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Unformatted text preview: 1 P L AT O The Divided Line
Plato of Athens (c. 429–347 B.C.E.) stands with Aristotle as one of the two
most important philosophers of Antiquity and as a major shaper of the
Western intellectual history as a whole. Descended from a wealthy and
aristocratic family, his intellectual outlook was decisively formed by his
teacher, Socrates. Socrates’ judicial murder at the instance of political opponents helped turn Plato into a critic of democracy and a supporter of aristocracy, in his special sense of the term, that is, rule by the wise and virtuous
(or “philosopher-kings”). From Socrates Plato learned a mode of inquiry that
consisted of subjecting received opinions to systematic cross-examination
(“dialectic”), as well as certain moral doctrines such as the view that the source
of wrongdoing is ignorance, or that the gods’ approval or disapproval does
not render actions right or wrong. Plato attempted to put his political ideas
into practice by serving as counselor to Dionysius II, tyrant of Syracuse, but
the young ruler’s sporadic enthusiasm for philosophy did not survive political reality, and the two men were ﬁnally estranged. Plato was more successful as the founder of a philosophical school, the Academy, which he
established in a grove dedicated to the hero Academus outside Athens during the early fourth century B.C.E. The school continued for several centuries and was instrumental in preserving Plato’s teachings and writings.
Plato’s surviving writings are cast in dialogue form, to force the reader to
make up his or her own mind about the positions and arguments presented.
Plato himself never appears, though students of the dialogues often assume,
perhaps correctly, that his point of view is represented by Socrates. Modern
scholarship largely agrees in dividing the dialogues into three broad groupings: early, middle, and late. Attempts to coordinate these groupings with
known events in Plato’s life or with the development of his thought, however, are more controversial.
The Republic, Plato’s most famous dialogue, is considered a work of
Plato’s mature, or middle period, where his ethical and political beliefs have
struck root in more fundamental metaphysical and epistemological convictions. The major question animating the dialogue is the nature of justice.
Plato’s Socrates defends the view that justice consists in a harmony of soul
stemming from a vision of transcendental Good, which in turn provides a
“The Divided Line,” from The Republic, by Plato, translated by Desmond Lee, revised
second edition, copyright © 1974 by Desmond Lee, 249–255. Reprinted by permission of
Penguin Books Ltd. 2 THE DIVIDED LINE standard for rational control of the passions and appetites, leading to happiness. In this famous passage from Book VI, Socrates compares cognitive experience with the nature of reality; he concludes that knowledge and opinion
correspond respectively to intelligible and sensible objects of cognition, and
argues that sense-objects are derivative from objects of the intellect. §6. THE DIVIDED LINE The analogy of the Divided Line is, Plato makes clear, a sequel to the Sun
simile, its purpose being to illustrate further the relation between the two
orders of reality with which the Sun simile dealt. But it does so from a
particular point of view, that of the states of mind (pathemata: 511d, [in
the second to last paragraph of this selection]) in which we apprehend
these two orders or realms. The purpose of the Line, therefore, is not, primarily, to give a classiﬁcation of objects. Both of the two states of mind
correlated with the intelligible realm deal with the same kind of object
(the forms), though each deals with them in a different way; and though
in the physical world there is a difference between physical things and
their shadows, that difference is used primarily to illustrate degrees of
‘truth’ or genuineness in what is apprehended—we know very little
about a thing if our knowledge is conﬁned to shadows or images of it or,
for that matter, to its superﬁcial appearance. . . .
Broadly speaking, the mental states comprised by the four subdivisions
are: (A) Intelligence. Full understanding, culminating in the vision of
ultimate truth. This understanding is reached by philosophy, or as Plato
often calls it ‘dialectic’; a term whose modern associations are quite misleading in interpreting the Republic, but which, with that caution,
remains a convenient translation. (B) Reason. The procedure of mathematics, purely deductive and uncritical of its assumptions. (C) Belief.
Commonsense beliefs on matters both moral and physical, which are a
fair practical guide to life but have not been fully thought out. (Later, in
the Timaeus, Plato includes the natural sciences in this sub-section, as
they can never reach ultimate truth, being concerned with a changeable
world.) (D) Illusion. All the various illusions, ‘secondhand impressions
and opinions’, of which the minds of ordinary people are full. In this section ‘illusion’ merely appears as the perception of shadows and reﬂections.
But the wider interpretation is demanded by the Cave simile, which
elaborates in a more graphic form the classiﬁcation set out in the Line.
And it is also clearly implied in Book X that all works of poetry and art
are to be included in this sub-section. THE DIVIDED LINE 3 To look forward for a moment, Plato is not entirely consistent in his use
of terms. In Part VII the contrast is frequently between doxa and gnosis,
another word for knowledge. Noe is sometimes used of sub-section A of
the Line, but, perhaps because the content of the whole ‘region’ AB is
called noeton, it is also used of intellectual operations more generally. And
at one place episteme is used of sub-section A. The content of CD, com¯¯
monly referred to in the Line as to horaton, the visible, is in this diagram
also called the physical world. Though there is an emphasis in the simile on
purely visual terms, Plato instances animals, plants and manufactured
objects as examples in sub-section C, and for example a donkey eating hay
in a barn is not a purely visual object. Besides, it is made quite clear in Part
VIII that CD is the world perceived by our senses (aisthe ), the world
of material change (genesis). The diagram assumes that both noesis and
dianoia deal with forms and that dianoia has no separate type of object. It 4 THE DIVIDED LINE is sometimes claimed that Plato implies that there are special mathematical
objects in sub-section B; but his language at 510d suggests rather that the
mathematicians deal with forms, but in a not fully adequate way.
This brief dogmatic summary can hardly do justice to the problems
raised by the Line and its two companion similes and to the controversies
which they have occasioned. Some suggestions for further reading will be
found in the bibliography. But the reader should ﬁrst study what Plato
himself has to say about the way in which the similes are to be interpreted
‘You must suppose, then,’ I went on, ‘that there are these two powers1 of
which I have spoken, and that one of them is supreme over everything in
the intelligible order or region, the other over everything in the visible
region—I won’t say in the physical universe or you will think I’m playing with words.2 At any rate you have before your mind these two
orders3 of things, the visible and the intelligible?’
‘Yes, I have.’
‘Well, suppose you have a line divided into two unequal parts, and
then divide the two parts again in the same ratio,4 to represent the visible
and intelligible orders. This gives you, in terms of comparative clarity and
obscurity, in the visible order one sub-section of images (D): by “images”
I mean ﬁrst shadows, then reﬂections in water and other close-grained,
polished surfaces, and all that sort of thing, if you understand me.’
‘Let the other sub-section (C) stand for the objects which are the
originals of the images—the animals around us, and every kind of plant
and manufactured object.’
‘Would you be prepared to admit that these sections differ in that one
is genuine,5 one not, and that the relation of image to original is the same
as that of the realm of opinion to that of knowledge?’
‘I most certainly would.’
‘Then consider next how the intelligible part of the line is to be
‘In one sub-section (B) the mind uses the originals of the visible order
in their turn as images, and has to base its inquiries on assumptions6 and
proceed from them not to a ﬁrst principle but to a conclusion: in the
other (A) it moves7 from assumption to a ﬁrst principle which involves
no assumption, without the images used in the other sub-section, but
pursuing its inquiry solely by and through forms themselves.’ THE DIVIDED LINE 5 ‘I don’t quite understand.’
‘I will try again, and what I have just said will help you to understand.
I think you know that students of geometry and calculation and the like
begin by assuming there are odd and even numbers, geometrical ﬁgures
and the three forms of angle, and other kindred items in their respective
subjects; these they regard as known, having put them forward as basic
assumptions which it is quite unnecessary to explain to themselves or
anyone else on the grounds that they are obvious to everyone. Starting
from them, they proceed through a series of consistent steps to the conclusion which they set out to ﬁnd.’
‘Yes, I certainly know that.’
‘You know too that they make use of and argue about visible ﬁgures,8
though they are not really thinking about them, but about the originals
which they resemble; it is not about the square or diagonal which they
have drawn that they are arguing, but about the square itself or diagonal
itself, or whatever the ﬁgure may be. The actual ﬁgures they draw or
model, which themselves cast their shadows and reﬂections in water—
these they treat as images only, the real objects of their investigation
being invisible except to the eye of reason.’9
‘That is quite true.’
‘This type of thing I called intelligible, but said that the mind was
forced to use assumptions in investigating it, and did not proceed to a
ﬁrst principle, being unable to depart from and rise above its assumptions; but it used as illustrations the very things (C) which in turn have
their images and shadows on the lower level (D), in comparison with
which they are themselves respected and valued for their clarity.’
‘I understand,’ he said. ‘You are referring to what happens in geometry and kindred sciences.’10
‘Then when I speak of the other sub-section of the intelligible part of
the line you will understand that I mean that which the very process of
argument grasps by the power of dialectic; it treats assumptions not as
principles, but as assumptions in the true sense, that is, as starting points
and steps in the ascent to something which involves no assumption and
is the ﬁrst principle of everything; when it has grasped that principle it
can again descend, by keeping to the consequences that follow from it, to
a conclusion. The whole procedure involves nothing in the sensible
world, but moves solely through forms to forms, and ﬁnishes with
‘I understand,’ he said; ‘though not fully, because what you describe
sounds like a long job. But you want to distinguish that part (A) of the
real and intelligible (A + B) which is studied by the science11 of dialectic 6 THE DIVIDED LINE as having greater clarity than that (B) studied by what are called “sciences”.12 These sciences treat their assumptions as ﬁrst principles and,
though compelled to use reason13 and not sense-perception in surveying14 their subject matter, because they proceed in their investigations
from assumptions and not to a ﬁrst principle, they do not, you think,
exercise intelligence on it, even though with the aid of a ﬁrst principle it
is intelligible.15 And I think that you call the habit of mind of geometers
and the like reason but not intelligence, meaning by reason something
midway between opinion (C + D) and intelligence (A).’
‘You have understood me very well,’ I said. ‘So please take it that
there are, corresponding to the four sections of the line, these four states
of mind; to the top section intelligence, to the second reason, to the third
belief, and to the last illusion.16 And you may arrange them in a scale,
and assume that they have degrees of clarity corresponding to the degree
of truth possessed by their subject-matter.’
‘I understand,’ he replied, ‘and agree with your proposed arrangement.’ EXPLANATORY NOTES
1. The form of the good and the sun.
2. The Greek words for ‘visible’ and for ‘physical universe’ (or more literally
‘heaven’) bear some resemblance to each other, and it has been suggested
that there was some connection between them.
3. Eidos: a good example of Plato’s non-technical use of the term, to mean
‘kind’, ‘sort’, ‘type’ (as also at 511a, ‘type of thing’). The technical (theory of
‘forms’) use is a natural sequel because things of a particular kind have a particular form.
4. See diagram.
5. Lit: true.
6. Greek hypothesis, of which the English ‘hypothesis’ is a transliteration. But
the English word means ‘something that may be true but needs testing’: the
Greek word ‘something assumed for the purpose of argument.’
7. 510b6, omit το
8. Eidos, non-technical again.
9. The translation is intended to bring out the strong visual metaphor. More
literally, ‘seeking to see those very things that one cannot see except with the
reason’. The word translated ‘reason’ (dianoia) will be appropriated later in
the passage as a quasi-technical term to designate the mathematical reasoning of sub-section B. ‘As images’: as we might say ‘as illustrations’.
10. Techne see note .
11. Episte ¯.
¯me THE DIVIDED LINE 7 12. Lit: ‘the so-called technai’. The wide range of meaning of techne was noted
on p. 15 [of this source text]. Here the reference is to sub-section B of the
line, and techne has already (note ) been used in the phrase ‘geometry and
kindred technai’, which describes its contents. Plato certainly does not mean
the arts or practical skills, and Adam’s ‘mathematical sciences’ gets the reference right.
14. A strongly visual word—‘gazing at’. So also the word translated ‘studied’
has a basic meaning ‘looked at’, ‘contemplated’.
15. Plato uses ‘intelligible’ to describe the whole section A + B, which is the
‘intelligible order’ or ‘region’. But here he seems to be referring to subsection A only and to be indicating the deﬁciency of sub-section B, which is
none the less dealing with material which if rightly handled is ‘intelligible’ in
the full (A) sense. The meaning of the phrase is, however, uncertain. It reads
literally ‘it is intelligible (noe
¯ton) with (with the aid of? in conjunction
with?) a (ﬁrst) principle’ or ‘and has a ﬁrst principle’. The interpretation
here suggested gives a particular meaning to this more general wording.
It is worth adding that, at 511a and 511e, Plato emphasizes degrees of
clarity, linked at 511e with truth; and that his four ‘states’ or ‘habits’ of mind
are said to entail different degrees of clarity and truthfulness and apprehension, which need not correspond to a difference of object. Both shadow and
object throwing it are in a sense physical things; it is our fault if we confuse
them. If we speak of shadow and reﬂection as less true or genuine than their
original this is really a comment on our own tendency to misapprehend
them. Similarly, here, the mathematician has, compared to the philosopher, a
defective apprehension of the same realities (the forms).
16. The words used for ‘belief’ and ‘illusion’ do not (with the possible exception of a use of pistis in Book x [of this source text]) occur elsewhere in Plato
in the sense in which they are used here. Pistis, ‘belief’, conveys overtones of
assurance and trustworthiness: ‘commonsense assurance (Cross and Woozley, p. 226). Eikasia, ‘illusion’, is a rare word whose few occurrences elsewhere in Greek literature give us little guidance. It can mean ‘conjecture’,
‘guesswork’, and some prefer so to translate it here. But ‘illusion’ is perhaps
more appropriate for a ‘state of mind’. ...
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