Parry - The Uniqueness Proof for Forms in Republic 10

8/20/2019 Parry - The Uniqueness Proof for Forms in Republic 10

1/19

Journal of the History of Philosophy, Volume 23, Number 2, April 1985,

pp. 133-150 (Article)

DOI: 10.1353/hph.1985.0026

For additional information about this article

Access provided by Universidad Complutense de Madrid (2 Sep 2015 13:29 GMT)

http://muse.jhu.edu/journals/hph/summary/v023/23.2parry.html

http://muse.jhu.edu/journals/hph/summary/v023/23.2parry.htmlhttp://muse.jhu.edu/journals/hph/summary/v023/23.2parry.html


2/19

T h e U n i q u e n e s s P r o o f fo r

o r m s i n

e p u b l i c l o

R I C H A R D D . P A R R Y

I N T H IS PA PER I o f f e r a n i n t e r p r e t a t i o n o f t h e a r g u m e n t a t t h e b e g i n n i n g o f

R e p t t b l i c l o ( 59 7 cl -d 3 ). T h e a r g u m e n t - - s o m e t i m e s c a l le d t h e T h i r d B e d A r -

g u m e n t ( T B A ) - - s h o w s t h a t t he F o r m o f b e d is u n i q u e . T h e a r g u m e n t i s

i n t e r e s t i n g b e c a u s e i t u s e s t h e O n e - O v e r - M a n y p r i n c i p l e ( O M ) , w h i c h j u s ti -

f ie s p o s i t i n g F o r m s . B u t u n l i k e t h e u s e o f O M i n t h e f i rs t T h i r d M a n A r g u -

m e n t ( T M A ) o f P a r m e n i d e s ( 1 3 1a l -b 2 ) , t h e u s e o f t h e O M i n T B A d o e s n o t

p r o d u c e a n a r g u m e n t w h i c h i s l ia b le to b e c o m i n g a n i n f in i te r e g r e s s . S i n ce

t h e T B A is i n e v e r y o t h e r r e s p e c t a c la ss ic s t a t e m e n t o f t h e t h e o r y o f F o r m s

u s u a l l y a s s o c i a te d w i t h t h e m i d d l e d i a l o g u e s , w e c a n c o n c l u d e t h a t t h is t h e -

o r y is n o t m e t a p h y s i c a l l y b a n k r u p t , a s i t is s o m e t i m e s c l a im e d . W h a t e v e r t h e

p r o b l e m s w i t h t h e T M A , t h e y d o n o t i n f e c t t h e w h o le t h e o r y o f F o r m s i n th e

m i d d l e d i a l o g u e s b e c a u s e t h e r e is a t le a s t o n e i n s t a n c e o f a c l e a r e n u n c i a t i o n

o f t h e t h e o r y w h i c h d o e s n o t f al l p r e y t o th e i n f i n it e r e g r e s s o f t h e T M A .

I n S e c t i o n 1 o f t h i s p a p e r , w e a n a l y z e t h e T B A a n d a d d t h r e e a s s u m p -

t io n s n e c e s s a r y t o m a k e i t v a li d . A s w el l, w e e x p l a i n t h e s e a s s u m p t i o n s a n d

o f f e r t e x t u a l e v i d e n c e f o r t h e m . I n S e c t i o n 9, w e s u r v e y r e c e n t c o m m e n t a r -

ie s o n t h e T B A a n d d e f e n d o u r i n t e r p r e t a t i o n a g a i n s t t h es e c o m m e n t a r i e s .

I n p a r t i c u l a r w e s h o w t h a t, u n d e r o u r i n t e r p r e t a t i o n , t h e T B A i s n o t li ab l e

t o b e i n g t u r n e d i n t o a n i n f i n i t e r e g r e s s o f F o r m s o f b e d . I n S e c t i o n 3, w e s ee

w h a t i m p l i c a t i o n s t h is l a t te r f a c t h a s f o r a th e o r y o f F o r m s w h i c h h o l d s t h a t

t h e F o r m o f f is , i n s o m e w a y , i t s e lf f . W e s h o w i n w h a t w a y t h is c e n t r a l

d o c t r in e o f t h e m i d d l e d i a lo g u e s t h e o r y o f F o r m s c a n be h e ld w i t h o u t t h r e a t

o f i n c o n s i s t e n c y o r i n f i n i t e r e g r e s s . I n S e c t io n 4 , w e a p p l y o u r i n t e r p r e t a t i o n

o f t h e T B A t o th e T M A , s h o w i n g t h a t th e fa l l ac io u s s t ep o f t h e T M A c a n b e

I would like to thank Anthony Nemetz, Nicholas Smith, and E. W. van Steenburgh who

were kin d en oug h to discuss this pap er with me, as well as an anonymous r eferee fo r

the Journal

of the History of Philosophy All internal references to the Greek text are from Burnet s edition.

[ 33]


3/19

I 4 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

b r o u g h t t o l ig h t b y c o n s i d e r i n g t h e i m p o r t a n t d i f f e r e n c e s b e t w e e n t h e t w o

a r g u m e n t s .

1

A t

R e p u b l i c

lO 5 9 7 c l -d 3 ) S o c r a t e s a r g u e s t h a t t h e r e w ill b e o n ly o n e F o r m o f

b e d , w h i c h h e c a ll s t h a t w h i c h i s b e d . H e s a y s t h a t t h e g o d w i ll n o t m a k e

m o r e t h a n o n e b e d i n n a t u r e - - b y t h e la t t e r p h r a s e is m e a n t a F o r m - - n o r

w ill t w o s u c h t h i n g s a r is e . T h e a r g u m e n t t o b ac k u p a t l e as t t h e f i rs t p a r t o f

t h is c l a i m i s s i m p l y p u t : i f h e m a d e a s f e w a s t w o ~ t h e n a g a i n a o n e b e d i n

n a t u r e ) w o u l d a r is e , w h o s e f o r m t h e tw o o r i g in a l b e d s ) w o u l d h a v e , a n d t h i s

o n e w o u l d b e t h a t w h i c h is b e d a n d n o t t h e t w o . S o, t h e g o d , k n o w i n g a ll t h is

a n d w i s h i n g t o b e t h e r e a l b e d m a k e r o f t h e r e a l b e i n g a n d n o t j us t) a m a k e r

o f a b e d , m a k e s o n e b e d ) i n n a t u r e .

T h e c a l c u l a t i o n i n v o l v e d i n t h i s p a s s a g e c o u l d b e r e n d e r e d :

I ) I f h e m a d e a s fe w a s t w o

x ) a ) a g a i n a o n e b e d ) w o u l d a p p e a r

b ) w h o s e f o r m t h e tw o w o u l d h a v e a n d

2 ) a ) t h is o n e w o u l d b e th a t w h i c h is b e d a n d

b ) n o t t h e t w o .

I f w e l o o k a t t h e c a l c u l a t io n c l o se l y w e s e e t h a t s o m e a s s u m p t i o n s a r e

m a d e . F o r t h e c a l c u la t io n t o w o r k , t h e n , t h e s e s u p p r e s s e d a s s u m p t i o n s n e e d

t o b e a d d e d t o d e r i v e b o t h p a r t 1 ) a n d p a r t 2 ). I n th is s e c ti o n w e a d d t h e s e

a s s u m p t i o n s . I n e f f e c t , t h e a s s u m p t i o n s s h o w t h a t th e o n e w h i c h a p p e a r s i s

t h e o n e F o r m o v e r m a n y a n d t h a t e v e r y t h i n g w h i c h is a b e d besides t h i s o n e

F o r m d e r i v e s its c h a r a c t e r f r o m t hi s F o r m . T h e l a tt e r a s s u m p t i o n i s o f c r u -

c ia l i m p o r t a n c e b e c a u s e i t a ll o w s t h e F o r m o f f t o b e f w i t h o u t p a r t i c i p a t i n g

i n a n o t h e r F o r m o f f ; t h e F o r m is n o n - d e r i v a t i v e l y f . T h e s i g n if i ca n c e o f t h is

a s s u m p t i o n w il l b e e x p l o r e d i n s u b s e q u e n t s e c ti o n s; b u t , f o r t h e p r e s e n t ,

s u f f i c e i t t o s a y t h a t u s i n g i t, w e a r g u e t h a t t h e T B A is n o t l i a b le t o a n

i n f in i te r e g r e s s . I n a n y e v e n t , f r o m t h e s e a s s u m p t i o n s w e c o n s t r u c t t h e i n t e r -

p r e t a t i o n w h o s e o u t l in e i s t h e f o l lo w i n g . T h e g o d m a k e s th e F o r m o f b e d

c a ll e d t h a t w h i c h i s b e d ) . T h i s F o r m is a p a r a d i g m w h i c h h a s o r e x h ib i t s t h e

c h a r a c t e r f o r w h i c h i t is a p a r a d i g m T h e r u l i n g m e t a p h o r o f t h e p a ss a ge is

c r a f t , i n w h i c h t h e c r a f t s m a n l o o k s t o a p a r a d i g m a s h i s g u i d e [ c f . Cratylus

3 8 9 a 5 - b 6 ] ) . I f t h e g o d w e r e m i s g u i d e d , h e w o u l d m a k e t w o s u c h t h i n g s - -

t w o F o r m s w h i c h a r e d u p l i c a t e s o f o n e a n o t h e r . J u s t a s t h e f ir s t w a s a b e d ,

t h e t w o w o u l d b e b e d s . B u t t h e i r b e in g d i f f e r e n t m e a n s t h a t, b y o u r a s s u m p -

The Rep ublic of P lato James A llen, ed. Cambridge: the U niversity Press, 1969), 2:3 91,

note for 597Cl9.


4/19

T H E U N I Q U E N E S S P R O O F ~ 3 5

t i o n s , n e i t h e r c a n b e

t h e

F o r m o f b e d ( t h a t w h i c h i s b e d ) n o r t h e p a r a d i g m .

T h u s , t h e o n e o v e r m a n y p r i n c i p l e d i c t a t e s t h a t t h e r e b e a n o t h e r F o r m , i .e . ,

t h a t w h i c h i s b e d . T h e t w o h a v e i t s c h a r a c t e r - - i . e . , t h e i r b e i n g b e d s d e p e n d s

o n i t - - b e c a u s e i t i s t h e p a r a d i g m a n d t h e y a r e n o t .

W e t u r n t o t h e s p e c i f i c a s s u m p t i o n s . T o ( 1 ) t h e r e n e e d s t o b e a d d e d s o m e

v e r s i o n o f t h e O n e - o v e r - M a n y p r i n c i p l e J T h e j u s t i f i c a t i o n f o r a d d i n g t h e

O M i s n o t f a r t o f i n d . A t t h e b e g i n n i n g o f t h i s w h o l e p a s s a g e ( 5 9 6 a 5 - 8 )

P l a t o s t a t e s a v e r s i o n o f t h e p r i n c i p l e : l e t u s b e g i n o u r i n v e s t i g a t i o n u s i n g

o u r a c c u s t o m e d m e t h o d : w e a r e a c c u s t o m e d t o p o s i t i n g s o m e o n e f o r m

( e i d o s ) f o r e a c h g r o u p o f m a n y , w h i c h b e a r t h e s a m e n a m e . 3 T h e a d d i t i o n o f

O M d e p e n d s o n t a k i n g t h e t w o t o b e b e d s i n s o m e s e n s e , o t h e r w i s e t h e t h i r d

b e d c o u l d n o t b e t h e F o r m o f b e d , a s i t i s s a i d t o b e . 4

W e c a n a d d t h i s p r i n c i p l e t o t h e c a l c u l a t i o n :

( I ) I f h e m a d e a s f e w a s t w o s u c h t h i n g s 5

S e e H . C h e r n i s s ,

Aristotle's Criticism of Plato and the Academy

( B a h i m o r e : t h e J o h n s H o p k i n s

Pre ss , 194~) ,

t

2 6 0 , n o t e 1 7 o ; C o l i n S t r a n g , P l a t o a n d t h e T h i r d M a n , Plato: A Collection of

CriticalEssays,

e d i t e d b y G . V l a s t o s ( G a r d e n C i t y : D o u b l e d a y , a 9 7 1 ) , l : 1 9 2 .

T h i s f o r m u l a t i o n s h o u l d b e c o m p a r e d w i t h t h a t a t 5 o 7 a 6 - b l o , w h i c h is v e r y c lo s e t o t h e

p r e s e n t o n e . J . A . S m i t h , i n G e n e r a l R e l a ti v e C l a u s e s i n G r e e k

(Classical Rev iew

3 1 [ 1 9 1 7 ] : 6 9 -

7 1 ), a r g u e s t h a t t h is p a s s a g e i n B o o k l o m e a n s e i t h e r t h a t

every

g r o u p b e a r i n g t h e s a m e n a m e

h a s a F o r m o r t h a t t h e F o r m p o s i t e d i n e a c h c a s e i s o n e . F o r g r a m m a t i c a l r e a s o n s h e d e n i e s t h e

f o r m e r , a f f i r m i n g t h e l a tt e r . I n t h e l i g h t o f 5 o 7 a 6 - b l o w e c a n se e t h a t w e a r e n o t r e s t r i c te d t o

t h e s e t w o a l te r n a t i v e s . T h e p r i n c i p l e a t 5 9 6 a 5 - 8 c a n al s o m e a n t h a t w e p o s i t o n e F o r m f o r e a c h

g r o u p w h i c h w e p o s i t a s a m a n y , l e a v i n g it i n d e t e r m i n a t e w h a t c o n s t it u t e s a m a n y .

4 S e e D . R . D u f f - F o r b e s , T h e R e g r e s s A r g u m e n t i n t h e

Republic, Mind

77 (x968) : 4o7 ; I .

M . C r o m b i e , D u f f - F o r b e s o n R e p u b l i c l O ,

M i n d

8 o ( ] 9 7 1 ) : 2 8 6 ; K . W . M i ll s, C r o m b i e o n

Republic

597c , '

M i n d

8 2 0 9 7 3 ) : 6 o 2 .

5 T h e f i rs t s t a t e m e n t i n t h e c a l c u l a ti o n is n o t d e f i n i t e a b o u t t h e t w o t h i n g s t h e g o d i s

m a k i n g . T h e n a t u r a l a s s u m p t i o n s e e m s t o b e th a t h e is m a k i n g t w o b e d s in n a t u r e o r t w o F o r m s

o f b e d . I f w e u s e t h e p h r a s e b e d i n n a t u r e w e h a v e n o d if f ic u l ty i n s ta t i n g s u c h a c as e . B u t i f

w e u s e t h e p h r a s e ( w h i c h o c c u r s j u s t b e f o r e t h e c a lc u l a ti o n ) , t h a t w h i c h is b e d , w e h a v e

c o n s i d e r a b l e d i f f ic u l t y in e v e n s t a t i n g t h e c a s e. W e c a n n o t s a y t h a t t h e g o d i s m a k i n g t w o t h a t

w h i c h is b e d ; a n d s u b s t i t u t i n g t h o s e w h i c h a r e b e d s s e e m s u t t e r l y u n w a r r a n t e d . T h e d if f ic u l ty

s e e m s t o b e t h a t t h e p h r a s e t h a t w h i c h is b e d i n d i c a t e s u n i q u e n e s s . U s i n g t h e p h r a s e to

d e s c r i b e a c a s e w h e r e u n i q u e n e s s is v io l a t ed i s im p o s s i b l e . F o r t h i s r e a s o n , p r o b a b l y , a t 5 9 7 c 4

P l a t o s a y s t h a t t h e g o d d i d n o t m a k e

two such

t h i n g s . T h e v a g u e n e s s o f t h i s p h r a s e a l l o w s t h e

f o l l o w i n g r e a d i n g . S u p p o s e t w o c as e s o f b e d m a k i n g . T h e f i rs t c a se ( a t 5 9 7 c a - 3 ) i s t h e o n e i n

w h i c h t h e g o d m a k e s o n e b e d i n n a t u r e , t h a t w h i c h is b e d . T h e s e c o n d c a s e is d e s c r i b e d i n ( I) ,

t h e o n e i n w h i c h h e m a k e s t w o s u c h t h i n g s . ( T h i s l a s t r e s u l t c o u l d b e a c c o m p l i s h e d i n t w o w a ys .

T h e g o d c o u l d m a k e t h a t w h i c h i s b e d a n d t h e n d u p l i c a t e it ; o r h e c o u l d s im u l t a n e o u s l y m a k e

t w o i t e m s e x a c t ly a l i k e, o n e o f w h i c h c r e a t e d a l o n e w o u l d b e t h a t w h i c h is b e d . S i n c e t h e f o r m e r

is th e e a s i e r f o r m y a r g u m e n t , I s u p p o s e t h e la t t er . ) B o t h F o r m s o f b e d d o n o t h a v e to b e t h a t

w h i c h i s b e d ; t h e y a r e t w i n s o n e o f w h o s e m e m b e r s w o u l d b e t h a t w h i c h i s b e d i f i t o c c u r r e d

a l o n e . T h i s r e a d i n g a l lo w s u s t o s a y t h a t t h e t w o a r e b e d s a n d , i f w e c h o o s e , t h a t e a c h is a F o r m .

B u t i t d o e s n o t n e c e s s i t a te o u r s a y i n g t h a t e a c h i s t h a t w h i c h i s b e d , i .e ., t h e F o r m o f b e d .


5/19

1 3 6 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

( 1 ) ( [ i ] G i v e n t h a t w e a r e a c c u s t o m e d t o p o s i t i n g s o m e o n e f o r m f o r

e a c h g r o u p o f m a n y 6) ( a) a g a i n a o n e ( b e d i n n a t u r e ) w o u l d a p -

p e a r , ( b ) w h o s e f o r m t h e t w o w o u l d h a v e a n d

( 9 ) ( a ) t h i s o n e w o u l d b e t h a t w h i c h i s b e d a n d

( b ) n o t t h e t w o .

T h i s f o r m u l a t i o n o f O M e x p l a i n s w h y t h e o n e i s r e q u i r e d i n t h e f o l l o w i n g

w a y . T h e o n e w h i c h a p p e a r s a n s w e r s t o t h e O M b e c a u s e w i t h o u t t h e o n e

t h e r e w o u l d n o t b e o n e F o r m o v e r m a n y a n d t h e p o s i t i n g m e n t i o n e d i n ( i )

w o u l d b e i l l e g i t i m a t e . T h u s t h e o n e w h i c h a p p e a r s i s t h e o n e F o r m o v e r

m a n y .

N o w w e t u r n t o t h e j u s t i f i c a t i o n f o r t h e n e x t s t e p s . ( l b ) s a y s t h a t t h e t w o

b e d s h a v e t h e f o r m o r c h a r a c t e r o f t h e o n e . I n o u r i n t e r p r e t a t i o n , s a y i n g

t h a t t h e t w o h a v e t h e c h a r a c t e r o r f o r m o f t h e o n e d o e s n o t te l l u s p r i m a r i l y

a b o u t t h e i n t r i n s i c q u a l i t i e s o f t h e t w o b e d s ; r a t h e r i t t e l l s u s a b o u t a r e l a t i o n

T h i s r e a d i n g a l l o w s u s t o s e e w h a t i s w r o n g w i t h t h e a t t e m p t s o f S t r a n g a n d C r o m b i e t o t r e a t

t h i s a r g u m e n t a s a

reduct io ad absurdum

w h e r e t h e a b s u r d i t y i s a c o n t r a d i c t i o n . S t r a n g ' s v e r s i o n

o f t h e c o n t r a d i c ti o n : T h e r e c a n n o t b e t w o F o r m s ; f o r s u p p o s e t h e r e w e r e tw o , t h e y w o u l d n o t

b e F o r m s a t a ll , b u t s o m e t h i n g e l s e w o u l d b e t h e F o r m

192) .

T h i s r e a d i n g is c o n s i s t e n t w i t h

t h e s e n s e o f

d u o t o ia u ta i

( t w o s u c h t h i n g s ) if t h e r e w e r e t w o i s e l ip t ic a l a n d m e a n s t h e r e w e r e

t w o F o r m s o f b e d . W h a t f o ll o w s in t h e t e x t is n o t t h a t t h e y a r e n o t F o r m s a t al l, as S t r a n g s a ys ,

b u t t h a t t h e y a r e n o t t h e F o r m o f b e d . S t r a n g d o e s n o t d i s t i n g u i sh b e t w e e n th e t w o b e d ' s b e i n g

F o r m s o f b e d a n d e a c h 's b e i n g t h e F o r m o f b e d . C r o m b i e ' s v e rs i o n o f t h e c o n t ra d i c t io n is b e t t e r

o n t h is l a tt e r p o i n t b e c a u s e i t h a s ea c h o f t h e t w o b e d s b e i n g b o t h t h e F o r m o f b e d a n d n o t t h e

F o r m o f b e d . B u t t h e n h e t a k e s

duo to iau ta i

t o b e m o r e s p e ci fi c t h a n s e e m s s e n s i b l e; h e a s s u m e s

t h e g o d t o m a k e t w o t h a t w h i c h i s b e d ( 2 8 6 ) .

B o t h i n t e r p r e t a t i o n s h a v e a f u r t h e r d i ff i cu l ty . N o t o n l y d o b o t h a b s t r a c t f r o m i ts c o n t e x t t h e

a r g u m e n t ; t h e y s e e m t o f o r g e t t h e c o n t e x t . I t is s i g n i f ic a n t t h a t b o t h e x p u r g a t e t h e l a n g u a g e o f

m a k i n g ; r e s t o r i n g i t s h o w s a c o n t r a d i c t i o n c a n n o t b e i n t e n d e d . I f m a k i n g t w o o f th e s e th i n g s is

i m p o s s ib l e b e c a u s e c o n tr a d i c to r y , e i t h e r t h e m i s g u i d e d g o d w o u l d m a k e t w o t h i n g s w h i c h b o t h

a r e a n d a r e n o t F o r m s ( S t r an g ) o r h e w o u l d m a k e t w o t h i n g s e a c h o f w h i c h b o t h is a n d is n o t

t h e F o r m o f b e d ( C r o m b i e ) - - t h i s r e s u l t c a n n o t b e s t a te d s e n si bl y. B u t f u r t h e r , f r o m a c o n t ra d i c -

t io n e v e r y t h i n g o r n o t h i n g f ol lo w s : t h e g o d - - w h o is s a id t o k n o w t h e i m p o r t o f t h e a r g u m e n t - -

c a n n o t c o n c l u d e f r o m t h e a r g u m e n t t h a t h e w ill e n d u p m a k i n g a b e d in s t e ad o f the F o r m o f

b e d . O n t h e o t h e r h a n d , o u r i n t e r p r e t a t i o n p r e s e r v e s t h e r e s u l t o f th i s c a lc u l at io n : i f t h e g o d

m a k e s t w o s u c h t h in g s - - -t w o F o r m s o f b e d b o t h p r e t e n d i n g t o b e th a t w h ic h is b e d - - h e e n d s u p

n o t m a k i n g the F o r m o f b e d , t h a t w h i c h is b e d , c o n t r a r y t o h i s i n t e n t i o n . I f o u r i n t e r p r e t a t i o n i s

a reductio, i t i s no t a reductio t o a c o n t r a d i c t i o n . S e e a l s o K . W . M i ll 's o b j e c t i o n in C r o m b i e o n

Rep u b l i c

5 9 7 c , ' 6 o 2 .

6 T h e r e is o n e o b v i o u s d i f f ic u l ty w i t h a d d i n g t h i s v e r s i o n o f O M . T h e a s s u m p t i o n , i n i ts

f o r m u l a t i o n a t 5 9 6 a 5 , t a l k s i n t e r m s o f f o r m eidos), w h i c h i s a n e u t e r n o u n i n G r e e k . O a ) t a lk s

i n t e r m s o f o n e i n t h e f e m i n i n e , n o t i n t h e n e u t e r . I n fa c t, t h e o n e i n O a ) r e f e r s t o t h e o n e

b e d i n n a t u r e a t 5 9 7 c~ ; b e d i n n a t u r e is f e m i n i n e . H o w e v e r , t h e b e d i n n a t u r e a t 5 9 7 c ~ i s t h e

F o r m o f b e d m e n t i o n e d e a r l ie r a t 5 9 7 c t - 3 . W e k n o w t h is b e c a u se t h e b e d i n n a t u r e a t 5 9 7c 2 is

c a ll e d in t h e n e x t l i n e t h a t w h i c h i s b e d ; t h a t w h i c h is b e d a n d t h e F o r m o f b e d a r e i d e n t if i e d

a t 5 9 7 a l - 2 . S o , o n e i n O a ) h a s a s i ts a n t e c e d e n t t h e f o r m u l a w h i c h , i n t u r n , r e f e r s t o t h e

F o r m o f b e d a t 5 9 7 c l - 3 ; t h e u s e o f O M is a p p r o p r i a t e a t (1 ).


6/19

T H E U N I Q U E N E S S P R O O F 1 3 7

t h e y n o w h a v e t o t h e o n e b e d o v e r t h e m a n y . W h e n t h e o n e a p p e a r s , t h e t w o

a r e a l r e a d y b e d s , e l s e t h e r e w o u l d b e n o n e e d f o r a o n e . N o w , t h e tw o g a i n a

n e w r e l a t i o n , i . e . , a r e l a t i o n t o t h e o n e b e d o v e r m a n y s u c h t h a t t h e f o r m

h a d b y t h e t w o i s m o r e p r o p e r l y a t t r i b u t e d t o t h e o n e . T h u s , t h e o n e F o r m

o v e r m a n y i s , i n s o m e s e n s e , a b e d a l t h o u g h i t n e e d n o t b e a b e d i n th e s a m e

s e n s e a s A g a t h o n ' s b e d is a b e d . T h e n , t h e t w o a r e s e e n as r e l a t e d t o t h e o n e

i n s u c h a w a y t h a t t h e f o r m o r c h a r a c t e r t h a y h a v e is t o b e i d e n t i f i e d a s i ts

f o r m ( e . g . , J u n i o r h a s h i s d a d ' s n o s e , n o t v ic e v e r s a ) . T h e locus c lass icus f o r

t h i s i m p o r t a n t a s p e c t o f t h e t h e o r y o f F o r m s i n t h e m i d d l e d i a l o g u e s is a

f a m o u s p a s s a g e i n t h e P h a e d o (1 o o c 4 - 6 ) . " I f a n y t h i n g is b e a u t i f u l b e s i d e s t h e

b e a u t i f u l i t se l f i t i s b e a u t i f u l o n l y t h r o u g h p a r t i c i p a t i o n i n t h e b e a u t i f u l

i t s e l f " ( e i t i e s t i n a l lo k a l o n p l a n a u t o t o k a lo n , o u d e d i ' h e n a l lo k a l o n e i n a i ~ d i o ti

m e t e c h ei e k e i n o u t o u k a l o u ) . 7

W e o f f e r , t h e n , t h i s a s s u m p t i o n a s t h e f i rs t s t e p t o f il l t h e g a p : " ( ii ) g i v e n

t h a t i f a n y t h i n g h a s t h e f o r m o f b e d b e s i d e s t h a t w h i c h i s b e d t h e n i t h a s t h e

f o r m o n l y t h r o u g h p a r t i c i p a t i o n i n t h a t w h i c h is b e d . " T h i s a s s u m p t i o n c a n

b e p a r a p h r a s e d t o r e a d " t h a t w h i c h i s b e d i s t h e p r i m a r y b e d f r o m w h i c h a l l

o t h e r b e d s d e r i v e t h e i r f o r m o r c h a r a c t e r . ' '8

7 V l a s to s a t o n e p o i n t ad v an c ed a t r i p a r t i t e o n t o l o g y o f ( a) p a r ad i g ma t i c F o r ms , ( b ) t h i n g s , (c )

t h e ch a r ac t e r o f t h o s e t h i n g s (Platonic Studies, 2 3, 85 , p a s s im) . O u r i n t e r p r e t a t i o n d ep en d s o n

n o t h i n g s o f o r m a l . C l ea r l y t h e r e i s a p a r ad i g m. T h e r e a r e a l so tw o t h i n g s w h i ch a r e b ed s ; b u t to

s ay t h a t t h ey h av e t h e c h a r ac t e r o f b ed i s j u s t a n o t h e r w ay o f s ay i n g t h a t t h ey a r e b ed s . I n t h i s

i n t e r p r e t a t i o n i t is n o t n eces s a r y t o g i v e th e ch a r ac t e r o f b ed t h e q u as i - s u b s t an t i a l s t a tu s g i v en t h e

i m m a n e n t c h a r ac t er s i n Phaedo ~2oD f f n o r e v e n t o g o b e y o n d o r d i n a r y l a n g u a g e i n t o A r i st o te -

l i an me t ap h y si c s . W e s h a l l, h o w ev e r , ad o p t V l a st o s' s u s ag e o f 'Fo r m ' - - w i t h u p p e r ca s e 'F ' - - a s

r e f e r r i n g t o t h e p a r a d i g m - - a n d ' f o r m ' w i t h l o w e r c a se ' f ' - - a s r e f e r r i n g t o th e p e r c e p t u a l c h a r ac -

t e r i s t i c . O u r p r e s en t p a s s ag e u s e s eidos in bo th those senses (c f . Platonic S tudies, 344 , no te 7 ) .

s T h i s s e c t i o n o f t h e i n t e r p r e t a t i o n o f f e r e d i n th is p a p e r o w e s m u c h t o th o s e c o m m e n t a t o r s

w h o a r e i n s y mp a t h y w i t h t h e p o s i t i o n o n P l a t o ' s t h eo r y o f Fo r ms p r o p ag a t ed b y R . E . A l l en ' s

" Pa r t i c i p a t i o n an d P r ed i c t i o n i n P l a t o ' s Mi d d l e D i a l o g u es , "

Stud ies in P lato's Metaphysics,

ed i t ed

b y R . E . A l l e n ( L o n d o n : R o u t l e d g e a n d K e g a n P a u l 1 9 65 ), 4 3 - 6 o . C f . T h o m a s W h e a t o n B e s t o r ,

" P l a to ' s s eman t i c s an d P l a t o 's Parmenides, Phronesis 2 5 ( 1 9 8 o ) : 3 8 ; Ro b e r t Ba r f o r d , " T h e Co n -

t e x t o f t h e T h i r d M a n A r g u m e n t i n P l a t o ' s Parmen ides, Journal of the History of Philosophy 16

( 19 78 ): 4 - 5 . T h e p o i n t a b o u t t h e n o n - d e r i v a t i v e n a t u r e o f t h e F o r m i s m o s t e x p li c it ly m a d e b y

W i l l ia m J . P r i o r i n " P a r m e n i d e s 1 3 2 c - 1 3 3 a a n d t h e D e v e l o p m e n t o f P l a to ' s T h o u g h t , " Phronesis

~ 4 ( 19 79 ) 2 3 o - 4 o . P r i o r 's a r g u m e n t d e a l s w i th t h e i m i t a t i o n a r g u m e n t , o r t h e s e c o n d v e rs i o n o f

t h e T h i r d M a n A r g u m e n t . B u t w h a t i t ha s t o s ay a p p li e s to F o r m s i n t h e m i d d l e d i a lo g u e s i n

g en e r a l . " T h u s , w h i l e i t i s n o t il l eg i ti ma t e t o d em an d an a c c o u n t o f t h e a t t r i b u t i o n o f t h e

p r o p e r t y t o t h e p a r a d i g m ( t h e F o r m ) , i t d i sp l a y s a m i s u n d e r s t a n d i n g c o n c e r n i n g t h e n a t u r e o f a

p a r a d i g m t fi e o ry t o d e m a n d t h e same kind of acc oun t g iven fo r o the r ob jec t s" (237) . I t ake i t t ha t

t h is c la i m p r e c l u d e s l o o k i n g t o a n o t h e r F o r m , i n a o n e o v e r m a n y s t ra t eg y , f o r a n a c c o u n t o f

w h y t h e Fo r m i s f. A n d i f o n e l o o k s to t h e F o r m i t se l f f o r an acco u n t o f it s b e i n g f , s u r e l y t h e

Fo r m i s n o n - d e r i v a t i v e l y f . A c t u a l ly , l o o k i n g t o t h e Fo r m i t se l f f o r s u ch an acc o u n t s eems t o

c o ll a ps e t h e n o t i o n o f a n a c c o u n t .

O t h e r e v i d en c e f o r t h e p o s i t i o n t h a t Fo r m s a r e n o n - d e r i v a t i v e i s i n Fu j is aw a ' s s t u d y n


7/19

138 JOURN AL OF THE HISTORY OF PHILO SOPHY

W e t a k e ( ii) t o i m p l y t h a t t h e F o r m o f b e d i s a p a r a d i g m a n d t h u s is a b e d

i n t h e w a y i n w h i c h a p a r a d i g m is t h a t f o r w h i c h i t is a p a r a d i g m . 9 I n t w o

p la c es t h e a r g u m e n t i m p l ie s t h a t t h e F o r m h a s t h e c h a r a c t e r o f b e d . F ir st o f

a ll, t h e a r g u m e n t i m p l i e s t h a t t h e f i rs t F o r m o f b e d - - i . e . , th e o n e at w h o s e

c r e a t i o n a r i g h t t h i n k i n g g o d w o u l d s t o p - - i s i ts e lf a b e d , a s w e c a n s e e f r o m

t h e f o l l o w i n g a r g u m e n t . L e t X b e t h e f ir s t F o r m ; a n d l e t Y a n d Z b e t h e p a i r

w h i c h t h e w r o n g t h i n k i n g g o d w o u l d m a k e . Y a n d Z a r e s a id t o b e t w o s u c h

t h i n g s scil. a s X i s); p r e s u m a b l y t h e y w o u l d b e l ik e X e x c e p t t h a t t h e y w o u l d

b e d o u b l e s w h i l e X is si n g le . B u t Y a n d Z a r e b o t h b e d s ( i f Y a n d Z w e r e n o t

b e d s t h e r e w o u l d b e n o n e e d f o r a o n e t o a ri se ). I t is i m p o s s i b l e to c o n c e i v e

t h a t X a l o n e d o e s n o t h a v e t h e c h a r a c t e r o f b e d b u t t h a t m a k i n g t w o X ' s

c o n f e r s t h a t c h a r a c t e r . S e c o n d , t h e g e n i t i v e o f p o s s e ss i on i n ( l b ) i m p l i e s t h a t

t h e o n e w h i c h a r is e s h a s t h e c h a r a c t e r o f b e d . T h e t w o b e d s a r e sa id t o h a v e

t h e c h a r a c t e r o r f o r m o f t h e o n e w h i c h a r i s e s h ~ s e k e i n a i a n a u a m p h o t e r a i t o

e i d o s e c h o i e n ) ; s i n c e b e i n g a b e d i s t h e c h a r a c t e r t h e t w o h a v e , b e i n g a b e d i s

t h e c h a r a c t e r o f t h e o n e w h i c h a r i s e s - - i . e . , t h e o n e is a b e d . '~

which he argues that the language of participation is proper to particulars. Cf. Norio Fnjisawa,

l~XEtv, bt~e~etv, and Idioms of 'paradeigmatism' in Plato's Theory of Forms,

P h r o n e s i s 1 9

(1974): 34-3 6. Fujisawa also says that the F orm d oes not have f although it is f. This seems to

contradict what we have previously said about serf-predication. However, Fujisawa seems to

assume that some thin g has f if and only if it participates in the Form o f f. This assumpti on is an

overinterpretation of

P h a e d o

lo oc 4- 6 , upon which he relies heavily. The oth er evidence in his

study shows only that a particular 's having f should be explicated by that particular's participat-

ing in the Form of f. It d oes not show t hat every instance of having f is an instance of

participation. In any event, it is not clear that the re is a substantive disagreem ent with Fujisawa's

reading of participation. We are not maintaining that the Form has f through participation;

indeed, we are denying precisely that notion.

Unfortunately, his reading

o f P h a e d o

lOOC 4- 6 is not as definit ive as he thinks. Fujisawa seems

to take this stat ement by itself to mean that the beautiful itself does not participate in anything. But

this stat ement merely does not requi re t he beautiful itself to participate in anything.

9 Cf. G. C. Nerlich, Regress Argu ment s in Plato,

M i n d

59 (196~ 88- 9o; of course, we do

not agree that the TBA is liable to an infinite regress.

~o A position, such as Strang's 093) , which denies that the Form o f bed-has the character

because it

is

the character does not square with the text. If that which is bed is the character of

bed it would be w ro ng -- if not i mpos sibl e-- to say, as Plato does, that the two beds would have

the form or character of that which is bed

h~s eke inai an au amphotera i to e idos echoien) .

If ' that

which is bed' means the character of bed, such a statement implies that the two beds have the

character of the character of the bed. But then they would not have the character of bed but

whatever character characters might be supposed to have. Rather, one ought to say, as Cherniss

does, that the two beds would have that which is bed. Of course, one might object that a less

rigorous readin g of this Greek phrase would allow whose to be analogous to the whose in

the brow n whose color the two had. Even if this usage is not grammatically questionable

( whose color seems to mean only which ) at least whose would be ambiguous between the

genitive of possession and this oth er genitive, which is not possession (brown does not have its

color; it is its color). But Strang's point is that Plato meant to deny, in this very statement, that

the Form possesses the character. It is very difficult to believe that Plato introduces this denial


8/19

TH UNIQU N SS PROOF 39

O f c o u r s e , e v e n i f ( ii) s ay s th a t t h a t w h i c h i s b e d is t h e p r i m a r y b e d f r o m

w h i c h a ll o t h e r b e d s d e r i v e t h e i r c h a r a c t e r , i t s ay s n o t h i n g a b o u t t h e o n e

( F o r m ) w h i c h w o u l d a p p e a r i f t h e g o d w e r e t o m a k e t w o b ed s . B u t ( l b ) sa ys

t h a t th e t w o w o u l d h a v e t h e c h a r a c t e r o f t h e o n e w h i c h w o u l d a p p e a r . T h u s ,

(ii) b y i t s e l f c a n n o t e x p l a i n w h y t h e t w o h a v e t h e f o r m o r c h a r a c t e r o f t h e

o n e w h i c h a p p e a r s , i . e ., ( lb ) . I n o r d e r t o e x p l a i n w h y th e t w o h a v e t h e f o r m

o r c h a r a c t e r o f th e o n e w e m u s t m a k e a n o t h e r a s s u m p t i o n . F i r st , w e r ec a l l

t h a t t h e o n e w h i c h a p p e a r s is t h e o n e F o r m o v e r m a n y . N o w , i f w e a s s u m e

t h a t t h e o n e F o r m o v e r m a n y is t h a t w h i c h is b e d - - ( i i i ) g i v e n t h a t t h e o n e

F o r m o v e r m a n y is t h a t w h i c h i s b e d - - t h e n , w i t h (iii) , w e c a n e x p l a i n w h y

t h e tw o h a v e t h e f o r m o r c h a r a c t e r o f t h e o n e w h i c h a p p e a r s . F r o m (ii) a n d

(iii) w e c a n c o n c l u d e t h a t , s i n c e t h e o n e w h i c h a p p e a r s is t h e o n e F o r m o v e r

m a n y , i t is al so t h e b e d i ts e l f f r o m w h i c h a l l o t h e r b e d s d e r i v e t h e i r f o r m .

T h u s , t h e tw o b e d s w o u l d d e r i v e t h e i r f o r m o r c h a r a c t e r f r o m t h e o n e w h i c h

a p p e a r s , i . e ., (a b ). M o r e o v e r , s i n c e t h e o n e w h i c h a p p e a r s is t h e o n e F o r m

o v e r m a n y , b y ( iii) i t w o u l d b e t h a t w h i c h is b e d , i .e ., ( 2 a) .

T h i s i d e n t if i c a t i o n o f t h e o n e F o r m o v e r m a n y a n d t h a t w h i c h is b e d - -

i .e ., ( ii i) - - i s c o n t a i n e d i n t h e i m m e d i a t e c o n t e x t o f t h e T B A , a t 5 9 7 a l - 9 :

d i d w e n o t j u s t s a y t h a t h e [ t h e m o r t a l c r a f t s m a n ] d o e s n o t m a k e t h e F o r m ,

w h i c h w e s ay is t h a t w h i c h is b e d , b u t s o m e p a r t i c u l a r b e d . T h e r e f e r e n c e t o

t h e p r e v i o u s s t a t e m e n t - - d i d w e n o t j u s t s a y - - s h o w s t h a t ' F o r m ' i n th e

p r e s e n t p a s s a g e r e f e r s t o t h e o n e F o r m o v e r m a n y a t 5 9 6 a 5 - b l o . T h e r e i s

a l s o t h e s a m e i d e n t i f ic a t io n b e t w e e n t h e o n e F o r m o f f o v e r m a n y a n d t h a t

w h i c h is f i n B o o k 6 ( 5 o 7 a 6 - b l o ) - - a p a s s a g e w i t h s t r ik i n g s im i la r it ie s to

5 9 6 a 5 - b l o a n d 5 9 7 a l - 2 .

W e p r e d i c a te ' to b e ' o f m a n y b e a u t if u l t h i n g s a n d m a n y g o o d t h in g s , s ay i n g o f th e m

s e v e r a l l y t h a t t h e y are a n d s o d e f in e t h e m in o u r s p e e c h . . . A n d a g a in , w e s p e ak o f a

s e l f -b e a u t i f u l a n d o f a g o o d t h a t is o n l y a n d m e r e l y g o o d , a n d s o , i n t h e c as e o f all

t h e t h i n g s t h a t w e t h e n p o s i t e d a s m a n y , w e t u r n a b o u t a n d p o s i t e a c h a s a s i n g le id e a

o r a s p e c t , a s s u m i n g i t t o b e a u n i t y a n d c al l i t t h a t w h i c h e a c h r e al ly i s . . . A n d t h e

o n e c la s s o f t h i n g s w e s a y c a n b e s e e n b u t n o t t h o u g h t , w h i l e th e i d e a s c a n b e t h o u g h t

bu t no t seen .~

P u t t i n g t h e s e t w o a s s u m p t i o n s i n t o t h e c a l c u l a t i o n w e o b t a i n :

( I ) I f h e m a d e a s f e w a s t w o ( s u c h t h i n g s ),

us ing an am biguo us ph rase one of whose meanings--- in fact , the more obviou s-- i s the very

opposi te o f what h e m eant . C herniss a l so argues tha t the Form o f bed i s the charac ter of bed;

but i t i s unclear whether he i s a l so denying a l together tha t the Form is a bed because his

asser tion of the d enia l i s so guar ded (296 -97) .

1 Plato: The Republic

t ranslated b y Paul Shore y (Cambridge: H arv ard Universi ty Press,

1935), 2: 97.


9/19

14o

x ) a )

b )

2 ) a )

J O U R N L O F T H E H I ST O R Y O F PH I L O SO P H Y

([i] given that we are accustomed to positing some one Form for

each group of many) again a one (bed in nature) would appear

([ii] given tha t if anything is a bed besides that which is bed then it

has the form of bed only through participation in that which is

bed. And [iii] given that the one Form over many is that which is

bed) the two would have the form of the one,

this one would be that which is bed and (b) not the two.

The logic of the ar gum ent at 5 97 cl -d 3 should be clear so far. Ther e is

one outstanding question, however. Why are the two not that which is bed,

i.e., what explains (2b)? (ii) answers this question. I f that which is bed is the

primary bed from which all other beds derive their form or character then

neither of the two beds can be that which is bed, as we can see from the

following arg ument.

Let us suppose two cases, modelled on the two cases of the calculation. In

one case, X is the f itself from which all other f's derive their form. Of X it is

true to say that if anything is f besides X it is f only through participation in

X. Let us suppose another case in which there are two duplicate items like X

insofar as possible. We label these items Y and Z. They stand in the same

relations--i.e., if Y stands in any relation R so does Z, and vice versa; thus

both are pr eten der s to the title the f itself from which all other f's derive

their form. Th en either (a) Y and all othe r f's derive their form only by

participation in Z and Z and all the other f's derive their form only by

participation Y; or (b) Y does not derive its form only by participation in Z

and Z does not derive its form only by participation in Y.

If (a) is true, then neither Y nor Z will be f's only by participating in the

other, cont rary to hypothesis. Und er (a), both of the following would be

true: (1) if anything is f besides Y it is f only by participation in Y; (2) if

anything is f besides Z it is f only by participation in Z. Th e anything in (1)

covers Z; thus Z is f only th rough participat ion in Y. In turn, any thing in

(2) covers Y and thus Y is f only through participation in-Z. However,

mutual participation, under the conditions of (ii), is ontological bankruptcy.

Compare: if Jones has money on y by borrowing from Smith and Smith has

money on y by borrowing from Jones, then neither could earn, steal, inherit,

and so on. Nor could either have any originally. But then, if neithe r has any

originally, earns any, etc., neither can borrow from the other. Consequently,

neither has any money. If Y and Z are both f only by participation in the

other, then neither is f only by participation in the other.

If (b) is true the n nei ther Y nor Z is the f itself from which all other f's

derive their form or character. Y does not derive its form from Z and vice

versa. Thus, neither of the following will be true: (l) if anything is f besides


10/19

TH E UNIQUENESS PROOF 141

Y i t is f o n l y t h r o u g h p a r t i c i p a t i o n i n Y a n d ( 2) i f a n y t h i n g i s f b e s i d e s Z i t is

f o n l y t h r o u g h p a r t i c ip a t i o n i n Z . T h u s t h e a r g u m e n t m i g h t b e s u m m a r i z e d :

Y a n d Z c a n n o t b o t h b e t h e p r i m a r y f f r o m w h i c h al l o t h e r f 's d e r i v e t h e i r

c h a r a c t e r ; s i nc e Y a n d Z a r e d u p l i c a t e s , n e i t h e r c a n b e t h e p r i m a r y f . S o b y

(ii) n e i t h e r o f t h e t w o b e d s c a n b e t h e p r i m a r y b e d f r o m w h i c h a ll o t h e r b e d s

d e r i v e t h e i r c h a r a c t e r . B y ( iii) , n e i t h e r c a n b e t h e o n e F o r m o v e r m a n y a n d

t h i s t i t l e g o e s t o a t h i r d .

F i n a l ly , i t is c l e a r t h a t P l a t o t h o u g h t t h a t n e i t h e r o f t h e t w o b e d s is t h e

F o r m o f b e d a n d t h a t s o m e h o w t h e i r d u p l i c a ti o n d is q ua l i fi es t h e m f r o m

b e i n g t h e F o r m o f b e d . (ii) g i v e s a r e a s o n f o r th i s d i s q u a l i f i c a t io n w h i c h

d e p e n d s o n t h e d u p l i c a t i o n . I n f a ct , t h i s a r g u m e n t b e a r s m a n y s t r ik i n g p a r-

a ll el s t o t h e a r g u m e n t a t T i m a e u s 3 o c l - 3 1 b 3 . T h e r e t h e F o r m o f t h e I n te l l i-

g i bl e A n i m a l w h i c h e m b r a c e s a ll o t h e r I n t e ll i g ib l e A n i m a l s is s ai d t o b e

u n i q u e b e c a u s e t h e r e c o u l d n o t b e tw o su c h t h in g s . O n l y o n e F o r m c a n

i n c l u d e a ll t h e o t h e r s . '~ I n t h e R e p u b l i c , t h e F o r m o f b e d i s n o t , o f c o u r s e , al l

i n cl u si v e; b u t i t d o e s s t a n d i n a u n i q u e r e l a t i o n t o a ll o t h e r b e d s . B y u n i q u e

is m e a n t a o n e - m a n y r e l a t i o n s u c h t h a t o n l y o n e t h i n g c a n b e t h e o n e - - -e . g .,

t h e l a r g e s t t o m a t o i n G e o r g i a . J u s t a s t h e I n t e ll i g ib l e A n i m a l w h i c h e m b r a c e s

a ll o t h e r I n t e l li g i b le A n i m a l s s t a n d s i n s u c h a u n i q u e r e l a t i o n t o al l o t h e r

I n t el l ig i b le A n i m a l s , s o th e F o r m o f b e d f r o m w h i c h all o t h e r b e d s d e r i v e

t h e i r c h a r a c t e r s t a n d s i n a u n i q u e r e l a t i o n t o a ll o t h e r b e d s . I n b o t h c a se s,

o n l y o n e s u c h t h i n g c a n h o l d t h e s u p e r o r d i n a t e p o s it io n .

2

T h i s i n t e r p r e t a t i o n d i f f e r s i n i m p o r t a n t r e s p e c t s f r o m t h o s e g i v en b y a

g r o u p o f c o n t e m p o r a r y c o m m e n t a t o r s . T h e s e c o m m e n t a t o r s ca n b e i de n ti -

f ie d b y th e f a c t t h a t t h e y r e a d t h e a r g u m e n t a t R e p u b l i c l o i n t h e l i g h t o f t h e

i n fi n it e r e g r e s s a r g u m e n t a t P a r m e n i d e s 1 3 2 a l - b 2 , a s t h a t a r g u m e n t h a s

b e e n a n a l y z e d b y G r e g o r y V l a st o s i n h is a r t ic le s T h e T h i r d M a n A r g u m e n t

i n t h e

P a r m e n i d e s

a n d P la to 's ' T h i r d M a n ' A r g u m e n t

( P a r m .

1 3 2 a x - b g ) :

T e x t a n d L o g i c ( T M A I I ) ? s S u c h c o m m e n t a t o r s , w h i l e n o t al wa ys a g r e e i n g

w i t h V l as t o s in d e ta i ls , d o i m p o r t i s su e s s u r r o u n d i n g V l a st o s' s t r e a t m e n t o f

,2 Cf. my Th e Unique World of the Timaeus 'Journal of the His tory of Philosophy 17 097 9):

X-lO. Cf. A. Nehamas, Self-Predication and Plato's Th eor y of Forms American Philosophical

Quarterly 16 0979): 97-98.

'~ Gregory Vlastos, Th e Th ird M an Argument in the Parmenides , S tudies in Plato 's Meta-

physics,

R. E. A llen, ed. (London: Routledge & Ke gan Paul, 1965): 231-63; Gregory Vlastos,

Pla to 's 'Third Man' Argument ( P a r m . 132Ax-B2); Text and Logic, in his Platonic Studies,

(Princeton: Princeton University Press, 1973), 342-65. Th e latter will be h ereafter refe rred to

as T M A H .


11/19

4 2 J O U R N A L O F T H E H I ST O R Y O F PH I L O SO P H Y

the TMA and some of the assumptions---or versions of those assumptions--

he in troduce d. 14 In conse quenc e most think that the ar gum ent at

R e p u b l i c

lO

is at least liable to becoming an infinite regress in the way that TMA does.

We will consider these interpretations in this section. Doing so will help us to

see that the TBA, according to our interpretation, is not liable to an infinite

regress.

It will be recalled that Vlastos adds to the text of the argument in the

P a r m e n i d e s

two assumptions: (SP) Self Predication Assumption: Any Form

can be predicated by itself and (NI) Non- Iden tity Assumption: If anythi ng

has a certain character, it cannot be identical with the Form in virtue of

which we ap pr eh en d that character. ' ' '5 From these as sumptions and the

premises in the text, Vlastos derives the infinite regress which is the conclu-

sion of the TMA.

Using these assumptions in the TBA, one could reason (a) that the two

Forms of bed are beds (SP) and (b) that neither can be that by which they are

ap pr eh en de d as beds (NI). Thus , there must be a third bed. However, if SP

and NI are assumed in the TBA then it too generates, in the by now familiar

fashion, an infinite regress o f Forms of bed.

First of all, what we wish to show is that NI, in its various formulations, is

not appropriate in

R e p u b l i c

lO, 59 7c l- d 3. If NI is not approp riat e then the

TBA is not liable to an infinite regress generated by NI. Second, we wish to

show that without NI, or some equivalent principle, the TBA cannot be

tu rne d into an infinite regress at all. Thus, we concl ude that the TB A is not

liable to an infinite regress.

The reason given by Vlastos for introducing NI in the TBA is that with-

out it we can not explain why on e of the two beds is not the one ov er many. '6

But we h ave seen that NI is not n ee de d to do this; (ii) is sufficient. More -

over, in the context of the argument at the beginning of R e p u b l i c l o , (ii) is

pre fe rab le to NI. First of all, (ii) occu rs in the mid dle dial ogues in an explicit

fashion; NI does not. Second, as we have seen the two beds are disqualified

,4 K. W. Mills applies P. T. Geach's analysis of the TMA to this argument. Geach's analysis

is an answer to Vlastos's first article on the TMA. While Mills does not say that the argument in

Republ ic lo is doomed to an infinite regress, he does import into his analysis of the argument

enough of Geach's analysis of the TMA to make an infinite regress possible. Cf. Duff-Forbes,

The Regress Argument ; Nerlich Regress Arguments ; Mills, Crombie on Republic ; Strang,

Plato and the Third Man ; and S. Marc Cohen, The Logic of the Third Man, Philosophical

Rev iew 8o 097 l): 448-75, especially 469-71.

,5 Vlastos, The Third Man Argument, 236-37; the subsequent modifications of these

assumptions made in T M A H do not affect the points being made here.

,6 Vlastos, The Third Man Argument, 263. We also agree with Bluck in denying the

universality of NI in Plato's theory of Forms, referred to by Vlastos in this passage.


12/19

TH UNIQU N SS PROOF 43

f r o m b e i n g t h e F o r m o f b e d b e c a u s e t h e y a r e d u p l i c a te s . ( ii) g iv e s a r e a s o n

f o r t h i s d i s q u a l i f i c a t i o n w h i c h d e p e n d s s p e c if i c al ly o n t h e d u p l i c a t i o n ; i t is

b e c a u s e t h e r e a r e t w o o f t h e s e t h i n g s t h a t n e i t h e r c a n b e t h e f i ts e lf f r o m

w h i c h a ll o t h e r f 's d e r i v e t h e i r c h a r a c t e r . B u t N I w o r k s i ts d i s q u a li f ic a t io n

w i t h o u t s p e ci fi c r e f e r e n c e t o d u p l i c a t i o n ; t h e t w o a r e d is q u a l if i e d b y N I

b e c a u s e t h e y a r e b e d s , n o t b e c a u s e t h e y a r e d u p l i c a t e s . T h i r d , N I d o e s n o t

e x p l a i n ( l b ) - - i . e . , t h a t t h e t w o b e d s h a v e t h e f o r m o r c h a r a c t e r o f th a t o n e

w h i c h a p p e a r s . N I a s s u m e s t h a t t h e y b o t h h a v e t h e c h a r a c te r ; t h e n i t o n l y

e x p l a i n s w h y t h e t w o a r e n o t t h e o n e w h i c h a r i s e s - - ( 2 b ) . I n f a c t, u s i n g S P ,

N I , a n d O M , ( ~b ) b e c o m e s o ti o se ; t h e T B A o u g h t t o r e a d : i f t h e g o d m a d e

t w o su c h t h i n g s ( t h e y w o u l d b o t h b e b e d s - - S P ) , a g a i n a o n e w o u l d a p p e a r - -

O M . T h e t w o a r e n o t t h a t w h i c h is b e d - - N I ; t h e o n e is t h a t w h i c h is b e d .

( l b ) i s l e ft o u t a l t o g e t h e r . I f w e i n c l u d e it , w e n e e d s o m e f u r t h e r a s s u m p t i o n

t o e x p l a i n w h y t h e t w o b e d s h a v e a r e l a t io n t o t h e o n e w h i c h a p p e a r s s u c h

t h a t t h e y h a v e i t s f o r m o r c h a r a c t e r .

T h e i m p o r t a n t d i f f e r e n c e b e t w e e n (ii) a n d N I is t h a t t h e f o r m e r d o e s n o t

r e q u i r e a F o r m t o p a r t i c ip a t e i n a n o t h e r F o r m i n o r d e r t o b e f b u t t h e l a t t e r

d o e s. T h e d i f f e r e n c e i m p l i e s t h a t t h e T B A a v o id s a n i n fi n it e r e g r es s o f

F o r m s , W e c a n s e e th i s c o n s e q u e n c e o f a s s u m i n g (ii) i n s t e a d o f N I i f w e t ry

t o g e n e r a t e a n i n f in i te r e g re s s f r o m t h e T B A , u n d e r o u r i n t e r p r e t a t io n . I f

w e a p p l y O M t o t h e g r o u p c o n s is t in g o f th e t w o b e d s a n d t h e F o r m , w e sh al l

p o s it a o n e f o r t h i s n e w g r o u p . A n i n f in i t e r e g r e s s s e e m s j u s t t o a b o u t to

s ta r t. B u t b e f o r e w e s e t o f f o n t h is r e g r e s s , w e m u s t a sk , in s p i r e d b y V la s to s ,

w h e t h e r t h e o n e p o s i te d f o r t h e n e w g r o u p is t h e s a m e as t h e t h i r d b e d o r

w h e t h e r i t is d i f f e r e n t f r o m t h e t h i r d , i . e. , is i t a f o u r t h b e d ? I f t h e y a r e n o t

d i f f e r e n t , t h e r e i s n o i n f i n i t e r e g r e s s .

B u t n o n e o f o u r a s s u m p t i o n s f o r ce s u s t o s ay t h a t t h e o n e F o r m p o s i te d

f o r t h e n e w g r o u p , c o n s t i t u t e d b y th e t h i r d b e d a n d t h e tw o , is d i f f e r e n t

f r o m t h e t h i r d b e d . B y c o n t r a s t w i t h th e w a y N I g e n e r a t e s a n i n fi n it e n u m -

b e r o f F o r m s , t h e T B A g e n e r a t e s o n l y t h e t h i r d b e d . F i r s t o f a ll , (ii) a n d ( iii)

d o n o t r e q u i r e a s e p a ra t e , f o u r t h b e d i n w h i c h t h e th i r d b e d m u s t p a r t i c ip a t e

i n o r d e r t o b e a b e d s i n c e ( iii) s a ys t h a t t h e t h i r d b e d i s t h a t w h i c h is b e d a n d

(ii) e x p li c it ly e x e m p t s t h a t w h i c h is b e d f r o m h a v i n g t o p a r t i c i p a t e in a F o r m

o f b e d i n o r d e r t o b e a b e d . S e c o n d , (ii) a n d (ii) w o u l d r e q u i r e a s e p a r a t e ,

f o u r t h F o r m o f b e d o n l y if t h e t h i rd b e d w e r e a d u p li c a te . I f t h e r e w e r e

a n o t h e r F o r m o f b e d e x a c tl y l ik e t h e t h i r d b e d n e i t h e r c o u l d b e t h a t w h ic h is

b e d . B u t o u r h y p o t h e t i c a l c as e d o e s n o t e n v i s i o n a d u p l i c a t e f o r t h e t h i r d

b e d . T h u s , w i t h o u t s o m e f u r t h e r a s s u m p t i o n t o d i f f e r e n t i a t e t h e t h i r d a n d

f o u r t h b e d s , (ii) a n d (iii) d o n o t s h o w th e f o u r t h b e d p o s i t e d b y O M is

d i f f e r e n t f r o m t h e t h i rd b e d .

O f c o u r s e , o n e m i g h t o b j e c t t h a t O M b y it se l f- -- i. e ., (i ) -- i s s u f f ic i e n t t o


13/19

44 JOURNAL OF THE HISTORY OF PHILOSOPHY

g e n e r a t e a n i n fi n it e r e g r e s s . O n e m i g h t c l a i m t h a t, a c c o r d i n g t o O M , t h e

o n e is a l w a y s a d i f f e r e n t e n t i t y f r o m e a c h o f t h e m a n y . ~7 T h i s p o s i t i o n

w o u l d i m p l y t h a t n o m a t t e r w h a t k i n d o f t h in g s c o n st i tu t e th e m a n y - - - e v e n

i f i t c o n t a i n e d a F o r m o f f a s w e ll a s f t h i n g s - - t h e o n e F o r m p o s i t e d b y

O M w o u l d h a v e t o b e d i s ti n c t f r o m t h a t o r ig i n a l F o r m . I t w o u l d b e h a r d t o

i m p r o v e o n V l a s to s 's c o u n t e r a r g u m e n t t o t h i s c l a i m in t h e c o n t e x t o f t h e

T M A . ' s I n w h a t f o l lo w s w e w il l a r g u e t h a t , i n th e r e l e v a n t p a s s a g e s o f

B o o k s 6 a n d 1 o, O M b y i t s e lf is n o t s u f f i c i e n t t o g e n e r a t e a n i n f i n it e

r e g r e s s .

N e i t h e r i n B o o k 6 n o r l o d o e s O M s a y t h a t t h e F o r m is a n e n ti t y d i s t in c t

f r o m e a c h o f t h e m a n y n o m a t t e r w h a t k i n d o f t h in g s c o ns t i t u te t h e m a n y . I t

is c l e a r f r o m 5 o 7 b 1 - 1 o , f o r i n s t a n c e , t h a t t h e e n v i s i o n e d c a se o f a p p l i c a t i o n

o f O M is w i t h a g r o u p o f p e r c e p t u a l p a r t i c u l a r s a n d t h a t th e o n e is d i s t in c t

f r o m t h e m a n y b e c a u s e i t is a d i f f e r e n t k i n d o f e n t it y f r o m t h e p a r t ic u l a r s ;

t h e F o r m is i n te l ]i g ib l e a n d t h e m a n y p e r c e p t u a l . I n B o o k 1o a s w e l l , t h e o n e

is a n i n te l li g ib l e e n t i t y a n d t h e m a n y a r e p e r c e p t u a l . I n b o t h c a se s , t h e F o r m

is s a id t o b e a n o n t o l o g i c a l l y d i f f e r e n t k i n d o f t h i n g f r o m p a r t ic u l a r s . T h e

i m p l i c a t i o n is t h a t , in t h e s e c o n t e x t s , o n e a n d m a n y a r e d is t in c t b e c a u s e o f

t h i s o n t o l o g i c a l d i f f e r e n c e .

S i m p l y b e c a u s e t h e o n e i s a l w a y s o n t o l og i c a ll y d i f f e r e n t i n k i n d f r o m

s e n si b le p a r t i c u l a r s , w e c a n n o t c o n c l u d e t h a t, w h e n t h e m a n y i n cl u d e s b o t h

t h e F o r m o f f a n d f s e n s i b l e p a r t i c u l a r s , t h e o n e i s d i s ti n c t f r o m e a c h o f t h e

m a n y , i n c l u d i n g t h e F o r m o f f. C o n s i d e r t h e fo l lo w i n g . A t R e p . 5 9 7 c l - d 3

t h e O M p o s i t s s o m e o n e F o r m o f b e d f o r t h e t w o b e d s. A c c o r d i n g t o R e p .

5 9 7 a l - 2 t h is F o r m is t h a t w h i c h is b e d - - i . e . , t h e F o r m o f b e d . T h e n , i n o u r

h y p o t h e t i c a l c a s e , w e m a y g r o u p t h i s F o r m w i t h t h e t w o b e d s . B y O M , a g a i n

w e m a y p o s i t s o m e o n e F o r m o f b e d f o r th is n e w g r o u p . A g a i n , a c c o r d i n g t o

R e p . 5 9 7 a a - 2 , t h e F o r m w e j u s t p o s i t e d is t h a t w h i c h is b e d - - i . e . , t h e F o r m

o f b ed . N o w w e h a v e u s e d t h e s a m e d e f i n i te d e s c r i p t i o n t o i ' e f e r t o w h a t w e

p o s i t e d i n t h e t w o c a s e s. H o w d o w e k n o w t h a t w h a t w e p o s i t e d i n t h e f ir s t

c a se is d i f f e r e n t f r o m w h a t w e p o s i t e d i n th e se c o n d ? N o t h i n g i n t h e f o r m u -

l a ti o ns o f O M a t 5 o 7 b 1 - 1 o a n d a t 5 9 6 a 5 - 8 te lls u s h o w t o a n s w e r th is

,7 Cf. Hen ry Teloh and David Jam es Louzecky, Plato 's Th ird M an Argument, Phronesis

17 097 2): 87- 88. T he autho rs incorporate nonidentity into a version of the OM ; they claim

that the TM A could not get started without incorporating nonidentity. Cf. Bestor, Plato's

semantics, 73- 74 , n ote 12. How ever, the passages from the

Republic

do not require anything as

sweeping as nonidentity to be incorporated into OM.

,8 See Vlastos, Th e Thi rd M an Arg um ent, ~38, where he says that without NI there

i s . . . nothin g to keep us fro m saying that they (a, b, c, and F-ness) are all app reh end ed as F in

virtue of F-ness itself. Cf.

T M A H

in

Platonic Studies

35 L


14/19

T H E U N I Q U E N E S S P R O O F 1 4 5

q u e s t io n . I n th e s e tw o f o r m u l a t i o n s , t h e d i f f e r e n c e b e t w e e n o n e a n d m a n y

d e p e n d s o n a d i f f e r e n c e i n k i n d ; b u t w e a r e n o t n o w d e a l in g w i th th e

d i f f e r e n c e b e t w e e n i n t e l l i g i b l e s a n d p a r t i c u l a r s .

I n f a c t , a t R e p . 5 o 7 b 1 - 1 o a n d 5 9 6 a 5 - 8 , w h a t te ll s u s h o w t o d i s t i n g u i sh

o n e f r o m m a n y is t h e c o n t e x t w h e r e t h e c o n c e r n is w i th t he d i f f e r e n c e

b e t w e e n i n te l li g ib l es a n d s e n s ib l es . A n d i t is t h e c a r e f u l l y c o n t r i v e d c o n t e x t

o f t h e T M A w h i c h m a k e s i t p l au s i b l e t o a p p l y O M t o a g r o u p c o n s i s t in g o f

F o r m a n d p a r t i c u l a r s . E v e n t h e n , i n o r d e r t o po s i t a s e p a r a t e F o r m f o r th is

g r o u p i t is n e c e s s a r y t o a s s u m e N I . U n d u e f ix a t i o n o n t h e n o t i o n t h a t th e

T M A is a u n i v e r s a l a r g u m e n t c a n m a k e u s o v e r l o o k t h e f u n c t i o n o f i t s

c o n t e x t i n g u i d i n g t h e a p p l i c a t i o n o f O M . T h e p r o b l e m w i th o u r h y p o t h e t i -

c a l c a s e is t h a t t h e r e is n o c o n t e x t t o h e l p u s t o se e w h a t is t h e n a t u r e o f th e

d i f f e r e n c e b e t w e e n o n e a n d m a n y . A s s u m i n g N I i n th is c as e w o u l d p r o v i d e

c o n t e x t . B u t t o d o s o w e p r o b a b l y w o u l d d r o p t h e c o n t e x t u a l d i s ti n c t i o n

b e t w e e n o n e a n d m a n y w h i c h d e p e n d s o n t h e d i f f e r e n c e b e t w e e n i n t el li g i bl e

a n d p a r t i c u l a r a n d s u b s t i t u t e t h e d i s t i n c t i o n i n t r o d u c e d b y N I . M i x i n g t h e

t w o d i s t i n c t i o n s , b a s e d a s t h e y a r e o n v e r y d i f f e r e n t p r i n c i p l es , c o u l d l e a d to

l o g i c a l i m p r o p r i e t y .

T h e p o i n t is , h o w e v e r , t h a t O M b y i ts e lf ( w e a r e a c c u s t o m e d t o p o s i t i n g

s o m e o n e F o r m f o r e a c h m a n y ) d o e s n o t i m p l y a n y t h i n g a b o u t t h e s t at us o f

t h e o n e . '9 W e m u s t d e p e n d o n t h e c o n t e x t t o te ll u s a b o u t t h is s ta tu s . O n e

c a n n o t w i t h O M a l o n e g e n e r a t e a n i n f in i te r e g r e s s . A n d w e h a v e s e e n t h a t

O M - - i . e . , ( i )- - (i i ) , a n d (iii) d o n o t g e n e r a t e a n i n f i n it e r e g r e s s . T h u s , t h e

T B A , u n d e r o u r i n t e r p r e t a t i o n , is n o t l ia b l e to b e c o m i n g a n in f in i t e r e g r e ss .

T h e p r e s e n t i n t e r p r e t a t i o n c al l s i n t o q u e s t i o n t h e in f l u e n t ia l c la i m th a t t h e

t h e o r y o f F o r m s i n t h e m i d d l e d i a l o g u e s i s b a s ic a ll y f l aw e d . V l a s t o s 's i n te r -

p r e t a t i o n h a s i t t h a t t h e in f i n i t e r e g r e s s o f t h e T M A i n t h e

P a r m e n i d e s

( 1 3 2 a l - b 2 ) r e v e a l s a d e e p a n d s e r io u s p r o b l e m b e c a u s e t h e c o r r e c t a n a l ys i s

s h o w s P l a t o c o m m i t t e d t o b o t h N I a n d S P . H o w e v e r , i f o u r i n t e r p r e t a t i o n i s

c o r re c t , P l a to d o e s n o t u se N I i n t h e T h i r d B e d A r g u m e n t o f

R e p u b l i c l o .

S i n c e R e p u b l i c lO c o n t a i n s a l l t h e o t h e r e l e m e n t s o f t h e t h e o r y o f F o r m s i n

,9 Ind eed , Fine arg ues th at OM nev er posi ts an ontological ly separate o ne but only a

univo~a

lis in rebus. Gai l Fine, Th e One Over Many, Philosophical Review 89

1980):

197-94o . On page

235 we read I t is t empt ing to infer tha t Plato uses hi s one over many assumpt ion only where

non-sepa ra t ed forms a re i n v i ew; once sepa ra ted forms a re i n t roduced , t he one ove r many i s

quiet ly replaced . . . . Th e pres ent interpre ta t ion o f 59 7c l -d 3 cont radic ts this c la im as does the

passage at 5o 7b 5- 1o . I t is no t so clear, however, that ei ther contradicts the claim that OM by itself

does no t w arra nt the p osi t ing a Fo rm w hich is separate. Cf. Fine 's t reatm ent o f the passages in

Rep. 596a f f and 59 7a - b (236-4o) . She does no t deal wi th t he a rgum ent a t 597c l -d3 .


15/19

1 4 6

JOURN L OF TI IE HISTORY OF PHILOSOP HY

t h e m i d d l e d i a l o g u e s b u t d e p e n d s u p o n (ii) r a t h e r t h a n N I , i t w o u l d a p p e a r

t h a t t h e t h e o r y i s n o t b a s e d , a t l e a s t i n a l l i t s i n s t a n c e s , u p o n N I . S i n c e N I

r e q u i r e s t h e F o r m o f f t o p a rt i c ip a t e i n a n o t h e r F o r m i n o r d e r t o b e f a n d

(ii) d o e s n o t s o r e q u i r e , w e c a n c o n c l u d e a t l e a st t h a t t h e t h e o r y d o e s n o t , in

a ll o f i ts i n s ta n c e s , d e p e n d o n t h e F o r m o f f p a r t i c i p a t i n g in a n o t h e r F o r m i n

o r d e r t o b e f . I n f a c t , i n w h a t f o l l o w s w e s h a ll a r g u e t h a t P l a t o is n o t

c o m m i t t e d t o N I e v e n i n t h e T M A . B u t f ir st w e w ill s h o w t h a t N I is n o t

p e r v a s i v e i n t h e t h e o r y o f F o r m s b y c o n s i d e r i n g V l a st o s's c la i m i n b o t h o f h is

a r t i c l e s o n t h e T M A .

V l a st o s a r g u e d i n hi s fi rs t a n a ly s is o f th e a r g u m e n t t h a t t h e T M A is a

' r e c o r d o f h o n e s t p e r p l e x i t y ' - - a n e x p r e s s i o n o f p h i lo s o p h ic a l p u z z l e m e n t

d u e t o th e f a i l u r e t o id e n t i f y t h e t a c it a s s u m p t i o n s w h i c h e n t e r e d i n t o th e

p r e m i s e s o f th is a n d o t h e r o b j e c t i o n s m a r s h a l l e d i n t h e

Parmenides

a g a i n s t

t h e t h e o r y o f I d e a s . ''~ ~ P l a t o , i t is t h o u g h t , w a s f a c e d i n t h e T M A w i t h t h e

e f f e c t s o f a n i n c o m p a t i b l e s e t o f a s s u m p t i o n s i n hi s t h e o r y o f F o r m s in th e

m i d d l e d i a l o g u e s . I n p a r t i c u l a r , t h e s e p a r a t i o n b e t w e e n F o r m s a n d p a r t i c u -

la rs , o n t h e o n e h a n d , a n d t h e s e lf - p r e d ic a t i o n o f F o rm s , o n t h e o t h e r , a r e - -

w h e n t h e i r i m p l i c a t io n s a r e e x p o s e d - - i n c o n s i s t e n t . ~' I n t h e w a k e o f th i s

a c c o u n t , w e a r e l e f t t o s u p p o s e t h a t e i t h e r P l a t o d i d n o t s e e t h e i n c o n s i s t e n c y

a n d c o n t i n u e d t o m u d d l e t h r o u g h o r h e d id s ee t h e in c o n s is t en c y a n d c o u r a -

g e o u s ly g a v e u p o n e o f t he s u p p o r t s o f h is m i d d l e d i a l o g u e t h e o r y - -

a l t h o u g h w e c o n t i n u e t o f in d v e s ti g es o f b o t h p a r t s o f th is t h e o r y i n P l a to ' s

l a t e r t e c h n i c a l v o c a b u l a r y .

I n

T MA H

V l a s to s r e v i s e s s o m e o f th e s t e p s a n d a s s u m p t i o n s o f hi s

e a r l i e r a n a ly s is i n o r d e r t o ta k e i n t o a c c o u n t s o m e o f t h e c ri ti ci sm s . T h e

f o l l o w i n g a r e t h e n e w f o r m u l a t i o n s : ( 1) I f a n y s et o f t h i n g s s h a r e a g i v e n

c h a r a c t e r t h e n t h e r e e x is ts a u n i q u e F o r m c o r r e s p o n d i n g t o t h a t c h a r a c t e r ;

a n d e a c h o f t h e s e t h i n g s h a s t h a t c h a r a c t e r b y p a r t i c i p a t i n g i n t h a t F o r m . ''22

( T h e l a t t e r , o f c o u r s e , is a v e r s i o n o f O M . ) S P is e f f e c t i v e l y t h e s a m e . N I

r e a d s : I f a n y t h i n g h a s a g i v e n c h a r a c t e r b y p a r t i c i p a t in g i n a F o r m , it is n o t

i d e n t i c a l w i t h t h a t F o r m . ''~3 ( I n w h a t f o ll o w s , ' N I ' w i ll s t a n d f o r t h i s v e r s i o n . )

T h e s e s t ep s i m p l y t h a t L a r g e n e s s p a r t i c ip a t e s in L a rg e n e s sH ; i n t u r n , t h is

r e s u l t c o n t r a d i c t s (~ ) s i n c e i t s a y s t h a t t h e r e i s m o r e t h a n o n e F o r m f o r l a r g e .

( 1), SP , a n d N I a r e a n i n c o n s i s t e n t t r i a d ; S P a n d N I a r e n o l o n g e r i n co n s is -

t e n t b y t h e m s e l v e s .

I n t h i s v e r s i o n ( 1 ) i s s o m e w h a t d i f f e r e n t f r o m i t s o r i g i n a l v e r s i o n . O f

~~ Vlastos, TM A II, 343-

~ Vlastos, T he Th ird Man Argument, 253-54.

~ V lastos, TMA II, 348.

3 Ibid.

351.


16/19

TH UNIQU N SS PROOF

1 4 7

s p e c i a l n o t e is th a t i t is n o w a u n i v e r s a l p r o p o s i t i o n d e s i g n e d t o a p p l y t o

F o r m s a s w e l l a s p a r t i c u l a r s . V l a s t o s a r g u e s t h a t 1 3 e a 2

( h o t a n p o l l a t t a m e g a l a

s o i d o x e i e i n a i )

w h e n t h e r e is a n u m b e r o f th i n gs w h i c h s e e m t o y o u t o b e

g r e a t T is a u n i v e r s a l c l a i m , m e a n t t o c o v e r a ll c a s es , i n c l u d i n g t h o s e i n

w h i c h a F o r m is a m o n g t h e l a r g e t h i n g s /5 H e a d m i ts t h a t t h e s e c o n d p a r t o f

( 1) . . . a n d e a c h o f t h e s e t h i n g s h a s th a t c h a r a c t e r b y p a r t i c i p a t io n i n t h a t

F o r m , h a s n o e x p l i c i t l y t e x t u a l w a r r a n t . ~6 O f c o u r s e , i t is p a r t o f t h e e a r l i e r

c o n t e x t o f th e a r g u m e n t t h a t p a r t i c u l a r s p a r ta k e o f F o r m s ( 1 3 o e 5 - 1 3 1 a t ) ;

b u t i n fa c t ~ 3 2 a 2 - 4 d o e s n o t m e n t i o n p a r t ic i p a t i o n . F u r t h e r o n , h o w e v e r , a t

1 3 9 a 7 - 8

( h O i t a u t a p a n t a m e g a l a p h a i n e s th a i )

a n d a t 1 3 ' ) b l

( h 6 i t a u t a p a n t a

m e g a l a e s t a i )

w e f in d p h r a s e s w h i c h s e e m t o i m p l y p a r t ic i p a t i o n . I n o r d e r t o

e x p l a i n h o w t h e s e p h r a s e s a p p l y t o F o r m a n d p a r t i c u l a r , t h u s m a k i n g t h e

r e g r e s s p o s s ib l e , it is a s s u m e d t h a t t h e m a n y p a r t i c i p a t e i n th e o n e a n d t h a t,

i f t h e m a n y c o n t a i n a F o r m , t h a t F o r m w o u l d p a r t ic i p a t e in t h e F o r m o v e r

t h a t m a n y , i .e ., (a ) a ll f 's p a r t i c i p a t e i n a u n i q u e F o r m w h i c h c o r r e s p o n d s t o f

( e v e n w h e n t h e f is t h e F o r m o f f ) . T h i s l a t t e r is, o f c o u r s e , r e a ll y t h e s e c o n d

p a r t o f ( 1 ). B u t t h e p o i n t is t h a t ( a) is a n a s s u m p t i o n a n d n o t p a r t o f t h e t e x t.

( l ) - - m i n u s ( a ) - - S P , a n d N I a r e n o t i n c o n si s te n t a n d d o n o t g e n e r a t e a n

i n f in i t e r e g r e s s , w h e r e a s ( a) , S P , a n d N I d o g e n e r a t e t h e r e g r e s s . B u t w h a t is

i m p o r t a n t is th a t w e h a v e f o u n d i n (a ) t h e r e a l c u l p r i t i n th e c a se o f t h e

h o n e s t p e r p l e x i t y . ( a ) a s s e r t s t h a t a l l f ' s p a r t i c i p a t e i n a F o r m ; w e c a n c a l l t h i s

a s s e r t io n t h e u n i v e r s a l i t y o f p a r t i c i p a t i o n . W h e n t h e F o r m o f f is i n q u e s t i o n

( a ) r e q u i r e s t h a t t h e F o r m p a r t i c i p a t e i n a n o t h e r F o r m o r i n i t s e l f . N I c l o s e s

t h e p o s s i b i l i t y o f p a r t i c i p a t i o n i n i t s e l f ; t h u s t h e F o r m i s r e q u i r e d t o p a r t i c i -

p a t e i n a n o t h e r . B u t g i v e n t h e w a y N I i s n o w f o r m u l a t e d , e v e r y t h i n g t u rn s

o n ( a ) i i . e . , t h e u n i v e r s a l i t y o f p a r t i c i p a t i o n . W i t h o u t (a ), N I d o e s n o t a p p l y

t o F o r m s ; t h e n F o r m s d o n o t h a v e t o p a r ti c i p a t e in a F o r m t o b e f. M o r e -

o v e r , w h e n w e c o n t r a s t ( a ) w i t h ( i i ) w e r e c a l l t h a t ( i i ) d o e s n o t r e q u i r e t h e

F o r m t o p a r t i c i p a t e i n a n y t h i n g , i n c l u d i n g i t s e l f , i n o r d e r t o b e f # 7

W h i c h o f t h e t w o , (a ) o r (ii) , is m o r e a p p r o p r i a t e a s P l a t o n ic d o c t r i n e ?

z4 Plato: Cratylus, Parmenides, Greater Htppias, Lesser H~ppias,

translated by H. N. Fowler

(London: W illiam Heineman, 1926), 217.

'~ Vlastos, TM A II, 344 -45, note lo.

~ Ibid., 348-49, note 28.

47 Cf. Alexander Neham as, Participation and Predication in Plato's Later Th oug ht, Re-

view o f Metaphysics

36 (De cemb er 1989): 343-74- Neham as denies that participation of Forms is

a part of the middle dialogue the ory of Forms. He does interpret passages in the second hall of

the

Parmenides

as allowing, but n ot requiring, se lf participation--and as, thus, introducing a

radically different theory of Form s. If , however, we assume--as Nehamas seems to---that the

first part of the dialogue is a discussion o f the middle dialogue theory o f Forms, the present

point stands.


17/19

x 8 J O U R N 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

G i v e n t h a t ( a) d o e s n o t o c c u r e x p l i c i t ly i n t h e t e x t a n d t h a t (ii) d o e s - - i n t h e

P h a e d o t h e

l a t t e r h a s m o r e t e x t u a l w a r r a n t . M o r e o v e r , (ii) is c l e a r l y c e n t r a l

t o t h e t h e o r y o f F o r m s i n t h e m i d d l e d i a l o g u e s . B u t w e c a n s ti l l a sk , i f P l a to

h a d e x p l ic i t l y c h o s e n (ii) o v e r (a ), a n d a d d e d i t t o t h e se t S P a n d N I , w o u l d

h e h a v e l o s t s o m e t h i n g e s s en t ia l t o t h a t t h e o r y o f F o r m s ? D o e s t hi s t h e o r y

r e q u i r e a F o r m o f f t o p a r t i c i p a t e i n a F o r m o f f i n o r d e r t o b e f? T h e T B A

s h o w s t h a t t h e F o r m o f b e d h a s t h e f o r m o f b e d i n s o m e s e n s e ; it is c a l le d

b e d a s m u c h a s a n y o t h e r F o r m i n t h e m i d d l e d i a l o g u e s i s c a l l e d b y i ts

a p p r o p r i a t e t e r m . B u t t h e a r g u m e n t c o n t a i n s n o a s s u m p t i o n w h i c h r e q u i r e s

t h e F o r m o f b e d t o p a r t i c i p a t e i n i ts e l f o r a n o t h e r F o r m o f b e d . S i n c e

e s t a b l i s h i n g t h e v a l i d i t y o f a n a r g u m e n t - - i . e . , t h e T M A - - w a s t h e o n l y r e a -

s o n f o r a s s u m i n g (a ) i n t h e f i rs t p la c e , w e h a v e n o r e a s o n f o r a s s u m i n g ( a) i n

t h e T B A s in c e it is n o t n e c e s s a r y f o r t h e v a l id i ty o f t h a t a r g u m e n t .

W h a t d o e s t hi s an a ly s is o f t h e T B A h a v e t o d o w i th t h e T h i r d M a n

A r g u m e n t o f t h e Parmenides? S i n c e t h a t a r g u m e n t is q u i t e c o m p l e x , w i t h

m a n y h i d d e n d e p t h s , a n d s in c e th is p a p e r is r e al ly a b o u t t h e T B A - - a n

a r g u m e n t w i th d i f f e r e n t n u a n c e s - - o n l y a s u g g e s t i o n c a n b e o f f e r e d . A s w e

h a v e s e e n , t h e i m p o r t a n t e l e m e n t i n o u r i n t e r p r e t a t i o n is t h e r e j e c t io n o f ( a)

in f a v o r o f (ii) . T h u s , t h e T B A s t a n d s , r e g r e s s f r e e , o n (i i) , w h i c h d o e s n o t

r e q u i r e t h e F o r m o f b e d t o p a r t i c i p a t e i n it se lf o r in a n o t h e r F o r m o f b e d i n

o r d e r t o b e a b e d ; b y c o n t r a s t t h e a p p l i c a t i o n o f N I t o t h e F o r m o f la r g e i n

t h e T M A r e q u i r e s t h a t F o r m t o p a r t ic i p a te i n a n o t h e r F o r m o f l a rg e in

o r d e r t o b e l a r g e . (ii) i n e f f e c t s a y s t h a t o n l y f ' s b e s i d e s t h e p r i m a r y f r e q u i r e

a s e p a r a t e F o r m o f f i n o r d e r t o b e f , i m p l y i n g t h a t N I d o e s n o t a p p l y t o th e

F o r m o f f , t h e f i t s e lf f r o m w h i c h a ll o t h e r f ' s d e r i v e t h e i r f o r m . B u t i f N I

d o e s n o t a p p l y t o t h e F o r m o f f, n o r e g r e s s r e su l t s. M o r e o v e r , i f N I d o e s n o t

a p p l y t o t h e F o r m o f f, t h e n a p p l y i n g i t t o t h e F o r m o f f is a f a ll a cy . ~8 F i n a l ly ,

i f t h e a p p l i c a t i o n o f N I t o th e F o r m o f f is a fa l la c y t h e n i t s h o u l d b e p o s s ib l e

~s Some of the c om me nta tors o n wh om we have rel ied a lso hold tha t the T M A is fa llac ious

and they do so on the bas is tha t the F orm is in some way pr ima ry-- i .e . , non -der iva t ive --and i ts

participants are derivative. Cf. Allen, Predication an d Participation, 46 -4 7 an d 59; Bestor,

Plato 's semantics , 57 -58 ; Barford, Con text of the Th i rd Man, 4- 5; Fuji sawa, l~xetv, 3 4-

39. However , unl ike the present interpre ta t ion, these const rue the di ffe rence be tween Form

and par t icular in such a way tha t f is not predica ted of Form and p ar t icular wi th the same

sense . The n the c la im i s made tha t OM does n ot apply in the second s tep of the f irst TM A

because a, b, c , and F-ness are n ot all f in the same w ay. How ever, i t is no t at all clear that an y of

these interpr etat ions avoids the di lem m ma posed in Ro ger Shiner, Self-Predicat ion an d the

' T h i r d M a n ' A r g u m e n t , Jou rna l of the History of Philosophy 8 (197o): 371 -86 . By cont ras t , the

interpre ta t ion offere d here a l lows there to be some s imi lar ity of me aning be tween f in der i-

vat ively f and f in non-derivat ively f. T he regress does no t de pe nd on part iculars and Fo rm

being in some sense al l f 's but upon the fai lure to see the difference between derivat ive and

non-derivative f.


18/19

TIl UNIQU N SS PROOF 149

t o a v o i d s o a p p l y i n g it . T h e r e s h o u l d be a s u s p i c io u s s t e p i n w h i c h t h e

o p p o r t u n i t y t o a p p l y N I t o t h e F o r m o f f a ri se s b e c a u se o f a m i s u n d e r s t a n d -

i n g o r a n a m b i g u i t y .

C o m m e n t a t o r s h a v e p o i n t e d o u t t h a t P l a t o s e e m s t o h a v e i n d i c a t e d t h a t

t h e s u s p i c i o u s s t e p o f t h e T M A is t h e s e c o n d ( 1 3 2 a l ) . ~9 I f i n th e s a m e w a y

y o u r e g a r d , i n y o u r m i n d , a ll t h e s e t h i n g s - - t h e l a rg e i ts e lf a n d t h e o t h e r

l a r ge t h i n g s - - w o u l d n o t s o m e o n e l a rg e a g a i n a p p e a r , b y w h i c h all t h e se

m u s t a p p e a r l a r g e ? (T i d au to to mega k a i taUa to meg a la , ean h6sau t6s t~ i p such~ i

e p i p a n t a i d ~ i s , o u c h i h e n t i a u m e g a p h a n e i t a i , h 6 i t a u ta p a n t a a n a g k ~ m e g a l a

pha ines tha i ; ) I f o n e c a n n o t s o r e g a r d t h e la r g e i ts e l f a n d l a r g e t h i n g s , t h e n

t h e re g r e s s d o e s n o t be g i n. N o w , i n t h e s a m e w a y c a n m e a n a n u m b e r o f

t h i n g s : ( a) a s a l l f , ( b) a s a l l h a v i n g a c o m m o n c h a r a c t e r [ e. g. , f o r f , ] , o r

(c) i n t h e s a m e w a y a s b e f o r e [ i. e., i n th e s a m e w a y a s t h e fi rs t g r o u p ] . T h e

s u g g e s t i o n o f f e r e d h e r e is t h a t (c) is t h e r e a d i n g w h i c h s h o w s th e T M A t o b e

f a ll a c io u s . I t is w r o n g t o lo o k a t th e g r o u p c o n t a i n i n g t h e F o r m o f f a n d f

p a r t i c i p a n t s i n t h e s a m e w a y a s o n e l o o k s a t t h e g r o u p c o n t a i n i n g o n l y f

p a r t i c ip a n t s . T h e g r o u p c o n t a i n i n g t h e F o r m a n d t h e pa r t ic i p a n ts c a n n o t be

r e g a r d e d i n t h e s a m e w a y a s t h e g r o u p o f l a rg e t h i n g s i n t h e f ir s t s t e p a r e

r e g a r d e d b e c a u s e a l l t h e f 's t h e r e a r e d e r i v a t iv e l y f a n d t h e g r o u p c o n t a i n i n g

t h e F o r m a n d t h e o t h e r f 's c o n t a i n s s o m e m e m b e r w h i c h, t h o u g h i t is f i n

s o m e s e n s e , i s n o t d e r i v a t i v e l y f.

T h e F o r m s t a n d s i n a n e p is t e m o l o g ic a l a n d m e t a p h y s ic a l p r io r i ty t o th e

p a r t ic u l a rs ; t h e y d e p e n d o n i t f o r e x p l a i n i n g a n d f o r h a v i n g w h a t e v e r p r o p -

e r t y t h e F o r m is t h e F o r m f o r. T h e F o r m , i n t u r n , d e p e n d s o n n o o t h e r

F o r m f o r h a v i n g w h a t e v e r p r o p e r t y i t is t h e F o r m f o r; n o r d o e s i t d e p e n d o n

a n o t h e r F o r m f o r e x p l a i n i n g o r c l a r if y i n g t h a t p r o p e r t y . I f o n e r e a l iz e d t h a t

d i f f e r e n c e b e t w e e n F o r m a n d p a r t ic i p a n t , it w o u l d b e i m p o s si b le t o r e g a r d

t h e F o r m a n d t h e o t h e r f 's i n th e s a m e w a y a s t h e f 's a l o n e . A f t e r s e e i n g t h e

d i f f e r e n c e b e t w e e n t h e F o r m a n d p a r ti c ip a n t s, o n e w o u l d se e th a t t he f 's

a l o n e i n th e f i rs t s t ep n e e d g r o u n d i n g b u t t h a t F o r m a n d t h e o t h e r f 's ar e a

c l o s e d s y st e m . T h e g r o u p c o n s i s t i n g o f F o r m a n d f p a r t i c ip a n t s is n o t in

n e e d o f g r o u n d i n g ; t h e f 's a re d e r i v a ti v e f r o m t h e F o r m a l r e a d y t h e r e a n d

t h a t F o r m is n o t d e r i v a t iv e o f a n y t h i n g . I f o n e r e g a r d e d t h e tw o g r o u p s

d i f f e r e n t l y f o r t h is r e a s o n h e w o u l d n o t s e e t h e s e c o n d g r o u p i n s u c h a w a y

t h a t a n o t h e r L a r g e n e s s w o u l d a p p e a r b y w h i c h t he m e m b e r s o f t h e s e c o n d

g r o u p a r e l a r g e , i .e ., th e o p p o r t u n i t y t o a p p l y N I d o e s n o t ar is e u n d e r t h is

u n d e r s t a n d i n g .

E v e n i f th i s s u g g e s t i o n f o r s e e i n g t h e f a ll a c y i n t h e T M A is n o t a c c e p t e d ,

~9 Cherniss, Aristotle s Criticism, 297; Ba rford, Context of the Third Man, 3.


19/19

1 5 0 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

t h e p r e s e n t i n t e r p r e t a t i o n o f t h e T B A s til l c all s i n t o q u e s t i o n t h e i n f lu e n t i a l

c la im t h a t t h e c o r r e c t u n d e r s t a n d i

Documents

Parry - The Uniqueness Proof for Forms in Republic 10