dividing of the line.
The “Divided Line” is the mathematical figure for an implicit logos and the possibility of learning what is yet unknown. The choice of a linear figure is itself meaningful, for the line, as the unique connection of two point-monads, stands for the closest of all relationships, that of like to like, of which the knower and the known are the paradigm (cf. Aristotle, On the Soul, 404b23, citing Plato; Metaphysics 1036b13 f., on the Pythagoreans); it stands as well for the possibility of incommensurable and hence irrational, i.e., not directly expressible, relations. To understand this explication of the sun image, Glaucon will have to exercise his dianoia.
The word dianoia can be used quite generally for what we would call “mental activity.” For instance, Socrates himself says (476d5): “Why may we not call the mental activity (dianoia) [cf. Sophist 263d] of one who knows, ‘gnomi,’ and of one who opines, ‘doxa’?” This word, doxa, too, will be “restored” by Socrates to its full significance. The dianoia, which goes with the third section from the bottom of the line, is, then, the power used in thinking or, as the phrase goes, in “thinking things through;” this thinking is the soul organ’s restless scanning of the articulations of being for distinctions and comparisons. It means attending to, or searching for, that in things which can be grasped in thoughtful words, such as the Greeks call logoi. This scanning involves a higher kind of eikasia, which may be termed “dianoetic eikasia.” For sensible things, when caught in speech, reveal themselves as mere imitations of something which the logos is truly about—as the “visible aspects” (horomena eide, 510d5) copying the true invisible “looks” (eide) of the thing itself. Likewise, in the Phaedo (100a2), Socrates intimates that those who look at things in terms of logoi are less involved in images than those who look at them more literally with their physical eyes. In the Sophist (261e), it turns out that this is because logoi are “manifestations” (delomata) of being. The natural objects considered by the dianoia are, therefore, described primarily as “images;” in the dianoetic section, the soul proceeds by “using the very things before imitated [i.e., the natural objects that were imitated in the lowest section] as images” (510b4, 511a7). The originals of these new images are—somehow—caught in what speech says: recall that the term logos stands for the meaning as well as for the words that convey it. By entrusting its inquiry to this logos, the dianoia is, in effect, “supposing” such originals; it is literally “hypothesizing” them so that they may serve as the basis of all distinctions, comparisons, inferences, and deductions.
Now, in an inquiry by means of logoi, certain results turn out to be primary and pervasive (522c8). Among these are the fact that a thing can always be called “one,” and together with another, “two,” that counting seems the inevitable concomitant of naming; furthermore, that in different things the same shape can be discerned and that it is caught accurately only in speech and never in a representation. To work out the parts and interconnections—they seem to be inherently perspicuous—of these objects that speech has discovered, it is necessary to recognize them as pure and separate. Hence arise the mathematicals, the “objects of study” par excellence, which form an especially important province of the dianoetic realm. On the highest level, they supply the subjects of that indispensable pre-dialectical “exercise” in which Parmenides engaged Socrates in his youth (Parmenides 135e); for the Platonic Parmenides, the most important hypotheses to be investigated are, of course, the two suppositions concerning the “One;” namely, that it is or is not. However, any common name is, in fact, a dianoetic hypothesis as well, and any sentence is a dianoetic structure—both are worthy objects of study.
3b. If, for Socrates, the philosophical poet, the fundamental nature of the present discourse is eikastic, for Glaucon, the mathematical enthusiast, it is dianoetic. Summarizing in his own words, but accurately, what he has learned from the division of the line, Glaucon perceptively brings out a central fact only implicit in Socrates’ words; namely, that the objects of the dianoia are the same as the noeta of the uppermost part—that they are these noeta before that complete logos, which brings the thinker up to the thing itself, has been reached. In fact, he ends by treating the divided line as if the whole purpose of the division had been only to set the terms for defining the dianoia. For, observing that the very name of dianoia suggests something in-between, or a mean, Glaucon defines it, in analogy to his earlier definition of doxa, as “something between doxa and nous” (511d4), as the naturally intermediate faculty par excellence (cf. Symposium 202, where Eros as daimon is the corresponding intermediary).
3c. Socrates, of course, depends on the mathematical predisposition of his young philosopher—mathematics being after all the young rulers’ childhood amusement—in introducing him to the exercise of this, the lower noetic faculty (cf. 508c4, 509d11). In Book VII, Socrates takes the act of beginning the long description of the formal mathematical education, that is, the “prelude” to dialectic (531d7), as an opportunity to engage Glaucon in a serious “methodical” dianoetic exercise. When Glaucon, accurately recalling the musical education of the guardians, perceptively concludes that this training cannot be the study that the future philosophers need, Socrates asks him: “O my marvelous Glaucon, what would be such a study…?” Glaucon eagerly interrupts to ask in turn what study might indeed remain to them (522b6). Socrates now invites him pointedly to become his “fellow viewer” (523a7) while, as he says, he makes divisions within himself about the studies that might lead toward being; he is to “say ‘I agree’ or ‘I disagree,'” watching carefully that Socrates is “oracling” correctly. The discussion that follows shows Glaucon that arithmetic is precisely the study wanted, since it is “inviting to the dianoia” (524d3) and “arousing to noesis” (d5), and that all the best natures should be educated in it—to which his slyly docile response is: “I agree” (526c7). Socrates proceeds to initiate him into the very study of “the one and the two and the three” (522c-526c) that Parmenides had once taught him. This is Glaucon’s first and only step on the dialectical way; here and nowhere else in the Republic is undisguised direct philosophical work done—a “huge work,” as he begins to realize (511c3, 531d5). Glaucon intends to do it seriously, and when Socrates asks him whether he means to carry on as if demonstrating before others or in his own behalf, he wants to converse chiefly for his own sake. But, as Socrates says, suddenly speaking straight out to us beyond the dialogue, “if someone else should be able to profit in some way, you won’t grudge him that” (528a2).
3d. But why should Glaucon need to be especially invited to this dialogue, since they are already in the midst of one and have indeed come precisely, as Polemarchus says in the beginning, to converse (328a9)? Evidently there are various ways to “converse.” In fact, three meanings of dialegesthai can be distinguished within this dialogue.
First, it can mean a conversation in which anyone may and can take part. This, despite Thrasymachus’s efforts to stage an exclusive rhetorical display, is its meaning in the “prelude” (357a2) of the dialogue, Book I. It can also mean that “power of dialectic” proper (511b4, 532d8, 533a8), in which the logos, the account-giving power, leaves all sense perception behind and is moved “by the eide themselves,” advancing “through them and into them” (511c1). This activity is what is imitated by sight (532a2); as the soul ranges over noetic “sights,” as the name eidos, “sight, look, aspect,” indicates, so the eye sees things at once distinct and together. It is clear that Socrates regards the soul as truly moving (cf. Timaeus 36e1) both upward and downward only in dialectic, which is thus repeatedly called a “way,” meaning a pursuit or a method, a “journey” (533b3, 532e1, 3; 533b3, c7; 532e3). In contrast, the conclusive motion of the dianoia is downward (510b6, d2) as in deduction, that of the lowest power, eikasia, is back and forth as in comparisons, and the next-to-lowest power, pistis, enjoys rarely disturbed rest. In the use of its lower powers, the soul is therefore said to be bogged down and made sluggish (533d1, 611c). The cause is its association with the body; the soul is never quick with bodily life but only with the logos, and its proper motion is a “heavenly journey” (cf. Phaedrus 256d8). But this dialectic is only praised in the Republic (532a1); its actual exercise is impossible to one who is not already “practiced” (533a9) in dianoetic studies (and perhaps to any mortal), for dialectic is thought out thinking itself. And indeed, the “propaedeutic” (536d6) mathematical studies are carefully trimmed: They exclude not merely all “banausic,” i.e., applied, elements, but also any explicit “eidetic” admixture as well; for instance, nothing is said of Plato’s arithmological teaching, the “eidetic numbers” (cf. Metaphysics 1080a12), although, as we shall see, allusions to dialectical terms abound.
There remains a middle dialegesthai, which happens to be the one characteristic of this central conversation. This is speech between two souls. Such speech must have a sensible clothing of sound, the audible dialogue. Such dialogue is strongly distinguished from myth telling and hearing (e.g., Protagoras 320c, 324d, Gorgias 523a, Timaeus 26c), since the latter appeals to trust and imagination, while the former involves primarily the dianoia. For the dianoia supervenes as soon as sense perception is expressed in words, which inevitably gives rise to a dilemma, especially to self contradiction (524e3). In supplying hypotheses to solve these dilemmas, the dianoia brings in noeta and thus invites the uppermost faculty of thought, noesis (523a1). In itself, the dianoia is the faculty of differences, distinctions, and contradictions. As such, it ever ranges betwixt and between and is called out by human perplexities as well as by mathematical problems (530b6). Unguided, it can easily become an aporetic or “wayless” affection (524a7). Therefore, in such a dialogue, one of the interlocutors must know somewhat more than the other, must have advanced into dialectic, so that he will be able “to ask and answer most knowledgeably” (534d9, 528b8; cf. Phaedrus, 276e5). In this dialogue with Glaucon, Socrates exercises such a superiority even more than usually since their conversation is “synoptic” and requires a large foreknowledge. The introduction to arithmetic mentioned above displays precisely the required relation of the interlocutors: Socrates makes dialectical divisions “within himself ” (523a6), which he then “shows” to Glaucon (a9), while Glaucon is to look on with him and to respond to Socrates’ affirmations or negations (cf. Sophist 263e12) with his own agreement or disagreement. But this dialogic superiority is evident most of all in the very naming of the powers of the soul with which Book VI closes. For these powers are, as it were, named from above, from a synoptic point of view. Anyone who has not left the first three sections cannot possibly know their true names: doxa, as used ordinarily, means the faculty of judgment; people rarely think that they have what to Socrates is “mere opinion,” but they think that they know their minds; in fact, the various provinces of the dianoia, such as the arts and mathematics (511c6, d3), are particularly highly regarded by their devotees, as producing nothing less than knowledge (533d4). For Socrates, of course, the dianoia is below knowledge.
This is the sixth essay in this series. The other essays may be found here: I, II, III, IV, V, VII, VIII, IX, and X. We highly recommend Eva Brann’s The Music of the Republic: Essays on Socrates’ Conversations and Plato’s Writings. This essay originally appeared in the St. John’s Review (Volume 39, Number 1 and 2, 1989 – 1990) and is republished here with gracious permission of the author. Miss Brann welcomes questions/comments via mail: Dr. Eva Brann, St. John’s College, 60 College Avenue, Annapolis, MD, 21401-1655 (she does not use computers).
 See Klein, A Commentary on Plato’s Meno (Chapel Hill 1965), pp. 112-15.
 See Meno 80c, The Meno of Plato, E. S. Thompson (Cambridge 1961), p. 112.
 Throughout the dialogue Socrates’ reiteration of themes, such as the “oft-told” tale of the one and the many, as well as the recapitulations he often elicits from Glaucon, have the effect of making Glaucon “recollect” (e.g., 507a7, 522b1, 544b4) from time to time the springs and the course of the argument. This is, obviously, not genuine Socratic recollection (see above, IV E 4d) but an exercise of that power of memory which philosophers must possess as part of their natural endowment (535cl). Such memory-recollection (anamnesis) was especially cultivated by the Pythagoreans: “A Pythagorean man does not arise from his bed before he has recollected what happened yesterday. And he performs the recollections in this way. He tries to recover by means of the dianoia what he first said or heard . . .” (Iamblichus, Life of Pythagoras 163, 20). The passage goes on to describe the discipline of completely recalling the logoi and erga of the previous day, a discipline that was considered part of the training needed for the acquisition of knowledge. It is obviously a technique Socrates himself had mastered.
 The most important ancient reports of the “Unwritten Teachings” are conveniently collected in Gaiser, Platons ungeschriebene Lehre (Stuttgart 1963), pp. 445 ff. See also J. N. Findlay, Plato, the Written and Unwritten Doctrines (New York 1974).
 Klein, op. cit. (supra, 25), pp. 115-25, “The Dianoetic Extension of Eikasia.”