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8/20/2019 kolb - Pythagoras bound. Limit and unlimit in Plato´s Philebus
1/16
Journal of the History of Philosophy, Volume 21, Number 4, October
1983, pp. 497-511 (Article)
DOI: 10.1353/hph.1983.0093
For additional information about this article
Access provided by Universidad Complutense de Madrid (2 Sep 2015 13:25 GMT)
http://muse.jhu.edu/journals/hph/summary/v021/21.4kolb.html
http://muse.jhu.edu/journals/hph/summary/v021/21.4kolb.htmlhttp://muse.jhu.edu/journals/hph/summary/v021/21.4kolb.html
8/20/2019 kolb - Pythagoras bound. Limit and unlimit in Plato´s Philebus
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Pythagoras Bound: Limit and
U nl im ited in Plato s hilebus
D A V I D A . K O L B
W H Y ARE T HIN GS t h e w a y t h e y a r e ? P l a t o a n d D e m o c r i t u s p r e s e n t o p p o s e d
a n s w e r s t o t h i s q u e s t i o n . N o t o n l y i s o n e a m a t e r i a l i s t w h i l e t h e o t h e r i s n o t ,
b u t f u r t h e r , t h e y e m p l o y d i f f e r e n t o n t o l o g i c a l s t r a t e g i e s t o a n s w e r t h e q u e s -
t i o n w h y ? D e m o c r i t u s t r a c e s t h e v is ib le f e a t u r e s o f t h i n g s, t h e i r c o l o r s a n d
s h a p e s a n d h a bi ts o f m o v e m e n t , b a ck to d e t e r m i n a t e f u n d a m e n t a l e n ti ti es ,
t h e a t o m s . A b o u t t h e f e a t u r e s o f t h e a t o m s t h e m s e l v e s t h e r e is n o t h i n g m o r e
t o s a y t h a n t h a t t h e y a r e t h e w a y t h e y a re . W e c a n d i s t i n g u i s h h e r e p h y s i ca l
a t o m i s m f r o m o n t o l o g i c a l a to m i s m . P h y s ic a l a t o m i s m is a d o c t r i n e a b o u t t h e
u l t i m a t e c o n s t i t u e n t s o f m a t t e r . O n t o l o g i c a l a t o m i s m is a d o c t r i n e a b o u t h o w
e n t it i es o f w h a t e v e r k i n d c o m e t o h a v e t h e f e a t u r e s t h e y h a v e , t h e cl a im t h a t
t h e r e a r e b a s ic e n ti t ie s w h i c h j u s t a r e w h a t t h e y a r e a n d w h i c h a r e r e s p o n s i -
b le f o r t h e f e a t u r e s o f o t h e r e n t i ti e s b y s o m e p r o c e s s o f c o m b i n a t i o n . T h e
q u e s t i o n w h y ? c o m e s t o a n e n d a t t h e ba s ic e n t it i es a n d t h e i r f e a t u r e s p lu s
a d e s c r i p t i o n o f th e p r o c e s s o f c o m b i n a t i o n . D e m o c r i t u s is a n a t o m i s t i n b o t h
t h e s e s e n s e s , t h e m a t e r i a l a t o m s p l a y i n g t h e r o l e o f o n t o l o g i c a l l y b a si c u n it s .
T h e s a m e o n t o l o g i c a l a t o m i s t s t r a t e g y c a n b e f o u n d , h o w e v e r , in t h o s e w h o
d e n y t h e e x i s t e n c e o f p h y s i c a l a t o m s . C l as s ic a l po s i ti v is t s a n d e m p i r i c i s t s w h o
p o s t u l a t e s e n s e d a t a d e n y p h y s i c al a to m s b u t k e e p t h e s t r a t e g y of r e g r e s s t o
e n t i t i e s w h o s e f e a t u r e s h a v e n o f u r t h e r e x p l a n a t i o n .
P l at o , a s r e p r e s e n t e d i n t h e
Timaeus
w a s a p h y s i c a l a t o m i s t . B u t h e r e j e c t s
t h e o n t o l o g i c a l u l t i m a c y o f p h y si c a l a t o m s , g e n e r a t i n g t h e m o u t o f a f o r m l e s s
e n e r g y - s p a c e a n d b as ic m a t h e m a t i c a l p a t t e r n s . I n th is a r ti c le I a r g u e t h a t
P l a t o i s n o w h e r e a n o n t o l o g i c a l a t o m i s t , n e i t h e r i n t h e p h y s i c a l w o r l d n o r i n
h is p s y c h o l o g y n o r i n t h e r e a h n o f t h e e t e r n a l F o r m s .
P l a to i s o f t e n i n t e r p r e t e d , h o w e v e r , i n w a y s w h i c h i n s e r t o n t o l o g ic a l
a t o m i s m i n t o h is v ie w s. T h e m o s t c o m m o n w a y is t o h o l d t h a t t h e F o r m s a r e
b r u t e l y g iv e n. S o m e D e m o c r i t e a n a t o m s a r e r o u n d a n d o t h e r s h a v e h o o k s
a n d t h e r e is n o t h i n g f u r t h e r t o b e s ai d a b o u t w h y ; s o t h e F o r m s o f c o u r a g e
[497]
8/20/2019 kolb - Pythagoras bound. Limit and unlimit in Plato´s Philebus
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498
JOURN L OF THE HISTORY OF PHILOSOPH Y
i: 4
O C T 983
a n d c o w - n es s j u s t a r e e t e r n a l l y w h a t t h e y a r e . A f t e r c o n t a c t i n g t h e F o r m s w e
s h o u l d h a v e n o m o r e w h y q u e s t i o n s . I n t h e l a t e r P l at o , t h e d o c t r i n e o f t h e
c o m m u n i o n o f t h e F o r m s in o n e a n o t h e r w e a k e n s t h e pl au s ib i li ty o f th is
i n t e r p r e t a t i o n , a n d t h e P y t h a g o r e a n g e n e r a t i o n o f t h e F o r m s d e s c r i b e d b y
A r i s t o t l e r e f u t e s i t . '
T h e r e is a s e c o n d w a y o n t o l o g i c a l a t o m i s m c a n b e s m u g g l e d i n t o P la t o.
E m p i r i c i s t n o t i o n s o f t h e r e l a t i o n o f u n i v e r s a l a n d p a r t i c u l a r c a n m a k e u s
r e a d h is d i s c u s s io n s o f c o l le c t i o n a n d d i v is i o n a n d o f t h e l im i t a n d t h e u n -
l i m i t e d a s i f w h a t w a s a t s t a k e w a s t h e c o r r e c t c l a s s if i c at i o n o f a r e a l m o f
a l r e a d y g i v e n a t o m i c p a r t i c u l a r s. G i v e n w h a t P l a to sa ys a b o u t t h e d e r i v e d
s t a t u s o f s e n s ib l e o b j e c t s w e a r e n o t l i k e ly t o r e a d h i m a s a n o n t o l o g i c a l
a t o m i s t o n t h a t l e ve l . H i s p s y c h o l o g i c a l d is c u s s i o n s , h o w e v e r , c a n t e m p t u s t o
r e a d h i m a s b u i l d i n g u p e x p e r i e l l c e f r o m a t o m i c u n i t s o f i n t e ll e c t u al o r
s e n s i b l e p e r c e p t i o n .
T h i s a r t i c l e t a k e s u p t h e
P h i b u s ,
w h e r e o n t o l o g i c a l d i s cu s s io n s o f t h e
m i x t u r e o f li m it a n d u n l i m i t e d a r e a p p l i e d i n e t h ic a l d i s cu s s i o ns o f p l e a s u r e
a n d p a i n . M y a im is t o sh o w t h a t i n t e r p r e t e r s o f t h e d i a l o g u e h a v e b e e n
w r o n g i n a s s u m i n g t h a t P l a to i s d i s c u s s i n g t h e r e c la s s if i ca t io n o f a r e a l m o f
g i v e n a to m i c e x p e r i e n c e s . W h e n t h is p s y c h o l o g ic a l a t o m i s m i s a b a n d o n e d
t h e d i a l o g u e g a in s i n u n i t y a n d c o g e n c y . S t a n d a r d i n t e r p r e t a t i o n s o f t h e
P h i b u s s u g g e s t P l a t o w i s he s u s t o r e c l a ss i fy t h e s e t o f a t o m i c e x p e r i e n c e s o f
p l e a s u r e a n d p a i n . J u d g i n g t h e b e t t e r li fe w o u l d t h e n i n v o l v e f i n d i n g r e l e -
v a n t s u b s e t s a n d c o m p a r i s o n s w e h a d n o t p r e v i o u s l y n o t i c e d . I f , h o w e v e r , w e
a v o i d p s y c h o l o g i c a l a t o m i s m , t h e d i s c u s s i on s o f p l e a s u r e a n d p a i n c a n b e
s e e n i n a n e w l i g h t. P l a t o is a s k i n g u s a l so t o i n d i v i d u a t e p l e a s u r e s a n d p a i n s
i n n e w w a y s, s o t h a t i n s o m e c a s e s w h a t c o u n t s a s a p l e a s u r e c h a n g e s ; a s a
r e s u l t o f t h i s n e w i n d i v i d u a t i o n a n d c l a s s i f i c a t i o n w e w i l l u s e n e w s t a n d a r d s
o f e v a l u a t i o n .
A f t e r c o n s i d e r i n g p s y c h o lo g i c al a t o m i s m w e t u r n t o t h e F o r m s , s h o w i n g
t h a t P l a t o a l s o a v o i d s o n t o l o g i c a l a t o m i s m i n t h i s r e a l m . R e c a l l i n g h i s c l e a r
r e j e c t i o n o f t h e u l t i m a c y o f p h y s i ca l a t o m s , I c o n c l u d e t h a t f o r P l a to t h e r e
a r e n o e n t i ti e s w h o s e d e t e r m i n a t i o n s a r e m e r e l y g iv e n , b e t h e y F o r m s o r
s e n s i b l e p a r t i c u l a r s , i n b e i n g o r i n k n o w l e d g e .
W h e n P l a to t al ks in g e n e r a l t e r m s a b o u t t h e li m i t a n d t h e u n l i m i t e d
(Phi bus 15
a - 1 8 d ) i n t e r p r e t e r s c o m m o n l y s u g g e s t w e a r e f a c e d w i t h a m u l t i -
t u d e o f d i s t i n c t p a r t i c u l a r s w h i c h w e h a v e t o c l a s s i f y . P l a t o i s s a i d t o b e
w a r n i n g u s n o t t o u s e c l a s s i f i c a t i o n s w h i c h a r e t o o b i g o r t o o s m a l l , t o o
' This article refe rs to the unwritten doctrines of Plato. Th e relevant passages from
Aristotle. along with many others referring to these doctrines, are translated in J. N. Findlay,
Plato: The Written and Unwritten Doctrines
(New Yor k: Humanities Press, 1974), pp. 4x3-4 54 .
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P Y T H A G O R A S B O U N D 4 9 9
e l a b o r a t e o r t o o s k e tc h y . W h e t h e r w e st a r t w i t h t h e p a r t i c u l a r s , b u i l d s m a l l
c l a ss e s a n d a r r i v e a t t h e g e n e r i c c l as s , o r s t a r t w i t h t h e g e n u s , d i v i d e it i n t o
s p e c i e s a n d a r r i v e a t t h e p a r t i c u l a r s , w e a r e n o t t o r e s t c o n t e n t u n t i l w e h a v e
t h e i n t e r m e d i a t e c l as s es a s w e ll a s t h e e x t r e m e s . F o r i n s t a n c e , H a c k f o r t h
s ay s, a p r o p o s o f P l a to ' s e x a m p l e a b o u t s o u n d , b e t w e e n ' s o u n d ' o r ' u t t e r -
a n c e ' a s a g e n u s a n d t h e i n f in i t y o f p a r t i c u l a r s o u n d s w e m u s t i n t e r p o s e t h e
s p e c i e s , v o w e l s , s o n a n t s , a n d m u t e s . ''2 W e a r e t o a r t i c u l a t e t h e g e n u s - s p e c i e s
s t r u c t u r e o f u n i v e r s a l s t o b e a p p l i e d t o a s e t o f f i x e d i n d i v i d u a l s .
G o s l i n g h a s a r g u e d c o n v i n c i n g l y a g a i n s t t h e m a n y i n t e r p r e t a t i o n s w h i c h
t a k e t h e d i s c u s s i o n o f t h e l i m i t a n d u n l i m i t e d a s a d o c t r i n e a b o u t g e n u s -
s p e c i es r e l a t i o n s a m o n g u n i v e r s a l s a l o n e . 3 T h i s d o e s n o t m e a n t h a t w e m u s t
t a k e t h e u n i v e r s a l s a s s im p l y g i v en . C l e a r l y P l at o m e a n s u s to b e w o r k i n g o u t
t h e i r a r t i c u l a t i o n s . I t w o u l d b e a m i s t a k e , h o w e v e r , t o s u p p o s e t h a t w e m u s t
a s s u m e t h a t o n e f a c t o r , e i t h e r u n i v e r s a l o r p a r t i c u l a r , i s f i x e d w h i l e t h e o t h e r
is i n d e f i n i t e a n d a d j u s t a b l e . B o t h a c h i e v e d e f i n i t e n e s s t o g e t h e r . P l a t o ' s e x -
a m p l e s p o i n t t h i s o u t . C o n s i d e r t h e s t o ry o f T h e u t h t h e E g y p t i a n :
W h e n o n e i s f o r c e d t o s t a rt w it h w h a t i s i n d e t e r m i n a t e , o n e s h o u l d n o t i m m e d i a t e l y
l o o k t o t h e u n i t a r y a s p e c t , b u t a g a i n n o t e s o m e n u m b e r e m b r a c i n g e v e r y p l u r a l i t y ,
a n d f r o m a ll t h e s e e n d u p a t t h e o n e . L e t u s t a k e u p t h e p r e s e n t p o i n t a g a i n in
c o n n e c t i o n w i t h l e t t e r s - - H o w d o y o u m e a n ? - - W e l l , o n c e , I s u p p o s e , s o m e g o d , o r
s o m e m a n v e r y li k e a g o d , n o t i c e d t h e i n d e t e r m i n a c y o f v oc a l s o u n d . T h e E g y p t i a n s
h a v e a s to ry t h a t i t w a s s o m e o n e c a l l e d T h e u th w h o f i rs t n o t i c e d th a t i n t h is i n d e t e r -
m in a t e v a r i e ty t h e r e w e re s e v e ra l v o c a b les (v o we l s) , n o t j u s t o n e , a n d th e n th a t t h e r e
w e r e o t h e r s t h a t c o u l d b e s o u n d e d b u t w e r e n o t v o we l s a n d t h a t t h e r e w a s a d e f i n i t e
n u m b e r o f t h e s e , a n d f i n a lly h e d i s t i n g u i s h e d a t h i rd c l a ss o f l e t t e r s t h a t w e n o w c a l l
m u t e s. H e t h e n d i s t i n g u i s h e d t h e s o u n d l e s s o n e s o r m u t e s d o w n t o s i n gl e l e t te r s , a n d
d id t h e s a m e w i th th e v o w e l s a n d s e m iv o w e l s . W h e n h e h a d th e fu l l c o u n t h e g a v e
t h e m , i n d i v i d u a l l y a n d c o l le c t iv e l y, t h e n a m e ' e l e m e n t . ' A s h e r e a l i z e d t h a t n o n e o f u s
R . Ha c k fo r t h ,
Plato s Examination of Pleasure
(C a mbr i dge : C a m br i dg e Un i ve r s i t y P re s s
1945) , p . 24. Co mp are G uth r ie : P la to he r e uses ~ tnetQov numer ica l ly , for the un cou nta ble
mu l t i tu de of pa r t icula rs in a spec ies (W. K. C. Gu thr ie ,
History of Greek Philosophy,
6 vols.
(C a mbr i dg e : C a m br i dg e Un i ve r s i t y P res s , 1978) , vo l. V , p. 2o9) . C rombi e ' s i n t e rp re t a t i on i s
more nua nc e d a nd re fuse s t o s e t t he un l i mi t e d t o t al ly on t he s ide o f t he un i ve r sa l s o r o f
pa r t icula rs , but he too seems to presume tha t we a re dea l ing a t a l l t imes wi th se t s of f ixed
par t icula rs . (Cf . I . M. Crom bie ,
An Examination of Plato s Doctrines, 2
vols . (New York: Humani -
t ie s Press , 1963) , vol . I I , pp . 365, 425, 428-9 , 436-7) .
:~ J . C .B . G osl ing , Plato s Philebus (Oxfo rd : Ox fo rd Un i ve r s i t y P re s s 1975), pp . 16o -165 . I t
is no t e n t i r e l y c l ea r w he re Gos l i ng s t a nds o n t he r e l a t i on o f i nd i v i dua t i o n a nd c la s si f ic a ti on. He
c a re fu ll y d i s t i ngu i she s t he l i m it a nd un l i mi t e d a s P la t o 's P y t ha go re a n t e c hn ic a l too ls f rom t he
i n t e rna l c ons t i t u t i on o f t he ob j e c t s t ud i e d by me a ns o f t he se t oo l s ( c f . p . ~ 77 ) - W he t he r t he se
ob j e c t s a re i nd i v i dua t e d i nde pe nde n t l y o f t he u se o f t he t oo l s t o c l a s s i fy t he m se e ms t o va ry ,
pe rhaps r ight ly so , s ince in Gosl ing ' s v iew Pla to i s d i scuss ing the appl ica t ion of technai t o p h e n o -
me na , no t t he c ons t i t u t i on o f ob je c ts . C f. p . 86 a nd pp . 177 - 18o fo r pa s sa ges t ha t c ou l d be
i n t e rp re t e d e i t he r wa y, a nd p . 172 fo r a n e xa mpl e , d i s c usse d bel ow, t ha t p re suppose s i nd e pe n -
de n t p syc ho l ogi c a l g i ve nne s s o f t he pa r t i c u la r s .
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5 J O U R N A L O F T H E H I S T O R Y O F P H I L O S O P H Y 2 1 : 4 O C T 198 3
would ever l ea rn about them in i so la t ion f rom the res t , he conc luded tha t th i s
cons t i tu ted a s ingle bond tha t somehow made them a s ingle uni t , and pronounced
the s ingle skill that cove red th em ' the ar t of le t ters . ' (17 b- d, Gosl ing 's t ranslat ion)
W h a t is it t h a t T h e u t h f ir st n o t ic e s ? H e i s n o t c r e a t i n g s p e e c h ; h e is
d i s c e r n i n g i ts s t r u c t u r e . H e n o t i c e s dpovilv ~ t e t Q o v ; G o s l i n g t r a n s l a t e s t h is a s
t h e i n d e t e r m i n a c y o f v o c al s o u n d , H a c k f o r t h a s u n l i m i t e d va r i et y o f
s o u n d . B o t h t h e s e m a k e ~ tz te tQ ov t h e m a i n n o u n , b u t i t is a n a d j e c t i v e :
i n d e t e r m i n a t e s o u n d . E a r li e r, P la to h a s d e s c r i b e d s o u n d a s s o m e h o w o n e
( ~ o v ~ a ) a n d i n d e t e r m i n a t e i n its m u l t i t u d e ( 6 ~ t Q o v ~ kv ]0 ~t) ( 1 7b ) . I t is
t e m p t i n g t o g lo s s t hi s a s h e a r i n g a s e q u e n c e o f i n d i v i d u a l s o u n d s w i t h o u t
k n o w i n g t h e m i n d e ta il , s o m e t h i n g l ik e s e e i n g a c r o w d o f p e o p l e w i t h o u t
k n o w i n g t h e i r o c c u p a t io n s . B u t T h e u t h d o e s n o t a r r iv e at h e a r i n g i n d i v id u a l
s o u n d s a s i n d i v i d u a l s u n t i l t h e e n d of h i s p r o c e s s . A l t h o u g h f o r P l a to t h i n g s
a r e o n t o l o g ic a l ly d e f i n i t e q u i te i n d e p e n d e n t l y o f o u r a w a r e n e s s o f t h e m , it
d o e s n o t a u t o m a t i c a l l y f o l l o w t h a t o u r a w a r e n e s s is a p r o c e s s w o r k i n g u p
f r o m c l e a r ly i n d i v i d u a t e d b u t u n c l a s s if i e d it e m s . T o c o n c l u d e t h is o n e m u s t
a s s u m e t h a t , o n t h e b a s i c l ev e l, c r i t er i a o f i n d i v i d u a t i o n a r e i n d e p e n d e n t o f
t h e n a t u r e s o f t h e i t e m s i n d i v i d u a t e d , w h i c h is o n t o l o g i c a l a t o m i s m i n it s
e m p i r i c is t v e rs i o n. I f w e r e je c t th is a s s u m p t i o n t h e n u n c e r t a i n t y a b o u t n u m -
b e r a n d a b o u t k i n d s m a y a ls o b e u n c e r t a i n t y a b o u t i n d iv i d u a t io n . H e n c e t h e
p h r a s e & ~r tQ o v = ~.fi0 et s h o u l d m e a n u n b o u n d e d i n it s m u l t i p li c i ty , w h e r e
n o t o n l y a r e t h e n u m b e r a n d k i n d s o f i t e m s i n d is t in c t , h u t t h e i r b o u n d a r i e s
f r o m o n e a n o t h e r a s w e l l ?
M o s t d i s c u s s i o n s o f c l a s s if i c a ti o n u s e a d o m a i n o f e n t i t i e s a l r e a d y i n d i -
v i d u a t e d b y s o m e other c l a s s i f i c a t i o n . T h e u b i q u i t o u s t r a d e s p e o p l e w h o m
S o c r a t e s f o r e v e r r e cl a ss i fi e s a r e a l r e a d y i n d i v i d u a t e d b y t h e i r b o d i e s. I f w e
r e g r o u p t h e m i n t o n e w c l as se s , w e h o l d s t a b l e o u r w a y s o f i n d i v i d u a t i n g
t h e m a s p e o p l e . T h e t a b le s a n d c h a i r s w h i c h fill m o d e r n d i s c u ss i o n s o f
p e r c e p t i o n a r e i n d i v i d u a t e d b y t h e i r g l u e a n d n a il s a n d i n d e p e n d e n t m o v -
a b il it y. T h e s e s o r ts o f e x a m p l e s f e e d t h e p r e j u d i c e t h a t c la s si fi c at io n i n v o lv e s
o n l y r e g r o u p i n g . B u t t h e r e a r e o t h e r s o rt s o f e x a m p l e s w h e r e it is n o t so
o b v i o u s w h a t m a k e s u p o n e i n d i v id u a l a n d w h e r e a c h a n g e i n h o w w e c la s-
s if y m a y b e t ie d t o a c h a n g e i n h o w w e i n d i v i d u a t e . T h e s e a r e c as e s w h e r e
t h e r e a r e n o i n d e p e n d e n t c r i t e ri a o f i n d i v i d u a t i o n a v a il a b le , o r t h o s e a v a il -
a b l e a r e m i s t r u s t e d . C o n s i d e r a L i b e r t a r i a n c o n v e r t e d t o M a r x i s m : h e w ill
4 GiselaStriker Peras und Apeiron: Das Problem der Formen in P aaatons Philebus (Gottingen:
Vandenhoeck & Rup rech t, 197 o) translates ~trtetQov ~tk~j0et as un beg ren zt zahlreich. I am
suggesting that fiJt~tQov need not ap ply only to the nu mb er o f particulars involved, but to their
individuation and hence to the kind of m ultiplicity as well. In her discussion of ~.ovr Striker
presu ppo ses that speech comes before Th eu th with its items already individuated but not yet
classified (p. 95).
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P Y T H A G O R A S B O U N D 5 1
now see things as part of the gove rnm ent which he did not before, for
instance Citibank. He will see more complex individuals where before he saw
simpler ones; a labor union will have mor e kinds of comp onen ts and more
interrelat ions among them. Closer to the P h i l e b u s , there is the difficulty we
experience in deciding what counts as one field of knowledge.
In such cases we do not have a crowd of particulars which need only to be
classified. N o r do we have an undifferentiated continuum, some pure poten-
tial to be cut as we choose. We have s omet hing already diffe rentia ted as to its
generic character but still indeterminate in more specific ways. Theuth starts
with speech sound indeterminate in its multiplicity. This is neither a blank
con tin uum nor a crowd of individual sounds but an indeterminately mul-
tiple and various stretch of speech sou nd. He has already distinguished this
generically fr om sights, smells, etc. He discovers stretches of s oun d which
contrast with other stretches. He classifies more and more finely, creating
more precisely bounded and contrasting species until he arrives at firm
particulars arranged in the lowest species as well as at the articulated genus.
He classifies and individuates; he arrives at his universals and his particulars
together. Th er e is no sharp s eparat ion between recognizing an individual
sound
as
individual, and kno wle dge of what sort of individual it is. 5
In the Th eu th examp le (as earlier in 17 a- b ) Plato evokes the exper ience
of learning to read an d wri te. We mod ern s should rem emb er that in his t ime
this involved analyzing heard sound by taking dictation and reading aloud.
One did not learn to read silently while facing letters which were already
spatially distinct; there was always the flowing indeterminacy of vocal
sound. 6 Nor were t here neat packets o f sound just waiting to be assigned to
distinct letters. Th e sou nd equivalents of one letter are frequen tly quite
varied al lophones of the same phon eme. One must learn to segmen t the
sound stream. Are the p of pin and that of spin the same sound? The
answer varies in English and in Greek. The same articulation can be part of
d i fferent phonemes.
Gosling seems to miss the point when he discusses learning one's letters in
5 Cf. J. Stenzel, Plato s Method ofDDDialectic, tr. D. Allen (Oxford: OxfordUniversity Press,
194o), p. 142 and p. 125: The particular only is in so far as it is this; and Io be th~ means to
have, or to fall under, this ~6og. Otherwise it is quite impossible to grasp the object, and even
&~o0 qotg can only do so in a spurious way. Until we have grasped how the ~6og and the sensible
particular are correlated, the latter remains unknowable; it is not 'one' but 'indefinite'
(6n~tQov). Stenzel assumes, however, that one and ~tnetQov apply here only to the particu-
lars, which seems unlikely. On this cf. A. E. Lloyd, Plato's Description of Division, in R. Allen,
Studies in Plato s Metaphysics (New York: Humanities Press, 1965), p. 225.
6 In his Confessions (VI, 3) Augustine records his puzzled astonishment at discovering
Ambrose reading silently to himself. Augustine's forced explanations of why Ambrose would
read in this unusual way testify to the opposite custom.
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5 0 2 J O U R N A L O F T H E H I S T O R Y O F P H I L O S O P H Y 2 1 : 4 O C T 1 9 8 3
t e r m s o f a v i su a l e x a m p l e . T h e l e t t e r C c a n b e
recognized,
b u t
knowing
it is
k n o w i n g it is a c o n s o n a n t , n o t a v o w e l, a n d w h a t k i n d o f c o n s o n a n t i t is , a n d
s o o n ( 1 72 , m y e m p h a s i s ) . H e is r i g h t , t h e p r i n t e d
letter
C c a n b e r e c o g -
n i z e d , b u t t h is is b e c a u s e w e a l r e a d y h a v e a n o t h e r c l as s if i ca t io n i n d i v i d u a t i n g
w r i t t e n l e t t e r s b y sp a t i a l s e p a r a t i o n . W o u l d i t b e s o e a s y to r e c o g n i z e in a
s t r a n g e - f l o w i n g s c r i p t ? B u t t h e
sound
C c a n n o t e v e n b e
recognized
e x c e p t b y
l e a r n i n g t h e r e l e v a n t c o n t r a s t s a n d c l as s if i ca t io n . I n P l a t o' s e x a m p l e t h e r e is
n o p l a c e f o r G o s l i n g 's s h a r p s e p a r a t i o n b e t w e e n r e c o g n i t i o n o f t h e l e t te r a s
a n i n d i v i d u a l a n d k n o w l e d g e o f w h a t s o r t o f in d i v i d u a l it is. T h e u t h r e a l i z e d
w e c o u l d n o t l e a r n l e t t e r s i n i s o l a t i o n f r o m o n e a n o t h e r , b e c a u s e t h e i r i d e n -
t it y c o m e s t h r o u g h t h e c o n t r a s t s i n w h i c h th e y s t a n d. I n d i v i d u a t i o n a n d
c l a s s if i c a ti o n o c c u r t o g e t h e r . 7
I t m i g h t s e e m t h a t t h e p o in t I h a v e b e e n m a k i n g c o n c e r n s o u r k n o w l e d g e
o f en t i ti e s a n d n o t t h e e n t it i es t h e m s e l v e s . B u t s o u n d s a r e e x p e r i e n c e s a n d
e x p e r i e n c e s a r e e n t i t i e s . T h e
Philebus
is c o n c e r n e d w i th o u r e x p e r i e n c e s i n ce
it s m a i n s u b j e ct , p l e a s u r e , r e s i d e s t h e r e . I t is p a r t i c u l a r l y a p p r o p r i a t e t o h i s
e t h i c a l d i s c u s s i o n t h a t P l a t o d is c u s s t h e c l as s i f ic a t io n a n d i n d i v i d u a t i o n o f
e x p e r i e n c e s . E x p e r i e n c e , h o w e v e r , is a d a n g e r o u s w o r d t o u s e s i n ce it is a
m o d e r n n o t i o n w i th c o n n o t a t i o n s f r o m D e s c a rt e s a n d K a n t. W e m u s t r e -
m e m b e r t h a t, f o r t h e G r e e k s t h e s u b j e c t - o b je c t d i v is i o n w a s n o t t h e f u n d a -
m e n t a l c l e ft in t h e w o r l d it l a t e r b e c a m e . W h e n P l a to t a lk s o f s en s a t i o n s o r
p l e a s u r e s h e is t a l k i n g o f t h e m o n t o l o g i c a ll y as i t em s o n a p a r w i t h t r e e s a n d
t r a d e s p e o p l e , n o t a s i t e m s i n s o m e p r i o r e p i s t e m o l o g i c a l r e a l m . E x p e r i e n c e s
a r e e n t i t i e s l i k e a n y o t h e r . I n s o f a r a s a l l e n t i t i e s h a v e m e a s u r e a n d l i m i t i n
t h e i r c o n s t i t u t i o n , s o will e x p e r i e n c e s . I t m a y s o u n d p a r a d o x i c a l t o s a y t h a t
w e ca n b e u n s u r e a b o u t t h e c o m p l e x i t y o f t h e i n d i v id u a t i o n o f o u r e x p e r i -
e n c e s, b u t t h is b e t r a y s h o w d e e p l y w e a r e i n f l u e n c e d b y a n a t o m i s t i c p s y c h o l-
o g y t h a t b u i l d s u p e x p e r i e n c e f r o m b i t s w h i c h a r e u n c l a s s i f i e d b u t a l r e a d y
i n d i v i d u a t e d a s o n e s e n s a t i o n o r o n e e x p e r i e n c e e a c h .
P l a t o ' s p h y s i o l o g y d o e s n o t s u g g e s t a n a t o m i s t p s y c h o l o g y . P l a t o c o r r e -
l at es p l e a s u r es t o p r oc e s s es o f b u i l d u p a n d b r e a k d o w n w i t hi n th e o r g a n i s m
Philebus
3 3 f f ) . S o m e o f t h e s e m a y r e a c h t h e s o ul . T h e r e a r e m a n y s u c h
r h y t h m i c p r o c es s e s g o i n g o n a t a n y o n e t i m e ; m a n y o f t h e m r e a c h t h e s ou l
t o g e t h e r . I n a d d i t i o n , t h e s o u l ha s its o w n r h y t h m i c p r oc e s s e s. T h e s e
7 p la to s o t h e r e x a m p l e , m u s i c al n o t e s ( 1 7 b - e ) , c a n b e r e a d i n a w a y c o n s o n a n t w i t h t h a t o f
T h e u t h . O n e s t a rt s w i th i n d e t e r m i n a t e l y m u l t i p l e s o u n d , w i t h a r e a s o f d i f f e r i n g p i t ch , t h e n
d i s t i n g u i s h e s i n te r v a ls a s p h e n o m e n a r e p e a t a b l e a t d i f f e r e n t p i t c h e s , t h e n t o n e s a s t h e e n d s o f
in t e r va l s, t he n a r r i ve s a t s ca l e s a s spe c i e s c on t a in ing r u l e s f o r i nd iv idua t in g sou nd in to no t e s
r e l a t e d b y c o n t r as t s a n d m e a s u r e s . T h e m u s i c e x a m p l e is l es s c o n v i n c i n g, p e r h a p s b e c a u s e w e
have eas i ly ava i lab le
oth r
w a ys o f i nd iv idua t ing m us i c a l sounds ( by s t r i ngs on a l y r e , ho l e s i n a
f lute , e tc . ) .
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PYTHAGORAS BOUND 5 3
r h y t h m s a r e all s u p e r p o s e d u p o n e a c h o th e r . T h e s u p e r p o s i t i o n o f v a r y i ng
f r e q u e n c i e s d o e s n o t o b l i g i n g l y s o r t i t s e lf o u t i n t o a li n e a r s e r i e s o f d i s c r e t e
a t o m i c s t im u l i t o b e c o r r e l a t e d w i t h a p a r a l l e l l i n e a r s er i es o f d i s c r e t e a t o m i c
e x p e r i e n c e s .
I f w e r e j e c t p s y c h o lo g i c a l a t o m i s m w e o b t a i n a s t r o n g e r i n t e r p r e t a t i o n o f
t h e et h ic a l a r g u m e n t i n t h e d i a lo g u e . C o n s i d e r t h e p a s s a g e w h e r e P l a to
d i s cu s s e s a l if e o f p u r e p l e a s u r e w i t h o u t i n t e l li g e n c e . P r o t a r c h u s s u g g e s t s a
l if e o f c o m p l e t e p l e a s u r e w o u l d b e j u s t f in e . S o c r a t e s r e p l ie s :
But i f you l acked thought , me mo ry , know ledge , and t rue opin ion , sure ly to begin
wi th , you co uldn ' t know even w hethe r you were en joying yours e l f or not , s ince you
would l ack a l l in te l l igence . - -True . - -What i s more , in the same way, as you would
l ac k m e m or y , you w ou l d be una b le t o r e m e m be r t ha t you d id e n j oy you r s e l f on a ny
occas ion , and no recol lec t ion a t a l l o f p leasure a t one moment would surv ive to the
next . S ince you would l ack the capac ity for t rue jud gm en t you would not jud ge tha t
you we re en joying yo urse l f when y ou were , and l acking the ab il ity to predic t you
would be unab le to predic t y our fu ture p leasures . I t wo uldn ' t be a hum an l ife a t all,
but a je l ly-fish exis tence, or the l i fe of o ne of those sea- things that l ive in shel ls .
Aren ' t I r igh t? Philebus 2 lC, Gosl ing 's Translat ion.)
G o s l i n g r e a d s t h is p a s s a g e w i t h a n a t o m i s t p s y c h o l o g y . A l if e o f p u r e p l e a -
s u r e w o u l d b e a s t r e a m o f c o n s t a n t p l e a s u r e - e x p e r i e n c e s , b u t th e e x p e r i -
e n c e r w o u l d b e u n a b l e t o r e fl e ct iv e ly j u d g e ( o r r e m e m b e r o r p r e d ic t ) t h a t h e
w a s e n j o y i n g . T h e s t r e a m o f e x p e r i e n c e s w o u l d l ac k i n t e ll e c tu a l a n d r e f le c -
t iv e a d d i t i o n s t o t h e p l e a s u r e e x p e r i e n c e s . T h u s it w o u l d b e a m e r e a n i m a l
s t r e a m o f l if e. G o s l i n g s h o w s t h a t t h is f a il s t o p r o v e t h a t t h e p l e a s u r e s o f
s u c h a b e i n g w o u l d n o t b e m o r e p l e a s u r a b le , a n d c o n c l u d e s
Socrates ' point gets i ts pul l , of course, as an appeal to the individual honest ly to
dec la re h i s pre fe rences . Doubt less mos t of us would show some oppos i t ion to a
prop osal to red uce us to the condi t ion of co nten ted jel ly-f ishes, a t least a t the level of
dec la red prefe rence . I t may be tha t Socra tes should be read as conduct ing an ad
hom inem exam ina t ion of Pro ta rchus , which Pla to hopes will e li ci t the sam e admiss ion
f rom any hones t reader (182) .
T h e r e m a y b e m o r e t o t h e a r g u m e n t t h a n G o s l i n g s ee s. H is i n t e r p r e t a -
t io n p r e s u p p o s e s t h a t t h e s t r e a m o f p l e a s u r e - e x p e r i e n c e s w i t h o u t in te ll i-
g e n c e is i n it s e lf u n i f i e d a n d d i s t in c t a n d t h a t i n te l l ig e n c e w o u l d e n t e r t h e
s t r e a m o f e x p e r i e n c e s s i m p l y as a n e w k i n d o f e x p e r i e n c e , l i k e a n e w c o l o r
b e a d o n a s t r in g . I f w e q u e s t i o n t h e s e p r e s u p p o s i t i o n s w e se e t h e r o l e o f
i n te l li g e nc e a s m o r e c o m p l e x . T h a t f e w h u m a n s w o u l d c h o o s e i t d o e s n o t
p r o v e t h e l i f e o f a n o y s t e r o r j e l ly - f is h i n h u m a n ; it m i g h t b e o n e o f t h o s e
p r e c i o u s t h i n g s t h a t a r e a s d i f f ic u l t as t h e y a r e r a r e . R a t h e r P l a t o cl a im s w e
n e e d i n t e l l ig e n c e i n o r d e r t o h a v e a n y t h i n g t h a t c o u l d b e c a ll e d one t e m p o -
r a l l y u n i f i e d
l i fe
o f e n j o y m e n t . G o s l i n g s u g g e s t s t h a t P l a to is t r y i n g t o p r o v e
t h a t r e a l i z i n g o n e i s e n j o y i n g o n e s e l f is p r e f e r r e d t o j u s t e n j o y i n g o n e s e l f
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5 4 JOURNAL OF THE HISTO RY OF PHILOSOPHY 2 1 : 4 OCT 983
(183). But p erhaps Plato's point is tha t one cannot enjoy oneself without
realizing one is enjoying oneself'.
Plato has argued in the earlier examples that we need the limit and the
unlimited to have knowledge. It is striking that the modes of knowledge
Plato suggests to avoid the fate of the oyster are explicitly correlated to the
three parts of time. Without memory you would not know that you have
enjoyed (~X(xtQegIpast). Wit hout true op inion abou t your sel f you would not
know you were enjoying (XctiQovzctIpresent). Without calculated expecta-
tions about the future you would not expect future pleasure ()~cttffr~oetg
future). A human life, as opposed to any oyster's, demands temporal unity.
This time-binding demands knowledge which will make a one out of indefi-
nitely multiple temporal flux. Applying Theuth's method, we can only di-
vide the moments from one another ( I am experiencing
this
pleasure
now )
when we have intermediate contrasting unities for the parts of time. It is
only because we can unify time into a one and divide it into the intermedi-
ates of the three temporal dimensions that we can experience the present
pleasure as one individual pleasure among many, as a pleasure, and as our
own. Without this temporal one-and-many the stream of experiences is
neither a stream nor experience.
Plato has two Kant ian insights: the need of a concep tual structure for
there to be experience of individuals, and the need of temporal synthesis fi)r
there to be experience at all. Plato links these by making the temporal
synthesis one sort of conceptual synthesis. None of this turns Plat() into
Kant. Plat() does not make the distinctively Kantian move of reversing the
dependence and holding temporal synthesis essential to our possessing con-
cepts. Nor does he in the
Philebus
separate transcen dental categories from
empirical concepts except by generality. Plato also differ s from Kant in
subordinating discussion of experience to the more general ontological dis-
cussion of limit and unlimited; the examination of knowledge has no special
privilege. Plato is not doing epistemology but onto logy; he gives necessary
ontological conditions for entities, including experiences, but not transcen-
dental conditions for experience as such.
This read ing o f the oyster passage does not make it a fully convincing
argument. It remains to be shown that the human life is better than the
oyster's existence. This value ju dg me nt is implied since hum an life contains
more complex unity, but such a criterion would not convince Philebus. Still,
on this reading Plato is making more than an ad hominem argument. It is
more than men's preferences which keep them from choosing the life of
pure pleasure without intelligence. Plato is trying to show the inconsistency
of the picture of a life containing nothing but pleasures which can still be
called
my life
in any me anin gful sense.
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PYTHAGORAS BOUND 5 5
T h e u t h h a s t a u g h t u s th a t w e n e e d d i f f e r e n t i a t e d c o n c e p t s i f w e a r e t o
k n o w i n d i v i d u a l s . N o k n o w l e d g e w i t h o u t n u m b e r . T h e o y s t e r t e a c h e s u s t h a t
w e n e e d k n o w l e d g e t o a ch i e v e th e t e m p o r a l u n i t y o f a l if e o f p l e a s u r e . N o
p l e a s u r e w i t h o u t k n o w l e d g e . T h e f u r t h e r c o n c lu s i on P la to dr a w s t h r o u g h -
o u t t h e d ia l o g ue : n o p l e a s u re w i t h o u t n u m b e r . W h a t m a y s e e m t h e g r e a te s t
p l ea s u re s , g r e a t j u s t b e c a us e t h e y g o b e y o n d n u m b e r a n d m o d e r a t i o n , b y
t h a t v e r y ex ces s t h r ea t en t o d i s o r g an i ze l i f e s o t h a t t h e ex p e r i en ce o f p l ea -
s u r e i s d e s t r o y ed .
I t is n o t s u r p r i s i n g , t h en , t h a t a t t h e en d o f t h e d i a l o g u e i t is t h e f am i l y o f
k n o w l e d g e t h a t is a ll o w e d t o e x c l u d e s o m e o f t h e f a m i l y o f p l e a s u r e s w h i c h
w il l p r e v e n t u s [ k n o w l ed g e ] f r o m ev e r co m i n g i n t o ex i s t en ce ( 6 3d ) . T o
ex i s t a t a ll i n a w o r l d w h e r e b e i n g s a r e m i x t u r e s o f li m i t an d u n l i m i t ed
d e m a n d s c o n s t a n t c a r e f o r b a l a n c e a n d p r o p o r t i o n , l es t w e lo se re a li ty . I f
p l e a s u r e s b e c o m e i m m o d e r a t e t h e y w ill d i s r u p t t h e t i m e - b i n d i n g a n d d e t e r -
m i n i n g m i x t u r e o f l im i t a n d u m l i m i t e d ; h u m a n e x p e r i e n c e w i ll s to p . A s
a lways in P l a to , t he fu l l oppo s i t e o f an o r de re d l i f e is no l i fe a t a ll .
I n t h e c o u r s e o f h is a r g u m e n t s f o r m e a s u r e P l at o n o t o n l y re c la s si fi es b u t
r e i n d i v i d u a t e s p l e a su r e s . 8 I f w h a t w a s s a id e a r l i e r a b o u t t h e c o n n e c t i o n o f
c l a s s i f i ca t i o n an d i n d i v i d u a t i o n i s t r u e , t h en t h e n ew s p ec i e s i n t o w h i ch
S o c r a t e s d i v i d es t h e g en u s o f p l ea s u r e s c a r r y t h e p o s s ib i li ty o f n ew m o d es o f
i n d i v i d u a t i o n . W e c a n n o t s u p p o s e w e a r e d e a l i n g w it h a f ix e d d o m a i n o f
e x p e r i e n c e s a l r e a d y c l e a rl y i d e n t i f ie d a s o n e p l e a s u r e o r o n e p a i n e a c h . I n
fac t , P l a to tr i es t o show tha t no t a ll p l easu re s a re s imp le f e l t s t a t es ; he
ch a n g e s t h e k i n d s o f i n d i v i d u a l i t y s o m e p l ea s u r e s p o s s es s .
P h i l eb u s 's o r i g i n a l d e s c r i p t i o n (1 l b ) s u g g es t s p l ea s u r e s a r e u n i t ex p e r i -
e n c e s t o b e e v a l u a t e d b y c ri t e ri a o f i n t e n s i ty a n d q u a n t i t y . B y t h e e n d o f t h e
d i a l o g u e P l at o h a s a r r i v e d a t a v a ri e t y o f k i n d s o f p l e a s u r e s o n m a n y d i f f e r -
en t l ev e ls o f i n d i v i d u a l i t y : s i m p l e t r u e p l ea s u r e s , m i x e d p l ea s u r e s , p l ea s u r e
a t d e s i re s o f p l e a s u r e , p l e a s u r a b l e c o m p a r a t i v e j u d g m e n t s o f p l e a su r e , p le a -
s u r a b l e m e m o r i e s o f p l e a s ur e s , p l e a s u r a b l e a n t i c i p a ti o n s , p l e a s u r e s a t th e
r e l a t i o n s o f p l ea s u r e s , n o t t o m e n t i o n a ll t h e v a r i e t ie s o f p a i n an d t h e m i x -
t u r e s o f p l e a s u r e a n d p a i n. S e e m i n g l y s i m p l e p l e as u r e s , s u c h a s e n j o y i n g a
g la ss o f w a t e r o r l a u g h i n g a t a c o m e d y , a r e s h o w n t o b e c o m p l e x e s o f m a n y
k i n d s o f i n t e r l o c k i n g e x p e r i e n c e . W e d o n o t j u s t r e c l as s if y o u r p l e a s u r e a t
t h e c o m e d y ; w e a n a l y z e it a n d d i s c o v e r it h a s i n t e r n a l c o m p l e x i t y . O n e
p l e a s u re o r p a i n c a n b e a c o m p o n e n t o f a n o t h e r . O u r a m u s e m e n t a t t h e
co m e d y i s a p l ea s u r e , b u t i t is a co m p l ex o f o t h e r ex p e r i en ces a s w e ll .
I f i t i s t r u e t h a t p l ea s u r e s m u s t b e i n d i v i d u a t ed i n t h i s m o r e v a r i ed w ay ,
Plato also re-individuates fields of knowledge, as is clear from the discussion of the two
arithmetics and the summary at 57 D.
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5 6 JOURNAL OF THE HISTORY OF PHILOSOPHY 21: 4 OCT 198 3
that pleasures d o not all have the same kinds of individuality, then it is diffi-
cult to apply the simple criterion of quantity to their evaluation. Truth and
falsity, mixture and purity, will assume a new importance in our evaluations.
This reading might also open an approach to Plato's notion of true and
false pleasures. When pleasures are taken as atomic experiences the ir fal-
sity can only mean the falsity of a related ju dg me nt which leaves the plea-
sure itself unch anged . If, however, pleasures can be individuated in other
ways, if something can be a compound experience and still be a pleasure,
then ju dg me nt can be built into pleasures more intimately and pleasures
may be false in a stro nger sense. Tr ue pleasures, on the oth er hand , are
not true by virtue of any related judg ment. Their truth is that of true
reality. Th ei r interna l st ructure is simple; in themselves, in their q~oLg
(52b3) they require no reference to another temporal moment to complete
them or to make them harmoniously pleasurable. This would seem to pose
problems for my int erpr etat ion since true pleasures look suspiciously like
psychological atoms. Tr ue pleasures might, however, be thoug ht of as the
pleasure-equivalents of prime numbers and harmonious ratios, not psycho-
logical atoms so much as self-contained units like those musical chords that
imply no build-up and de ma nd no resolution. In his physiological section
Plato does not speak of a series of discrete bodily states but of superposed
rhythms; analogously, the true pleasures might be thought of as the experi-
enced correlates of har moniousl y bound body or soul rhythms, as the physi-
cal atoms of the
Timaeus
are mathematically bou nd flux.
I have tried to purge a residual empiricism from the interpretatio n of the
Philebus
by removing psychological atomism from Plato's examples and ethi-
cal argument. It is a familiar theme in Plato's writings that complex entities
like cities or personalities are built from components whose mixture is cor-
rect when it approaches a norm given by the Form of the object or quality in
question. Joining the rejection of psychological atomism with the account of
physical atoms given in the
Timaeus
we see that the physical and psychologi-
cal components themselves contain measure and limit rather than brutely
given qualities.
What of the Forms? Most interpretations of Plato treat the Forms much
as the myth in the
Timaeus
presents them, as given eternal exemplars, with
all questions terminated in the claim that a certain form
just does
contain a
certain quality in its definition.
The
Philebus
however, speaks of our arriving at pro per classifications and
prop er divisions of genera by a process of finding measure. Th eu th works at
making his classifications. In so doing he not only determines the indefinite
plurality of speech sound into individual units, he determines the generic
universal speech sound into species in a har mon iou s and complete man-
ner. As he e ncounters the indefinitely multiple sound already distinguished
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PYTHAGORAS BOUND 507
i n s o m e w a y ( f r o m s m e l ls a n d s ig h ts ), s o h e e n c o u n t e r s u n i t y a s a d e f i n i t e
g e n u s n e e d i n g f u r t h e r s p e ci fi c at io n . T h e s e a r e n o t t w o e n c o u n t e r s , b u t tw o
s id es o f th e s a m e p r o c e s s . W e e n c o u n t e r n e i t h e r i n d e f in i t e ne s s n o r u n i ty b y
t h e m s e l v e s , n o r c a n w e e n c o u n t e r e i t h e r i n a p u r e s t a te .
T o c o m e t o k n o w a F o r m is t o g r a s p t h e s t r u c t u r e d m o d u l a t i o n o f u n i t y
i n s o m e a p p r o p r i a t e f ie ld . T h e u t h ' s a c ti v e s p e c i f y in g o f t h e g e n e r i c u n i v e r s a l
r e p r e s e n t s o u r a r r i v i n g a t k n o w l e d g e o f t h e F o r m s . T h e r e is a n o t a b l e a b -
s e n c e h e r e o f t h e a p p e a l s t o i n t u i t i o n m a d e i n e a r l i e r d i a lo g u e s . A l s o a b s e n t
is a p ro c e s s o f a b s t r a c ti o n f r o m a l r e a d y g i v e n d e t e r m i n a t e p a r t ic u l a rs . T h e
u n i v e r s a l is s p e c i f ie d a n d t h e p a r t i c u l a r s d e t e r m i n e d t o g e t h e r . T h i s p r o c e s s
s e e m s t o m i r r o r , i n o u r k n o w i n g , th e g e n e r a t i o n o f t h e F o r m s t h e m s e l v e s .
A r i s to t le s p e a k s o f t h e g e n e r a t i o n o f th e f o r m s o u t o f th e o n e a n d t h e
i n d e f i n i t e d y a d
(Metaphysics
I , 6 ; XI V , 1 , e t c .) . W hi l e t he de t a i l s o f t h i s
d o c t r i n e a r e f a r f r o m c l e a r, e n o u g h c a n b e m a d e o u t t o s h o w t h a t t h e
p i c t u r e o f P l a t o p o s i t i n g b r u t e l y g i v e n F o r m s is w r o n g . I t is n o t e n o u g h t o
c l ai m t h a t t h e F o r m s a r e i n t e r re l a t e d a n d m i x e d w i th o n e a n o t h e r i n t h e
f a s h i o n d e s c r i b e d i n t h e Sophist. T h e r e is a n o r d e r o f g e n e r a t i o n i n v o l v e d a s
w e ll . I t is t r u e t h a t t h e F o r m s a r e e t e r n a l l y w h a t t h e y a r e . Y e t t h is is n o t a
b r u t e f ac t. T h e F o r m s a r e a s t h e y a r e b e c a u s e t he y a re t h e h a r m o n i o u s
m o d u l a t i o n s o f u n i t y in t o m u lt ip l ic i ty . T h e y c o u l d n o m o r e b e d i f f e r e n t t h a n
t h i r t e e n c o u l d c e a s e t o b e a p r i m e n u m b e r . B u t t h i r t e e n is n o t a b r u t e f a ct ; i t
a ri se s f r o m t h e g e n e r a t i o n o f t h e n u m b e r s b y t h e m i x i n g o f u n i ty a n d t h e
i n d e f i n i t e d y a d . 9
I t s e e m s l ik e l y P l a t o h o p e d t h a t al l t h e F o r m s , t h e i r q u a l i ti e s a n d i n t e r -
r e l a t i o n s h i p s , c o u l d b e d e r i v e d a s h a r m o n i o u s s et s o f r a ti o s , n a t u r a l p o i n t s o f
u n i ty i n t h e c o m b i n i n g o f l im i t a n d u n l i m i te d . T h e p r o p o s a l h o p e d f o r a
s y s t em o f n e c e s s a r y t r u t h s a b o u t t h e n a t u r e s o f all t h in g s , d e r i v e d f r o m t h e
f u n d a m e n t a l r e l at i o n s o f u n i ty a n d m u l ti p li c it y . T h o u g h n e v e r r e a li z ed , th is
p r o g r a m c o u l d h a v e i n s p i r e d m a n y r e s e a r c h p r o je c t s a t t h e A c a d e m y .
A s s u m i n g t h a t A r i s t o t le i s n o t t o t al ly m i s r e p r e s e n t i n g P l a to , t h e r e is t h e
p r o b l e m o f r e l a t i n g t h e u n w r i t t e n d o c t r i n e s w i t h t h e o n t o l o g i c a l d i s cu s -
s i ons i n t he
Philebus.
E n o u g h o f th e u n w r i t t e n d o c t r i n e s c a n b e r e l a te d t o th e
Philebus t o s h o w t h a t P l a t o is n o t t h e r e a n o n t o l o g i c a l a t o m i s t c o n c e r n i n g t h e
F o r m s . T h e c l a i m a t 1 6c t h a t a ll e n t it i e s a r e c o m p o s e d o f l i m it a n d u n l i m i t e d
fits w i th , t h o u g h it n e e d n o t e x p r e s s d i r e c t ly , t h e u n w r i t t e n d o c t r i n e s ? ~ T h e
q u e s t i o n is m o r e o b s c u r e i n c o n n e c t i o n w i t h th e f o u r f o l d d i v i s i o n o f e n t it i e s
Cf. Findlay's intriguing conjectures on how this might have been envisaged, an d the
special role played by the prime numbers
(Plato,
pp. 67- 7o )
' As is clear from the general mo vem ent of this essay, I accept the traditional translation
of 16c9 as refe rrin g to all entitles, r ath er th an Striker's revised translation refe rrin g only to the
Forms. The arguments used by Pamela Huby in her review of Striker's book
(Classical Review
XXII (197~), p. 333) and Gosling
(Plato s Philebus,
p. 84) seem convincing.
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5 8 J OURNA L OF THE HI STORY OF PHI LOS OPHY 2 1 :4 OCT 983
into limited, unlimited, mixed, and cause (23c-26d) . Explaini ng this
division, Plato states that the m ixt ur e of limit and unlimi ted is car ried o ut by
nous with reference to both our souls and the world soul. This mixing
activity is also connected to wisdom and knowledge, which are said not to
exist except in souls. This poses no problem for the mixture of limit and
unli mited rele vant to the ethical topics discussed. But were we to appl y this
description to the Forms themselves we would be blocked. For there is no
sense of cause accep table to Plato in which one could say that soul is the
cause of the generat ion of the Forms fr om the one and the indefini te dyad.
To read the unwrit ten doctrine s straight into the four| old classification of
the Philebus requires serious reinterpret at ion. With Jackson, one could turn
Plato's doctrine into idealism, but this seems anachronistic in the extreme.
With the Neoplatonist s and Findlay one could read the cause,
nous
not as
single souls but as the F or m o f soul, an eternal Intellect which bot h is a For m
and contains the Forms. '~ This, however, would be to read the entire Neo-
platonic hierarchy into the Philebus a move which, I argue below, goes
against Plato's intent. In a similar vein one could interpret wisdom and
knowledge as referring to Forms from which others could be derived. While
this could be made congruent with Plato's overall doctrine, i t is expressly
excluded as a meaning for this text.
We should conclude that the unwritten doctrines are not expressed di-
rectly in the fourfold classification, though the doctrines are not excluded
either. In addition, as Striker argues, both some Forms (e.g., Heat) and some
concr ete objects (e.g., impu re pleasures) are included in the genus of the
unlimited. Th e ethical application of the fo urf old classification suggests that
unlimite d or indefinite includes those Forms and those particulars which
lack a definite ratio or n um be r that makes them perf ect of their kind, and
are always relative to a more-and-less and to contrasting items. There is no
highest heat nor any definite temperature which is perfect heat, while there
are such rules a nd ratios fo r Forms such as horse or man. '~ The se points
suggest that the unwrit ten doctrines be seen in the background. Had the
Henry Jackson, in a series of articles in the Journal of Philology which appeared from
1882 through 1886 (vols. X through XV) argued that after the self-criticism found in the
Parmenides Plato modified his theory in a way which eliminated the presence of the Forms in
sensible particulars and made of the theory a thoroughgoing idealism in which each Form is
a thought which is eternally present in the universal mind (or which would be eternally present
in the universal mind, if in passing into time and space it retained its universality). Particulars
are the same thought imperfectly actualized by finite minds in [perceived] time and space (Vol.
XIII, p. ~43). The phenomenalistic use to which the concept of mind is put in this theory is
more nineteenth-century than Greek.
'~ Cf. Findlay, pp. 281-295 for an account in this spirit.
~:~ Striker, pp. 41-68.
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PYTHAGORAS BOUND 5 9
pr og ra m which Aristotle repor ts been capable of being carried out, i t would
have provided an explanat ion why the rat ios that determine a horse are
what they are, and why some Forms need f urthe r determin ation, given their
place in the generative scheme.
Striker also wishes to argue, however , that the unlimited cann ot be
seen as an ele ment in entities. '4 This concl usion seems unnece ssar ily strict.
Th e ter m ~t~etOov can be app lied on a variety of levels. Striker her sel f
shows several: the gen eric universal, the multiplicity of particulars, particu-
lar individual pleasures. These all have in common that in themselves or in
their context they demand or al low further determination. While we can-
not make any simple equat ion of the unlimited with one constant element
in all entities, we can see it describing many different levels of indetermina-
t ion. The need of measure and determination holds equally and with no
special p rimac y fo r atoms of fire, pleasures, politics, percept ions, and per-
sonalities, with all their dif fer ing kinds of comp one nts and of indefinite-
ness. This is not so dif fer ent fr om Aristotle's flexibility with matt er an d
potentiality.
When Theuth is inventing letters, he faces indeterminately multiple
sound, already distinguished in a generic way fr om othe r kinds of experi-
ence. Presumably we never face the simply indeterminate, for to do so would
be to lack any experience. In so far as we can experience the indeterminate
it is already de-scribed or de-limited in some generic way. So too whenever
entities, be they Forms or particulars, are described as indeterminate the
entities will be already determinate in some other way. Thus the fact that the
unli mite d of the four fo ld classification is a gen us of entities and no t som e
pur e potential l ike Aristotle's prima ry matter need not force us to deny that
determinate entities can be composed, on various different levels, of the
inde term inat e plus meas ure or limit. '5
The unwrit ten doctrines again stand in the background, unit ing this
flexible use of the ter m unli mite d into a gene rati ve series of specifications
of the indetermina te dyad. Th e dyad would be a purely indetermi nate
principle, but it is not an entity. To make such a generative series plausible it
,4 Striker, pp. 45-5 o. I do not deal with all of Striker's arguments on this question nor
with her overly restrictive hermeneutic principle about what it means to take the text on its
own. Striker (and Gosling's) various other arguments against seeing limit and unlimited as
elements in things can be met, I think, by a position which (a) refuses to separate knowing
particulars from knowing universals, (b) links classification and individuation, (c) has more
flexible and multi-leveled notions of the limit and unlimited, and (d) makes unifying back
ground reference to the unwritten doctrines. The interpretation still has difficulties with 16el-
2 (dismissing units into the indeterminate).
~ I am bypassing the question whether the hilebt~ does or does not presuppose the
distinction drawn in the
Statesman
between limit in general and normative measure (283-285).
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1 9 8 3
would be necessary to link the indefinite dyad and the Receptacle discussed
in the
Timaeus.
Th e Receptacle can be seen as a specification of the indefinite
dya d into the realm of space. 16 Th e two are related as a generically deter-
mined to a simply indefinite principle. Plato seems to have thought that the
progressive limitation of the dyad described in geometrical terms eventually
produced the spatio-temporal indeterminate, which by the fact of its spatial-
ity is generically determinate. Aristotle indicates in his criticism of Plato in
Metaphysics
lo9oa 23 - 9 that the re is one indefin ite principle, which cries
out at the way it gets dra gge d about into what Aristotle thinks are too many
different generative processes.
The unwritten doctrines stand behind the
Philebus
not as necessary pre-
suppositions but as a fuller story which, had Plato been able to complete it,
would have unified the discussion of limit and unlimited and would have
explained the details of their application to Forms and particulars. This
means that the
Philebus
suggests and the unwritten doctrines confirm that
Plato is nowhere an ontological atomist. There are no beings which are
brutely given as what they are. All determinations are generated by pro-
cesses which are ideally those of harmonious measure; the question why? is
in principle answerable for any determination, based only on the notions of
unity and indefinite miltiplicity and their combination into a set of necessary
structures.'7
Plato could have reconciled his dualisms more easily had he asserted the
unchalle nged primacy of the principle of unity and m ade it the source of the
principle o f indet ermi nati on, as do the Neoplatonists. Plato himself has little
or nothing to say about the basic principles of unity and indefiniteness
themselves. This is not coyness; as the ontological conditions of possibility
for any definite entity, the limit and the unlimited are not themselves defi-
nite entities to be spoken about. The Neoplatoists do ask and answer ques-
tions about the ultimate principles in themselves. Emanation and ~ntoxQoq~,
the power of the One which by its being makes a counterspace as it over-
,5 According to Plato the one and the indefinite dyad, which he spoke of as the great and
small, are the principles of all things and even of the Forms themselves. So Aristotle reports in
his work On the Good (Alexander, quoted by Simplicius in his comment ary on
Physics 187a12
translated by Findlay, Plato p. 4x4). Cf. also the passages translate d on p. 44 x con cer nin g the
Timae~
and Aristotle,
Metaphysics
~o85a 7- 14 for the series numb er, line, surface, volume and
the referenc e to species of the indefinite dyad.
,7 Thi s is not quite true. Plato, like Aristotle, seems to dismiss accidental determinations as
not knowable by a science of dialectic such as he proposes. Th e d octr ine of
infimae species
implies
this conclusion for both thinkers; cf. PosteriorAnalyticsI, 4(73b15ff). The problem whether (and
if so where) to draw the line between determinat ions which are accidental and those which can
be necessarily known plagues thinkers who reject ontological atomism.
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