Psychology, Philosophy, and Plato's Divided Line

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Contents


Introduction

PLATO's Divided Line, his Cave Allegory and the Sun analogy, occur together in the central section of the Republic and arguably express the core message of this most important of philosophical works. Of the Divided Line, Smith (1996, p. 25) wrote: "Scholars seem generally to agree that what Plato is doing here is extremely important; but they cannot seem to agree about exactly what Plato means to be doing."

The Divided Line contains much in a few short paragraphs. As Raven (1965, p. 144) put it: "One of Plato's more baffling tendencies is to condense his writing in proportion as his thought becomes more profound. This particular tendency is especially pronounced throughout the whole of the Divided Line." Whether this condensation is "baffling," or instead a highly productive feature of Plato's literary genius is perhaps an open question. But in any case it is clear that the Divided Line requires attentive reading and reflection.

The Divided Line is supplied at the end of Book 6 of the Republic, with additional remarks in Book 7 (Rep 6.509d–6.511e; 7.533c–7.534b).

The basic features are as follows:

  • Using a line for illustration, Plato divides human knowledge into four grades or levels, differing in their degree of clarity and truth. First, imagine a line divided into two sections of unequal length (Figure 1, hash mark C). The upper level corresponds to Knowledge, and is the realm of Intellect. The lower level corresponds to Opinion, and concerns the world of sensory experience. Plato says only that the sections are of "unequal" length, but the conventional view is that the Knowledge section is the longer one.

  • Then bisect each of these sections (hash marks B and D). This produces four line segments, corresponding to four cognitive states and/or modes of thinking. From highest to lowest, these are:

    • noesis (immediate intuition, apprehension, or mental 'seeing' of principles)
    • dianoia (discursive thought)
    • pistis (belief or confidence)
    • eikasia (delusion or sheer conjecture)


    Figure 1. The Divided Line

  • Plato admits to being loose with terms. For example, while noesis mainly refers to the highest of the four cognitive states, sometimes he uses it to denote the intellectual sphere generally. Also, he sometimes calls the highest grade episteme, but also uses that term in a more general sense to refer to technical sciences.

  • In any case, it is evident that these four states correspond to the stages of prisoners' ascent in the Cave Allegory (Rep. 7.514a–7.521d).

  • The line image lets Plato point out instructive ratios concerning truth quality amongst the states. Specifically:

    1. As Being is to becoming, so Knowledge is to Opinion.
    2. As Knowledge is to Opinion, so noesis is to pistis,
    3. And dianoia is to eikasia,
    4. And (though Plato does not say this explicitly, but rather lets us see it ourselves) noesis is to dianoia.

Interpretation

Plato certainly placed the Divided Line in the center of the Republic for a reason. Thus we must begin by understanding what the nature and purpose of the Republic is. To facilitate inquiry we will make the following assumptions:

  1. The Republic is mainly an ethical and psychological work. That is, we accept the view expressed by Hoerber (1944), Guthrie (1986), Waterfield (1993), Annas (1999), Blössner (2007) and others that any interest Plato may have had within the work in actual civil government is secondary and subordinate to his psychological and ethical interests. As Socrates states explicitly in 2.368d–2.369a and reminds us frequently, the ideal City-State is presented as a conceptual tool that enables us to better understand our own inner, psychic life.

  2. The model works because the human psyche may indeed be accurately likened to a commonwealth of citizens. Such psychic pluralism is recognized by dozens of modern theories of human personality (for reviews see Lester 1995, 2007; Rowan, 1990; Schwartz, 1995). Different theories give different names for these personality elements, but overall the terms subpersonalities or sub-egos seem adequate, at least if understood very generally.

    We have, in short, a separate subpersonality or sub-ego associated with every one of our social roles and relationships, jobs and projects, goals, hopes, plans and ambitions, appetites and desires, passions and emotions, dispositions and inner voices, styles, self-images and self-concepts. And these are only our conscious elements. Who knows how many more 'people' there are within us operating at an entirely sub- or unconscious level!

  3. The commonwealth of our psyche — psychopolis — can well or poorly governed, congenial or conflict-ridden, integrated or fragmented, harmonious or discordant. Plato's aim in the Republic — identical with his and Socrates' overall project — is to instruct us how to achieve a well-governed, harmonious psyche by means of philosophia, the love of Wisdom.

  4. A distinctive and important feature of the Platonic/Socratic system is that ethics and epistemology are inseparable. In an oppressive, conflicted soul-city, each subpersonality seeks only its own narrow interests. In the ideal soul-city each subpersonality looks to the good of all. For example, in a vicious soul-city, the money subpersonality may seek to acquire wealth by questionable means, putting it into conflict with other subpersonalities. Harmony of the soul-city (personality integration) is accomplished when subpersonalities instead seek direction from a higher source — a separate faculty (or faculties?) concerned with Wisdom, noesis, higher intuition, inspiration, etc., and a justice which benefits the entire self-community

  5. The Republic must offer sound practical advice for our daily mental life, or it would not be so singularly admired and acclaimed. Its aim is to teach us how to think and how to live.
Salvation from Egoism by Higher Knowledge
Now let's try to put the pieces together. To begin, we are probably on solid ground to suggest that the Divided Line is principally concerned with moral epistemology: how do we know what to do (i.e., what is best for us), both in general and at any given moment? Upon the answer to this eminently practical question all our well-being depends. It is true that Plato includes mathematical examples in the Divided Line. But this doesn't mean he's spliced in an investigation of mathematical or scientific epistemology amidst his great work on personal ethics. It's more plausible to see these as examples drawn from a fairly explicit domain (mathematics) to illustrate corresponding aspects of a less clear one (moral experience).

If we accept this view then what Plato seems to be saying in the Divided Line is that there is a special form of knowledge, noesis, which is a much better basis for guiding our thoughts and actions than other, lesser forms of knowledge. It takes little sophistication to recognize that noesis is better than the more degenerate kinds of 'knowing' — i.e., the eikasia and pistis displayed by prisoners of the Cave. What is far more subtle and interesting, and what is therefore perhaps more important for Plato here, is the contrast between dianoia, ordinary discursive ratiocination, and noesis.

This distinction is vital. While dianoia thinking certainly has benefits, we have a distinct tendency to over-rely on it and to forget its limitations. The weakness of dianoia is that it must begin by taking as true unproven assumptions. We are, in effect, presupposing a model of reality before we begin our deliberations. But any model, be it logical, geometrical, or moral, is only imperfect. Its conclusions may be, and frequently are, wrong. Our selection of assumptions, moreover, is bound to be influenced by our passions and prejudices. Our dianoia thinking tends to reflect the values and prejudices of whatever subpersonality is currently activated. We then see reality partly — through a glass darkly. Moreover, the principle of cognitive dissonance may cause us to ignore, distort, or rationalize away any data which do not fit our preconceived model.

In contrast, noesis presupposes a soul that has turned away from specific selfish concerns to seek the Good itself. With this change in mental orientation — this Pauline metanoia or Plotinian epistrophe we may then begin to see things more truly, and in their proper relation to one another. We may better think, judge — and therefore act — according to natural law and right reason. We will consequently be more harmonized with the external world as well as within ourselves.

Noesis (Peters, 1967, 121ff.) is the mental power or faculty associated with an immediate apprehension of first principles (Forms) of mathematics, logic, morals, religion, and perhaps other things. So understood, noesis, when concerned with moral Forms, is very close to, if not the same thing as what is traditionally called Conscience. By Conscience we mean not a Freudian super-ego formed by the internalization of arbitrary social conventions, but an innate sense, something divine, and something perhaps closely associated with consciousness itself (let us not forget that in some languages, such as French, the same word denotes both consciousness and Conscience.) We need not commit ourselves to a particular religious creed to say that this moral noetic sense is a phenomenological reality — a clarifying, integrating, joyful, loving faculty of human consciousness.

The characteristic human flaw of turning away from the Good — and instead relying on our own fallible substitutes for divine Wisdom — is hubris, the fundamental sin against which Greek philosophy and literature so forcefully and persistently warns us. This great concern of Homer, Hesiod, and the tragic poets is also Plato's.

Dialectic
As Plato explains in Book 7 (7.532e ff.), it is by dialectic that we rise from the cave of ignorance to noesis. By dialectic the eye of the soul, which, as in the Orphic myth, is otherwise buried in a slough of mud, is by her gentle aid lifted upwards (7.533c-d).

For Plato, dialectic is more than logical analysis. It is a focusing of ones attention and intentions on the search for and reconnection with Truth. It coincides with a turning away from sensual pleasure as the organizing principle of ones thought life.

In a broad sense dialectic might include any activity by which, through the exertion of one's intellect and will, greater mental sharpness occurs. Plato does seem to suggest that this mental ability can be improved by the study of mathematics (and also of music, gymnastics, and astronomy — or whatever these serve as allegories for in Book 7).

Dialectic is a topic of central importance to Plato, and he also discusses it throughout his other dialogues (e.g., Meno, Parmenides, Phaedo, Phaedrus, Philebus, Sophist, Statesman, and Theaetetus).

The late Neoplatonist, Proclus, in a famous passage of his commentary on the Parmenides, describes three different forms — or, as he calls them energies — of dialectic: (1) arguing both sides of an issue; (2) trying to uncover truth; and (3) refutation of a false view (In Parm. 653; Morrow & Dillon, p. 43f; cf. section 989).

Specific Platonic/Socratic techniques for the second of Proclus' categories include collection (gathering together of similar examples), division (seeking principles which distinguish some examples from others), and the method of hypothesis (exploring the implications of a hypothesis). For further details see Benson (2010), Kinney (1983), Robinson (1953), etc.

Note that the very effort to define dialectic and discover its essence is a form of dialectic.

Platonic Ascents
In his dialogues Plato presents three methods of ascent to the Good (see Plotinus, Enneads 1.3). In the Republic there is the ascent of dialectic. In the Symposium, there is the famous ascent by Love of Beauty. The Phaedrus, especially in the Chariot Allegory, describes the ascent by Moral Virtue (harmonia). These three methods first ascend to the second-highest tier of Forms: Truth, Beauty, and Justice, respectively. One may then ascend higher to their common essence, the Form of the Good, or Goodness itself.

Are there other avenues? Plato's emphasis on just these three certainly doesn't rule out the existence of more. Could prayer and religious ritual, for example, comprise another? What about yoga? Communing with nature? The practice of charity?

Before proceeding to final discussion let us summarize our observations thus far in the form of Table 1.

Table 1. The Divided Line
Level (highest to lowest) Name Meaning Cave Allegory Example
1 noesis Higher Reason; direct apprehension or intuition of moral, logical, relational, or religious first principles outside cave, seeing Forms (e.g., direct apprehension of moral truths) seeing another person in the light of spiritually-based compassion
2 dianoia discursive thought; ratiocination; lower reason outside cave, seeing images of Forms (e.g., verbal, conceptual representations of moral truths) a logical acceptance of truth that one should treat another person with compassion
3 pistis plausible opinion; trust; confidence seeing objects in cave (e.g., egoistic distortion of a moral concept) noticing a person's faults instead of their virtues and goodness (selective, egoistic perception)
4 eikasia baseless opinion; delusion; fantasy- or wishful-thinking seeing only shadows on wall of cave (e.g., moral opinion fully detached from reality) imagining faults or attributing false motives (e.g., psychological projection) to another person

Discussion

In this section we will make some observations and suggestions concerning the further study of Plato's Divided Line and associated themes, especially as they relate to modern psychology. First, though, two observations of a more general nature are offered.

The first concerns Plato's mysticism here. In the sense that Plato is suggesting modes of knowledge above discursive reasoning, then, by a broad definition at least, he could considered a mystic. He is, however, able to approach this mysticism rationally, so that what is being effected is an integration of our epistemological faculties. In any case, it is important to see that what Plato offers is a practical mysticism of everyday life — something that enriches our 'ordinary' experience. He is not merely presenting an ascetical, otherworldly life of pure contemplation, suitable only for a monastic existence.

The second general point is that we have here at best only scratched the surface of the Divided Line. In 7.534 Plato explicitly alludes to there being other categories of opinion and knowledge, such as would require a discussion many times longer to flesh out. Perhaps, however, he's supplied some clues in 7.516 when he alludes to the prisoner newly emerged from the cave only being able to see the Sun (i.e., the Form of the Good) after preliminary stages of seeing, in order, shadows and reflections of objects, objects, the light of the moon, stars, and heavens, and the light of the Sun.

Maslow's Being-psychology

Some possible connections between Platonic philosophy and the Being-psychology of the influential humanistic psychologist Abraham Maslow (1968; 1971) should be noted.

Maslow argued that once human beings meet their basic life necessities their attention turns naturally to higher things — to what Maslow called growth (as opposed to deficiency) motivation and Being (as opposed to becoming) experience. Associated with this higher life are certain intense but brief peak experiences, and somewhat more durable, if less powerful plateau experiences. These superior states of consciousness, which most people experience to some extent, are characterized by such things as enhanced clarity of perception, a feeling of deeper meaning, truth, and completeness of experience, a sense of timelessness, egolessness, sacredness, innocence, and absence of negative thoughts and emotions. Just as in peak or plateau experience our external vision may suddenly come into greater focus, revealing more depth, detail, and beauty, so may our inner moral, intellectual, and philosophical vision. In sum, these states are perhaps as close to pure happiness and wisdom as any we can identify.

For Maslow, in such states it feels as though we are perceiving true reality, eternal verities — Being. In contrast, our usual modes of perception and consciousness allow us only to experience the transitory realm of becoming. Maslow's language clearly alludes to the Being-becoming distinction in Platonism — a distinction nowhere more explicitly presented than in the Republic. Nevertheless, Maslow is muted in his explicit enthusiasm for Plato, and perhaps for at two reasons. First, Maslow was a committed materialist and atheist, and this constrained how much of Plato, a theist, his theories could accommodate. Second, if Maslow had explored in more detail the implications of Platonism, his audience would likely not have cared. At the time of Maslow's peak influence (the 1960's and early 70's), Plato had long since been banished from the university. Free-spiritism was the zeitgeist. The last thing people were interested in was Plato, the very symbol, in their minds, of obsolete and oppressive Western values and moralism.

Nevertheless the times have changed, and the inevitable engagement of modern humanistic psychology with Plato should not be put off longer. The entire positive psychology movement, of which Maslow is arguably the founder, or at least a major forerunner and influence, lacks two things which Platonism can supply: (1) a moral focus: a recognition that man is a moral being and that upon his moral life all his happiness depends; and (2) a plausible theory of epistemology that admits knowledge higher than rationalism. Without these, the success of positive psychology is questionable.

Brain Hemisphere Specialization and Integration
McGilchrist (2009, 2012) has recently recalled to our collective scientific attention the issue of lateralization of brain function, an important topic which laid strangely dormant for several decades. The basic premises of this work as relates to our discussion are as follows:
  • There is a marked asymmetry in function (and anatomy) between the left and right hemispheres of the human brain.
  • The left brain hemisphere (for the typical right-handed person) is more specialized for logical, linear thinking, focused attention, and certain verbal skills.
  • As human technology and language have progressed in recent centuries and millennia, the 'left brain' has become increasingly dominant.
  • This has thrown our brains, as well as our culture generally, into a state of conflict and disequilibrium. We need to learn to reintegrate or reharmonize our brain hemispheres.

A further important hypothesis of McGilchrist is that there is a definite connection between left-brain dominance and egoism. This is the meaning of the title, The Master and His Emissary, which alludes to a parable of Nietzsche. The proper role of our rational ego is to serve as the emissary, steward, or chief executive officer for the much larger organism, the Self. But the ego habitually oversteps its proper bounds, producing myriad problems.

Translated to the Divided Line, McGilchrist's left-brain ego would seem to correspond reasonably well to dianoia-dominated thinking and morality. Plato, in teaching us about noesis, and perhaps drawing from a store of cultural wisdom deposited before modern rationalism took over, is then in a sense helping us to re-harmonize the audacious left brain with the rest of the psyche.

There is a limit to how closely we can map McGilchrist's bicameral model of the brain to Plato's tri-partite psychology. Further, all agree that the 'two-brain' model is more than a little oversimplified. Nevertheless, the work of McGilchrist and others offers some hope that there are identifiable neurophysiological correlates of the kind of moral and cognitive egoism (and its remedies) that Plato is concerned with.

Towards the Scientific Study of Noesis

We close by posing the question: can noesis be studied scientifically?

We do have reasonable evidence that noesis exists and that it is at least phenomenologically distinct from other forms of knowing. First is the literary evidence. Noesis, or at least some form of reason above ratiocination, has a long history in Western tradition. Plato's distinction between noesis and dianoia was taken up and developed by a long series of subsequent writers (for review see Uebersax, 2013), starting with Aristotle. It was considered by Plotinus (and later Neoplatonists), from whom it reached St. Augustine. From Augustine it became a standard concept of Medieval scholasticism, which codified the distinction as one between ratio superior and ratio inferior, or higher and lower reason. The distinction persisted in the intellectual mainstream at least until the time of the Cambridge Platonists.

With the Enlightenment, however, the distinction between higher and lower reason more or less vanished. Ratiocination was held as the highest epistemologically level. The word Reason itself, by which the Cambridge Platonists meant higher reason, something divine, now became broadened to include dianoia. Without a means of verbally distinguishing between lower and higher reason, the rarer and subtler of the two faded from the cultural mind. This change coincided with the emergence of naturalist ethics, which had no room for an innate sense that might inform us of genuine, non-relativistic, spiritually based moral principles.

A second line of evidence is colloquial language. We maintain many expression in English that suggest a common sense of there being noesis or similar forms of knowing. We say, for example, "Ah, I see it now", referring to a new concept or logical principle. Or similarly, "I see what you mean," "She had a flash of insight," or "It suddenly dawned on him that...."

Taken by themselves these lines of evidence are perhaps inconclusive. But they do imply that the existence of a distinct faculty of noesis is plausible enough to warrant further investigation.

Given this, the extent of modern scientific and academic neglect of noesis is striking. Aside from a brief reference in William James' Varieties of Religious Experience (1903, p. 380) it is hard to find any well-known psychologist even mentioning it. Modern philosophical literature is little better, dominated as it is by a hyper-rationalistic, analytic approach. A rare exception is an excellent article by Wallis (1976).

There are certainly many today who feel that we have reached a cultural impasse associated with an inability to collectively grapple with issues of meaning — that is, with the moral dimension of life. Crucial to any paradigm shift is the question of whether noesis does exist, and, if so, how to integrate it with rationalism in our culture.

Clearly any advance in noetic science must begin with the preliminaries: to establish basic terms and definitions, identify examples, and survey previous literature. Among the questions we may wish to address are:

  • What is noesis?
  • If it has different forms (e.g. moral noesis and logical noesis), what is common to all, and how do they differ?
  • What is the relationship of noesis to Wisdom? To Conscience?
  • Is an explicit distinction between higher and lower reason also found in other traditions(Buddhism, Vedantism, etc.)
  • Are there distinct and detectable neurophysiological correlates of noetic activity?

These are all worthy questions. To pursue them, however, it would seem vital to first equip scholars and scientists to investigate them with a more interdisciplinary education than is commonly found today. Psychologists — standing as it were halfway between science and phenomenology — may have an especially valuable role to play here.  


References

The references in this section apply to the discussion above. An extended bibliography on Plato's Divided Line in the philosophical literature appears following the text.

Annas, Julia. Understanding and the Good: Sun, Line, and Cave. In: Julia Annas, An Introduction to Plato's Republic, Oxford, 1981, pp. 242–271. Repr. in: Richard Kraut (ed.), Plato's Republic: Critical Essays, Oxford, 1997 (pp. 143–168).

Annas, Julia. The Inner City: Ethics Without Politics in the Republic. In: Julia Annas, Platonic Ethics, Old and New, Ithaca, 1999, pp. 72–95 (Ch. 4).

Benson, Hugh H. Plato's Method of Dialectic. In: Hugh H. Benson (ed.), A Companion to Plato, Malden, Mass., 2006 (Ch. 7, pp. 85–99).

Benson, Hugh H. Plato's Philosophical Method in the Republic: The Divided Line (510b–511d) . In: Mark L. McPherran (ed.), Plato's Republic: A Critical Guide, Cambridge, 2010, pp. 188–208.

Blössner, Norbert. The City-Soul Analogy. In: Ed. G. R. F. Ferrari, The Cambridge Companion to Plato's Republic, (Ch. 13, pp. 345–385 ), Cambridge University Press, 2007.

Boyle, Anthony J. Plato's Divided Line: Essay 1: The Problem of dianoia. Apeiron 7: 1–11, 1973.

Burnyeat, M. F. Plato on Why Mathematics is Good for the Soul. In: Timothy J. Smiley (ed.), Mathematics and Necessity, Oxford, pp. 1–81, 2000.

Dorter, Kenneth. The Divided Line and the Structure of Plato's Republic. History of Philosophy Quarterly, 21(1), 2004, pp. 1–20.

Fischer, Franck. La nature de l'objet dianoétique en République VI : bilan de l'interprétation contemporaine. Laval théologique et philosophique, vol. 59, no. 2, 2003, pp. 279–310.

González, Francisco J. Dialectic and Dialogue: Plato's Practice of Philosophical Inquiry. Evanston, 1998. (See n. 19, p. 363.)

James, William. The Varieties of Religious Experience. New York, 1902.

Jowett, Benjamin (translator). The Dialogues of Plato in Five Volumes. 3rd ed. Vol. 3. Republic, Timaeus, Critias. Oxford, 1892.

Lester, David. Theories of Personality: A Systems Approach. Washington, DC: Taylor & Francis, 1995.

Lester, David. A Subself Theory of Personality. Current Psychology, 26, March 2007, pp. 1–15.

Maslow, Abraham H. Toward a Psychology of Being, 2nd edition. New York: Van Nostrand, 1968.

Maslow, Abraham H. The Farther Reaches of Human Nature. New York: Viking, 1971.

McGilchrist, Iain. The Master and His Emissary: The Divided Brain and the Making of the Western World. New Haven, 2009.

McGilchrist, Iain. The Divided Brain and the Search for Meaning. New Haven, 2012.

Morrow, Glenn R.; Dillon, John M. (translators). Proclus: Commentary on Plato's Parmenides (In Parm.). Princeton, 1992.

Murdoch, Iris. The Sovereignty of Good (excerpt). In: Richard Kraut (ed.), Plato's Republic: Critical Essays, Oxford, 1997 (pp. 169–180).

Peters, Francis E. Greek Philosophical Terms. New York, 1967. (See: 'dianoia', p. 37; 'noesis', pp. 121–128;)

Reeve, CDC (translator). The Republic of Plato. Indianapolis, 2004.

Rowan, John. Subpersonalities: The People Inside Us. Routledge, 1990 (repr. 2013)

Schwartz, Richard C. Internal Family Systems Therapy. New York: Guilford, 1995 (repr. 2013).

Shorey, Paul (translator). Plato: The Republic (2 Volumes). Loeb Classical Library. Cambridge, Mass., 1935.

Smith, Nicholas D. Plato's Divided Line. Ancient Philosophy 16: 25–46, 1996. Repr. in Nicholas D. Smith (ed.). Plato: Critical Assessments, vol. 2, New York, 1998. pp. 292–317.

Taylor, Thomas (translator). Plotinus: Ennead 1.3 (On Dialectic). In: Thomas Taylor, Select Works of Plotinus, London, 1817, pp. 18–28. Accessed from www.prometheustrust.co.uk (Prometheus Trust), 15 September 2014.

Uebersax, John S. Higher Reason and Lower Reason. 2013. Accessed from www.john.uebersax.com, 20 October 2014.

Wallis, Richard T. NOUS as Experience. In: R. Baine Harris (ed.), The Significance of Neoplatonism, SUNY Press, 1976, pp. 121–153.

Waterfield, Robin (translator). The Republic of Plato. (Introduction) Oxford, 1993 (re-issued 1998).

 

Text

The full text, from public domain translation of Benjamin Jowett (1892), is supplied below. Stephanus numbers are added, as are links to the Greek text at the Perseus Project. Comments in square brackets ([ ]) and italicized glosses are mine.

Source: Benjamin Jowett (translator). The Dialogues of Plato in Five Volumes. 3rd ed. Vol. 3. Republic, Timaeus, Critias. Oxford, 1892.

The Divided Line

[509d]
Socrates: You have to imagine, then, that there are two ruling powers, and that one of them is set over the intellectual world, the other over the visible. I do not say heaven, lest you should fancy that I am playing upon the name [i.e., a pun: ouranou (heaven), oratou (visible world)]. May I suppose that you have this distinction of the visible and intelligible fixed in your mind?

Glaucon: I have.

divide a line in two, and subdivide each part

Socrates: Now take a line which has been cut into two unequal parts, and divide each of them again in the same proportion, and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness,

lower subsection of the visible realm

[509e]
and you will find that the first section in the sphere of the visible consists of images. And by images I mean,

[510a]
in the first place, shadows, and in the second place, reflections in water and in solid, smooth and polished bodies and the like: Do you understand?

Glaucon: Yes, I understand.

higher subsection of the visible realm

Socrates: Imagine, now, the other section, of which this is only the resemblance, to include the animals which we see, and everything that grows or is made.

Glaucon: Very good.

Socrates: Would you not admit that both the sections of this division have different degrees of truth, and that the copy is to the original as the sphere of opinion is to the sphere of knowledge?

[510b]

Glaucon: Most undoubtedly.

Socrates: Next proceed to consider the manner in which the sphere of the intellectual [noetic] is to be divided.

Glaucon: In what manner?

the two subdivisions of the intellectual realm

Socrates: Thus: — There are two subdivisions, in the lower of which the soul uses the figures given by the former division as images; the enquiry can only be hypothetical, and instead of going upwards to a principle descends to the other end; in the higher of the two, the soul passes out of hypotheses, and goes up to a principle which is above hypotheses, making no use of images as in the former case, but proceeding only in and through the ideas themselves.

Glaucon: I do not quite understand your meaning.

Socrates: Then I will try again;

[510c]
you will understand me better when I have made some preliminary remarks. You are aware that students of geometry, arithmetic, and the kindred sciences assume the odd and the even and the figures and three kinds of angles and the like in their several branches of science; these are their hypotheses, which they and everybody are supposed to know, and therefore they do not deign to give any account of them either to themselves or others; but they begin with them,

[510d]
and go on until they arrive at last, and in a consistent manner, at their conclusion?

Glaucon: Yes, I know.

Socrates: And do you not know also that although they make use of the visible forms and reason about them, they are thinking not of these, but of the ideals which they resemble; not of the figures which they draw, but of the absolute square and the absolute diameter,

[510e]
and so on — the forms which they draw or make, and which have shadows and reflections in water of their own, are converted by them into images, but they are really seeking to behold the things themselves, which can only be seen

[511a]
with the eye of the mind?

Glaucon: That is true.

Socrates: And of this kind I spoke as the intelligible, although in the search after it the soul is compelled to use hypotheses; not ascending to a first principle, because she is unable to rise above the region of hypothesis, but employing the objects of which the shadows below are resemblances in their turn as images, they having in relation to the shadows and reflections of them a greater distinctness, and therefore a higher value.

[511b]
Glaucon: I understand, that you are speaking of the province of geometry and the sister arts.

the higher subdivision of the intellectual realm

Socrates: And when I speak of the other division of the intelligible, you will understand me to speak of that other sort of knowledge which reason herself attains by the power of dialectic, using the hypotheses not as first principles, but only as hypotheses — that is to say, as steps and points of departure [Shorey: "springboards so to speak"] into a world which is above hypotheses, in order that she may soar beyond them to the first principle of the whole; and clinging to this and then to that which depends on this, by successive steps she descends again

[511c]
without the aid of any sensible object, from ideas, through ideas, and in ideas she ends.

Glaucon: I understand you; not perfectly, for you seem to me to be describing a task which is really tremendous; but, at any rate, I understand you to say that knowledge [episteme] and being, which the science of dialectic contemplates, are clearer than the notions of the arts [techne], as they are termed, which proceed from hypotheses only: these are also contemplated by the understanding [dianoia], and not by

[511d]
the senses: yet, because they start from hypotheses and do not ascend to a principle, those who contemplate them appear to you not to exercise the higher reason [noesis] upon them, although when a first principle is added to them they are cognizable by the higher reason. And the habit which is concerned with geometry and the cognate sciences I suppose that you would term understanding [dianoia] and not reason [noesis], as being intermediate between opinion [doxa] and reason [noesis].

Socrates: You have quite conceived my meaning; and now, corresponding to these four divisions, let there be four faculties in the soul — reason [noesis] answering to the highest,

[511e]
understanding [dianoia] to the second, faith (or conviction) [pistis; confident opinion, not religious faith] to the third, and perception of shadows [eikasia; literally 'picture-thinking'] to the last — and let there be a scale of them, and let us suppose that the several faculties have clearness in the same degree that their objects have truth.

Glaucon: I understand, and give my assent, and accept your arrangement.

~ End of Book 6 ~

Book 7 begins with the famous Cave Allegory (7.514–7.520). From there it to proceeds to the education of Guardians (7.521–7.531). This culminates in a discussion of dialectic (7.532ff), which begins with a restatement of the Divided Line.

[533c]
...
Socrates: Then dialectic, and dialectic alone, goes directly to the first principle and is the only science which does away with hypotheses in order to make her ground secure; the eye of the soul, which is literally buried

the word 'science' (epistime) is ambiguous, and all terms here only approximate

[533d]
in an outlandish slough [or mud, an Orphic motif], is by her gentle aid lifted upwards; and she uses as handmaids and helpers in the work of conversion, the sciences [technais] which we have been discussing. Custom terms them sciences [epistimas], but they ought to have some other name, implying greater clearness than opinion [doxa] and less clearness than science [epistime]: and this, in our previous sketch, was called understanding [dianoia]. But why should we dispute about

[533e]
names when we have realities of such importance to consider?

Glaucon: Why indeed, he said, when any name will do which expresses the thought of the mind with clearness?

Socrates: At any rate, we are satisfied, as before, to have four divisions; two for intellect [noesis, but in the broader sense] and two for opinion [doxa], and to call the first division science [1. episteme], the second understanding [2. dianoia],

[534a]
the third belief [3. pistis], and the fourth perception of shadows [4. eikasia], opinion being concerned with becoming, and intellect with being; and so to make a proportion: —

    As being is to becoming, so is pure intellect [1 & 2; knowledge] to opinion [3 & 4].

    And as intellect [1 & 2] is to opinion [3 & 4], so is science [1] to belief [3],

    and understanding [2] to the perception of shadows [4].

But let us defer the further correlation and subdivision of the subjects of opinion and of intellect, for it will be a long enquiry, many times longer than this has been.

[534b]
Glaucon: As far as I understand, he said, I agree.

~ * ~


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