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A refutation of the principle of the Identity of Indiscernibles Timmis, Mark William 1984

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A REFUTATION OF THE PRINCIPLE OF THE IDENTITY OF INDISCERNIBLES By MARK WILLIAM TIMMIS B.A., The University of B r i t i s h Columbia, 1984 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (Department of philosophy) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1984 © Mark William Timmis, 1984 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requ i rement s f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Co lumb ia , I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s tudy . I f u r t h e r agree tha t p e r m i s s i o n f o r e x t e n s i v e copy ing of t h i s t h e s i s f o r s c h o l a r l y purposes may be g ranted by the head of my department or by h i s o r her r e p r e s e n t a t i v e s . I t i s unders tood that copy ing or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a in s h a l l not be a l lowed w i thout my w r i t t e n p e r m i s s i o n . Department of ?W\[ybS>0?&/ The U n i v e r s i t y of B r i t i s h Columbia 1956 Main M a l l Vancouver , Canada V6T 1Y3 Date i i ABSTRACT The p r i n c i p l e of the I d e n t i t y of I n d i s c e r n i b l e s s t a t e s tha t q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s are n e c e s s a r i l y n u m e r i c a l l y i d e n t i c a l . The purpose of t h i s t h e s i s i s to o f f e r what I b e l i e v e i s a c o n c l u s i v e r e f u t a t i o n of t h i s p r i n c i p l e . S ince the p r i n c i p l e of the I d e n t i t y of I n d i s c e r n i b l e s was f i r s t s t a t e d by L e i b n i z i n 1684, a number of p h i l o s p h e r s have argued tha t the p r i n c i p l e i s f a l s e . C e n t r a l to t h e i r arguments has been the c l a i m tha t i t i s l o g i c a l l y p o s s i b l e f o r n u m e r i c a l l y d i s t i n c t o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and t h e r e f o r e q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s are not n e c e s s a r i l y n u m e r i c a l l y i d e n t i c a l . However, the d i f f i c u l t y w i th t h i s argument i s tha t i t merely a s s e r t s tha t d i s t i n c t i n d i s c e r n i b l e s are a l o g i c a l p o s s i b i l i t y and t h i s of course i s something which proponents of the I d e n t i t y of I n d i s c e r n i b l e s would o b v i o u s l y deny. Thus type of argument, which i s termed an i n d i v i d u a t i o n argument, does not then p r o v i d e c o n c l u s i v e grounds on which to r e j e c t the I d e n t i t y of I n d i s c e r n i b l e s . My argument a g a i n s t the I d e n t i t y of I n d i s c e r n i b l e s i s not an i n d i v i d u a t i o n argument, tha t i s , i t does not seek to e s t a b l i s h tha t d i s t i n c t i n d i s c e r n i b l e s are a l o g i c a l . p o s s i b i l i t y . Rather, what my argument endeavours to show i s t h a t the I d e n t i t y of I n d i s c e r n i b l e s i m p l i e s an unacceptable view of the nature of o b j e c t s . T h i s argument i s e s t a b l i s h e d , f i r s t , by i n d i c a t i n g those f e a t u r e s of recognized o n t o l o g i e s which are incompatible with the I d e n t i t y of I n d i s c e r n i b l e s and, t h e r e f o r e , through a process of e l i m i n a t i o n , those f e a t u r e s which are compatible with the p r i n c i p l e . These f e a t u r e s together form the view of the nature of o b j e c t s to which proponents of the I d e n t i t y of I n d i s c e r n i b l e s are committed, and which i s i n turn shown to be unacceptable. i v TABLE OF CONTENTS A b s t r a c t i i I n t r o d u c t i o n 1 Chapter One: EU-Onto logy 20 Chapter Two: R e l a t i v e Space and Time 39 I. B l a c k ' s I n d i v i d u a t i o n Argument 42 II. A Second I n d i v i d u a t i o n Argument 47 I I I . The Argument from the Nature of Ob jec t s 54 Chapter T h r e e : Abso lu te Space and Time 86 B i b l i o g r a p h y 93 1 INTRODUCTION The p r i n c i p l e of the Identity of Indiscernibles was f i r s t stated by Leibniz in his correspondence with Clark in the following form: "there i s no such thing as two individuals indiscernible from each other" (Loemker 1956, p. 1117). The basis of this metaphysical claim was the pr i n c i p l e of S u f f i c i e n t Reason. According to Leibniz, God could have no s u f f i c i e n t reason for putting one set of properties at one place and a second set of precisely the same properties at another place rather than the other way round. In contemporary philosophy, epistemological claims about how objects are i d e n t i f i e d have replaced the p r i n c i p l e of S u f f i c i e n t Reason and, as a r e s u l t , the Identity of Indiscernibles has remained the subject of recurring int e r e s t . At the turn of the century, for example, G.E. Moore claimed to have refuted the p r i n c i p l e (Moore 1901). This claim was further substantiated by Bertrand Russell's analysis of space and time in his Presidential Address to the A r i s t o t e l i a n Society (Russell 1911). However, by mid-century, epistemological considerations had led Russell 2 to abandon h i s e a r l y view of space and time and wi th i t h i s case a g a i n s t the I d e n t i t y of I n d i s c e r n i b l e s ( R u s s e l l 1948). A l though R u s s e l l was to r e a f f i r m t h i s . v i e w ( R u s s e l l 1959), h i s argument d i d not go uncha l l enged . In 1952, Max B lack p u b l i s h e d what i s w ide l y regarded as the most s u c c e s s f u l a t t a c k a g a i n s t the I d e n t i t y o f I n d i s c e r n i b l e s (B lack 1976). However, many p h i l o s o p h e r s , such as A . J . Ayer and D . J . O 'Conner , have remained unconv inced. A . J . Aye r , f o r example, has argued tha t d e s p i t e a l l tha t B lack urges a g a i n s t the p r i n c i p l e he i s s t i l l " i n c l i n e d " to ho ld that the p r i n c i p l e i s n e c e s s a r i l y t rue (Ayer 1976) wh i l e D . J . O 'Conner has c r i t i c i z e d not j u s t B lack but the gene ra l u n w i l l i n g n e s s of opponents of the p r i n c i p l e to d i s c u s s f u r t h e r i s sues which might bear upon the v a l i d i t y of the p r i n c i p l e (O'Conner 1976 ) . The purpose o f t h i s t h e s i s , however, w i l l not be to reach a consensus on the v a r i o u s i s sues i n v o l v e d , but to o f f e r a c o n c l u s i v e r e f u t a t i o n of the I d e n t i t y o f I n d i s c e r n i b l e s , h e r e a f t e r r e f e r r e d to as I I. T h i s w i l l be done by showing that the metaphy s i ca l c o n c l u s i o n that i t i s n e c e s s a r i l y the case that " t h e r e i s no such t h i n g as two i n d i v i d u a l s i n d i s c e r n i b l e from each o t h e r " e n t a i l s an unacceptab le o n t o l o g y . In o rde r to e s t a b l i s h t h i s argument i t i s neces sa ry to determine what I I a s s e r t s . But , be fo re t u r n i n g to t h i s q u e s t i o n , i t i s important to d i s t i n g u i s h my 3 argument for this thesis from those of the early Russell, Black and Moore. Both the early Russell and Black endeavour to show that two indiscernible objects are not necessarily i d e n t i c a l . The reason, they suggest, i s that i t i s in fact l o g i c a l l y possible for there to be two q u a l i t a t i v e l y indistinguishable and yet numerically d i s t i n c t objects. Consequently, i f I I were true, there would be no basis for t e l l i n g the two objects apart, as the objects would quite l i t e r a l l y be i n d i s c e r n i b l e . This l i n e of argument is commonly referred to as the "individuation argument". My argument for this thesis d i f f e r s from the early Russell's and Black's thesis in three ways. F i r s t , I do not take the individuation argument to be strong enough to conclusively refute I I. (This may also explain Ayer's " i n c l i n a t i o n " to support I I.) Second, my case against I I rests on another argument: the argument from the nature of objects. This argument demonstrates that I I e n t a i l s an unacceptable view of the nature of objects and therefore i t is this argument, and not the individuation argument, which i s conclusive. Thirdly, the view of objects to which my thesis reduces I I is not the view of objects which the early Russell and Black reje c t . In fact, this point can be stated more strongly than t h i s . Those philosophers who have either accepted or rejected I I agree that I I implies that the nature of objects i s such that i f 4 two o b j e c t s share a l l t h e i r p r o p e r t i e s then they are n e c e s s a r i l y n u m e r i c a l l y i d e n t i c a l . Opponents o f I I have not then found t h i s c l a i m to e n t a i l an unacceptab le view of the nature of o b j e c t s . Ra ther , the ground of c r i t i c i z i n g I I has been to show tha t i f i t i s l o g i c a l l y p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and ye t n u m e r i c a l l y d i s t i n c t , then the q u a l i t a t i v e i n d i s t i n g u i s h -a b i l i t y o f o b j e c t s does not guarantee tha t they are n u m e r i c a l l y i d e n t i c a l . Proponents of I I have a c c o r d i n l y defended I I by de fend ing the view tha t q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s are n u m e r i c a l l y i d e n t i c a l ; i n o the r words, they have den ied tha t the i n d i v i d u a t i o n argument a g a i n s t I I has any f o r c e at a l l on the grounds that d i s t i n c t i n d i s c e r n i b l e s are not a l o g i c a l p o s s i b i l i t y . The p o i n t on which advocates andopponents of I I have t r a d i t i o n a l l y d i s a g r e e d , then , i s whether t h i s view of the nature of o b j e c t s can guarantee the numer i ca l d i s t i n c t n e s s of o b j e c t s , bu t , more i m p o r t a n t l y , the p o i n t on which they do agree i s tha t i t i s t h i s view of the nature of o b j e c t s which i s e n t a i l e d by I I. I t i s my argument that t h i s view of the nature of o b j e c t s i s on l y s u p e r f i c i a l l y imp l i ed by I I and tha t the view o f the nature o f o b j e c t s which i s a c t u a l l y i m p l i e d i s u n a c c e p t a b l e . Consequent l y , wh i l e my argument i s c o n s i s t e n t wi th the e a r l y R u s s e l l ' s and B l a c k ' s in tha t i t seeks to r e f u t e I I , i t may a l s o be taken as a c r i t i c i s m of t h e i r arguments. The connec t i on between my argument and Moore ' s argument in ' I d e n t i t y ' i s remote. I t i s e v i d e n t tha t Moore f i n d s the on to logy i m p l i e d by I I u n a c c e p t a b l e . However, Moore ' s reasons f o r t h i n k i n g t h i s are not at a l l c l e a r . I t i s p o s s i b l e tha t what Moore has i n mind i s an i n d i v i d u a t i o n argument not u n l i k e the e a r l y R u s s e l l ' s or B l a c k ' s . I f t h i s i s the c a s e , then i t i s not the nature of o b j e c t s imp l i ed by I I which Moore f i n d s u n a c c e p t a b l e , but the i n a b i l i t y of t h i s s o r t of on to logy to account f o r the d i f f e r e n c e between d i s t i n c t i n d i s c e r n i b l e s . I t i s a l s o p o s s i b l e tha t Moore i s o f f e r i n g a more s o p h i s t i c a t e d argument i n which the i n d i v i d u a t i o n argument i s based on an a n a l y s i s of the nature of o b j e c t s i m p l i e d by I I. There are two c l a ims which Moore makes which suggest tha t t h i s i s the s o r t of argument he has in mind. The f i r s t c l a i m i s tha t sentences such as "A i s r e d " p re sen t us w i th a l i n g u i s t i c p i c t u r e of the nature of o b j e c t s and, s e c o n d l y , tha t the s t r u c t u r e of t h i s p i c t u r e , w i th "A" on the one s i de and " r e d " on the o t h e r , i n d i c a t e s a r e l a t i o n between an i n d i v i d u a l o b j e c t and a p r o p e r t y . Moore t h e r e f o r e seems to b e l i e v e tha t the nature of o b j e c t s i s such tha t they are not r e d u c i b l e to the p r o p e r t i e s which are p r e d i c a b l e of them — as t h i s would t rans fo rm p r e d i c a t i o n from a r e l a t i o n between an o b j e c t and i t s p r o p e r t i e s i n t o a r e l a t i o n among a bundle of p r o p e r t i e s — but that they are 6 in some sense d i s t i n c t from the properties which are predicable of them. As Moore sees i t , i f two objects are numerically i d e n t i c a l where the same properties are predicable of them, as advocates of I I claim, then the objects of I I cannot be d i s t i n c t from their properties but must be reducible to them. Moore therefore concludes, f i r s t , that in reducing objects to a bundle of properties, the advocate of I I i s forced to acknowledge that to a predicate red of A i s r e a l l y to predicate red of a constituent of A. In other words, rather than predicating red of the object A, the advocate of I I i s forced to predicate red of a constituent of A such as square. The second conclusion that Moore draws i s that this view of the nature of objects implies that objects are equivalent to a single property. That i s to say, in predicating red of A where A i s reducible to the properties red and square, the advocate of I I must ide n t i f y the object A with the single property square. Consequently, not only i s the advocate of I I committed to the absurd view that objects are equivalent to a single property but, as Moore suggests, i t is considerably more d i f f i c u l t to individuate objects where objects are equivalent not to a bundle of properties but to a single property. If this i s in fact Moore's objection to I I, then, even though this argument appears impressive, i t i s extremely 7 weak. In the f i r s t p l a c e , Moore ' s argument r e q u i r e s tha t o n e ' s m e t a p h y s i c a l a n a l y s i s c o r r e l a t e e n t i t i e s to o r d i n a r y sentences such as "A i s r e d " and, f u r t h e r m o r e , tha t the r e l a t i o n between A and red must be one of p r e d i c a t i o n , r a t h e r than a s p e c i a l r e l a t i o n which, f o r example, b inds a bundle o f p r o p e r t i e s . Consequent l y , i f one takes the r e l a t i o n between A and red to ho ld between a bundle of p r o p e r t i e s r a t h e r than an i n d i v i d u a l o b j e c t and a p r o p e r t y , "A i s r e d " w i l l , when i n t e r p r e t e d i n accordance wi th Moore ' s r equ i rement , expres s a r e l a t i o n between two p r o p e r t i e s , namely, a c o n s t i t u e n t of A such as square and r e d . Moore ' s o b j e c t i o n to the on to logy i m p l i e d by I I i s not then tha t t h i s view of the nature of o b j e c t s i s u n a c c e p t a b l e , but that i n v iewing o b j e c t s i n t h i s way, h i s p r i m i t i v e theory of language i s a l t e r e d . However, i t i s not necessary to accept Moore ' s i m p l i c i t theory that the s t r u c t u r e of o b j e c t s must m i r r o r the s t r u c t u r e of sen tences . T h i s theory i s by no means o b v i o u s , nor f o r tha t matter does Moore defend the theo ry . A second reason f o r d i s m i s s i n g Moore ' s o b j e c t i o n i s tha t by r e j e c t i n g o n t o l o g i e s which suggest tha t sentences of the form "A i s r e d " t e l l us something about the c o n s t i t u t i o n o f o b j e c t s , Moore i s i m p l i c i t l y committed to r ega rd ing o b j e c t s as u n d e f i n a b l e . Consequent l y , wh i le Moore c l a ims to have r e f u t e d I I, i t i s c l e a r tha t i f Moore i s o f f e r i n g something more than the i n d i v i d u a t i o n arguments o f f e r e d by 8 the e a r l y R u s s e l l and B l a c k , then i t i s not an o b j e c t i o n to the nature of o b j e c t s i m p l i e d by I I but r a t h e r an o b j e c t i o n to the view of language which i s imp l i ed by an onto logy of t h i s s o r t . No p h i l o s o p h e r s , t hen , i n c l u d i n g the e a r l y R u s s e l l , B lack and Moore, have r e j e c t e d I I on the grounds that i t i m p l i e s the unacceptab le view of the nature of o b j e c t s tha t I w i l l show that i t does i n f a c t imp ly . The e a r l y R u s s e l l and B l ack r e j e c t I I on the grounds tha t the on to logy which i t i m p l i e s cannot guarantee the i d e n t i t y of o b j e c t s wh i l e Moore ' s grounds f o r r e j e c t i n g I I are l i n g u i s t i c . The po s -s i b i l i t y of r educ ing I I to a view of the nature of o b j e c t s which i s unacceptab le i s not then a p o s s i b i l i t y which has been con s i de red i n the l i t e r a t u r e on I I. The purpose of t h i s t h e s i s i s t h e r e f o r e to s u b s t a n t i a t e the c l a i m that an unacceptab le view o f the nature o f o b j e c t s i s i n f a c t e n t a i l e d by I I. T h i s argument r e q u i r e s an a n a l y s i s of what I I a s s e r t s . One way o f f o r m u l a t i n g I I i s to a s s e r t tha t i t i s a necessary t r u t h tha t two o b j e c t s are n u m e r i c a l l y i d e n t i c a l i f and o n l y i f they are q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e . In o t h e r words, i f two o b j e c t s agreed e x a c t l y i n a l l t h e i r p r o p e r t i e s so tha t they were i n d i s c e r n i b l e from each o t h e r , then there would not be two o b j e c t s but on l y one. T h i s p r i n c i p l e i s supported by e p i s t e m o l o g i c a l c l a i m s p e r t a i n i n g to the i d e n t i f i c a t i o n o f o b j e c t s . Most o b j e c t s tha t we 9 commonly observe are d i s s i m i l a r enough as to present few d i f f i c u l t i e s as to t h e i r i d e n t i t y . However, where two objects are not readily distinguished, i t i s supposed that i f the objects r e a l l y are two, then a q u a l i t a t i v e difference w i l l emerge on closer inspection. Consequently, i f every-thing that we can observe of an object can in p r i n c i p l e be stated, then a complete description of the object w i l l be s u f f i c i e n t to individuate the object beyond any shadow of doubt. In other words, epistemological claims about perceived differences in objects w i l l support the view that identity consists in q u a l i t a t i v e i n d i s t i n g u i s h a b i l i t y . This argument rests heavily on the sort of things that are allowed to count as properties. If the property of being s e l f - i d e n t i c a l and the property of being d i f f e r e n t are allowed, then I I i s c l e a r l y true. But as advocates and opponents of I I agree, this sense i s t r i v i a l . To claim that "A has the property of being i d e n t i c a l with A" and that "B has the property of being d i f f e r e n t from A" is merely to assert that A i s A and that B is not A, that i s , that d i f f e r e n t objects are d i f f e r e n t . In order to avoid this t r i v i a l i t y , advocates have interpreted I I as holding not between A and A but between A and B. Accordingly, A and B w i l l be numerically i d e n t i c a l i f and only i f they have a l l their properties in common. But, once again, this argument i s contingent upon the sort of things which count as properties. If i d e n t i t y and difference 10 are aga in coun ted , then a l though I I w i l l not be t r i v i a l , i t w i l l be s e l f - r e f u t i n g . For even though A and B may share a l l t h e i r n o n - r e l a t i o n a l p r o p e r t i e s such as c o l o u r , shape, s i z e , e t c . , i f A has the p r o p e r t y of be ing i d e n t i c a l w i th A and d i f f e r e n t from B and, c o n v e r s e l y , i f B has the p r o p e r t y of be ing i d e n t i c a l w i th B and d i f f e r e n t from A, then A and B w i l l not be i d e n t i c a l but n u m e r i c a l l y d i s t i n c t . The p h i l o s -opher who wishes to ma in ta in tha t A and B are n u m e r i c a l l y i d e n t i c a l i s t h e r e f o r e r ep re sen ted as say ing that he cannot d i s t i n g u i s h A and B when he has a l r e a d y recogn i zed A and B to be d i s t i n c t . However, proponents o f I I have been qu i ck to p o i n t out tha t the d i f f i c u l t y l i e s not so much i n the p r o p e r t i e s of i d e n t i t y and d i f f e r e n c e as i n the l i n g u i s t i c f a c t tha t the names "A" and "B" presuppose d i s t i n c t o b j e c t s . Advocates such as Ayer (Ayer 1976) have t h e r e f o r e proposed rephra s i ng c l a i m s about o b j e c t s as c l a ims about the p r o p e r t i e s which c o n s t i t u t e them. In t h i s way, any r e f e r e n c e to an o b j e c t by name or to a p r o p e r t y which c o n t a i n s a name such as the p r o p e r t y o f " b e i n g - i d e n t i c a l - w i t h - A " or the p r o p e r t y o f " b e i n g - d i f f e r e n t - f r o m - B " i s cashed out in terms of a gene ra l d e s c r i p t i o n . Thus i n s tead of a s s e r t i n g tha t the o b j e c t s A and B are i n f a c t n u m e r i c a l l y i d e n t i c a l i f they have a l l and on l y the same p r o p e r t i e s in common, the p r i n c i p l e may be more p l a u s i b l y taken to a s s e r t tha t one and on l y one o b j e c t 11 s a t i s f i e s a g i ven g e n e r a l d e s c r i p t i o n . For example, i f an o b j e c t wh ich , on one o c c a s i o n , we named " A " , and another o b j e c t wh ich , on another o c c a s i o n , we named " B " , tu rn out to s a t i s f y the same genera l d e s c r i p t i o n , f o r i n s t ance red square l a r g e hard then A and B are n e c e s s a r i l y n u m e r i c a l l y i d e n t i c a l . Ayer c a l l s t h i s v e r s i o n of I I i n t e r e s t i n g , tha t i s , where q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s are n u m e r i c a l l y i d e n t i c a l or A=B i n o rder to d i s t i n g u i s h i t from the t r i v i a l c l a i m tha t o b j e c t s are i d e n t i c a l w i th themselves or A=A. However, wh i l e i t i s t h i s v e r s i o n which i s of p h i l o s o p h i c a l i n t e r e s t , not a l l advocates of I I have found t h i s f o r m u l a t i o n s a t i s f a c t o r y . D .J . O 'Conner , f o r example, has argued tha t r e f e r e n c e to o b j e c t s cannot be e n t i r e l y rephrased as a g e n e r a l d e s c r i p t i o n (O'Conner 1976). The r e a s o n , O 'Conner suggests i s tha t u n l i k e n o n - r e l a t i o n a l p r o p e r t i e s which are g e n e r a l , s p a t i a l l o c a t i o n s and temporal l o c a t i o n s are un ique. T h i s uniqueness w i l l then be r e f l e c t e d in t h e i r d e s c r i p t i o n s . For example, A might be d e s c r i b e d as r e d , square , and l a r g e , and as hav ing the s p a t i o - t e m p o r a l c o - o r d i n a t e X i , Y]_, Z i a t t i i n a system of axes. A c c o r d i n g l y , I I w i l l be d e f i n a b l e i n terms o f a complete d e s c r i p t i o n where a complete d e s c r i p t i o n i n c l u d e s r e l a t i o n a l as w e l l as n o n - r e l a t i o n a l p r o p e r t i e s . The most obv ious d i f f e r e n c e between A y e r ' s v e r s i o n and 0 ' C o n n e r ' s v e r s i o n concerns the s o r t of t h ing s which the term " p r o p e r t y " i s taken to connote . For A y e r , s p a t i o -temporal l o c a t i o n s are f o r c e d o u t s i d e the conno ta t i on of the term by the requ i rement tha t a complete d e s c r i p t i o n be a g e n e r a l d e s c r i p t i o n whereas f o r 0 'Conner t h i s r e s t r i c t i o n does not a p p l y . However, the f a c t tha t the d i f f e r e n c e between the two v e r s i o n s reduces to a q u e s t i o n of whether s p a t i o - t e m p o r a l l o c a t i o n s are p r o p e r t i e s does not imply tha t the d i f f e r e n c e i s merely one of degree r a t h e r than k i n d , tha t i s , tha t a l l tha t i s at s take o n t o l o g i c a l l y i s the r e c o g n i t i o n o f one more or one fewer k inds of e n t i t y . On the c o n t r a r y , these two forms of the i n t e r e s t i n g v e r s i o n o f I I are o n t o l o g i c a l l y i n c o m p a t i b l e . I f , as 0 'Conner sugges t s , o b j e c t s can be i d e n t i f i e d by t h e i r s p a t i o - t e m p o r a l l o c a t i o n s , then i n any g i ven case an o b j e c t w i l l be i d e n t i -f i a b l e i ndependent l y of o t h e r o b j e c t s by r e f e r e n c e to i t s s p a t i o - t e m p o r a l l o c a t i o n or c o - o r d i n a t e . T h i s view i m p l i e s tha t space and time are a b s o l u t e , tha t i s , tha t the s p a t i o -tempora l p o s i t i o n of an o b j e c t w i l l not be determined by r e f e r e n c e to i t s r e l a t i v e p o s i t i o n to o the r o b j e c t s , r a t h e r , the o b j e c t w i l l be i d e n t i f i a b l e i n i t s own r i g h t or a b s o l u t e l y as occupy ing a unique and n u m e r i c a l l y d i s t i n c t 1 3 s p a t i o - t e m p o r a l p o s i t i o n . C o n v e r s e l y , where s p a t i o - t e m p o r a l p r o p e r t i e s are exc luded from the bundle o f p r o p e r t i e s to which an o b j e c t i s r e d u c i b l e , the i d e n t i t y of an o b j e c t w i l l r e s i d e i n the uniqueness o f i t s bundle of n o n - r e l a t i o n a l p r o p e r t i e s . For example, A might be r e d , square , l a r ge and h a r d , whereas B i s r e d , square , l a r g e , and s o f t . A may a l s o be s a i d to have a c e r t a i n s p a t i o - t e m p o r a l l o c a t i o n , but i n o rde r to determine t h i s l o c a t i o n we must f i r s t be ab le to i d e n t i f y A. In o t h e r words, s p a t i o - t e m p o r a l p o s i t i o n s presuppose the e x i s t e n c e of the o b j e c t in q u e s t i o n and are r e l a t i v e to the l o c a t i o n of o t h e r o b j e c t s . On A y e r ' s v iew, then , space and time are r e l a t i v e and thus o f the form " t o - t h e - l e f t - o f " or "above" wh i l e on 0 ' C o n n e r ' s view space and time are a b s o l u t e and thus of the form " X j , Y±, Z± a t t l - " The a n a l y s i s to date may t h e r e f o r e be summarized as f o l l o w s . The important d i s t i n c t i o n s were made. F i r s t , the t r i v i a l v e r s i o n o f I I was d i s t i n g u i s h e d from ' the i n t e r e s t i n g v e r s i o n . The t r i v i a l v e r s i o n made I I t rue by coun t i ng as p r o p e r t i e s n o n - r e l a t i o n a l p r o p e r t i e s such as c o l o u r , shape, and s i z e as w e l l as the p r o p e r t i e s of i d e n t i t y and d i f f e r e n c e . The t r i v i a l i t y of t h i s v e r s i o n l a y i n the f a c t tha t by count ing i d e n t i t y and d i f f e r e n c e as p r o p e r t i e s A and B cou ld not p o s s i b l y have a l l t h e i r p r o p e r t i e s in common as A would have the p r o p e r t i e s of be ing 14 i d e n t i c a l with A and not being i d e n t i c a l with B, which B could not share. The t r i v i a l version of I I therefore makes the obvious claim that objects are i d e n t i c a l with themselves, that i s , that A=A. Both advocates and opponents of I I agree that the t r i v i a l version of I I is true. But they also agree that this version i s philosophically uninteresting. Thus in order to make I I interesting , I I has been interpreted as holding not between A and A but between A and B where id e n t i t y and difference are not counted as properties. The interesting version of I I thus states that i f A and B have a l l the same properties in common, with the exception of i d e n t i t y and difference, then A and B w i l l necessarily be numerically i d e n t i c a l . The second d i s t i n c t i o n which was drawn d i f f e r e n t i a t e d two versions of the interesting form of I I, namely, Ayer's and 0'Conner's. On Ayer's view, r e l a t i o n a l properties are not included in the bundles of properties to which objects are reducible on the ground that they presuppose the i d e n t i t i e s of the objects in question. This view commits Ayer to a r e l a t i v e view of space and time as i t is on this view of space and time that r e l a t i o n a l properties presuppose the i d e n t i t i e s of objects. On O'Conner's view, on the other hand, r e l a t i o n a l properties are included in the bundle of properties to which objects are reducible. Consequently, i f relations are to function as properties in the manner of 15 non-relational properties, r e l a t i o n a l properties must constitute rather than presuppose the i d e n t i t i e s of objects. Accordingly, O'Conner i s committed to an absolute view of space and time as i t is on this view of space and time that r e l a t i o n s constitute rather than presuppose the i d e n t i t i e s of objects. The argument of this thesis may now be more f u l l y stated. If the ide n t i t y of A and B depends solely on non-relational properties, then a p a r t i c u l a r ontology w i l l be implied while i f identity ultimately resides in common r e l a t i o n a l properties another ontology w i l l be implied. The c r u c i a l point is that both versions of the interesting form of I I w i l l imply a d e f i n i t e ontology and that both of these ontologies w i l l be unacceptable. Consequently, any philosopher who supports I I is i m p l i c i t l y committed to an unacceptable ontology. My argument for this thesis w i l l be divided into three chapters. The f i r s t chapter defines the ontology which i s implied by the interesting form of the r e l a t i v e space-time version of I I. This ontology can be e x p l i c i t l y defined. However, as I make the strong claim that only one ontology is implied by this version of I I and that this ontology is unacceptable, i t is important to demonstrate why a l l other ontologies are incompatible with this version of I 1.1 The approach in this f i r s t chapter, then, w i l l be to consider in 16 more d e t a i l what i s a s s e r t e d 'by I I. T h i s w i l l provide a b a s i s on which to t e s t o n t o l o g i e s f o r t h e i r c o m p a t i b i l i t y with I I. In t h i s way, through a process of e l i m i n a t i o n , i t i s p o s s i b l e to argue that only a c e r t a i n s o r t of ontology i s compatible with the r e l a t i v e space-time v e r s i o n of I I. The second chapter a t t a c k s the ontology which i s im p l i e d by the r e l a t i v e space-time v e r s i o n of I I and which i s d e f i n e d i n chapter one. T h i s s e c t i o n w i l l be d i v i d e d i n t o three s u b - s e c t i o n s . The f i r s t s u b - s e c t i o n w i l l c o n s i d e r Black's v e r s i o n of the i n d i v i d u a t i o n argument and, the second, an e l a b o r a t i o n of an argument o f f e r e d by R.M. Adams. Even though most p h i l o s o p h e r s would w i l l i n g l y grant that i n d i v i d u a t i o n arguments do not provide c o n c l u s i v e grounds on which to r e f u t e I I, there are a number of reasons f o r d i s c u s s i n g t h i s type of argument. F i r s t of a l l , the i n d i v i d u a t i o n argument i s s t i l l though to o f f e r the best ground f o r r e j e c t i n g I I. Secondly, s i n c e the i n d i v i d u a t i o n argument remains at the f o r e f r o n t of the debate over I I, any s y s t e m a t i c a t t a c k a g a i n s t I I must respond to t h i s argument e i t h e r by s u p p o r t i n g i t as most p h i l o s o p h e r s have done, or e l s e by demonstrating that there i s another l i n e of argument which i s more e f f e c t i v e as i s done i n t h i s t h e s i s . F i n a l l y , while i t i s the argument from the nature of o b j e c t s which c o n c l u s i v e l y r e f u t e s I I , i t does not r a i s e some of the i s s u e s which are r a i s e d by the i n d i v i d u a t i o n argument. 1 7 Therefore, the i n d i v i d u a t i o n argument must be included i n an account of the issues surrounding I I i f t h i s account i s to be complete. In the f i r s t two sub-sections of chapter two, then, an account of the i n d i v i d u a t i o n argument w i l l be given as w e l l as a b r i e f account of the reasons why advocates of I I have found t h i s type of argument i n c o n c l u s i v e . The t h i r d sub-section o f f e r s what has been termed the argument from the nature of o b j e c t s . Unlike the i n d i v i d u a t i o n argument which o f f e r s e s s e n t i a l l y one o b j e c t i o n to I I , the argument from the nature of objects o f f e r s a number of o b j e c t i o n s . These o b j e c t i o n s are not independent of each other, but form a continuum i n which each successive o b j e c t i o n r e v e a l s more of the ontology to which proponents of I I are committed. Consequently, while some advocates of I I might not f i n d the f i r s t o b j e c t i o n persuasive, the case against I I gets p r o g r e s s i v e l y stronger with each o b j e c t i o n . The argument from the nature of objects might then be c h a r a c t e r i z e d as a s e r i e s of o b j e c t i o n s i n which the st a t u s of I I goes from bad to unacceptable. The t h i r d chapter deals with the i n t e r e s t i n g form of I I where space and time are viewed as absolute and, i n p a r t i c u l a r , the views of O'Conner and the l a t e R u s s e l l . U nlike the r e l a t i v e space-time v e r s i o n of I I , which i s shown to reduce to an unacceptable view of the nature of 18 o b j e c t s , t h e c o n c e r n o f t h i s c h a p t e r i s l i m i t e d t o an e x a m i n a t i o n o f t h e n a t u r e o f r e l a t i o n a l p r o p e r t i e s w h i c h a r e c l a i m e d t o u l t i m a t e l y d i s t i n g u i s h o b j e c t s i n a b s o l u t e s p a c e and t i m e . What t h i s a r g u m e n t w i l l show i s t h a t a b s o l u t e s p a t i o - t e m p o r a l p o s i t i o n s a r e n o t i n f a c t u n i q u e and f u r t h e r m o r e t h a t t h e o n l y s e n s e i n w h i c h t h e y c o u l d be s a i d t o be u n i q u e i s i n a s e n s e w h i c h i s i n c o m p a t i b l e w i t h I I. The a b s o l u t e s p a c e - t i m e v e r s i o n o f I I w i l l t h e r e f o r e be shown t o be a v i e w w h i c h d o e s n o t s u p p o r t I I a n d , f o r t h a t m a t t e r , a v i e w w h i c h d o e s n o t p r o v i d e a s a f e r e t r e a t f r o m t h e d i f f i c u l t i e s o f t h e r e l a t i v e s p a c e - t i m e v e r s i o n o f I I. 19 Notes to I n t r o d u c t i o n 1 I t i s p o s s i b l e that two or more of the o n t o l g i e s that I c l a i m to be incompatible with the r e l a t i v e space-time v e r s i o n of I I could be combined to produce another o n t o l -ogy. However, t h i s i s a p o s s i b i l i t y which i s not of concern. In the f i r s t p l a c e , an ontology of t h i s s o r t i s not one which i s l i k e l y to be held as the f u n c t i o n of at l e a s t some of i t s components w i l l be redundant and, secondly, i n s o f a r as i t combines d i s t i n c t o n t o l o g i e s which are themselves incompatible with the r e l a t i v e space-time v e r s i o n of I I, i t f o l l o w s that i t too w i l l be i n c o m p a t i ble. 20 CHAPTER ONE EU-ONTOLOGY I I s t a t e s t h a t i f two o b j e c t s are q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e then they are n e c e s s a r i l y n u m e r i c a l l y i d e n t i c a l . The term "object" i s taken to denote a bundle of p r o p e r t i e s w h i c h , i n keep ing w i t h A y e r , i s d e s c r i b e d i n such a way as not to presuppose the i d e n t i t y o f the o b j e c t i n q u e s t i o n . A c c o r d i n g l y , A and B are n u m e r i c a l l y i d e n t i c a l i f and o n l y i f they s a t i s f y the same g e n e r a l d e s c r i p t i o n . A l t h o u g h t h i s f o r m u l a t i o n i s most common, another way of s t a t i n g I I i s to a s s e r t , c o n v e r s e l y , tha t i f there are two n u m e r i c a l l y d i s t i n c t o b j e c t s , then one o b j e c t must possess a t l e a s t one p r o p e r t y not possessed by the o t h e r . 1 I f A i s n u m e r i c a l l y d i s t i n c t from B , then there i s no d i f f e r e n c e between A and B t h a t cannot be expressed as a d i f f e r e n c e between p r o p e r t i e s . For example, i f A and B are both r e d , s q u a r e , and l a r g e , t h e n , i f they are i n f a c t n u m e r i c a l l y d i s t i n c t , A w i l l possess a p r o p e r t y not possessed by B; f o r example , A might be hard whereas B i s s o f t . Of the two f o r m u l a t i o n s o f I I the second p o i n t s more c l e a r l y to the o n t o l o g y which I I e n t a i l s ; o r , a t l e a s t a t 21 t h i s s t a g e , i t i n d i c a t e s which o n t o l o g i e s w i l l not be c o m p a t i b l e w i t h I I . To b e g i n w i t h , i f the d i f f e r e n c e between o b j e c t s i s not e x p r e s s e d as a d i f f e r e n c e between p r o p e r t i e s , then the o n t o l o g y i m p l i e d w i l l not be c o m p a t i b l e w i t h I I . In o t h e r words, i f i t i s not a n e c e s s a r y c o n d i t i o n f o r o b j e c t s t o be n u m e r i c a l l y d i s t i n c t t h a t they d i f f e r i n a p r o p e r t y , i t w i l l be l o g i c a l l y p o s s i b l e f o r two o b j e c t s t o have a l l t h e i r p r o p e r t i e s i n common and y e t s t i l l be n u m e r i c a l l y d i s t i n c t . T h e r e f o r e , a l l o n t o l o g i e s which are i n c o m p a t i b l e w i t h I I w i l l p o s t u l a t e the e x i s t e n c e o f a component o t h e r than q u a l i t a t i v e d i f f e r e n c e which i s i t s e l f s u f f i c i e n t t o d i s t i n g u i s h o b j e c t s . These components w i l l by d e f i n i t i o n be capable of making o b j e c t s unique and t h e r e f o r e w h i l e a l l the o b j e c t s i n the w o r l d may d i f f e r from one a n o t h e r i n a t l e a s t one p r o p e r t y i t i s not n e c e s s a r y on these views t h a t they do so i n o r d e r to be n u m e r i c a l l y d i s t i n c t . I w i l l now c o n s i d e r a number o f o n t o l o g i e s which p o s t u l a t e such a component and are t h e r e f o r e i n c o m p a t i b l e w i t h I I . By d o i n g t h i s , I w i l l i n d i r e c t l y narrow down the k i n d s o f o n t o l o g y t h a t are c o m p a t i b l e w i t h I I . I s h a l l c o n s i d e r t h r e e k i n d s o f components which have been c l a i m e d t o be c a p a b l e o f i n d i v i d u a t i n g o b j e c t s w i t h o u t r e l y i n g on q u a l i t a t i v e d i f f e r e n c e . These components, which w i l l be examined i n t u r n , are i n s t a n t i a t e d p r o p e r t i e s , bare 22 p a r t i c u l a r s and s u b s t r a t a . Ob jec t s have sometimes been c la imed to be r e d u c i b l e to i n s t a t a t i o n s of p r o p e r t i e s where i t ' i s he ld tha t there may be n u m e r i c a l l y d i s t i n c t i n s t a n t a t i o n s o f the very same determina te p r o p e r t y . For example, i f A i s r e d u c i b l e to the p r o p e r t i e s r e d , square , and l a r g e , then these p r o p e r t i e s w i l l be p a r t i c u l a r i n the sense tha t they are n u m e r i c a l l y d i s t i n c t from the p r o p e r t i e s r e d , square , and l a r g e which c o n s t i t u t e B. T h i s on to logy has been deve loped a long f ou r separa te l i n e s . Moore and the e a r l y Rus se l have argued that p r o p e r t i e s such as red are i n s t a n c e s or p a r t i c u l a r i z a t i o n s o f s u b s i s t e n t u n i v e r s a l s . 2 In s tances are t h e r e f o r e e a s i l y d e f i n e d by the way i n which they d i f f e r from t h e i r s u b s i s t e n t u n i v e r s a l s . For example, s u b s i s t e n t u n i v e r s a l s do not e x i s t i n space and time and are ak i n to " forms" which are e t e r n a l and t i m e l e s s whereas t h e i r i n s t a n c e s e x i s t i n space and t ime. A l though i n s t a n c e s and s u b s i s t e n t u n i v e r s a l s d i f f e r o n t o l o g i c a l l y , i t i s n e v e r t h e l e s s i n v i r t u e of the form or s u b s i s t e n t u n i v e r s a l red that an e n t i t y i s s a i d to be red and, f u r t h e r , tha t the s i m i l a r i t y between two i n s t a n c e s i s accounted f o r . T h e r e f o r e , wh i le the red of A i s n u m e r i c a l l y d i s t i n c t from the red o f B, and a l l o the r i n s t a n c e s of r e d , i t i s by reason of t h e i r r e l a t i o n to the s u b s i s t e n t u n i v e r s a l red that both i n s t ance s are s i m i l a r . A second i n t e r p r e t a t i o n , which i s o f f e r e d by G.F. i 23 S t o u t , d i f f e r s from Moore ' s and the e a r l y R u s s e l l ' s i n two r e s p e c t s . F i r s t , " r e d " i s not taken to r e f e r to a t i m e l e s s e n t i t t y of which " t h i s r e d " and " t h a t r e d " are p a r t i c u l a r i n s t a n c e s or examples, but to a c l a s s which i s e q u i v a l e n t to the sum of a l l c onc re te i n s t a n c e s of r e d . Second ly , S tout does not regard p r o p e r t y i n s t a n c e s as d e r i v i n g t h e i r d i s t i n c t n e s s from the d i s t i n c t n e s s of the o b j e c t s to which they be l ong , as Moore and the e a r l y R u s s e l l seem to b e l i e v e , but as d i s t i n c t i n t h e i r own r i g h t . In S t o u t ' s words, a p r o p e r t y o f an o b j e c t i s "as p a r t i c u l a r as the th ing or i n d i v i d u a l which i t c h a r a c t e r i s e s " (Stout 1930, p. 386). F i n a l l y , two o the r r ecogn i zed v e r s i o n s o f t h i s onto logy are suggested by D.C. W i l l i a m s and R.I. S i k o r a . Both v e r s i o n s , i n keep ing w i th S t o u t , take p r o p e r t i e s to be p a r t i c u l a r i n t h e i r own r i g h t . Where W i l l i a m s ' v e r s i o n d i f f e r s i s i n h i s r e j e c t i o n o f S t o u t ' s idea of t h e c l a s s as a unique form of u n i t y , tha t i s , as a u n i t y which cannot be f u r t h e r reduced to s i m i l a r i t y . W i l l i a m s ' v e r s i o n a l s o d i f f e r s in tha t he c l a ims tha t i n s t a n t i a t e d p r o p e r t i e s o r , what he terms, " f i n e p a r t s " c o u l d c o n c e i v a b l y e x i s t by themselves and, t h e r e f o r e , c o n t r a r y to S t o u t , the e x i s t e n c e o f p r o p e r t i e s i s not dependent on the o b j e c t s to which they be l ong . S i k o r a , on the o the r hand, argues that many of the t r a d i t i o n a l d i f f i c u l t i e s i m p l i e d by c l a s s terms and the r e l a t i o n of s i m i l a r i t y are e l i m i n a t e d i f g e n e r a l terms are 24 viewed as denot ing groups o f l o g i c a l p o s s i b i l i t i e s and i n s t a n t i a t e d p r o p e r t i e s as i n s t a n c e s of these p o s s i b i l i t i e s . De sp i te the obv ious d i f f e r e n c e s between these o n t o l o g i e s , they are s i m i l a r to the ex ten t tha t the p r o p e r t i e s of o b j e c t s are i n some sense p a r t i c u l a r . T h i s means tha t on each view the red of A w i l l be n u m e r i c a l l y d i s t i n c t from the red of B and, t h e r e f o r e , where A and B have a l l and on l y the same p r o p e r t i e s in common, A and B w i l l s t i l l be n u m e r i c a l l y d i s t i n c t by reason of the numer i ca l d i s t i n c t n e s s of t h e i r p r o p e r t y i n s t a n t i a t i o n s . On these v iews, t h e n , q u a l i t a t i v e i n d i s t i n g u i s h a b i l i t y does not n e c e s s a r i l y imply numer i ca l i d e n t i t y and t h e r e f o r e o n t o l o g i e s o f t h i s s o r t , which p o s t u l a t e the e x i s t e n c e of p a r t i c u l a r p r o p e r t y i n s t a n t i a t i o n s , are i ncompat ib l e w i th I I. Over and above t h e i r o t h e r d i f f e r e n c e s , these views a l s o d i f f e r i n t h e i r account o f the s i m i l a r i t y between o b j e c t s . However, t h i s i s something which some p h i l o s o p h e r s f e e l t ha t these o n t o l o g i e s cannot e x p l a i n . Acco rd ing to E.B. A l l a i r e ( A l l a i r e 1976, p. 282) there must be e n t i t i e s to account f o r A and B be ing the same, tha t i s , there must be e n t i t i e s which are q u i t e l i t e r a l l y one and the same i n both o b j e c t s i n o rde r to e x p l a i n the word " r e d " be ing t r u l y p r e d i c a t e d of A and B. I n s t a n t i a t e d p r o p e r t i e s cannot then be p a r t i c u l a r s but must be e n t i t i e s which are capab le of 25 enjoying a spatio-temporally divided mode of existence. A l l a i r e therefore believes that the properties of objects must be universal. But, unlike the universals to which Moore and the early Russell refer, these universals do not subsist but rather e x i s t and therefore may be termed "existent" universals. However, the d i f f i c u l t y with this theory i s that while i t accounts for the s i m i l a r i t y between objects, i t does not account for their difference. In other words, i f i t is l o g i c a l l y possible for two objects to share a l l their properties and yet be numerically d i s t i n c t , then this theory must provide some other basis other than q u a l i t a t i v e difference on which to distinguish the two objects. To solve this problem A l l a i r e postulates the existence of a special kind of p a r t i c u l a r termed a "bare" p a r t i c u l a r which supposedly accounts for the difference between objects. T r a d i t i o n a l l y , bare p a r t i c u l a r s have been viewed with suspicion. The early Russell, for example, referred to them as a mere unknowable substratum, or an i n v i s i b l e peg from which propereties would hang l i k e hams from the beams of a farmhouse (Russell 1959, p. 120). However, the early Russell's view of bare p a r t i c u l a r s i s not one which i s shared by A l l a i r e . Instead, A l l a i r e characterizes bare p a r t i c u l a r s as "the c a r r i e r s of numerical difference as d i r e c t l y presented to us" ( A l l a i r e 1976, p. 290) . T h i s means, f i r s t of a l l , tha t bare p a r t i c u l a r s are not i n v i s i b l e pegs from which p r o p e r t i e s hang, but r a t h e r one of a number of p r o p e r t i e s which together form an o b j e c t . I t a l s o means that bare p a r t i c u l a r s and e x i s t e n t u n i v e r s a l s are not p r o p e r t i e s of the same o n t o l o g i c a l type as e x i s t e n t u n i v e r s a l s are not c a r r i e r s of numer i ca l d i f f e r e n c e . F o r , even though e x i s t e n t u n i v e r s a l s such as red and green are themselves n u m e r i c a l l y d i f f e r e n t , the numer i ca l d i f f e r e n c e of o b j e c t s cannot be guaranteed by the p o s s e s s i o n of an e x i s t e n t u n i v e r s a l . T h i r d l y , wh i l e bare p a r t i c u l a r s cannot be i d e n t i f i e d i n the manner i n which e x i s t e n t u n i v e r s a l s a r e , they can be known. A c c o r d i n g to A l l a i r e , the argument tha t bare p a r t i c u l a r s are unknowable f a i l s to d i s t i n g u i s h two senses i n which th i ng s can be known. I f by knowing something we mean tha t we are ab le to " r e c o g n i z e " i t , then A l l a i r e admits tha t bare p a r t i c u l a r s are not the s o r t of th ing s tha t can be known. For example, i f we are p re sen ted a second time wi th A and B, t h e n , because we can o n l y t e l l tha t the two o b j e c t s tha t we now see have a l l the p r o p e r t i e s tha t the two o b j e c t s tha t we saw e a r l i e r had, i t f o l l o w s tha t i f each o b j e c t c o n t a i n s a bare p a r t i c u l a r , the bare p a r t i c u l a r s i n themselves are not r e c o g n i z a b l e . However, i f by knowing something we mean that we are " a c q u a i n t e d " w i th i t , A l l a i r e then c l a i m s tha t we can know bare p a r t i c u l a r s . A l l a i r e ' s 27 rea son ing seems to be that i f , i n d i s t i n g u i s h i n g A and B, we are p re sen ted w i th numer i ca l d i f f e r e n c e and i f bare p a r t i c u l a r s are c a r r i e r s of numer i ca l d i f f e r e n c e , then we must i n some sense be acqua in ted w i th bare p a r t i c u l a r s . But as A l l a i r e admi t s , I cannot get away w i th j u s t m a i n t a i n i n g that they [ i . e . , bare p a r t i c u l a r s ] are mere ly n u m e r i c a l l y d i f f e r e n t . I must show i n what sense one i s acqua in ted w i th them. Not to r e c o g n i z e t h i s o b l i g a t i o n would be to confuse aga in the two uses of "know". N e v e r t h e l e s s , i n p o i n t i n g out tha t i n d i v i d u a l s [ i . e . , bare p a r t i c u l a r s ] are not r e c o g n i z a b l e , i . e . , are merely n u m e r i c a l l y d i f f e r e n t , one has a r r i v e d a t the hea r t o f the m a t t e r . I n d i v i d u a l s [ i . e . , bare p a r t i c u l a r s ] are j u s t those e n t i t i e s which do ground the numer i ca l d i f f e r e n c e of two th ing s which are the same i n a l l ( n o n r e l a t i o n a l ) r e s p e c t s ( A l l a i r e 1976, p. 288). What these e n t i t e s a r e , however, i s s t i l l not a l t o g e t h e r c l e a r . But , as p r o b l e m a t i c as they a r e , i t i s n e v e r t h e l e s s by reason of these e n t i t i e s tha t o b j e c t s are u l t i m a t e l y s a i d to d i f f e r . On a view such as A l l a i r e ' s , then, i t i s p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and y e t n u m e r i c a l l y d i s t i n c t by reason of t h e i r bare p a r t i c u l a r s and t h i s , as we have seen, i s c o n t r a r y to I I. The t h i r d type of i n d i v i d u a t i n g component i s what i s termed a " s u b s t r a t u m " . Acco rd ing to t h i s t h e o r y , be s ide s the v a r i o u s p r o p e r t i e s of an o b j e c t , there i s an e n t i t y that i n some sense " s u p p o r t s " those p r o p e r t i e s . There are four ways i n which one might come to ho ld t h i s v iew. An advocate of i t h i s view might ho ld tha t the nature of language commits us 28 to an on to logy of t h i s s o r t . From the s t r u c t u r e of sentences such as "A i s r e d " i t might seen to f o l l o w that an o b j e c t i s something d i f f e r e n t from the sum of p r o p e r t i e s which are p r e d i c a b l e o f i t . A second reason i s tha t s u b s t r a t a are thought to be necessary to b ind the v a r i o u s p r o p e r t i e s of an o b j e c t t o g e t h e r . A c c o r d i n g to a t h i r d v iew, s u b s t r a t a are needed i n o rde r to make s u b s i s t e n t u n i v e r s a l s a c t u a l , tha t i s , to i n s t a n t i a t e them. And, f i n a l l y , s u b s t r a t a might be regarded as the o n l y s o r t of component which i s capab le of d i f f e r e n t i a t i n g q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s . However, d e s p i t e the d i v e r s i t y of reasons f o r h o l d i n g the substratum t h e o r y , s u b s t r a t a a r e , on a l l f ou r grounds, regarded as something which i s not i t s e l f a p r o p e r t y but as something which suppor t s p r o p e r t i e s . The substratum theory i s t h e r e f o r e i n compa t i b l e w i th I I s i n c e i t i s l o g i c a l l y p o s s i b l e f o r two o b j e c t s to have a l l t h e i r p r o p e r t i e s in common and ye t s t i l l be n u m e r i c a l l y d i s t i n c t by reason of t h e i r s u b s t r a t a . A l though none of these reasons f o r h o l d i n g the substratum theory i n f l u e n c e the nature of s u b s t r a t a , they do i n some cases i n f l u e n c e the nature of o b j e c t s . Of the four rea sons , the f i r s t two do not have any bea r ing on the nature of o b j e c t s . The f i r s t s imp ly a s s e r t s a d i f f e r e n c e between s u b s t r a t a and p r o p e r t i e s based on f e a t u r e s o f language, and the second , the same d i f f e r e n c e , but based on the need to b ind p r o p e r t i e s t o g e t h e r . O b j e c t s , on these two v iews, may 29 t h e r e f o r e be composed of e i t h e r i n s t a n t i a t e d p r o p e r t i e s or e x i s t i n g u n i v e r s a l s . On the t h i r d v iew, o b j e c t s cannot be composed of e x i s t -ent u n i v e r s a l s but must be composed of i n s t a n t i a t e d p r o p e r -t i e s as s u b s t r a t a are s p e c i f i c a l l y p o s t u l a t e d i n o rder to make s u b s i s t e n t u n i v e r s a l s a c t u a l . In o t h e r words, wh i l e s u b s i s t e n t u n i v e r s a l s are e t e r n a l and t i m e l e s s , t h e i r i n s t a n t i a t e d p r o p e r t i e s cannot e x i s t by themselves but r e q u i r e s u b s t r a t a i n which to i n h e r e . In keeping w i th S t o u t , W i l l i a m s and S i k o r a , i n s t a n t i a t e d p r o p e r t i e s may be regarded as p a r t i c u l a r i n t h e i r own r i g h t . But t h i s view seems u n l i k e l y , f o r wh i l e s u b s t r a t a would s t i l l be r e q u i r e d to i n s t a n t i a t e e x i s t e n t u n i v e r s a l s , the d i f f e r e n c e between o b j e c t s cou ld be accounted f o r i n terms of s u b s t r a t a as w e l l as the p a r t i c u l a r i t y of t h e i r p r o p e r t i e s . The d i f f e r e n t -i a t i n g f u n c t i o n o f s u b s t r a t a would t h e r e f o r e be redundant. However, sho r t of a c t u a l l y abandoning s u b s t r a t a , and o f f e r i n g an account of the nature of o b j e c t s s imply i n terms o f p a r t i c u l a r p r o p e r t i e s as S t o u t , W i l l i a m s and S i k o r a do , the substratum t h e o r i s t might argue that wh i l e p r o p e r t i e s are not e x i s t e n t u n i v e r s a l s they are not p a r t i c u l a r s e i t h e r . A more p l a u s i b l e i n t e r p r e t a t i o n of t h i s t h i r d v iew, t h e n , i s tha t i n s t a n t i a t e d p r o p e r t i e s are not e n t i t i e s which are p a r t i c u l a r i n t h e i r own r i g h t but r a t h e r e n t i t i e s which d e r i v e t h e i r p a r t i c u l a r i t y from s u b s t r a t a . I t i s worth no t i ng how c l o s e l y t h i s view resembles the view o f Moore and 30 the e a r l y R u s s e l l . Both Moore and the e a r l y R u s s e l l c l a i m tha t the red of A i s n u m e r i c a l l y d i f f e r e n t from the red o f B, but tha t p r o p e r t i e s such as red are not p a r t i c u l a r i n t h e i r own r i g h t . But , s i n c e Moore and the e a r l y R u s s e l l e x p l i c i t l y r e j e c t the substratum t h e o r y , i t would seem tha t r a t h e r than p o s t u l a t e the e x i s t e n c e o f an "unknowable subs t ra tum" from which p r o p e r t i e s cou ld d e r i v e t h e i r p a r t i c u l a r i t y , Moore and the e a r l y R u s s e l l are content to l eave the nature of o b j e c t s u n e x p l a i n e d . A c c o r d i n g to Moore, i t i s c l e a r tha t something i s t rue of a g i ven o b j e c t which i s not t rue of o the r o b j e c t s and that t h i s cannot mean that the o b j e c t has one or more p r o p e r t i e s which noth ing e l s e has . In f a c t , says Moore, there i s an ambigu i ty i n the e x p r e s s i o n , " t h a t which i s t rue of a t h i n g , " to p o i n t out which i s a l l I can do i n the way o f d e f i n i n g a s u b j e c t [ i . e . , o b j e c t ] (Moore 1901, p. 122) . The f o u r t h reason f o r h o l d i n g the substratum theory i s t ha t s u b s t r a t a are b e l i e v e d to be the on l y s o r t of components which are capab le of d i f f e r e n t i a t i n g q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s . T h i s view immediate ly p r e c l u d e s c o n s t r u i n g p r o p e r t i e s as p a r t i c u l a r i n s t a n t i a t i o n s as o b j e c t s cou ld a l s o d i f f e r by reason of the p a r t i c u l a r i t y of t h e i r p r o p e r t i e s . P r o p e r t i e s must t h e r e f o r e be cons t rued e i t h e r as e n t i t i e s which d e r i v e t h e i r 31 p a r t i c u l a r i t y from s u b s t r a t a or e l s e as e x i s t e n t u n i v e r s a l s . I f p r o p e r t i e s are cons t rued i n the f i r s t way, then t h i s i n t e r p r e t a t i o n e n t a i l s an on to l ogy which i s i m p l i e d by the t h i r d view and, as sugges ted, by Moore and the e a r l y R u s s e l l . However, wh i l e t h i s i n t e r p r e t a t i o n i s not i n c o n s i s t e n t w i th the f o u r t h v iew, i t i s not c o n s i s t e n t w i th the reasons f o r h o l d i n g i t . U n l i k e the t h i r d v iew, which p o s t u l a t e s s u b s t r a t a i n o r d e r to g i ve i n s t a n t i a t i o n s of s u b s i s t e n t u n i v e r s a l s something i n which to i n h e r e , the f o u r t h view seeks to e x p l a i n the s i m i l a r i t y and d i f f e r e n c e between o b j e c t s i n terms of t h e i r p r o p e r t i e s . I f the red of A and B are t h e r e f o r e i n some sense p a r t i c u l a r , then the s i m i l a r i t y between A and B cannot be e x p l a i n e d i n terms of t h e i r p r o p e r t i e s but must be e x p l a i n e d by r e f e r e n c e to t h e i r r e l a t i o n to another e n t i t y such as a s u b s i s t e n t u n i v e r s a l . 3 On the o t h e r hand, i f p r o p e r t i e s are regarded as e x i s t e n t u n i v e r s a l s , the s i m i l a r i t y between A and B can be accounted f o r i n terms of t h e i r p r o p e r t i e s s i n c e A and B w i l l q u i t e l i t e r a l l y possess one and the same p r o p e r t y . Sub s t r a t a w i l l then be p o s t u l a t e d i n o r d e r to d i f f e r e n t i a t e q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s . There i s some sugges t i on tha t substratum and, i n p a r t i c u l a r , t h i s f o u r t h reason f o r h o l d i n g the substratum theory i s what A l l a i r e a c t u a l l y had i n mind when he s t a t e d h i s bare p a r t i c u l a r s t heo ry . A l though A l l a i r e e x p l i c i t l y den ie s t h i s i n t e r p r e t a t i o n , the bare p a r t i c u l a r s theory and the substratum theory share a number of s i m i l a r i t i e s . F i r s t , both views e x p l a i n the s i m i l a r i t y between o b j e c t s i n terms of e x i s t e n t u n i v e r s a l s . Second, both views d i s t i n g u i s h the component which d i f f e r e n t i a t e s o b j e c t s from the o b j e c t ' s e x i s t e n t u n i v e r s a l s . And, t h i r d l y , both views regard the i n d i v i d u a t i n g component as p r o p e r t y l e s s . In A l l a i r e ' s words, wh i l e e x i s t e n t u n i v e r s a l s such as red and green d i f f e r i n t r i n s i c a l l y (as w e l l as n u m e r i c a l l y ) , bare p a r t i c u l a r s and s u b s t r a t a on l y d i f f e r n u m e r i c a l l y ( A l l a i r e 1976, p. 286). Where the bare p a r t i c u l a r s theory and the substratum theory d i f f e r i s i n the way i n which they conce i ve of the r e l a t i o n between an o b j e c t ' s i n d i v i d u a t i n g component and i t s e x i s t e n t u n i v e r s a l s . On the substratum t h e o r y , s u b s t r a t a " s u p p o r t " e x i s t e n t u n i v e r s a l s o r , c o n v e r s e l y , e x i s t e n t u n i v e r s a l s " i n h e r e " i n s u b s t r a t a . E x i s t e n t u n i v e r s a l s and s u b s t r a t a do not then combine to form a bund le . Ra the r , e x i s t e n t u n i v e r s a l s themselves form a bundle which i n tu rn i s supported by or which inheres i n a s u b s t r a t a . In o the r words, on the substratum theory o b j e c t s are not e q u i v a l e n t to a bundle of e x i s t e n t u n i v e r s a l s , but to a bundle of e x i s t e n t u n i v e r s a l s p l u s a s u b s t r a t a . A l l a i r e , on the o the r hand, suggests tha t the i n d i v i d u a t i n g component, tha t i s , the bare p a r t i c u l a r , i s not " connec ted " w i th a bundle of e x i s t e n t u n i v e r s a l s but a c t u a l l y " c o n t a i n e d " i n i t . 33 Acco rd ing to A l l a i r e , i n say ing tha t an o b j e c t (denoted by " t h i s " ) i s composed of the e x i s t e n t u n i v e r s a l s R, S and C, there i s a temptat ion to c l a i m tha t R, S, and C are the c o n s t i t u e n t s of " t h i s " . But here we have i d e n t i f i e d d e s c r i p t i o n w i th p r e d i c a t i o n and so have exc luded the p o s s i b i l i t y of i n c l u d i n g i n our d e s c r i p t i o n tha t which accounts f o r the " t h i s n e s s " o f " t h i s " . In d e s c r i b i n g a s i n g l e t h i n g , the omi s s ion does not d i s t u r b . But i n d e s c r i b i n g two th ing s hav ing the same c h a r a c t e r s [ i . e . , p r o p e r t i e s ] , the omis s ion does d i s t u r b . One thus says that th ing s c o n t a i n bare p a r t i c u l a r s , which a r e , l i k e c h a r a c t e r s , p r e s e n t e d . However, a p a r t i c u l a r i s d i f f e r e n t i n k i n d from a c h a r a c t e r and i s thus squeezed out of the d e s c r i p t i o n . One cannot p e d i c a t e a p a r t i c u l a r of a t h i n g . For p a r t i c u l a r s , be ing ba re , cannot be named as c h a r a c t e r s can be. P a r t i c u l a r s are i n tha t sense i n e f f a b l e ( A l l a i r e 1976, p. 290). A l though A l l a i r e c l a ims tha t bare p a r t i c u l a r s are con ta ined i n o b j e c t s and not mere ly connected w i th them and t h e r e f o r e that bare p a r t i c u l a r s are not subs t ra tum, i t may s t i l l be argued tha t the two s o r t s of e n t i t i e s d i f f e r on l y i n name. The d i f f e r e n c e between A l l a i r ' s theory and the substratum theory would not then l i e i n the nature of the i n d i v i d u a t i n g component, but i n whether the i n d i v i d u a t i n g component i s con ta ined i n or connected w i th o b j e c t s . However, wh i l e bare p a r t i c u l a r s may w e l l reduce to subs t ra tum, i t i s not impor tant , f o r the purposes of t h i s t h e s i s , to e i t h e r support or r e j e c t t h i s c l a i m . For whether or not bare p a r t i c u l a r s and substratum are the same, both 34 t h e o r i e s are i n c o m p a t i b l e w i t h I I as on e i t h e r view i t i s l o g i c a l l y p o s s i b l e f o r two o b j e c t s t o have a l l t h e i r p r o p e r t i e s i n common and y e t s t i l l be n u m e r i c a l l y d i s t i n c t by r e a s o n o f t h e i r i n d i v i d u a t i n g component whatever t h e i r i n d i v i d u a t i n g may t u r n out t o be. T h i s a n a l y s i s thus s u b s t a n t i a t e s the c l a i m which gave r i s e t o t h i s d i s c u s s i o n , namely, t h a t o n t o l o g i e s which p o s t u l a t e the e x i s t e n c e o f an i n d i v i d u a t i n g component w i l l be i n c o m p a t i b l e w i t h I I on the grounds t h a t i t w i l l be by r e a son of the i n d i v i d u a t i n g component, and not a d i f f e r e n c e i n p r o p e r t i e s , t h a t o b j e c t s d i f f e r , t h e r e b y r a i s i n g the p o s s i b i l i t y o f d i s t i n c t i n d i s c e r n i b l e s . But what t h i s a n a l y s i s a l s o i n d i c a t e s are the types of p r o p e r t i e s which are sometimes c l a i m e d t o c o n s t i t u t e o b j e c t s but which are i n c o m p a t i b l e w i t h I I , and, i n t h i s way, i t i n d i r e c t l y p o i n t s t o the o n t o l o g y e n t a i l e d by I I . By s t i p u l a t i n g the s o r t s o f p r o p e r t i e s which are i n c o m p a t i b l e w i t h I I , i t i s t h e r e f o r e p o s s i b l e , through a p r o c e s s o f e l i m i n a t i o n , t o deduce the p r o p e r t i e s which are c o m p a t i b l e w i t h I I . The o n t o l o g y e n t a i l e d by I I can t h e r e f o r e be s t a t e d i n t h i s n e g a t i v e way as f o l l o w s . (1) S i n c e I I i s i n c o m p a t i b l e w i t h the e x i s t e n c e o f i n d i v i d u a t i n g components, the p r o p e r t i e s which c o n s t i t u t e o b j e c t s must be n o n - p a r t i c u l a r o r u n i v e r s a l . (2) Moreover, s i n c e u n i v e r s a l s are components of p h y s i c a l o b j e c t s , they must e x i s t . A c c o r d i n g l y , a p r o p e r t y 35 such as red i s an e x i s t e n t u n i v e r s a l and t h e r e f o r e may be r e f e r r e d to as the " e x i s t e n t u n i v e r s a l r e d " . (3) T h i s means t h a t , because the p r o p e r t i e s of o b j e c t s are not p a r t i c u l a r but u n i v e r s a l and t h e r e f o r e capab le of be ing shared by more than one o b j e c t , p r o p e r t i e s such as the e x i s t e n t u n i v e r s a l red are capab le of e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e . ( 4 ) I t a l s o means tha t the red of A and the red of B cannot be d i s t i n c t p a r t s of the e x i s t e n t u n i v e r s a l r e d : f i r s t , because i t i s one and the same p r o p e r t y which i s s a i d to e x i s t i n s p a t i o - t e m p o r a l l y separa te o b j e c t s and, s econd l y , because i f the red of A and the red of B were d i s t i n c t p a r t s of the same e x i s t e n t u n i v e r s a l , i t would be l o g i c a l l y p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and ye t n u m e r i c a l l y d i s t i n c t by reason of t h e i r p a r t s . (5) E x i s t e n t u n i v e r s a l s are t h e r e f o r e the on l y c o n s t i t u e n t s o f o b j e c t s f o r i f o b j e c t s were composed o f i n s t a n t i a t e d p r o p e r t i e s or con ta ined bare p a r t i c u l a r s , i t would not f o l l o w tha t q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s are n e c e s s a r i l y i d e n t i c a l . ( 6 ) S i m i l a r l y , o b j e c t s cannot be connected w i th any th ing such as a substratum as i t would p o s s i b l e f o r two o b j e c t s to have a l l t h e i r p r o p e r t i e s i n common and y e t s t i l l be n u m e r i c a l l y d i s t i n c t by reason of t h e i r s u b s t r a t a . The on to logy which i s i m p l i e d by I I can t h e r e f o r e be p o s i t i v e l y d e f i n e d as f o l l o w s : 36 (1) o b j e c t s are composed of e x i s t e n t u n i v e r s a l s ; (2) e x i s t e n t u n i v e r s a l s e x i s t r a t h e r than s u b s i s t ; (3) e x i s t e n t u n i v e r s a l s are capab le of e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e ; (4) e x i s t e n t u n i v e r s a l s are not d i v i s i b l e i n t o p a r t s ; (5) e x i s t e n t u n i v e r s a l s are the on l y c o n s t i t u e n t s of o b j e c t s ; and f i n a l l y , (6) o b j e c t s are r e d u c i b l e to t h e i r c o n s t i t u e n t e x i s t e n t u n i v e r s a l s r a t h e r than r e q u i r i n g i n a d d i t i o n a subs t ra tum. T h i s means (7) tha t i f A and B possess a l l and on l y the same p r o p e r t i e s , then A and B are n e c e s s a r i l y n u m e r i c a l l y i n d e t i c a l o r , i n L e i b n i z ' s words, " t h e r e i s no such t h i n g as two i n d i v i d u a l s i n d i s c e r n i b l e from each o t h e r " (Loemker 1956, p. 1117). C o n v e r s e l y , (8) i f A pos ses ses at l e a s t one p r o p e r t y not possessed by B, then A and B are n e c e s s a r i l y n u m e r i c a l l y d i s t i n c t and t h e r e f o r e there i s no sense of d i f f e r e n c e o the r than a d i f f e r e n c e i n p r o p e r t i e s , s i n c e " t h e r e i s no such t h i n g as two i n d i v i d u a l s i n d i s c e r n i b l e from each o t h e r " (Loemker 1956, p. 1117). T h i s on to logy i s r e a d i l y d i s t i n g u i s h e d from the o n t o l o g i e s of Moore, the e a r l y R u s s e l l , S t o u t , W i l l i a m s and S i k o r a by i t s c o n s t r u a l of p r o p e r t i e s as e x i s t e n t u n i v e r s a l s and from A l l a i r e ' s bare p a r t i c u l a r s theory and the substratum theory by i t s r e d u c t i o n of o b j e c t s to on l y e x i s t e n t u n i v e r s a l s . For ease of r e f e r e n c e , i t i s a p p r o p r i a t e to r e f e r to t h i s on to logy as the EU -on to logy , 37 tha t i s , as the on to logy of E x i s t e n t U n i v e r s a l s . The term "EU" or " E U - o n t o l o g y " , i n s o f a r as i t denotes the on to logy e n t a i l e d by I I, w i l l t h e r e f o r e be used synonymously w i th the term " I d e n t i t y o f I n d i s c e r n i b l e s " or "I I". A c c o r d i n g l y , p h i l o s o p h e r s who s u b s c r i b e to I I w i l l be r e f e r r e d to as " E U - o n t o l o g i s t s " . 38 Notes to Chapter One 1 Any r e f e r e n c e to an o b j e c t by name or to a p r o p e r t y which c o n t a i n s a name such as the p r o p e r t y of " b e i n g -i d e n t i c a l - w i t h A" or the p r o p e r t y of " b e i n g - d i f f e r e n t - f r o m -B" must be cashed out i n terms of a g e n e r a l d e s c r i p t i o n . Where I I i s s t a t e d i n the conver se , t h i s means that the d i f f e r e n c e between A and B cannot l i e i n the f a c t tha t A possesses the p r o p e r t i e s of be ing i d e n t i c a l w i th i t s e l f and d i f f e r e n t from B. 2 A l though Moore and the e a r l y R u s s e l l c l a i m that one i n s t ance of red i s n u m e r i c a l l y d i s t i n c t from another i n s t ance of r e d , they do not i n d i c a t e why the two i n s t a n c e s are n u m e r i c a l l y d i s t i n c t . Moore, f o r example, suggests tha t the p a r t i c u l a r i t y of p r o p e r t y i n s t a n c e s i s d e r i v e d from the uniqueness of the o b j e c t s to which they be l ong . But , as Moore a l s o admi t s , a bundle of p r o p e r t i e s i s no more unique than each p r o p e r t y s i n g l y . T h i s p o i n t I w i l l r e t u r n to l a t e r i n t h i s c h a p t e r . The nature of i n d i v i d u a t i n g components i s a l s o dubious where they are viewed as bare p a r t i c u l a r s or s u b s t r a t a . However, wh i l e a c r i t i c a l a n a l y s i s of these p r o p e r t i e s would prove i n t e r e s t i n g , i t i s not w i t h i n the scope of t h i s t h e s i s to do so . Ra the r , what t h i s chapter seeks to e s t a b l i s h i s t h a t , whatever t h e i r n a t u r e , i n d i v i d u a t i n g components are i n p r i n c i p l e i ncompat ib l e w i th I I. 3 S i k o r a argues that the s i m i l a r i t y between o b j e c t s can be e x p l a i n e d by r e f e r e n c e to l o g i c a l p o s s i b i l i t i e s i n s t e a d o f s u b s i s t e n t u n i v e r s a l s . In t h i s way, one avo ids p o s t u l a t i n g the e x i s t e n c e of P l a t o n i c e n t i t i e s which many p h i l o s o p h e r s f i n d p r o b l e m a t i c . 39 CHAPTER TWO RELATIVE SPACE AND TIME The e a r l y Rus se l and B lack r e j e c t I I on the grounds that i t i s l o g i c a l l y p o s s i b l e f o r two o b j e c t s to have a l l t h e i r p r o p e r t i e s i n common and y e t be n u m e r i c a l l y d i s t i n c t and t h e r e f o r e q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s are not n e c e s s a r i l y n u m e r i c a l l y i d e n t i c a l . However, be fo re t u r n i n g to t h i s argument, which i s termed the i n d i v i d u a t i o n argument, i t i s important to f i r s t d i sm i s s what might appear to be two obv ious and c o n c l u s i v e arguments a g a i n s t EU -onto logy . Some c r i t i c s have argued tha t i n o rde r f o r u n i v e r s a l s to be shared by two or more o b j e c t s they must be " a b s t r a c t " and t h e r e f o r e , as a b s t r a c t e n t i t i e s , i n some sense l e s s r e a l than o b j e c t s (Loux 1976, p. 11 ) . The o b j e c t i o n i s tha t t h i s l eads to the absurd consequence tha t o b j e c t s are composed of p r o p e r t i e s tha t are l e s s than r e a l . But c l e a r l y , as no E U - o n t o l o g i s t would knowingly ho ld t h i s , i t must be assumed t h a t i n r e f e r r i n g to u n i v e r s a l s as a b s t r a c t , the E U - o n t o l o g i s t i s not c l a i m i n g tha t u n i v e r s a l s s u b s i s t r a t h e r than e x i s t , but tha t they can be shared by more than one o b j e c t and, i n t h i s sense , they are not p a r t i c u l a r i n the 40 manner i n which o b j e c t s a r e . R.I. Aa ron , f o r example, remarks tha t I understand how p a r t i c u l a r th ing s r e t a i n t h e i r p a r t i c u l a r i t y w h i l s t y e t be ing c l a s s e d t o g e t h e r , f o r they share some of t h e i r q u a l i t i e s i n common. But I do not see how q u a l i t i e s , here i n t h e i r bare s i m p l i c i t y , can be i d e n t i f i e d and y e t remain d i s t i n c t p a r t i c u l a r s (p .179, 1939). The E U - o n t o l o g i s t 1 s c l a i m tha t e x i s t e n t u n i v e r s a l s are a b s t r a c t or e n t i t i e s which are capab le o f e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e does not then mean that e x i s t e n t u n i v e r s a l s are i n some sense l e s s than r e a l , but tha t e x i s t e n t u n i v e r s a l s are a d i f f e r e n t type of e n t i t y than p h y s i c a l o b j e c t s . A second o b j e c t i o n to e x i s t e n t u n i v e r s a l s i s tha t there may not be an i n s t a n c e o f a s p a t i o - t e m p o r a l l y d i v i d e d e x i s t e n t u n i v e r s a l . In o the r words, i f we were ab le to determine the p r e c i s e shade of a l l o c cu r rence s of r e d , we might f i n d tha t no two shades of red are i n f a c t p r e c i s e l y the same. I t might then be supposed that because the red of A i s not one and the same wi th the red of B, red i s not sha reab le but p a r t i c u l a r . However, t h i s i s not a good argument a g a i n s t EU-onto logy f o r two rea sons . F i r s t , as Dawes-Hicks n o t e s , e m p i r i c a l ev idence of t h i s o rde r i s not p o s s i b l e (Dawes-Hicks 1923, p. 126) . But , s e cond l y , even i f such ev idence were p o s s i b l e , i t would not i n d i c a t e that p r o p e r t i e s are not s h a r e a b l e , but o n l y tha t of a l l 41 occu r rence s of the p r o p e r t y no two occu r rence s happen to be p r e c i s e l y the same. E m p i r i c a l ev idence of t h i s s o r t would not then be s u f f i c i e n t to deny the l o g i c a l p o s s i b i l i t y of e x i s t e n t u n i v e r s a l s . EU-onto logy cannot then be r e f u t e d on the grounds that e x i s t e n t u n i v e r s a l s are i n some sense l e s s than r e a l or tha t the e x i s t e n c e of e n t i t i e s which are capab le of e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e i s not a l o g i c a l p o s s i b i l i t y . T h i s means tha t c r i t i c i s m of EU-onto logy must be based on whether a s a t i s f a c t o r y account of o b j e c t s can be g i ven i n terms of p r o p e r t i e s which are e x i s t e n t u n i v e r s a l s . The common argument a g a i n s t the nature of the o b j e c t s of EU-onto logy i s the i n d i v i d u a t i o n argument. C e n t r a l to the many v e r s i o n s o f t h i s argument i s the c l a i m tha t i t i s l o g i c a l l y p o s s i b l e f o r two o b j e c t s to have a l l t h e i r e x i s t -ent u n i v e r s a l s i n common and y e t s t i l l be n u m e r i c a l l y d i s t i n c t . In t h i s c h a p t e r , I w i l l c o n s i d e r B l a c k ' s w e l l -known v e r s i o n of t h i s argument as w e l l as a more e l a b o r a t e v e r s i o n of an argument o f f e r e d by Adams. The d i f f e r e n c e between the two v e r s i o n s l i e s i n the use tha t i s made of the argument ' s c e n t r a l c l a i m . B l a c k , f o r i n s t a n c e , devotes h i s a r t i c l e to c o n s t r u c t i n g a mean ing fu l example of two q u a l -i t a t i v e l y i n d i s t i n g u i s h a b l e but n u m e r i c a l l y d i s t i n c t o b j e c t s . Adams' v e r s i o n , on the o the r hand, suggests tha t i f the E U - o n t o l o g i s t accept s the l o g i c a l p o s s i b i l i t y of a lmost i d e n t i c a l o b j e c t s then he shou ld a l s o be w i l l i n g to accept 42 the l o g i c a l p o s s i b i l i t y of i d e n t i c a l o b j e c t s . The way i n which I e l a b o r a t e upon Adams' argument a l s o d i f f e r s from B l a c k ' s argument i n tha t I c o n s i d e r whether p r o p e r t i e s , as they are conce ived of by E U - o n t o l o g i s t s , are by t h e i r very nature capab le of guarantee ing tha t n u m e r i c a l l y d i s t i n c t o b j e c t s are i n f a c t q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e . However, d e s p i t e the obv ious d i f f e r e n c e between these two v e r s i o n s of the i n d i v i d u a t i o n argument, both v e r s i o n s are d i r e c t e d toward the same end , namely to demonstrate tha t d i s t i n c t i n d i s c e r n i b l e s are a l o g i c a l p o s s i b i l i t y and t h e r e f o r e tha t where two o b j e c t s are q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e , the E U - o n t o l o g i s t has no b a s i s on which to i n d i v i d u a t e or t e l l the two o b j e c t s a p a r t . I. Black's Individuation Argument In his paper e n t i t l e d "The Identity of Indiscernibles", Black o f f e r s the following instance of two objects which have a l l their existent universals in common. I s n ' t i t l o g i c a l l y p o s s i b l e tha t the un i ve r se shou ld have con ta ined no th ing but two e x a c t l y s i m i l a r pheres? We might suppose that each was made of c h e m i c a l l y pure i r o n , had a d iameter of one m i l e , tha t they had the same temperature, c o l o u r , and so o n , and tha t no th ing e l s e e x i s t e d . Then every q u a l i t y and r e l a t i o n a l c h a r a c t e r i s t i c of the one would a l s o be a p r o p e r t y of the o t h e r . Now i f what I am d e s c r i b i n g i s l o g i c a l l y p o s s i b l e , i t i s not impos s i b l e f o r two th ing s to have a l l t h e i r p r o p e r t i e s i n common. T h i s seems to me to r e f u t e the P r i n c i p l e (B lack 1976, p. 253-54) . 43 In o the r words what B lack i s c l a i m i n g i s tha t i f i t i s not l o g i c a l l y impos s i b l e f o r two n u m e r i c a l l y d i s t i n c t o b j e c t s to have a l l t h e i r e x i s t e n t u n i v e r s a l s in common/ then q u a l -i t a t i v e l y i n d i s t i g u i s h a b l e o b j e c t s w i l l not n e c e s s a r i l y be n u m e r i c a l l y i d e n t i c a l as the E U - o n t o l o g i s t c l a i m s . However, E U - o n t o l o g i s t s have not found t h i s argument p e r s u a s i v e . In f a c t , they f l a t l y deny the l o g i c a l p o s s i b i l i t y of d i s t i n c t i n d i s c e r n i b l e s . A c c o r d i n g to the E U - o n t o l o g i s t , i f A and B a r e , i n f a c t , n u m e r i c a l l y d i s t i n c t , then , by d e f i n i t i o n , A must possess an e x i s t e n t u n i v e r s a l not possessed by B, o therwi se A and B w i l l be n u m e r i c a l l y i d e n t i c a l . One reason f o r suppos ing t h i s i s tha t most d i s t i n c t o b j e c t s which at f i r s t s i g h t appear to have the same p r o p e r t i e s i n common prove to d i f f e r q u a l i t a t i v e l y on c l o s e r i n s p e c t i o n . The E U - o n t o l o g i s t might then suppose that there w i l l not a c t u a l l y be two o b j e c t s i n the wor ld which are q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and ye t n u m e r i c a l l y d i s t i n c t . However, i f t h i s i s what the E U - o n t o l o g i s t takes I I to a s s e r t , then , wh i l e the E U - o n t o l o g i s t may be r i g h t , he i s not making an i n t e r e s t i n g c l a i m as the t r u t h of I I w i l l be con t i n gen t on whether a t any g i ven time there e x i s t d i s t i n c t i n d i s c e r n -i b l e s . In o t h e r words, what the E U - o n t o l o g i s t would be c l a i m i n g i s not tha t there cannot be d i s t i n c t i n d i s c e r n -i b l e s , but tha t i t happens to be the case that there a r e n ' t 44 any. Therefore, i f the EU-ontologist wants to deny the l o g i c a l p o s s i b i l i t y of Black's two q u a l i t a t i v e l y i n d i s t -inguishable spheres, he must hold that I I i s necessarily true and not merely contingently true. As Ayer states, Philosophically, the grounds for a denial of existence are always a p r i o r i . The proof that nothing does answer to a given description i s that nothing could, and the proof of this is that the description in question i s meaningless or s e l f -contradictory (Ayer 1976, p. 264). Another way of defending I I against the individuation argument, then, i s to claim that not only does nothing answer Black's description, but that nothing could answer i t . This, as Ayer states, means that Black's description of two numerically d i s t i n c t but q u a l i t a t i v e l y indistinguishable spheres must be either meaningless or self-contradictory. But i t i s cle a r , f i r s t of a l l , that Black's description i s not self-contradictory. For, as we have just seen, even though there may not be two objects with a l l their existent universals in common, i t i s not outside the bounds of l o g i c a l p o s s i b i l i t y to say that at some other point in time there might be. However, what the EU-ontologist might question i s the meaningfulness of Black's description. The EU-ontologist might argue, for example, that i t i s a misuse of the term "object" to speak of objects in the p l u r a l where 4 5 there i s commonal i ty. T h i s s o r t of o b j e c t i o n i s r a i s e d by Ayer at the c o n c l u s i o n o f h i s paper "The I d e n t i t y o f I n d i s c e r n i b l e s " . A c c o r d i n g to A y e r , B l a c k ' s a b i l i t y to c r e a t e a counter -example to I I r e s t s on h i s f r e e use of the d i s t i n c t i o n between o b j e c t s and the p r o p e r t i e s which compose o b j e c t s . Because B lack does not c l e a r l y equate o b j e c t s w i th the bundle of p r o p e r t i e s which compose them, t h i s i n turn a l l ows him to r e f e r to two spheres and then r a i s e the q u e s t i o n o f whether two spheres , ' which he has a l r e a d y d i s t i n g u i s h e d , are n u m e r i c a l l y d i s t i n c t even though they have a l l t h e i r p r o p e r t i e s i n common. In t h i s way B lack takes f o r g ranted what I I i s in tended to deny, namely, the numer i ca l d i s t i n c t n e s s of the two spheres . However, the f a c t tha t B lack r e f e r s to two spheres i s not i n i t s e l f s u f f i c i e n t to d i f f e r e n t i a t e the spheres . In f a c t , says A y e r , i t i s j u s t t h i s tendency to r e f e r to o b j e c t s w i thout enumerat ing t h e i r p r o p e r t i e s which leads us to t r e a t the spheres as n u m e r i c a l l y d i s t i n c t . Ayer t h e r e f o r e c l a ims tha t B l a c k ' s use of the term " o b j e c t " i n v o l v e s an i l l e g i t i m a t e e x t e n s i o n of the concept o f number as i t i s on l y where there i s a d i f f e r e n c e i n p r o p e r t i e s t ha t Ayer b e l i e v e s tha t i t makes any sense to t a l k of the p l u r a l i t y of o b j e c t s . A l though B lack does not a n t i c i p a t e t h i s o b j e c t i o n , i t i s f a i r to assume that he would response by a rgu ing tha t s i n c e i t i s l o g i c a l l y p o s s i b l e f o r two o b j e c t s to be 46 q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and ye t n u m e r i c a l l y d i s t i n c t there may be p l u r a l i t y even where there i s commonal i ty. In f a c t , even though Ayer a t t aches some weight to the argument tha t p l u r a l i t y i m p l i e s q u a l i t a t i v e d i f f e r e n c e , he n e v e r t h e l e s s concedes tha t t h i s i s not an a l t o g e t h e r c o n v i n c i n g argument. A t the same t ime, however, Ayer i s d i s t u r b e d by the consequences of r e j e c t i n g I I . I f I I were f a l s e , t hen , i n the words of B l a c k ' s f i c t i t i o u s proponent of I I, we cou ld not d e f i n e i d e n t i t y s i n c e the f a c t tha t we see one o b j e c t would not prove that there i s on ly one o b j e c t and not three or f ou r more o b j e c t s which are q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e but n u m e r i c a l l y d i s t i n c t from each o t h e r . Proponents of I I consequent l y f e e l tha t i t i s on l y i f o b j e c t s d i f f e r i n at l e a s t one p r o p e r t y tha t they can be i d e n t i f i e d . As Ayer admi t s , I t may be tha t I am unduly s u s p i c i o u s o f the ca tegory of subs tance , but I s t i l l cannot see how a s s e r t i n g tha t an i n d i v i d u a l e x i s t s can be to a s s e r t any th ing more than that some p r e d i c a t e , or se t o f p r e d i c a t e s , i s i n s t a n t i a t e d . No doubt there are many p h i l o s o p h e r s f o r whom t h i s q u e s t i o n p r e s e s n t s no d i f f i c u l t y ; but I am not of t h e i r number. And the p roo f of t h i s i s t h a t , i n s p i t e of a l l tha t can be urged a g a i n s t i t , I am s t i l l i n c l i n e d to ho ld that the p r i n c i p l e of the i d e n t i t y o f i n d i s c e r n i b l e s i s n e c e s s a r i l y t rue (Ayer 1976, p. 270) . E u - o n t o l o g i s t s such as Ayer t h e r e f o r e b e l i e v e tha t wh i le B l a c k ' s l i n e of argument i s p e r s u a s i v e , the 47 d i f f i c u l t i e s which i t r a i s e s f o r I I are f a r l e s s severe than those which would a r i s e i f I I were abandoned. II. A Second I n d i v i d u a t i o n Argument In s t a t i n g h i s v e r s i o n of the i n d i v i d u a t i o n argument, B l ack sought to d e s c r i b e a l o g i c a l l y p o s s i b l e wor ld i n which two o b j e c t s were q u a l i t a t i v e l y i d e n t i c a l and ye t n u m e r i c a l l y d i s t i n c t . B l a c k ' s assumption was that i f such a word cou ld be d e s c r i b e d i n a way tha t was mean ing fu l and not s e l f -c o n t r a d i c t o r y , then there would be no l o g i c a l reason why i t cou ld not e x i s t . Whi le Adams' argument a l s o seeks to e s t a b l i s h the l o g i c a l p o s s i b i l i t y of d i s t i n c t i n d i s c e r n -i b l e s , i t goes about do ing t h i s i n a d i f f e r e n t way. Rather than a t tempt ing to d e s c r i b e a f a n t a s t i c wor ld s i m i l a r to B l a c k ' s , Adams shows tha t the l o g i c a l p o s s i b i l i t y o f d i s t i n c t i n d i s c e r n i b l e s can be p l a u s i b l y i n f e r r e d from the l o g i c a l p o s s i b i l i t y of a lmost i d e n t i c a l o b j e c t s . Where my argument e l a b o r a t e s on Adams' argument and, f o r tha t ma t te r , B l a c k ' s argument, i s i n the s t r e s s i t p l a c e s on the nature o f e x i s t e n t u n i v e r s a l s which are c l a imed to c o n s t i t u t e o b j e c t s . As we have seen, e x i s t e n t u n i v e r s a l s are d e f i n e d i n EU-onto logy as e n t i t i e s which are capab le o f e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e . T h i s means tha t 48 the red of A i s q u i t e l i t e r a l l y one and the same as the red o f B. I t a l s o means that i t i s l o g i c a l l y p o s s i b l e f o r A and B to share o the r p r o p e r t i e s such as t h e i r shape, s i z e , t e x t u r e , and so on. For example, i t i s p o s s i b l e f o r A and B to both be square and l a r g e as w e l l as r e d . In f a c t , says Adams, i f we accept the p o s s i b i l i t y of A and B s h a r i n g a l l but one e x i s t e n t u n i v e r s a l , we can i n f e r the p o s s i b i l i t y o f A and B sha r i n g a l l t h e i r e x i s t e n t u n i v e r s a l s w i thout l o s s of t h e i r separa te i d e n t i t i e s . The q u e s t i o n i s , then: how would the E U - o n t o l o g i s t i n d i v i d u a t e A and B? Or, to put i t l e s s t e n d e n t i a l l y , how would the E U - o n t o l o g i s t go about enumerat ing the o b j e c t s which s a t i s f y a l i s t such as t h i s : red square l a r g e hard I t i s c l e a r tha t the E U - o n t o l o g i s t would argue that i f r e d , square , l a r ge and hard are toge ther apt f o r e x i s t e n c e , then on l y one o b j e c t can s a t i s f y t h i s l i s t . T h i s does not mean that B cannot have these p r o p e r t i e s , but on l y tha t i f B does , t hen , i f B i s n u m e r i c a l l y d i s t i n c t from A, B must possess a f u r t h e r p r o p e r t y which A does not po s se s s , o t h e r -wise A and B w i l l be n u m e r i c a l l y i d e n t i c a l . But suppose tha t the on l y q u a l i t a t i v e d i f f e r e n c e between A and B i s tha t A i s 49 h a r d whereas B i s s o f t and, f u r t h e r , t h a t i t was o n l y a f t e r l o n g and c l o s e e x a m i n a t i o n t h a t t h i s d i f f e r e n c e emerged, s a y , a t t ^ . 1 I f we c o n s i d e r A and B a t t ] _ , t h e E U - o n t o l -o g i s t would r e a d i l y a g r e e t h a t A and B a r e n u m e r i c a l l y d i s t i n c t o b j e c t s as i t i s a t t h i s p o i n t t h a t t h e i r n u m e r i c a l d i s t i n c t n e s s i s e s t a b l i s h e d by r e a s o n o f t h e i r q u a l i t a t i v e d i s c e r n i b i l i t y . On t h e o t h e r hand, i f we c o n s i d e r A and B p r i o r t o t±, t h e E U - o n t o l o g i s t i s c o mmitted t o r e g a r d i n g A and B as n u m e r i c a l l y i d e n t i c a l as t h e r e i s no q u a l i t a t i v e d i f f e r e n c e between A and B. The E U - o n t o l o g i s t i s t h e r e f o r e f o r c e d t o c l a i m t h a t A and B a r e i d e n t i c a l p r i o r t o t ^ y e t n u m e r i c a l l y d i s t i n c t a t t i e v e n though the c o n s t i t u t i o n o f A and B has r e m a i n e d u n c h a n g e d . The E U - o n t o l o g i s t may o f c o u r s e a r g u e t h a t i n d e t e r m i n i n g t h e n u m e r i c a l d i s t i n c t n e s s o f A and B a t t± he i s r e a l l y a f f i r m i n g t h e s e p a r a t e i d e n t -i t i e s o f A and B e v e n t h o u g h he t h o u g h t th e two o b j e c t s were i d e n t i c a l p r i o r t o t i . B u t , as Adams p o i n t s o u t i n t h e c a s e o f t h e t w i n s , t h e n u m e r i c a l d i s t i n c t n e s s o f two o b j e c t s a l r e a d y e x i s t i n g c a n n o t depend on s o m e t h i n g t h a t has n o t y e t h appened. In o t h e r words, A and B a r e a l r e a d y d i s t i n c t from e a c h o t h e r t h o u g h n o t h i n g has y e t happened t o d i s t i n g u i s h them q u a l i t a t i v e l y . The n u m e r i c a l d i s t i n c t n e s s o f A and B must t h e r e f o r e be i n d e p e n d e n t o f t h e q u a l i t a t i v e d i f f e r e n c e w h i c h l a t e r a r i s e s a t t i . C o n s e q u e n t l y , i t i s l o g i c a l l y p o s s i b l e f o r two o b j e c t s , s u c h as A and B p r i o r t o 50 t i , to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and y e t n u m e r i c a l l y d i s t i n c t . However, the E U - o n t o l o g i s t may respond to the c l a i m that d i f f e r e n c e i s independent o f q u a l i t a t i v e d i s c e r n i b i l i t y by a r gu ing tha t the above l i s t o f p r o p e r t i e s does not i n c l u d e r e l a t i o n a l p r o p e r t i e s and that i t i s these p r o p e r t i e s which are capab le of d i f f e r e n t i a t i n g o b j e c t s . T h e r e f o r e , wh i l e A and B may have a l l t h e i r n o n - r e l a t i o n a l p r o p e r t i e s i n common, such as c o l o u r , shape, s i z e , and t e x t u r e , e t c . , A and B w i l l not be n u m e r i c a l l y i d e n t i c a l l y un le s s they a l s o have the same s p a t i o - t e m p o r a l l o c a t i o n . A c c o r d i n g to t h i s argument, t hen , on l y one o b j e c t can s a t i s f y a l i s t which i n c l u d e s a r e l a t i o n a l p r o p e r t y . 2 For example, on l y A can s a t i s f y the l i s t : red square l a r g e hard t o - t h e - l e f t - o f However, even i f we assume tha t r e l a t i o n a l p r o p e r t i e s are i n some sense un ique , we can never say tha t A d i f f e r s from B i n v i r t u e o f hav ing a d i f f e r e n t s p a t i o - t e m p o r a l l o c a t i o n . In o the r words, i f we assume tha t " t h e r e are two o b j e c t s , A and B" i s e q u i v a l e n t to "A has a p r o p e r t y B does not have" and tha t t h i s unshared p r o p e r t y i s r e l a t i o n a l , the f a c t tha t t h i s r e l a t i o n i s unshared cannot serve to d e s c r i b e A i n a 51 way which does not also describe B. For i f A i s to-the-l e f t - o f - B i s to say that the complex of existent universals: red, square, large, and hard, i s to the l e f t of the complex of existent universals: red, square, large, and hard, then whatever we say about the complex A, w i l l also be true of the complex B. Or, to put i t less charitably, one and the same complex of existent universals w i l l be to the l e f t of i t s e l f . The EU-ontologist i s consequently faced with the following dilemma. If objects are composed only of existent universals, then s t r i c t l y speaking r e l a t i o n a l properties must also be existent universals and so, l i k e red, square, large, and hard, they must be capable of enjoying a spatio-temporally divided mode of existence. Therefore, while the apparent difference between A and B i s that A i s to-the-l e f t - o f - B , B may also be described as possessing the property to-the-lef t-of, even though i t i s to C that B has this r e l a t i o n . However, i f we ignore the requirement that r e l a t i o n a l properties must also be capable of a spatio-temporally divided mode of existence and grant, as above, that there i s some sense in which r e l a t i o n a l properties are unique and, further, that their uniqueness provides a basis on which to individuate objects, then i t must be in the sense that they are symmetrical. That i s , there must be some sense in which A has this r e l a t i o n to B but which B does not 52 have to A, o therwi se i t cou ld be one and the same o b j e c t which stands i n t h i s r e l a t i o n to i t s e l f . But i n assuming t h i s one assumes that there are two o b j e c t s to begin w i t h , t ha t i s , t h a t A and B are d i s t i n c t o b j e c t s and tha t A happens to be t o - t h e - l e f t - o f - B . In s h o r t , i f r e l a t i o n a l p r o p e r t i e s are e x i s t e n t u n i v e r s a l s , then, l i k e n o n - r e l a t i o n a l p r o p e r t i e s , they can be shared by more than one o b j e c t and t h e r e f o r e a l i s t which unc ludes r e l a t i o n a l p r o p e r t i e s w i l l be no more unique than one which does not . On the o the r hand, i f r e l a t i o n a l p r o p e r t i e s are not e x i s t e n t u n i v e r s a l s , t hen , wh i l e t h i s c l a i m r e q u i r e s tha t we over look the f a c t tha t r e l a t i o n a l p r o p e r t i e s are p a r t i c u l a r and t h e r e f o r e , s t r i c t l y s peak ing , i n compat ib l e wi th I I, r e l a t i o n a l p r o p e r t i e s w i l l not c o n s t i t u t e but r a t h e r presuppose the i d e n t i t i e s of the o b j e c t s i n q u e s t i o n . Consequent l y , something o the r than a d i f f e r e n c e i n e i t h e r n o n - r e l a t i o n a l or r e l a t i o n a l e x i s t e n t u n i v e r s a l s must p r o v i d e the b a s i s f o r i n d i v i d u a t i o n . For example, o b j e c t s might be c l a imed to d i f f e r i n v i r t u e of t h e i r c o n t a i n i n g p a r t i c u l a r p r o p e r t i e s o r bare p a r t i c u l a r s or e l s e they might be c la imed to d i f f e r i n v i r t u e of t h e i r be ing connected wi th a subs t ra tum. But , i n t h i s c a se , a f u r t h e r sense of d i f f e r e n c e emerges: d i f f e r i n g w i th r e s p e c t to such i n d i v i d u a t o r s as d i s t i n c t from d i f f e r i n g i n an e x i s t e n t u n i v e r s a l . But t h i s , as we saw in the p r e v i o u s c h a p t e r , i s unacceptab le to the E U - o n t o l o g i s t s i n c e i t i m p l i e s tha t i t i s l o g i c a l l y p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and y e t s t i l l n u m e r i c a l l y d i s t i n c t by reason of t h e i r i n d i v i d u a t i n g components. The E U - o n t o l -o g i s t ' s o n l y r e c o u r s e , then , i s to contend that e n t i t i e s o t h e r than e x i s t e n t u n i v e r s a l s need o n l y be recogn i zed once the p o s s i b i l i t y of d i s t i n c t i n d i s c e r n i b l e s has been admit ted and t h i s of course i s something which the E U - o n t o l o g i s t does not do. A l though E U - o n t o l o g i s t s such as Ayer f e e l some d i s c o m f o r t i n s imp ly deny ing t h i s p o s s i b i l i t y , A y a r 1 s r a t i o n a l e i s tha t the consequences of de fend ing I I are f a r l e s s severe than those of deny ing i t . Consequent l y , wh i le Ayer would no doubt f i n d my e l a b o r a t i o n of Adams' i n d i v i d -u a t i o n argument p e r s u a s i v e , he wou ld , as i n the case of B l a c k ' s argument, remain i n c l i n e d to accept I I as a neces sa ry t r u t h . The shortcoming of i n d i v i d u a t i o n arguments, then, i s tha t they are not ab le to generate consequences that would make I I unacceptab le to any p h i l o s o p h e r . As a r e s u l t , the debate between advocates and opponents of I I has remained a l i v e . In the next s e c t i o n I o f f e r an argument which p h i l o s -ophers w i l l f i n d c o n c l u s i v e and which has not been o f f e r e d 1 any p l a c e e l s e . T h i s i s ach ieved through a c l o s e examinat ion o f EU -on to logy , s p e c i f i c a l l y , the r e l a t i o n between o b j e c t s and t h e i r p r o p e r t i e s or e x i s t e n t u n i v e r s a l s . 54 I I I . The Argument From The Nature of O b j e c t s The purpose of the argument from the nature of o b j e c t s i s to show tha t the on to l ogy which I I e n t a i l s i s u n a c c e p t a b l e . As the focus o f t h i s argument i s on the nature o f o b j e c t s imp l i ed by EU -on to logy , i t i s not important to c o n s i d e r h e r e , as i n the i n d i v i d u a t i o n argument a ga in s t I I, whether i t i s l o g i c a l l y p o s s i b l e f o r two n u m e r i c a l l y d i s t i n c t o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e . The q u e s t i o n i s r a t h e r whether a p l a u s i b l e on to logy can be r e c o n c i l e d w i th t h i s v iew. A l l the argument from the nature of o b j e c t s r e q u i r e s i s tha t we g rant tha t the E U - o n t o l o g i s t i s committed to the s i x tenet s se t out at the c o n c l u s i o n of the I n t r o d u c t i o n . The argument from the nature of o b j e c t s i s d i v i d e d i n t o two s t a ge s . The f i r s t s tage e s t a b l i s h e s tha t the on l y e n t i t i e s to which e x i s t e n t u n i v e r s a l s are r e l a t e d are the o b j e c t s to which they b e l o n g . In o the r words, e x i s t e n t u n i v e r s a l s do not have a second r e l a t i o n to s u b s i s t e n t u n i v e r s a l s , l o g i c a l p o s s i b i l i t i e s or c l a s s e s . T h i s i s shown by c o n s i d e r i n g what i t means to c l a i m that p r o p e r t i e s are e x i s t e n t u n i v e r s a l s . The second stage of the argument examines the r e l a t i o n between o b j e c t s and t h e i r e x i s t e n t u n i v e r s a l s where, as the f i r s t stage shows, t h i s i s the on l y r e l a t i o n i n which e x i s t e n t u n i v e r s a l s are r e l a t a . The f i r s t stage of the argument from the nature of o b j e c t s t h e r e f o r e 5 5 examines the r i g h t hand s i de of the diagram below and the second stage of the argument, the l e f t hand s i d e . 1) s u b s i s t e n t u n i v e r s a l o b j e c t A x 2) l o g i c a l p o s s i b i l i t y /3 ) c l a s s who lS -par t 1) r e l a t i o n of e x e m p l i f i c a t i o n r e l a t i o r r ^ 2) r e l a t i o n o f a c t u a l i z a t i o n 3 ]yc lass -member r e l a t i o n 'red ( e x i s t e n t u n i v e r s a l ) The f i r s t s tage o f the argument from the nature of o b j e c t s r e s t s on an examinat ion of e x i s t e n t u n i v e r s a l s . As we have seen, o b j e c t s are d e f i n e d i n EU-onto logy as e q u i v a l e n t to the p r o p e r t i e s which c o n s t i t u t e them. These p r o p e r t i e s are i n tu rn d e f i n e d as e n t i t i e s which are capab le o f e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e , tha t i s , as u n i v e r s a l s which e x i s t r a t h e r than s u b s i s t . The red o f A and the red of B are t h e r e f o r e he ld to be q u i t e l i t e r a l l y one and the same. Or, to put i t another way, no d i s t i n c t i o n i s made in EU-onto logy between the d e n o t a t i o n of " r e d " where i s i t used as a g e n e r a l term and the d e n o t a t i o n of " r e d " where i t i s used i n sentences such as "A i s r e d " . 3 In both ca se s , " r e d " denotes a s i n g l e e n t i t y which e x i s t s and which i s capab le of be ing a c o n s t i t u e n t of more than one o b j e c t a t one and the same t ime. T h i s view of p r o p e r t i e s t h e r e f o r e p r e c l u d e s the E U - o n t o l o g i s t from r e c o g n i z i n g 56 s u b s i s t e n t forms of p r o p e r t i e s , f i r s t , because p r o p e r t i e s are not s p a t i o - t e m p o r a l l y d i v i d e d and t h e r e f o r e n u m e r i c a l l y d i s t i n c t e x e m p l i f i c a t i o n s of s u b s i s t e n t u n i v e r s a l s , but one and the same i n a l l t h e i r i n s t a n t a t i o n s and, s econd l y , because p r o p e r t i e s do not exemp l i f y s u b s i s t e n t u n i v e r s a l s but are themselves u n i v e r s a l s , i n t h i s c a se , u n i v e r s a l s which e x i s t r a t h e r than s u b s i s t . In o the r words, what the E U - o n t o l o g i s t i s c l a i m i n g i s tha t P l a t o ' s rea lm of e t e r n a l a n d . t i m e l e s s forms i s i n f a c t e x i s t e n t . The p o s t u l a t i o n of a rea lm of s u b s i s t e n t u n i v e r s a l s , which are i n tu rn exemp-l i f i e d by e x i s t e n t u n i v e r s a l s , would t h e r e f o r e be super -f l u o u s . The c l a i m tha t u n i v e r s a l s are l o g i c a l p o s s i b i l i t i e s i s a l s o i n compa t i b l e w i th EU-onto logy because i t cont rues u n i v e r s a l s as e x i s t e n t and l o g i c a l p o s s i b i l i t i e s are not e x i s t e n t s . A t h i r d s o r t of r e l a t i o n which might be c l a imed to ho ld between the e x i s t e n t u n i v e r s a l red and x i n the diagram above i s a c lass-member r e l a t i o n . The red of A and the red of B might be thought of as members of the c l a s s of red p r o p e r t i e s which i s denoted by the g e n e r a l term " r e d " . However, there are a number of reasons why t h i s view i s i n compat ib l e w i th EU -on to logy . F i r s t , as we have seen, the d i f f e r e n c e between " r e d " as i t appears i n the sentences "A i s r e d " and " red i s my f a v o u r i t e c o l o u r " i s not o n t o l o g i c a l . In both s en tence s , " r e d " r e f e r s to the e x i s t e n t u n i v e r s a l 57 r e d . In the f i r s t sentence the e x i s t e n t u n i v e r s a l red i s a t t r i b u t e d to a p a r t i c u l a r o b j e c t and i n the second sentence i t i s merely r e f e r r e d t o . Second ly , p r o p e r t y c l a s s e s would not be an i n f o r m a t i v e f e a t u r e of EU -onto logy . Each p r o p e r t y c l a s s would always have one member, as a l l p r o p e r t i e s e x i s t , and no more than one member, as a l l o c cu r rence s of a g i ven p r o p e r t y are one and the same. P rope r t y c l a s s e s would not then t e l l us anyth ing about p r o p e r t i e s tha t i s not expressed by the term " e x i s t e n t u n i v e r s a l " . And, f i n a l l y , the f u n c t i o n of c l a s s e s i n onto logy has t r a d i t i o n a l l y been to account f o r the s i m i l a r i t y between n u m e r i c a l l y d i s t i n c t o ccu r rences of a g i ven p r o p e r t y . For example, S tout argues that the reason why r\ and r2 are red i s tha t they are members of the same c l a s s . 4 But , s i n c e the E u - o n t o l o g i s t does not th ink of r^ and r2 as n u m e r i c a l l y d i s t i n c t but as one and the same, he does not need to account f o r t h e i r s i m i l a r i t y . The class-member r e l a t i o n , l i k e s u b s i s t e n t u n i v e r s a l s and l o g i c a l p o s s i b i l i t i e s , i s t h e r e f o r e i ncompat ib l e wi th EU-onto logy . However, the f a c t tha t these three r e l a t i o n s and, i n p a r t i c u l a r , the r e l a t i o n s of e x e m p l i f i c a t i o n and a c t u a l i z a t i o n are i ncompat ib l e w i th EU -on to logy , commits the E U - o n t o l o g i s t to the view tha t even though there may not be any o b j e c t s which possess the e x i s t e n t u n i v e r s a l r e d , r e d , 58 as an " e x i s t e n t " u n i v e r s a l , must n e v e r t h e l e s s e x i s t . In o ther words, because the E U - o n t o l o g i s t d e f i n e s p r o p e r t i e s as e x i s t e n t u n i v e r s a l s , he cannot ho ld that where no o b j e c t possesses a g i ven p r o p e r t y tha t p r o p e r t y does not e x i s t as t h i s would be tantamount to c l a i m i n g tha t some e x i s t e n t u n i v e r s a l s do not i n f a c t e x i s t . The E U - o n t o l o g i s t i s t h e r e f o r e f o r c e d i n t o the untenab le p o s i t i o n of c l a i m i n g tha t a l l l o g i c a l l y p o s s i b l e shades o f red e x i s t , and, f u r t h e r , tha t these shades e x i s t even though they may not be possessed by an o b j e c t . The E U - o n t o l o g i s t might o b j e c t tha t a l l shades of red can e x i s t because t h e i r e x i s t e n c e i s not dependent on o b j e c t s . T h i s l i n e of argument i s s i m i l a r to W i l l i a m s ' view that p r o p e r t i e s such as red are f i n e p a r t s where the term " p a r t " i s used i n i t s o r d i n a r y sense to r e f e r to an e x i s t e n t i a l l y independent e n t i t y or an e n t i t y which i s apt f o r e x i s t e n c e by i t s e l f . However, the two views are not i d e n t i c a l . Where W i l l i a m s ' view d i f f e r s from EU-onto logy i s i n what W i l l i a m s takes " e x i s t e n t i a l l y independent " to mean. A c c o r d i n g to W i l l i a m s , a p r o p e r t y i s e x i s t e n t i a l l y independent i f i n p r i n c i p l e i t can be removed from the o b j e c t to which i t be longs w i thout l o s s o f i d e n t i t y . W i l l i a m s t h e r e f o r e i m p l i e s tha t e x i s t e n t i a l l y independent p a r t s must f i r s t be p a r t s of o b j e c t s . For example, i f red i s 59 e x i s t e n t i a l l y independent , then i t must f i r s t have belonged to an o b j e c t , f o r i n s t a n c e , i t must have belonged to a p i e c e of c l o t h i n the form of red dye from which i t was then e x t r a c t e d . W i l l i a m s a l s o ho lds tha t once the red dye has been e x t r a c t e d from the c l o t h , the r e s i d u e of red dye a s -sumes the s t a t u s of an o b j e c t . However, t h i s view i s incom-p a t i b l e w i th EU-onto logy . F o r , f i r s t of a l l , the e x i s t e n t i a l independence o f p r o p e r t i e s cannot depend on t h e i r be long ing to o b j e c t s from which they may then be e x t r a c t e d s i n ce t h i s i m p l i e s tha t i n o rder f o r a p r o p e r t y to e x i s t i t must f i r s t belong to an o b j e c t and, t h e r e f o r e , where no o b j e c t po s -sessed a g i ven p r o p e r t y , the e x i s t e n t u n i v e r s a l cou ld not be s a i d to e x i s t . Second ly , e x i s t e n t i a l l y independent p a r t s cannot be e q u i v a l e n t to o b j e c t s f o r i f the r e s i d u e of red dye from one p i e c e of c l o t h i s an i n s t ance of the e x i s t e n t u n i v e r s a l red and the r e s i d u e o f red dye from a second p i e c e of c l o t h another i n s t a n c e , then the two s p a t i a l l y separate r e s i d u e s must be one and the same. In o the r words, i f both r e s i d u e s are o b j e c t s , t h e n , as q u a l i t a t i v e l y i n d i s t i n g u i s h -ab le o b j e c t s they are n e c e s s a r i l y n u m e r i c a l l y i d e n t i c a l . Or, c o n v e r s e l y , i f the two r e s i d u e s are not n u m e r i c a l l y i d e n t -i c a l , as the E u - o n t o l o g i s t would no doubt want to c l a i m , then the o n l y way i n which the d i s t i n c t n e s s of the two r e s i d u e s can be e x p l a i n e d i s i f something o the r than an 60 e x i s t e n t u n i v e r s a l were to account f o r t h e i r d i s t i n c t n e s s . But t h i s , t oo , would be i ncompat ib l e w i th EU-onto logy s i n ce i t would be l o g i c a l l y p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and ye t n u m e r i c a l l y d i s t i n c t by reason of t h e i r i n d i v i d u a t i n g components. The E U - o n t o l -o g i s t must t h e r e f o r e r e j e c t W i l l i a m s ' d e f i n i t i o n of an e x i s t e n t i a l l y independent p r o p e r t y as a p r o p e r t y whose e x i s t e n c e i s t i e d to i t s be long ing to an o b j e c t from which i t may then be e x t r a c t e d . I n s t e a d , the E U - o n t o l o g i s t must c l a i m tha t p r o p e r t i e s are capab le of e x i s t i n g by themse lves , per se and i n s e . Some advocates o f I I may f i n d t h i s f e a t u r e of EU-onto logy u n a c c e p t a b l e . Other advocates may remain i n c l i n e d to accept I I on the grounds that t h i s consequence i s s t i l l l e s s severe than the d i f f i c u l t i e s which a r i s e as soon as I I i s abandoned. These E U - o n t o l o g i s t s might argue tha t wh i l e they are f o r c e d to c l a i m tha t a l l l o g i c a l l y p o s s i b l e p r o p e r t i e s e i x s t , i t i s on l y i f p r o p e r t i e s are cons t rued as e x i s t e n t u n i v e r s a l s tha t the i d e n t i t y of o b j e c t s can be guaranteed . In o ther words, these E U - o n t o l -o g i s t s might c l a i m tha t i f o b j e c t s are not composed on l y of e x i s t e n t u n i v e r s a l s but e x i s t e n t u n i v e r s a l s p l u s , f o r example, a bare p a r t i c u l a r , i t w i l l be l o g i c a l l y p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and 61 ye t s t i l l be n u m e r i c a l l y d i s t i n c t by reason of t h e i r bare p a r t i c u l a r s . Consequent ly , one ' s o b s e r v a t i o n of a red o b j e c t would not be s u f f i c i e n t to guarantee that what one i n f a c t observed was one o b j e c t and not two. E U - o n t o l o g i s t s of t h i s s o r t are t h e r e f o r e w i l l i n g to accept the c l a i m tha t a l l l o g i c a l l y p o s s i b l e p r o p e r t i e s e x i s t i n o r d e r to account f o r the i d e n t i t y of o b j e c t s . The E U - o n t o l g i s t ' s i n c l i n a t i o n to ho ld t h i s view r e s t s on two assumpt ions . The f i r s t assumption i s tha t i d e n t i t y and d i f f e r e n c e cannot be accounted f o r i n terms of p r o p e r t i e s which are l e s s p r o b l e m a t i c . T h i s i s an assumption which I do not i n tend to c h a l l e n g e as the problems of i d e n t i t y and d i f f e r e n c e are c o n t i n g e n t upon whether d i s t i n c t i n d i s c e r n -i b l e s are a l o g i c a l p o s s i b i l i t y , and t h i s , as we have seen, i s something which the E U - o n t o l o g i s t f l a t l y d e n i e s . The second assumption i s tha t an a c c e p t a b l e account o f the nature of o b j e c t s can be g i ven i n terms of e x i s t e n t u n i v e r s a l s . Advocates o f I I c l e a r l y see EU-onto logy as o f f e r i n g a s u p e r i o r account of o b j e c t s than o ther o n t o l o g i e s d e s p i t e the c o t r o v e r s i a l i t y of the c l a ims that a l l l o g i c a l l y p o s s i b l e p r o p e r t i e s e x i s t and tha t these p r o p e r t i e s are capab le o f e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e . In t h i s second stage of the argument from the nature o f o b j e c t s , which corresponds to the l e f t hand s i d e 6 2 of the diagram above, I w i l l show tha t even i f the c o n t r o v e r s i a l i t y of these c l a ims i f i g n o r e d , an a c c e p t a b l e account of the nature of o b j e c t s cannot be g i ven i n terms of e x i s t e n t u n i v e r s a l s . T h i s w i l l be done by examining the r e l a t i o n s which might be c la imed to ho ld between o b j e c t s and t h e i r e x i s t e n t u n i v e r s a l s , i n p a r t i c u l a r , the who le -pa r t r e l a t i o n and the bundle r e l a t i o n . As we have seen, the E U - o n t o l o g i s t i s committed to r e g a r d i n g p r o p e r t i e s as e n t i t i e s which are capab le of e x i s t i n g by themse lves , per se and i n se . However, in o rder to d i s t i n g u i s h the who le -pa r t and bundle r e l a t i o n , I w i l l use the term " p a r t " , as i t i s o r d i n a r i l y unders tood , to r e f e r to an e n t i t y which i s a bundle of p r o p e r t i e s and which i s capab le of e x i s t i n g independent l y of the o b j e c t of which i t i s s a i d to be long . The who le -pa r t r e l a t i o n w i l l t h e r e f o r e be s a i d to e x i s t between a bundle of p r o p e r t i e s , such as a s t e e r i n g whee l , and a c a r . The term " p r o p e r t y " , on the o ther hand, w i l l be used to r e f e r to a s i n g l e e x i s t e n t u n i v e r s a l . The bundle r e l a t i o n w i l l t h e r e f o r e ho ld between a bundle of e x i s t e n t u n i v e r s a l s which c o n s t i t u t e an o b j e c t and one such e x i s t e n t u n i v e r s a l . Another way of d i s t i n g u i s h i n g the who le -pa r t and bundle r e l a t i o n , then , i s to say tha t wh i le both are bund l i ng r e l a t i o n s , " w h o l e - p a r t " denotes a r e l a t i o n on which ho lds between an o b j e c t and a p a r t which i s i t s e l f 63 ( a bundle of e x i s t e n t u n i v e r s a l s whereas the term "bundle r e l a t i o n " i s r e s e r v e d f o r the r e l a t i o n between an o b j e c t and a s i n g l e e x i s t e n t u n i v e r s a l . A c c o r d i n g l y , the whole i n the who le -pa r t r e l a t i o n i s composed of p a r t s whereas the bundle i n the bundle r e l a t i o n i s not composed of p a r t s but of s i n g l e p r o p e r t i e s . In o r d e r f o r the who le -pa r t r e l a t i o n to be compat ib le w i th EU -on to l ogy , wholes and p a r t s must themselves be e x i s t e n t u n i v e r s a l s . There are two reasons f o r t h i s . F i r s t , a bundle of e x i s t e n t u n i v e r s a l s i s no l e s s apt to e x i s t i n d i s c o n t i n u o u s r eg i on s of space and time than i s a s i n g l e e x i s t e n t u n i v e r s a l . Second ly , i f the bundle of e x i s t e n t u n i v e r s a l s which form a p a r t of one whole were c la imed to be n u m e r i c a l l y d i s t i n c t from the same bundle of e x i s t e n t u n i v e r s a l s which form a p a r t of another o b j e c t , then the d i f f e r e n c e between the two bundles cou ld not be accounted f o r i n terms of a p r o p e r t y of d i f f e r e n c e , as both p a r t s are bundles o f the same e x i s t e n t u n i v e r s a l s , but must be accounted f o r i n terms of an i n d i v i d u a t i n g component such as a bare p a r t i c u l a r . In t h i s case i t would be l o g i c a l l y p o s s i b l e f o r two wholes o r p a r t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and ye t n u m e r i c a l l y d i s t i n c t by reason of t h e i r bare p a r t i c u l a r s . The w h o l e - p a r t r e l a t i o n must t h e r e f o r e be d e s c r i b e d as h o l d i n g between bundles of 64 e x i s t e n t u n i v e r s a l s which c o n s t i t u t e an o b j e c t and one such bundle where both the whole and i t s p a r t s are themselves e x i s t e n t u n i v e r s a l s . In the case of the c a r , f o r example, the bundle o f e x i s t e n t u n i v e r s a l s which c o n s t i t u t e the s t e e r i n g wheel form a p a r t o f the c a r . The o t h e r bundles of e x i s t e n t u n i v e r s a l s such as the c h a s s i s and engine are a l s o p a r t s of the c a r ; and, thus , toge ther w i th the s t e e r i n g wheel they c o n s t i t u t e the whole of the c a r . An immediate o b j e c t i o n to t h i s view i s tha t i f p a r t s are e x i s t e n t u n i v e r s a l s , and t h e r e f o r e capab le of e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode o f e x i s t e n c e , then i t i s l o g i c a l l y p o s s i b l e f o r car A and car B to have a l l t h e i r p a r t s i n common and y e t be n u m e r i c a l l y d i s t i n c t . But , as we saw e a r l i e r , the E U - o n t o l o g i s t might o b j e c t tha t t h i s i s mere ly another v e r s i o n of the i n d i v i d u a t i o n argument, tha t i s , i t r a i s e s the p o s s i b i l i t y of t h e i r be ing two q u a l i t a t -i v e l y i n d i s t i n g u i s h a b l e o b j e c t s which are not n u m e r i c a l l y i d e n t i c a l , and t h i s , as we have seen, i s a p o s s i b i l i t y which the E U - o n t o l g i s t d e n i e s . A c c o r d i n g to the E U - o n t o l o g i s t , i f car A and ca r B are i n f a c t n u m e r i c a l l y d i s t i n c t , then there w i l l be a t l e a s t one p a r t which A and B do not sha re . But t h i s c l a i m r a i s e s a second and more p e r s u a s i v e prob lem. Un les s the two ca r s over l apped s p a t i a l l y , and t h e r e f o r e cou ld q u i t e l i t e r a l l y be s a i d to share a p a r t , i t i s not 6 5 c l e a r what i t means to say tha t car A and ca r B are capab le of s h a r i n g a p a r t l e t a lone a l l but one p a r t . The no t i on o f a shared or common p a r t i s t h e r e f o r e e n i g m a t i c . The second s o r t of r e l a t i o n which might be c la imed to account f o r the nature of o b j e c t s i s the bundle r e l a t i o n where the term "bundle r e l a t i o n " i s used i n the r e s t r i c t e d sense to denote the r e l a t i o n between an o b j e c t and a s i n g l e p r o p e r t y . On t h i s v iew, the e x i s t e n t u n i v e r s a l red i s s a i d to combine w i th the e x i s t e n t u n i v e r s a l s square , l a r g e , and hard to form a bund le . I t i s a l s o p o s s i b l e f o r the e x i s t e n t u n i v e r s a l r e d , as an e n t i t y which i s capab le of e x i s t i n g i n d i s c o n t i n u o u s reg i on s of space and time s i m u l t a n e o u s l y , to combine w i th o the r e x i s t e n t u n i v e r s a l s such as square , l a r g e and s o f t to form another bund le , B. The bundle r e l a t i o n i s t h e r e f o r e compat ib le w i th EU-onto logy as i t support s the E U - o n t o l o g i s t ' s c l a i m tha t s p a t i o - t e m p o r a l l y separa te o b j e c t s can share one and the same p r o p e r t y . However, as we have seen, both the who le -pa r t and bundle r e l a t i o n are bund l i ng r e l a t i o n s where the d i f f e r e n c e between the two r e l a t i o n s l i e s i n the comp lex i t y of the e n t i t i e s between which the r e l a t i o n s h o l d . Consequent l y , wh i l e we cannot t a l k of the w h o l e - p a r t r e l a t i o n as h o l d i n g between an o b j e c t and a s i n g l e p r o p e r t y i f the term " p a r t " i s used i n the o r d i n a r y sense to denote an e n t i t y which i s capab le of e x i s t i n g 6 6 i ndependent l y of the o b j e c t to which i t be long s , we can t a l k of the bundle r e l a t i o n as h o l d i n g between an o b j e c t and a bundle of e x i s t e n t u n i v e r s a l s . In o the r words, bundles of e x i s t e n t u n i v e r s a l s which are themselves apt f o r e x i s t e n c e can i n tu rn combine to form s t i l l l a r g e r bund le s . But , at t h i s s t age , bundles are e q u i v a l e n t to p a r t s , that i s , l i k e p a r t s , they are capab le of e x i s t i n g i ndependent l y of the l a r g e r bund le . In f a c t , t h i s i s j u s t the sense i n which the who le -pa r t r e l a t i o n i s s a i d to be a bundle r e l a t i o n . However, because the r e l a t i o n between a complex bundle and a s m a l l e r e x i s t e n t i a l l y independent bundle i s e q u i v a l e n t to the r e l a t i o n which we termed the " w h o l e - p a r t r e l a t i o n " , the same d i f f i c u l t i e s a r i s e . In o the r words, where the c o n n o t a t i o n o f the term "bundle r e l a t i o n " i s extended to cover not j u s t the r e l a t i o n between an o b j e c t and a s i n g l e p r o p e r t y but the r e l a t i o n between a complex bundle and a s m a l l e r e x i s t e n t i a l l y independent bund le , i t i s u n c l e a r what two complex bundles cou ld have i n common un le s s they over l apped s p a t i a l l y . The E U - o n t o l o g i s t i s t h e r e f o r e f o r ced to make the more modest c l a i m tha t wh i l e he i s ab le to account f o r the r e l a t i o n between an o b j e c t and a s i n g l e p r o p e r t y , he i s unable to account f o r the more complex bundle r e l a t i o n , or what has been termed the "who le -pa r t r e l a t i o n " , which ho lds between o b j e c t s and s m a l l e r 67 e x i s t e n t i a l l y independent bundles of e x i s t e n t u n i v e r s a l s . The E U - o n t o l o g i s t might respond to t h i s o b j e c t i o n i n one o f two ways. He might argue tha t to say that there e x i s t s a commonality between two o b j e c t s i s to say that the two o b j e c t s share one or more e x i s t e n t u n i v e r s a l s and t h e r e f o r e to say tha t two o b j e c t s have a p a r t in common i s r e a l l y j u s t to say tha t the two o b j e c t s share a number of e x i s t e n t u n i v e r s a l s . But , suppose tha t A and B are s p a t i a l l y separa te o b j e c t s and that a , b, c , e t c . are p r o p e r t i e s which c o n s t i t u t e A and B. A B a 1 a b 2 b c 3 c d 4 d e 5 e f 6 f g 7 g h 8 h i 9 i x 10 y I f we c o n s i d e r p r o p e r t i e s (a) through ( i ) s e p a r a t e l y , „the E u - o n t o l o g i s t would agree tha t each one of these p r o p e r t i e s i s common to A and B. In f a c t , he would want to make the s t r onge r c l a i m that the f i r s t n ine p r o p e r t i e s are common to both o b j e c t s and tha t i t i s o n l y by reason of a d i f f e r e n c e 68 i n the ten th p r o p e r t y tha t A and B are n u m e r i c a l l y d i s t i n c t . However, i f the e x i s t e n t u n i v e r s a l s 1-5 and 6-10 form p a r t s which c o n s t i t u t e A and B i n the o r d i n a r y sense that they are capab le of e x i s t i n g i ndependent l y o f A and B, then the E U - o n t o l o g i s t , because he regards p r o p e r t i e s 1-5 as common to A and B, i s committed to the view tha t s p a t i a l l y separate o b j e c t s can have a common p a r t . The on l y means by which the E U - o n t o l o g i s t can avo id making t h i s c l a i m i s by s imp ly denying i t . T h i s would mean that wh i l e o b j e c t s can be composed of p a r t s , p a r t s would be d e f i n e d as n u m e r i c a l l y d i s t i n c t e n t i t i e s , tha t i s , as e n t i t i e s which are i n capab le of be ing shared by s p a t i o -t e m p o r a l l y separa te o b j e c t s . The grounds f o r t h i s second argument might then be that because p a r t s , l i k e o b j e c t s , are e x i s t e n t i a l l y independent , they must e i t h e r be n u m e r i c a l l y i d e n t i c a l and t h e r e f o r e q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e or e l s e n u m e r i c a l l y d i s t i n c t by reason of a d i f f e r e n c e i n at l e a s t one p r o p e r t y . The f a c t tha t A and B are n u m e r i c a l l y d i s t i n c t i s t h e r e f o r e taken to imply tha t the p a r t s of A w i l l be d i s t i n g u i s h a b l e from the p a r t s o f B; o r , more p r e c i s e l y , two o therw i se q u a l i t a t i v e l y i n d i s c e r n i b l e p a r t s w i l l be d i s t i n g u i s h e d by the f a c t tha t one has the p r o p e r t y of b e l o n g i n g - t o - A whereas the o the r possesses the p r o p e r t y of b e l o n g i n g - t o - B . However, t h i s d e f i n i t i o n of p a r t s i s f a r 69 too s t r o n g . In the f i r s t p l a c e , where two o b j e c t s such as A and B o v e r l a p s p a t i a l l y , the shared p a r t cou ld not be s a i d to be common to A and B f o r i f the e n t i t y i s a p a r t of A, then , by d e f i n i t i o n , i t must be n u m e r i c a l l y d i s t i n c t from the e n t i t y which i s a p a r t of B even though the e n t i t y i s one and the same in both A and B. Second ly , as we have seen, any r e f e r e n c e to an o b j e c t o r , i n t h i s c a se , a p a r t i n a way which presupposes the i d e n t i t y of the p a r t i n q u e s t i o n must be cashed out i n terms of a gene ra l d e s c r i p t i o n i f I I i s to be more than t r i v i a l l y tue . The i d e n t i t y of a g i ven p a r t cannot then l i e i n the f a c t tha t i t has the p r o p e r t y of b e l o n g i n g - t o - A as t h i s immediate ly presupposes that i t i s n u m e r i c a l l y d i s t i n c t from the p a r t which be l ong s - t o -B by v i r t u e o f i t s p o s s e s s i o n of t h i s p r o p e r t y . In the case where A and B o v e r l a p s p a t i a l l y , t h i s i s of course something which the E U - o n t o l o g i s t would want to deny.5 F i n a l l y , i f p a r t s are c l a imed to be n u m e r i c a l l y d i s t i n c t not by reason of the uniqueness of the p r o p e r t i e s which compose them but by d e f i n i t i o n , i t w i l l be l o g i c a l l y p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and ye t n u m e r i c a l l y d i s t i n c t by reason of the numer i ca l d i s t i n c t n e s s of t h e i r p a r t s . Consequent l y , the problem which the E u - o n t o l o g i s t f ace s i s tha t i n c l a i m i n g tha t p r o p e r t i e s are capab le of e x i s t i n g i n d i s c o n t i n u o u s r eg i on s of space and time 70 s i m u l t a n e o u s l y , he i s a l s o committed to the view tha t p a r t s , as bundles of e x i s t e n t u n i v e r s a l s , are a l s o capable o f e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e . The E U - o n t o l o g i s t must t h e r e f o r e s e t t l e f o r the more modest c l a i m tha t i t i s o n l y the nature of non-complex o b j e c t s , tha t i s , o b j e c t s which are not composed of e x i s t e n t i a l l y independent bundles or p a r t s , and not complex o b j e c t s tha t he i s ab le to account f o r . What the argument from the nature of o b j e c t s must now show i s tha t even t h i s modest v e r s i o n of EU-onto logy us u n a c c e p t a b l e . As we have seen , the c l a i m tha t o b j e c t s are composed on ly of e x i s t e n t u n i v e r s a l s i s c e n t r a l to the defense of I I . Un les s p r o p e r t i e s are capab le of e x i s t i n g i n two p l a c e s at one and the same t ime, o b j e c t s which have a l l t h e i r p r o p e r t i e s i n common w i l l not n e c e s s a r i l y be n u m e r i c a l l y i d e n t i c a l . The red of A, f o r example, i s t h e r e f o r e c la imed to be q u i t e l i t e r a l l y one and the same wi th the red of B and A and B i n tu rn n u m e r i c a l l y i d e n t i c a l i f they share not on l y the p r o p e r t y r e d , but a l l t h e i r o the r p r o p e r t i e s as w e l l . However, t h i s v iew, that o b j e c t s are bundles of e x i s t e n t u n i v e r s a l s , e n t a i l s two a d d i t i o n a l c l a i m s , both of which are un tenab le . I f " r e d " denotes an e x i s t e n t u n i v e r s a l which i s one and the same in a l l the o b j e c t s i n which i t i s p r e s e n t , then f i r s t o f a l l , the amount of red i n the wor ld i s not i n c rea sed by the number of o b j e c t s i n which i t i s found and, s e c o n d l y , there must be as much red i n a sma l l o b j e c t as in a l a r g e one. In o the r words, because a l l o ccu r rences of red are i d e n t i c a l , there w i l l be as much red i n the wor ld i f there i s one red o b j e c t as i f there are one hundred red o b j e c t s . S i m i l a r l y , even though the s u r f a c e of A i s s m a l l e r than the s u r f a c e of B, the amount of red w i l l not vary s i n c e the red of A i s i d e n t i c a l w i th the red of B. These two c l a i m s are a l s o t rue of o t h e r p r o p e r t i e s such as sound, hea t , we i gh t , e t c . For example, the amount o f heat at s e v e n t y - f i v e degrees i s the same whether there are one or one hundred ovens at s e v e n t y - f i v e degrees and, s econd l y , the t o t a l amount of heat p re sen t i n one oven at s e v e n t y - f i v e degrees i s one and the same wi th the amount of heat p re sen t in one hundred ovens at s e v e n t y - f i v e degrees . Consequent ly , the E U - o n t o l o g i s t i s f o r c e d to c l a i m tha t what appear to be d i v e r s e occu r rence s of v a r y i n g amounts of red are i n f a c t one and the same. T h i s consequence i s the r e s u l t of c o n s t r u i n g p r o p e r t i e s as e x i s t e n t u n i v e r s a l s . But , as we have seen throughout t h i s t h e s i s , p r o p e r t i e s must be cons t rued i n t h i s way i f I I i s n e c e s s a r i l y t r u e . The d i f f i c u l t y which c o n f r o n t s the E u - o n t o l o g i s t i s t h e r e f o r e one of e x p l a i n i n g what i t means to say tha t A i s red w i thout imp ly ing that p r o p e r t i e s such as red do not i n c r e a s e i n number or amount wi th an i n c r e a s e 72 in the number or s i z e of o b j e c t s which possess them. In o t h e r words, the E U - o n t o l o g i s t must r e c o n c i l e the f a c t tha t A i n some sense pos ses ses red w i th the f a c t t h a t , g i ven the nature o f e x i s t e n t u n i v e r s a l s , the red of A i s i d e n t i c a l w i th the red of B even though the amount of red possessed by B i s g r e a t e r than the amount of red possessed by A. There are two ways i n which the E U - o n t o l o g i s t can go about t h i s . He can argue tha t wh i l e red belongs to both A and B, e x i s t e n t u n i v e r s a l s can be d e f i n e d i n such a way as to a l l ow f o r the v a r y i n g number and amount of t h e i r occur rences or e l s e he can argue that red i s not i n f a c t a component of A. In t h i s next segment, I w i l l c o n s i d e r these two arguments in t u r n . The f i r s t argument, which examines two a l t e r n a t i v e d e f i n i t i o n s of e x i s t e n t u n i v e r s a l s , w i l l be shown to be unacceptab le on the grounds tha t i t i s not compat ib le w i th the tene t s of EU-onto logy s p e l l e d out at the the c o n c l u s i o n of Chapter One. The second argument, on the o ther hand, i s compat ib le w i th EU-onto logy . I t i s t h e r e f o r e to t h i s view tha t a l l remain ing E U - o n t o l o g i s t s w i l l be committed. However, as I w i l l a l s o show, t h i s view of the nature of o b j e c t s i s u n a c c e p t a b l e . The f i r s t a l t e r n a t i v e d e f i n i t i o n of e x i s t e n t u n i v e r s a l s suggests tha t i f B i s t r e a t e d as c o n t a i n i n g a second occu r rence of the same e x i s t e n t u n i v e r s a l red and, f u r t h e r m o r e , a l a r g e r amount or more of the e x i s t e n t 73 universal red than A, then properties such as red can be claimed to vary in number and amount. However, this argument i s misleading. If a l l occurrences of red are in fact numerically i d e n t i c a l , there cannot be a second occurrence of red and therefore the existent universal red cannot increase in number or amount. Or, to say the same thing d i f f e r e n t l y , i f properties such as red were capable of increasing in number and amount, a l l occurrences of red would not be numerically i d e n t i c a l but numerically d i s t i n c t . In this case, i t would be l o g i c a l l y possible for two objects to be q u a l i t a t i v e l y indistinguishable and yet numerically d i s t i n c t on the grounds that either the red of B would not be one and the same with the red of A but more of the same sort of red which i s present in A or else the amount of red present in B w i l l be greater than the amount of red present in A. The second d e f i n i t i o n of existent universals i s es s e n t i a l l y a more elaborate version of the above view. Instead of claiming that the red of A and the red of B are themselves i d e n t i c a l occurrences of the existent universal red, what i s claimed i s that the two occurrences are of one and the same shade. In other words, unlike the above view, i t i s the shade of red and not the actual occurrences of red which are i d e n t i c a l and therefore various occurrences of red may be claimed to d i f f e r in number and amount. However, 74 wh i l e i t i s not the a c t u a l s p a t i o - t e m p o r a l d imens ions of the red of A and the red of B which are c la imed to be i d e n t i c a l but the shade of the two o c c u r r e n c e s , the f a c t tha t two n u m e r i c a l l y d i s t i n c t o b j e c t s are of one and the same shade must l i e i n something e l s e . In o the r words, i f the two s p a t i o - t e m p o r a l expanses of a g i ven shade of red are not themselves i d e n t i c a l , then the f a c t tha t the two occur rences are of the i d e n t i c a l shade must l i e i n the f a c t tha t they possess the same r e l a t i o n to something e l s e . For example, the shades of the two s p a t i o - t e m p o r a l expanses of red which belong to A and B may be c l a imed to be i d e n t i c a l on the grounds tha t they are i n s t a n t a t i o n s of the same s u b s i s t e n t u n i v e r s a l or l o g i c a l p o s s i b i l i t y or e l s e on the grounds that they are members of the same c l a s s . However, as we saw e a r l i e r , these three accounts are i ncompat ib le w i th E u - o n t o l o g y . For i f A and B are c l a imed to be of the i d e n t i c a l shade o f red by reason o f t h e i r r e l a t i o n to a s u b s i s t e n t u n i v e r s a l , l o g i c a l p o s s i b i l i t y or c l a s s , then the red of A w i l l not be one and the same wi th the red of B. Or to say the same t h i n g d i f f e r e n t l y , p r o p e r t i e s such as red w i l l not be capab le of e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e and t h e r e f o r e , c o n t r a r y to I I, i t w i l l be l o g i c a l l y p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and y e t n u m e r i c a l l y d i s t i n c t by reason of the numer i ca l d i s t i n c t n e s s of t h e i r p r o p e r t i e s . The 75 E U - o n t o l o g i s t i s t h e r e f o r e unable to avo id c l a i m i n g that the number or amount of red i n the wor ld does not i n c r e a s e w i th the occu r rence of a d d i t i o n a l red o b j e c t s by argu ing tha t there i s a sense of the term " e x i s t e n t u n i v e r s a l " which does not have t h i s i m p l i c a t i o n . As we saw e a r l i e r , the E U - o n t o l o g i s t i s unable to account f o r the nature of complex o b j e c t s , tha t i s , where the bund l ing r e l a t i o n i s one of whole to p a r t ; and, as we now see , i n a ccoun t ing f o r the nature of non-complex o b j e c t s , where the bund l ing r e l a t i o n ho lds between an o b j e c t and a s i n g l e p r o p e r t y , the E U - o n t o l o g i s t i s committed to suppo r t i n g the numer i ca l i d e n t i t y of the red of A and the red of B even though B has a g r e a t e r complement of red than A. The E U - o n t o l o g i s t 1 s i n a b i l i t y to o f f e r an a ccep tab le account o f both complex and non-complex o b j e c t s i s the r e s u l t of two c l a i m s . The f i r s t c l a i m i s tha t p r o p e r t i e s are e x i s t e n t u n i v e r s a l s and, the second c l a i m , tha t o b j e c t s are bundles of e x i s t e n t u n i v e r s a l s . In the case of the who le -pa r t r e l a t i o n t h i s means that i t i s l o g i c a l l y p o s s i b l e f o r s p a t i a l l y separa te o b j e c t s to share one and the same p a r t w h i l e , i n the case of the bundle r e l a t i o n which ho lds between an o b j e c t and a s i n g l e p r o p e r t y , t h i s means that the red of A i s n u m e r i c a l l y i d e n t i c a l w i th the red of B even though the s u r f a c e area of B i s g r e a t e r than that of A.6 The E U - o n t o l o g i s t i s of course unable to deny the f i r s t of these 76 two c l a i m s as i t i s o n l y i f p r o p e r t i e s are e x i s t e n t u n i v e r s a l s t hat I I w i l l be n e c e s s a r i l y t r u e . However, the E u - o n t o l o g i s t may argue that i t i s not incompatible with the tenets of EU-ontology to deny the second c l a i m that p r o p e r t i e s are components of o b j e c t s . In other words, the E U - o n t o l o g i s t might argue that he i s only committed to the untenable p o s i t i o n t h at the number and amount of a p r o p e r t y does not i n c r e a s e with an i n c r e a s e i n the o b j e c t s which possess the p r o p e r t y i f e x i s t e n t u n i v e r s a l s are components of o b j e c t s . T h e r e f o r e , by denying t h i s second c l a i m , the E U - o n t o l o g i s t might hope to avoid t h i s unacceptable consequence. T h i s defense might then be supported on the grounds t h a t sentences such as "A i s red" do not i n d i c a t e a r e l a t i o n between an o b j e c t A and one of i t s component p r o p e r t i e s , but a r e l a t i o n between an o b j e c t and a p r o p e r t y where the p r o p e r t y i s not a component of A but, r a t h e r , i s e x e m p l i f i e d by A.7 i n . t h i s way, the E U - o n t o l o g i s t does not commit h i m s e l f to the view that the red of A and the red of B are n u m e r i c a l l y i d e n t i c a l even though B's complement of red i s g r e a t e r than A's s i n c e red i s not claimed to be a component of A or B. T h i s view t h e r e f o r e appears to have the advantage of e x p l a i n i n g the r e l a t i o n between o b j e c t s and t h e i r p r o p e r t i e s without implying that p r o p e r t i e s cannot vary i n number or amount. The q u e s t i o n i s , does t h i s view e n t a i l an a c c e p t a b l e ontology? 77 The view tha t p r o p e r t i e s are not components of o b j e c t s i s a view tha t has been espoused most no tab l y by substratum t h e o r i s t s . Substratum t h e o r i s t s argue t h a t , among o the r rea sons , s u b s t r a t a are needed to ho ld toge ther the v a r i o u s p r o p e r t i e s a t t r i b u t e d to o b j e c t s . T h i s view has f ou r i m p l i c a t i o n s . F i r s t , c o n t r a r y to the theory o f bundle r e l a t i o n s , o b j e c t s are not r e d u c i b l e to the p r o p e r t i e s which compose them, but to a group o f p r o p e r t i e s p l u s a subs t ra tum. Second, a l though the group of p r o p e r t i e s and t h e i r substratum are s a i d to form an o b j e c t , s t r i c t l y speak ing , the term " o b j e c t " denotes the substratum and the term " p r o p e r t y " the p r o p e r t i e s which are a t t r i b u t a b l e to the o b j e c t o r subs t ra tum. (Some substratum t h e o r i s t s c l a i m tha t t h i s o n t o l o g i c a l d i s t i n c t i o n i s determined by the nature of o r d i n a r y language. For example, sentences such as "A i s r e d " are c l a imed to imply tha t the o b j e c t i t s e l f must be d i s t i n c t from a l l o f i t s p r o p e r t i e s . ) T h i r d , p r o p e r t i e s are not components of o b j e c t s . Acco rd ing to the s u b s t r a t a t h e o r i s t , o b j e c t s o r s u b s t r a t a are p r o p e r t y l e s s . And, f o u r t h l y , the group of p r o p e r t i e s which are a t t r i b u t a b l e to an o b j e c t do not themselves form a bundle which i s i n tu rn supported by a subs t ra tum. Ra ther , i t i s s u b s t r a t a and not a bundle r e l a t i o n which b inds p r o p e r t i e s t o g e t h e r . In Dr. S i k o r a ' s words, substratum can be thought of 78 as i f i t were a lump of m o d e l l i n g c l a y and p r o p e r t i e s as the shapes tha t may be g i ven to the m o d e l l i n g c l a y ( S i ko ra undated, p. 2) . T h e r e f o r e , wh i l e the substratum has p r o p e r t i e s , these p r o p e r t i e s are not components of the substratum i n the sense tha t subs t ra tum, or mode l l i n g c l a y , i s not r e d u c i b l e to i t s p r o p e r t i e s . Another way of c h a r a c t e r i z i n g the substratum t h e o r y , then , i s to say tha t the substratum or mode l l i n g c l a y e x e m p l i f i e s i t s p r o p e r t i e s . For example, The f e a t u r e o f the substratum theory which i s most a t t r a c t i v e to the E U - o n t o l o g i s t i s the c l a i m tha t p r o p e r t i e s are not components of o b j e c t s but r a t h e r e x e m p l i f i e d by o b j e c t s . However, i t i s a l s o c l e a r tha t the substratum theory and EU-onto logy are not compa t i b l e . F o r , as we saw e a r l i e r , i t i s l o g i c a l l y p o s s i b l e on the substratum theory f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and y e t n u m e r i c a l l y d i s t i n c t by reason of t h e i r substratum o r , i n terms of Dr. S i k o r a ' s ana logy , by reason of the numer i ca l d i s t i n c t n e s s of the c l a y from which p r o p e r t i e s such as shape substratum e x e m p l i f i e s .red .square •large hard 79 and s i z e emerge. Therefore, i n order f o r the EU-ontologist to preserve the cla i m that p r o p e r t i e s are not components of o b j e c t s , o b j e c t s must be c h a r a c t e r i z e d i n some other way than as substratum. There are three ways i n which the p r o p e r t i e s of objects might be claimed to be exem p l i f i e d by o b j e c t s . The f i r s t way i s to argue that i f r e d , square, l a r g e , and hard are a t t r i b u t a b l e to A, then sentences such as "A i s red" mean that square, l a r g e , and hard exemplify red, i . e . , square large hard -exemplify. -red A c c o r d i n g l y , i f red i s not a component of the object A but exe m p l i f i e d by A and i f the object A i s , i n t h i s case, i d e n t i f i e d w ith square, l a r g e , and hard, the colour red must emerge when the e x i s t e n t u n i v e r s a l s square, l a r g e , and hard are combined together. However, t h i s view, which i s termed the p r i n c i p l e of emergence, i s incompatible with EU-ontology. To begin w i t h , an account of what binds square, l a r g e , and hard together i s re q u i r e d . I f i t i s a bundle r e l a t i o n , then square, large and hard must be components of A. On the other hand, i f i t i s a substratum, square, large 80 and hard w i l l be supported by an e n t i t y which i s capable o f i n d i v i d u a t i n g q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s , and t h e r e f o r e q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e o b j e c t s w i l l not n e c e s s a r i l y be n u m e r i c a l l y i d e n t i c a l . Moreover , the E U - o n t o l o g i s t cannot assume t h a t s q u a r e , l a r g e , and hard i n some sense form an o b j e c t which i s d i s t i n c t from red s i n c e A can be s a i d to e x e m p l i f y square or l a r g e or h a r d . In o ther words , i f A i s c la imed to be square or l a r g e or h a r d , then the problems s t a t e d w i t h r e g a r d to the e x e m p l i f i c a t i o n o f red w i l l a l s o a p p l y to these p r o p e r t i e s as w e l l . A second and s i m i l a r concept o f o b j e c t s i s the view t h a t s q u a r e , l a r g e , and hard do not e x e m p l i f y red as a group but i n d i v i d u a l l y . U n l i k e the p r e c e d i n g v iew, the E U - o n t o l o g i s t i s not r e q u i r e d to p r o v i d e a b i n d i n g r e l a t i o n such as a s u b s t r a t u m , or bundle r e l a t i o n as there a r e , s t r i c t l y s p e a k i n g , no p r o p e r t i e s to b i n d t o g e t h e r . A diagram of t h i s view would l o o k l i k e t h i s : square e x e m p l i f i e s red l a r g e e x e m p l i e i e s red hard e x e m p l i f i e s red A c c o r d i n g to t h i s v i ew , s q u a r e , f o r example, i s i n some sense accompanied by l a r g e and hard b u t , more to the p o i n t , square i s c l a imed to e x e m p l i f y r e d . I t i s t h e r e f o r e p o s s i b l e on t h i s view f o r an e x i s t e n t u n i v e r s a l such as square to be c o l o u r , shape , s i z e , e t c . However, t h i s c l a i m i f c l e a r l y 81 u n a c c e p t a b l e . F i r s t of a l l , i t i s not c l e a r what sense square i s accompanied by l a r g e and ha rd . And, s econd l y , not on l y i s i t absurd to say tha t a s i n g l e e x i s t e n t u n i v e r s a l such as square can be r e d , but i f we d e s c r i b e d A as r e d , square , l a r g e , and hard and then s a i d tha t A was a l s o g reen , i t would f o l l o w that each of the e x i s t e n t u n i v e r s a l s would be green i n c l u d i n g the e x i s t e n t u n i v e r s a l r e d . F i n a l l y , the t h i r d and most p l a u s i b l e v e r s i o n of the theory tha t the p r o p e r t i e s of o b j e c t s are not components of o b j e c t s i s the view tha t A denotes a s p a t i o - t e m p o r a l l o c a t i o n . Sentences such as "A i s r e d " are t h e r e f o r e i n t e r p r e t e d as s t a t i n g tha t red occup ie s a c e r t a i n s p a t i o - t e m p o r a l l o c a t i o n . S i m i l a r l y , square , l a r g e , and hard w i l l a l s o be c l a imed to occupy the same p o s i t i o n i n space and t ime. However, there are two ways i n which the r e l a t i o n between s p a t i o - t e m p o r a l l o c a t i o n s and p r o p e r t i e s can be c o n s t r u e d . F i r s t , the s p a t i o - t e m p o r a l l o c a t i o n together w i th square , l a r g e , and hard can exemp l i f y r e d . For example, s p a t i o - t e m p o r a l l o c a t i o n square l a r g e hard -exempl i f y- -red But , i n t h i s c a se , the E U - o n t o l o g i s t i n c u r s the d i f f i c u l t y 82 above, namely, tha t s p a t i o - t e m p o r a l l o c a t i o n , square , l a r g e , and hard must e i t h e r form a bundle or e l s e be supported by a subs t ra tum. The second way i s to c l a i m tha t the s p a t i o - t e m p o r a l l o c a t i o n e x e m p l i f i e s red as w e l l as square , l a r g e , and h a r d . In o the r words, s p a t i o - t e m p o r a l l o c a t i o n e x e m p l i f i e s < £ ^ — > - s q u a r e ^^^SLarge >_iard Sentences such as "A i s r e d " would t h e r e f o r e imply tha t p r o p e r t i e s l i k e red are d i s t i n c t from but a t t r i b u t a b l e to A i n much the same way tha t p r o p e r t i e s are d i s t i n c t from but a t t r i b u t a b l e to subs t ra tum. However, the d i f f i c u l t y w i th t h i s view i s tha t we cannot say tha t a g i ven s p a t i o - t e m p o r a l l o c a t i o n e x e m p l i f i e s r e d , square , l a r g e , and hard s i n c e l o c a t i o n does not c o n s t i t u t e the i d e n t i t y of o b j e c t s but presupposes i t . In o the r words, i t i s o n l y a f t e r we have f i r s t i d e n t i f i e d an o b j e c t as r e d , square , l a r g e and hard and then determined i t s s p a t i o - t e m p o r a l p o s i t i o n w i th r e s p e c t to o ther o b j e c t s tha t we can say that an o b j e c t has a c e r t a i n p o s i t i o n . Moreover, t h i s p o s i t i o n w i l l be r e l a t i v e to the p o s i t i o n s of the o b j e c t s w i th which i t i s compared and t h e r e f o r e the same o b j e c t may be v a r i o u s l y d e s c r i b e d as occupy ing the p o s i t i o n s l e f t , r i g h t , above, and below 83 w i thout ever moving.8 T h i s l a t t e r v iew, which a s s e r t s (1) tha t p r o p e r t i e s are not components of o b j e c t s and (2) t ha t o b j e c t s are s p a t i o - t e m p o r a l p o s i t i o n s , i s the most p l a u s i b l e onto logy to which the r e l a t i v e space and time v e r s i o n of I I can be reduced . However, the d i f f i c u l t y w i th t h i s view i s tha t i t does not o f f e r an account of the nature of o b j e c t s l e t a lone an a c c e p t a b l e account . T h i s i s due to the f a c t tha t s p a t i o - t e m p o r a l p o s i t i o n s cannot be i d e n t i f i e d w i th o b j e c t s s i n c e they presuppose r a t h e r than c o n s t i t u t e the i d e n t i t i e s of the o b j e c t s i n q u e s t i o n . The E U - o n t o l o g i s t ' s f i n a l l i n e of defense might then be to argue tha t i t i s on l y i f s p a t i o - t e m p o r a l p o s i t i o n s are p l a c e d w i t h i n a framework i n which they c o n s t i t u t e the i d e n t i t i e s of o b j e c t s tha t i t i s p o s s i b l e to o f f e r an account of the nature of o b j e c t s which i s compat ib le w i th I I. Some p h i l o s o p h e r s such as D .J . O 'Conner f e e l tha t ab so lu te space and time p r o v i d e s j u s t such a c o n t e x t . 84 Notes to Chapter Two 1 T h i s argument p a r a l l e l s Adams' case of twins whose l i v e s are q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e u n t i l a t the age o f 27 they have d i f f e r e n t dreams (Adams 1979, p. 17 -19) . 2 The p r i n c i p l e which t h i s argument i s r e q u i r e d to p r e s e r v e i s tha t d e s c r i p t i o n s or l i s t s must be genera l i n o r d e r to avo id p resuppos ing the i d e n t i t y of the o b j e c t i n q u e s t i o n . A l i s t may not then c o n t a i n r e f e r e n c e to any o b j e c t which i s not i t s e l f cashed out i n t h i s g e n e r a l way. A ' s hav ing the r e l a t i o n of be ing i d e n t i c a l to i t s e l f or the r e l a t i o n of be ing d i f f e r e n t from B are not then a c c e p t a b l e . S i m i l a r l y , s p e c i f i c s p a t i o - t e m p o r a l c o - o r d i n a t e s such as xi , Y l r z l a t fcl a r e a l s o unacceptab le as they are not g e n e r a l but p a r t i c u l a r . 3 The E U - o n t o l o g i s t can of course use " r e d " as a g e n e r a l term. However, the d i f f e r e n c e between the two uses does not l i e i n the type of e n t i t y deno ted , but r a t h e r i n what i s s a i d . For example, the statement "A i s r e d " a t t r i b u t e s red to a p a r t i c u l a r o b j e c t whereas " r e d i s my f a v o u r i t e c o l o u r " merely r e f e r s to the c o l o u r red wi thout a t t r i b u t i n g i t to any o b j e c t . 4 i t i s worth no t i n g tha t S tout does not regard the c lass-member r e l a t i o n as a r e l a t i o n but as a "fundamentum r e l a t i o n i s " or fundamental u n i t y and tha t W i l l i a m s i n tu rn c l a i m s tha t S t o u t ' s fundamental u n i t y can be reduced to a r e l a t i o n o f resemblance. But , h e r e , t o o , the concept of resemblance would not be of use to the E U - o n t o l o g i s t . 5 A f u r t h e r problem i s tha t i f p a r t s are c la imed to be n u m e r i c a l l y d i s t i n c t by v i r t u e of be long ing to n u m e r i c a l l y d i s t i n c t o b j e c t s , then the same w i l l be t rue of s i n g l e p r o p e r t i e s . For example, the red of A w i l l be n u m e r i c a l l y d i s t i n c t from the red o f B by v i r t u e of i t s be long ing to A and t h i s of course i s c o n t r a r y to the E U - o n t o l o g i s t ' s c l a i m t h a t p r o p e r t i e s such as red are capab le of e n j o y i n g a s p a t i o - t e m p o r a l l y d i v i d e d mode of e x i s t e n c e . 6 T h i s argument may a l s o be used a g a i n s t complex o b j e c t s . In t h i s c a se , i t would be c la imed tha t the number o f p a r t s , which are composed of a l l and on l y the same e x i s t e n t u n i v e r s a l s , i s always the same. S i m i l a r l y , two p a r t s , which are composed of a l l and on ly the same e x i s t e n t u n i v e r s a l s , are n u m e r i c a l l y i d e n t i c a l even though one p a r t may be c o n s i e r a b l y l a r g e r than the o t h e r . 85 7 The term " e x e m p l i f y " can be used i n one of two ways: (1) as e x p r e s s i n g a r e l a t i o n between an o b j e c t and a p r o p e r t y where the p r o p e r t y i s con ta ined i n the o b j e c t or (2) as e x p r e s s i n g a r e l a t i o n between an o b j e c t and a p r o p e r t y where the p r o p e r t y i s not con ta ined i n the o b j e c t . In the argument that f o l l o w s , I w i l l use the term i n the second sense . 8 A f u l l e r account o f the c o n d i t i o n s which the r e l a t i v e view of space and time imposes an EU-onto logy i s g i ven i n Chapter One. 86 CHAPTER THREE ABSOLUTE SPACE AND TIME I n h i s p a p e r i n s u p p o r t o f t h e c o n t r o v e r s i a l f o r m o f I I , D.J. O'Conner a r g u e s t h a t t h e r e a r e o t h e r f a c t o r s w h i c h b e a r upon t h e t r u t h o f I I b u t w h i c h have g e n e r a l l y been t h o u g h t o f as p e r i p h e r a l . One s u c h f a c t o r c o n c e r n s th e d e n o t a t i o n o f t h e term " p r o p e r t y " . T r a d i t i o n a l l y , t h e t e r m has e x c l u d e d th e r e l a t i o n a l p r o p e r t i e s o f s p a t i a l l o c a t i o n and t e m p o r a l l o c a t i o n , s i n c e t h e s e p r o p e r t i e s have been f e l t t o p r e s u p p o s e t h e e x i s t e n c e o f o b j e c t s s u c h t h a t i f A e x i s t s t h e n and o n l y t h e n c a n A be s a i d t o have a g i v e n r e l a t i o n . R e l a t i o n s have t h e r e f o r e been c o n s i d e r e d as i r r e l e v a n t t o t h e i d e n t i t y o f o b j e c t s and t h e r e f o r e t o t h e c o n s t i t u t i o n o f o b j e c t s . B u t , a c c o r d i n g t o O'Conner, t h i s c u s t o m begs the q u e s t i o n i n f a v o u r o f o p p o n e n t s o f I I . F o r , i f s p a t i o - t e m p o r a l p r o p e r t i e s were r e c o g n i z e d p r o p e r t i e s o f o b j e c t s , t h e n d i s t i n c t o b j e c t s would have d i f f e r e n t s p a t i o - t e m p o r a l l o c a t i o n s . A d i f f e r e n c e between o b j e c t s w ould t h e r e f o r e n e c e s s a r i l y i m p l y a d i f f e r e n c e between p r o p e r t i e s . 0 ' C o n n e r ' s v i e w i s s i m i l a r t o E U - o n t o l o g y i n one 87 important r e s p e c t : O 'Conner does not regard i n s t a n c e s o f n o n - r e l a t i o n a l p r o p e r t i e s as i n some sense n u m e r i c a l l y d i s t i n c t as t h i s , r a t h e r than s p a t i o - t e m p o r a l l o c a t i o n , would p r o v i d e a b a s i s f o r i n d i v i d u a t i o n . L i k e E U - o n t o l -o g i s t s , O 'Conner cons t rues n o n - r e l a t i o n a l p r o p e r t i e s as e x i s t e n t u n i v e r s a l s . However, d e s p i t e t h i s agreement on the nature of n o n - r e l a t i o n a l p r o p e r t i e s , i t i s e v i d e n t from 0 ' C o n n e r ' s r ecour se to r e l a t i o n a l p r o p e r t i e s tha t he does not f e e l tha t n o n - r e l a t i o n a l p r o p e r t i e s can guarantee the t r u t h o f I I. A c c o r d i n g to O 'Conner , t h i s guarantee must i n s t e a d come wi th r e l a t i o n a l p r o p e r t i e s bu t , more impor t -a n t l y , w i th r e l a t i o n a l p r o p e r t i e s which do not presuppose the i d e n t i t y of o b j e c t s . As we have seen, t h i s type of a n a l y s i s has been r e j e c t e d on the grounds tha t r e l a t i o n a l p r o p e r t i e s such as " t o - t h e - l e f t - o f " presuppose the i d e n t i t y of A as w e l l as the i d e n t i t y of B to which A i s to the l e f t . However, O'Conner argues tha t the s p a t i o - t e m p o r a l p o s i t i o n of A need not be determined by i t s r e l a t i v e p o s i t i o n to B, but tha t the p o s i t i o n of A can be s t a t e d independent l y of B, tha t i s , i t can be s t a t e d i n i t s own r i g h t or a b s o l u t e l y . The s o r t of system O'Conner has i n mind i s one i n which the s p a t i o -tempora l p o s i t i o n s of o b j e c t s are a s s i gned a c o - o r d i n a t e i n a network of axes i n ab so lu te space and t ime. For example, A, which i s r e d , square , and l a r g e , might have the 88 ass ignment , y i , z± a t t i whereas B, which i s a l s o r e d , square , and l a r g e , might be found at X2, Y2t z 2 a t t-2* A n Y o b j e c t w i l l t h e r e f o r e be i d e n t i f i a b l e by r e f e r e n c e to i t s c o - o r d i n a t e . But , more i m p o r t a n t l y , the v a l i d i t y of I I w i l l be guaranteed by the f a c t tha t s p a t i o - t e m p o r a l p r o p e r t i e s are i n t r i n s i c a l l y i n capab le of be ing shared by more than one o b j e c t . In o the r words, c o n t r a r y to the r e l a t i v e space- t ime v e r s i o n o f I I, i d e n t i c a l o b j e c t s must share t h e i r r e l a t -i o n a l as w e l l as a l l t h e i r n o n - r e l a t i o n a l p r o p e r t i e s . Con-v e r s e l y , a d i f f e r e n c e between i n d i v i d u a l s w i l l be expressed as a d i f f e r e n c e between p r o p e r t i e s where those p r o p e r t i e s are u l t i m a t e l y s p a t i o - t e m p o r a l . U n f o r t u n a t e l y , O 'Conner does not o f f e r an account of ab so lu te space and t ime. In f a c t , he d o e s n ' t e x p l i c i t l y mention i t o the r than to say tha t c o n s i d e r a t i o n s of space and time c l e a r l y bear upon the t r u t h of I I. However, an account has been o f f e r e d by the l a t e R u s s e l l ( R u s s e l l 1948). A c c o r d i n g to R u s s e l l ' s a n a l y s i s , o b j e c t s form a "complete complex o f compresence" , t ha t i s , a compresence which c o n s i s t s of both n o n - r e l a t i o n a l p r o p e r t i e s such as c o l o u r , shape and s i z e and the r e l a t i o n a l p r o p e r t i e s of space and t ime. As we have seen, n o n - r e l a t i o n a l p r o p e r t i e s are not s u f f i c i e n t to d i s t i n g u i s h o b j e c t s f o r even though the time o r d e r of my expe r i ence of c o l o u r s might be the e x i s t e n t u n i v e r s a l s r e d , g r e e n , r e d , i t w i l l f o l l o w tha t the 89 e x i s t e n t u n i v e r s a l red i s exper i enced be fo re i t s e l f . S i m i l a r l y , i f the th ree c o l o u r expe r i ence s are l e f t , c e n t e r , and r i g h t i n my v i s u a l f i e l d , the e x i s t e n t u n i v e r s a l red w i l l be to the l e f t (or r i g h t ) of i t s e l f . T h i s , however, i s not the case w i th r e l a t i o n a l p r o p e r t i e s . I f A i s a t t i and B i s a t t2/ then A w i l l precede B. S i m i l a r l y , i f A i s to the l e f t of B, then A cannot a l s o be to the r i g h t of B. A c c o r d i n g to R u s s e l l ' s t h e o r y , t hen , i t i s necessary to e s t a b l i s h a space - t ime o rde r i n o rde r to d i s t i n g u i s h o b j e c t s or i n d i v i d u a l e x p e r i e n c e s , tha t i s , i n o rde r to as i t were t i e n o n - r e l a t i o n a l p r o p e r t i e s to p o i n t s i n space and time which are i n t r i n s i c a l l y un ique. A complete complex of compresence i s t h e r e f o r e enumerated by l i s t i n g both i t s n o n - r e l a t i o n a l and r e l a t i o n a l p r o p e r i e s . For example, A might be d e s c r i b e d as c o n s i s t i n g of the e x i s t e n t u n i v e r s a l red and l e f t a t t i , where " l e f t " denotes the l e f t s i de of my v i s u a l f i e l d and t i e i t h e r the time on a c l o c k or a sense of s u b j e c t i v e pa s t o r p r e s e n t n e s s . Thus, i n s t e a d of say ing " T h i s i s r e d " , we might say tha t "Red i s comprescent w i th l e f t a t t i " . There a r e , however, a number of s e r i o u s o b j e c t i o n s to t h i s a n a l y s i s . F i r s t of a l l , i t i s not c l e a r what e x a c t l y would make d i s t i n c t p o i n t s i n space and time d i f f e r e n t . We cou ld n o t , f o r example, say tha t the s p a t i o - t e m p o r a l l o c a t i o n of A i s d i f f e r e n t from tha t of B, tha t i s , tha t A i s e i t h e r to the l e f t of or be fo re B, as t h i s would imply 90 tha t A ' s p o s i t i o n i s determined by r e f e r e n c e to i t s r e l a t i o n to B. Ra ther , we must be ab le to determine s p a t i o - t e m p o r a l p o s i t i o n s o u t r i g h t o r i n themse lves . The s o r t of t h i n g R u s s e l l has i n mind r e l i e s h e a v i l y on our p e r c e p t i o n o f space and t ime. For example, a l though my p e r c e p t i o n of the n o n - r e l a t i o n a l p r o p e r t i e s o f A ye s te rday may be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e from my p e r c e p t i o n of B today, as a complete complex of compresence, that i s , as a bundle which i n c l u d e s r e l a t i o n a l p r o p e r t i e s , A w i l l d i f f e r from B i n s o f a r as i t was p e r c e i v e d y e s t e r d a y . S i m i l a r l y , i f A occup ied the l e f t of my v i s u a l f i e l d , then even though B, which i s l o c a t e d to the c e n t e r of my f i e l d of v i s i o n , has the same n o n - r e l a t i o n a l p r o p e r t i e s , A w i l l be d i s t i n g u i s h e d by i t s p o s i t i o n . A can t h e r e f o r e be d e s c r i b e d as o c c u r r i n g y e s t e r d a y or as l o c a t e d to the l e f t of my v i s u a l f i e l d w i thout r e f e r e n c e to i t s r e l a t i v e p o s i t i o n to B. There i s perhaps some sense i n which o b j e c t s of p e r c e p t i o n have the c h a r a c t e r of o b s o l u t e n e s s . For example, i n r e c a l l i n g my p e r c e p t i o n of A y e s t e r d a y , i t i s not necessary to add that t h i s o ccu r red p r i o r to my p e r c e p t i o n of B today. But t h i s i s not the p o i n t of the o b j e c t i o n . The p o i n t i s t ha t i f s p a t i o - t e m p o r a l l o c a t i o n s are p r o p e r t i e s as R u s s e l l c l a i m s , then how i s one space - t ime p o i n t d i s t i n g u i s h e d from another? What, f o r example, i s the d i f f e r e n c e between the p r o p e r t i e s t]_, t2r and t3 or l e f t , 91 center, and right or, for that matter, l e f t on one occasion and l e f t on another occasion? Put in this way, i t is evident that there i s no difference, that space-time points are voids in which non-relational properties inhere and in this sense they are q u a l i t a t i v e l y indistinguishable. This means that spatio-temporal properties do not constitute the identity of objects as spatio-temporal positions are, f i r s t of a l l , q u a l i t a t i v e l y indistinguishable and secondly, something which a l l spatio-temporally located objects have in common. A further consequence i s that absolute space-time bears adversely upon the I I. If A i s constituted by red, square, l e f t at t i , then A w i l l be q u a l i t a t i v e l y indistinguishable from B although B i s reducible to red, square, center at t2» for not only w i l l A and B share the same non-relational properties but the same r e l a t i o n a l properties insofar as " l e f t " and "center", " t i " and " t 2 " denote q u a l i t a t i v e l y indistinguishable voids. In other words, the late Russell and O'Conner w i l l be forced to say that even though A and B are located at a d i f f e r e n t time and at a d i f f e r e n t place they are i d e n t i c a l . Conversely, i f i t is argued that l e f t and center and t i and t2 are in some sense d i s t i n c t , then, contrary to I I, spatio-temporal locations w i l l be d i s t i n c t even though they are q u a l i t a t i v e l y indistinguishable. Accordingly, i f the voids to which the r e l a t i o n a l properties 92 of A and B are r e d u c i b l e are i n d i s c e r n i b l e but d i s t i n c t , then i f A and B a l s o have t h e i r n o n - r e l a t i o n a l p r o p e r t i e s in common i t w i l l be p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and y e t n u m e r i c a l l y d i s t i n c t . Consequent l y , i f s p a t i o - t e m p o r a l p r o p e r t i e s are i n d i s c e r n i b l e and t h e r e f o r e i d e n t i c a l , they w i l l not c o n s t i t u t e the i d e n t i t y of o b j e c t s . On the o the r hand, i f they are i n d i s c e r n i b l e but not n u m e r i c a l l y i d e n t i c a l , t h e n , c o n t r a r y to I I, i t w i l l be l o g c a l l y p o s s i b l e f o r two o b j e c t s to be q u a l i t a t i v e l y i n d i s t i n g u i s h a b l e and ye t n u m e r i c a l l y d i s t i n c t . 93 BIBLIOGRAPHY Aa ron , R.I. 1967. The Theory o f U n i v e r s a l s . London: C la rendon P r e s s . 1939. "Two Senses of ' U n i v e r s a l ' " . Mind. 48: 168-185. 1945. "Our Knowledge of U n i v e r s a l s " . B r i t i s h Academy P r o c e e d i n g s . 31: 17-42. Adams, R.M. 1979. " P r i m i t i v e Th i sne s s and P r i m i t i v e I d e n t i t y " . J o u r n a l of P h i l o s o p h y . 76: 5-26. A l l a i r e , E.B. 1976. 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A r i s t o t e l i a n S o c i e t y Supplementary Volume. 15: 1-15. 1940. " T h i n g s , P r e d i c a t e s and R e l a t i o n s " . A u s t r a l a s i a n J o u r n a l o f Psycho logy and P h i l o s o p h y . 18: 117-130. ( W i l l i a m s , D.C. 1953. "The Elements of Be ing : P a r t I". Review  o f Me taphys i c s . 7: 3-18. 1953. "The Elements of Be ing : P a r t II". Review of Metaphys i c s . 7: 171-192. 

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