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New work for a theory of universalsDavid Lewis aa Princeton University,

Online Publication Date: 01 December 1983

To cite this Article Lewis, David(1983)'New work for a theory of universals',Australasian Journal of Philosophy,61:4,343 377To link to this Article DOI 10.1080/00048408312341131URL http://dx.doi.org/10.1080/00048408312341131

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Au s tr a la s ia n J o u r n a l o f P h i l o s o p h yVol. 61 , No . 4 , D ece m be r 1983

N E W W O R K F O R A T H E O R Y O F U N I V E R S A L S

D a v i d L e w i s

I n t r o d u c t i o n . D . M . A r m s t r o n g o f f e r s a t h e o r y o f u n i v er s a ls a s t h e o n l y

a d eq u at e a n s w e r t o a ' c o m p u l s o r y q u e s t i o n ' f o r s y s t e m a t i c p h i l o s o p h y : t h ep r o b le m o f O n e o v e r M a n y. 1 I f in d th i s l in e o f a r g u m e n t u n p e r s u a s v i e . B u tI t h in k t h e r e is m o r e t o b e s a i d f o r A r m s t r o n g ' s t h e o r y t h a n h e h i m s e l f h a ssa id . F o r a s I b e a r i t i n m i n d c o n s i d e r i n g v a r i o u s t o p i c s i n p h i l o s o p h y, I n o t i c etim e a n d a g a i n t h a t i t o f f e r s s o l u t io n s t o m y p r o b l e m s . W h a t e v e r w e m a yth in k o f t h e p r o b l e m o f O n e o v e r M a n y, u n i v e r sa l s c an e a r n t h e i r l iv i n g d o i n go th er m u c h - n e e d e d w o r k .

I d o n o t s a y t h a t t h e y a r e i n d i s p e n s a b l e . T h e s e rv i c es t h e y r e n d e r c o u l dbe m a t c h e d u s i n g r e s o u r c e s t h a t a r e N o m i n a l i s t i c i n l e t t e r, i f p e r h a p s n o tin s p ir it . 2 B u t n e i t h e r d o I h o l d a n y p r e s u m p t i o n a g a i n s t u n i v e r s a l s , t o t h ee ffe ct t h a t t h e y a r e t o b e a c c e p t e d o n l y i f w e h a v e n o a l t e r n a t i v e . I t h e r e f o r es us pe nd j u d g e m e n t a b o u t u n i v e r s a l s t h e m s e l v e s . I o n l y in s i st t h a t , o n e w a yo r a n o t h e r , t h e i r w o r k m u s t b e d o n e .

I s h a ll i n v e s t i g a t e t h e b e n e f i ts o f a d d i n g u n i v e r s a l s t o m y o w n u s u a lo n to l og y. T h a t o n t o l o g y , t h o u g h N o m i n a l i s t i c , is i n o t h e r r e sp e c t s g e n e r o u s .I t c o n s i s t s o f p o s s i b i l i a - p a r t i c u l a r , i n d i v i d u a l t h in g s , s o m e o f w h i c hc om p r i s e o u r a c t u a l w o r l d a n d o t h e r s o f w h i c h a r e u n a c t u a l i s e d 3 - - t o g e t h e r

w ith t h e i t e r a t i v e h i e r a r c h y o f c la s se s b u i l t u p f r o m t h e m . T h u s I a l r e a d yh av e a t m y d i s p o s a l a t h e o r y o f p r o p e r t i e s a s c l a s se so f p o s s i b i l i a . P r o p e r t i e s ,so u n d e r s t o o d , a r e n o t m u c h l ik e u n i v e r s a l s . N o r c a n t h e y, u n a i d e d , t a k eo ve r t h e w o r k o f u n i v e r sa l s . N e v e r t h e l e s s t h e y w i l l f ig u r e i m p o r t a n t l y i n w h a t

D. M. A rmstrong,Universals an d Scientific Realism(Ca mb ridge University Press, 1978),henceforth cited a sUniversals see also his Against 'Ostrich' Nominalism: A Rep ly to M ichaelDevitt ,Pacific Philosophical Qua rterly61 (1980) pp. 440-449.

z In this pa per, I follow Armstrong's tra ditio nal terminology: 'universals' are repeatable entities,wholly present w herever a particu lar instantiates them; 'Nom inalism ' is the rejection of suchentities. In the conflicting m od ern term ino logy of H arva rd, classes cou nt as 'univ ersals' and'Nominalism' is pred om inan tly the reje ction of classes. C onfu sion o f the terminologies canresult in grave misunderstanding; see W . V. Q uine, 'S oft Impeachment Disowned',PacificPhilosophical Quarterly61 (1980) pp. 450-451.A,laong things' I m ean to include al l the gerrym andered wholes and undem arcated partsadmitted by the m ost permissive sort of m ereolog y. Fu rthe r, I include such physical ob jectsas spatiote m poral regions and force fields, unless an eliminative red uction o f them shou ldprove desirable. Furth er, I include such no nphysical objects as gods and spook s, thoughnot - I hope -- as parts o f the same world as us. W orlds themselves need no special treatment.They are things -- big ones, for the m ost part .

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3 4 4 Ne w W ork fo r a Theory o f Universa ls

f o l l o w s , s in c e f o r m e t h e y a r e p a r t o f t h e e n v i r o n m e n t i n w h i c h u n i v e rs a lsm i g h t o p e r a t e .

T h e f r ie n d o f u n i v e rs a ls m a y w o n d e r w h e t h e r t h e y w o u l d b e b et te re m p l o y e d n o t a s a n a d d i t io n t o m y o n t o l o g y o fp o s s i b i l i a a n d c l a s s e s , b u tr a t h e r a s a r e p l a c e m e n t f o r p a r t s o f it . A f a i r q u e s t i o n , a n d a n u rg e n t o n e;n e v e r t h e l e s s , n o t a q u e s t i o n c o n s i d e r e d i n t h is p a p e r.

I n t h e n e x t s e c t i o n , I s h al l s k e t c h A r m s t r o n g s t h e o r y o f u n i v e r sa l s,c o n t r a s t i n g u n i v e r s a l s w i th p r o p e r t i e s u n d e r s t o o d a s cl as s esofposs ib i l i a . T h e nI s h al l s a y w h y I a m u n c o n v i n c e d b y t h e O n e o v e r M a n y a r g u m e n t . T h e nI s h a l l t u r n t o m y p r i n c i p a l t o p i c : h o w u n i v e r s a l s c o u l d h e l p m e i n c o n n e c t i o nw i t h s u c h t o p i c s a s d u p l i c a t i o n , s u p e r v e n i e n c e , a n d d i v e rg e n t w o r l d s ; a

m i n i m a l f o r m o f m a t e r i a l is m ; l a w s a n d c a u s a t i o n ; a n d t h e c o n te n t o f la n g ua g ea n d t h o u g h t . P e r h a p s t h e l is t c o u l d b e e x te n d e d .

U n i v e r s a l s a n d P r o p e r t i e s . L a n g u a g e o f f e r s u s s e v e r a l m o r e o r l e s si n t e r c h a n g e a b l e w o r d s : u n i v e r s a l ; p r o p e r t y , q u a l i t y , a t t r i b u t e , f e a tu r e ,a n d c h a r a c t e ri s ti c ; t y p e , k i n d , a n d s o r t ; a n d p e r h a p s o t h e r s. A n dp h i l o s o p h y o f f e r s u s s e v e r a l c o n c e p t i o n s o f t h e e n ti ti es t h a t s u c h w o r d s r ef ert o . M y p u r p o s e is n o t t o fix o n o n e o f th e s e c o n c e p t i o n s ; b u t r a t h e r tod i st in g u i sh t w o ( a t o p p o s i t e e x t r e m e s ) a n d c o n t e m p l a t e h e l p in g m y s e l f tob o t h . T h e r e f o r e s o m e r e g i m e n t a t i o n o f l a n g u a g e i s c a ll e d f o r; I a po lo g is ef o r a n y i n c o n v e n i e n c e c a u s e d . L e t m e r e s e rv e t h e w o r d u n i v e r s a l f o r th o see n ti ti es , i f s u c h th e r e b e , t h a t m o s t l y c o n f o r m t o A r m s t r o n g s a c c o u n t . A n dl et m e r e s e r v e t h e w o r d p r o p e r t y f o r c l as s es - a n y c la s s es , b u t I h a vef o r e m o s t i n m i n d c la s se s o f t h in g s . T o h a v e a p r o p e r t y is t o b e a m e m b e ro f t h e c l a s s . 4

W h y c a ll t h e m p r o p e r t i e s a s w e l l a s c l a s se s ? - J u s t to u n d e r l in e t h e fa ctt h a t t h e y n e e d n o t b e c l as se s o fa c t u a l t h in g s . T h e p r o p e r t y o f b e i n g a d o n k e y,f o r i n s t a n c e , is t h e c l a ss o fal l t h e d o n k e y s . T h i s p r o p e r t y b e l o n g s to - th isc l as s c o n t a i n s - n o t o n l y t h e a c t u a l d o n k e y s o f th i s w o r l d w e li v e i n , b u ta l s o a ll t h e u n a c t u a l i s e d , o t h e r w o r l d l y d o n k e y s .

L i k e w i s e I r e s e rv e t h e w o r d r e l a t i o n f o r a r b i t r a r y c la s se s o f o r d e r e d p a ir s,t r ip l e s . . . . . T h u s a r e l a t i o n a m o n g t h i n g s is a p r o p e r t y o f t u p l e s o f th in g s.A g a i n , t h e r e is n o r e s t r i c t io n t o a c t u a l t h in g s . C o r r e s p o n d i n g r o u g h l y tot h e d i v i s io n b e t w e e n p r o p e r t i e s a n d r e l a t i o n s o f t h i n g s , w e h a v e t h e d iv is io nb e t w e e n m o n a d i c a n d p o l y a d i c u n i v e rs a ls .

U n i v e r s a l s a n d p r o p e r t i e s d i f f e r i n t w o p r i n c i p a l w a y s . T h e f i r s t d i f f e r e n c e

c o n c e r n s t h e i r i n s t a n t i a t i o n . A u n i v e r s a l i s s u p p o s e d t o b e w h o l l y p r e s e n tw h e r e v e r i t is i n s t a n ti a t e d . I t is a c o n s t i t u e n t p a r t ( t h o u g h n o t a s p a t i o t e m p o r a lp a r t ) o f e a c h p a r t i c u l a r t h a t h a s i t. A p r o p e r t y, b y c o n t r a s t , is s p r e a d a r o u n d .T h e p r o p e r t y o f b e i n g a d o n k e y is p a r tl y p r e s e n t w h e r e v e r t h e re i s a d o n ke y,

4 M y conc eption of properties resembles the doc trine o f C lass Nom inalism considered inUniversals I, pp. 28-43. But, strictly speaking, a Class Nominalist would be som eone whoclaims to solve the O ne ov er Man y problem simply by m eans of properties taken as classes,and that is far from my intention.

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David Lew is 345

in th is o r a n y o t h e r w o r l d . F a r f r o m t h e p r o p e r t y b e i n g p a r t o f th e d o n k e y,it is c l o se r t o t h e t r u t h t o s a y t h a t t h e d o n k e y is p a r t o f t h e p r o p e r t y . B u tth e p r e ci se t ru t h , r a t h e r , is t h a t t h e d o n k e y is a m e m b e r o f t h e p r o p e r t y.

T h u s u n i v e r s a ls w o u l d u n i f y r e a li tyCf. Universals, I , p . 1 0 9 ) i n a w a yth a t p r o p e r t i e s d o n o t . T h i n g s t h a t s h a r e a u n i v e r s a l h a v e n o t j u s t j o i n e da s in g le c la ss . T h e y l it e ra l ly h a v e s o m e t h i n g i n c o m m o n . T h e y a r e n o t e n t i re l yd i s t i n c t . T h e y o v e r l a p .

B y o c c u r r i n g r e p e a t e d l y, u n i v e r s a l s d e f y in t u i t iv e p r i n c i p l e s . B u t t h a t isn o d a m a g i n g o b j e c t i o n , s in c e p l a i n l y t h e i n t u it i o n s w e r e m a d e f o r p a r t ic u l a r s .F o r i n s t a n c e , c a l l t w o e n t i ti e scopresent i f b o t h a r e w h o l l y p r e s e n t a t o n ep o s it io n i n s p a c e a n d t im e . W e m i g h t i n t u it o f f h a n d t h a t c o p r e s e n c e is

t ra n s it iv e . B u t it is n o t s o , o b v i o u s l y, f o r u n i v e r s a l s . S u p p o s e f o r t h e s a k eo f a rg u m e n t t h a t t h e r e a r e u n i v e rs a l s: r o u n d , s il ve r , g o l d e n . S i lv e r a n d r o u n da re c o p r e s e n t , f o r h e r e is a s ilv e r c o i n ; g o l d e n a n d r o u n d a r e c o p r e s e n t , f o rt he re is a g o l d c o i n ; b u t s i lv e r a n d g o l d e n a r e n o t c o p r e s e n t . L i k e w i s e , i fw e a d d u n i v e r s a ls t o a n o n t o l o g yofpossibi l ia , f o r t h e r e l a ti o n o f b e in g p a r to f t h e s a m e p o s s ib l e w o r l d : I a n d s o m e o t h e r w o r l d l y d r a g o n a r e n o tw o r l d m a t e s ; b u t I a m a w o r l d m a t e o f th e u n i v e r s a l g o l d e n , a n d s o is t h ed r ag o n . P r e s u m a b l y I n e e d e d a m i x e d c a se i n v o l v i n g b o t h u n i v e r s a ls a n dp a rt ic u la r s. F o r w h y s h o u l d a n y t w o u n i v e r s a ls e v e r f a il t o b e w o r l d m a t e s ?L a c k in g s u c h f a il u re s , t h e w o r l d m a t e r e l a t io n a m o n g u n i v e r s a ls a l o n e i sff iv i a lly t r an s i t i ve .

T h e s e c o n d d i f fe r e n c e b e t w e e n u n i v e r sa l s a n d p r o p e r t i e s c o n c e r n s t h e ira b u n d a n c e . T h i s is t h e d i f f e r e n c e t h a t q u a l if ie s t h e m f o r d i f f e r e n t w o r k , a n dt h e re b y g i v e s r is e t o m y i n te r e s t i n h a v i n g u n i v e r s a l s a n d p r o p e r t i e s b o t h .

A d i st in c t iv e f e a t u r e o f A r m s t r o n g s t h e o r y is t h a t u n i v e r s a ls a r e s p a r se .T h e r e a r e t h e u n i v e r s a l s t h a t t h e r e m u s t b e t o g r o u n d t h e o b j e c t i v er es e m b la n c es a n d t h e c a u s a l p o w e r s o f th i n g s , a n d t h e r e i s n o r e a s o n t o b e l ie v e

in a n y m o r e . A l l o f t h e f o l l o w i n g a l l eg e d u n i v e r s a ls w o u l d b e r e j e c te d :n o t g o l d e n ,g o l d e n o r w o o d e n ,me ta l l i c ,s e l f - iden t i c a l ,o w n e d b y F r e d ,b e l o n g i n g t o c l as s C ,g rue ,

f i r s t e x a m i n e d b e f o r e 2 0 0 0 A . D . ;b e i n g i d e n t i c a l ,b e i n g a l i k e i n s o m e r e s p e c t ,b e i n g e x a c t l y a l i k e ,b e i n g p a r t o f ,o w n i n g ,b e i n g p a i r e d w i t h b y s o m e p a r t i n R

If universals are to do the new wo rk I have in store for them, they must be capable o f repeatedoccurrence not only within a w orld but also across worlds. They would then be an exceptionto m y usual principle - mean t fo r particulars, o f course - tha t nothing is who lly presentas par t o f two different w orlds. But I see no harm in that. If two worlds are said to o verlapby having a coin in co m m on, and if this coin is supposed to be wholly roun d in one worldand wholly octagonal in the o ther, I stubbornly ask what shape it is, and insist tha t shapeis no t a relation to w orlds. (See m y Individuation by A cquaintance and by S tipulation ,PhilosophicalReview92 (1983), pp . 3-32.) I do n ot see any parallel objection if worlds aresaid to ov erlap by sharing a universal. W hat contingent, nonrelational property o f the universalcould we put in place of shape o f the coin in raising the problem? I can not think of any.

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3 4 6 N ew W ork fo r a T h eo ry o f U n iv ersa ls

( w h e r e C a n d R a r e u t t e r l y m i s c e l l a n e o u s c la s s e s) . T h e g u i d i n g i d e a , r o u g h l y,is t h a t t h e w o r l d s u n i v e r s a l s s h o u l d c o m p r i s e a m i n i m a l b a s i s f o rc h a r a c t e r i s i n g th e w o r l d c o m p l e t e l y. U n i v e r s a l s t h a t d o n o t c o n t r i b u t e a t allt o t h i s e n d a r e u n w e l c o m e , a n d s o a r e u n i v e r s a l s t h a t c o n t r i b u t e o n l yr e d u n d a n t l y. A s a t i s f a c t o r y in v e n t o r y o f u n i v e r sa l s is a n o n - li n g u is t icc o u n t e r p a r t o f a p r i m i t iv e v o c a b u l a r y f o r a la n g u a g e c a p a b l e o f d e sc r ib in gt h e w o r l d e x h a u s t i v e l y.

( T h a t i s r o u g h : A r m s t r o n g d o e s n o t d i s m is s r e d u n d a n t u n i v e rs a ls o u t o fh a n d , a s t h e s p ir it o f h is t h e o r y m i g h t s e e m t o d e m a n d . C o n j u n c t i v e u n iv e r sa l s

a s it m i g h t b e , g o l d e n - a n d - r o u n d - a r e a c c e p t e d , t h o u g h r e d u n d a n t ; soa r e a n a l y s a b l e s t r u c t u r a l u n i v e r s a l s. T h e r e a s o n i s t h a t i f t h e w o r l d w e re

i n fi n it e ly c o m p l e x , t h e r e m i g h t b e n o w a y t o c u t d o w n t o a m i n i m a l b a si s.T h e o n l y a l t e rn a t iv e t o r e d u n d a n c y m i g h t b e i n a d e q u a c y, a n d i f s o w e h adb e t t e r t o le r a t e r e d u n d a n c y. B u t t h e r e d u n d a n c y is m i t i g a te d b y th e f a c t th a tc o m p l e x u n i v e r s al s c o n si st o f t h e i r s i m p l e r - - i f p e r h a p s n o t a b s o l u t e l y si m p le- c o n s t i t u e n t s . T h e y a r e n o t d i s t in c t e n t i t ie s . S e eU n i v e r s a l s I I , p p . 3 0 -4 2a n d 6 7 - 7 1 . )

I t i s q u i t e o t h e r w i s e w i t h p r o p e r t i e s . A n y c l a s s o f t h i n g s , b e i t e v e r s og e r r y m a n d e r e d a n d m i s c e ll a n e o u s a n d i n d e s c r ib a b l e in t h o u g h t a n d l a n g u ag e ,a n d b e i t e v e r s o s u p e r f l u o u s i n c h a r a c t e r i s i n g t h e w o r l d , i s n e v e r t h e l e s s a

p r o p e r t y. S o t h e r e a re p r o p e r t ie s in im m e n s e a b u n d a n c e . ( I f t h e n u m b e r o ft h i n g s , a c t u a l a n d o t h e r w i s e , i s b e t h - 2 , a n e s t i m a t e I r e g a r d a s m o r e l ik e lyl o w t h a n h i gh , t h e n t h e n u m b e r o f p r o p e r t ie s o f t h in g s i s b e t h -3 . A n d t ha tis a b i g in f in i ty i n d e e d , e x c e p t t o s t u d e n t s o f t h e o u t e r r e a c h e s o f s e t t h e o r y. )T h e r e a r e s o m a n y p r o p e r t i e s t h a t t h o s e s p e c if ia b le i n E n g l is h , o r i n t h e b r a in sl a n g u a g e o f s y n a p t i c i n te r c o n n e c t i o n s a n d n e u r a l s p i k e s, c o u l d b e o n l y ani n f in i t e si m a l m i n o r i t y.

B e c a u s e p r o p e r t i e s a re s o a b u n d a n t , t h e y a r e u n d i s c r i m i n a t in g . A n y t w ot h i n g s s h a r e i n f i n it e ly m a n y p r o p e r t i e s , a n d f a i l t o s h a r e i n fi n it e ly m a n yo t h e r s . T h a t i s s o w h e t h e r t h e t w o t h i n g s a r e p e r f e c t d u p l i c a t e s o r u t t e r l yd i s si m i la r. T h u s p r o p e r t i e s d o n o t h i n g t o c a p t u r e f a c t s o f r e s e m b l a n c e . T h a tis w o r k m o r e s u i t e d t o t h e s p a r s e u n iv e r s a l s. L i k e w i s e , p r o p e r t i e s d o n o t h i n gt o c a p t u r e t h e c a u s a l p o w e r s o f t h in g s . A l m o s t a l l p r o p e r t i e s a r e c a u sa ll yi r r e l e v a n t , a n d t h e r e i s n o t h i n g t o m a k e t h e r e l e v a n t o n e s s t a n d o u t f r o mt h e c r o w d . P r o p e r t i e s c a r v e re a l i t y a t th e j o i n t s - - a n d e v e r y w h e r e els e a sw e l l. I f i t s d is t in c t i o n s w e w a n t , t o o m u c h s t r u c t u r e i s n o b e t t e r t h a n n o n e .

I t w o u l d b e o t h e r w i s e i f w e h a d n o t o n l y th e c o u n t l e ss t h r o n g o f all

p r o p e r t i e s , b u t a l s o a n 6 1ite m i n o r i t y o f s p e c i a l p r o p e r t i e s . C a l l th e s e th en a t u r a l p r o p e r t i e s . 6 I f w e h a d p r o p e r t i e s a n d u n i v e r s a l s b o t h , t h e u n i v er sa ls

See Universals I, pp. 38-41; Anthon y Q uinton, Properties and Classes ,Proceedings o fthe Aristotelian Society48 (1957) pp. 33-58; and W . V . Q uin e, Natural Kinds , in hisOntological Relativity(Colum bia University Press, 1969). See also Geo rge Bealer,Qualityand Concept(Oxford University Press, 1982), especially pp. 9-10 and 177-187. Like me,Bealer favou rs an inegalitarian wofold conception of p roperties: there are ab und ant conceptsand sparse qualities , and the latter are the o ne s that determine t.he logical, causal, andphenomenal order of reality . (p. 10) Despite his point of agreement, however, Bealer sviewsand mine differ in many ways.

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D a v i d L e w i s 347

could serve to pick out the natural properties. After wards the universals couldretire if they liked, and leave their jobs to the natural properties. Naturalproperties would be the ones whose sharing make s f or resemblance, and theones relevant to causal powers. Most simply, we could call a p r o p e r t y p e r f e c t lynatural if its members are all and only those things that share some oneuniversal. But also we would have othe r less-than-perfectly natu ral properties,made so by families of suitable r elated universals. 7 Thu s we might have animperfectly natur al pro per ty o f being metallic, even if we had no such singleuniversal as metallic, in virtue of a close-knit family of genuine universalsone or another of which is instantiated by any metallic thing. Theseimperfectly natural properties would be natural to varying degrees.

Let us say that an a d e q u a t e theory of properties is one that recognises anobjective difference between natural and unnatural properties; preferably,a difference that admits of degree. A combined theory of properties anduniversals is one sort of adequate theory of properties.

But not the only sort. A Nominalistic theory of properties could achieveadequacy by other means. Instead of employing universals it could drawprimitive distinctions among particulars. Most simply, a Nominalist couldtake it as a primitive fact that some classes of things are perfectly naturalproperties; others are less-than-perfectly natural to various degrees; and mostare not at all natural. Such a Nominali st takes nat ura l as a primitivepredicate, a nd offers no analysis o f what he means in predicating it of classes.His intention is to select the very same classes as natural properties that theuser of universals would select. But he regards the universals as idlemachinery, fictitiously superimposed on the primative objective differencebetween the n atura l properties and the others. 8

Alternatively, a Nominalist in pursuit of ade quacy might prefer to rest withprimitive objective resemblance among things. (He might not think that

natural was a very natur al primitive, perhaps because it is to be predicatedof classes.) Then he could u nder take to define natural properties in termsof the mutua l re semblance o f their member s and the failure of resemblancebetween their members and their non-members. Unfortunately, the projectmeets with well-known technical difficulties. These can be solved, but at adaunting price in complexity and artificiality of our primitive. We cannotget by with the familiar dyadic resembles . I nstead we need a predicate ofresemblance that is both contrastive and variably polyadic. Something like

xl, x2 . . . . resemble one anothe r and do no t likewise resemble any of yl,Y2, . . .

7 Here I assume that some solution to the problem of resemblance of universals is possible,perhaps along the lines suggested by Armstrong in UniversalsII, pp. 48-52 and 101-131;and that such a solution could be carried over into a theory of resemblance of perfectlynatural properties, even if we take naturalness of properties as primitive.

8 This is the Moderate Class Nominalism considered in UniversalsI, pp. 38-41. It is akinto the view of Quinton, op. cit.;but plus the unactualised members of the natural classes,and minus any hint that natural could receive a psychologistic analysis.

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348 N e w Wo r k f o r a T h e o r y o f U n i v e r s a l s

w h e r e t h e s t ri n g s o f v a r i a b le s m a y b e i n f in i te , e v e n u n c o u n t a b l e ) m u s t b et a k e n a s u n d e r s t o o d w i t h o u t f u r t h e r a n ai y si s. 9 I f a d e q u a t e N o m i n a li s mr e q u i r e s u s to c h o o s e b e t w e e n t h is a n d a p r i m i t i v e p r e d i c a t e o f c la s se s , w em i g h t w e l l w o n d e r w h e t h e r t h e g a m e is w o r t h t h e c a n d l e . I o n l y s a y w e m i g h tw o n d e r ; I k n o w o f n o c o n s i d e r a t i o n t h a t s e e m s t o m e d e c is iv e .

A t t h i s p o i n t , y o u m a y s ee v e r y w e ll w h y i t c o u l d b e a g o o d i d e a t o b e li ev ei n u n i v e r s a l s a s w e l l a s p r o p e r t i e s ; b u t y o u m a y s e e n o p o i n t i n h a v i n gp r o p e r t i e s a s w el l a s u n i v e r s a ls . B u t p r o p e r t i e s h a v e w o r k o f t h e i r o w n , a n du n i v e r s a l s a r e i l l - s u i t e d t o d o t h e w o r k o f p r o p e r t i e s .

I t i s p r o p e r t i e s t h a t w e n e e d , s o m e t i m e s n a t u r a l a n d s o m e t i m e s n o t , t op r o v i d e a n a d e q u a t e s u p p l y o f s e m a n t i c v a l u e s f o r l i n g u i s t i c e x p r e s s i o n s .

C o n s i d e r s u c h s e n t e n c e s a s t h e s e :1 ) R e d r e se m b l e s o r a n g e m o r e t h a n it r e s e m b l e s b l u e .2 ) R e d is a c o l o u r.3 ) H u m i l i t y is a v i r t u e .4 ) R e d n e s s i s a s i g n o f r i p e n e s s .

P r i m a f a c ie t h es e s e n te n c e s c o n t a i n n a m e s t h a t c a n n o t b e t a k e n t o d e n o t ep a r t i c u l a r , i n d i v i d u a l t h in g s . W h a t i s t h e s e m a n t i c ro l e o f t h e s e w o r d s ? I f

w e a r e to d o c o m p o s i t i o n a l s e m a n t i c s i n t h e w a y t h a t is b e s t d e v e l o p e d , w en e e d e n t i t i e s t o a s s i g n a s s e m a n t i c v a l u e s t o t h e s e w o r d s , e n t i t i e s t h a t w i l le n c o d e t h e i r s e m a n t i c r o l e s . P e r h a p s s o m e t i m e s w e m i g h t f i n d p a r a p h r a s e st h a t w i ll a b s o l v e u s f r o m t h e n e e d t o s u b j e c t t h e o r i g i n a l s e n t e n c e t o s e m a n t ic

S u c h a t h e o r y i s a f o r m o f R e s e m b l a n c e N o m i n a l i s m , i n A r m s t r o n g s c l a s si f ic a t io n , b u t iti s u n l i k e t h e f o r m t h a t h e p r i n c i p a l l y c o n s i d e r s . S e eUniversals, I , pp . 44 -63 . Fo r d i s cus s ionso f t h e p r o b l e m o f d e f in i n g n a t u r a l c l a s s es in t e r m s o f r e s e m b l a n c e , a n d o f t h e t r i c k e r y t ha tp r o v e s u s e f u l i n s o lv i n g t h is p r o b l e m , s e e N e l s o n G o o d m a n ,Th e S t ru c t u re o f Ap p ea ran ce( H a r v a r d U n i v e r s i ty P r e s s , 1 951 ), C h a p t e r s I V- V I ; W . V . Q u i n e , N a t u r a l K i n d s ; a n d A d a mM o r t o n , C o m p l e x In d i v id u a l s a n d M u l t ig r a d e R e l a t io n s ,No Ds 9 (1975) pp. 309-318.

To ge t f rom pr imi t ive re sem blance to pe r fec t ly na tu ra l p rope r t i e s , I have in min d a de f ini tiona s f o l l o w s . We b e g i n w i t h R a s o u r c o n t r a s t iv e a n d v a r i a b ly p o l y a d i c p r i m i ti v e . We w a n ti t t o t u r n o u t t h a tx~,x2, . Ry l, Y 2 . . . . i f f s o m e p e r f e c t l y n a t u r a l p r o p e r t y is s h a r e d b ya l l o f x~, x2 , . bu t by n on e o f y l , Y2 , . W e w an t to de f ine iV, an o th e r v a r i ab ly po lyad icp r e d i c a t e , s o t h a t i t w il l t u r n o u t t h a tN x b x 2 . . . . i f f x ~, x 2 . . . a r e a ll a n d o n l y t h e m e m b e r so f s o m e p e r f e c t ly n a t u r a l p r o p e r t y. A g a i n w e m u s t a l l o w f o r , a n d e x p e c t , t h e c a s e w h e ret h e r e a r e i n f i n it e ly m a n y x s . W e d e f i n eNxl,x2, . . . as:3yl ,y2 . . . . Yz z, xl ,x 2, . . Rye,y 2 . . . . ~ z= x~ v z= x2 v . . . ) .T h e n w e f i n i s h t h e j o b b y d e f i n i n g a p e r f e c t l y n a t u r a l p r o p e r t y a s a c l a s s s u c h t h a t , i f x l,x2 . . . . a r e al l a n d o n l y i ts m e m b e r s , t h e nN x l , x2 . . . . .

W e m i g h t h a v e t a k e n N a s p r i m i t iv e in s t e a d o f R . B u t w o u l d t h a t h a v e b e e n s i gn if ic a nt lyd i f f e r e n t , g i v e n t h e i n t e r d e f i n a b i l it y o f t h e t w o ? O n t h e o t h e r h a n d , t a k i n g N a s p r im i t iv ea l s o s e e m s n o t s i g n i f i ca n t l y d i f f e r e n t f r o m t a k i n g p e r f e c t n a t u r a l n e s s o f c l a s s e s a s p r im i t iv e .I t i s on ly a d i f fe ren ce be tw een speak ing in the p lu ra l o f ind iv idua l s and speak ing in the s ingu la ro f t h e i r c l a s s e s , a n d t h a t s e e m s n o r e a l d i f f e r e n c e . I s p l u r a l t a l k a d i s g u i s e d f o r m o f cla sst a l k ? O r vice versa? ( S e e t h e d i s c u s s i o n i nUniversals, I , p p . 3 2 -3 4 ; a ls o M a x B l a c k , T h eE l u s i v e n e s s o f S e t s ,R e v i e w o f M e t a p h y s i c s 24 (1971) pp . 614-636 ; Er ic S ten ius , Se t s ,S y n t h e s e 2 7 (1 9 74 ) , p p . 1 61 -1 88 ; a n d K u r t G 6 d e l , R u s s e l l s M a t h e m a t i c a l L o g i c , i n P. A .S c h i l p p , e d . ,T h e P h i l o s o p h y o f B e r t r a n d R u s s el l ( C a m b r i d g e U n i v e r s i t y P r e s s , 1 94 4).) A ta n y r a t e , i t i s n o t a t a ll c l e a r t o m e t h a t M o d e r a t e C l a s s N o m i n a l i s m a n d R e s e m b l an c eN o m i n a l i s m i n it s p r e s e n t f o r m a r e t w o d i f f e r e n t th e o r i e s , a s o p p o s e d t o a s in g le t he o ryp r e s e n t e d i n d i f f e r e n t s t y l e s .

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ana lys is . Th a t i s t he case wi th (1 ) , fo r i n s t ance . I Bu t even i f such pa rap h ra sess o m e t i m e s e x is t - - e v e n i f t h e yalways e x i s t, w h i c h s e e m s u n l i k e l y - t h e yw o r k p i e c e m e a l a n d f r u s t r a t e a n y s y s t e m a t i c a p p r o a c h t o s e m a n t i c s .

A r m s t r o n g t a k e s i t t h a t s u c h se n t e n c e s p r o v i d e a s u b s i d i a r y a rg u m e n t f o ru n iv er sa ls , in d e p e n d e n t o f hi s m a i n a r g u m e n t f r o m t h e O n e o v e r M a n yp r o b l e m . Universals, I , p p . 5 8 -6 3 ; a l so A g a i n s t 'O s t r i c h ' N o m i n a l i s m . n )I q u it e a g r e e t h a t w e h a v e h e r e a n a r g u m e n t f o r s o m e t h i n g . B u t n o t f o ru n i v e r s a l s a s o p p o s e d t o p r o p e r t i e s . P r o p e r t i e s c a n s e r v e a s t h e r e q u i s i t es em a n t ic v a l u e s . I n d e e d , p r o p e r t i e s a r e m u c h b e t t e r s u i te d t o t h e j o b t h a nu n iv e rs a ls a re . T h a t is p l a i n e v e n f r o m t h e e x a m p l e s c o n s i d e r e d . I t i s u n l i k e l yt h a t t h e r e a r e a n y s u c h g e n u i n e u n i v e r s a l s a s t h e c o l o u r s ( e s p e c i a l l y

d e t e rm i n a b l e c o l o u r s , l i k e r e d , r a t h e r t h a n d e t e r m i n a t e s h a d e s ) , o r r i p en e s s ,o r h u m i l i ty. A r m s t r o n g a g r e e sUniversals,I , P. 61 ) t ha t he ca nn o t t ake (1 )- (4 )as s t r a i g h t f o r w a r d l y m a k i n g r e f e r e n c e t o u n i v e rs a l s. H e m u s t f i rs t s u b j e c tt he m t o p a r a p h r a s e . E v e n i f t h e r e a l w a y s is a p a r a p h r a s e t h a t d o e s r e f e r t o ,o r q u a n t i f y o v e r , g e n u i n e u n i v e r sa l s , s ti ll t h e n e e d f o r p a r a p h r a s e is a t h r e a tto s y s te m a t i c s e m a t i c s . T h e p r o b l e m a r is e s e x a c t l y b e c a u s e u n i v e r s a ls a r esp ars e. T h e r e i s n o c o r r e s p o n d i n g o b j e c t i o n i f w e t a k e t h e r e q u i s i t e s e m a n t i cva lues as p roper t i e s .

O t h e r s e n t e n c e s m a k e m y p o i n t m o r e d r a m a t i c a l l y.

(5 ) G r u e n e s s d o e s n o t m a k e f o r r e s e m b l a n c e a m o n g a ll i ts i n s ta n c e s .(6 ) W h a t is c o m m o n t o a ll w h o s u f f e r p a i n is b e i n g i n s o m e o r a n o t h e r

s t a t e t h a t o c c u p i e s t h e p a i n r o l e , p r e s u m a b l y n o t t h e s a m e s t a t e i nal l cases .

T h e p o i n t is n o t t h a t t h e s e s e n t e n c e s a r e t r u e - - t h o u g h t h e y a r e - - b u t t h a tt he y r e q u i r e s e m a n t i c a n a l y s i s . ( I t is i r r e l e v a n t t h a t t h e y a r e n o t o r d i n a r yl a ng u a g e. ) A u n i v e r s a l o f g r u e n e s s w o u l d b e a n a t h e m a ; a s w o u l d a u n i v e r s a lsu ch t h a t , n e c e s s a r i ly, o n e h a s i t i f h e i s i n s o m e s t a t e o r o t h e r t h a t o c c u p i e s

10 I n v i r t u e o f t h e c l o s e r e s e m b l a n c e o f r e d a n d o r a n g e , i t is p o s s i b l e f o r a r e d t h i n g t o r e s e m b l ea n o r a n g e o n e v e r y c lo s e ly ; i t i s n o t p o s s i b l e f o r a r e d t h i n g t o r e s e m b l e a b l u e o n e q u i t es o cl os e ly. G i v e n o u r o n t o l o g yofpossibilia allposs i b i l it i e s a r e r ea l is ed . So w e cou l d pa r aph ase(1) by

(1 ' ) S o m e r ed t h i n g r e s e m b l e s s o m e o r a n g e t h i n g m o r e t h a n a n y r e d t h in g r es e m b l e sa n y b l u e t h i n g .

s o l o n g a s it is u n d e r s t o o d t h a t t h e t h i n g s in q u e s t i o n n e e d n ' t b e p a r t o f o u r w o r l d , o r o f

a n y o n e w o r l d . O r i f w e d i d n o t w i s h to s p e a k o f u n a c t u a l i s e d t h i n g s , b u t w e w e r e w i l li n gt o t a k e o r d i n a r y - l a n g u a g e m o d a l i d i o m s a s p r im i t i v e , w e c o u l d i n s t e a d g i v e t h e p a r a p h r a s e :( 1 ) A r e d t h i n g c a n r e s e m b l e a n o r a n g e th i n g m o r e c l o se l y t h a n a r e d t h i n g c a n r e s e m b l e

a b l u e t h i n g .I t i s n e c e s s a r y t o u s e t h e o r d i n a r y - l a n g u a g e i d i o m s , o r s o m e a d e q u a t e f o r m a l i s a t i o n o f t h e m ,r a th e r t h a n s t a n d a r d m o d a l l o g ic . Yo u c a n n o t e x p r e s s (1 ' ') i n m o d a l l o g i c ( e x c l u d in g a ne n ri c he d m o d a l l o g ic t h a t w o u l d d e f e a t t h e p o i n t o f t h e p a r a p h r a s e b y q u a n t i f y i n g o v e r d e g r e e so f r e s e m b l a n c e o r w h a t n o t ) b e c a u s e y o u c a n n o t e x p r e s s c r o s s - w o r l d re l a t io n s , a n d i n p a r t i c u l a rc a n n o t e x p re s s t h e n e e d e d c r o s s - w o r l d c o m p a r i s o n o f s i m i l a r i ty.

n H e d e ri v es t h e a r g u m e n t , a n d a s e c o n d s e m a n t i c a r g u m e n t to b e c o n s i d e r e d s h o rt l y, f r o mA r t h u r P a p , ' N o m i n a l i s m , E m p i r i c i s m , a n d U n i v e rs a l s : I ',Philosophical Quarterly 9(1959)p p . 3 30 -3 4 0, a n d F. C . J a c k s o n , ' S t a t e m e n t s a b o u t U n i v e r s a l s ',M i n d 86 (1977) pp . 427 - 429 .

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3 5 0 New Work for a Theory of Universals

t h e p a i n r o l e i n h is c as e .l Z B u t t h e c o r r e s p o n d i n g p r o p e r t i e s a r e n o p r o b l e m .I n d e e d , w e h a v e a c o m p r e h e n s i o n s c h e m a a p p l y i n g t o a n y p r e d ic a t e p h ra s e

w h a t e v e r, h o w e v e r c o m p l i c a t e d . ( L e t i t e v e n b e i n f i n i t e l y l o n g ; l e t i t e v e ni n c lu d e i m a g i n a r y n a m e s f o r e n ti ti es w e h a v e n ' t r e a ll y n a m e d . ) L e t x ra n g eo v e r t h i n g s , P o v e r p r o p e r t i e s ( c l a ss e s) o f t h i n g s. T h e n :

31PV7x x h a s P =-- l~x).

W e c o u l d a p p r o p r i a t e l y c a l l t h is ' th e p r o p e r t y o f I t -i n g ' i n t h o s e c a s e s w h e ret h e p r e d i c a t e p h r a s e is s h o r t e n o u g h t o f o r m a g e r u n d , a n d t a k e th i s p r o p e r t yt o b e t h e s e m a n t i c v a l u e o f th e g e r u n d . C o n t r a s t t h is w i t h t h e v e r y d if f e re n tr e l a t io n s h i p o f u n i v e r s a ls a n d p r e d i c a t e s s e t f o r t h i nUniversals, I I , pp . 7 -59 .

C o n s i d e r a l s o t h o s e s e n t e n c e s w h i c hprima facie i n v o l v e s e c o n d - o r d e rq u a n t i f i c a t i o n . F r o mUniversals, I , p . 6 2, a n d A g a i n s t ' O s t r i c h ' N o m i n a l i s mw e h a v e t h e s e .

( 7) H e h a s t h e s a m e v i r t u e s a s h is f a t h e r.( 8) T h e d r e s s e s w e r e o f t h e s a m e c o l o u r.(9 ) T h e r e a r e u n d i s c o v e r e d f u n d a m e n t a l p h y s i ca l p r o p e r t ie s .( 10 ) A c q u i r e d c h a r a c t e r i s t ic s a r e n e v e r i n h e r i te d .( 11 ) S o m e z o o l o g i c a l s p e c i e s a r e c r o s s - f e r t i le .

Prima facie, w e a r e q u a n t i f y i n g e i t h e r o v e r p r o p e r t i e s o r o v e r u n i v e r s a l s .A g a i n , p a r a p h r a s e s m i g h t d e f e a t t h a t p r e s u m p t i o n , b u t i n a p i e c e m e a l w a yt h a t t h r e a t e n s s y s t e m a t i c s e m a n t i c s . I n e a c h c a s e , p r o p e r t i e s c o u l d s e r v e a st h e v a l u e s o f t h e v a r i a b l e s o f q u a n t i f i c a t i o n . O n l y in c a s e (9 ) c o u l d u n i v e r s al ss e r v e e q u a l l y w e l l . To t r e a t t h e o t h e r c a s e s , n o t t o m e n t i o n

( 12 ) S o m e c h a r a c t e r i s ti c s , s u c h a s t h e c o l o u r s , a r e m o r e d i s j u n c t i v e t h a nt h e y s e e m .

a s q u a n t i f ic a t i o n s o v e r u n i v e r s a l s, w e w o u l d a g a i n h a v e t o r e s o r t to s o m ep r e l i m i n a r y p a r a p h r a s e . ( A r m s t r o n g a g a i n a g re e s:Universals, I , p . 63 . ) Th iss e c o n d s e m a n t i c a r g u m e n t , l ik e t h e f ir st , a d d u c e s w o r k f o r w h i c h p r o p e r ti e sa r e b e t t e r q u a l i f i e d t h a n u n i v e r s a l s .

W h i c h is n o t t o d e n y t h a t a p a r t n e r s h i p m i g h t d o b e t t e r s til l. L e t it b eg r a n t e d t h a t w e a r e d e a l in g w i t h q u a n t i f i c a t io n s o v e r p r o p e r t i e s . S t il l, th e seq u a n t i f i c a t i o n s - l ik e m o s t o f o u r q u a n t i f ic a t i o n s - m a y b e t a c i tl y o re x p l ic i tl y r e st r i c te d . I n p a r t i c u l a r , t h e y u s u a l l y a r e r e s t r ic t e d t o n a t u ra l

p r o p e r t i e s . N o t t o p e r f e c t l y n a t u r a l p r o p e r t i e s t h a t c o r r e s p o n d t o s in gleu n i v e r s a l s , e x c e p t i n s p e c i a l c a s e s l i k e ( 9 ) , b u t t o p r o p e r t i e s t h a t a r e a t l e a s ts o m e w h a t m o r e n a t u r a l t h a n t h e g r e a t m a j o r i t y o f t h e u t te r l y m is c el la n eo u s.T h a t is s o f o r a ll o u r e x a m p l e s , e v e n ( 12 ). T h e n e v e n t h o u g h w e q u a n t i f yo v e r p r o p e r t i e s , w e s ti ll n e e d e i t h e r u n i v e r s a l s o r t h e r e s o u r c e s o f a n a d e q u a t eN o m i n a l i s m i n o r d e r t o s a y w h i c h o f th e p r o p e r t i e s w e m o s t l y q u a n t i f y o v er.

12 Or b etter, in the case of creatures of his kind. See my 'Mad Pain and M artian Pain', in NedBlock, ed .,Readings in Philosophy of Psychology, I (H arvard University Press, 1980).

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I a l so t h i n k t h a t i t is p r o p e r t i e s t h a t w e n e e d i n c h a r a c t e r i s i n g t h e c o n t e n to f o u r i n t e n t i o n a l a t t i t u d e s . I b e l i e v e , o r I d e s ir e , t h a t I l iv e i n o n e o f th e

w o r l ds in a c e r t a i n c l a s s , r a t h e r t h a n a n y w o r l d o u t s i d e t h a t c l as s . T h i s c la s so f w o r l d s i s a p r o p e r t y h a d b y w o r l d s . I b e l ie v e , o r I d e si r e, t h a t m y w o r l dh a s t h a t p r o p e r t y . ( T h e c l a ss o f w o r l d s a l s o m a y b e c a ll e d ap r o p o s i t i o n ,in o n e o f th e l e g i t im a t e se n se s o f t h a t w o r d , a n d m y ' p r o p o s i t i o n a l a t t i tu d e 'o f b e l i e f o r d e s i r e h a s t h is p r o p o s i t i o n a s it s ' o b j e c t ' . ) M o r e g e n e r a l l y,s u b s u m i n g t h e p r e v i o u s c a s e , I b e l ie v e o r I d e si r e t h a t I m y s e l f b e l o n g t oa ce r t a in c l asso f p o s s i b i l i a . I a s c r i b e a c e r t a i n p r o p e r t y t o m y s e l f , o r I w a n tto h a v e it . O r I m i g h t a s c r i b e a p r o p e r t y t o s o m e t h i n g e ls e , o r e v e n t o m y s e l f ,u n d er a r e l a t io n o f a c q u a i n t a n c e I b e a r t o t h a t t hi ng .1 3 S u r e l y t h e p r o p e r t i e s

t ha t g i v e t h e c o n t e n t o f a t t i t u d e s i n t h e s e w a y s c a n n o t b e r e li e d o n t o b ep e r f ec t ly n a t u r a l , h e n c e c a n n o t b e r e p l a c e d b y u n i v e r s a l s . I t is in t e r e s ti n gto a s k w h e t h e r t h e r e i s a n y l o w e r l i m i t t o t h e i r n a t u r a l n e s s ( se e t h e f in a l s e c ti o no f t hi s p a p e r ) , b u t s u r e l y n o v e r y e x a c t in g s t a n d a r d is p o s s i b l e . H e r e a g a i np r o p e r t i e s a r e r i g h t f o r t h e j o b , u n i v e r s a l s a r e n o t .

O n e O v e r M a n y .A r m s t r o n g ' s m a i n a r g u m e n t f o r u n i v e r s a l s i s t h e ' O n eo v er M a n y ' . I t is b e c a u s e I f in d t h is a rg u m e n t u n c o n v i n c i n g t h a t I a mi n v e s t i g a t i n g a l t e r n a t i v e r e a s o n s t o a c c e p t a t h e o r y o f u n i v e r s a l s .

H e r e is a co n c is e s t a t e m e n t o f t h e a r g u m e n t , t a k e n b y c o n d e n s a t i o n f r o mA g a i n st ' O s t r i c h ' N o m i n a l i s m , p p . 4 4 0- 44 1 . A v e r y s im i l a r s t a t e m e n t c o u l d

h av e b e e n d r a w n f r o m t h e o p e n i n g p a g e s o fUn iv er sa l s .

I w o u l d w i s h t o s t a rt b y s a y i n g t h a t m a n y d i f f e r e n t p a r t i c u la r s c a n a ll h a v ew h a t a p p e a r s t o b e t h e s a m e n a t u r e a n d d r a w t h e c o n c l u s io n t h a t , a s aresu l t , t h e re i s ap r i m a f a c i e c a s e f o r p o s t u l a t i n g u n i v e r s a l s . We a r ec o n t i n u a ll y t a lk i n g a b o u t d i f f e r e n t th i n gs h a v i n g t h e s a m e p r o p e r t y o rq u a l it y, b e i n g o f th e s a m e s o r t o r k i n d , h a v i n g th e s a m e n a t u r e , a n d s o

o n . P h i l o s o p h e r s d r a w t h e d i s t in c t io n b e t w e e n s a m e n e s s o f to k e n a n ds a m e n e s s o f t y p e . B u t t h e y a r e o n l y m a k i n g e x p l ic i t a d i s ti n c t i o n w h i c ho r d i n a r y l a n g u a g e ( a n d s o , o r d i n a r y t h o u g h t ) p e r f e c t l y r e c o g n i s e s. I su g g e s tt h a t t h e f a c t o f s a m e n e s s o f t y p e is a M o o r e a n f a c t: o n e o f t h e m a n y f a c t sw h i ch e v e n p h i l o s o p h e r s s h o u l d n o t d e n y, w h a t e v e r p h i lo s o p h i c a l a c c o u n to r a n a ly s is t h e y g iv e o f s u c h f a c ts . A n y c o m p r e h e n s i v e p h i l o s o p h y m u s tt ry t o g iv e s o m e a c c o u n t o f M o o r e a n f a c ts . T h e y c o n s t it u te t h e c o m p u l s o r yq u e s t i o n s i n t h e p h i l o s o p h i c a l e x a m i n a t i o n p a p e r.

F r o m t h is p o i n t o f d e p a r t u r e , A r m s t r o n g m a k e s h i s c a s e b y c r it ic i si n g ri v a la t te m p t s t o a n s w e r t h e c o m p u l s o r y q u e s t i o n , a n d b y r e je c t in g v ie w s t h a tdecl ine to answer i t a t a l l .

S till m o r e c o n c i s e l y, t h e O n e o v e r M a n y p r o b l e m is p r e s e n t e d a s t h ep ro b le m o f g iv in g s o m e a c c o u n t o f M o o r e a n f a ct s o f a p p a r e n t s a m e n e s s o fty pe . T h u s u n d e r s t o o d , I a g r e e th a t t h e q u e s t i o n i s c o m p u l s o r y ; I a g r e e t h a t

1t See my 'AttitudesDe D ictoand D e S e , Philosophical Review88 (1979) pp. 513-543; and'Individuation by Acq uaintance and by Stipulation'.

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352 N ew W ork fo r a Theory o f Universals

A r m s t r o n g s p o s t u l a t i o n o f s h a r e d u n i v e r sa l s a n s w e r s i t; b u t I t h i n k t h a t a na d e q u a t e N o m i n a l i s m a l s o a n s w e r s i t .

A n e f f o r t a t s y s t e m a t i c p h i l o s o p h y m u s t i n d e e d g i v e a n a c c o u n t o f a n yp u r p o r t e d f a c t . T h e r e a r e t h r e e w a y s t o g iv e a n a c c o u n t . ( 1 ) I d e n y it -t h i s e a r n s a f a i l in g m a r k i f t h e f a c t is r e a l l y M o o r e a n . ( 2) I a n a l y s e i t t h u s

t h is i s A r m s t r o n g s r e s p o n s e t o t h e f a c t s o f a p p a r e n t s a m e n e s s o f ty p e.O r ( 3 ) I a c c e p t i t a s p r i m i t i v e . N o t e v e r ya c c o u n t i s an analysis A systemt h a t t a k e s c e r t a i n M o o r e a n f a c t s a s p r i m i t i v e , a s u n a n a l y s e d , c a n n o t b ea c c u s e d o f f a il i n g t o m a k e a p l a c e f o r th e m . I t n e i t h e r s h ir k s t h e c o m p u l s o r yq u e s t i o n n o r a n s w e r s i t b y d e n i a l . I t d o e s g iv e a n a c c o u n t .

A n a d e q u a t e N o m i n a l i s m , o f c o u r s e , is a t h e o r y th a t t a k e s M o o r e a n fa cts

o f a p p a r e n t s a m e n e s s o f t y p e as p r i m i t i v e . I t p r e d i c a t e s m u t u a l r e se m b l a n c eo f t h e t h i n g s w h i c h a r e a p p a r e n t l y o f th e s a m e t y p e ; o r i t p r e di c at e sn a t u r a l n e s s o f s o m e p r o p e r t y t h a t t h e y a ll sh a r e ,i.e. t h a t h a s t h e m a l l a sm e m b e r s ; a n d i t d e c l in e s t o a n a l y s e t h e s e p r e d i c a t i o n s a n y f u r t h e r. T h a t isw h y t h e p r o b l e m o f O n e o v e r M a n y, r ig h t ly u n d e r s t o o d , d o e s n o t p ro v id em o r e t h a n ap r i m a f a c ie r e a s o n t o p o s t u l a t e u n i v e r s a l s . U n i v e r s a l s a f f o r do n e s o l u t i o n , b u t t h e r e a r e o t h e r s .

I f e a r th a t t h e p r o b l e m d o e s n o t r e m a i n r i g h t ly u n d e r s t o o d . E a r l y inUniversalsi t u n d e rg o e s a n u n f o r t u n a t e d o u b l e t r a n s f o r m a t i o n . I n t h e co u rs eo f a f e w p a g e s(Universals, I , pp . 11-16) the l eg i timate dem an d fo r an accoun to f M o o r e a n f a c ts o f a p p a r e n t s a m e n e ss o f ty p e tu r n s i n t o a d e m a n d f o r ana n a l y s i s o f p r e d i c a t i o n i n g e n e r a l . T h ea n a l y s a n d u m b e c o m e s t h e s c h e m aa h a s t h e p r o p e r t y F . T h e t u r n i n g p o i n t t a k e s o n l y t w o s e n t e n c e s (p . 12):

H o w is [ th e N o m i n a l i s t ] t o a c c o u n t f o r t h e a p p a r e n t ( i f u s u a l l y pa rt ia l)i d e n t i t y o f n u m e r i c a l l y d i f f e r e n t p a r t ic u l a r s ? H o w c a n t w o d i f f e r e n t th in gsb o t h b e w h i te o r b o t h b e o n a ta b l e ?

A n d v e r y s o o n ( p p . 1 6 -1 7 ) t h o s e w h o r e f u s e t o c o u n t e n a n c e u n i v e r s al s b utw h o a t t h e s a m e t i m e s ee n o n e e d f o r a n y r e d u c t i v e a n a ly s e s [ o f t h e s c he m ao f p r e d i c a t i o n ] , t h o s e a c c o r d i n g t o w h o m t h e r e a r e n o u n i v e rs a l s b u t th ep r o p o s i t i o n t h a t a is F i s p e r f e c t l y a ll r i g h t a s i t i s s t a n d a c c u s e d o f d o dg in gt h e c o m p u l s o r y q u e s t i o n .

W h e n t h e d e m a n d f o r a n a c c o u n t - f o r a p l a c e i n o n e s s y s t e m - t u rn e di n t o a d e m a n d f o r a n a n a l y s is , t h e n I s a y th a t t h e q u e s t i o n c e a s e d t o bec o m p u l s o ry. A n d w h e n t h ea n a l y s a n d u ms w i tc h e d , f r o m M o o r e a n f ac ts o fa p p a r e n t s a m e n e s s o f t y p e to p r e d i c a t i o n g e n e r a l ly, t h e n I s a y t h a t the

q u e s t i o n c e a s e d t o b e a n s w e r a b l e a t a ll . T h e t r a n s f o r m e d p r o b l e m o f O neo v e r M a n y d e s e r v e s o u r n e g l e c t . T h e o s t r i c h t h a t w i ll n o t l o o k a t i t is a w iseb i r d i n d e e d .

D e s p i t e hi s w o r d s , I d o n o t t h i n k t h a t A r m s t r o n g r e a l ly m e a n s t o d e m a n d ,e i th e r f r o m N o m i n a l is t s o r f r o m h i m s e l f , af u l l y g e n e r a l a n a l y s i s o fp r e d i c a t i o n . F o r n o n e i s s o r e a d y a s h e t o i n s i s t t h a t n o t j u s t a n y s h a r e dp r e d i c a t e m a k e s f o r e v e n a p p a r e n t s a m e n e s s o f t y p e . ( T h a t i s w h a t g i ve s hist h e o r y i ts d i s ti n c t i v e i n t e r e s t a n d m e r i t . ) I t w o u l d b e b e t t e r t o p u t th et r a n s f o r m e d p r o b l e m t h u s: o n e w a y o r a n o t h e r , a ll p r e d i c a t io n is t o be

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354 N ew W ork fo r a T heory o f Universa ls

i n s t an t i a t es un iver sa l F ' o r 't h i s e l ec t ron has un i t charge ' . N o o ne -o ff analys isa p p l i e s t o t h i s s p e c if ic p r e d i c a t e . ' S u c h i d e n t i t y i n n a t u r e [ as r e s u lt s f r o m t heh a v i n g o f o n e u n i v e r s a l i n m a n y p a r t i c u l a r s ] is l i t e r a ll y i n e x p l i c a b l e , i n th es e n se t h a t i t c a n n o t b e f u r t h e r e x p l a i n e d . '(Un iv er sa l s , I , p . 109 . ) Nei therd o p r e d i c a t i o n s o f ' i n s t a n t i a t e s ' f a l l u n d e r A r m s t r o n g ' s g e n e r a l a n a l y s i s o f( o t h e r w i s e u n a n a l y s e d ) p r e d i c a t i o n . H i s i s an o n - r e l a t i o n a l R e a l i s m : h ed e c l in e s , w i t h g o o d r e a s o n , t o p o s t u l a t e a d y a d i c u n i v e r s a l o f in s t a n ti a ti o nt o b i n d p a r t i c u l a r s t o t h e i r u n i v e r s a l s. ( A n d i f h e d i d , i t w o u l d o n l y p o s tp o n et h e n e e d f o r p r i m i t i v e p r e d i c a t i o n . ) S o l e t a ll w h o h a v e f e l t t h e b i t e o fA r m s t r o n g ' s r e l a t i o n r e g r e s s r i s e u p a n d c r y' T u q u o q u e ' A n d l e t u s m a rkw e ll t h a t A r m s t r o n g is p r e p a r e d t o g i v eo n e p r e d i c a t e ' w h a t h a s b e e n s a i d

t o b e t h e p r i v i le g e o f t h e h a r l o t : p o w e r w i t h o u t r e s p o n s i b i li t y. T h e p r e d ic a tei s i n f o r m a t i v e , i t m a k e s a v i t a l c o n t r i b u t i o n t o t e l l i n g u s w h a t i s t h e c a s e ,t h e w o r l d is d i f f e r e n t i f i t is d i f f e r e n t , y e t o n t o l o g i c a l l y it i s s u p p o s e d n o tt o c o m m i t us . N i c e w o r k : i f y o u c a n g e t i t. ' ( C o m p a r e A r m s t r o n g o n Q u i ne 'st r e a t m e n t o f p r e d i c a t i o n , A g a i n s t ' O s t r ic h ' N o m i n a l i s m , p. 4 4 3 .)

L e t u s d u m p t h e p r o j e c t o f g e t ti n g r id o f p r i m i t i v e p r e d i c a t i o n , a n d r et ur nt o t h e s e n si b le - t h o u g h n o t c o m p u l s o r y - p r o j e c t o f a n a l y s i n g M o o r e a nf a c ts o f a p p a r e n t s a m e n e s s o f t y p e . N o w d o e s t h e r e l a t i o n r e g re s s serveA r m s t r o n g b e t t e r ? I t h i n k n o t . I t d o e s m a k e b e t t e r s e n s e w i t h i n t h e m o r es e n s i b le p r o j e c t , b u t i t st il l b i t es A r m s t r o n g a n d h i s r i v a l s w i t h e q u a l f o rc e .L e t th e N o m i n a l i s t s a y ' T h e s e d o n k e y s r e s e m b l e e a c h o t h e r , s o li ke w i se dot h o s e s t a r s , a n d t h e r e a n a l y s i s e n d s . ' L e t t h e P l a t o n i s t s a y 'T h i s s ta tu ep a r t i c ip a t e s i n t h e F o r m o f b e a u t y, l i k e w is e t h a t l e c t u r e p a r ti c i p a t e s i n theF o r m o f t r u t h , a n d t h e r e a n a ly s is e n d s . ' L e t A r m s t r o n g s a y 'T h i s e le ctro ni n s t a n t i a t e s u n i t c h a rg e , l i k e w i s e t h a t p r o t o n i n s t a n t i a t e s t r i p a r t i t e n e s s , a n dt h e r e a n a l y s i s e n d s . ' I t is p o s s i b l e t o c o m p l a i n i n e a c h c a s e t h a t a f a c t o fs a m e n e s s o f t y p e h a s g o n e u n a n a l y s e d , t h e t y p e s b e i n g r e sp e ct iv e ly

r e s e m b l a n c e , p a r t i c i p a t i o n , a n d i n s t a n t i a t io n . B u t it is f a r f r o m e v i d e n t th atthe a l l eged f ac t s a re M oo re an , an d s ti ll l es s ev id en t t ha t t h e f i rs t tw o a re moreM o o r e a n t h a n t h e th i r d . N o n e o f t h e m a r e re m o t e l y t h e e q u a ls o f t h e genuin eM o o r e a n f a c t t h a t , i n s o m e s e n se , d i f f e r e n t l u m p s o f g o l d a r e t h e sa m e ink i n d .

M i c h a e l D e v i t t h a s d e n o u n c e d t h e O n e o v e r M a n y p r o b l e m a s a m irageb e t t e r l e f t u n s e e n . 15 I h a v e f o u n d D e v i t t 's d i s c u s s i o n i n s t r u c t i v e a n d I ag reew i t h m u c h o f w h a t h e s ay s . B u t D e v i t t h a s j o i n e d A r m s t r o n g i n t ra n s fo r m i n gt h e O n e o v e r M a n y p r o b l e m . H e t a k e s i t t o b e t h e p r o b l e m o f a n a ly s in g the

s c h e m a

a a n d b h a v e t h e s a m e p r o p e r t y ( a r e o f t h e s a m e t y p e ) , F - n e s s

o t h e r w i s e t h a n b y m e a n s o f a o n e - o f f a n a l y si s f o r s o m e s p e c if ic F. To th atp r o b l e m i t i s f a i r t o a n s w e r a s h e d o e s t h a t

'Ostrich Nominalism' or 'Mirage Realism'? ,Pacific Philosophical Quarterly61 (1980)pp. 433-439. De vitt speaks on behalf o f Qu ine as w ell as himself; Qu ine indicates agreementwith Dev itt in 'Soft Impe achm ent Disowned'.

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a is F; b is F

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is a n a ly s is e n o u g h , o n c e w e g iv e o v e r th e a i m o f d o i n g w i t h o u t p r i m i t iv ep r e d i c a ti o n . B u t D e v i t t h a s s e t h i m s e l f t o o e a s y a p r o b l e m . I f w e a t te n d t oth e m o d e s t , u n t r a n s f o r m e d O n e o v e r M a n y p r o b l e m , w h i c h is n o m i ra g e ,w e w i ll a s k a b o u t a d i f f e r e n tan a ly s an d u m:

a a n d b h a v e s o m e c o m m o n p r o p e r t y ( ar e s o m e h o w o f th e s a m e t y pe )

in w h i c h i t i s n o t s a i d w h a t a a n d b h a v e i n c o m m o n . T h i s l e ss d e fi n i teana lysandumis n o t c o v e r e d b y w h a t D e v i t t h a s s a id . I f w e t a k e a c l e a rl yM o o r e a n c a se , h e o w e s u s a n a c c o u n t : e i t h e r a n a n a l y s i s o r a n o v e r t r e s o r tto p r i m i ti v e p r e d i c a t i o n o f r e s e m b l a n c e .

Dupl ica t ion Superven ience an d D ivergen t W or lds .H e n c e f o r t h I s h a l lspeak o n l y o f m y n e e d f o r t h e d i s t in c t i o n b e t w e e n n a t u r a l a n d u n n a t u r a l ,o r m o r e a n d l es s n a t u r a l , p r o p e r t i e s . I t is t o b e u n d e r s t o o d t h a t t h e w o r kI h a ve i n s t o r e f o r a n a d e q u a t e l y d i s c r i m i n a t o r y t h e o r y o f p r o p e r t i e s m i g h tbe n e w w o r k f o r a t h e o r y o f u n i v e r s a ls , o r i t m i g h t i n s t e a d b e w o r k f o r t h er e s o u r c e s o f a n a d e q u a t e N o m i n a l i s m .

I b e g i n w i t h t h e p r o b l e m o f a n a l y s i n g d u p l i c a t i o n . W e a r e f a m i l i a r w i t hcases o f a p p r o x i m a t e d u p l i c a t i o n ,e.g. w h e n w e u s e c o p y i n g m a c h i n e s. A n dwe u n d e r s t a n d t h a t i f t h e se m a c h i n e s w e r e m o r e p e r f e c t t h a n t h e y a r e , t h ecopies t h e y m a d e w o u l d b e p e r f e c t d u p l i c a t e s o f t h e o r i g i n a l. C o p y a n do rig in al w o u l d b e a l i k e in s iz e a n d s h a p e a n d c h e m i c a l c o m p o s i t i o n o f t h eink m a r k s a n d t h e p a p e r , a l ik e in t e m p e r a t u r e a n d m a g n e t i c a l i g n m e n t a n de le c tr o st at ic c h a rg e , a l i k e e v e n in t h e e x a c t a r r a n g e m e n t o f t h e i r e l e c t r o n sand q u a r k s . S u c h d u p l i c a t e s w o u l d b e e x a c t l y a l ik e , w e s a y. T h e y w o u l d m a t c hp e rf ec tl y, t h e y w o u l d b e q u a l i t a t i v e l y i d e n t i c a l , t h e y w o u l d b e i n d i s c e r n i b le .

B u t t h e y w o u l d n o t h a v e e x a c t l y t h e s a m e p r o p e r t i e s , i n m y s e ns e o f th ew ord . A s i n t h e c a s e o f a n y t w o t h i n g s , c o u n t l e s s c l a ss b o u n d a r i e s w o u l dd iv id e t h e m . I n t r i n s i c a l l y, l e a v i n g o u t t h e i r r e l a t i o n s t o t h e r e s t o f t h e w o r l d ,they w o u l d b e j u s t a l ik e . B u t t h e y w o u l d o c c u p y d i f f e r e n t s p a t i o - t e m p o r a lpos itions; an d th ey m igh t h ave d i ff e ren t owne rs , be f i r st exam ined in d i ff e ren tcenturies, an d so on .

S o i f w e w i s h t o a n a l y s e d u p l i c a t i o n i n t e r m s o f s h a r e d p r o p e r t i e s , i t se e m sthat we m us t f i rs t d i s t i ngu i sh theintrinsic ( o r i n t e r n a l ) p r o p e r t i e s f r o m t h e

extrinsic( o r e x t e r n a l o r r e l a ti o n a l ) p r o p e r t i e s . T h e n w e m a y s a y t h a t t w oth in gs a r e d u p l i c a t e s i f f t h e y h a v e p r e c i s e l y t h e s a m e i n t r in s i c p r o p e r t i e s ,h ow ev er m u c h t h e i r e x t ri n s ic p r o p e r t i e s m i g h t d i f f e r. B u t o u r n e w p r o b l e mo f d iv id in g t h e p r o p e r t i e s i n t o i n t r in s i c a n d e x t r i n s i c is n o e a s ie r t h a n o u ro rig in al p r o b l e m o f a n a l y s i n g d u p l i c a t i o n . I n f a c t , t h e t w o p r o b l e m s a r ejo in ed i n a ti g h t l i tt le c i r c le o f i n t e r d e f i n a b i l i ty. D u p l i c a t i o n is a m a t t e r o fsh arin g i n t ri n s ic p r o p e r t i e s ; i n t ri n s i c p r o p e r t i e s a r e j u s t t h o s e p r o p e r t i e s t h a tn ev er d i f f e r b e t w e e n d u p l i c a t e s . P r o p e r t y P i s i n t r in s i c i ff , f o r a n y t w od u p l i c a t e t h i n g s , n o t n e c e s s a r i l y f r o m t h e s a m e w o r l d , e i t h e r b o t h h a v e P

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3 5 6 N e w W o r k f o r a T h e o r y o f U n iv er sa ls

o r n e i t h e r d o e s . P i s e x t r i n s i c i f f t h e r e i s s o m e s u c h p a i r o f d u p l i c a t e s o f w h ic ho n e h a s P a n d t h e o t h e r l a c k s p .1 6

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

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

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

t h i s f o r w a r d a s a d e f i n i t i o n ? B u t s u c h a ' d e f i n i t i o n ' i s n o a n a l y s i s . I t

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

a n d k n o w n a p o s t e r i o r i . T h e d e f i n i t i o n d o e s n o t a p p l y t o d u p l i c a t i o n a t

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

t h a t d i f f e r in t h e i r p h y s i c s . N o r d o e s i t c a p t u r e w h a t t h o s e i g n o r a n t o f p h ys ic s

m e a n w h e n t h e y s p e a k - a s t h e y d o - o f d u p l i c a t i o n .

T h e p r o p e r c o u r s e , I s u g g e s t , i s t o a n a l y s e d u p l i c a t i o n i n t e r m s o f s h a r e dp r o p e r t i e s ; b u t t o b e g i n n o t w i t h t h e i n t r i n s ic p r o p e r t i e s b u t r a t h e r w i t h n a t u ra l

p r o p e r t i e s . Tw o t h i n g s a r e q u a l i t a t i v e d u p l i c a t e s i f t h e y h a v e e x a c t l y t h e sa m ep e r f e c t l y n a t u r a l p r o p e r t i e s . 17

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

16 Given du p l ica t ion , we ca n a l so sub d iv ide the ex t r in s ic p rop er t i es , d i s t ingu ish ing pu re casesf rom var ious mix tu res o f ex t rin s ic and in t rin s ic . Par t i t ion the th ings , o f th i s and o ther wor lds,i n t o e q u i v a l e n c e cl as s es u n d e r t h e r e l a t i o n o f d u p l i c a t io n . A p ro p e r t y ma y d i v i d e a nequ iva lence c las s, ma y inc lude i t , o r ma y exc lude i t. A p ro per ty P i s ex t r in s ic , a s we said ,i f it d iv ides a t l eas t some o f the c las ses . We hav e fo u r subcases . (1 ) P d iv ides every c lass ;t h e n w e m a y c a llPp ur ely extr ins ic .(2) P d iv ides some classes , includes som e, a nd excludesnon e ; then P i s the d i s junc t ion o f an in t r in s ic p ro per ty and a pu re ly ex t r in s ic p rope r ty. (3)P d iv ides some, exc ludes some, a nd inc ludes non e ; then P i s the co n jun c t ion o f an in t r in s icp rop er ty a nd a pu re ly ex t r in s ic p rop er ty. (4) P d iv ides some, inc ludes some, a nd exc ludess o me ; t h e n P i s t h e c o n j u n c t i o n o f a n i n t r i n s i c p ro p e r t y a n d a n i mp u re l y e x t ri n s ic pro p e rt yo f the so r t cons idered in the second case , o r equ iva len t ly i s the d i s ju nc t ion o f an in tr in sicp ro p e r t y a n d a n i mp u re l y e x t r in s i c p ro p e r t y o f t h e s o r t c o n s i d e re d i n t h e t h i rd c a se .

W e can a l so c lass i fy re la t ions as in t r in s ic o r ex t r in s ic , bu t in two d i ffe ren t ways . Takea dyad ic re la t ion ,i.e. a c las s o r o rdered pa i rs . Ca l l the re la t ionintrinsic to its relataiff,

w h e n e v e r a a n da ' are dup l ica tes (o r iden t ica l) and b and b ' a re du p l ica tes (o r iden t ica l ),then bo th o r n e i ther o f the pa ir s < a ,b > and < a ' , b ' > s t and in the re la t ion . Ca l l the re la tionintrinsic to itsp air si f f , when ever the pa i r s< a , b > a n d < a ' , b > them selve s are duplicates,then bo th o r ne i ther o f them s tand in the re la t ion . In the second case , a s t ronger requ iremen ti s impo sed on the pa i r s . F o r in s tance they migh t fa i l to be dup l ica te pa i r s because the d is tanceb e t w e e n a a n d b d i f fe r s f ro m t h e d is t a n c e b e t w e e n a ' a n d b ' , e v e n t h o u g h a a n da ' aredup l ica tes and b and b ' a re dup l ica tes . In trad i t iona l te rm ino log y, ' i n te rna l re la t ions ' a rein t r in s ic to the i rrelata; ' ex te rna l re la t ions ' a re in t r in s ic to the i r pa i r s bu t n o t to th e i rrelata;and rela t ions extr ins ic even to the ir pairs , such as the re la t ion of be longing to the sam e owner,ge t l e f t ou t o f th e c las s i f i ca tion a l toge ther.

O ur defin i t ion of in t r ins ic prop ert ies in term s o f du pl icat ion closely resemb les the defini tionof 'd i ffe ren t ia l p rop er t i es ' g iven by Michae l S lo te in 'Some T hou gh ts on G oo dm an 's R idd le ',Analys i s27 (1967) pp . 128-132, an d inReason and Scepticism(Geo rge Allen Un win , 1970).Bu t where I quan t i fy overpossibilia, Slote appl ies mo dal i ty to o rd ina ry, p resu m ably actualist ,quan t i f i e rs . Th a t m akes a d i ffe rence . An ex t r in s ic p rop er ty m igh t d i ffe r be twe en dup lica tes ,b u t o n l y w h e n t h e d u p l i ca t e s in h a b i t d i f f e r e n t w o r ld s ; t h e n S l o te w o u l d c o u n t t h e p ro p e rt ya s d i f f e r e n t ia l . A n e x a mp l e i s t h e p ro p e r t y o f b e i n g a s p h e re t h a t i n h a b i t s a w o r l d w h eret h e re a r e p i gs o r a c u b e t h a t i n h a b i t s a w o r l d w i t h o u t p i g s.

See my 'Ex t r in s ic Proper t i es ' ,Phi losophical Studies 44(1983) fo r fu r ther d i scuss ion o ft h e c i r c le f ro m d u p l i c a t i o n t o i n t r i n s ic n e s s a n d b a c k .

17 Likewise< a , b > a n d < a ' , b > a n d d u p l i c a t e p a i r s i f f a a n da ' have exac t ly the samep e r f e c t l y n a t u ra l p ro p e r t i e s , a n d s o d o b a n db ' , and a l so the per fec t ly na tu ra l re la t ionsb e t w e e n a a n d b a r e e x ac t ly th e s a me a s t h o s e b e t w e e n a ' a n d b ' .

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a n al ys is o f c a u s a l c o u n t e r f a c t u a l s a n dde re m o d a l i t y. I f n o t , s u c h p r o j e c t sa re d o o m e d f r o m t h e s ta r t, a n d w e n e e d n t l o o k a t t h e d e ta i ls o f th e a t t e m p t s .

B ut w e c a n n o t e v e n r a is e th e s e q u e s t i o n s o f s u p e r v e n i e n c e u n l e s s w e c a n s p e a ko f d u p l i c a t e w o r l d s . A n d t o d o t h a t , I h a v e s u g g e s t e d , w e n e e d n a t u r a lp ro p er t i e s .

( N o t e t h a t i f p o s s i b l e w o r l d s o b e y a p r i n c ip l e o f i d e n t it y o f q u a l it a t iv ei nd is c er n ib le s , t h e n a ll t h e s e s u p e r v e n i e n c e t h e s e s h o l d a u t o m a t i c a l l y. I f n otw o w o r l d s a r e d u p l i c a t e s , t h e na f o r t i o r i n o t w o a r e d u p l i c a t e s t h a t d i f f e rin t h e i r p r o b a b i l i t i e s , l a w s . . . . . o r a n y t h i n g e l se . )

We m i g h t a l s o a s k w h e t h e r q u a l it a ti v e c h a r a c t e r s u p e r v e n e s o n a n y t h i n gl e s s . F o r i n s t a n c e , w e m i g h t a s k w h e t h e r g l o b a l q u a l i t a t i v e c h a r a c t e r

s u p e rv e n e s o n l o c a l q u a l i t a ti v e c h a r a c t e r. S a y t h a t t w o w o r l d s a r elocalduplicates i f f t h e y a r e d i v is ib l e i n t o c o r r e s p o n d i n g s m a l l p a r t s i n s u c h a w a yt h a t ( 1 ) c o r r e s p o n d i n g p a r t s o f t h e t w o w o r l d s a r e d u p l i c a t e s , a n d ( 2 ) t h ec o r r e s p o n d e n c e p r e s e r v e s s p a t i o t e m p o r a l r e l a t i o n s . ( T h e e x a c t m e a n i n gd e pe n ds , o f c o u r s e, o n w h a t w e m e a n b y s m a l l . ) I f tw o w o r l d s a r e l o c a ld u p li ca te s , t h e n m u s t t h e y b e d u p l i c a t e ss impl ic i ter?O r c o u l d t h e y d i f f e r inw a ys t h a t d o n o t p r e v e n t l o c a l d u p l i c a t i o n -e g i n e x t e r n a l r e l a t i o n s , o t h e rt ha n t h e s p a t i o t e m p o r a l r e l a t io n s t h e m s e l v e s , b e t w e e n s e p a r a t e d t h i n g s ?A g a in , w e m u s t m a k e s e n s e o f d u p l i c a t i o n - t h is ti m e , b o t h i n t h e la rg ean d in th e sm al l - ev e n to a sk th e q u e s t io n . 19

N e x t , d i v e rg e n t w o r l d s . I s h a l l s a y t h a t t w o p o s s i b l e w o r l d sdiverge i f f t h e yare n o t d u p l ic a t e s b u t t h e y d o h a v e d u p l i c a t e in i ti a l t e m p o r a l s e g m e n t s . T h u so ur w o r l d a n d a n o t h e r m i g h t m a t c h p e r f e c t l y u p t h r o u g h t h e y e a r 1 94 5, a n dgo t h e ir s e p a r a t e w a y s t h e r e a f t e r.

N o t e t h a t w e n e e d n o i d e n ti ty o f t im e s a c r o s s w o r l d s. O u r w o r l d t h r o u g ho u r 1945 d u p l i c a t e s a n i n it ia l s e g m e n t o f t h e o t h e r w o r l d ; t h a t o t h e r w o r l d l ys eg m e n t e n d s w i t h a y e a r t h a t i n d e e d r e s e m b l e s o u r 1 94 5, b u t it is p a r t o fo t h e rw o r l d ly ti m e , n o t p a r t o f o u r t i m e . A l s o , w e n e e d n o s e p a r a t i o n o f t i m ea nd s p a c e t h a t c o n t r a v e n e s R e l a t i v i ty - w e h a v e i n it ia l t e m p o r a l s e g m e n t s ,o f th is o r a n o t h e r w o r l d , i f w e h a v e s p a t i o t e m p o r a l r e g io n s b o u n d e d b ys p a c e l i k e s u r f a c e s t h a t c u t t h e w o r l d i n t w o .

I d is t ingu ishdivergenceo f w o r l d s f r o mbranch ingo f w o r l d s . I n b r a n c h i n g ,i ns te a d o f d u p l i c a t e s e g m e n t s , o n e a n d t h e s a m e i n it ia l s e g m e n t is a ll e g e d ly

s ha re d a s a c o m m o n p a r t b y t w o o v e r l a p p i n g w o r ld s . B r a n c h i n g i sp r o b l e m a t i c i n w a y s t h a t d i v e rg e n c e is n o t . F i r s t, b e c a u s e a n i n h a b i t a n t o fth e s h a r e d s e g m e n t c a n n o t s p e a k u n e q u i v o c a l l y o fthe w o r l d h e l iv e s i n . W h a tif h e sa y s t h e r e w il l b e a s e a f ig h t t o m o r r o w , m e a n i n g o f c o u r s e t o s p e a ko f t h e f u t u r e o f h is o w n w o r l d , a n d o n e o f th e t w o w o r l d s h e l iv e s i n h a s

19 Sucha thesis of supervenienceof the global on the local resembles he holographichypothesisconsidered and rejected by Saul Kripke in Identity Through Time , presented at the 1979conference of the Am erican Philosophical Association, Eastern Division, and elsewhere.

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a sea fight the next day and the other doesn t? Sec ond, b ecause overlap ofworlds interferes with the most salient principle of demarcation for worlds,v i z . that two possible individuals are p art of the same world iff they are linkedby some chain o f external relations, e . g . of spa tiotem poral relations. (I knowof n o oth er example.) Neither of these difficulties seems insuperable, but bothare better avoided. That makes it reasonable to prefer a theory ofnonover lappin g divergent worlds to a th eory o f branching worlds. Then weneed to be able to speak of qualitative dupli cation of world-segments, whichwe can do in terms of shared natural properties.

Divergent (or branchin g) worlds are o f use in defining Determinism. Theusual definitions are not very satisfactory. If we say that every event has a

cause, we overlo ok probabilistic causation u nder Indeterminism. If we speakof what could be predicted by a superhuman calculator with unlimitedknowledge of history and the laws of nature, we overloo k obstacles that mightprevent prediction even under Determinism, or else we try to makenonvacuous sense of counterfactuals about what our predictor could do ifhe had some quite impossible combination of powers and limitations.

A better approach is as follows. First, a system of laws of nature isDeterministic iff no two divergent worlds bo th co nf or m perfectly to the lawsof that system. Second, a world is Deterministic iff its laws comprise aDeterministic system. Third, Determinism is the thesis that our world isDetermin istic. E

(Alternative versions of Determinism can be defined in similar fashion.For instance, we could strengthen the first step by prohibiting convergenceas well as divergence of law-abiding worlds. Or we could even require thatno two law-abiding worlds have duplicate momentary slices without beingduplicates throughout their histories. Or we could define a weaker sort ofDeterminism: we could call a world f o r t u i t o u s l y Deterministic, even if itslaws do n ot comprise a Deterministic system, iff no world b oth diverges fromit and co nfor ms to its laws. The laws an d early histo ry of such a world sufficeto determine later histo ry, but only because the situations in which the lawsfall short o f Determinism never arise. We mig ht equivalently defirae fortuitousDeterminism as follows: for any historical fact F and any initial segment Sof the world, there are a true proposition H about the history of S-and atrue pro posi tion L abo ut the laws of nature, such tha t H and L together

2strictly imply F. Does this definition bypass our need to speak of duplicationof initial segments? Not so, for we must ask what it means to say that H

20 This approach is due, in essence, to Richard Montague, Deterministic Theories , in Decisions,Values and Group s,II (Pergamon Press, 1962), and in his Formal Philosophy YaleUniversityPress, 1974). But Montague did not speak as I have done of duplication of initial segmentsof worlds in virtue of the sharing of certain 61ite properties. Instead, he used sameness ofdescription in a certain vocabulary, which vocabulary was left as an unspecified parameterof his analysis. For he wrote as a logician obliged to remain neutral on questions ofmetaphysics.

21 A closely related definition appears in Peter van Inwagen, The Incompatibility of Free Willand Determinism , Philosophical Studies27 (1975) pp. 185-199.

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is a b o u t t h e h i s t o r y o f S . I t a k e t h a t t o m e a n t h a t H h o l d s a t b o t h o r n e i t h e ro f a n y t w o w o r l d s t h a t b o t h b e g i n w i t h s e g m e n t s t h a t a r e d u p l i c a t e s o f S .)

D i v e r g e n t w o r l d s a r e i m p o r t a n t a l so i n c o n n e c t i o n w i th t h e s o r t o fc o u n t e r f a c t u a l c o n d i t i o n a l t h a t f ig u r e s i n p a t t e r n s o f c a u s a l d e p e n d e n c e . S u c hc o u n t e r f a c t u a ls t e n d t o b e t e m p o r a l l y a s y m m e t r i c , a n d t h i s is w h a t g iv e s r is eto t h e a s y m m e t r y o f c a u s a t i o n i ts e lf . C o u n t e r f a c t u a l s o f t hi s s o rt d o n o tb a c k t r a c k : i t is n o t t o b e s a id t h a t i f t h e p r e s e n t w e r e d i f f e r e n t a d i f f e r e n t

p as t w o u l d h a v e l e d u p t o i t, b u t r a t h e r t h a t i f t h e p r e s e n t w e r e d i f f e r e n t ,th e s a m e p a s t w o u l d h a v e h a d a d i f fe r e n t o u t c o m e . G i v e n a h y p o t h e s i s e dd i ff e re n c e a t a c e r t a i n t i m e , t h e e v e n t s o f f u t u r e t i m e s n o r m a l l y w o u l d b ev er y d i f f e r e n t i n d e e d , b u t t h e e v e n t s o f p a s t t i m e s ( e x c e p t p e r h a p s f o r t h e

v er y n e a r p a s t ) w o u l d b e n o d i f f e r e n t . T h u s a c t u a l i t y a n d its c o u n t e r f a c t u a la l te r n a ti v e s a r e d i v e rg e n t w o r l d s , w i t h d u p l i c a t e i n it i a l s e g m e n t s , z2

Minimal Mater ia l i sm. T h e r e is a d i ff i c u lt y th a t a r is e s i f w e a t t e m p t t of o r m u l a t e c e r t a i n r e d u c t i o n i s t v i e w s , f o r i n s ta n c e M a t e r i a l i s m , a ss u p e r v en i e n c e t h e s e s . A s o l u t i o n t o t h i s d if f i c u lt y e m p l o y s n a t u r a l p r o p e r t i e sn ot o n l y b y w a y o f d u p l i c a t i o n b u t i n a m o r e d i r e c t w a y a l s o .

R o u g h l y s p e a k i n g , M a t e r i a l i s m is t h e t h e si s t h a t p h y s i c s - s o m e t h i n g n o tto o d i f fe r e n t f r o m p r e s e n t - d a y p h y s ic s , t h o u g h p r e s u m a b l y s o m e w h a ti m p r o v e d - is a c o m p r e h e n s i v e t h e o r y o f t h e w o r l d , c o m p l e t e a s w e ll a sc o rr e ct . T h e w o r l d i s a s p h y s ic s s a y s it is , a n d t h e r e s n o m o r e t o s a y. W o r l dh is to r y w r i t t e n i n p h y s i c a l l a n g u a g e is al l o f w o r l d h i s t o r y. T h a t i s r o u g hs p e ak i ng i n d e e d ; o u r g o a l w ill b e t o g iv e a b e t t e r f o r m u l a t i o n . B u t b e f o r eI t ry t o s a y m o r e p r e c i s e l y w h a t M a t e r i a l i s m i s, l et m e s a y w h a t i t is n o t .(1) M a t e r i a l i s m is n o t a th e s i s o f f i n it e t r a n s l a t i b i l i t y o f a l l o u r l a n g u a g e i n t oth e l a n g u a g e o f p h y s i c s . ( 2 ) M a t e r i a l i s m is n o t t o b e i d e n t if ie d w i t h a n y o n eM a t e r ia l is t t h e o r y o f m i n d . I t is a t h e si s t h a t m o t i v a t e s a v a r i e t y o f t h e o r i e s

o f m i n d : v e r s io n s o f B e h a v i o u r i s m , F u n c t i o n a l i s m , t h e m i n d - b o d y i d e n ti t yt h eo r y, e v e n t h e t h e o r y t h a t m i n d is a ll a m i s t a k e . (3 ) M a t e r i a l i s m is n o t j u s tth e t h e o r y t h a t t h e r e a r e n o t h i n g s e x c e p t th o s e r e c o g n i s e d b y p h y s ic s . Tob e s u r e, M a t e r i a l is t s d o n t b e l i e v e in s p i ri ts , o r o t h e r s u c h n o n p h y s i c a l t h i n g s .B u t a n t i m a t e r i a l i s t s m a y n o t b e l i e v e i n s p i ri ts e it h e r - t h e i r c o m p l a i n t n e e d n tb e t h a t p h y s ic s o m i t s s o m e o f t h e t h in g s t h a t t h e r e a r e . T h e y m a y c o m p l a i ni ns te a d t h a t p h y s i c s o v e r l o o k s s o m e o f t h e

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