Meno 5 ended with the boy
in an error. Socrates made sure that Meno noticed it, and then he asked him: ‘Now watch his progress in recollecting, when he
uses recollection step by step (e0fech/j), and does so properly
(w(j dei=).’ (82e13-14) These words of Socrates imply
that the Boy was led into error by recollection, used improperly.
Socrates
turns from Meno to the boy: And you (su\ de/), tell me (moi le/ge). Do you say we get the double space from the
double line (a0po\
th=j diplasi/aj grammh=j fh\|j to\ dipla/sion xwri/on gi/gnesqai;)? The space I speak of (toio/nde le/gw)
***
Socrates
does not mention ‘the space’; he is pointing at the square, using an adjectival
pronoun toio/nde, which expresses the gesture of pointing – for
which the translator supplies ‘the space’. Socrates’ pointing affects the whole
questioning of the boy, and the translator does his best to give us a notion of
it, which ‘the space’ allows him to do. The problem is, that the referring ‘to the
space’ in the English language is performed within the framework of the language
by language itself; Socrates’ questions thus become leading questions. In Greek,
just like the opening toio/nde, all Socrates’ questions are performed by
Socrates’ gestures: by what he is pointing to the boy, and how he is doing it.
***
Let
Socrates begin from the start the sentence I interrupted by my remark: The
space I speak of (toio/nde
le/gw) is not long one way and short the
other (mh\ tau/th| me\n makro/n,
th|= de\ braxu/), but must be
equal each way like this one (a0lla\
i1son pantaxh=| e1stw w#sper touti/),
while being double its size (dipla/sion
de\ tou/tou) – eight square feet (o0ktw&poun). Now see (a0ll’ o3ra|)
if you still think we get this from a doble length of line (ei0 e1ti soi a0po\ th=j diplasi/aj dokei=
e1sesqai).
Boy:
I do (E!moige)
Socrates:
Well then, double (diplasi/a) this one (au3th,
Socrates is pointing at the side of the double size, i.e. the eight square feet,
quadrangle) of this one (tau/thj, Socrates points at the side of the smaller
quadrangle, which is half the size of the bigger one) becomes (gi/gnetai [Socrates points to the side of the bigger space]),
if another (a2n e9te/ran) just as big (tosau/thn [Socrates
points out/at the size of the side of the smaller, four square feet space]) we add
to it (prosqw/men) from here (e0nqe/nde).
Boy:
Certainly (Pa/nu ge).
Socrates:
From this [line] then (A0po\
tauth=j dh/ [Socrates points at the four feet long
line; in Greek “line” is indicated by the feminine pronoun tauth=j]),
you say (fh/|j) will be (e1stai) the eight-foot
space (to\ o0ktw&poun
xwri/on), if four (a2n te/ttarej) this big [lines] (tosau=tai) come to be (ge/nwntai)?
Boy:
Yes (Nai/).
Socrates:
Let us draw then (A0nagrayw&meqa
dh/) from it (a0p’ au0th=j
[from this line]) equal (i1saj) four (te/ttaraj). This will be
what you say is the eight-foot figure, will it not (a1llo ti h2 touti\ a2n ei1h o4 fh\|j
to\ o0ktw&poun ei]nai;)?
Boy:
Certainly (Pa/nu ge).
Socrates:
And here in it (Ou0kou=n
e0n au0tw~|) are (e0sti/)
these four (tauti\
te/ttara [Socrates points at four squares],
each of which (w{n
e3kaston) is equal to this (i1son tou/tw| e0sti/) quadrangle (tw~| tetra/podi).
Boy:
Yes (Nai/).
Socrates:
How large it (Po/son) then (ou]n) becomes (gi/gnetai;)? Isn’t it (ou0)
four times (tetra/kij) this large (tosou=ton;
[Socrates points at one of the quadrangles, the side of each being two feet
long])?
Boy:
It must be (Pw~j d’ ou1;).
Socrates:
Twice as big is then (Dipla/sion
ou]n e0sti/) that which is four times as big (to\ tetra/kij tosou=ton;)?
Boy:
Not by Zeus (Ou0 ma\
Di/a).
Socrates:
But how many times (A0lla\
posapla/sion;)?
Boy:
Four times (Tetrapla/sion).
Socrates:
From the double size line thus (A0po\ th=j diplasi/aj a1ra),
boy (w} pai=), not twice as big (ou0 dipla/sion) but four times as big a place becomes (a0lla\ tetrapla/sion gi/gnetai xwri/on).
Boy:
That is true (A0lhqh=
le/geij).
Socrates:
And if it is four times four it is sixteen, is it not (Tetta/rwn ga\r tetra/kij e0sti\n
e9kkai/deka, ou0xi/;)?
Boy:
Yes (Nai/).
Socrates:
What line will give us a space of eight feet (O)ktw&poun d’ a0po\ poi/aj grammh=j;)? This one gives us a fourfold space, does it
not (ou0xi\ a0po\ me\n
tau/thj tetrapla/sion;)?
Boy:
It does (Fhmi/).
Socrates:
And a space of four feet is made from this line of half the length (Tetra/poun de\ a0po\ th=j h9mise/aj
tauthsi\ touti/;)?
Boy:
Yes (Nai/).
Socrates:
Very well (Ei]en); and is not a space of eight feet double the
size of this one, and half the size of this other (to\ de\ o0ktw/poun ou0 tou=de me\n
dipla/sio/n e0sti, tou/tou de\ h3misu;)?
Boy:
Yes (Nai/).
Socrates:
Will it not be made from a line longer than the one of these, and shorter than
the other (Ou0k
a0po\ me\n mei/zonoj e1stai h2 tosau/thj grammh=j, a0po\ e0la/ttonoj de\ h2 toshsdi/;
h2 ou1)?
Boy:
I think so (E!moige
dokei= ou3twj).
Socrates:
Excellent (Kalw~j): always answer just what you think (to\ ga/r soi dokou=n tou=to a0pokri/nou). Now tell me (kai/ moi le/ge),
did we not draw this line two feet (ou0x h3de me\n duoi=n podoi=n h]n),
and that four (h9
de\ tetta/rwn;)?
Boy:
Yes (Nai/).
Socrates:
Then the line on the side of the eight-foot figure should be more than this of
two feet (Dei=m
a1ra th\n tou= o0ktw&podoj xwri/ou grammh\n mei/zw me\n ei]nai th=sde th=j di/podoj), and less than the other of four (e0la/ttw de\ th=j tetra/podoj)?
Boy:
It should (Dei=).
Socrates:
Try and tell me how much you would say it is (Peirw~ dh\ le/gein phli/khn tina\ fh\|j
au0th\n ei]nai).
Boy:
Three feet (Tri/poda).
Socrates:
Then if it is to be three feet (Ou0kou=n a1nper tri/pouj h]|),
we shall add on a half to this one (to\ h3misu tau/thj proslhyo/meqa),
and so make it three feet (kai\
e1stai tri/pouj)? For here we
have two (du/o me\n
ga\r oi3de), and here one more (o9 de\ ei[j), and so again on that side there are two (kai\ e0nqe/nde w(sau/twj du/o me\n oi3de), and another one (o9 de\ ei[j); and that makes the figure of which you
speak (kai\ gi/gnetai
tou=to to\ xwri/on o4 fh/|j).
***
It
is worth noticing that the pointing and adding is made only in Socrates’ and the
boy’s mind. Had Socrates drawn it on sand, it would have become immediately
obvious that the figure thus achieved would be larger than the eight-foot
square, the side of which the boy is asked to find.
***
Boy:
Yes (Nai/).
Socrates:
Now if it be three this way (Ou0kou=n
a1n h]| th=de triw~n) and three that
way (kai\ th=|de
triw~n), the whole space will be thrice
three feet, will it not (to\
o3lon xwri/on triw~n tri\j podw~n gi/gnetai;)?
Boy:
So it seems (Fai/netai).
Socrates:
And thrice three feet are how many (Trei=j de\ tri\j po/soi ei0si\ po/dej;)?
Boy:
Nine (E)nne/a).
Socrates:
And how many feet was that double one to be (E1dei de\ to\ dipla/sion po/swn ei]nai podw~n;)?
Boy: Eight (O)ktw&).
Socrates: So we fail to get our eight-foot
figure from this three-foot line (Ou0d’ a1ra a0po\ th=j tri/podo/j pw to\ o0ktw&poun xwri/on
gi/gnetai).
Boy: Yes, indeed (Ou0 dh=ta).
Socrates: But from what line shall we
get it (A0ll’ a0po\ poi/aj;)? Try and tell us exactly (peirw~ h9mi=n ei0pei=n a0kribw~j); and if you would rather not reckon it out (kai\ ei0 mh\ bou/lei a0riqmei=n), just show what line it is (a0lla\ dei=con a0po\ poi/aj).
Boy: Well, on my word (A0lla\ ma\ to\n Di/a), Socrates (w} Sw&kratej),
I for one do not know (e1gwge
ou0k oi]da).
Socrates turns to Meno: There now,
Meno, do you observe what progress he has already made in his recollection (E)nnoei=j au], w} Me/nwn, ou[ e0sti\n
h1dh badi/zwn o3de tou= a0namimnh/skesqai;)?
At first he did not know (o3ti
to\ me\n prw~ton h1|dei me\n ou1)
what is the line that forms the figure of eight feet (h3 tij e1stin h9 tou= o0ktw&podoj
xwri/ou gammh/), and he does not know even now (w#sper ou0de\ nu=n pw oi]den): but at any rate he thought he knew then (a0ll’ ou]n w!|eto/ g’ au0th\n to/te ei0de/nai), and confidently answered as though he knew
(kai\ qarrale/wj
a0pekri/neto w(j ei0dw&j), and was
aware of no difficulty (kai\
ou0x h9gei=to a0porei=n); whereas now he
feels the difficulty he is in (nu=n
de\ h9gei=tai a0porei=n h1dh), and
besides not knowing (kai\
w#sper ou0k oi]den) does not think
he knows (ou0d’ oi1etai ei0de/nai).
Meno: That is true (A0lhqh= le/geij).
Socrates: And is he not better off (Ou0kou=n nu=n be/ltion e1xei) in respect of the matter (peri\ to\ pra=gma) which he did not know (o4 ou0k h]|dei)?
Meno: I think that too is so (Kai\ tou=to/ moi dokei=).
