Complete Works (56 page)
1
. The words ‘wise’ and ‘wisdom’ in the argument which begins here represent the Greek
sophos
and
sophia
. The point of the argument will come across more naturally in English if readers substitute in their mind the words ‘expert’ and ‘expertise’.
2
. ‘Powers’ is a mathematical term for squares. By contrast, at 148a–b ‘power’ is given a new, specially defined use to denominate a species of line, viz. the incommensurable lines for which the boys wanted a general account. It may be useful to give a brief explanation of the mathematics of the passage.
Two lines are incommensurable if and only if they have no common measure; that is, no unit of length will measure both without remainder. Two squares are incommensurable
in length
if and only if their sides are incommensurable lines; the areas themselves may still be commensurable, i.e., both measurable by some unit of area, as is mentioned at 148b. When Theodorus showed for a series of powers (squares) that each is incommensurable in length with the one foot (unit) square, we can think of him as proving case by case the irrationality of
,
, …
. But this was not how he thought of it himself. Greek mathematicians did not recognize irrational
numbers
but treated of irrational quantities as geometrical entities: in this instance, lines identified by the areas of the squares that can be constructed on them. Similarly, we can think of the boys’ formula for powers or square lines at 148a–b as making the point that, for any positive integer
n,
is irrational if and only if there is no positive integer
m
such that
n = m
×
m
. But, once again, a Greek mathematician would think of this generalization in the geometrical terms in which Theaetetus expounds it.
3
. The name means ‘She who brings virtue to light’.
4
. Aristides is one of the two young men whose education Socrates discusses in
Laches
(see 178a–179b).
5
. A famous Sophist. See
Protagoras
315d, 337a–c, 340e–341c, 358a–b.
6
. Protagoras of Abdera was a fifth century
B.C.
philosopher and sophist; this appears to have been the title of his book.
7
. Heraclitus was famous for holding that ‘everything flows’ (cf. 179d ff.). Empedocles described a cosmic cycle in which things are constituted and dissolved by the coming together and separating of the four elements earth, air, fire, and water. Epicharmus made humorous use of the idea that everything is always changing by having a debtor claim he is not the same person as incurred the debt. Parmenides remains outside the chorus of agreement because he held that the only reality is one single, completely changeless thing (cf. 183e).
8
.
Iliad
xiv.201, 302.
9
. The Greek could equally be translated ‘that the soul gains and preserves knowledge’; the reader may perhaps be expected to hear the clause both ways.
10
.
Iliad
viii.17–27. Zeus boasts that if he pulled on a golden cord let down from heaven, he could haul up earth, sea and all, bind the cord fast round the peak of Mt. Olympus, and leave the lot dangling in mid-air.
11
. Cf.
Hippolytus
612.
12
.
Theogony
265. ‘Thaumas’ means wonder, while Iris, the messenger of the gods, is the rainbow which passes between earth and heaven.
13
. An alternative translation would be: ‘the suggestion that nothing is, but rather becomes, good, beautiful or any of the things we were speaking of just now’.
14
. A reference to a notorious declaration by Protagoras (Diog. Laert. 9.51): ‘Concerning gods I am unable to know whether they exist or do not exist, or what they are like in form; for there are many hindrances to knowledge, the obscurity of the subject and the brevity of human life’.
15
. A wealthy Athenian famous for his patronage of the sophists: ‘a man who has spent more money on sophists than everyone else put together’ (
Apology
20a). The discussion of Plato’s
Protagoras
is set in his house, where Protagoras and other visiting sophists are staying.
16
. Literally, ‘the sophist’.
17
. A legendary highwayman who attacked travellers on the coast between Megara and Corinth. His most famous ‘method’ was to compel them to wash his feet, and kick them over the cliff into the sea while they were so doing.
18
. Antaeus was said to have lived in a cave and compelled all passers-by to wrestle with him, with results invariably fatal to them.
19
.
Odyssey
xvi.121.
20
. This quotation from a lost poem of Pindar’s is listed as his frag. 292 (Snell).
21
. The first founder of Greek natural philosophy (sixth century
B.C.
), about whom we have anecdotes but little solid information.
22
. Reading, with Madvig,
taü chrusion
.
23
. An alternative text (accepting the conjecture of
d
ē
for
m
ē
at 179a1 and retaining the mss’
haut
ō
i
at a3) yields: ‘if he really was in the habit of persuading his pupils that, even about the future, neither a fortune-teller nor anyone else can judge better than one can for oneself’.
24
. I.e., the principle that everything is really motion (156a).
25
. Both the text and the sense of this quotation are uncertain.
26
. Melissus of Samos was a fifth-century follower of Parmenides.
27
. This is the first occurrence in Greek of the word
poiot
ē
s
, ‘quality’ or ‘what-sort-ness’, coined by Plato from the interrogative adjective
poios
, ‘of what sort?’.
28
.
Iliad
iii.172.
29
. A reference probably to the discussion between Socrates and Parmenides in
Parmenides
.
30
. Viz., the eyes and ears.
31
. Cf. 143e.
32
. Reading [
anti tinos
] for Burnet’s [
ti
] at 189c1; the latter reading would yield: ‘when a man asserts that one of the things which are is another of the things which are, having substituted one for the other in his thought’.
33
. The Greek idiom here could be used to say either that some particular beautiful thing is ugly, or that beauty is ugliness.
34
. In the Greek the opposition here between ‘one’ and ‘the other’ is expressed by the repetition of the word meaning ‘other’—thus yielding, literally, the unparadoxical tautology ‘the other is other’. As Socrates refrained at 189c–d from taking up the paradoxical construal of Theaetetus’ ‘truly false’, so Theaetetus must refrain from taking up this unparadoxical construal of Socrates’ ‘one is the other’.
35
. A transliteration of a variant Greek expression for ‘other-judging’ that Socrates uses here.
36
.
Iliad
ii.851, xvi.554. The word for ‘heart’ attributed to Homer here is
kear
, which has a superficial resemblance to the word for wax,
k
ē
ros
.
37
. According to the scholiast the story was: some travellers came to the bank of a river, which they wished to cross at the ford; one of them asked the guide, ‘Is the water deep?’ He said, ‘It will show you’, i.e., you must try it for yourself.
38
. ‘Account’ translates
logos,
which can also mean ‘statement,’ ‘argument’, ‘speech’, and ‘discourse’.
39
. The parenthesis may alternatively be translated: ‘(that was the word he used)’. The translation in the text expresses surprise about the claim that some things are not knowable at all. The alternative translation calls attention to the particular Greek word used for ‘knowable’.
40
. ‘Letters’ translates
stoicheia
, which can also mean ‘elements’ more generally (and is so translated sometimes below). ‘Syllables’: in Greek
sullabai
, also translated below as ‘complexes.’
41
. I.e., the seven vowels of ancient Greek, as contrasted with two classes of consonant: mutes like B, which cannot be pronounced without a vowel, and semivowels like S, which can.
42
. The word translated ‘sum’ (
pan
) and the word translated ‘all’ (
panta
) in the phrase ‘all the parts’ are singular and plural forms of the same Greek word.
43
. At 204a.
44
. See 203d–e.
45
. Alternatively (accepting the conjecture of
to
for
touto
at 205d): ‘And is there any other reason for this than that it is single in form and indivisible into parts?’
46
. ‘Giving an account’ here translates
legein
, the ordinary Greek word for ‘say, speak, speak of’, which corresponds to
logos
in its wider meanings ‘speech, discourse, statement’.
47
.
Works and Days
456.
48
. The pictorial technique referred to (
skiagraphia
) seems to have been one which depended on contrasts between light and shade to create the appearance of form and volume. A more familiar comparison for modern readers would be a pointilliste painting by Seurat.
49
. Reading
Ei ge d
ē
… for
Eipe d
ē
at 209e5.
*
Alternatively, this sentence could be translated: ‘What we must do is to make use of our midwife’s art to set Theaetetus free from the thoughts which he has conceived about the nature of knowledge’.
Translated by Nicholas P. White.
The day following their conversation in
Theaetetus,
the geometer Theodorus,
together with his Athenian pupils Theaetetus and Socrates’ young namesake, rejoins
Socrates for further discussion. They bring with them a philosopher visiting
from Elea, a Greek town of Southern Italy famous as home to the great philosopher
Parmenides and his pupil, the logician Zeno—both of whom Socrates
had encountered in yet another dialogue closely linked to this one,
Parmenides.
Socrates asks whether this visitor and the others at Elea treat the philosopher,
the statesman, and the sophist as actually being just one thing—a single
sort of person, though appearing to different people as falling under just one or
another of these headings—or rather as having three distinct intellectual capacities,
as their three names indicate. Hearing that the latter is the Eleatics’ view,
he thus initiates two successive, complex discussions. First, in
Sophist,
the visitor,
opting to use Socrates’ favorite procedure of question and answer, displays
in full detail his own conception of the sophist. In
Statesman
he then continues
in a similar way with the statesman. There is no third discussion of the
philosopher, despite occasional suggestions that the initial agenda calls for one.
The visitor, after all,
is
a distinguished philosopher. Perhaps Plato’s intention
is to mark the philosopher off for us from these other two through showing a
supreme philosopher at work defining them and therein demonstrating his own
devotion to truth, and the correct method of analysis for achieving it: for Plato
these together define the philosopher.