UBC Theses and Dissertations

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UBC Theses and Dissertations

Logic and existence Skosnik, Jeffrey Paul 1977

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LOGIC AND EXISTENCE by J e f f r e y Paul Skosnik B.A., Michigan State U n i v e r s i t y , 1968 M.A., Simon Fraser U n i v e r s i t y , 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OFllGRADUATE STUDIES Department of Philosophy We accept t h i s t h e s i s as conforming to the req u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1977 J e f f r e y Paul Skosnik In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that . the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Depa rtment The University of Brit ish Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Research Supervisor: Professor Steven S a v i t t ABSTRACT This t h e s i s i s a l o g i c a l / h i s t o r i c a l i n q u i r y i n t o the concept of being. R e l a t i v e to t h i s concept, there are ( I contend) two great t r a d i t i o n s i n Wes-t e r n philosophy. According to the one, the p r s d i c a t i o n a l use of the verb •to be* i s not independent of i t s e x i s t e n t i a l use} according to the other, i t i s . That i s to say, the f i r s t t r a d i t i o n assumes that 'a i s F* e n t a i l s *a e x i s t s ' , while the other t r a d i t i o n denies t h i s entailment. There are prima f a c i e problems i n both t r a d i t i o n s , and the t h e s i s attempts to r e s o l v e those a r i s i n g on the assumption that the entailment holds. The t h e s i s does not assume t h a t e i t h e r t r a d i t i o n as such i s wrong. I t i s r a t h e r maintained that we may adopt e i t h e r forms of language i n which the p r e d i c a t i o n a l use of *to be* i s not independent of i t s e x i s t e n t i a l use, £r e l s e forms of l a n -guage i n which the two uses are independent. When we make the f i r s t move, the r e s u l t i s a Fregean s t y l e of q u a n t i f i c a t i o n theory i n which e x i s t e n t i a l g e n e r a l i z a t i o n holds as an u n c o n d i t i o n a l l y v a l i d form of i n f e r e n c e ; when we make the second move, the r e s u l t i s a f r e e l o g i c such as we f i n d i n the sys-tems of Lambert and van Fraassen. Though I do not attempt to d i s c r e d i t e i t h e r t r a d i t i o n as a whole, I do c r i t i c i z e s p e c i f i c c l a i m s made by the ad-herents of both t r a d i t i o n s . On the whole, however, I am f a r more c r i t i c a l of those i n the t r a d i t i o n to which the f r e e l o g i c i a n s belong than I am of those i n the t r a d i t i o n to which Frege belongs. The t h e s i s attempts to show tha t i n Frege's q u a n t i f i c a t i o n theory we have a s a t i s f a c t o r y e x p l i c a t i o n of our concept of e x i s t e n c e . The t h e s i s o f f e r s some reasons f o r t h i n k i n g that i n the a l t e r n a t i v e t r a d i t i o n of the f r e e l o g i c i a n s no such e x p l i c a t i o n has yet emerged. The t h e s i s concludes wit h a b r i e f account of modality i n which i t i s not assumed t h a t i n d i v i d u a l s can possess c h a r a c t e r i s t i c s independently of t h e i r e x i s t e n c e . iv CONTENTS INTRODUCTION TO THESIS 1_5 PART I: GREEK THOUGHT 6-91 1 Parmemides 7-65 2 Aristotle . , 66-90 PART II: MEDIEVAL THOUGHT 92-175 3 Anselm. 93-134 4 Leibniz. 135-174 PART III: MODERN THOUGHT 176-310 5 Frege 177-220 6 Russell 221-309 SELECTED BIBLIOGRAPHY 311-314 ACKNOWLEDGEMENTS To the Bertrand R u 3 s e l l Archives f o r permission to study and quote from R u s s e l l ' s unpublished w r i t i n g s . To Ken B l a c k w e l l of the R u s s e l l Archives f o r p r o v i d i n g me wi t h copies of R u s s e l l ' s unpublished w r i t i n g s . To Norman C a l l e g a r o f o r expert b i b l i g r a p h i c a l a s s i s t a n c e . To Kim Floeck f o r t r a n s l a t i n g some of Kant's h i t h e r t o u n t r a n s l a t e d Ger-man i n t o i n t e l l i g i b l e E n g l i s h . To my wif e f o r w a i t i n g more or l e s s p a t i e n t l y w h i l e I wrote a very long t h e s i s . To the members of my Ph.D. committee, t o whom I am indebted i n the ways that one would expect. 1 INTRODUCTION In t h i s t h e s i s I w i l l d i s c u s s seme f a m i l i a r problems concerningtthe ap-p l i c a t i o n of q u a n t i f i c a t i o n theory to n a t u r a l languages. My aim w i l l be to defend what I regard as a b a s i c a l l y Fregean approach to the concept of e x i s -tence, but to do so i n a way which ensures greater f i d e l i t y to the workings of n a t u r a l languages than Frege himself thought necessary or perhaps even d e s i r a b l e . In terms of pr e d i c a t e extensions r e l a t i v e to a given domain, Frege of-f e r s what I take to be a comprehensive account of e x i s t e n t i a l p r o p o s i t i o n s . On t h i s account, the p r o p o s i t i o n 'unicorns do not e x i s t ' (£.£.) means: i n the domain of animals (of which unicorns would be members i f there were any) the extension of the pr e d i c a t e 'unicorn* i s n u l l . When I say that Frege's account of e x i s t e n t i a l p r o p o s i t i o n s i n terms of predicate extensions i s com-prehensive, I do not mean that s i n g u l a r e x i s t e n t i a l p r o p o s i t i o n s are somehow re d u c i b l e to general ones. On the c o n t r a r y , I b e l i e v e t h a t there are no s i n - g u l a r e x i s t e n t i a l p r o p o s i t i o n s . With Frege I hold t h a t , i f 'a' were used as a s i n g u l a r term i n 'a e x i s t s * , then t h i s combination of words would be mean-i n g l e s s . Unlike Frege, however, I do not b e l i e v e that ' J u l i u s Caesar e x i s t s ' (§_.£.) i s meaningless. I w i l l contend that i n t h i s p r o p o s i t i o n ' J u l i u s Caesar* i s f u n c t i o n i n g not as a name but as a general term with an a s c e r t a i n -able e x t e n s i o n . Thus, on the account I w i l l defend ' J u l i u s Caesar e x i s t s ' i s r e t a i n e d as a s i g n i f i c a n t , though g e n e r a l , p r o p o s i t i o n . There are p h i l o -sophers who would t r e a t i t as a genuine s i n g u l a r p r o p o s i t i o n . In t h e i r sys-tems, u n l i k e Frege's, ' e x i s t s ' occurs as a predicate of i n d i v i d u a l s . There i s a s u b s t a n t i a l d i f f e r e n c e between the philosophers who t r e a t 2 • e x i s t s * as a pred i c a t e of i n d i v i d u a l s and those who do not. H i s t o r i c a l l y the philosophers who have wished to t r e a t ' e x i s t s * as a pr e d i c a t e of i n -d i v i d u a l s b e l i e v e d that i t i s p o s s i b l e to frame p r o p o s i t i o n s about what does not e x i s t . The p r o p o s i t i o n 'Pegasus i s a winged horse* (f_.£.) they would regard as a true p r o p o s i t i o n about Pegasus. So regarded, however, t h i s p r o p o s i t i o n i n v i t e s the i n f e r e n c e : t h e r e f o r e , winged horses e x i s t . To block t h i s inference these philosophers would amend e x i s t e n t i a l g e n e r a l i z a -t i o n by adding 'Pegasus e x i s t s * as a premise to the inference here i n ques-t i o n . Thus, they would a l t e r the character of a fundamental inference i n Frege's system. Moreover, they would do so by adding a premise whose unana-l y s e d form at l e a s t i s thought i l l e g i t i m a t e by Frege. Frege himself would avoid the problems which a r i s e i n connection w i t h non-designating s i n g u l a r terms simply by excluding such terms from the ' l o g i c a l l y p e r f e c t ' language i n which e x i s t e n t i a l g e n e r a l i z a t i o n holds u n c o n d i t i o n a l l y . In one sense, the dispute between Frege and h i s c r i t i c s i s a t r i v i a l one. For, i f we r e q u i r e every s i n g u l a r term to have a r e f e r e n t , then e x i s -t e n t i a l g e n e r a l i z a t i o n w i l l hold u n c o n d i t i o n a l l y ; but, i f we drop t h i s r e -quirement, i t w i l l not. We can t h e r e f o r e c o n s t r u c t formal languages of the type Frege p r e f e r s , and we can c o n s t r u c t some of the type h i s c r i t i c s p r e f e r . We must, t h e r e f o r e , r e s i s t r e p r e s e n t i n g the dispute between Frege and h i s c r i t i c s as though i t concerned the v a l i d i t y of e x i s t e n t i a l g e n e r a l i z a t i o n : e x i s t e n t i a l g e n e r a l i z a t i o n i s v a l i d i n some languages but not i n others;. Our aim i n t h i s t h e s i s t h e r e f o r e cannot be to pronounce upon the v a l i d i t y of an i n f e r e n c e ; i t i s rat h e r to judge the adequacy of the language i n which i t i s admittedly v a l i d or admittedly i n v a l i d . Our concern i s to e x h i b i t the s t r u c t u r e of inference i n n a t u r a l languages, p a r t i c u l a r l y i n E n g l i s h . 3 Therefore, the formal language which best e x h i b i t s t h a t s t r u c t u r e i s , f o r our purposes, the most adequate. I s h a l l contend t h a t a formal language i n which e x i s t e n t i a l g e n e r a l i z a t i o n holds u n c o n d i t i o n a l l y i s more adequate i n t h i s sense than one i n which t h i s inference r e q u i r e s the a d d i t i o n of an e x i s t e n t i a l premise. This i s prima f a c i e s u r p r i s i n g because E n g l i s h abounds i n such apparently nondesignating s i n g u l a r terms as •Pegasus'. Having made these remarks about the aims of the t h e s i s , I w i l l conclude t h i s i n t r o d u c t i o n w i t h a few unguarded (and perhaps naive) remarks concern-ing the p r i n c i p l e s which have guided the i n v e s t i g a t i o n s of which t h i s t h e s i s i s the record. Throughout t h i s work I t r e a t past philosophers s e r i o u s l y , c a r e f u l l y . There i s u s u a l l y more to be l e a r n t from understanding a L e i b n i z than from misunderstanding him. I have f o r t h i s reason o c c a s i o n a l l y been l e d i n t o e x e g e t i c a l d i s p u t e s . The t h e s i s , however, i s nevertheless not a manual i n the h i s t o r y of philosophy. For I have not t r i e d to c h a r a c t e r i z e anyone's h i s t o r i c a l p o s i t i o n . My aim has r a t h e r been to i l l u m i n a t e c e r t a i n problems from a v a r i e t y of p e r s p e c t i v e s . I have f o r t h i s reason permitted myself to s e l e c t , ignore, extend, and otherwise d i s t o r t the views of a c t u a l f i g u r e s . But, as Mark Twain observed, 'you have to have the f a c t s before you can per-v e r t them'. I a t t a c h importance to the h i s t o r y of philosophy p a r t l y because of the view I take of philosophy i t s e l f , I see philosophy as being r e l a t e d to i t s h i s t o r y i n a way that the n a t u r a l sciences are not r e l a t e d to t h e i r h i s t o r i e s . The n a t u r a l s c i e n t i s t , people say, hopes to extend our knowledge of non-ana-l y t i c f a c t , and t h e r e f o r e bases h i s work upon observation. ( I hope t h i s com-monplace i s t r u e . ) I t i s hardly s u r p r i s i n g , t h e r e f o r e , that s c i e n t i f i c 4 t h e o r i e s should be d i s c r e d i t e d by an advancing technology which gives us such wonders as the telescope and microscope; Newton c e r t a i n l y would not have been r e f u t e d without the i n v e n t i o n of some q u i t e s o p h i s t i c a t e d a s t r o -nomical instruments. The d i s c r e d i t e d t h e o r i e s then cease to be important as s c i e n c e , and become mere h i s t o r y . In c o n t r a s t , there i s a view of p h i l o - sophy according to which the philosopher, u n l i k e the n a t u r a l s c i e n t i s t , hopes to e s t a b l i s h a n a l y t i c a l (or conceptual) t r u t h s , t r u t h s which i n p r i n -c i p l e cannot be d i s c r e d i t e d by o b s e r v a t i o n , however r e f i n e d . Thus, the work of past p h i l o s o p h e r s , when i t i s good, r e t a i n s i t s value as philosophy. There are unbroken t r a d i t i o n s i n Western thought from the time of the ancient Greeks t o the present day. These t r a d i t i o n s are a part of our i n -t e l l e c t u a l h e r i t a g e as a s p e c i e s , and place us i n a s c h o l a r l y community ex-tended through time. When we see ideas p r o j e c t e d through vast streches of h i s t o r y and i n the process formed by the a r t of great philosophers, i t helps us to f i n d a d i r e c t i o n f o r our own thoughts, and to advance beyond the a l l -to-near p o i n t at which our unaided r e f l e c t i o n leaves us. There are p h i l o s o -phers who, apparently not seeing t h e i r own work as a chapter i n a l a r g e r h i s -t o r y , b e l i e v e that t r a d i t i o n a l d o c t r i n e s are f o r the most part devoid of cog-n i t i v e meaning. For them t r a d i t i o n a l problems (£.£., the problem of r e a l i s m versus nominalism) become i n t e l l i g i b l e only i n t h i s century. But I s h a l l r e s i s t t h i s p r o v i n c i a l a t t i t u d e and the arrogance which accompanies i t . The reader who does not l i k e w i s e r e s i s t i t , however, may w e l l f i n d the e a r l i e r p a r t s of my work devoid of c o g n i t i v e meaning. In these parts I t r y to give expression to some c o n f l i c t i n g , p r e - t h e o r e t i c a l i n t u i t i o n s which i n various ways have been captured i n the formal systems which purport to e x h i b i t the s t r u c t u r e of sound t h i n k i n g . These i n t u i t i o n s , though i n h e r e n t l y c r e d i b l e , 5 are demonstrably i n c o n s i s t e n t . Thus, to b r i n g consistency to our t h i n k i n g we must choose from amongst them. The major d i f f e r e n c e s amongst l o g i c a l l y -minded philosophers often r e s u l t from t h e i r adhering to d i f f e r e n t p o r t i o n s of our i n t u i t i v e b e l i e f i n t h e i r attempts to b r i n g consistency to our common thought. We w i l l see how d i f f e r e n t p o r t i o n s of our i n t u i t i v e b e l i e f are em-bodied i n the a l t e r n a t i v e q u a n t i f i c a t i o n t h e o r i e s of L e i b n i z and Frege. We w i l l a l s o see how, at an e a r l i e r stage i n Western thought, P l a t o ' s system c o l l a p s e s i n t o incoherence through h i s attempt to maintain too much of our i n t u i t i v e b e l i e f concerning e x i s t e n c e . Consistency demands that we s a c r i f i c e a p o r t i o n of our i n t u i t i v e b e l i e f , but i t does not t e l l us which p o r t i o n must go. I do not say that my choices i n i n t u i t i v e b e l i e f are the only rea-sonable ones to make. But I do say that these choices b r i n g consistency to our t h i n k i n g about existence while they minimize the r e q u i s i t e s a c r i f i c e s i n i n t u i t i v e b e l i e f . 6 P A R T I : GREEK THOUGHT P A R T I I S INTRODUCTORY I N N A T U R E . I T S A i m I S M E R E L Y TO A C Q U A I N T THE READER WITH THE P R E - T H E O R E T I C A L P R O B L E M S L A T E N T I N THE CONCEPT OF E X I S T E N C E . TO SOME T H E S E P R O B L E M S MAY S E E M UNWORTHY OF C O N S I D E R A T I O N . B U T WE W I L L MEET THEM A G A I N IN A MUCH MORE R E C A L C I T R A N T FORM WHEN WE A T T E M P T TO F O R M A L I Z E OUR CONCEPT OF E X I S T E N C E . 7 PARWENIDES 1.0 I n t r o d u c t i o n In t h i s chapter uie w i l l show that» con t r a r y to popular commentary, c e r t a i n paradoxes i n Parmenides are not due to any e l e -mentary confusions, but f o l l o w from i n t u i t i o n s having a widespread appeal. We w i l l then show th a t P l a t o ' s attempt to res o l v e these paradoxes f a i l s . 1.1 'To be' and VdC The E n g l i s h verb 'to be* i s used i n two s y n t a c t i c a l l y d i s t i n c t ways—i..e., i t has what grammarians c a l l (1) a com- p l e t e use and a l s o (2) an incomplete use. The complete use i s e x h i b i t e d i n contexts such as * i s * , where we may generate a complete sentence from t h i s schema simply by r e p l a c i n g the * ' with a t e r m — , 'God*. The i n -complete use i s e x h i b i t e d i n contexts such as * . i s where i n order to generate a complete sentence from t h i s schema the ' ' and the '...' must each be replaced by terms—e_.g_., r e s p e c t i v e l y , 'God' and 'omnipotent'. 'I am* (as i n *I t h i n k ; t h e r e f o r e , I am') i s an example of the complete use; and 'I am wealthy' i s an example of the incomplete use. I t i s c l e a r t h a t i n i t s complete use 'to be' means 'to e x i s t ' ; and we s h a l l a c c o r d i n g l y speak of t h i s use as the e x i s t e n t i a l use of 'to be'. I t i s e q u a l l y c l e a r t h a t i n i t s incomplete use 'to be' expresses the r e l a t i o n between subj e c t and p r e d i c a t e ; and we s h a l l a c c o r d i n g l y speak of t h i s use as the p r e d i c a t i o n - a l use of 'to be'. Philosophers o f t e n attach great importance to the d i s t i n c t i o n between these two uses of 'to be'. W i l l , £.£., w r i t e s : * W i l l , J . , A System of Logic (London: 1965), p. 50. (Bk I , Ch i v , sec. 1) 8 Many volumes might be f i l l e d with the f r i v o l o u s specula-t i o n s concerning the nature of Being ... which have a r i s e n from o v e r l o o k i n g t h i s double meaning ^ e x i s t e n t i a l and p r e d i c a t i o n a l j of the word to b_e; from supposing t h a t when i t s i g n i f i e s t£ e x i s t , and when i t s i g n i f i e s to be some s p e c i f i e d t h i n g , as to be a man, to b_e Socrates, to be_ seen or spoken o f , even to be a nonen t i t y , i t must s t i l l , a t bottom, answer to the same idea; and that a meaning must be found f o r i t which s h a l l s u i t a l l these cases. The fog which rose from t h i s narrow spot d i f f u s e d i t s e l f a t an e a r l y p e r i o d over the whole surface of meta-phy s i c s . This passage may serve as the locus c l a s s i c u s of a view which we s h a l l here d i s p u t e — v i z . , t h a t the t r a d i t i o n a l d i s c u s s i o n s of o n t o l o g i c a l questions are v i t i a t e d by an unconscious equivocation between the e x i s t e n t i a l and p r e d i c a -t i o n a l uses o f *to be' and i t s e q u i v a l e n t expressions i n other languages. Though mill does not mention him,.Rarmenides..is u s u a l l y regarded as the g r e a t e s t offender i n t h i s respect. Our view i s t h a t , although the f a l l a c y of e q u ivocation (on 'to be*) has o c c a s i o n a l l y been committed, we must attend to s p e c i f i c arguments and show how the f a l l a c y has been committed t h e r e i n . Scholars f o r the most p a r t , however, do not attempt to show i n a p a r t i c u l a r  argument how the f a l l a c y has been committed, but have ( l i k e W i l l ) simply used the charge of equivocation to j u s t i f y d i s m i s s i n g a whole p o s i t i o n (£.£., th a t of Parmenides). The Greek verb '/tV^t* i s u s u a l l y t r a n s l a t e d as *to be'; and, l i k e *to be*, i t has a complete use and an incomplete use. In p_e S o p h i s t i c i s E l e n c h i s , 167a3-5, A r i s t o t l e d i s t i n g u i h e s the complete use from the incomplete use of ^lYcO?* as f o l l o w s : . . . i t i s not the same t h i n g "not to be x" and "not to be" at a l l : i t looks as i f i t were because of the closeness of the e x p r e s s i o n , i . e . because "to be x_" i s but l i t t l e d i f f e r e n t from "to be", and "not to be £" from "not to be". The t r a n s l a t o r (W. A. Pickard-Cambridge) has here rendered 'dtVgti' as 'to be*. 9 C l a s s i c a l s c h o l a r s , however, have r e c e n t l y noted c e r t a i n p e c u l i a r i e s of which d i s t i n g u i s h i t from 'to be*. v l a s t o s w r i t e s : 1 ^rom the Greek "is" {£(fpp we get d i r e c t l y the p a r t i c i p l e 0V, the noun, Q\ATccu> and t n o adverb, Qy-gf" From the Eng-l i s h " i s " a l l we can get d i r e c t l y i s t h e - p a r t i c i p l e , be- i n g , but no noun or adverb. We can't say "beingness" or " b e i n g l y " , and have to s h i f t to " r e a l i t y " and " r e a l l y " . But when we do t h i s we los e a verb from the same stem: we can't say, "Socrates r e a l s a man" or "Socrates r e a l s wise". ... I f we want t o t a l k E n g l i s h , we w i l l have to break up the consanquineous Greek quartet i n t o two etymo-l o g i c a l l y u n r e l a t e d groups, p i c k i n g our verbs from the f i r s t , our noun and adverb (and a l s o the e x c e p t i o n a l l y u s e f u l a d j e c t i v e , " r e a l " ) from the second. As we noted, the E n g l i s h verb 'to be' i n i t s complete use simply means 'to e x i s t * . But i t i s h i g h l y d o u b t f u l whether '^iVcd* i n i t s complete use c a r r i e s q u i t e t h i s sense. V l a s t o s favors t r a n s l a t i n g i t as 'to be r e a l or genuine', and notes the c l o s e connection f o r Greeks between t r u t h and r e a l i -t y . A r i s t o t l e , e.£., defines ' t r u t h * and ' f a l s i t y * as f o l l o w s : 3 To say of what i s that i t i s not, or of what i s not that i t i s , i s f a l s e , while to say of what i s that i t i s , or of what i s not th a t i t i s not, i s t r u e . In h i s well-reasoned a r t i c l e Kahn concludes:^ •< ...the most fundamental value of; e i n a i when used alone [ i . . e . , i n i t s complete usej i s not "to e x i s t " but "to be the case", or "to be t r u e " . I t i s worth noting t h a t t h i s meaning of the verb, which appears among the four uses l i s t e d i n the chapter of Wet. De l t a ... i s l a t e r described by A r i s t o t l e as the " s t r i c t e s t " or "most a u t h o r i t a t i v e " sense of "to be". (Wet. Theta 10, 1051b 1) I v l a s t o s , G., 'Degrees of R e a l i t y i n P l a t o ' , as contained i n : Bambrough, R., ed., New Essays on P l a t o and A r i s t o t l e (London: 1965), p. 1. 2See i b i d . , pp. 1^3. Sffletaphysica 1011b27. Also see P l a t o , C r a t y l u s 385b; Sophist 263b. 4Kahn, C., 'The Greek verb " t o be" and the Concept of Being",' Founda- t i o n s of Language, v o l . 2 (1966), p. 248. ID In t h i s connection i t i s worth noting (as Kahn does, p. 254n6) that the Ox- f o r d E n g l i s h D i c t i o n a r y l i s t s the f o l l o w i n g as one of the recognized meanings of 'to be' i n E n g l i s h : 'to be the case or the f a c t ' , as i n 'so be i t * (s_.v. •be', B.I.3). Kahn s t a t e s t h a t 'the Greeks d i d not have our notion of e x i s t e n c e ' . * This strong c l a i m , i f t r u e , must obviously a f f e c t our i n t e r p r e t a t i o n of Greek philosophy profoundly, given the importance of o n t o l o g i c a l questions i n Greek thought. Indeed, the issue of r e a l i s m versus nominalism i s one which we i n -h e r i t from P l a t o and A r i s t o t l e . There are passages i n the Greeks ( p a r t i c u l a r -l y i n P l a t o ) which suggest that t h e i r concept of ex i s t e n c e i s d i f f e r e n t from ours; e_.£. (Rep., 476e-477b): ...Does he who knows know something or nothing? ... I w i l l r e p l y , he s a i d , t h a t he knows something. Is i t something that i s or i s not? That i s . How could that which i s not be known? Ule are s u f f i c i e n t l y assured of t h i s , then, even i f we should examine i t from every po i n t of view, that that which e n t i r e l y is_ i s e n t i r e l y knowable, and that which i n no way i s i s i n every way unknowable? most s u f f i c i e n t l y . Good. I f a t h i n g , then, i s so co n d i t i o n e d as both to be and not to be, would i t not l i e between that which abso-l u t e l y i s and t h a t which i n no way i s ? Between. Then si n c e knowledge p e r t a i n s t o that which i s and i g n o r -ance of n e c e s s i t y to t h a t which i s not, f o r t h a t which l i e s between we must seek f o r something between nescience and s c i e n c e , i f such a t h i n g there be. As t h i s passage continues (477b-8e), P l a t o concludes that opinions have as 'The Greek verb "to be" and the Concept of Being', p. 248. 11 t h e i r o b j e c t s t h i n g s which are immediate between the extremes of existence and nonexistence. As we conceive i t , however, e x i s t e n c e , u n l i k e anger, does not come by degrees; things do not more or l e s s e x i s t . I f , however, we t h i n k of VfVctL' as meaning *to be genuine' (as V l a s t o s suggests), then per-haps t h i s passage i s not s t r a i g h t f o r w a r d nonsense. For, as V l a s t o s suggests, there i s sense i n speaking of 'degrees of genuineness': a p a i n t i n g done p a r t -l y by Rubens and p a r t l y by h i s students working under h i s d i r e c t i o n , , i s arguably 'more genuine' than an o u t r i g h t fake. We may wish to say that such a p a i n t i n g i s more n e a r l y genuine than a fake. But we should never wish to say that something i s more nearly an e x i s t e n t than i s something else.^-The views of Kahn and V l a s t o s are engaging. But I think i t d i f f i c u l t to decide whether (a) P l a t o had our concept of e x i s t e n c e and simply reason-ed i l l o g i c a l l y from i t , or (b) had a d i f f e r e n t concept a l t o g e t h e r and rea-soned w e l l from that one. How are we to decide whether the Greeks possessed 3 our concept of e x i s t e n c e or not? One c o u l d not decide t h i s issue a b s o l u t e l y ( i f indeed i t can be decided a b s o l u t e l y ) without a d e t a i l e d study of the Greek language, which u n f o r t u n a t e l y I am not competent to do. In p a r t i c u l a r , Isee 'Degrees of R e a l i t y ' , pp. 4-6. ^'The reading of [ P l a t o ' s ^ d i a l o g u e s ' , says Bochenski ( i n Ancient For- mal Logic (Amsterdam: 1963), p. 17), ' i s almost i n t o l e r a b l e to a l o g i c i a n , so many elementary blunders are contained i n them. I t w i l l be enough to men-t i o n h i s s t r u g g l i n g w i t h the f a l s e p r i n c i p l e ^ a P > S a P 1 or the d i f f i c u l t y he ha^ s i n grasping that one who does not admit rSaP must not n e c e s s a r i l y ad-mit SeP . (See I b i d . , p. 17, footnotes f o r references i n P l a t o f o r h i s a l -leged l o g i c a l b l u n d e r s ) . Sprague, R., r e p l i e s to Bochenski*s charges i n P l a t o ' s Use of F a l l a c y (London: 1962), pp. 86-97. On the general question of how we are to decide whether the same con-cept i s expressed i n two languages, see Bennett, J . , Kant's A n a l y t i c (Cam-brid g e : 1966), pp. 73-4. 12 i t would be necessary to examine the no n - p h i l o s o p h i c a l uses of *£iva(i*, sin c e f o r reasons sometimes good and sometimes bad philosophers are apt to deviate from normal usage. I t i s c e r t a i n l y r e l e v a n t , however, to study the key argu-ments of Greek philosophers i n which the concept of existence plays a p a r t ; t h i s we s h a l l do. Our c o n c l u s i o n then w i l l be that P l a t o probably reasoned i l l o g i c a l l y from a concept of existence not u n l i k e our own. To the c l a s s i -c a l s c h o l a r s who th i n k that the Greek concept of exi s t e n c e was d i f f e r e n t from our own, I concede a t once t h a t the Greeks d i d use 'tfTV<*v.' ( i n i t s complete sense) d i f f e r e n t l y from how we use 'to be '^T( iin; i t s complete sense). But every t r a n s l a t o r w i l l admit that they sometimes used i t i n a way f o r which 'to be' seems not only the best t r a n s l a t i o n but an adequate one. Our concept of existence thus appears embodied i n par t of t h e i r usage of '4i\roH. *» which suggests that '£-tWi* i s ambiguous. Perhaps because 'to e x i s t ' i s not s i m i -l a r l y ambiguous, i t appears that the Greeks may have had a d i f f e r e n t concept of e x istence when i n f a c t a Greek philosopher has simply equivocated i n a way that i s not p o s s i b l e i n E n g l i s h or other modern European languages. 1.2 Parmenides Only 161 l i n e s of Parmenides' work remain—146 com-p l e t e l i n e s of hexameter posty, nine fragments of a l i n e , and s i x l i n e s of L a t i n t r a n s l a t i o n . Though i t would c e r t a i n l y be disputed by some s c h o l a r s , 1 I f i n d P l a t o ' s Parmenides a u s e f u l adjunct to these meager sources. Admit-t e d l y , the Parmenides i s a d i f f i c u l t , obscure dialogue whose o v e r - a l l pur-pose i s unclear. The dialogue i s supposed to be the record-jaf a meeting i n Athens •••Some s c h o l a r s would not even a t t r i b u t e a s e r i o u s purpose to the Parmeni- des. A. E. Ta y l o r , £.£., i n P l a t o : the Wan and h i s Work (London: 1960), p. 541, w r i t e s : 'Wore than any other P l a t o n i c work of any considerable com-pass, the Parmenides bears throughout the stamp of being an " o c c a s i o n a l " com-p o s i t i o n . I t s purpose i s to "have some f u n " with Wonists who regard the sen-s i b l e as i l l u s i o n , and very l i t t l e more'. 13 between Parmenides as an ol d man and Socrates as a youth. Though chrono-logy does not exclude the p o s s i b i l i t y of such a meeting, the character of tha t meeting ( i f i t took place a t a l l ) must have been d i f f e r e n t from P l a t o ' s d e s c r i p t i o n of i t . For i n the e a r l i e r part of the dialogue the youth Soc-r a t e s expounds, and Parmenides c r i t i c i z e s , P l a t o ' s theory of Forms. In t h i s p a r t of the dialogue Parmenides deduces a b s u r d i t i e s from P l a t o n i c premises. In the l a t e r p a r t of the dialogue (with which we are here concerned), i t i s Parmenidean fflonism which i s under a t t a c k , and Parmenides i s made to deduce a b s u r d i t i e s i n h i s own p o s i t i o n . I t would, o f course, be f o o l i s h to assume that the h i s t o r i c a l Parmenides ever e n t e r t a i n e d q u i t e the arguments unfolded i n t h i s part of the dialogue. But (1) there would be no po i n t to t h i s part of the dialogue i f the premises from which the a b s u r d i t i e s are deduced were not accepted by the h i s t o r i c a l Parmenides. Furthermore, (2) f o r us to un-derstand what these premises meant to Parmenides i t helps to see what k i n d of argument a sympathic Greek philosopher thought they support. Having made these remarks about sources, l e t us now t u r n to the ques-t i o n of i n t e r p r e t a t i o n . In t h e i r e x c e l l e n t study of the P r e - S o c r a t i c s K i r k and Raven see i n Parmenides an a t t a c k upon 'those who b e l i e v e , as a l l men a l -ways had b e l i e v e d , t h a t i t i s p o s s i b l e to make a negative p r e d i c a t i o n ' . * Ac-cording to K i r k and Raven, the Parmenidean philosophy r e s t s upon an elemen-t a r y confusion of the e x i s t e n t i a l 2 and p r e d i c a t i o n a l uses of '£fVaf. In lf<-irk, G, and Raven, J . , The P r e - S o c r a t i c Philosophers (Cambridge: 1966), p. 270. ^Igno r i n g the issues r a i s e d by Kahn and V l a s t o s , K i r k and Raven t r e a t '^oVcH* as meaning ( i n i t s complete use) 'to e x i s t * . K i r k and Raven are of course concerned s p e c i f i c a l l y w i t h what the verb meant to Parmenides; how they stand on the l a r g e r issues r a i s e d by Kahn and V l a s t o s , I do not know. 14 t h i s s e c t i o n we w i l l o f f e r an i n t e r p r e t a t i o n of Parmenides which i s opposed to t h a t of K i r k and Raven. We w i l l accept t h e i r t r a n s l a t i o n s of the f r a g -ments, and deny th a t the f a l l a c y of equ i v o c a t i o n must have been committed t h e r e i n . I t i s thus s u f f i c i e n t f o r our purposes to show t h a t , where K i r k and Raven t h i n k they see the f a l l a c y of e q u i v o c a t i o n , there i s i n f a c t a va-l i d argument--or, a t any r a t e , one which does not commit t h i s f a l l a c y . Given the fragmentary s t a t e of the t e x t , we cannot say wi t h c e r t a i n t y that Parmeni-des intended t h i s v a l i d argument rat h e r than some i n v a l i d one. But t h i s d i f -f i c u l t y i s present f o r any i n t e r p r e t a t i o n of h i s w r i t i n g s , and as we w i l l see the K i r k and Raven i n t e r p r e t a t i o n does not i n any case seem supported by the t e x t . In fragment 346 of K i r k and Raven, Parmenides says: 'Never s h a l l t h i s be proved, that t h i n g s that are not are*. In modern symbolism I express t h i s c l a i m as f o l l o w s : (1) - ^ ( g x ) - E x , where 'Ex* stands f o r *x e x i s t s * and 'fy' f o r ' p o s s i b l y * . I_,e.*» i s n o t p o s s i b l e that there should be something which does not e x i s t . (1) i s e q u i -v a l e n t to the f o l l o w i n g : (I*) U(V*)E:X, where *Q' stands f o r ' n e c e s s a r i l y ' . I_.£_.# n e c e s s a r i l y , e v e r y t h i n g e x i s t s . One c o u l d , of course, object to (1) on the grounds th a t 'existence* i s not a p r e d i c a t e . But t h i s i s a c o n t r o v e r s i a l p o i n t about which i t would be premature a t t h i s time to be dogmatic. Naknikian and Salmon* argue (perhaps See Naknikian, G. and Salmon, W., ' " E x i s t s " as a P r e d i c a t e ' , P h i l o s o - p h i c a l Review, v o l . 66 (1957). 15 cogently) t h a t the t r a d i t i o n a l o b j e c t i o n s to 'existence* as a predicate are not well-founded, moreover, they a s s e r t (p. 538): (2) (Vx)Ex, which i s of course i m p l i e d by ( 1 ) . By the l o g i c of q u a n t i f i c a t i o n theory, ( l i ) e n t a i l s the f o l l o w i n g : (3) (Vx)(-Ex - -Gx), where *G* stands f o r any p r e d i c a t e . J_.e_., f o r a l l x, i f x does not e x i s t s no p r e d i c a t e i s t r u e of i t . 1 K i r k and Raven (pp. 269-70) seem to c r i t i c i z e Parmenides f o r saying i n fragment 344 that 'thou c o u l d s t not know that which i s - n o t ' . But, i f i n (3) we may i n t e r p r e t 'G' as 'knowable', then the unknow-a b i l i t y of the nonexistent emerges as a v a l i d consequence of the apparent tautology '-(-Jx)-Ex'. I t might be objected that we are reading too much i n t o Parmenides, Granted, the o b j e c t o r might might say, (3) i s i m p l i e d by ( 1 ) , and Parmenides accepted ( 1 ) . Parmenides may nevertheless not have seen the i m p l i c a t i o n , and there i s no fragment i n which (3) i s c l e a r l y expressed as such. This ob-j e c t i o n has some weight perhaps, but not much i n view of the many passages i n P l a t o where Parmenides i s represented as h o l d i n g ( 3 ) . Here are two such •••The s c h o l a s t i c s accepted (3) i n the form of t h e i r maxim, ' N i h i l i n u l - l a e p r o p r i e t a t e s s u n t ' — i . e . , Nothing has no p r o p e r t i e s . 2 j u s t as Parmenides argues t h a t the nonexistent i s unknowable, Sextus Empiricus (second century AD) argues that the nonexistent i s unteachable: 'Now the nonexistent qua nonexistent w i l l not be taught; f o r i f i t i s taught i t i s teachable, and being teachable i t w i l l become an e x i s t e n t . But i t i s not p o s s i b l e f o r the same t h i n g to be both e x i s t e n t and nonexis-t e n t ; t h e r e f o r e the nonexistent qua nonexistent Is not t a u g h t — A l s o , the nonexistent has no property, and what has no property w i l l not have the property of being taught'. Bury, R., t r , Works of Sextus Empiricus (London: 1959), v o l . 4, p. 9, 16 passages: I f a t h i n g i s not, you cannot say that i t "has" anything or t h a t there i s anything " o f " i t . Consequently, i t can-not have a name or be spoken o f , nor can there be any know-ledge or perception or opinion pjf i t . I t i s not named or spoken o f , not an object of opinion or of knowledge, not perceived by any c r e a t u r e . (Parmenides, 142a-b) Again, we cannot a t t r i b u t e to "what i s not" anything t h a t i s ; we< cannot say i t i s "something" or " t h i s t h i n g " , or that i t i s so-and-so "of t h i s " or "of another", or tha t i t i s at any time, past, present, or f u t u r e , or t h a t there i s anything "of i t " — a n y knowledge or o p i n i o n , or perception of i t — o r t hat i t has anything, even a name, so as to be the subject of di s c o u r s e . Thus a one which i s not cannot have any charac t e r whatsoever. ( l b . , 164b-c) The l a s t sentence of the second quotation i n p a r t i c u l a r r e v e a l s that Greeks were quick to see t h a t Parmenides i s committed t o ( 3 ) , and t h i s t e l l s us something about how h i s c l a i m 'nothing nonexistent e x i s t s ' (see Wetaphysica, 986b27-30) i s to be understood and was understood by the Greeks themselves. moreover, i t i s u n l i k e l y that Parmenides himself would have missed what others so q u i c k l y saw. I suggest t h e r e f o r e that (3) i s the connecting premise which leads from h i s c l a i m that nothing nonexistent e x i s t s to h i s c o n c l u s i o n t h a t the nonexistent i s p r o p e r t y l e s s and consequently unknowable. Thus understood, h i s reasoning does not ( i n t h i s instance) commit the f a l l a c y of eq u i v o c a t i o n . Let me now c i t e fragment 344 i n f u l l , f o l l o w i n g i t w i t h the K i r k and Raven commentary on i t (pp. 269-70): Come now, and I w i l l t e l l t h e e — a n d do thou hearken and c a r r y my word away—the only ways of enquiry t h a t can be thought of [ l i t e r a l l y , t hat e x i s t f o r t h i n k i n g , the o l d da t i v e sense of the i n f i n i t i v e ] : the one way, that i t i s and cannot not-be, i s the path of Persuasion, f o r i t attends upon Truth; the other, t h a t i t i s - n o t and needs must not-be, that I t e l l thee i s a path a l t o g e t h e r un-t h i n k a b l e . For thou c o u l d s t not know th a t which i s - n o t ( t h a t i s impossible) nor u t t e r i t ; f o r the same t h i n g can be thought as can be [ c o n s t r u c t i o n as above, l i t -e r a l l y the same t h i n g e x i s t s f o r t h i n k i n g and f o r b e i n g ] . 17 The brackets and the m a t e r i a l enclosed t h e r e i n are i n K i r k and,Raven exact-l y as c i t e d ; t h i s a p p l i e s to both the fragment and t h e i r commentary, which I now g i v e : The goddess begins her i n s t r u c t i o n by d e f i n i n g "the on-l y two conceivable ways of enquiry", which are d i r e c t l y c o n t r a r y one to the other: I f you accept one premise, then l o g i c compels you to r e j e c t the other. The choice i n f a c t , as Parmenides l a t e r puts i t i n i t s b r i e f e s t form (347, 1. 16) i s simply t h i s : & m o i V f r I ' f P z i V . Unfor-t u n a t e l y even to t r a n s l a t e these apparently simple words i s l i a b l e to be m i s l e a d i n g , because of the ambiguity, of which Parmenides himself was unconscious, between the pre-d i c a t i v e and the e x i s t e n t i a l senses of the Greek word £jTr_L* The usual t r a n s l a t i o n , " i t i s or i t i s not", too e a s i l y gives r i s e t o the question what " i t " i s . ... At t h i s e a r l y stage i n h i s poem Parmenides's premise has no d e f i n i t e s ubjec^ a t a l l : i t i s necessary to t r a n s l a t e the sen-tence &tTCiVi\ (AJH tVtiV* then perhaps the l e a s t misleading rendering i s : " E i t h e r a t h i n g i s or i t i s not". Parmenides i s a t t a c k i n g those who b e l i e v e , as a l l men always had be-l i e v e d , t h a t i t i s p o s s i b l e to make a s i g n i f i c a n t negative p r e d i c a t i o n ; but he i s enabled t o a t t a c k them only because of h i s own confusion between a negative p r e d i c a t i o n and a negative e x i s t e n t i a l judgment. The g i s t of t h i s d i f f i c u l t and important fragment i s t h e r e f o r e t h i s : " E i t h e r i t i s r i g h t only to t h i n k or say of a t h i n g , ' i t i s ...' (_i.e_., * i t i s so-and-so, e.g. w h i t e ' , or e l s e i t i s r i g h t t o t h i n k or say only ' i t i s not ...' (i_.e_., ' i t i s not some-t h i n g e l s e , e.g. b l a c k ' . The l a t t e r i s to be f i r m l y r e -j e c t e d on the ground £a mistaken one, owing to the confu-s i o n between e x i s t e n t i a l and predicative]] t h a t i t i s im-p o s s i b l e to conceive of Not-Being, the non-existent. Any p r o p o s i t i o n s about Not-Being are n e c e s s a r i l y meaningless; the only s i g n i f i c a n t thought or statements concern Being". I have quoted at length from the K i r k and Raven commentary because I do not understand t h e i r argument w e l l enough to s t a t e i t myself. Whatever the argu-ment, however, l e t us at l e a s t note the extreme i m p l a u s i b i l i t y of the i n -d i v i d u a l claims i n t h i s passage. F i r s t , i t seems u n l i k e l y t h a t Parmenides set out to a t t a c k 'those who b e l i e v e ... that i t i s p o s s i b l e t o make a s i g n i -f i c a n t negative p r e d i c a t i o n ' : his^ownvwork abounds i n such c l a i m s ; he says, e.£., 'what i s i s uncreated and imperishable, f o r i t i s e n t i r e , immovable 18 and without end* (fragment 347). Second, K i r k and Raven appear to th i n k t h a t i t was due to some confusion over negative p r e d i c a t i o n s and negative e x i s t e n t i a l s that Parmenides b e l i e v e d ( i n t h e i r words): 'Any p r o p o s i t i o n s about Not-Being are n e c e s s a r i l y meaningless} the only s i g n i f i c a n t thought or statements concern Being'. But I th i n k i t f a r more l i k e l y t h a t Parmeni-des was l e d to t h i s view by the f e a t u r e l e s s character of the nonexistent r a t h e r than by some confusion over negative p r e d i c a t i o n s and negative e x i s -t e n t i a l s ( f o r which confusion the t e x t u a l evidence i s at best i n c o n c l u s i v e ) . Note t h a t (3) above i s eq u i v a l e n t to the f o l l o w i n g : (3*) ( V x ) ( G x - E x ) i . . e_.» i f any pr e d i c a t e a p p l i e s to x, i t e x i s t s . (3*) e n t a i l s t h a t , however 'G* i s understood, we could not know something t o be G . unless i t e x i s t s ; hence, we could not i s o l a t e the c h a r a c t e r i s t i c s of the nonexistent, and iden-t i f y i t . Thus, (3*) might w e l l be thought to imply that ' p r o p o s i t i o n s about Not-Being are n e c e s s a r i l y meaningless', s i n c e we could never i s o l a t e a sub-j e c t f o r our dis c o u r s e . As we have i n t e r p r e t e d him, Parmenides i s concerned, not with the prob-lem of a t t r i b u t i n g negative p r e d i c a t e s to something, but r a t h e r with the problem of a t t r i b u t i n g any pr e d i c a t e s ( p o s i t i v e or negative) t o what does not e x i s t . In the Parmenides there i s an acute passage (I60c-2e) where Par-menides i s made to unfold the problems i n h i s own philosophy, as f o l l o w s : Now suppose one says, " i f largeness does not e x i s t " , or " i f smallness does not e x i s t " , or any other statement of that type. Obviously i n each case i t i s a d i f f e r e n t t h i n g t h a t i s spoken of as nonexistent. And so i n the present case, i f a man says " i f a one does not e x i s t " , i t i s p l a i n that the t h i n g he i s saying does not e x i s t i s something d i f f e r e n t from other t h i n g s , and we know what he i s speaking o f . So i n speaking of a "one" he i s speaking, i n the f i r s t p l a c e , of something knowable, and i n the second of something d i f f e r e n t from other 19 t h i n g s , no matter whether he a t t r i b u t e s e xistence to i t or nonexistence; even i f he says i t i s nonexistent, we nevertheless know what i s s a i d not to e x i s t , and that i t i s d i s t i n g u i s h a b l e from other t h i n g s . S t a r t i n g a f r e s h , then, from t h i s s u p p o s i t i o n , " i f a one does not e x i s t " , we are to consider what consequences f o l l o w . F i r s t , i t seems, t h i s must be true of i t , t h at there i s knowledge of i t ; otherwise the very meaning of the sup-p o s i t i o n t h a t "a ons does not e x i s t " would be unknown. The point i n Parmenides's philosophy which perplexes P l a t o comes t o t h i s : The a s s e r t i o n s ( i ) Largeness does not e x i s t , and ( i i ) Smallness does not e x i s t . are p l a i n l y d i f f e r e n t . Since ( i ) and ( i i ) have the same p r e d i c a t e , the as-s e r t i o n s as wholes must d i f f e r because of a d i f f e r e n c e i n t h e i r s u b j e c t s . Assuming ( i ) and ( i i ) are t r u e , however, how could largeness d i f f e r from smallness? When things d i f f e r , they d i f f e r i n t h e i r p r o p e r t i e s . But on Par-menides's p r i n c i p l e s what does not e x i s t i s p r o p e r t y l e s s . Today, we may be i n c l i n e d simply to dismiss P l a t o ' s d i f f i c u l t y . We are not t r o u b l e d by the f a c t t h a t 'largeness' and 'smallness' do not d i f f e r i n extension (assuming ( i ) and ( i i ) to be true) because we know that they d i f f e r i n i n t e n s i o n . I t i s t h i s i n t e n s i o n a l d i f f e r e n c e , we would say, which ex-p l a i n s the d i f f e r e n c e between ( i ) and ( i i ) . But, of course, the d i s t i n c t i o n between i n t e n s i o n and extension was unknown to P l a t o and Parmenides. Even when we make i t , however, there w i l l be a problem on Parmenides's p r i n c i p l e s i n accounting f o r the t r u t h of negative e x i s t e n t i a l s : i f there i s n ' t any-t h i n g which does not e x i s t , then Pegasus, e.£., cannot be something which does not e x i s t . On the other hand, we do not want to say that Pegasus i s 20 something which does exist. Recalling that Kahn said that 'the Greeks did not have our concept of existence*, let us set aside the charge of equivocation and consider Kahn's view relative to Parmenides. Though Russell claimed that his philosophy of logical analysis put an end to the twenty five centuries of .'metaphysical-error' allegedly begun by Parmenides, there are in fact a number of significant parallels between Par-menides and Russell. E..£»» in connection with the Parmenidean belief that •propositions about Not-Being are necesssarily meaningless', note Russell's related view that failure of reference for a proper name suffices to make meaningless the propositions in which it occurs as subject; he writes:* Whenever the grammatical subject of a proposition can be supposed not to exist without rendering the proposi-tion meaningless, i t is plain that the grammatical sub-ject is not a proper name. Moreover, a somewhat more sophisticated version of (3*) above is embodied in *14.21 of Principia Mathematica, about which Russell comments: 'If Ox)Fx 2 has any property whatever, i t must exist'. A good deal of the Parmenidean outlook in fact finds its way into modern 3 quantification theory; Quine, £.£.» writes: To say that somethinq does not exist, or that there is something which is not, is clearly a contradiction in terms; hence "(yxT(x exists)" must be true. Moreover, we should certainly expect leave to put any primitive name of our language for the "x" of any matrix "...x...", •'•Russell, B.,and Whitehead, A., Principia Mathematica (Cambridge: 1967), vol. I, p. 66. 2Ibid., vol. I, pp. 174-5. 3Quine, U., Mathematical Logic (New York: 1962), p. 150. 21 and to i n f e r the r e s u l t i n g s i n g u l a r statement from "(Vx)(••• ••)"> i t i s d i f f i c u l t to contemplate any a l -t e r n a t i v e l o g i c a l r u l e f o r reasoning with names. But t h i s r u l e of inference leads from the t r u t h "(Vx)(x e x i s t s ) " not only to the t r u e c o n c l u s i o n "Europe e x i s t s " but a l s o to the c o n t r o v e r s i a l c o n c l u s i o n "God e x i s t s " and the f a l s e c o n c l u s i o n "Pegasus e x i s t s " , i f we accept "Europe", "God", and "Pegasus" as p r i m i t i v e names i n our language. The a-t h e i s t seems c a l l e d upon to repudiate the very name "God", thus d e p r i v i n g h i m s e l f of vocabulary i n which to a f f i r m h i s atheism; and those of us who d i s b e l i e v e i n Pegasus would seem to be i n a s i m i l a r p o s i t i o n . As we a l l know, Quine would avo i d these t r o u b l e s by not t r e a t i n g 'Europe', 'God' and 'Pegasus' as ' p r i m i t i v e names i n our language'. This move a l s o suggests the Parmenidean philosophy, as i s shown by the f o l l o w i n g passage (Parmenides, 164b), i n which Parmenides says: ' Concerning "what i s not" there cannot be any knowledge or o p i n i o n , or p e r c e p t i o n of i t ; we cannot say that i t has anything, even a name, so as to be the s u b j e c t of d i s c o u r s e . L i k e o u r s e l v e s , Parmenides i s tempted (but u n l i k e us does not r e s i s t the temptation) t o t r e a t negative e x i s t e n t i a l s as untrue on the: grounds that there i s n ' t anything nonexistent. Again l i k e o u r s e l v e s , he r e j e c t s the no-t i o n of an intermediate between the e x i s t e n t and the nonexistent, saying: The words " i s not" mean simply the absence of being from anything t h a t we say i s not. We do not mean that the t h i n g i n a sense i s not, though i n another sense i t i s . The words mean without any q u a l i f i c a t i o n t h a t the t h i n g which i s not i n no sense or manner i s , and does not pos-sess being i n any way. (Parmenides, 163c-d) These remarks tend to undermine V l a s t o s ' s 'degrees of r e a l i t y ' t h e s i s . In 'The Greek verb "To Be" and the Concept of E x i s t e n c e ' (p. 248) Kahn disputes the adequacy of q u a n t i f i c a t i o n theory f o r expressing the Greek con-cept of e x i s t e n c e . But we have seen that q u a n t i f i c a t i o n theory seems very w e l l s u i t e d indeed to express Parmenides's c l a i m s , and t h a t , thus expressed, 22 the c l a i m s are c o n s i d e r a b l e . To understand the t e x t , t h e r e f o r e , we do not seem c a l l e d upon to a t t r i b u t e a f o r e i g n concept of ex i s t e n c e to Parmenides, A f t e r r e f e r r i n g to Wetaphysica, D e l t a 7, i n which A r i s t o t l e g i v e s 'to be t r u e * as a fundamental meaning f o r VXVpti*» Kahn o f f e r s h i s i n t e r p r e t a t i o n of Parmenides as f o l l o w s : * Parmenides' t h e s i s JL 6-8~xj. means " i t i s the case", where I t i s the s u b j e c t (or the o b j e c t ) which we know, Parmenides i s making the obvious, but not e n t i r e l y tri«* v i a l c l a i m that whatever we know, whatever can be known, i s — a n d must b e — d e t e r m i n a t e l y so, that i t must be ac-t u a l l y the case i n r e a l i t y or i n the world. I f we r e -s t a t e Parmenides* c l a i m i n the modern, fformal mode, i t might run: "m knows that £" e n t a i l s "p". On Kahn's account, Parmenides's poem i s more a t r e a t i s e i n epistemology than 2 ontology. I agree that the verb 'c:XVgtt* c a r r i e s the sense of 'to be t r u e ' , but disagree with Kahn over what i s fundamental i n Parmenides. I t i s hard f o r me to b e l i e v e that Parmenides would have s a i d ' i t i s the case* to mean 'whatever we know must be t r u e * ; the l a t t e r view c o u l d a t most be a conse-quence of the former. There i s an e p i s t e m o l o g i c a l s i d e to Parmenides's d o c t r i n e ; but my i n t e r p r e t a t i o n does j u s t i c e to i t . I f we may take:Kahn's ' a c t u a l l y the case i n r e a l i t y ' to mean ' e x i s t e n t * , then as we saw the un-k n o w a b i l i t y of what i s not ' a c t u a l l y the case i n r e a l i t y ' emerges as an im-mediate consequence of (1) above. But I t h i n k that e p i s t e m o l o g i c a l s i d e i n Parmenides i s l a r g e l y undeveloped; f o r i t s development we must t u r n to the s o p h i s t s and P l a t o , ^ a h n , C , 'The Thesis of Parmenides', Review of Metaphysics, v o l . 22 (1968/9), p. 711. ^Kahn's i n t e r p r e t a t i o n of Parmenides i s a n t i c i p a t e d by H i n t i k k a , who c r e d i t s 'the o l d man' with an ' e a r l y r e c o g n i t i o n of the i m p o s s i b i l i t y of " f a l s e knowledge",' H i n t i k k a , J . , Knowledge and B e l i e f ( I t h a c a , New York), p. 22n7. 23 1,3 The Sophists The s o p h i s t s were i t i n e r a n t teachers i n ancient G r e e c e — o r , as P l a t o p r e f e r s to put i t (Sophist 223b), 'paid hunters of r i c h young men'. Apart from i t s h i s t o r i c a l c o n t e x t , n e i t h e r the s o p h i s t movement nor P l a t o ' s r e a c t i o n to i t i s i n t e l l i g i b l e . Therefore, though of course the h i s t o r y of Greece i s f a m i l a r to a l l , l e t us begin our d i s c u s s i o n of the sop-h i s t s with some reminders of the cimcumstances which caused them to prosper. S c h o o l s — i.e_., immovable places of education—came r a t h e r l a t e to Greece; and, when they d i d come, they were not welcomed by a l l . For i n the o l d a r i s -t o c r a t i c t r a d i t i o n (which many were r e l u c t a n t to abandon) education had meant an inti m a t e union between a youth and an o l d e r man, i n which the o l d e r man assumed r e s p o n s i b i l i t y f o r the c h a r a c t e r of the youth and served as h i s quide and model. I would guess that t h i s h i g h l y personal system of education f e l l i n t o d i s r e p u t e p a r t l y because of the large p a r t which pederasty i n e v i t a b l y played i n i t . 1 But i n any case the r i s e of democratic commonwealths made the a r i s t o c r a t i c ways obsolete. S k i l l i n o r a t o r y became more important than s k i l l i n hunting and other s p o r t s . The s o p h i s t s , and a f t e r them the s c h o o l s , developed out of the new educational needs of the p o l i s . For t h e i r s e r v i c e s the s o p h i s t s p r e f e r r e d a fee to the favors ofyoung men. For t h i s preference they were roundly condemned by P l a t o , an a r i s t o c r a t who r e s i s t e d the spread 2 of democracy. lFor a ' p a i n s t a k i n g a n a l y s i s of what i s a f t e r a l l a d r e a d f u l a b e r r a t i o n ' , I r e f e r the reader to Marrou, H., A H i s t o r y of Education i n A n t i q u i t y (New York: 1956), pp. 50-62. 2 Needless to say, not every c l a s s i c a l s c h o l a r would agree with my r e -marks concerning P l a t o ' s antipathy toward the s o p h i s t s . For a balanced ac-count of the r e l a t i o n s between P l a t o and the S o p h i s t s , I r e f e r the reader to Jowett's t h o u g h t f u l commentary, as contained i n : Jowett, B., t r , The  Dialogues of P l a t o (Oxford: 1964), v o l . I l l , pp. 321-31. On the s o p h i s t s g e n e r a l l y , I r e f e r the reader t o G u t h r i e , Ui., The Sophists (Cambridge: 1971). 24 Economic c o n s i d e r a t i o n s r e q u i r e d the s o p h i s t s t o aim at a broad appeal. No doubt, given the s t a t e of t h e i r s o c i e t y , 1 the moral r e l a t i v i s m f o r which the s o p h i s t s are famous today found a r e c e p t i v e audience, p a r t i c u l a r l y s i n c e moral r e l a t i v i s m i s i n any case a popular p o s i t i o n with those who have given 2 moral problems a l i t t l e thought. For the s o p h i s t s , however, moral r e l a t i -vism was but a s p e c i a l case of an all-encompassing r e l a t i v i s m , which must have seemed p a r a d o x i c a l t o t h e i r audience; "everything i s t r u e ' , remarked Pro-tagoras, the g r e a t e s t s o p h i s t . 3 Truth and f a l s i t y , not only i n moral d i s -course but i n a l l d i s c o u r s e , seem to have been a matter of mere convention w i t h the s o p h i s t s . U n f o r t u n a t e l y , not much s o p h i s t w r i t i n g has s u r v i v e d . But from P l a t o and other near contemporary sources we know the s o p h i s t s taught t h a t any o p i n i o n , however absurd, can be e s t a b l i s h e d by argument; and, coming t o us v i a P l a t o and A r i s t o t l e , we have a number of simply awful sop-h i s t arguments p u r p o r t i n g to prove patent a b s u r d i t i e s . For example, i n Euthy-demus 298a-e P l a t o has the s o p h i s t Euthydemus argue t h a t the puppies of Ctesippus's dog are the brothers' of Ctesippus,- as f o l l o w s : s i n c e t h i s dog i s a f a t h e r and yours, i t i s your f a t h e r ; t h e r e f o r e , i t s puppies are your broth e r s . iSee de S e l i n c o u r t , A., t r , Herodotus: the H i s t o r i e s (Middlesex, Eng-l a n d : 1972), pp. 219-20; and Warner, R., t r , Thucydidest The H i s t o r y of the Peloponnesian War (Middlesex, England: 1970), pp. 126-7, ^ S p e c i a l i s t s doubtless would object to my speaking of 'the s o p h i s t s ' as i f they were a sc h o o l or movement w i t h a common p r a c t i c e and body of be-l i e f . To be exact, when I speak of 'the s o p h i s t s ' , I mean (unless a p a r t i -c u l a r f i g u r e outside the group i s named) 'Protagoras and h i s people'. (Euthy- demus 286c) Even then our concern i s not w i t h Protagoras's p o s i t i o n as he understood i t , but r a t h e r with that p o s i t i o n as P l a t o understood i t and pre-sented i t i n the dialogues. J H i c k s , R., t r , Diogenes L a e r t i u s : L i v e s of Eminent Philosophers (Har-vard: 1958), v o l . I I , p. 465. 25 Wost of the s u r v i v i n g sophisms co u l d f o o l only a r e a l d u l l a r d ; and so, i f there weren't more a r t to some of them, the s o p h i s t s c o u l d hardly have sustained the heated i n t e r e s t of P l a t o and A r i s t o t l e . I t i s , I t h i n k , c h i e f -l y the ambiguity of ViV«U' which made some of the sophisms p h i l o s o p h i c a l l y important to P l a t o and A r i s t o t l e . For, when we recall,' that 'fMfWL' meant both 'to e x i s t ' and 'to be t r u e ' , then i n Parmenides's d e n i a l of non-being we may a l s o see Protagoras's d e n i a l of falsehood. Thus, i n the C r a t y l u s 429d-e we f i n d t h i s exchange: Socrates: Does your statement amount to t h i s , that i t i s a l t o g e t h e r impossible to speak f a l s e l y ? For there are many who say t h i s , my dear C r a t y l u s , and there have been many i n the past. C r a t y l u s : Why, Socrates, how can a man say that which i s n o t ? — s a y something and yet nothing? For i s not falsehood saying the t h i n g which i s not? Diogenes L a e r t i u s says that Protagoras was the f i r s t t o hold that 'there are two s i d e s to every que s t i o n ' . * . For t h i s seemingly bland truism i t i s odd to see authorship a s c r i b e d , but what Protagoras meant by i t was something 2 w i l d l y p a r a d o x i c a l . As P l a t o p o i n t s out i n d i r e c t l y , he meant t h a t , given any p r o p o s i t i o n A and i t s negation -A, both are t r u e — j i . e _ . , there i s no con-t r a d i c t i o n , s i n c e everything i s t r u e . I f one c l a i m cannot be s a i d to con-t r a d i c t , however, then (as P l a t o saw) the very p o s s i b i l i t y of i n t e l l i g e n t disagreement i s l o s t . The e p i s t e m o l o g i c a l analogue to the Parmenidean paradoxes over nonexistence i s the problem of f i n d i n g a place f o r e r r o r i n one's theory of judgment, and t h a t task i n turn r e q u i r e s that a place f o r * L i v e s of Eminent Ph i l o s o p h e r s , v o l . I I , p. 465. 2See Euthydemus 385d-386e. Protagoras's views i n t h i s connection are r i d i c u l e d by P l a t o i n Euthydemus 287a-b, 297a-b, 300b-e, and f i n a l l y 303d-e. 26 falsehood be found i n one's theory of t r u t h . I t i s , I t h i n k , i n t h i s l a t t e r connection that the s o p h i s t s were p r i m a r i l y of i n t e r e s t to P l a t o . 1.4 The Euthydemus 1 Though r a r e l y s t u d i e d or even read, the Euthy- demus e x h i b i t s that p e r f e c t i o n of form which i s c h a r a c t e r i s t i c of P l a t o ' s f i n e s t work. The s t r u c t u r e of the Euthydemus i s bound to be p l e a s i n g to tho u g h t f u l readers, who must enjoy seeing i t s apparently u n r e l a t e d t o p i c s introduced unexpectedly only to f i n d them i n the end drawn together i n P l a t o ' s usual manner when they are r e l a t e d by i m p l i c a t i o n to a s i n g l e theme of over-r i d i n g importance. That theme f o r the Euthydemus i s the f a l l a c y of equivo-9 c a t i o n . The Euthydemus, as Jowett remarks, 'may f a i r l y c l a i m to be the old e s t t r e a t i s e on l o g i c * ; i t i s p a r t l y f o r t h i s reason t h a t I here o f f e r a commentary on t h i s neglected work, but we w i l l see that i t i s r e l e v a n t to the o n t o l o g i c a l and e p i s t e m o l o g i c a l problems with which we are now concerned. Perhaps b e t t e r than any other dialogue does, the Euthydemus introduces us to the p r a c t i c e of s o p h i s t r y , and r e v e a l s P l a t o * s a t t i t u d e toward i t . The two s o p h i s t s , Euthydemus and Oionysodorus, have such s k i l l ' i n the war of words, t h a t they can r e f u t e any p r o p o s i t i o n whether true or f a l s e * . (272b) Socrates hopes th a t they w i l l apply t h e i r s k i l l i n d i s p u t a t i o n * to h i s young l A l l t r a n s l a t i o n s from the Euthydemus are by Jowett. ^The Euthydemus i s thus an important dialogue i n connection w i t h the charge t h a t Parmenides i s g u i l t y of an eq u i v o c a t i o n , 3 J o w e t t , B., t r , The Dialogues of P l a t o (Oxford: 1964), v o l . I , p. 193. * I am here using ' d i s p u t a t i o n ' as a name f o r what was almost a p a r l o r game w i t h the Greeks, i n which one person puts a s e r i e s of questions to anoth-e r , questions t h a t can be answered only w i t h a 'no' or 'yes'. (Notice i n the Euthydemus how the s o p h i s t s object to Socrates q u a l i f y i n g h i s answers; see, » 296a-b), The object of the game i s f o r the questioner to d r i v e the ans-werer i n t o c o n t r a d i c t i o n , and of course f o r the answerer to avoid being so d r i v e n . 27 f r i e n d C l e i n i a s , so t h a t through a d i s c u s s i o n of knowledge and wisdom h i s c h a r a c t e r might be improved. (275b) But the two s o p h i s t s , u n l i k e Socrates, care nothing about C l e i n i a s ' s character ' i f the young man i s only w i l l to answer*. (275b) Taking advantage of a m b i g u i t i e s only p a r t l y r e f l e c t e d i n E n g l i s h , Euthy-demus asks C l e i n i a s a s e r i e s of questions, beginning w i t h : 'Are those who l e a r n the wise or the ignorant?* (275d) Equating 'wise' with ' i n t e l l i g e n t ' , the boy answers 'the wise'. (276a) S h i f t i n g the ground somewhat, Euthydemus then draws out of C l e i n i a s the admission that l e a r n e r s must be ignorant of that which they are about to l e a r n (276a-c), and triumphantly concludes: 'Then the unlearned l e a r n , and not the wise, C l e i n i a s , as you imagine*. (276b) The dialogue continues i n t h i s v e i n u n t i l Socrates, seeing the boy ' i n deep water' (277d), warns him: ...you have j u s t gone through the f i r s t p art of the sop-h i s t i c a l r i t u a l , which, as Prodicus says, begins with i n s t r u c t i o n i n the c o r r e c t use of terms. The two f o -r e i g n gentlemen, p e r c e i v i n g that you d i d not know, want-ed t o e x p l a i n to you that the word "to l e a r n " has two meaninge, and i s used, f i r s t , i n the sense of a c q u i r i n g knowledge, and a l s o , when you have the knowledge, i n the sense of reviewing t h i s same matter, whether something done or spoken, by the l i g h t of t h i s newly acquired knowledge; the l a t t e r i s g e n e r a l l y c a l l e d "understanding" r a t h e r than " l e a r n i n g " , but the word " l e a r n i n g " i s a l s o used; and you d i d not see, as they explained to you, that the term i s employed of two opposite s o r t s o f men, of those who know, and of those who do not know. There was a s i m i l a r t r i c k i n the second qu e s t i o n , when they asked you whether men l e a r n what they know or what they do not know. These parts of l e a r n i n g are not s e r i o u s , and t h e r e f o r e I say t h a t the gentlemen are not s e r i o u s , but are only p l a y i n g with you. For i f a man had a l l that s o r t of knowledge t h a t ever was, he would not be at a l l wiser about the t r u t h of t h i n g s . ... (277e-8c) Toward the end of Socrates's warning to C l e i n i a s , we see P l a t o ' s judgment of s o p h i s t r y : i t i s a mere game which does n o t a d v a n c e understanding. *But, (/of 28 course, through h i s examination of s o p h i s t r y P l a t o hopes to advance under-sta n d i n g . And as the s o p h i s t r y becomes more s u b t l e , he does. When Socrates i s through with h i s warning and w i t h some d i s c u s s i o n be-tween C l e i n i a s and h i m s e l f , Dionysodorus asks him whether he and Ctesippus ( C l e i n i a s ' s l o v e r ) t r u l y wish C l e i n i a s to become wise, to which Socrates of course answers t h a t they do. (283b-c) 'You wish him to become what he i s not, and no longer to be what he i s ? ' asks Dionysodorus. (283d) At t h i s sug-g e s t i o n Socrates i s 'thrown i n t o c o n s t e r n a t i o n ' , as Dionysodorus equates the d e s i r e to see C l e i n i a s 'become what he i s not' with a d e s i r e t o see him des-troyed. (283d-e) That i s , Dionysodorus ( t o put the matter i n general terms) equates 'x i s not-F' with 'x i s not*, where the l a t t e r c l a i m i s taken to mean *x does not e x i s t ' . Dionysodorus thus confuses negative p r e d i c a t i o n a l c l a i m s with negative e x i s t e n t i a l claims i n p r e c i s e l y the way K i r k and Raven s a i d that Parmenides does; and so P l a t o ' s handling of the matter would not be without i n t e r e s t to us. But before Socrates can d i s c u s s Dionysodorus*s statements, he i s i n t e r r u p t e d by Ctesippus, who a t the suggestion that he and Socrates would wish C l e i n i a s destroyed 'got very angry (as a l o v e r w e l l might) and s a i d : "Stranger of T h u r i i — i f p o l i t e n e s s would a l l o w me I should say, A plague upon you! What can make you t e l l such a l i e about [ u s ] " , ' (283e) With t h i s i n t e r j e c t i o n , the t o p i c of d i s c u s s i o n changes.* Euthydemus, now speaking i n s t e a d of Dionysodorus, asks: 'do you t h i n k , Ctesippus, that x A t 285a-c, "Socrates '-returns, .to t h i s f a l l a c y i n which negative p r e d i c a -t i o n a l c l a i m s are confused with negative e x i s t e n t i a l c l a i m s , but i s content .there - t o d e a * ^ * If £the s o p h i s t s ] know how to destroy men i n such a way as. to make good and s e n s i b l e men out of bad and f o o l i s h ones let.them,, i n t h e i r phraseology, destroy the youth and create him again wise*. 29 i t i s p o s s i b l e to t e l l a l i e ? * (283e) Ctesippus of course answers t h a t i t i s (283e), and here i s the exchange which f o l l o w s J ( 2 8 3 e - 4 c ) : And i n t e l l i n g a l i e , do you t e l l the t h i n g of which you speak or not? You t e l l the t h i n g of which you speak. And he who t e l l s , t e l l s t h a t t h i n g which he t e l l s , and no other? Yes, s a i d Ctesippus, And t h a t i s a d i s t i n c t t h i n g apart from other t h i n g s ? C e r t a i n l y . And he who says that t h i n g says that which i s ? Yes. * And he who says t h a t which i s , says the t r u t h . And t h e r e f o r e Dionysodorus, i f he says t h a t which i s , says the t r u t h about you and no l i e . Yes, Euthydemus, s a i d Ctesippus; but i n saying t h i s , he says that which i s not. Euthydemus answered: And t h a t which i s not i s not? True. And t h a t which i s not e x i s t s nowhere? Nowhere. And can anyone do anything about t h a t which has no e x i s -tence? Can anyone, whosoever he be, act on t h i n g s which e x i s t nowhere? I think not, s a i d Ctesippus. To put the matter b r i e f l y , i f l y i n g i s saying the t h i n g which i s not, then l i a r s have nothing t o say. This i s perhaps a 'quibble', as P h i l i p Rouse sug-gests i n h i s e d i t i o n of the Euthydemus; 1 but i t i s one which has the support l-See Hamilton, E. and C a i r n s , H., eds, P l a t o : The C o l l e c t e d Dialoques (New York: 1964), p. 420. a  30 of Parmenides (Parmenides 142a-b): i f *a t h i n g i s not i t i s not named or spoken o f . Except f o r an b r i e f remark by Ctesippus a t 284c, 1 no r e p l y i s given to the s o p h i s t argument against falsehood and l y i n g . Instead, a s h o r t exchange on c o n t r a d i c t i o n (285d-6d) f o l l o w s , i n which Dionysodorus says that there can be no such t h i n g as c o n t r a d i c t i o n , s i n c e 'no man could a f f i r m a negative; f o r no one could a f f i r m t h a t which i s not*. (286a) Socrates then p o i n t s out that t h i s view of c o n t r a d i c t i o n i s i n v o l v e d with the Protagorean dictum that 'there i s no such t h i n g as f a l s e h o o d * , 2 a dictum to which Dionysodorus r e a d i -l y assents. (286c-d) But, i f everything a man says i s t r u e , continues Soc-r a t e s , i t would seem that there i s no such t h i n g as ignorance, s i n c e a man can speak t r u l y on any t o p i c . Again Dionysodorus assents. (286d-e) But, i f there i s no ignorance, then what, asks Socrates, have these s o p h i s t s come to teach? To t h i s question Dionysodorus responds by c a l l i n g Socrates 'an o l d f o o l ' . (287b) Having thus traded argumenta ad homines, e q u i v o c a t i o n again becomes the t o p i c , w i t h t h i s exchange between Dionysodorus and Socrates: Are the th i n g s which have sense a l i v e or l i f e l e s s ? They are a l i v e . And do you know of any word which i s a l i v e ? Awhere Ctesippus u n s a t i s f a c t o r i l y says that he who speaks f a l s e l y 'says what i s i n a c e r t a i n way and manner, and not as i t r e a l l y i s ' . ( S i g n i f i c a n t -l y , i t i s Ctesippus rather than Socrates who makes t h i s remark.) 2 p i a t o s l y l y says t h a t the Protagorean dictum of u n i v e r s a l t r u t h ' i s s u i c i d a l as w e l l as d e s t r u c t i v e ' . (286c) A r i s t o t l e l e s s s l y l y says (ffleta- p h y s i c a 1012bl5): 'he who says t h a t everything i s tr u e makes even the statement c o n t r a r y to h i s own t r u e , and ther e f o r e h i s own not t r u e ' . 31 I c e r t a i n l y do not. Then why d i d you ask me what sense my words had? Why, because I was s t u p i d and made a mistake.* At 293b-d Euthydemus undertakes to show Socrates, who had always made a p r o f e s s i o n of h i s own ignorance (see Apology 21a-3c), that he i s omniscient: . . . t e l l me [asks Euthydemus] do you know anything? Yes, I s a i d , I know many t h i n g s , but not anything of much importance. That w i l l do, he s a i d : And would you admit that any-t h i n g can be what i t i s , and a t the same time not be what i t i s ? C e r t a i n l y not. And d i d you not say) 1:that you knew something? I d i d . I f you know, you are knowing. C e r t a i n l y , of j u s t the knowledge which I have. That makes no d i f f e r e n c e j — a n d must you not, i f you are knowing, know a l l t h i n g s ? C e r t a i n l y not, I s a i d , f o r there are many other thing s which I do not know. And i f you do not know, you are not knowing. Yes, f r i e n d , p f ^ t h a t which-I do not know. S t i l l you are not knowing, and you s a i d j u s t now th a t you were knowing; and ther e f o r e you are and are not the i d e n t i c a l you, at the same time and i n reference to the same t h i n g s . -••Apparently missing the i r o n y of t h i s passage, E d i t h Hamilton says t h a t Dionysodoru8*s remarks 'are acknowledged ... to be a knockout blow', and i n -f e r s t h a t our t h i n k i n g i s more advanced than t h a t of the a n c i e n t s , whose •reasoning was l a r g e l y v e r b a l * . See Hamilton, E. and C a i r n s , H., eds, P l a t o :  The C o l l e c t e d Dialogues, p. 385. 32 Imagining himself to have reduced Socrates to c o n t r a d i c t i o n , Euthydemus t h i n k s t h a t he has won t h i s d i s p u t a t i o n . I t i s c l e a r , however, from how Soc-r a t e s q u a l i f i e s h i s answers that P l a t o Is not f o o l e d by t h i s sophism purport-ing to prove t h a t , i f Socrates knows anything, he knows e v e r y t h i n g . B e l i e v -i n g (or pretending t o b e l i e v e ) that '(3x)-(Socrates knows x ) * i s the c o n t r a -d i c t o r y of * (j y)(Socrates know y ) ' , Euthydemus I n f e r s t h a t '(By)(Socrates knows y ) * e n t a i l s the negation of '(^ x ) - ( S o c r a t e s knows x ) , which i s , of course, *-("3x)-(Socrates knows x ) ' . Since t h i s l a s t p r o p o s i t i o n i s equiva-l e n t to '(Vx)(Socrates knows x ) * , Euthydemus concludes that *(3y)(Socrates know y ) * e n t a i l s *(yx)(Socrates knows x ) ' — i_.e., he concludes t h a t , i f Soc-r a t e s knows anything, he knows eve r y t h i n g . Since, however, f(afy)(Socrates know y ) ' and ' ( J x ) - ( S o c r a t e s knows x ) * are not c o n t r a d i c t o r i e s , Socrates may know some th i n g s while being ignorant of others; and the argument i s there-f o r e f a l l a c i o u s . To us, the f a l l a c y i n Euthydemus's argument i s obvious. But consider the matter i n i t s context. By philosophers and s o p h i s t s a l i k e there had been a good deal of m y s t i f y i n g t a l k about knowledge. Protagoras had s a i d ( a t l e a s t by i m p l i c a t i o n ) t h a t we know e v e r y t h i n g ; whereas Georgias of L e o n t i n o i , anoth-er s o p h i s t , had s a i d that we know nothing. The obvious t r u t h , of course, i s that we know somethings and not others. But t h i s obvious t r u t h was ob-scured by the s o p h i s t confusion (perhaps d e l i b e r a t e ) of *x i s not-F* with *x i s not', where the l a t t e r p r o p o s i t i o n Is understood as a negative e x i s t e n t i a l . For, having thus equated negative p r e d i c a t i o n a l c l a i m s with negative e x i s t e n -t i a l c l a i m s , the s o p h i s t s c o u l d then invoke the a u t h o r i t y of Parmenides to prove that no negative p r e d i c a t i o n a l c l a i m i s t r u e : to see how e a s i l y the Parmenidean philosophy can be made to degenerate i n t o s o p h i s t r y , we have on-33 l y to r e c a l l the commentary of K i r k and Raven. As we saw,; Parmenides t r e a t e d 'x i s not*, understood e x i s t e n t i a l l y , as s e l f - c o n t r a d i c t o r y when •x' i s replaced by a name. The c l a i m 'Socrates does not know x* i s , of course, a negative p r e d i c a t i o n a l c l a i m . Therefore, i f , as the s o p h i s t s a r -gued, no such cla i m s are t r u e , then Socrates could not f a i l to know some-t h i n g and would be omniscient a f t e r a l l . The p e r f e c t l y good word 'know' had been thus ruined by the v a i n s p e c u l a t i o n s of s o p h i s t s and philosophers. By p u t t i n g matters i n concrete terms P l a t o t r i e s t o d i s p e l the mysteries c r e a t e d by these v a i n s p e c u l a t i o n s : I adjure you, s a i d Ctesippus, i n t e r r u p t i n g , give me some proof [ t h a t you are omniscient]]. What proof s h a l l I give you? [Dionysodorus askedj W i l l you t e l l me how many teeth Euthydemus has? and Euthydemus s h a l l t e l l how many teeth you have. W i l l you not take our word that we know a l l t h i n g s ? C e r t a i n l y not, s a i d Ctesippus: you must f u r t h e r t e l l us t h i s one t h i n g , and then we s h a l l know th a t you are speak-in g the t r u t h ; i f you t e l l us the number, and we count them, and you are found to be r i g h t , we w i l l b e l i e v e the r e s t . (295b-d) But the s o p h i s t s r e f u s e . I come at l a s t to the p a r t of the Euthydemus which i s always c i t e d to demonstrate how f a r t h i n k i n g has progressed s i n c e ancient times, I mean, of course, the famous s t o r y of Ctesippus and h i s dog. (298a-9e) I t would sure-l y be absurd to suggest that the argument purporting to e s t a b l i s h the kin-.-., s h i p of Ctesippus and h i s dog i s one which could have f o o l e d P l a t o ' s audience. On the c o n t r a r y , given the context i n which t h i s argument occurs, P l a t o can have but one purpose i n t e l l i n g i t : he i s reasoning with ' l o g i c a l a n a l o g i e s ' ; 1See Copi, I . , I n t r o d u c t i o n to Logic (New York: 1968), pp. 157-9, and then compare Euthydemus 293b-d to Euthydemus 297c-Bc. 34 t h a t i s , he i s presenting a c l e a r l y i n v a l i d argument and thereby r e v e a l i n g the i n v a l i d i t y of a pe r p l e x i n g argument of the same form. That perple x i n g argument i s , of course, the one which moves from '(-^yX Socrates knows y ) ' to '(yx)(Socrates knows x ) * . Let me c i t e the r e l e v e n t passages a t some l e n g t h , beginning as f o l l o w s : i . . i s P a t r o c l e 8 your brother [, Socrates]? Yes, he i s my h a l f - b r o t h e r , the son of my mother, but not of my f a t h e r . Then he i s and i s not your brother. Not by the same f a t h e r , my good man, I s a i d , f o r Chaere-demus was h i s f a t h e r , and mine was Sophroniscus. And was Sophroniscus a f a t h e r , and Chaeredemus a l s o ? Yes; the former was my f a t h e r , and the l a t t e r h i s . Then, he s a i d , Chaeredemus was other than a f a t h e r . Than my f a t h e r , I s a i d . But was he then a f a t h e r , being other than a f a t h e r ? or are you the same as a stone? I c e r t a i n l y do not think I am a stone, though I am a f r a i d t hat you may prove me to be one. Are you not other than stone? I am. And being other than stone, you are not stone; and being other than g o l d , you are not gold? Very t r u e . And so Chaeredemus, being other than a f a t h e r , i s not a f a t h e r ? I suppose t h a t he i s not a f a t h e r , I r e p l i e d . For i f , s a i d Euthydemus, t a k i n g up the argument, Chaere-demus i s a f a t h e r , then Sophroniscus, being other than a f a t h e r , i s not a f a t h e r ; and you, Socrates, are without a f a t h e r . (297d-8b) 35 I t i s sometimes s a i d (by R u s s e l l , £_•£•) that before our century r e l a t i o n s and r e l a t i o n a l inference had been r e j e c t e d f o r poor reasons or simply ignored a l t o g e t h e r . In t h i s passage, however, P l a t o i s c l e a r l y aware of the dis-ana-logy between 'x i s a stone' and 'x i s a f a t h e r ' a r i s i n g out of the f a c t t h a t 'being a f a t h e r ' , u n l i k e 'being a stone', i s a r e l a t i o n a l p r e d i c a t e . Given the n o n - r e l a t i o n a l predicate ' b B i n g a stone', from the c l a i m 'x i s other than a stone', i t f o l l o w s that x i s not a stone at a l l . But, given the r e l a t i o n -a l p r e d i c a t e 'being a f a t h e r ' , from the c l a i m 'x i s other than Socrates's . f a t h e r ' , i t does not f o l l o w that x i s not a f a t h e r at a l l , s i n c e x may be someone e l s e ' s f a t h e r . I t i s l e f t to the reader to observe t h a t 'to know' i s l i k e 'to f a t h e r ' , not l i k e 'to be stone'. The dialogue continues: Ctesippus, here t a k i n g up the argument, s a i d : And i s not your f a t h e r i n the same case [as Socrates's f a t h e r ] , f o r he i s other than my f a t h e r ? Assuredly not, s a i d Euthydemus. Then he i s the same? He i s the same. The idea does not please me; but i s he only my f a t h e r , Euthydemus, or i s he the f a t h e r of a l l other men? Of a l l other men. Do you suppose the same person t o be a f a t h e r and not a f a t h e r ? C e r t a i n l y , I d i d so imagine, s a i d Ctesippus. And do you suppose that gold i s not g o l d , or that a man i s not a man? (298b-c) Notice t h a t the s o p h i s t must again r e t u r n to n o n - r e l a t i o n a l p r e d i c a t e s , such as 'being g o l d ' or 'being a man', i n order to make i t seem that there i s a c o n t r a d i c t i o n i n v o l v e d i n a s s e r t i n g t h a t the same man may simultaneously be a f a t h e r [ t o some] and not be a f a t h e r [ t o o t h e r s ] . Again, i t i s l e f t to 36 the reader t o observe that a man may know some things and not o t h e r s , j u s t as he may f a t h e r some c h i l d r e n and not others. Ctesippus remarks that ' i t i s monstrous to suppose that your f a t h e r i s the f a t h e r of a l l ' . (298c) For that view e n t a i l s that he 'has a progeny of sea-urchins and gudeons and puppies and l i t t l e p i g s ' , (298d) I t i s f o l l o w -ing t h i s remark t h a t the oft-quoted s t o r y of Ctesippus and h i s dog comes: I f you w i l l answer my questions, s a i d Dionysodorus, I w i l l soon e x t r a c t the same admissions from you, C t e s i p -pus. You have a dog? Yes, a v i l l a i n of a one, s a i d Ctesippus. And he has puppies? Yes, and they are very l i k e h i m s e l f . And the dog i s the f a t h e r of them? Yes, he s a i d , I c e r t a i n l y saw him and the mother of the puppies come together. And i s he not yours? To be sure he i s . Then he i s a f a t h e r , and he i s yours; ergo, he i s your f a t h e r , and the puppies are your broth e r s . (298d-e) This t a l k of sea-urchins and gudgeons and dogs i s the death-blow to the sop-h i s t treatment of knowledge. Discounting a few t h e i s t s who t h i n k God i s the f a t h e r of a l l , no one would think that h i s f a t h e r , or anyone e l s e ' s , i s the f a t h e r of a l l . But on Protagoras's a u t h o r i t y someone who had been s u i t a b l y confused by Parmenides may w e l l have thought that man, being the measure of a l l t h i n g s , i s i n some sense omniscient. I t i s P l a t o ' s reasoned c o n c l u s i o n t h a t t h i s view of knowledge i s no l e s s absurd than the analogous view of fatherhood. Moreover, t h i s i s a c o n c l u s i o n f o r which the tho u g h t f u l reader i s s y s t e m a t i c a l l y prepared. 37 We conclude our commentary on the Euthydemus w i t h the f o l l o w i n g remarks. The Euthydemus f o l l o w s the p a t t e r n of the e a r l y dialogues i n t h a t i t r a i s e s q u i t e general questions while answering only s p e c i f i c arguments, and i s there-f o r e somewhat u n s a t i s f y i n g t o the reader. P l a t o has perhaps d i s c r e d i t e d c e r -t a i n s o p h i s t arguments. But we have already seen t h a t , c o n t r a r y to K i r k and Raven, the Parmenidean paradoxes about ex i s t e n c e and knowledge are not mere s o p h i s t r y . Given P l a t o ' s a l l i a n c e with Parmenides, t h e r e f o r e , we are l e f t wondering how he would account f o r the p o s s i b i l i t y of (1) f a l s e statement, and (2) s i g n i f i c a n t d e n i a l s of e x i s t e n c e . For h i s treatment of the general i s s u e s which make the Euthydemus i n t e r e s t i n g , we must turn to a l a t e d i a l o g u e , the Sophist. ^•5 P l a t o on False Statement; A Commentary on the Sophist 236e-9b and 260e-4c* The ostensive aim of the Sophist i s to define ' s o p h i s t r y ' , and P l a t o concludes the Sophist (268c-d) with the f o l l o w i n g d e f i n i t i o n : The a r t of c o n t r a d i c t i o n making, descended from an i n s i n -cere k i n d of conceited mimicry, of the semlilance-making breed, d e r i v e d from image making, d i s t i n g u i s h e d as a por-t i o n , not d i v i n e but human, of production, that presents a shadow play of words—such are the blood and l i n e a g e which can, with p e r f e c t t r u t h , be assigned t o the authen-t i c Sophist. One of the d e c e i t f u l things which the s o p h i s t s d i d i n the Euthydemus, as we saw, to argue t h a t , s i n c e there i s no falsehood, d e c e i t i s impossible. To give h i s d e f i n i t i o n of ' s o p h i s t r y * a non-empty ex t e n s i o n , P l a t o s e t s out i n the Sophist to f i n d c o r r e c t terms i n which one may say or think that falsehoods have a r e a l e x i s t e n c e , without being caught i n a c o n t r a d i c t i o n by the mere utterance of such words. (237a) 1 U n l e s s otherwise i n d i c a t e d , a l l t r a n s l a t i o n s from the Sophist are by Cornford. 38 Though the Euthydemus d i d not so much as mention Parmenides, the c h i e f speaker of the Sophist (the Stranger) i s introduced as one who 'belongs to the school of Parmenides and Zeno*. (216a) The reason f o r making the c h i e f speaker an E l e a t i c philosopher r a t h e r than a s o p h i s t i s that P l a t o sees i n Parmenides some unintended but p e r n i c i o u s p h i l o s o p h i c a l support f o r what would otherwise be an u n i n t e r e s t i n g a b s u r d i t y — v i z . , t h a t there i s no f a l s e -hood; thus he says: The audacity of the statement [ t h a t falsehood e x i s t s ] l i e s i n i t s i m p l i c a t i o n t h a t "what i s not" has being, f o r i n no other way cou l d a falsehood come to have being. But, my young f r i e n d [Theaetetus], when were were of your age the great Parmenides, from beginning t o end, t e s t i -f i e d a g a i n s t t h i s , c o n s t a n t l y t e l l i n g us what he a l s o says i n h i s poem, "Never s h a l l t h i s be p r o v e d — t h a t things that are not are". (237a-b) U n w i l l i n g to b e l i e v e t h a t there i s no falsehood, P l a t o proposes 'to put [Parmenides's] statement to a m i l d degree of t o r t u r e . . . , studying i t on i t s own m e r i t s ' . (237b) He begins by showing e x a c t l y how i n h i s view Parmenides's statement i m p l i e s t h a t there i s no falsehood, as f o l l o w s : Stranger: . . . t e l l us to what t h i s name can be a p p l i e d — " t h a t which i s not". ... Theaetetus: That i s a hard question. ... Stranger: W e l l , t h i s much i s c l e a r a t any r a t e , that the term "what i s not" must not be a p p l i e d to anything t h a t e x i s t s . Theaetetus: C e r t a i n l y not. Stranger: And s i n c e i t cannot be a p p l i e d to th a t which e x i s t s , n e i t h e r can i t p r o p e r l y be a p p l i e d to "something". Theaetetus: How so? Stranger: Surely we can see that t h i s expression "some-t h i n g " i s always used of a t h i n g t h a t e x i s t s . We cannot use i t j u s t by i t s e l f i n naked i s o l a t i o n from everything t h a t e x i s t s , can we? 39 Theaetetus: No Stranger: Is your assent due t o the r e f l e c t i o n that to speak of "something" i s t o speak of "some one thing"? Theaetetus: C e r t a i n l y . Stranger: Because you w i l l admit t h a t "something" stands f o r one t h i n g , as "some t h i n g s " stands f o r two or more. Theaetetus: Yes. Stranger: So i t seems to f o l l o w n e c e s s a r i l y t h a t to speak of what i s not "something" i s t o speak of no t h i n g a t a l l . Theaetetus: N e c e s s a r i l y . Stranger: Must we not even refuse t o allow that i n such a case a person i s saying something, though he may be speaking of nothing? Must we not a s s e r t t h a t he i s not even saying anything when he s e t s about u t t e r i n g the sounds "a t h i n g t h a t i s not"? Theaetetus: That would c e r t a i n l y end our bewilderment. (237d-e) P l a t o ' s . p o i n t i n t h i s passage i s that on Parmenides's premises every meaning-f u l a s s e r t i o n i s t r u e , implying t h a t apparently f a l s e a s s e r t i o n s are i n f a c t e i t h e r true or meaningless. Our a p p r e c i a t i o n of P l a t o p o i n t i s aided by the f o l l o w i n g passage i n A r i s t o t l e (Metaphysica 1051b31-2a5): As regards the "being" that answers to t r u t h and the "non-being" t h a t answers t o f a l s i t y , i n one case there i s t r u t h i f the subject and the a t t r i b u t e are r e a l l y combined, and f a l s i t y i f they are not combined; i n the other case, i f the o b j e c t i s e x i s t e n t i t e x i s t s i n a p a r t i c u l a r way, and i f i t does not e x i s t i n t h i s way i t does not e x i s t at a l l . And t r u t h means knowing these o b j e c t s , and f a l s i t y does not e x i s t , nor e r r o r , but only i g n o r a n c e — a n d not an ignorance which i s l i k e b l i n d n e s s ; f o r b l i n d n e s s i s a k i n to a t o t a l absence of the f a c u l t y of t h i n k i n g . I take i t that i n t h i s passage A r i s t o t l e i s saying something l i k e the f o l l o w -i n g : The p r o p o s i t i o n 'Socrates i s P e r s i a n ' , e.g., a s s e r t s the existence of 40 a c e r t a i n o b j e c t — v i z . , a P e r s i a n Socrates, and i s f a l s e because there i s no such o b j e c t . * On the other hand, 'Socrates i s Greek* l i k e w i s e a s s e r t s the existence of a c e r t a i n o b j e c t — v i z . , a Greek Socrates, but i s true be-cause i n t h i s case there i s such an o b j e c t . But, i f we f o l l o w Parmenides and hold t h a t everything e x i s t s , then i t would seem that the P e r s i a n Soc-r a t e s e x i s t s , implying (on the correspondence theory of t r u t h here assumed) t h a t 'Socrates i s P e r s i a n ' i s t r u e . On Parmenidean premises, then, the only a l t e r n a t i v e to t h i s r e s u l t which P l a t o can envisage would be to hold that •Socrates i s P e r s i a n ' i s not f a l s e but meaningless. In t h i s a l t e r n a t i v e Theaetetus t h i n k s he sees an 'end to our bewilderment*, (237e) But the . Stranger q u i c k l y c a u t i o n s him against t h i s c o n c l u s i o n . (237e) For, as P l a t o w e l l knows (see 261e-4c), there i s a d i f f e r e n c e between speaking f a l s e l y and c h a t t e r i n g without meaning. But before P l a t o can account f o r meaningful falsehood, he must make some general remarks about meaning, as f o l l o w s (261d-3e): Theaetetus: What are you going to ask me about words? Stranger: Whether they a l l f i t together, or none of them, or some w i l l and some w i l l not. Theaetetus: That i s p l a i n enough. Some w i l l , some w i l l not. Stranger: You mean perhaps something l i k e t h i s . Words which, when spoken i n s u c c e s s i o n , s i g h i f y something, do f i t together, while those which mean nothing when they are strung together, do not. Theaetetus: What do you mean? •••Elsewhere (metaphysics 1024b25-30) A r i s t o t l e says 'A f a i s e account i s the account of nonexistent o b j e c t s , i n so f a r as i t i s f a l s e ' . 41 Stranger: What I supposed you had i n your mind when you gave your assent. The signs we use i n speech to s i g n i f y being are s u r e l y of two ki n d s . Theaetetus: How? Stranger: One k i n d c a l l e d "names", the other "verbs". Theaetetus: Give me a d e s c r i p t i o n of each. Stranger: By "verb" we mean an expression which i s ap-p l i e d to a c t i o n s . Theaetetus: Yes. Stranger: And by a "name" the spoken s i g n a p p l i e d to what performs these a c t i o n s . Theaetetus: Quite so. Stranger: Now a statement never c o n s i s t s s o l e l y of names spoken i n succ e s s i o n , nor yet of verbs apart from names. Theaetetus: I don't f o l l o w t h a t . Stranger: E v i d e n t l y you had eomething e l s e i n mind when you agreed w i t h me j u s t now, because what I meant was j u s t t h i s — t h a t these words spoekn i n a s t r i n g i n t h i s way do not make a statement. Theaetetus: N a t u r a l l y . Stranger: And again, i f you say " l i o n stag horse" and any other names given to t h i n g s t h a t performcactions, such a s t r i n g never makes up a statement. Neither i n t h i s example nor i n the other do the sounds u t t e r e d s i g n i f y any a c t i o n performed or not performed or nature of anything that e x i s t s or does not e x i s t , u n t i l you com-bine verbs w i t h names. The moment you do t h a t , they f i t together and the simp l e s t combination becomes a statement of what might be c a l l e d the s i m p l e s t and b r i e f e s t k i n d . Theaetetus: Then how do you make a statement of th a t kind? Stranger: When one says "A man understands", do you agree that t h i s i s a statement of the simpest and s h o r t -e s t p o s s i b l e kind? Theaetetus: Yes. 42 Stranger: Because now I t gives i n f o r m a t i o n about f a c t s or events i n the present or past or f u t u r e ; i t does not merely name something but gets you somewhere by weaving together verbs with names. Hence we say i t " s t a t e s " something, not merely "names" something, and i n f a c t i t i s t h i s complex that we mean by the word "statement". The d i s t i n c t i o n s which P l a t o makes i n t h i s passage are doubtless taken from the grammarians of h i s day. But the d i f f i c u l t y which Theaetetus, an im-mensely c l e v e r l a d w e l l versed i n philosophy, has i n f o l l o w i n g them suggests that philosophers had neglected such d i s t i n c t i o n s . Indeed, we have some i n -dependent evidence f o r t h i s neglect i n the f a c t t h a t , although the dialogues abound i n l i n g u i s t i c a n a l y s i s , there i s n ' t a t r a c e of i t i n the p r e - S o c r a t i c s . The elementary char a c t e r of P l a t o ' s grammatical d i s t i n c t i o n s may thus b e l i e the h i s t o r i c a l l y important f a c t t h a t probably f o r the f i r s t time a p h i l o s o -pher i s attempting to r e s o l v e o n t o l o g i c a l problems through l i n g u i s t i c analy-s i s . Woreover, h i s main p o i n t — v i z . , that a p r o p o s i t i o n s t a t e s but does not name s o m e t h i n g — i s echoed by R u s s e l l i n these words: 1 I t i s very important t o r e a l i z e ... that p r o p o s i t i o n s  are not names f o r f a c t s . I t i s q u i t e obvious as soon as i t i s pointed out to you, but as a matter of f a c t I never had r e a l i z e d i t u n t i l i t was pointed out to me by a former p u p i l of mine, W i t t g e n s t e i n . I t i s p e r f e c t l y evident as soon as you think of i t , t h at a p r o p o s i t i o n i s not a name f o r a f a c t , from the mere circumstance that there are two p r o p o s i t i o n s corresponding t o each f a c t . Suppose i t i s a f a c t that Socrates i s dead. You have two p r o p o s i t i o n s : "Socrates i s dead" and "Socrates i s not dead". ,.. There are two d i f f e r e n t r e l a t i o n s , as you see, that a p r o p o s i t i o n may have to a f a c t : the one t h e : r e l a t i o n that, you "may.'.'call being true to the f a c t , and the other being f a l s e to the f a c t . Both are e q u a l l y e s s e n t i a l l y l o g i c a l r e l a t i o n s which may s u b s i s t between the two, whereas i n the case of a name, there i s only one r e l a -t i o n that i t can have to what i t names. A name can j u s t i R u s s e l l , B., 'The Philosophy of L o g i c a l Atomism', as contained i n : Marsh, R., ed., Logic and Knowledge (London: 1956), p. 187. 43 name a p a r t i c u l a r , o r , i f i t does not, i t i s not a name at a l l , i t i s a noise. I t i s important f o r both R u s s e l l and P l a t o to d i f f e r e n t i a t e p r o p o s i t i o n s from names, si n c e i n t h e i r view names ' s i g n i f y being* (261e) and are other-wise meaningless. Whereas, i f the s t a t e of a f f a i r s i n d i c a t e d by a pro p o s i -t i o n does not o b t a i n , the p r o p o s i t i o n i s not meaningless but f a l s e . P l a t o concedes to Parmenides (as would R u s s e l l a l s o ) t h a t 'Whenever there i s a statement, i t must be about something; i t cannot be about nothing*. (262e) How then are t r u e and f a l s e statements to be d i s t i n g u i s h e d ? P l a t o answers: Stranger: I w i l l make a statement to you, then, p u t t i n g together a t h i n g w i t h an a c t i o n by means of a name and a verb. You are to t e l l me what the statement i s about. Theaetetus: I w i l l do my best. Stranger: "Theaetetus s i t s " . . . . Now i t i s f o r you to say what i t i s a b o u t — t o whom i t belongs. Theaetetus: C l e a r l y about me: i t belongs t o me. Stranger: Now take another ... "Theaetetus (whom I am to at t h i s moment) f l i e s " . Theaetetus: That too can only be described as belonging to me and about me. Stranger: And moreover we agree that any statement must have a c e r t a i n c h a r a c t e r . Theaetetus: Yes, Stranger: Then what s o r t of character can we a s s i g n to each of these? Theaetetus: One i s f a l s e , the other t r u e . Stranger: And the true one s t a t e s about you the things that are ( o r the f a c t s ) as they are. Theaetetus: C e r t a i n l y . Stranger: Whereas the f a l s e statement s t a t e s about you things d i f f e r e n t from the things that are, 44 Theaetetus: Yes. Stranger: And a c c o r d i n g l y s t a t e s things that are-not as being. Theaetetus: No doubt. Stranger: Yes, but things t h a t e x i s t , d i f f e r e n t from things t h a t e x i s t i n your case. For we s a i d that i n the case of everything there are many things that are and a l s o many that are not. Theaetetus: Quite so. Stranger: So the second statement I made about you, i n the f i r s t p l a c e , according to our d e f i n i t i o n of the na-ture of a statement, must i t s e l f n e c e s s a r i l y be one of the s h o r t e s t p o s s i b l e . Theaetetus: So we agreed j u s t now. Stranger: And second i t must be about something, Theaetetus: Yes. Stranger: And i f i t i s not about you, i t i s not about anything e l s e . Theaetetus: C e r t a i n l y . Stranger: And i f i t were about nothing, i t would not be a statement a t a l l ; f o r we pointed out t h a t there c o u l d not be a statement that was a statement about nothing. Theaetetus: Quite t r u e . Stranger: So what i s s t a t e d about you, but so that what i s d i f f e r e n t i s s t a t e d as the same or what i s not as what i s — a combination of verbs and names answering to th a t d e s c r i p t i o n f i n a l l y seems to be r e a l l y and t r u l y a f a l s e statement. (262e-3d) As i n the Euthydemus (284c) we are s a i d to speak f a l s e l y when we say 'what i s i n a c e r t a i n way and manner, and not as i t r e a l l y i s ' . I t i s f a l s e to say 'Socrates wishes C l e i n i a s destroyed', £.3., though of course both Socrates and C l e i n i a s e x i s t , and there are d e s t r u c t i v e d e s i r e s . Thus, f a l s e p r o p o s i t i o n s are resolve d i n t o elements, a l l of which have being; and yet 45 the p r o p o s i t i o n as a whole a s s e r t s what i s not. How f a r P l a t o has come from the Euthydemus! There Ctesippus i s forced to admit that 'no one says that which i s not*, (2B4c) the very t h i n g which i s denied i n the Sophist. We may measure P l a t o ' s achievement i n the Sophist a g a i n s t t h i s passage from the C r a t y l u s (385b-d)s Socrates: ... You would acknowledge th a t there i s i n words a true and a f a l s e ? Hermogenes: C e r t a i n l y . Socrates: And there are tru e and f a l s e p r o p o s i t i o n s ? Hermogenes: To be sure. Socrates: And a true p r o p o s i t i o n says that which i s , and a f a l s e p r o p o s i t i o n says that which i s not? Hermogenes: Yes, what other answer i s p o s s i b l e ? Socrates: Then i n a p r o p o s i t i o n there i s a tru e and f a l s e ? Hermogenes: C e r t a i n l y . Socrates: But i s a p r o p o s i t i o n true as a whole o n l y , and are the p a r t s untrue? Hermogenes: No, the pa r t s are true as w e l l as the whole. Socrates: Would you say the l a r g e p a r t s and not the smaller ones, or every p a r t ? Hermogenes: I should say that every part i s t r u e . Socrates: Is a p r o p o s i t i o n r e s o l v a b l e i n t o any par t s m a l l e r than a name. Hermogenes: No, that i s the s m a l l e s t . Socrates: Then the name i s a part of the true p r o p o s i -t i o n ? Hermogenes: Yes. Socrates: Yes, and a tru e p a r t , as you say. Hermogenes: Yes. 46 Socrates: And i s not the part of a falsehood a l s o a falsehood? Hermogenes: Yes. Socrates: Then, i f p r o p o s i t i o n s may be true and f a l s e , names may be true and f a l s e ? Hermogenes: So we must i n f e r . In t h i s passage, where names and p r o p o s i t i o n s are a s s i m i l a t e d , P l a t o f a l l s f a r s h o r t o f the s o p h i s t i c a t i o n he d i s p l a y s i n the Sophist. In h i s l a t e r work he knows th a t p r o p o s i t i o n s and names do not belong to the same semantic category. I t i s f a l l a c i o u s then to i n f e r t h a t , i f a p r o p o s i t i o n i s t r u e , i t s terms are as w e l l , j u s t as i t i s f a l l a c i o u s to i n f e r t h a t , i f men are numerous, Socrates i s numerous. I t i s a l s o f a l l a c i o u s to i n f e r t h a t , i f there i s something which every term i n a p r o p o s i t i o n names, there i s some-t h i n g i n a d d i t i o n to these things which the p r o p o s i t i o n i t s e l f names, i n the absence of which the p r o p o s i t i o n would be meaningless. Because p r o p o s i t i o n s are not names, we can a s s e r t what i s not the case ( i . . e . , f a l s e ) without thereby a s s e r t i n g that there i s a name which names nothing. In t h i s f a c t we have P l a t o ' s answer to the Sophist d e n i a l of falsehood. P l a t o i s attempting t o f i n d a place f o r falsehood w i t h i n an e s s e n t i a l l y Parmenidean metaphysic. He concedes t o Parmenides: One cannot l e g i t i m a t e l y u t t e r the.words, or speak of that which j u s t simply i s not; i t i s unthinkable, not to be spoken of or u t t e r e d or expressed. (238c) He apparently a l l u d e s to these words when he l a t e r says: So f a r as any co n t r a r y of the e x i s t e n t i s concerned, we have long ago s a i d good-by to the question wheth-er there i e such a t h i n g or not and whether any ac-count can be given of i t or none whatsoever. (258e) Neither Parmenides nor P l a t o admit that there i s a l e g i t i m a t e use f o r nega-47 t i v e e x i s t e n t i a l c l a i m s — i _ . e , , there i s never an occasion on which '...does not e x i s t * can be s u p p l i e d w i t h a term such that i t expresses a t r u e propo-s i t i o n . Thus, he says (257b): When we speak of " t h a t which i s not", i t seems that we do not mean something c o n t r a r y t o what e x i s t s but only something t h a t i s d i f f e r e n t . 'x i s not', when t r u e , i s always (on t h i s view) e l l i p t i c a l f o r 'x i s d i f f e r -ent from y' and i s never the expression of x's nonexistence. 1 Jowett there-for e remarks r i g h t l y that i n the Sophist P l a t o a n t i c i p a t e s Hegel's 'expla-nation of "not-Being" as d i f f e r e n c e ' , but e r r s i n t h i n k i n g t h i s d e s i r a b l e . To s a t i s f y h i s Parmenidean i n c l i n a t i o n s , P l a t o assumed th a t a l l terms (both s i n g u l a r and general) are non-empty, and thereby committed himself to the view t h a t n o n e g a t i v e e x i s t e n t i a l p r o p o s i t i o n i s t r u e . To understand why P l a t o should have acquiesced i n t h i s view (which i s c e r t a i n l y counter-i n t u i t i v e ) , l e t us t u r n b r i e f l y to h i s theory of Forms. 'Any discourse we can have', P l a t o says (259e), 'owes i t s existence to the weaving together of forms'. I understand t h i s to mean that language i s impossible without general expressions. The forms, according t o P l a t o , are the f e a t u r e s of r e a l i t y which answer to general e x p r e s s i o n s — j L . e . , they are p r o p e r t i e s . x I n ' L o g i c a l S t r u c t u r e of P l a t o ' s Sophist ', Review of metaphysics, v o l . 22 (1969), pp. 482-98, van Fraassen c i t e s these very passages (257b and 258e) to show that P l a t o i s not even attempting an a n a l y s i s of the e x i s t e n t i a l uses of 'to be', but i s merely e l u c i d a t i n g v a r ious incomplete u s e s — e . g . , *x i s [ o r i s n o t j i d e n t i c a l to y' and 'x i s [ o r i s not] F'. But P l a t o c l e a r l y i n -tends h i s a n a l y s i s t o be comprehensive—.i.e., t o cover 'to be* i n a l l i t s i n -t e l l i g i b l e uses. At 251c he says 'we want our argument to be addressed to a l l a l i k e who have ever had anything to say about e x i s t e n c e * . In the pas-sages van Fraassen c i t e s P l a t o has not set aside the complete use of 'to be', perhaps to be analysed on a f u t u r e occasion: he has scraped i t , on the grounds th a t i t i s d i s c r e d i t e d by the paradoxes introduced at 236e-9b. 2 J o w e t t , B,, t r , The Dialogues of P l a t o (Oxford: 1964), v o l . I l l , pp. 335-6. 46 In the Euthydemus (299e-300c) P l a t o says: Why, Socrates, s a i d Dionysodorus, d i d you ever see a b e a u t i f u l t h i n g ? Yes, Dionysodorus, I r e p l i e d , I have seen many. Were they other than the b e a u t i f u l , or the same as the b e a u t i f u l ? Now I was i n a great quandary a t having to answer t h i s q u e s t i o n , and I thought t h a t I was r i g h t l y served f o r having opened my mouth at a l l : I s a i d however, They are not the same as absolute beauty, but they have a beauty present i n each of them. Is not the honourable honourable, and the base base [asks Socrates]? That, he s a i d , i s as I please. And do you please? C e r t a i n l y . In t h i s passage the property of beauty i s d i s t i n g u i s h e d from the p a r t i c u l a r s which i n s t a n t i a t e t h i s property,* but both the property and the i n d i v i d u a l s i n s t a n t i a t i n g i t are s a i d to be b e a u t i f u l . That F-ness i t s e l f i s F i s even more c l e a r l y a s s e r t e d i n the Protagoras (330c-d) than i n the Euthydemus (300c): Is there such a t h i n g as j u s t i c e or not? I think there i s . So do I , he s a i d . W e l l , i f someone asked you and me, " T e l l me, you two, t h i s t h i n g that you mentioned a moment a g o — j u s t i c e — i s i t i t s e l f : j u s t or u n j u s t ? " I myself should answer t h a t i t was j u s t . Which way, would you vote? The same as you, he s a i d . Then we would both answer t h a t j u s t i c e i s of such a na-tu r e as to be j u s t ? He agreed. •Lin P l a t o ' s language we would say here that the Form of Beauty i s d i s -t i n g u i s h e d from the v a r i o u s i n d i v i d u a l t h i n g s 'partaking' i n i t . 49 I f , as seems extremely l i k e l y , 1 P l a t o b e l i e v e d t h a t every property i s an i n -stance of i t s e l f , then i n h i s view there w i l l be no u n i n s t a n t i a t e d p r o p e r t i e s . I f , moreover, every negative e x i s t e n t i a l c l a i m has the form 'there i s nothing which i s F', then we cannot a s s e r t the nonexistence of anything without con-t r a d i c t i n g P l a t o ' s metaphysics. Thus, h i s metaphysics prepares him very w e l l indeed f o r t h a t Parmenidean r e j e c t i o n of non-Being t o which, as we saw, he commits hims e l f a t 258e. I t must not be supposed t h a t P l a t o ' s metaphysics commits him merely t o the view t h a t there i s a property answering t o every general term, while a l -lowing him t o say t h a t such a property c o u l d be u n i n s t a n t i a t e d by any i n d i v i d u -a l . I t might seem, e.£., that the c l a i m 'there are no unicorns' means f o r P l a t o t h a t there are no i n d i v i d u a l unicorns, although there i s a property of being a unicorn. On the c o n t r a r y , more than r e a l i s m i s i n v o l v e d i n P l a t o ' s p o s i t i o n . For, i f we introduce the term 'being an i n d i v i d u a l u n i c o r n * , then the property expressed by these words w i l l be i n s t a n t i a t e d by an i n d i v i d u a l , i f by anything: and i n P l a t o ' s view i t i s i n s t a n t i a t e d by something. In t h i s case, we have a Form which i s a l s o an i n d i v i d u a l . The d i s t i n c t i o n bet-ween s i n g u l a r and general ( i n d i v i d u a l and property) i s thus obviated i n P l a t o ' s metaphysics. As A r i s t o t l e remarks (Metaphysics 1086bl0), ' i t followed [on P l a t o ' s p r i n c i p l e s ] t h a t u n i v e r s a l e and i n d i v i d u a l s were almost the same \ s o r t of t h i n g ' . In h i s commentary on the Sophist Taylor c l a i m s t h a t P l a t o ' s a n a l y s i s of f a l s e statement i s i n a p p l i c a b l e to p r o p o s i t i o n s about witches because on A F o r an i n t e r e s t i n g (though I t h i n k mistaken) c o n t r a r y i n t e r p r e t a t i o n , see: A l l e n , R,, ' P a r t i c i p a t i o n and P r e d i c a t i o n i n P l a t o ' s Middle Dialogues', as r e p r i n t e d i n : V l a s t o s , G., P l a t o I (New York: 1970), pp. 167-83. 50 t h a t a n a l y s i s e x i s t e n t i a l import i s assumed f o r a l l the terms i n t o which a p r o p o s i t i o n i s analysed. In P l a t o : The Sophist and the Statesman (London: 1961), p. 68, A. E. Taylor remarks: 'There i s c e r t a i n l y a f i e l d of enquiry here which P l a t o has l e f t unexplored'. As we suggested e a r l i e r , however, P l a t o intends h i s a n a l y s i s t o be comprehensive; and i n f a c t to those who, l i k e T a y l o r , would object t h a t there are no witches, he can answer t h a t the Form of Witchness i s i t s e l f a w i t c h , and th a t consequently the property i s not u n i n s t a n t i a t e d a f t e r a l l . P l a t o i s thus d e l i v e r e d from the T a y l o r - o b j e c t i o n by the assumption t h a t , f o r every general expression 'F-ness', there i s a property of F-ness which i s i n s t a n t i a t e d at l e a s t by i t s e l f . This assumption, however, leads to c o n t r a d i c t i o n . The property of not being a s e l f - i n s t a n c e , e.g_., i s a s e l f - i n s t a n c e i f and only i f i t i s not. I t f o l l o w s that not every general expression p i c k s out a s e l f - i n s t a n t i a t i n g property. Moreover, a s e l f - c o n t r a -d i c t o r y general e x p r e s s i o n , such as 'round-square', must express an unin-s t a n t i a t e d property. Consequently, both P l a t o ' s metaphysics and h i s analy-s i s of f a l s e statement are mistaken, 1 (Though the a n a l y s i s of f a l s e s t a t e -iThough I have s a i d nothing I would wish to r e t r a c t , I apologize f o r having d e a l t so b r i e f l y w i t h the theory of Forms. Allow me, then; here to r e f e r t o some l i t e r a t u r e , and make some remarks i n a n t i c i p a t i o n of p o s s i b l e o b j e c t i o n . Cornford, F,, P l a t o ' s Theory of Knowledge (London: 1967); Mo-r a v c s i k , J . , 'Being and Meaning the S o p h i s t ' , Acta P h i l o s o p h i c a Fennica, v o l . 14 (1962); Ross, W., P l a t o ' s theory of Ideas"(Oxford: 1963); v l a s t o s , G., 'The T h i r d Man Argument i n the Parmenides, as r e p r i n t e d i n : A l l e n , R., Studies i n P l a t o ' s Metaphysics (London: 1967). The assumption t h a t there i s a property (Form) answering t o every general expression seems questioned at 130c-e and then accepted at 135a-d of the Parmenides. According to Ross (p. 168) and Cornford (p. 293), however, i n the P o l i t i c u s (262) P l a t o declares hi m s e l f a g a i n s t negative Forms (B_.(J., the n o t - B e a u t i f u l ) . But, as Ross and Cornford themselves remark, t h i s i s c e r t a i n l y not the view taken i n the Sop- h i s t , the dialogue with which we are here p r i m a r i l y concerned. Moreover, t h e i r i n t e r p r e t a t i o n of the P o l i t i c u s i s d o u b t f u l ; see Moravcsik, p. 72. I r e f e r the reader t o V l a s t o s f o r the best account of the conceptual d i f f i c u l -t i e s i n the theory of Forms. 51 ment could i n f a c t be separated from i t s ( P l a t o n i c ) metaphysical background, and made more p l a u s i b l e , t h i s i s not a task I w i l l undertake. For by making tru e negative e x i s t e n t i a l claims i m p o s s i b l e , that a n a l y s i s as i t stands helps us to understand P l a t o ' s confused treatment of the copula; and here we are more concerned with being than w i t h falsehood.) 1.6 P l a t o and the Copula: A Commentary on the Sophist 250a-60d I f there i s one great i s s u e on which the s c h o l a r l y i n t e r p r e t a t i o n of the Sophist i s d i v i d e d , i t i s t h i s : Did P l a t o i n 250a-6d d i s t i n g u i s h the e x i s t e n t i a l and p r e d i c a t i o n a l uses of 'to be'? According to the majo r i t y o p i n i o n * (here r e j e c t e d ) , he d i d ; according to the m i n o r i t y o p i n i o n 2 (here adopted), he d i d not. This i s a s u b s t a n t i a l dispute which cannot be s e t t l e d merely by attend-in g to P l a t o ' s syntax. S y n t a c t i c a l l y , an e l l i p t i c a l occurrence of '^Tvs^' i n i t s incomplete use i s i n d i s t i n g u i s h a b l e from a n o n - e l l i p t i c a l occurrence of *^rVo(L' i n i t s complete use. The s i t u a t i o n i s the same i n E n g l i s h . 'I am', e_.£., depending upon co n t e x t , may be (1) short f o r (say) * I am wealthy' or (2) an expression of personal e x i s t e n c e , as i n Descartes's famous argument. The context f o r P l a t o ' s use of i n the Sophist i s a c e r t a i n body of argument; and i t i s how we construe t h a t body of argument which determines whether P l a t o appears i n places to d i s t i n g u i s h the e x i s t e n t i a l and p r e d i c a -*For the majo r i t y o p i n i o n see the f o l l o w i n g : A c k r i l l , J . , 'Plato and the Copula', as r e p r i n t e d i n : V l a s t o s , G., ed., P l a t o I (New York: 1970), pp. 210-2; Cornford, F., P l a t o ' s Theory of Knowledge (London: 1967), p. p. 296; Moravcsik, J . , 'Being and Weaning i n the Sophist' ( c i t e d i n f t n 1, p. 50), pp. 42 and 51; Shorey, P., What P l a t o S a i d ( C h i c a g o : 1933), p. 298; Ta y l o r , A., P l a t o : The Sophist and the Statesman (London: 1961), pp. 81-2 2For the m i n o r i t y o p i n i o n , see the f o l l o w i n g : Malcolm, J . , 'Plato's A n a l y s i s of To ov and To i n the Sop h i s t ' , Phronesis, v o l . 12 (1967), pp. 130-45. Runciman, W . T P l a t o ' s L a t e r Eplstemoloqy (Cambridge: 1962), pp. 84-5. 52 t i o n a l uses of 'to be*. To r e f u t e the view that i n the Sophist P l a t o d i s t i n g u i s h e d the e x i s t e n -t i a l and p r e d i c a t i o n a l uses of 'to be', I cannot do b e t t e r than to c i t e Run-ciman, as f o l l o w s : 1 [ P l a t o ' s ] f a i l u r e to d i s t i n g u i s h the e x i s t e n t i a l sense as such i s c l e a r l y demonstrated by the argument of 256d-e, which runs as f o l l o w s : S t r . For the nature of D i f f e r e n c e makes each one of a l l the kinds d i f f e r e n t from Being i^o CM) and the r e f o r e something that i s not (ottfc  \5y*)> and on t h i s p r i n c i p l e we s h a l l be r i g h t i n speaking of a l l of them as things which i n t h i s sense "are not" (obK Qvtay)* and a l s o as t h i n g s which, s i n c e they partake i n Being ^ , UfrTcVet to*? D V f o f ) . have being and are (61V0U. Th. So i t seems. S t r . So about each of the Forms there i s much that i t i s and a countless number of t h i n g s t h a t i t i s not. This passage [continues Runciman] i s taken by both Corn-f o r d and A c k r i l l to be r e f e r r i n g at 256e3 to the e x i s t e n -t i a l sense of t~T\/o(,\. But that the phrase l^fcT^A^L TC$  fty-rpr cannot here be the philosopher's f o r m u l a t i o n of the e x i s t e n t i a l use i s shown by the Stranger's next r e -mark. For t h i s makes i t c l e a r t h a t i t i s the c o p u l a t i v e sense which i s covered by the phrase. The Stranger would be t a l k i n g nonsense i f he s a i d that f o r each one of the Forms "there are many things that i t e x i s t s " or " i t i s ex i s t e n c e i n many respec t s " . I t i s i n any case not the e x i s t e n c e of the Forms which r e q u i r e s t o be demonstrated, but the f a c t that they can both be and not be i n the co-p u l a t i v e sense. What the Stranger goes on to say (257a) i s t h a t Being CT^^A/) must ther e f o r e be marked o f f from the other k i n d s . This Is t r a n s l a t e d by Cornford " E x i s -tence". But from the previous sentence i t i s c l e a r t h a t t h i s i s not existence but the Being which each of the. Forms can be i n many res p e c t s . In f a c t , throughout the d i s c u s s i o n there i s an a s s i m i l a t i o n to each other of the e x i s t e n t i a l and c o p u l a t i v e senses. r1nH P o £ir£r J L r rF EP*»temoloqy> PP. 84-5. (The quotation which f o l l o w s i n -cludes a t r a n s l a t i o n from the Sophist by Runciman, not Cornford.) 53 Having warned the reader that there are various c o n f l i c t i n g ways of viewing the Sophist, we w i l l now adopt the c r i t i c a l p e r s p e c t i v e of Runciman and ana-l y s e the argument i n the Sophist a c c o r d i n g l y . For a l l h i s t a l k against non-Being, P l a t o recognizes that there i s a sense i n which we t a l k about what does not e x i s t . In a d d i t i o n to such prima  f a c i e falsehoods as 'Socrates i s P e r s i a n * , there are such prima f a c i e t r u t h s as 'Heracles does not e x i s t ' . But, i f we can say nothing about what does not e x i s t , then presumably even t h i s p r o p o s i t i o n would be meaningless, and we would not be able to d i s t i n g u i s h the nonexistent Heracles from what e x i s t s . For Heracles would not have a cha r a c t e r i n terms of which he could be iden-t i f i e d . How then c o u l d we know he does not e x i s t ? From such c o n s i d e r a t i o n s P l a t o seems t o have concluded that t h i n g s which do not e x i s t cannot be de-v o i d of character (see Parmenides 160c-2d). I f they were, observes P l a t o (238c), then we could a t t r i b u t e n e i t h e r p l u r a l i t y to 'things that are not* nor u n i t y to 'that which i s not'. In the oft-quoted fragment which I take as h i s fundamental premise, however, Parmenides himself speaks of 'things which are not', and thus v i o l a t e s h i s own p r o h i b i t i o n . I t i s c l e a r then t h a t we do a t t r i b u t e c h a r a c t e r i s t i c s (e.g_., s i n g u l a r i t y and p l u r a l i t y ) to the nonexistent. Thus, P l a t o says (25Bc), '"That which i s not" unquestiona-b l y i s a t h i n g that has a nature of i t s own*. We s h a l l understand the s u p p o s i t i o n t h a t the nonexistent 'has a nature of i t s own' to mean t h a t , f o r some empty expression <X> some p r o p o s i t i o n of the form (X i s 8 i s t r u e — . i . e . , to mean that 'Pegasus i s w i n g l e s s ' (or some other such p r o p o s i t i o n ) i s t r u e , though Pegasus does not e x i s t . The suppo-s i t i o n , thus understood, c o n t r a d i c t s the f o l l o w i n g : (3) (Vx)(-Ex - - E x ) , 54 which, as we saw i n s e c t i o n 1.2, i s e n t a i l e d by the fundamental Parmenidean premise: (1) -4Qx)-Ex. Thus, f o r Pl a t o to e s t a b l i s h that 'the nonexistent* has a nature of i t s own--. i . e . , f o r him to e s t a b l i s h the d e n i a l of ( 3 ) — h e must r e f u t e ( 1 ) , from which (3) f o l l o w s . (1) i m p l i e s that there i s n ' t anything which does not e x i s t . To argue aga i n s t i t i n any s t r a i g h t f o r w a r d f a s h i o n , t h e r e f o r e , one must argue that there e x i s t t h i n g s which do not e x i s t . This does not seem a very promising l i n e of argument, nor one which anybody would f o l l o w . But a f t e r c i t i n g the saying of Parmenides 'never s h a l l t h i s proved, that t h i n g s that are not a r e ' , A r i s t o t l e then adds that to avoid Parmenides's r e s u l t s c e r t a i n (unnamed) t h i n k e r s 'thought i t necessary to prove t h a t t h a t which i s not i s * . (Wetaphy-s i c a 1089a3-7) This i s i n f a c t p r e c i s e l y the course which P l a t o f o l l o w s : We s h a l l f i n d i t necessary i n se l f - d e f e n s e ... to e s t a -b l i s h by main f o r c e t h a t what i s not, i n some respect has being. ... (241d) A f t e r an argument purporting t o r e v e a l 'the r e a l c h a r a c t e r of "not-being"' (258e), P l a t o concludes: '"What i s not' has been found t o have i t s share i n e x i s t e n c e * . The argument by which t h i s absurd c o n c l u s i o n i s reached i s of consi d e r -able h i s t o r i c a l i n t e r e s t s i n c e j i t e x p l o i t s the e x i s t e n t i a l / p r e d i c a t i o n am-b i g u i t y of 'to be*. In the course of h i s counter-argument against Parmenides, P l a t o examines s e v e r a l negative predicates—e.£., ' n o t - b e a u t i f u l * and 'not-t a l l * . He r i g h t l y concludes t h a t what i s n o t - b e a u t i f u l or n o t - t a l l e x i s t s , and has a nature of i t s own. From t h i s unexceptional remark,! however, he llf t h i s remark were intended only as a r e f u t a t i o n of the so p h i s t view th a t 'a i s not-F* e n t a i l s 'a does not e x i s t ' and not a l s o as a step i n the r e f u t a t i o n of Parmenides, i t would not lead P l a t o i n t o t r o u b l e . 55 then makes the i l l i c i t step to *uie have shown that t h i n g s that are [do not e x i s t ] , are [do e x i s t ] ...'. (258e) In f a c t , however, a l l he has shown i s t h a t t h i n g s t h a t are n o t ( - F ) , are ( e x i s t ) . T h i s , however, was never i n doubt f o r Parmenides, 1 and does not imply t h a t anything both e x i s t s and does not e x i s t . The c o n t r a d i c t o r y of (1) t h e r e f o r e remains undemonstrated. R e a l i z i n g the a b s u r d i t y of '(Jx)^*'* P l a t o t r i e s to make i t out that he i s not r e a l l y a s s e r t i n g t h a t there e x i s t s something which does not e x i s t , (see 258e-9a) 'When we speak of " t h a t which i s not",' he says (257b), 'we do not mean something contrary to what e x i s t s but only something that i s d i f -f e r e n t ' . But at 256d-e he makes i t q u i t e c l e a r that he intends to c o n t r a - d i c t Parmenides's c l a i m 'Never s h a l l t h i s be proved, that t h i n g s that are not, are*. Dn our i n t e r p r e t a t i o n of t h i s c l a i m (which as we saw i s supported by P l a t o ' s Parmenides), P l a t o must a s s e r t '(3x)-Ex* I f he i s to c o n t r a d i c t t h i s c l a i m . Thus, P l a t o ' s remarks are worthless as a r e p l y to Parmenides i f we construe those remarks as applying only to 'what i s not-F' (the D i f f e r e n t ) and not a l s o 'what i s not' i n Parmenides's sense (the Nonexistent). The t r u t h of the matter i s t h a t , when P l a t o i s t r y i n g to make h i s t h e s i s sound p l a u s i b l e (even to h i m s e l f ) , he uses the p r e d i c a t i o n a l sense of 'to be'} and then, when he i s t r y i n g to r e f u t e Parmenides, he s h i f t s ( u nconsciously, I t h i n k ) to the e x i s t e n t i a l sense. On our i n t e r p r e t a t i o n , then, P l a t o more than Parmenides i s g u i l t y of the confusion he i s a l l e g e d to have recognized and exposed. In ray. view P l a t o made, these s e r i o u s mistakes i n handling the concept i..e_., on our i n t e r p r e t a t i o n , but r e c a l l the K i r k and Raven i n t e r p r e t a -t i o n . Perhaps they would be i n c l i n e d to t r e a t P l a t o ' s argument more sympathi-c a l l y than I; most commentators are. 56 of e x i s t e n c e because he c o n f l a t e d the o n t o l o g i c a l paradoxes of Parmenides w i t h the e p i s t e m o l o g i c a l puzzles of the s o p h i s t s . When we say * I know*, t h i s i s always e l l i p t i c a l f o r 'I know x'. The absolute c o n s t r u c t i o n *.,,know(s)* i s p a r a s i t i c a l on the incomplete c o n s t r u c t i o n '...know(s) '. In the Euthy- demus, as we saw, P l a t o used t h i s f a c t to r e f u t e the so p h i s t contention t h a t , i f a man knows anything, he knows everything. Owing to the incomplete charac-t e r of 'to know*, the p r o p o s i t i o n 'Socrates knows [ x ] and does not know £y3'» e.£., i s not s e l f - c o n t r a d i c t o r y — i _ , e _ . , Socrates can be both knowing and un-knowing. Now, j u s t as he re f u t e d the s o p h i s t s , so P l a t o hopes to r e f u t e Par-menides. J u s t as a man may know some things and not ot h e r s , so he may be some things and not others. Hence: (a) Things both are and are not. P l a t o t h i n k s (a) c o n t r a d i c t s the Parmenidean c l a i m t h a t there are no things which are not. In order to make (a) t r u e , however, we must understand i t s occurrences of 'to be' p r e d i c a t i o n a l l y , as i n *a man may be [ F ] and not be [ G ] ' . When (a) i s thus understood, however, i t does not c o n t r a d i c t the Parmenidean c l a i m . P l a t o r e f u t a t i o n t h e r e f o r e f a i l s . The reason f o r t h i s f a i l u r e , of course, i s th a t 'to be', understood e x i s t e n t i a l l y , i s l i k e 'to be g o l d ' or •to be a man' r a t h e r than 'to know* or 'to f a t h e r * : Socrates, £.£., can no more both e x i s t and not e x i s t than he can both be a man and not be a man. This i m p l i e s that *x i s ' , understood e x i s t e n t i a l l y , i s not e l l i p t i c a l f o r *x i s ', where ' • i s to be f i l l e d i n with some p r e d i c a t e — s a y , ' e x i s -t e n t ' , * Existence then i s not a r e l a t i o n which, l i k e fatherhood, a t h i n g But see Quine: 'We may indeed take "(3x)(x = a ) " as e x p l i c a t i n g "a e x i s t s " . John Bacon has noted a n i c e p a r a l l e l here: j u s t as "a e a t s " i s short f o r "a eats something", so "a i s " i s short f o r "a i s something",' •Existence and Q u a n t i f i c a t i o n * , as contained i n M a r g o l i s , J . , ed,, Fact and  Existence (Toronto: 1968), p. 3. 57 may bear to some things and not others.* I t i s f o r t h i s reason that 'to be*, understood e x i s t e n t i a l l y , r e s i s t s a n a l y s i s i n terms of the r e l a t i o n a l verb •to be d i f f e r e n t * . 1.7 The Greek Concept of Being Let us r e t u r n now to Kahn's view that 'the Greeks d i d not have our notion of being*. As we have understood P l a t o , he wrongly a s s i m i l a t e s the e x i s t e n t i a l (complete) and p r e d i c a t i o n a l (incomplete) uses of 'to be*. According to Kahn, however, the s y n t a c t i c a l d i s t i n c t i o n between the incomplete and complete c o n s t r u c t i o n s f o r 'to be' i s o f t e n t r e a t e d by Greek authors 'as of no consequence whatever'.2 But, as W i l l complained, E n g l i s h w r i t e r s o f t e n do the same t h i n g . Though Kahn doubts the firmness of the complete/incomplete d i s t i n c t i o n even i n E n g l i s h , I t h i n k fflill r i g h t l y thought i t a mistake to neglect the d i s t i n c t i o n . There-f o r e , I must understand Kahn's poi n t to be that i t i s p e r m i s s i b l e to do i n Greek what i t i s not p e r m i s s i b l e to do i n E n g l i s h — v i z . , a s s i m i l a t e the com-p l e t e and incomplete c o n s t r u c t i o n s of the verb f o r being. If so, then P l a t o ' s argument cannot be f a l l a c i o u s i n q u i t e the way I say i t i s ; and the Greeks may w e l l have had a concept of being d i f f e r e n t from ours. lAlthough i t makes no sense to say 'a e x i s t s F' or 'a does not e x i s t F', i t does make sense to say 'a e x i s t s at t ' or 'a does not e x i s t ajt t ' , Thus, Montague holds i n The Ways of Knowing (London: 1925), pp. 110-1, that e x i s - , tence i s hot a property but a r e l a t i o n between an i n d i v i d u a l and a moment. From t h i s p e r s p e c t i v e the same i n d i v i d u a l could both e x i s t [ a t t j and not e x i s t [ a t t ' J . But we w i l l ignore t h i s way of c o n t r a d i c t i n g Parmenides's c l a i m t h a t nothing can both e x i s t and not e x i s t * except to remark t h a t he, t h i n k i n g what e x i s t s to be sem p i t e r n a l , would not allow t h a t something which e x i s t s a t some time could f a i l t o e x i s t a t some other time. 2'The Greek Verb' "to be" and the Concept of Being", pp. 249-50. ^He even says ( w i t h what p l a u s i b i l i t y I leave the reader to judge): 'fflr. James fflill was, I b e l i e v e , the f i r s t who d i s t i n c t l y c h a r a c t e r i z e d the ambiguity [of "to be " J , and pointed out how many e r r o r s i n the recei v e d sys-tems of philosophy i t had to answer f o r ' . A System of L o g i c , pp. 50-1 58 But, i f the Greeks had a d i f f e r e n t concept of being and d i d not make a f i r m s y n t a c t i c a l d i s t i n c t i o n between the complete and incomplete construc-t i o n s of 'gtwiCt we should expect to see these d i f f e r e n c e s r e f l e c t e d i n other Greek authors besides P l a t o . When we turn to A r i s t o t l e , however, we f i n d the appropriate d i s t i n c t i o n c l e a r l y made: [ F a l l a c i e s ] that depend on whether an expression i s used a b s o l u t e l y or i n a c e r t a i n respect and not s t r i c t l y , oc-cur whenever an expression used i n a p a r t i c u l a r sense i s taken as though i t were used a b s o l u t e l y , e.g. i n the argu-ment " i f what i s not i s the obje c t of an o p i n i o n , then what i s not i s " : f o r i t i s not the same t h i n g "to be x" and "to be" a b s o l u t e l y . Or again "What i s , i s not, i f i t i s not a p a r t i c u l a r k i n d of being, e . g . i f i t i s not a man". For i t i s not the same t h i n g "not to be x" and "not to be" a t a l l : i t looks as i f i t were, because of the closeness of the expression, i.e_. because " t o be x" i s but l i t t l e d i f f e r e n t from "to be" and "not to be x" from "not t o be". (De S o p h i s t i c i s E l e n c h i s 166b37-8a7) Jus t as there were Greek t h i n k e r s who wrote about existence as we do, so there were non-Greek t h i n k e r s who wrote about existence as P l a t o d i d . Fredegisus of Tours ( d i e d 819), e.g., wrote: 1 The s i g n i f i c a t i o n of anything i s something that i s . But "nothing" s i g n i f i e s something. Therefore, the s i g n i f i c a t i o n of "nothing" i s something that i s , i..e., an e x i s t i n g t h i n g . Thus, P l a t o was not alone i n h i s odd b e l i e f that the nonexistent has ' i t s share i n e x i s t e n c e * . Theology sometimes forced a c u r i o u s ontology upon C h r i s t i a n philosophers, s i n c e they had to account f o r the appearance of e v i l In some s u i t a b l y pious way. E v i l , according to many C h r i s t i a n p h i l s o p h e r s , i s a ' p r i v a t i o n ' and, as such, does not e x i s t . But the world seems to abound i n these ' p r i v a t i o n s ' , the o n t o l o g l c a l s t a t u s of which i s rat h e r mysterious. Perhaps with these n t l l XAs c i t e d (without d i s a p p r o v a l , i n c i d e n t l y ) i n Rescher, N., Essays i n P h i l o s o p h i c a l A n a l y s i s ( P i t t s b u r g h : 1969), p. 84. " 59 words Boethius c l e a r s up the mystery:* ...Anyone [who turns to v i c e ] loses not only h i s strength but h i s very being. ... Perhaps i t may s t r i k e some as strange to say that e v i l men do not e x i s t , e s p e c i a l l y s i n c e they are so numerous; but i t i s not so strange. For I do not deny that those who are e v i l are e v i l } but I do deny that they are, i n the pure and simple sense of the term. For j u s t as you may c a l l a cadaver a dead man, but cannot c a l l i t simply a man, so I would concede that v i c i o u s men are e v i l , but I cannot say, i n an absolute sense, that they e x i s t . For a t h i n g i s which maintains i t s place i n nature and a c t s i n accord with i t s nature. Whatever f a i l s to do t h i s l o s e s the existence which i s proper to i t s nature. But you argue that e v i l men are capable of a c t i o n . I w i l l not deny, but such c a p a b i l i t y i s the product of weakness, not of s t r e n g t h . For they can do e v i l a c t s which they could not have done i f they had been able to remain capable of good. And that p o s s i b i l i t y of doing e v i l shows c l e a r l y t h a t they can do nothing. For, i f our e a r l i e r c o n c l u s i o n that e v i l i s nothing s t i l l stands, i t i s c l e a r t h a t the wicked can do nothing s i n c e they do only e v i l . Boethius's s u p p o s i t i o n that someone co u l d be something (e,£., e v i l ) without e x i s t i n g may sound s i l l y and unworthy of c o n s i d e r a t i o n . But i n 'Coqito, Ergo Sum: Inference or Performance?', P h i l o s o p h i c a l Review, v o l . 71 (1962), pp. 3-22, H i n t i k k a (who i s no f o o l ) o b j e c t s to the Coglto on the grounds that Descartes, l i k e Hamlet, could be t h o u g h t f u l without e x i s t i n g . I suppose t h a t someone could combine the a b s u r d i t i e s of F r e j e g i s u s w i t h those of Boethius, and conclude that e v i l , s i g n i f y i n g nothing, both e x i s t s (Fredegisus's view) and does not e x i s t (Boethius's view). This combination would have the dubious merit of c o n t r a d i c t i n g the Parmenidean premise that -(3x)-Ex. But the t r u t h i s , though others have shared P l a t o ' s confusions, Greek and non-Greek a l i k e can see that i t i s a mistake to t r e a t 'nothing' as Boethius, The Consolutions of Philosophy (New York: 1962), pp. 79-80. 60 as though i t were the name of something. 1 To my knowledge only one contemporary philosopher has, without hedging, a f f i r m e d the d e n i a l of '-(^xJ-Ex*, and i t i s Nicholas Rescher, who says: ' I propose now to adduce reasons f o r r e j e c t i n g the statement that a l l things 2 e x i s t ' , and proceeds to argue t h a t there e x i s t things which do not e x i s t . Such courage i s not often shown i n p h i l o s o p h i c a l argument; and Rescher him-s e l f , i t would seem, came to repent of I t . For, when he r e p r i n t e d t h i s es-say, he modified h i s c l a i m to the f o l l o w i n g : '...one must r e j e c t - - i n an un-q u a l i f i e d form, a t any r a t e — t h e t h e s i s t h a t a l l t h i n g s e x i s t ' . 3 Perhaps, i f he r e p r i n t s i t again, he w i l l t e l l us what the q u a l i f i c a t i o n i s . i , . _ _ Most philosophers who have been disposed to deny *-(3x)-Ex* have been more s o p h i s t i c a t e d than Rescher. To avoid o u t r i g h t c o n t r a d i c t i o n , they have m u l t i p l i e d the senses of 'existence'. Thus, we f i n d E. E* Jones s a y i n g : * ... In order to predicate non-existence i n one sphere i t i s necessary to p o s t u l a t e e x i s t e n c e i n another. I f I say (1) Dragons are non-existent, or (2) Round-squares are impossible, I do of course mean to imply the non-existence and im-In t h i s connection consider C a r r o l l ' s Through the Looking-Glass (New York: 1966), pp. 80-1: ' " I see nobody on the road", s a i d A l i c e . " I only wish I had such eyes", the King remarked i n a f r e t f u l tone. "To be able to see Nobody! and at t h a t distance too! Why, i t ' s as much as I can do to see r e a l people by t h i s l i g h t ! " . * ^Rescher, N.» 'On the Logic of Existence and Denotation', P h i l o s o p h i c a l  Review, v o l . 68 (1959), p. 160. 3Rescher, N., Topics i n P h i l o s o p h i c a l Logic (Holland: 1968), p. 141. 4 J p. 454. 4 o n e s , E., 'On the Nature of L o g i c a l Judgment', Mind, v o l . 3 (1893), 61 p o s s i b i l i t y of Dragons and Round-squares r e s p e c t i v e l y — but i t i s non-existence and I m p o s s i b i l i t y i n a c e r t a i n region t h a t i s n e i t h e r all-embracing nor even that to which I p r i m a r i l y r e f e r . Unless I r e f e r to something, e x i s t e n t somehow, i n some r e g i o n , what i s i t of which I p r e d i c a t e non-existence or i m p o s s i b i l i t y ( w i t h i n a given r e g i o n ) , what i s i t which I exclude from those regions to which "non-existent" and " i m p o s s i b l e " r e f e r ? Jones r e j e c t s the a b s o l u t e l y nonexistent and a b s o l u t e l y impossible. To say th a t something does not e x i s t or i s im p o s s i b l e , i n her view, i s j u s t to say tha t i t i s d i f f e r e n t from anything e x i s t i n g or p o s s i b l e ' i n a c e r t a i n r e g i o n ' . In connection w i t h t h i s view (which i s c e r t a i n l y reminiscent of P l a t o ' s treatment of negative e x i s t e n t i a l s ) , there are c e r t a i n obvious d i f f i c u l t i e s . The twin notions of ' e x i s t i n g i n a c e r t a i n r e g i o n ' and of 'being impossible i n a c e r t a i n region* are l e f t u n c l e a r . I t i s true t h a t , when we say 'Snakes do not e x i s t i n I r e l a n d ' or 'Honest p o l i t i c s are impossible i n the United S t a t e s ' , we leave open the p o s s i b i l i t i e s of snakes e x i s t i n g elsewhere and of honest p o l i t i c s being p o s s i b l e elsewhere. But do we commit ourselves to the exi s t e n c e of snakes outside of Ir e l a n d or to the p o s s i b i l i t y of honest p o l i -t i c s outside the United S t a t e s , when we say these t h i n g s ? C e r t a i n l y not. For, when we say t h a t unicorns do not e x i s t , e.g., we mean th a t they do not e x i s t anywhere; and, when we say that round-squares are im p o s s i b l e , we mean that they are impossible everywhere. In the P r i n c i p l e s of mathematics (London: 1903), pp. 449-50, R u s s e l l adopts a p o i n t of view s i m i l a r to that of Jones: Being i s that which belongs to every conceivable term, to every p o s s i b l e object of t h o u g h t — i n short to every-t h i n g that can p o s s i b l y occur i n any p r o p o s i t i o n . ... Numbers, the Homeric gods, r e l a t i o n s , chimeras and four dimensional spaces a l l have being, f o r i f they were not e n t i t i e s of a k i n d , we could make no p r o p o s i t i o n s about them. Thus being i s a general a t t r i b u t e of e v e r y t h i n g , and t o mention anything i s to show t h a t i t i s . 62 E x i s t e n c e , on the c o n t r a r y , i s the p r e r o g a t i v e of some only amongst beings. ... This d i s t i n c t i o n i s e s s e n t i a l , i f we are ever to deny the existence of anything. For what does not e x i s t must be something, or i t would be meaningless to deny i t s e x i s t e n c e . The reasoning i n these passages from Jones and R u s s e l l r e f l e c t s our confused i n t u i t i o n s about the nonexistent. On the one hand, we are i n c l i n e d to think t h a t there i s n ' t anything which doesn't e x i s t , s i n c e what e x i s t s i s a l l there i s . On the other hand, we are i n c l i n e d to t h i n k that there are l o t s of t h i n g s which do not e x i s t — u n i c o r n s , e_.£.. To s a t i s f y these c o n t r a d i c -t o r y i n c l i n a t i o n s , ' e x i s t s ' i s given two meanings. According to the f i r s t , 'to mention anything i s to show th a t i t i s * . According to the second, how-ever, i t i s not the case t h a t e v e r y t h i n g , i n c l u d i n g u n i c o r n s , e x i s t s . By a s s i g n i n g the f i r s t meaning to *"3' and the second to 'E*, we are able to con-t r a d i c t Parmenides without c o n t r a d i c t i n g ourselves as w e l l , which i s of course what P l a t o hoped t o do i n a s s e r t i n g ' ( j x J - E x ' . I t must be admitted, I t h i n k , that the views of P l a t o and h i s f e l l o w t r a v e l l e r s have very l i t t l e to recommend them. But i t must a l s o be admitted that such terms as 'unicorns' occur i n s t r a i g h t f o r w a r d , i n t e l l i g i b l e d i s -course. The semantic t h e o r i e s of the philosophers considered thus f a r , how-ever, simply were inadequate t o e x p l a i n our employment of empty expressions; and so a r b i t r a r y extensions were assigned ( i n another 'region') t° such ex-pressions as 'unicorn', 'round-square', e t c . . 'A p r o p o s i t i o n * says R u s s e l l , ' i s about the s u b j e c t , and the p r e d i c a t e i s what i s s a i d about the s u b j e c t ' . * Given '(\/x)(-Ex •* -Gx)', however, no p r e d i c a t e i s true of a nonexistent sub-j e c t . Therefore, i n R u s s e l l ' s sense we cannot frame p r o p o s i t i o n s about what •••Russell, B., 'On Weaning and Denotation*. This unpublished paper was w r i t t e n between the P r i n c i p l e s (1903) and 'On Denoting' (1905). 63 does not e x i s t . From the f a c t that there i s i n d i s p u t a b l y a sense i n which we do frame p r o p o s i t i o n s about unicorns ( i f only to deny that there are any), R u s s e l l I n f e r r e d i n the P r i n c i p l e s t h a t there must be a sense i n which u n i -corns e x i s t . This i s the o r i g i n of h i s much lamented o n t o l o g i c a l e x t r a v a -gance i n the P r i n c i p l e s . Thus, the acceptance of '(yx)(-Ex "* -Gx)', coupled w i t h c e r t a i n assump-t i o n s governing what i t i s to t a l k about something, forced philosophers i n -to a d i f f i c u l t p o s i t i o n . They had to argue e i t h e r that unicorns, £.£., do e x i s t ( i n a sense, of c o u r s e ) , or e l s e t h a t t a l k which appears to be about unicorns i s n ' t r e a l l y about them at a l l . The philosophers i n the P l a t o n i c camp accept the f i r s t horn of the dilemma. Other ph i l o s o p h e r s , however, rea-soning from the same b a s i c premises, accept the second horn. That i s to say, accepting the Parmenidean p r i n c i p l e 'tyx)(-Ex -»-Gx)', they reason: 1 By the word paraphrasis may be designated that s o r t of e x p o s i t i o n which may be affo r d e d by transmuting i n t o a p r o p o s i t i o n , having f o r i t s subject some r e a l e n t i t y , a p r o p o s i t i o n which has not f o r i t s subject any other than a f i c t i t i o u s e n t i t y . Nothing has no p r o p e r t i e s . A f i c t i t i o u s e n t i t y , being, as t h i s i t s name i m p o r t s — b e i n g , by the very s u p p o s i t i o n — a mere nothing, cannot of i t s e l f have p r o p e r t i e s : no p r o p o s i t i o n by which any property i s a s c r i b e d to i t can, t h e r e f o r e , be, i n i t s e l f and of i t s e l f , a true one? nor, t h e r e f o r e , an i n s t r u c t i v e one. Whatsoever of t r u t h i s capable of belonging to i t cannot belong to i t i n any character other than t h a t of the r e p r e s e n t a t i v e — o f the intended and supposed equivalent and adequate succedaneum— of some p r o p o s i t i o n having f o r i t s s u b j e c t some r e a l e n t i t y . 2 This p o i n t of view i s nea t l y encapsulated i n Broad's remark: Dragons do not e x i s t ... cannot be about dragons; f o r -••Ogden, C.> ed., Bentham's Theory of F i c t i o n s (London: 1932), p. 86. 2 B r o a d , C., R e l i g i o n , Philosophy and P s y c h i c a l Research (New York: 1953), p. 182. 64 there w i l l be no such things as dragons f o r i t to be about. Bentham and Broad are thus l a t t e r - d a y Parmenideans because, l i k e Parmeni-des, they hold that we cannot even t a l k about what does not e x i s t . Rather than a r t i f i c i a l l y i n f l a t e the c l a s s of e x i s t e n t objects (as P l a t o and h i s f e l l o w t r a v e l l e r s would do) , these philosophers r e s o r t t o l i n g u i s t i c para-phrase. In 1905 R u s s e l l s h i f t e d from the P l a t o n i s t camp to the 8entham-Broad camp. The Theory of D e s c r i p t i o n s i s the device by which t h i s t r a n s i t i o n was achieved. But we are g e t t i n g ahead of our s t o r y . Before we can accept some p r o p o s i t i o n A as g i v i n g the sense of 'Dragons do not e x i s t ' , we must have an adequate f e e l i n g f o r the unanalysed sense of 'Dragons do not e x i s t ' . Otherwise, we w i l l not be able t o judge the extent to which the a n a l y s i s f i t s the o r i g i n a l p r o p o s i t i o n . But the semantic assump-t i o n s common tb the l a t t e r - d a y Parmenideans and the P l a t o n i s t s seem to sug-gest t h a t 'Dragons do not e x i s t * i s sheer nonsense, and therefore t h a t our p r e - t h e o r e t i c a l grasp of t h i s p r o p o s i t i o n i s i l l u s o r y . How then can the l a t -t e r day Parmenideans f i n d a p r o p o s i t i o n which means the same as one which, on t h e i r p r i n c i p l e s , means nothing a t a l l ? Their program i s no more free of d i f f i c u l t y than t h a t of the P l a t o n i s t s . Admittedly, there are some s t r i k i n g d i f f e r e n c e s i n the views surveyed a l l too q u i c k l y i n t h i s s e c t i o n . Yet we have r e l a t e d these views to a f i x -ed set of p r e s u p p o s i t i o n s , which seem to e x p l a i n both the d i f f e r e n c e s and the s i m i l a r i t i e s i n the p h i l o s o p h i c a l s p e c u l a t i o n concerning e x i s t e n c e . This suggests t h a t there i s a c e n t r a l core of i n t u i t i o n common to philosophers i n the Western t r a d i t i o n a t l e a s t — a n d , t h e r e f o r e , that Kahn i s wrong i n h i s c l a i m t h a t the Greeks had a concept of exis t e n c e d i f f e r e n t from ours. Had he been r i g h t i n t h i s , perhaps the roo t s of our own philosophy would have 65 been i n a c c e s s i b l e to us. 1.8 Conclusion Most commentators, u n l i k e o u r s e l v e s , seem to think t h a t Parmenides was l e d to h i s b i z a r r e conclusions simply by overloo k i n g a small p o i n t (the ambiguity of 'to be') which was l a t e r detected by P l a t o and set r i g h t by him. To t h i s view I can only say the problems surrounding e x i s -tence must be s u f f i c i e n t l y s u b t l e t h a t these commentators have missed them a l t o g e t h e r , Jowett, , says:* The problem of "not-being" appears to us to be one of the most unreal d i f f i c u l t i e s of ancient philosophy. ... How could such a [problem] a r i s e at a l l , much l e s s be-come of ser i o u s importance? But we have seen that P l a t o ' s intended r e f u t a t i o n of Parmenides f a i l s , while our own r e s u l t s i n t h i s chapter have been almost wholly negative. U/e w i l l see t h a t we must advance many c e n t u r i e s beyond P l a t o before we can accumu-l a t e the m a t e r i a l s f o r an a n a l y s i s of e x i s t e n t i a l p r o p o s i t i o n s which w i l l d e l i v e r us from the paradoxes of Parmenides while yet sparing us from the s t i l l g reater paradoxes of P l a t o . *Jowett, B., t r , The Dialogues of P l a t o , p. 331. 66 ARISTOTLE 2.0 I n t r o d u c t i o n A r i s t o t l e i s a d i f f i c u l t philosopher whose mean-ing i s not always c l e a r . My A r i s t o t l e i s a l o g i c a l c o n s t r u c t i o n out of The  Works of A r i s t o t l e (Oxford: 1963), 12 volumes. I hope, but do not i n s i s t , t h at my A r i s t o t l e does not d i f f e r s u b s t a n t i a l l y from the h i s t o r i c a l one. Be-cause of the d i f f i c u l t i e s i n v o l v e d i n i n t e r p r e t i n g him, i t i s tempting to leave A r i s t o t l e to s p e c i a l i s t s . But i n t h i s philosopher we w i l l f i n d h i n t s of a s o l u t i o n to the Parmenidean paradoxes over nonexistence. A l s o , i n t h i s chapter our problems w i l l begin totake on a p r e c i s e enough form as to admit of s o l u t i o n . But i n t h i s chapter we w i l l not advocate an A r i s t o t e l i a n s o l u t i o n to the Parmenidean paradoxes. Tor A r i s t o t l e (at l e a s t on our i n t e r p r e t a t i o n ) , l i k e P l a t o , f a i l s to achieve consistency i n r e l a t i o n to the paradoxes. 2.1 A r i s t o t l e ' s Logic and i t s Presuppositions L i k e a f i g u r e cut from stone, one sees the science of l o g i c emerge g r a d u a l l y from the Orqanon. A f t e r a few u n c e r t a i n s t e p s , A r i s t o t l e c onfers upon l o g i c the form i n which i t w i l l remain f o r two thousand years. To the extent that one i s able to f o l l o w A r i s t o t l e ' s formation of t h i s s c i e n c e , one sees a mind of i n c a l c u l a -b l e power at work on problems of the f i r s t importance. I t would be ungra-c i o u s (and tedious) f o r us here to belabor the shortcomings of h i s l o g i c a l work. I t i s enough to note i t s l i m i t a t i o n s , and then seek the reasons f o r them i n h i s philosophy. Let us begin by s e t t i n g down (as examples) the f o l l o w i n g p r o p o s i t i o n s : (A) A l l men are mortal. (E) No men are s p i n e l e s s . ( I ) Some men are mortal. 67 (0) Some men are not s p i n e l e s s . Let us c a l l A-type p r o p o s i t i o n s ' u n i v e r s a l a f f o r m a t i v e ' ; E-type, ' u n i v e r s a l negative'} I-type, ' p a r t i c u l a r a f f i r m a t i v e * } 0-type, ' p a r t i c u l a r negative'. A p r o p o s i t i o n e x h i b i t i n g one of these four forms we w i l l say i s a c a t e g o r i - c a l p r o p o s i t i o n . A r i s t o t l e ' s l o g i c may be thought of as an attempt to char-a c t e r i z e the va r i o u s l o g i c a l r e l a t i o n s h o l d i n g between c a t e g o r i c a l p r o p o s i -t i o n s . But i t i s not my aim here to acquaint the reader with A r i s t o t l e ' s l o g i c a l w r i t i n g s } that I leave t o A r i s t o t l e h i m s e l f . Instead, I w i l l simply remind the reader of those p o r t i o n s of A r i s t o t l e ' s l o g i c a l work i n which we are p a r t i c u l a r l y i n t e r e s t e d . The ( I ) and the (0) p r o p o s i t i o n s , understood i n t h e i r most n a t u r a l way, p l a i n l y a s s e r t the existence of men who i n the one case ( I ) are mortal and i n the other (0) are not s p i n e l e s s — _ i . e _ . , e x i s t e n t i a l import i s assumed f o r the subject terms i n ( I ) and (0) p r o p o s i t i o n s . A r i s t o t l e holds that the ( I ) and the (0) p r o p o s i t i o n s are i m p l i e d , r e s p e c t i v e l y , by the (A) and the (E) p r o p o s i t i o n s . Given t h i s i m p l i c a t i o n ( c a l l e d s u b a l t e r n a t i o n ) , i t f o l l o w s that the exis t e n c e of men i s l i k e w i s e assumed f o r the p r o p o s i t i o n s (A) that a l l men are m o r t a l , and (E) that no men are s p i n e l e s s . Thus, e x i s t e n t i a l import i s assumed f o r the subject terms of c a t e g o r i c a l p r o p o s i t i o n s . I t i s assumed by A r i s t o t l e that both ( I ) and (E) can be converted sim- p l y — i . e . , i t i s assumed by A r i s t o t l e : (1) Some men are mortal i f and only i f ( I * ) some mortals are men. (2) No men are s p i n e l e s s i f and only i f (E*) no s p i n e l e s s t h i n g i s a man. Employing s u b a l t e r n a t i o n upon (E*)» we see that the existence of (1) mortals and (2) s p i n e l e s s t h i n g s i s assumed. Thus, e x i s t e n t i a l import i s a l s o assumed 68 f o r the pr e d i c a t e terms of c a t e g o r i c a l p r o p o s i t i o n s . Since e x i s t e n t i a l import i s assumed f o r the terms i n c a t e g o r i c a l propo-s i t i o n s , i t f o l l o w s that no term i n such a p r o p o s i t i o n as i t i s used i n a s y l l o g i s m a p p l i e s to everything. This we may demonstrate as f o l l o w s : To each general expression 'F* we a s s i g n a c l a s s of o b j e c t s , Z, c o n s i s t i n g of a l l and only those t h i n g s which are F. Z i s the extension of 'F'. Employ-ing the terminology of set theory, we may c h a r a c t e r i z e t h i s c l a s s as f o l l o w s : Z = [ x / F x ] , i..e_.» Z i s the c l a s s of obj e c t s such that a € Z i f and only i f 'a i s F' i s t r u e . From the general expression *F' we may form the general expression 'non-F', to which we a s s i g n the f o l l o w i n g extension: Z* = [x/-Fx] i^.e., Z* i s the c l a s s of objects such that a € Z* i f and only i f a i s not i n the extension of 'F'. Since A r i s t o t l e excludes empty general expressions from s y l l o g i s m s , i t f o l l o w s on h i s view t h a t both Z and Z* are non-empty i f they occur i n s y l l o g i s m s , and ther e f o r e t h a t *F' does not apply to everything i f i t occurs i n a s y l l o g i s m . The assumption that general expressions do not apply to everything i s necessary to v a l i d a t e c e r t a i n t r a d i t i o n a l inferences i n which c o n t r a p o s i t i o n i s i n v o l v e d . C o n t r a p o s i t i o n , £_.£.» guarantees the f o l l o w i n g equivalences: (1) No men are s p i n e l e s s i f and only i f (0*) some non-s p i n e l e s s t h i n g i s a man. (2) A l l men are mortal i f and only i f (A*) a l l non-mori t a l s are non-men. Employing s u b a l t e r n a t i o n upon ( A * ) , we see that the term 'non-mortal* i s i n -s t a n t i a t e d — a n d , hence, t h a t the term 'mortal' does not apply to everything. Given (0*), i t f o l l o w s t h a t the term 'non-spineless t h i n g ' i s a l s o i n s t a n t i -69 a t e d — a n d , hence, that the term ' s p i n e l e s s ' does not apply to ever y t h i n g . Having surveyed the assumptions i n v o l v e d i n A r i s t o t l e ' s l o g i c , we may now b r i e f l y c onsider i t s adequacy as a l o g i c a l system. The most popular view today i s th a t i t i s f o r m a l l y inadequate.* A system i s f o r m a l l y adequate only i f 2 any matter of e x t r a l i n g u i s t i c f a c t which must be known before an inference can be made s h a l l be stat e d as a premise of that i n f e r e n c e . 3 A r i s t o t l e accepts s u b a l t e r n a t i o n as a v a l i d form of immediate i n f e r e n c e . He e x p l i c i t l y says: ...when we have shown that a pred i c a t e belongs i n every case, we s h a l l a l s o have shown that i t be-longs i n some cases. (Topica 109a2-5) In t h i s passage A r i s t o t l e i s committing hims e l f e x p l i c i t l y to the i n f e r e n c e : i f (1) Every S i s P, then (2) Some S i s P. Today, we would symbolize (1) and ( 2 ) , r e s p e c t i v e l y , as f o l l o w s : (1«) (Vx)(Sx - Px) (2') Q x ) ( S x & Px) As everyone knows, the inference from (1') to (2') Is not f o r m a l l y v a l i d ; i n modern systems t h i s case of s u b a l t e r n a t i o n i s replaced by the f o l l o w i n g medi-a t e 4 i n f e r e n c e : -••See, e_.g., Church, A., 'The H i s t o r y of the Question of E x i s t e n t i a l Im-port of C a t e g o r i c a l P r o p o s i t i o n s ' , as contained i n : B a r - H i l l e l , Y., ed., Proceedings of the 1964 I n t e r n a t i o n a l Congress f o r L o g i c , Methodology, and  the Philosophy of Science (Amsterdam: 1965), pp. 418-9. 2 I b i d . , p. 419. 3An inference i s immediate i f i t proceeds from a s i n g l e premise. An inference i s mediate i f i t proceeds from more than one premise. 70 i f (1') (Vx)(Sx - Px) and (1") (3x)Sx, then (2«) (3x)(Sx & Px). In connection with the v a l i d i t y of s y l l o g i s t i c reasoning A r i s t o t l e does not d i s c u s s the question of e x i s t e n t i a l import f o r the terms i n c a t e g o r i c a l pro-p o s i t i o n s . Consequently, there i s room f o r s c h o l a r l y controversy as to how these p r o p o s i t i o n s are to be understood when they occur i n s y l l o g i s m s or i n immediate i n f e r e n c e s . But, i f we a l l o w (1*) and (2*) to stand, r e s p e c t i v e l y , as adequate expressions of (1) and ( 2 ) , then there can be no doubt that A r i s -t o t l e ' s system i s f o r m a l l y inadequate. 1 A r i s t o t l e ' s modern c r i t i c s , however, often d i s p l a y a c e r t a i n i n s e n s i t i v i t y to the p h i l o s o p h i c a l stumbling blocks which l o g i c i a n s before Frege faced i n connection with o n t o l o g i c a l questions. In order to preserve s u b a l t e r n a t i o n as a v a l i d immediate i n f e r e n c e , A r i s t o t l e must exclude empty general terms from the language i n which t h i s i nference holds. But i t i s , of course, open to A r i s t o t l e to view t h i s f a c t as a l i m i t a t i o n on the scope of s y l l o g i s t i c l o g i c , and to allow the p o s s i -b i l i t y of there being empty general terms i n n a t u r a l languages and i n more comprehensive l o g i c a l systems. But t h i s i s not what he does; i n s t e a d , he repeatedly (see, §_.£.» A n a l y t i c a P r i o r a 68bl2) t e l l s us that s y l l o g i s t i c rea-soning s u f f i c e s to prove a l l our d e r i v a t i v e b e l i e f s not founded upon induc-t i o n . He thus makes very s t r o n g , and u n j u s t i f i e d , claims f o r the adequacy of h i s system. Let us now note the s t a t e of philosophy which allowed A r i s -t o t l e to acquiesce i n h i s u n s a t i s f a c t o r y l o g i c a l r e s u l t s . I t i s p e r f e c t l y p o s s i b l e , of course, that Greek l o g i c i a n s d i d not aim at 'formal adequacy' and would not have considered i t important to achieve i t ; t h i s i s a matter f o r h i s t o r i a n s . Formal adequacy i s very important f o r our purposes, p a r t i c u l a r l y i n connection with Frege's q u a n t i f i c a t i o n theory and such inferences as e x i s t e n t i a l g e n e r a l i z a t i o n . 71 In the Phaedo P l a t o says that the s o u l i s p r e - e x i s t e n t , and that i n a p r i o r l i f e we acquire our understanding of the e s s e n t i a l nature of F-ness through an acquaintance with the Form of F-ness. (Phaedo 75c-e) A r i s t o t l e , of course, w i l l have none of t h i s ; he says ( A n a l y t i c a P o s t e r i o r a 97bl5-20): I f we were i n q u i r i n g what the e s s e n t i a l nature of p r i d e i s , we should examine instances of prou men we know of to see what, as such, they have i n common; , i f A l c i -diades was proud, or A c h i l l e s and Ajac were proud, we should f i n d , on i n q u i r i n g what they a l l had i n common, that i t was i n t o l e r a n c e of i n s u l t . In A r i s t o t l e ' s view we cannot l e a r n the e s s e n t i a l nature of F-ness except through seeing t h a t c h a r a c t e r i s t i c e x h i b i t e d i n p a r t i c u l a r s . 'A " d e f i n i t i o n * " , he says (Topica 101b35), ' i s a phrase s i g n i f y i n g a t h i n g ' s essence*. Thus, h i s b e l i e f that we cannot l e a r n the e s s e n t i a l nature of F-ness except through i t s instances may have prompted him to b e l i e v e that every term i s i n s t a n t i -ated, s i n c e otherwise i t s meaning would be unknowable. I f 'F-ness' were not a v a i l a b l e to us i n r a t i o n a l discourse unless '(^x)Fx' were t r u e , then to v a l i d a t e s u b a l t e r n a t i o n i t would not be necessary to s t a t e as a separate pre-mise of ' e x t r a l i n g u i s t i c f a c t * t h a t there are F's; f o r i n s t a n t i a t i o n would then be a p r e s u p p o s i t i o n the f a i l u r e of which would s u f f i c e to make 'F' mean-i n g l e s s . A r i s t o t l e says that before we can i n q u i r e i n t o a t h i n g ' s nature we must a s c e r t a i n that i t e x i s t s . ( A n a l y t i c a P o s t e r i o r a 89b30-5) 'No one', he says ( A n a l y t i c a P o s t e r i o r a 92b5), 'knows the nature of what does not e x i s t ' . He a l s o says: . . . c l e a r l y , i n j u s t the same way we cannot apprehend a th i n g ' s d e f i n a b l e form without apprehending-that i t e x i s t s , s i n c e while we are ignorant whether i t e x i s t s we cannot know i t s e s s e n t i a l nature. ( A n a l y t i c a Pos-t e r i o r a 93al7-21) ~ 72 ...to search f o r a thing's e s s e n t i a l nature when we are unaware that i t e x i s t s i s to search f o r nothing. (Analy- t i c s P o s t e r i o r a 93a27-8) A r i s t o t l e ' s point i n these passages may j u s t be that we cannot 'come to grasp u n i v e r s a l s except through i n d u c t i o n * ( A n a l y t i c a P o s t e r i o r a 81b3-4), so that we could never come to grasp an u n i n s t a n t i a t e d u n i v e r s a l . I f t h i s i s h i s p o i n t , however, we may ignore i t , s i n c e i t i s based upon a d i s c r e d i t e d theory i of concept formation. But there i s a way of viewing h i s c l a i m that to search f o r the nature of what does not e x i s t i s 'to search f o r nothing* which does not l i n k i t with h i s d i s c r e d i t e d theory of concept formation, and that i s to l i n k i t instead with the Parmenidean c l a i m ! that-(\/.x)(-Ex -* -Gx). '"What i s not*V A r i s t o t l e says i n De Generatione et Corruptione 318al6-7, * i s n e i t h e r a t h i n g , nor pos-sessed of a q u a l i t y , nor i n any pl a c e * . Here at l e a s t A r i s t o t l e seems to be accepting the Parmenidean premises from which he could conclude that we can-not know the nature of the nonexistent because i t has no nature. U n f o r t u n a t e l y , A r i s t o t l e does not di s c u s s h e l p f u l l y the problem of emp-ty general terms. He says (Ptetaphysica 1007b27-30): we 'must pr e d i c a t e of every subject the a f f i r m a t i o n or the negation of every a t t r i b u t e * . But we are concerned with the case where the subject-term does not pick out a sub-ject-m a t t e r (e_.£., as i n 'unicorns are F'). Given any p a i r of a t t r i b u t e s , F and not-F', i s i t true t h a t unicorns possess the one or the other? I f so, how are we to r e c o n c i l e t h i s view with A r i s t o t l e ' s c l a i m that '"What i s not" i s ... not possessed of a q u a l i t y ' ? •••Aristotle's theory of how we form general concepts i s a k i n to that of Locke. For an e f f e c t i v e c r i t i c i s m of Locke's theory, see Bennett, J . , Locke, Berkeley, Hume (Oxford: 1971), pp. 11-20. 73 I b e l i e v e t h a t f o r Parmenidean reasons A r i s t o t l e r e j e c t e d empty general terms as meaningless, and t h a t , t h e r e f o r e , he would not have viewed the ex-c l u s i o n of such terms from the s y l l o g i s m as i n any way l i m i t i n g the scope of h i s l o g i c a l system. But to best see h i s dependence upon the Parmenidean mode of t h i n k i n g we must turn from h i s treatment of c a t e g o r i c a l p r o p o s i t i o n s to h i s p u z z l i n g d i s c u s s i o n s of s i n g u l a r p r o p o s i t i o n s . 2.2 L o g i c a l Truth and Si n g u l a r P r o p o s i t i o n s In A r i s t o t l e ' s l o g i c , i f a term may appear i n the subje c t p o s i t i o n of a premise or c o n c l u s i o n , then i t may a l s o appear i n the pred i c a t e p o s i t i o n of a premise or c o n c l u s i o n . We may, e_.£., move back and f o r t h between 'Some mortals are men* and 'Some men are mortals'. General expressions such as 'mortals' and 'men* a r e , of course, i d e a l l y s u i t e d f o r t h i s k i n d of interchange of p o s i t i o n i n sentences. S i n -g u l a r terms are not. In A r i s t o t l e ' s view, s i n g u l a r terms are the names of substances; n o t i c e how he define s 'substance* (Categorise l b l 2 - 4 ) : Substance, i n the t r u e s t and primary and most d e f i n i t e sense of the word, i s th a t which i s n e i t h e r p r e d i c a b l e of a subject nor present i n a su b j e c t ; f o r in s t a n c e , the i n d i v i d u a l man or horse. The consequences of t h i s d e f i n i t i o n are evident a t once. No p r o p o s i t i o n con-t a i n i n g a s i n g u l a r term may appear as a premise or co n c l u s i o n i n a s y l l o g i s -t i c demonstration. S y l l o g i s t i c demonstration i s the only s o r t of l o g i c a l proof A r i s t o t l e thought p o s s i b l e . Therefore, he has excluded p r o p o s i t i o n s c o n t a i n i n g s i n g u l a r terms from the c l a s s of p r o p o s i t i o n s he thought l o g i c a l -l y demonstrable. A r i s t o t l e ' s system of s y l l o g i s t i c was q u i c k l y extended to include s i n -g u l a r p r o p o s i t i o n s , as i f he had merely f o r g o t t e n to cover t h i s case. As e a r l y as the f i r s t century AD we f i n d Sextus Empiricus g i v i n g the f o l l o w i n g 74 as an instance of 'the s o - c a l l e d " c a t e g o r i c a l " s y l l o g i s m , which i s c h i e f l y used by the P e r i p a t e t i c s * : 1 (1) Socrates i s a man. (2) Every man i s an animal. (3) Therefore, Socrates i s an animal. But, of course, a ' c a t e g o r i c a l * s y l l o g i s m contains only A, E, I , 0 p r o p o s i -t i o n s , of which 'Socrates i s a man* i s not one. In h i s w r i t i n g s A r i s t o t l e 2 d e l i b e r a t e l y r e f r a i n s from g i v i n g such 'in s t a n c e s ' of s y l l o g i s m s . A r i s t o t l e d i d not simply i n h e r i t h i s l o g i c from others but rat h e r c r e a t -ed the f i r s t l o g i c a l system. Therefore, l e t us examine h i s concept of l o g i -c a l t r u t h to understand why he thought i t proper to exclude s i n g u l a r propo-s i t i o n s from the c l a s s of l o g i c a l t r u t h s . In A n a l y t i c a P o s t e r i o r a (75b20-30) A r i s t o t l e w r i t e s : I f the premises from which the s y l l o g i s m proceeds are commensurately u n i v e r s a l , the co n c l u s i o n of such demon-s t r a t i o n — i..e_., demonstration i n the u n q u a l i f i e d s e n s e -must be e t e r n a l . Therefore no a t t r i b u t e can be demon-s t r a t e d nor known by s t r i c t l y s c i e n t i f i c knowledge t o i n -here i n p e r i s h a b l e t h i n g s . The proof can only be a c c i -d e n t a l because the a t t r i b u t e ' s connection with i t s per-i s h a b l e subject i s not commensurately u n i v e r s a l but tem-porary and s p e c i a l . I f such a demonstration i s made, one premise must be p e r i s h a b l e and not commensurately u n i v e r s a l ( p e r i s h a b l e because only i f i t i s p e r i s h a b l e w i l l the c o n c l u s i o n be p e r i s h a b l e ; not commensurately u n i v e r s a l , because the pr e d i c a t e w i l l be p r e d i c a b l e of some instances of the s u b j e c t and not of others; so t h a t the c o n c l u s i o n can only be th a t a f a c t i s true a t the mo-ment—not commensurately and u n i v e r s a l . ^-See Bury, R., t r , The Wortcs of Sextus Empiricus (Harvard: 1961), v o l . I , pp. 257-8. [Hyp. Pyrrh. i i , 174j 2 I n A r i s t o t l e ' s S y l l o g i s t i c (Oxford: 1972), pp. 5-7, Lukasiewicz e r r s s l i g h t l y i n saying t h a t i n the A n a l y t i c a P r i o r a A r i s t o t l e quotes no argument c o n t a i n i n g s i n g u l a r p r o p o s i t i o n s ; a t 70al6-20 he d o e s — a n i n v a l i d one i n Da-r a p t i . I t remains true t h a t A r i s t o t l e made a conscious e f f o r t to exclude s i n g u l a r p r o p o s i t i o n s from the s y l l o g i s m . 75 Despite an o c c a s i o n a l l y i l l - c h o s e n phrase, A r i s t o t l e ' s l o g i c a l i n t u i t i o n s i n t h i s passage are i n accord w i t h ours. Connections which hold only some-times or a c c i d e n t a l l y (i,.£.» not 'communsurately u n i v e r s a l ' ) cannot be de-monstrated l o g i c a l l y . Therefore, l o g i c w i l l not s u f f i c e to show that a c e r -t a i n contingent t h i n g w i l l be thus and so. 'Demonstrative knowledge', he says ( A n a l y t i c a P o s t e r i o r a 7 5 a l l - 2 ) , 'must be knowledge of a necessary nexus'. Therefore, 'the t r u t h obtained by demonstration w i l l be necessary'. (Analy- t i c a P o s t e r i o r a 73a20-2) Demonstration i n A r i s t o t l e ' s view has only to do w i t h essence; he w r i t e s : Of a c c i d e n t s that are not e s s e n t i a l according to our de-f i n i t i o n of e s s e n t i a l , there i s no demonstrative know-ledge. ( A n a l y t i c a P o s t e r i o r a 75al8-20) There i s a u n i v e r s a l i t y to l o g i c a l t r u t h s which i s i m p l i c i t i n the notion of essence; r e c o g n i z i n g t h i s , A r i s t o t l e w r i t e s ( A n a l y t i c a P o s t e r i o r a 79a27-9): essence must have a u n i v e r s a l c h a r a c t e r : e.g. man i s not two-footed animal i n any q u a l i f i e d sense, but u n i -v e r s a l l y . In s t r e s s i n g the u n i v e r s a l c h a r a c t e r of essence, A r i s t o t l e s i g n a l s h i s r e j e c -t i o n of what Quine c a l l s * ' A r i s t o t e l i a n e s s e n t i a l i s m * . Though o c c a s i o n a l l y c a r e l e s s , A r i s t o t l e expresses His considered opinion at Metaphysics 1030al0-2: Nothing, then, which i s not a s p e c i e s of a genus w i l l have an essence. I n d i v i d u a l s , then, not being s p e c i e s , w i l l not have essences. I take t h i s to mean that no p r o p o s i t i o n of the form OV i s 8 • s u b j e c t ' , he says i n Word and Object (Cambridge, Mass.: 1960), p. 199, 'to c o n t r a d i c t i o n by s c h o l a r s , such being the penalty f o r a t t r i b u t i o n s to A r i s t o t l e ' . 76 i s t r u e , where v i s a s i n g u l a r term. I t i s not d i f f i c u l t to see why A r i s -t o t l e held that p r o p o s i t i o n s of t h i s form are untrue. *A " d e f i n i t i o n " , * he says at Topica 102al, * i s a phrase s i g n i f y i n g a thi n g ' s essence*. Things designated by i n d e f i n a b l e terms then w i l l not have essences. A f t e r d i s m i s -s i n g the the p o s s i b i l i t y of d e f i n i n g (the names o f ) non-eternal i n d i v i d u a l s , A r i s t o t l e observes (Wetaphysica 1040a27-b4): The i m p o s s i b i l i t y of d e f i n i n g i n d i v i d u a l s escapes n o t i c e i n the case of e t e r n a l t h i n g s , e s p e c i a l l y those which are unique, l i k e the sun or the moon. For people e r r not on-l y by adding a t t r i b u t e s whose removal the sun would s u r -v i v e , e.g. "going round the e a r t h " or "night-hidden" ( f o r from t h e i r view i t f o l l o w s that i f i t stands s t i l l or i s v i s a b l e [ a t n i g h t ] , i t w i l l no longer be the sun; but i t i s strange i f t h i s i s so; f o r "the sun" means a c e r t a i n substance); but a l s o by the mention of a t t r i b u t e s which can belong to another s u b j e c t ; e.g. i f another t h i n g with the s t a t e d a t t r i b u t e s comes i n t o e x i s t e n c e , c l e a r l y i t w i l l be a sun; the formula i s ther e f o r e general. But the sun was supposed to be an i n d i v i d u a l , l i k e Cleon or Soc-r a t e s . D e f i n i t i o n s are ge n e r i c , and ther e f o r e of (terms f o r ) s p e c i e s , not (terms f o r ) i n d i v i d u a l s . " . • Taken together, A r i s t o t l e ' s v a r i ous views commit him to the t h e s i s that the foundation of a l l demonstration i s the r e l a t i o n of a species to i t s genus. Therefore, the r e l a t i o n of an i n d i v i d u a l to i t s p r o p e r t i e s w i l l not be a mat-t e r f o r l o g i c a l demonstration--i.e., no p r o p o s i t i o n of the form V i s 3 w i l l be l o g i c a l l y t r u e . I t i s f o r t h i s reason, I t h i n k , that A r i s t o t l e ex-cludes s i n g u l a r p r o p o s i t i o n s from the c l a s s of l o g i c a l t r u t h s ; he w r i t e s : * x a s c i t e d by H i n t i k k a i n Time and Necessity (Oxford: 1973), p. 76. H i n t i k k a ' s commentary (pp. 62-93) supports mine and e x p l a i n s c e r t a i n aspects of t h i s passage (Metaphysics 1039b27-40a5) which, though important, I must ignore ( f o r want of space). 77 Since substance i s of two k i n d s , the concrete t h i n g and the formula ( I mean that one k i n d of substance i s the formula taken w i t h the matter, while another k i n d i s the formula i n i t s g e n e r a l i t y ) , substances i n the former sense are capable of d e s t r u c t i o n ( f o r they are capable a l s o of g e n e r a t i o n ) , but there i s no d e s t r u c t i o n of the formula i n the sense that i t i s ever i n course of be-i n g destroyed ( f o r there i s no generation of i t e i t h e r } the being of house i s not generated, but only the be-ing t h i s house), but without generation and d e s t r u c t i o n formulae are and are not; f o r i t has been shown that no one begets nor makes these. For t h i s reason, a l s o , there i s n e i t h e r d e f i n i t i o n of nor demonstration about s e n s i -b l e i n d i v i d u a l substances, because they have matter whose nature i s such that they are capable both of being and of not being; f o r which reason a l l the i n d i v i d u a l i n -stances of them are d e s t r u c t i b l e . I f then demonstration i s of necessary t r u t h s and d e f i n i t i o n i s a s c i e n t i f i c process, and i f , j u s t as knowledge cannot be sometimes knowledge and sometimes ignorance, but the s t a t e which v a r i e s thus i s o p i n i o n , so too demonstration and d e f i n i -t i o n cannot vary thus, but i t i s opinion t h a t deals with that which can be otherwise than as i t i s , c l e a r l y there can n e i t h e r be d e f i n i t i o n of nor demonstration about sen-s i b l e i n d i v i d u a l s . For p e r i s h i n g t h i n g s are obscure to those who have the r e l e v e n t knowledge, when they have passed from our p e r c e p t i o n ; and though the formulae r e -main i n the s o u l unchanged, there w i l l no longer be e i t h -er d e f i n i t i o n or demonstration. And so when one of the definition-mongers d e f i n e s any i n d i v i d u a l , he must r e -cognize that he d e f i n i t i o n may always be overthrown; f o r i t i s not p o s s i b l e to define such t h i n g s . (Metaphysica 1039a20-40a8) I t i s evident from the above c o n s i d e r a t i o n s t h a t A r i s t o t l e ' s treatment of essence d i f f e r s markedly from that commonly a t t r i b u t e d to him; i n A_ H i s - t o r y of western Philosophy (New York: 1964), pp. 200-1, R u s s e l l (e_.£. ) w r i t e s : The n o t i o n of essence i s an intimate part of every p h i l o -sophy subsequent to A r i s t o t l e u n t i l we come to modern times. I t i s , i n my o p i n i o n , a h o p e l e s s l y muddle-head-ed n o t i o n , but i t s h i s t o r i c a l importance re q u i r e s us to say something about i t . The "essence" of a t h i n g appears to have meant "those of i t s p r o p e r t i e s which i t cannot change without l o s i n g i t s i d e n t i t y " . Socrates may be sometimes happy, sometimes sad; sometimes w e l l , sometimes i l l . Since he can change these p r o p e r t i e s without ceasing to be Socrates, they are 78 no part of h i s essence. But i t i s supposed to be of the essence of Socrates t h a t he i s a man, though a Pythago-rean, who b e l i e v e s i n t r a n s m i g r a t i o n , w i l l not admit t h i s . In f a c t [ c o n t r a r y to A r i s t o t l e , t h i n k s R u s s e l l ] , the ques-t i o n of "essence" i s one as to the use of words. This account overlooks the f a c t s that (1) A r i s t o t l e agrees t h a t 'essence' concerns the use of words: 'A " d e f i n i t i o n " , ' he says, ' i s a phrase s i g n i -f y i n g a th i n g ' s essence*} and (2) A r i s t o t l e held that i n d i v i d u a l s such as Socrates do not have essences. Of course, not every w r i t e r has abused the t e x t i n the way R u s s e l l does. For example, Lukasiewicz, always a c a r e f u l h i s t o r i a n , notes that A r i s t o t l e has excluded s i n g u l a r terms from s y l l o g i s m s . He sees i n t h i s , however, a mistake} i n A r i s t o t l e ' s S y l l o g i s t i c ; ( p . 6) he w r i t e s : I t i s f u r t h e r not c o r r e c t to say that i n d i v i d u a l or s i n -g u l a r terms, l i k e " C a l l i a s " cannot be t r u l y predicated of anything e l s e . A r i s t o t l e himself gives examples of true p r o p o s i t i o n s with a s i n g u l a r term, as "That white obje c t i s Socrates" or "That which approaches i s C a l l i a s " [see An. Pr_. 43a33], saying t h a t such p r o p o s i t i o n s are " i n c i d e n t a l l y " t r u e . There are other examples of t h i s k i n d which are not merely i n c i d e n t a l l y t r u e , as "Socrates i s Socrates". This o b j e c t i o n takes us r i g h t to the heart of t h i n g s . As Lukasiewicz says, A r i s t o t l e concedes that i n an i n c i d e n t a l sense a s i n g u l a r term may be p r e d i -cated of something, as when we say 'That white obj e c t i s Socrates or that which approaches i s C a l l i a s ' } see A n a l y t i c a P r i o r a 43a33. These p r o p o s i t i o n s , however, are obviously contingent, and the r e f o r e not demonstrable. But Luka-s i e w i c z c i t e s what he takes to be a necessary p r o p o s i t i o n — v i z . , 'Socrates i s S o c r a t e s ' — c o n t a i n i n g a s i n g u l a r term as p r e d i c a t e . How would A r i s t o t l e handle t h i s apparent counter-example to h i s t h e s i s that p r o p o s i t i o n s about i n d i v i d u a l s are never necessary? To answer t h i s question ws must look again at the Parmenidean background to A r i s t o t l e ' s s p e c u l a t i o n . 79 As we saw, i n De Generatione et Corruptione A r i s t o t l e appears to commit himse l f to the Parmenidean p r i n c i p l e t h a t (Vx)(-Ex -* -Gx)~i_.£., i f something does not e x i s t , i t possesses no c h a r a c t e r i s t i c s at a l l . On t h i s view, t h e r e -f o r e , i f Socrates had not e x i s t e d ^ the p r o p o s i t i o n 'Socrates i s Socrates' would have been untrue, s i n c e Socrates would not have possessed the charac-t e r i s t i c of being Socrates. I t i s , moreover, a contingent matter f o r A r i s -t o t l e (see Metaphysica 1039a20-40a8) whether Socrates e x i s t s , and therefore a contingent matter whether he i s s e l f - i d e n t i c a l . That A r i s t o t l e would have responded to Lukasiewicz i n the manner I sug-gest i s , I t h i n k , confirmed by the f o l l o w i n g passage (Cateqoriae 13bl4-35): "Socrates i s i l l " i s the c o n t r a r y of "Socrates i s w e l l " , but not even of such composite expressions i s i t true to say t h a t one of the p a i r must always be true and the other f a l s e . For i f Socrates e x i s t s , one w i l l be true and the other f a l s e , but i f he does not e x i s t , both w i l l be f a l s e ; f o r n e i t h e r "Socrates i s i l l " nor "Socrates i s w e l l " i s t r u e , i f Socrates does not e x i s t at a l l . In the case of " p o s i t i v e s ' and " p r i v a t i v e s " , i f the sub-j e c t does not e x i s t at a l l , n e i t h e r p r o p o s i t i o n i s t r u e , but even i f the s u b j e c t e x i s t s , i t i s not always the f a c t that one i s t r u e and the other f a l s e . For "Soc-r a t e s has s i g h t " i s the opposite of "Socrates i s b l i n d " i n the sense of the word "opposite" which a p p l i e s to pos-session and p r i v a t i o n . Now i f Socrates e x i s t s , i t i s not necessary that one should be true and the other f a l s e , f o r when he i s not yet able to acquire the power of v i -s i o n , both are f a l s e , as a l s o i f Socrates i s a l t o g e t h e r non-existent. But i n the case of a f f i r m a t i o n and negation, whether the subject e x i s t s or not, one i s always f a l s e and the other t r u e . For m a n i f e s t l y , i f Socrates e x i s t s , one of the two p r o p o s i t i o n s "Socrates i s i l l " , "Socrates i s not i l l " , i s t r u e , and the other f a l s e . This i s l i k e w i s e the case i f he does not e x i s t ; f o r i f he does not e x i s t , to say that he i s i l l i s f a l s e , to say that he i s not i l l i s t r u e , Thus i t i s i n the case of those opposites o n l y , which are opposite i n the sense i n which the term i s used with reference t o a f f i r m a t i o n and negation, that the r u l e holds good, that one of the p a i r must be true and the other f a l s e . 80 I taka i t that A r i s t o t l e i s arguing somewhat as f o l l o w s : Given the pre d i c a t e s F and non-F, an e x i s t e n t ( p a r t i c u l a r ) s u b j e c t a_ must be e i t h e r F or non-F. But, i f a does not e x i s t , then ( s i n c e i t i s not anything) i t i s n e i t h e r F nor non-F, Thus, i n that event the p r o p o s i t i o n s *a_ i s F' and 'a i s non-F' are both f a l s e . But t h i s does not v i o l a t e the f i r m e s t of a l l f i r s t p r i n c i p l e s ... th a t i t i s im-p o s s i b l e f o r the same t h i n g to belong and not to belong to the same t h i n g a t the same time i n the same respect. (ftetaphysica 1005bl9-23) For we must d i s t i n g u i s h the a s s e r t i o n t h a t something possesses a c e r t a i n ne-ga t i v e p r e d i c a t e from the d e n i a l t h a t i t possesses the p o s i t i v e c o r r e l a t i v e to t h a t p r e d i c a t e — I. £., (1) a i s non-F i e not equivalent to (2) I t i s not the case that a i s F, (1) i s f a l s e i f a does not e x i s t } f o r , I f a does not e x i s t , i t cannot be non-F, si n c e i n that event i t i s n ' t anything. Whereas, (2) i s true i f a does not e x i s t } f o r , i f a does not e x i s t , then (being nothing at a l l ) i t Is not F; and i n t h a t event i t i s not the case that i t i s F. This passage (Categoriae 13bl4-35) c l e a r l y presupposes the parmenidean p r i n c i p l e t h a t ( l / x ) ( - E x - ? - G x ) . 2.3 A r i s t o t l e on ' E x i s t s * In Metaphysics 1089al-25 A r i s t o t l e d i s -cusses the parmenidean c l a i m (1) - (^x)-Ex. His d i s c u s s i o n i s obscure, but i t i s at l e a s t c l e a r that he r e j e c t s P l a t o ' s view i n the Sophist that things c o n s i s t of Being and non-Being— j l . £ ., that there are things which are not. But i t i s perhaps not a l t o g e t h e r c l e a r how A r i s t o t l e would r e s o l v e the problems a r i s i n g out of Parmenides's philosophy; 81 and, as uie w i l l now see, these problems have a s p e c i a l s i g n i f i c a n c e f o r A r i s -t o t l e . In A n a l y t i c a P r i o r a 43a35-43 A r i s t o t l e remarks that demonstrations u s u a l l y concern n e i t h e r i n d i v i d u a l s nor terms of the great e s t g e n e r a l i t y , but 'whatever l i e s between these l i m i t s * , tele n o ticed e a r l i e r t h a t A r i s t o t l e cannot use i n s y l l o g i s m s terms having u n i v e r s a l a p p l i c a t i o n . A r i s t o t l e does not to my knowledge say that no general expression a p p l i e s t o ev e r y t h i n g ; but a t Metaphysics 998b22-7 he does, according to Bochenski i n Ancient For- mal Logic (Amsterdam! 1963), p, 34, argue f o r what Is ne a r l y the same t h i n g — v i z . , t h a t there i s no u n i v e r s a l c l a s s . Therefore, A r i s t o t l e i s under some conceptual pressure t o exclude p r o p o s i t i o n s of the form: ( ¥ ^ $ i As i t happens, the Parmenidean p r o p o s i t i o n (2) (Vx)Ex i s of the excluded form. Sin c e , however, A r i s t o t l e does not b e l i e v e t h a t there are things which do not e x i s t , he cannot a s s e r t the d e n i a l of ( 2 ) . Consistency, then, demands t h a t he analyse ' e x i s t s ' i n a way which commits him n e i t h e r to the a s s e r t i o n nor to the d e n i a l of ( 2 ) ; and he does i n f a c t o f f e r such an a n a l y s i s (metaphysics 998b22): I t i s not p o s s i b l e that e i t h e r u n i t y or being should be a s i n g l e genus of t h i n g s ; f o r the d i f f e r e n t i a e of any genus must each of them have being and be one. A r i s t o t l e r e fuses t o accept ' e x i s t s * as an independent general term which, l i k e (say) 'animal', has i t s own genus; ' e x i s t s ' , he says, must always be used w i t h a generic expression. In the Eudemian E t h i c s 1217b25-35, A r i s t o t l e w r i t e s t h a t the good has many senses, as numerous as those of being. For bein g , as we have seen, i s d i v i d e d i n t o many p a r t s . Notice that p r o p o s i t i o n ( 2 ) , the Parmenidean c l a i m , 82. i s of the excluded form. Since, however, A r i s t o t l e does not b e l i e v e that there are things which do not e x i s t , he cannot a s s e r t the d e n i a l of ( 2 ) . Consistency, then, demands that he analyse ' e x i s t s * i n a way which commits him n e i t h e r to the a s s e r t i o n nor to the d e n i a l of ( 2 ) ; and he does i n f a c t o f f e r such an a n a l y s i s (Metaphysics 99Bb22): I t i s not p o s s i b l e t h a t e i t h e r u n i t y or being should be a s i n g l e genus of things} f o r the d i f f e r e n t i a e of any genus must each of them have being and be one. A r i s t o t l e refuses to accept ' e x i s t s ' as an independent general term which, l i k e (say) 'animal*,has i t s own genus; ' e x i s t s ' , he says, must always be used with a generic expression. In the Eudemian E t h i c s 1217b25-35, A r i s t o t l e w r i t e s : ...the good has many sense, as numerous as those of be-i n g . For being, as we have d i v i d e d i t i n other works, s i g n i f i e s now what a t h i n g i s , now q u a l i t y , now q u a n t i t y , now time, and i n a d d i t i o n i t sometimes c o n s i s t s i n being changed, sometimes i n e f f e c t i n g change} and the good i s found i n each of these modes, i n substance as mind and God, i n q u a l i t y as j u s t i c e , i n q u a n t i t y as moderation, i n time as opportunity, while as example of i t i n change we have t h a t which teaches and that which i s being taught. As then being i s not one i n a l l that we have mentioned, so n e i t h e r i s good; nor i s there one science e i t h e r of being or of the good. Here A r i s t o t l e says t h a t there can be no s i n g l e science of being or of good-ness, s i n c e there i s no one character shared e i t h e r by a l l e x i s t e n t things or by a l l good t h i n g s , the nature of which we might i n v e s t i g a t e . Thus, he says (Metaphysics 992bl7-20): In g e n e r a l , i f we search f o r the elements of e x i s t i n g things without d i s t i n g u i s h i n g the many senses i n which t h i n g s are s a i d to e x i s t , we cannot f i n d them. Concerning the meaning of 'good*, he w r i t e s (Topica 107a5-10: "good" i n the case of food means "productive of pleasure", and i n the case of medicine "productive of h e a l t h " , whereas as a p p l i e d to the s o u l i t means to be of a c e r t a i n q u a l i -83: t y , e.g. temperate or courageous or j u s t : and l i k e w i s e a l s o , as a p p l i e d to "man". Here i t i s maintained t h a t d i f f e r e n t things are s a i d to be good i n d i f f e r e n t senses according t o the kinds of things they are. Thus, the question 'What i s i t f o r something to be good?* i s given up i n favor of the question 'What i s i t f o r ajn F_ to be good?*, where 'F' stands f o r some generic expression. Our concern, however, i s not with A r i s t o t l e ' s a n a l y s i s of moral terms; l e t us t u r n immediately to h i s analogous treatment of ' e x i s t s ' . At Metaphy- s i c s 1042bl2-3a2 he t e l l s us th a t to ask, e.£., whether a t h r e s h o l d e x i s t s i s to ask whether there i s something i n such and such a p o s i t i o n ; f o r us to ask whether i c e e x i s t s i s to ask whether there i s something which has been s o l i d i f i e d i n such and such a manner. And i n De Anima (415bl3) he says: • f o r l i v i n g t h i n g s , to be i s to be a l i v e ' . Thus, the question 'What i s i t to e x i s t ? ' i s given up i n favor of the question 'What i s it f o r an £ to e x i s t ? ' At Metaphysica 1053b26-7, he says: ' C l e a r l y we must i n every category ask ... what the e x i s t e n t i s , s i n c e i t i s not enough to say that i t s nature i s to e x i s t ' . We are now i n a p o s i t i o n to s t a t e A r i s t o t l e ' s answer to Parmenides; and i t i s as f o l l o w s : the expression ' e x i s t s ' , not being a generic term, hasn't an extension of i t s own. Consequently, existence i s not a property shared by e v e r y t h i n g , nor yet a property which only some,things possess. Therefore, both (2) (Vx)Ex and i t s d e n i a l are r e j e c t e d by A r i s t o t l e . Allowable e x i s t e n t i a l questions always take the form: 'Is there [ o r i s there not] something which i s F?' The question 'Is there something which i s F?* i s gene r a l , whereas the 84 question 'Is Socrates bald?' (e_.£.) i s s i n g u l a r . We w i l l answer the f i r s t question a f f i r m a t i v e l y i f the general p r o p o s i t i o n 'there are F's' i s t r u e ; we w i l l answer the second question a f f i r m a t i v e l y i f the s i n g u l a r p r o p o s i t i o n 'Socrates i s b a l d ' i s t r u e , A r i s t o t l e ' s answer to Parmenides may t h e r e f o r e be understood to assume the f o l l o w i n g t h e s i s : every e x i s t e n t i a l q uestion, p r o p e r l y framed, i s g e n e r a l ; and every e x i s t e n t i a l p r o p o s i t i o n , properly analysed, i s g e n e r a l . In connection w i t h t h i s t h e s i s the f o l l o w i n g passage from Kahn i s important:* In e a r l y Indo-European i n c l u d i n g c l a s s i c Greek, there was no verb to e x i s t , and a l l e x i s t e n t i a l sentences are formed by the ordinary i s . In Greek The gods e x i s t or There i s n_o Zeus i s expressed l i t e r a l l y as The gods are and Zeus i s not: el(J\ froC, Q\JK & T t i "Zftfe The p h i l o s o -pher may or may not be s u r p r i s e d to l e a r n that such t y -p i c a l l y e x i s t e n t i a l sentence—what I c a l l here "pure e x i s -t e n t i a l s " — w h i c h a s s e r t or deny the existence of a de-f i n i t e i n d i v i d u a l or a d e f i n i t e s o r t of i n d i v i d u a l , do not occur i n the e a r l i e s t t e x t s . Thus there are no such sentences i n Homer. The e a r l i e s t pure e x i s t e n t i a l s a t -t e s t e d i n Greece are from the p e r i o d of the S o p h i s t s , and they are n e a r l y always concerned with the e x i s t e n c e of the gods. E x i s t e n t i a l sentences of the form N i s or N i s not a r i s e almost as a t e c h n i c a l use which seems to be the r e s u l t of p h i l o s o p h i c s p e c u l a t i o n and t h e o l o g i -c a l controversy. But, of course, even i f 'Zeus does not e x i s t ' arose as a t e c h n i c a l use, i t i s now f i r m l y implanted i n our language. I f we are to t r e a t every e x i s t e n t i -a l p r o p o s i t i o n as g e n e r a l , we must e x p l a i n what i n general terms i s meant by t h i s p r o p o s i t i o n . Though I won't argue f o r i t i n t h i s chapter, I b e l i e v e that A r i s t o t l e ' s t h e s i s — v i z . , t h a t e x i s t e n t i a l p r o p o s i t i o n s are always g e n e r a l -i s true of E n g l i s h . I b e l i e v e , moreover, t h a t t h i s i s not an i n c i d e n t a l f a c t about how we happen i n E n g l i s h to express e x i s t e n t i a l c l a i m s . I w i l l xKahn, C , 'On the Thsory of the Verb "To Be"J' as contained i n : Munitz, M., ed., Logic and Ontology (New York: 1973), p. 7. 85 argue that the formal languages using our concept of exi s t e n c e a l s o exclude s i n g u l a r e x i s t e n t i a l p r o p o s i t i o n s . P a s c a l claimed t h a t , though ignorant of God's (general) c h a r a c t e r i s t i c s , he was at l e a s t sure of His e x i s t e n c e ; others have s a i d t h i s too. I f Pascal were r i g h t , i t would be hard to e x p l a i n 'God e x i s t s ' as a general p r o p o s i t i o n , s i n c e we would not know a Div i n e c h a r a c t e r i s t i c the i n s t a n t i a t i o n of which would f i x the t r u t h - v a l u e of 'God e x i s t s * f o r us. But I th i n k we can see that P a s c a l i s wrong. What evidence could we have f o r the existence of a t h i n g whose c h a r a c t e r i s t i c s we d i d not know? I f someone askBd us: 'Is there a ?* but refused t o t e l l us the s a l i e n t p r o p e r t i e s of the , how would we know what to look f o r ? Perhaps, the g e n e r a l i t y enters e x i s t e n t i a l propo-s i t i o n s because of how we i d e n t i f y t h i n g s — v i z . , i n terms of t h e i r general c h a r a c t e r i s t i c s . But we must ask: i s i t a contingent f a c t about human psy-chology t h a t we so i d e n t i f y t h i n g s , or would God Himself have to r e s o r t to such means i n l o c a t i n g t h i n g s ? This i s not a question I am prepared to ans-wer, but upon i t s answer depends the s t a t u s ( l o g i c a l or e m p i r i c a l ) of our t h e s i s t h a t e x i s t e n t i a l claims are always general. Let us conclude t h i s s e c t i o n w i t h the observation t h a t we cannot but marvel at the f a c t that a mere two c e n t u r i e s separates A r i s t o t l e ' s work from that of Thales, w i t h whom philosophy unpromisingly o r i g i n a t e d when he observed ( f a l s e l y ) t h a t ' A l l i s water'. Whether we agree with A r i s t o t l e ' s s o l u t i o n to Parmenides, we must at l e a s t appreciate i t s s o p h i s t i c a t i o n . In t r e a t i n g every e x i s t e n t i a l p r o p o s i t i o n as gen e r a l , A r i s t o t l e i m p l i c i t l y r e j e c t s ' e x i s t s ' as a p r e d i c a t e of i n d i v i d u a l s ; t h i s f r e e s him of (2) (V*)Ex and a l l t h a t i t e n t a i l s . 86 2.5 mistakes Eminent Philosophers Have Made To i l l u s t r a t e the d i f -f i c u l t i e s which the concept of ex i s t e n c e poses f o r p h i l o s o p h e r s , I w i l l con-clude t h i s chapter with a few examples ( s e l e c t e d from a la r g e fund) of how t h i s concept has o c a s s i o n a l l y been mishandled. (1) Consider the f o l l o w i n g passages from the Categories; "Socrates i s i l l " i s the con t r a r y of "Socrates i s w e l l " , but not even of such composite expressions i s i t true to say t h a t one of the p a i r must always be tru e and the other f a l s e . For i f Socrates e x i s t s , one w i l l be true and the other f a l s e , but i f he does not e x i s t , both w i l l be f a l s e ; f o r n e i t h e r "Socrates i s i l l " nor "Socrates i s w e l l " i s t r u e , i f Socrates does not e x i s t a t a l l . (13bl4-9) Take the p r o p o s i t i o n "Homer i s so-and-so", say "a poet"; does i t f o l l o w t h a t Homer I s , or does i t not? The verb " i s " i s here used of Homer only i n c i d e n t a l l y , the propo-s i t i o n being that Homer i s a poet, not t h a t he i s , i n the independent sense of the word. (21a25-30) In the f i r s t passage A r i s t o t l e commits himself to the view; t h a t any a t t r i b u -t i o n to a s i n g u l a r s u b j e c t i m p l i e s the exi s t e n c e of that s u b j e c t , whereas i n the second passage he says that 'Homer Is a poet* does not imply that Homer e x i s t s . (2) In Dialogues Concerning Natural R e l i g i o n , pt IX, Hume says: 'What-ever we conceive as e x i s t e n t , we can a l s o conceive as nonexistent*. But, as 2 Shaffer p o i n t s out, t h i s d o c t r i n e i s ' f l a t l y c o n t r a d i c t o r y ' of what i s s a i d i n A T r e a t i s e of Human Nature (Oxford: 1888), p. 66: 'Whatever we conceive, we conceive to be e x i s t e n t * . In the l a t t e r q u o t a t i o n Hume wants t o t r e a t ' e x i s t s ' as a vacuous p r e d i c a t e which, l i k e ' s e l f - i d e n t i c a l ' , a p p l i e s to *In 'On A r i s t o t l e ' s Square of Opposition' ( r e p r i n t e d i n Moravcsik, J . , ed., A r i s t o t l e [New York: 1967], pp. 56-7, Thomson t r i e s u n s u c c e s s f u l l y to r e c o n c i l e these.passages; see Dancy, R., Sense and C o n t r a d i c t i o n : A Study  i n A r i s t o t l e (Boston: 1975), p. 154. 2 Sh a f f e r , J . , 'Existence, P r e d i c a t i o n and the O n t o l o g i c a l Argument', as r e p r i n t e d i n : Hick, J . and M c G i l l , eds, The Many-Faced Argument (New York: 1967), p. 235. 87 e v e r y t h i n g ; i n the former, he wants to t r e a t i t as a p r e d i c a t e which, u n l i k e • s e l f - i d e n t i c a l ' , may properly be withheld from s u b j e c t s . (3) In h i s Logic H i l l e b r a n d maintains that ' " A l l i s 8" does not imply t h a t A e x i s t s * . But i t i s d i f f i c u l t to r e c o n c i l e t h i s view with h i s c l a i m t h a t , * In the acceptance of A the idea of A's existence i s i n c l u d e d ' . 1 (4) John Stuart W i l l i s another philosopher whose views lea d him i n t o o n t o l o g i c a l d i f f i c u l t i e s . In W i l l ' s case, however, the c o n f l i c t i s p a r t i c u -l a r l y s t r i k i n g , s i n c e he was not one to cloak a b s u r d i t y i n obscure language which l e f t h i s i n t e n t i n doubt. In A. System of L o g i c , p. 50, he w r i t e s : In the p r o p o s i t i o n , Socrates i s j u s t , i t may seem to be i m p l i e d not only that the q u a l i t y j u s t can be a f f i r m e d of Socrates, but moreover that Socrates is_, t h a t i s to say, e x i s t s . T h i s , however, only shows that there i s an ambiguity i n the word i s ; a word which not only per-forms the f u n c t i o n of the copula i n a f f i r m a t i o n s , but has a l s o a meaning of i t s own, i n v i r t u e of which i t may i t s e l f be made the p r e d i c a t e of a p r o p o s i t i o n . That the employment of i t as a copula does not n e c e s s a r i l y i n -clude the a f f i r m a t i o n of existence appears from such a p r o p o s i t i o n as t h i s : A centaur i s a f i c t i o n of the poets; where i t cannot p o s s i b l y be implied that a centaur e x i s t s , s i n c e the p r o p o s i t i o n i t s e l f e x p r e s s l y a s s e r t s t h a t the t h i n g has no r e a l e x i s t e n c e . Thus, W i l l wants to maintain t h a t , when we say (e.g_.) 'Socrates i s j u s t ' , our words do not imply t h a t Socrates e x i s t s , s i n c e ' e x i s t s ' i s an independent p r e d i c a t e which, l i k e any o t h e r , we sometimes withhold from s u b j e c t s to which other p r e d i c a t e s apply. However p l a u s i b l e t h i s view may seem i n i t s e l f , i t i s not one which W i l l can c o n s i s t e n t l y maintain; f o r elsewhere i n A Sys- tem of Logic (p. 73) he says: AAs c i t e d i n Jones, E., Review of H i l l e b r a n d ' s Die neuen Theorien der  Kateqorischen Schlusse, Wind, v o l . 3 (1893),' pp. 276-7; Jones p o i n t s out the apparent i n c o n s i s t e n c y i n H i l l e b r a n d . 88 No [ e s s e n t i a l p r o p o s i t i o n ] can be reckoned such which r e l a t e s to an i n d i v i d u a l by name, that i s , i n which the subjec t i s a proper name. I n d i v i d u a l s have no essences; Therefore, the p r e d i c a t i o n of j u s t i c e to Socrates must be a c c i d e n t a l , s i n c e , u n l i k e R u s s e l l , W i l l t r e a t s 'Socrates* as a genuine proper namB. However, W i l l a l s o b e l i e v e s (p. 73) th a t ' A l l a c c i d e n t a l or non-e s s e n t i a l a f f i r m a t i o n does imply the r e a l e xistence of the s u b j e c t ' , which c o n t r a d i c t s the o r i g i n a l s u p p o s i t i o n that 'Socratss i s j u s t ' does not imply t h a t he e x i s t s . In the cases of W i l l and A r i s t o t l e i t i s p a r t i c u l a r l y c l e a r that they wish, i n p l a c e s , to hold that '"a i s s'1 does not e n t a i l ^O- e x i s t s 1 . That i s to say, a g a i n s t Parmenides they wish to hold that the p r e d i c a t i o n a l use of 'to be' i s independent of i t s e x i s t e n t i a l use. Otherwise, we would not be able to frame p r o p o s i t i o n s about what does not e x i s t . As A r i s t o t l e observes: ...But i n the case of th a t which i s not, i t i s not true t o say t h a t because i t i s the ob j e c t of o p i n i o n , i t i s ; f o r the op i n i o n h e l d about i t i s that i t i s not, not that i t i s . (Categoriae 21a30-4) In t h i s passage i t looks as though A r i s t o t l e i s simply h e l p i n g himself to a view which i t would be convenient not to c o n t r a d i c t — v i z . , that we can say something (.i.e., a t t a c h some p r e d i c a t e s ) t o what does not e x i s t . The f a c t that we are t h i n k i n g about Pegasus, e.g_., s u r e l y does not imply t h a t he e x i s t s . S u r e l y , we can a t l e a s t say that Pegasus i s a f i c t i o n , and do so t r u t h f u l l y w i t h implying that he e x i s t s ; see Topica 121al0-bl0 and De S o p h i s t i c u s E l e n -c h i s 167al-7. A r i s t o t l e does, however, prepare us f o r the anti-Parmenidean c o n c l u s i o n he reaches i n Categoriae 21a25-34. At De I n t e r p r e t a t i o n s 21al2-5 he discusses the p r o p o s i t i o n s : (1) A man i s a good shoemaker. (2) A man i s good. 89 From h i s d i s c u s s i o n of these p r o p o s i t i o n s he c l e a r l y intends us to see that* when c e r t a i n expressions (such as •good') are used as p a r t s of l a r g e r expres-s i o n s (such as 'good shoemaker*)* t h e i r use i n these l a r g e r expressions i s o f t e n independent of t h e i r use alone. Thus, (1) does not e n t a i l ( 2 ) . For (1) means that someone i s s k i l l f u l at making shoes, whereas (2) means that someone i s v i r t u o u s ; and a s k i l l f u l shoemaker may w e l l not be v i r t u o u s . In De SophiBticus E l e n c h i s (166b35-7a2) A r i s t o t l e appears to reason somewhat as f o l l o w s : In i t s p r e d i c a t i o n a l context * i s . . . * , the expression ' i s * has a d i s t i n c t meaning from i t s meaning i n the e x i s t e n t i a l context ' i s * . There-f o r e , from the p r o p o s i t i o n 'Homer i s a poet* (e.g.) we cannot i n f e r 'Homer i s ' — j u s t as, owing to the ambiguity of 'good', we cannot i n f e r that a man i s good from the f a c t that he i s a good shoemaker. The t h r u s t of t h i s d i s c u s s i o n seems to be t h a t Parmenides was l e d to h i s paradoxes through the neglect of the e x i s t e n t i a l / p r e d i c a t i o n a l ambiguity of 'to be*. But, as we have already seen, t h i s i s not so. Moreover, A r i s -t o t l e accepts enough of the Parmenidean p o s i t i o n 1 to be l e d i n t o c o n t r a d i c -t i o n when he t r i e s t o a l l o w f o r discourse about the nonexistent; hence, the c o n f l i c t between Categoriae 13bl4-9 and 21a25-3D. 2.6 Conclusion There i s ample room f o r controversy over what A r i s -t o t l e ' s v a r i ous pronouncements on being mean. Ule have seen t h a t empty general terms cannot be employed i n h i s l o g i c a l sys-tem, and t h a t he appears t o accept enough of Parmenides's views to make us wonder how he would e x p l a i n the meaningfulness of empty terms, s i n g u l a r or general. A r i s t o t l e i s c e r t a i n l y not the only l o g i c i a n whose p h i l o s o p h i c a l See, e.g., De Generations e t Corruptlone 3 l 8 a l 6 - 7 . 90 views l i m i t h i s l o g i c . Even so recent a l o g i c i a n as DeWorgan s a i d , ' I t i s only as rep r e s e n t i n g existence that a term i s used i n l o g i c * . The concept of e x i s t e n c e i s one whose e x p l i c a t i o n r e q u i r e s a more s o p h i s t i c a t e d a n a l y s i s of language than was a v a i l a b l e to the t r a d i t i o n a l l o g i c i a n , though A r i s t o t l e seems a t times to transcend the l i m i t s of h i s theory and to a n t i c i p a t e Kant and Frege. T r a d i t i o n a l l o g i c i a n s b e l i e v e d t h a t , u l t i m a t e l y , every p r o p o s i -t i o n i s of the s u b j e c t - p r e d i c a t e form. In A_ System of L o g i c , p. 13, W i l l (£.£,) w r i t e s : Every p r o p o s i t i o n c o n s i s t s of two names; and every p r o p o s i t i o n a f f i r m s or denies one of these names of the other. Concerning t h i s view of the b a s i c s t r u c t u r e of p r o p o s i t i o n s , Bradley a c u t e l y 2 observed i n 1883: The d o c t r i n e i s erroneous. "B f o l l o w s A", "A and B co-e x i s t " , "A and B are equal", "B f o l l o w s A", "A i s south of B " — i n these instances i t i s unnatural to take A or B as the subject and the residue as p r e d i c a t e . And, where exi s t e n c e i s d i r e c t l y a s s e r t e d or denied, as i n , "The s o u l e x i s t s " , o r , "There i s a sea-serpent", o r , "There i s nothing here", the d i f f i c u l t i e s of the theory w i l l be found to culminate. Not having an adequate view of the v a r i e d s t r u c t u r e s which p r o p o s i t i o n s may e x h i b i t , the t r a d i t i o n a l l o g i c i a n could not e x p l a i n the use of empty expres-s i o n s . T r a d i t i o n a l l o g i c , t h e r e f o r e , when c o n s i s t e n t , was contaminated by powerful, though i r r e l e v e n t , e x i s t e n c e assumptions. DeWorgan, A,, Logic (London: 1860), p. 251 Bradley, F. H., The P r i n c i p l e s of Logic (Oxford: 1967), v o l . I, p. 13 91 CONCLUSION TO PART I The Greeks, to t h e i r h o r r o r , found t h a t t h e i r fundamental i n t u i t i o n s concerning mathematics were i n c o n s i s t e n t . The discovery of incommensurables wreaked havoc upon t h e i r mathematics. I t was the r e v i s i o n a r y mathematician Eudoxus who replaced the Pythagorean theory of p r o p o r t i o n by a s u p e r i o r theory which was a p p l i c a b l e t o commensurable and incommensurable q u a n t i t i e s . In t h i s century mathematicians found that t h e i r i n t u i t i o n s concerning se t s are i n c o n s i s t e n t and thus i n need of r e v i s i o n . Nor should we think that t h i s i s a problem a f f l i c t i n g only mathematics. The t r u t h r a t h e r seems to be t h a t , when as i n mathematics we attempt to f o r m a l i z e our reasoning, then the c o n t r a -d i c t i o n s l a t e n t i n our unanalysed thought surface and must be removed through an adjustment of the deeper s t r u c t u r e from which they came. I know of no a_ p r i o r i reason why our i n t u i t i o n s , anymore than our d e s i r e s , should be con-s i s t e n t , The a_ p o s t e r i o r i evidence i s c e r t a i n l y a g a i n s t t h e i r being so. I hope th a t our cursory survey of Greek philosophy was a t l e a s t thorough enough to suggest t h a t our fundamental i n t u i t i o n s concerning existence may be incon-s i s t e n t . In any event, the c h i e f purpose of Parts I and I I i s to p o i n t out the need f o r the r e v i s i o n s i n our t r a d i t i o n a l concepts which I w i l l advocate i n Part I I I as a s o l u t i o n to the p h i l o s o p h i c a l problems introduced i n P a r t s I and I I . P a r t s I and I I may t h e r e f o r e be understood as essays i n d e s c r i p -t i v e metaphysics, whereas Part I I I i s an essay i n r e v i s i o n a r y metaphysics.* I use ' d e s c r i p t i v e ' and ' r e v i s i o n a r y * i n the senses which-Strawson ex-p l a i n s i n I n d i v i d u a l s (London: 1959), p. 9. 92 PART I I : MEDIEVAL THOUGHT PART I I CONTINUES OUR INTRODUCTION TO THE PRE-THEORETICAL PROBLEMS ASSOCI-ATED WITH THE CONCEPT OF EXISTENCE. ITS CHIEF PURPOSE IS TWO FOLD: 1) TO ACQUAINT THE READER WITH A NONPARMENIDEAN ANALYSIS OF EXISTENCE AND 2) TO SHOW HOW EXTREMELY PLAUSIBLE, GIVEN THAT ANALYSIS, THE ONTOLOGICAL ARGUMENT IS. TOWARDS THE END OF PART I WE INTRODUCED THE FREGEAN ANALYSIS OF 'EXISTS', IN WHICH THIS TERM CAN OCCUR ONLY IN GENERAL PROPOSITIONS} TOWARDS THE END OF PART I I WE WILL BEGIN OUR DEFENSE OF FREGE'S ANALYSIS. 93 ANSEL.ro 3.0 I n t r o d u c t i o n In t h i s chapter I w i l l f i r s t d i s c u s s the d i f f e r -ences i n the Greek and C h r i s t i a n outlooks i n s o f a r as these d i f f e r e n c e s should a f f e c t t h e i r l o g i c a l analyses of ' e x i s t s ' . I w i l l argue t h a t , given the C h r i s t i a n b e l i e f i n s i n and i n the l i t e r a l c r e a t i o n of the world, C h r i s t i a n philosophers must o f f e r a r a d i c a l l y non-Parmenidean a n a l y s i s of ' e x i s t s ' . Then I w i l l r e l a t e that non-Parmenidean a n a l y s i s to the C h r i s t i a n d i s c u s s i o n s of the problem of e x i s t e n t i a l import f o r the p r o p o s i t i o n s i n s y l l o g i s m s . Af-t e r our d i s c u s s i o n of medieval l o g i c , I w i l l present Anselm's O n t o l o g i c a l Ar-gument, an argument which we w i l l see to be very p l a u s i b l e indeed i n i t s l o g i -c a l context. 3.1 Cautionary Note I w i l l not attempt to argue that anyone's ac- t u a l s p e c u l a t i o n concerning e x i s t e n c e was c o n s c i o u s l y i n f l u e n c e d by the con-s i d e r a t i o n s I am about to put f o r t h . I do b e l i e v e that C h r i s t i a n theology r e q u i r e s a c e r t a i n a n a l y s i s of ' e x i s t s ' , and that there i s evidence that c e r -t a i n Medieval t h i n k e r s o f f e r e d the r e q u i r e d a n a l y s i s . S t i l l , though we must recognize a tendency i n human thought towards c o n s i s t e n c y , that tendency i s u n c e r t a i n and o f t e n unconscious. Moreover, c o n s i d e r i n g the s t a t e of my own knowledge, the i d e a l i z e d p o s i t i o n s a s c r i b e d to a c t u a l persons are more apt here than elsewhere to deviate unknowingly from h i s t o r i c a l f a c t . Therefore, though I have of course t r i e d to be f a i t h f u l to h i s t o r i c a l f a c t , when I quote from a Medieval work, i t i s probably best to think of the q u o t a t i o n as mere-l y i l l u s t r a t i n g a p o s i t i o n perhaps not found i n the work as a whole. I w i l l not attempt t o represent Medieval philosophy i n i t s f u l l complexity, depth, or v a r i e t y . 94 3.2 God and Q u a n t i f i c a t i o n Theory In the C h r i s t i a n t r a d i t i o n God i s an a r t i s t whose work i s the world. In L e i b n i z (whom f o r our present pur-poses we may regard as the l a s t important Medieval philosopher) we f i n d an attempt to provide a reasoned account of t h i s t r a d i t i o n a l d o c t r i n e . Let us approach that account n e g a t i v e l y , d i s t i n g u i s h i n g i t from a view which L e i b -n i z r e j e c t s as incoherent. In the mind of God there cannot be a fund of f e a t u r e l e s s s o u l s from which God s e l e c t s one from time to time and then places i t i n the world where i t acquires a c h a r a c t e r appropriate to i t s circumstances. On the c o n t r a r y , the c r e a t i o n of the world d i d not proceed by means of a k i n d of d i v i n e l o t t e r y i n which f o r no s p e c i a l reason one s o u l enters the world to become a man of wealth and power i n v i r t u e of the p o s i t i o n i n t o which i t was t h r u s t , w h i l e another s o u l , as l u c k would have i t , s u f f e r s the very r e -verse of t h i s . As the p a r t i c i p a n t s i n the French Revolution would have seen, t h i s would have been an unjust way f o r God to manifest h i s beneficence. But, apart f r o m . i t s i n j u s t i c e , L e i b n i z would say t h a t t h i s account of c r e a t i o n must be wrong because God could not s e l e c t anything from a fund ' f e a t u r e l e s s s o u l s ' , s i n c e even He could not i d e n t i f y such a s o u l as the object of future c r e a t i o n . C h r i s t i a n theology r e q u i r e s that God created Adam—i.e., a de-f i n i t e i n d i v i d u a l . I t i s not enough then t h a t God created a man; f o r the concept of a man i s a p p l i c a b l e to more than one i n d i v i d u a l . But God began the human race with a c e r t a i n i n d i v i d u a l . In order f o r God's c r e a t i o n of Adam to be a r a t i o n a l , d e l i b e r a t e a c t , He must ( i n L e i b n i z ' s view) have a concept of Adam so s p e c i f i c that i n p r i n c i p l e , i t c o u l d not be a p p l i c a b l e to more than one i n d i v i d u a l . I f h i s concept of Adam were a p p l i c a b l e to more than one p o s s i b l e i n d i v i d u a l , how could He know which one of these i n d i v i d u -a l s He had created when He saw that concept r e a l i z e d i n the world? 95 No d e s c r i p t i o n which i s i n any way incomplete i s a p p l i c a b l e to only one p o s s i b l e i n d i v i d u a l . Even i f the d e s c r i p t i o n 'English philosopher born i n 1872 who had numerous a f f a i r s with women and ran f o r Parliament' i n f a c t ap-p l i e s to only one person, i t might have a p p l i e d to more than one person. Even i f the d e s c r i p t i o n 'the f i r s t man to d i e * can apply to only one person, i t c o u l d have a p p l i e d to someone other than the one to whom i t does apply, and i s i n that sense general, not i n d i v i d u a l . To e x p l a i n God's a c t s of par-t i c u l a r c r e a t i o n , L e i b n i z assumes that f o r any p o s s i b l e i n d i v i d u a l God has a complete concept from which He can produce a f u l l d e s c r i p t i o n of that i n -d i v i d u a l . Because of the i d e n t i t y of i n d e s c e r n i b l e s , no two p o s s i b l e i n d i v i -duals could answer t o the same i n d i v i d u a l concept. In v i r t u e of His complete concepts God i s able to i d e n t i -f y the varioue p o s s i b l e i n d i v i d u a l s and consider them as candidates f o r c r e -a t i o n . I t f o l l o w s that the d e s c r i p t i o n s a s s o c i a t e d w i t h these concepts en-able God t o i d e n t i f y t h i n g s independently of t h e i r e x i s t e n c e . Otherwise, He c o u l d not i d e n t i f y the as yet uncreated Adam and then confer existence upon him. Our natures t h e r e f o r e are something which God recognizes but does not c r e a t e . Thus, we cannot blame God f o r our not having been born r i c h , e.2., i He can no more choose our parents than we. Thus, L e i b n i z w r i t e s : 1 ...You w i l l o b j e c t that i t i s p o s s i b l e f o r you t o ask why God d i d not give you more st r e n g t h than he has. I answer: i f he had done t h a t , you would not e x i s t , f o r he would have produced not you but another c r e a t u r e . i G r u a , G., ed., G. W. L e i b n i z , Textes i n s d i t s ( P a r i s : 1948), p. 314, note 157. ( I c i t e t h i s passage as contained and t r a n s l a t e d i n : mates, 8., ' I n d i v i d u a l s and modality i n the Philosophy of L e i b n i z ' , Studia L e i b n i t i a n a , Band IV (1972), p. 104.) 96 With the famous exception of P l a t o i n the Tiroaeus (27d-8d), Creeks gen-e r a l l y r e j e c t e d the p o s s i b i l i t y of c r e a t i o n from nothing, as A r i s t o t l e does i n De Ceneratione e t Corruptione 317a24-6. According to P l u t a r c h , e.£. :* Xenophanes l e f t room n e i t h e r f o r c r e a t i o n nor destruc-t i o n , but claims t h a t the universe i s always the same. For i f i t were created there would have been a time when i t was non-existent. But the nonexistent cannot come i n -to e x i s t e n c e , n e i t h e r can i t make anything nor can any-t h i n g be made from i t . But, as we've been n o t i c i n g , c r e a t l o ex n i h i l o i s an important p a r t of C h r i s -t i a n theology. Thus, we f i n d Thomas Aquinas, e.£., saying: 'That God can 2 and does make something from nothing should be s t e a d f a s t l y h e l d * . But A-quinas was not b l i n d to the prima f a c i e d i f f i c u l t i e s i n v o l v e d i n t h i s aspect 3 of C h r i s t i a n theology; he w r i t e s : The maker gives being t o t h a t which i s made. I f then God makes a t h i n g out of nothing, he gives being to t h a t t h i n g . Hence e i t h e r there i s something that r e c e i v e s being, or there i s nothing. I f nothing, then nothing r e -c e i v e s being by t h a t a c t i o n of God's, and thus nothing i s made thereby. I f something, ... God makes a t h i n g from something already e x i s t i n g , and not from nothing. 4 I do not w e l l understand how Aquinas would answer t h i s o b j e c t i o n , but h i s answer seems to i n v o l v e him i n the L e i b n i z i a n assumption that God can under-stand the natures even of t h i n g s which do not yet e x i s t . Otherwise, He would 1As c i t e d i n Ehrhardt, A., The Beginning (Manchester: 1968), p. 168. 2 G i l b y , T., t r , S a i n t Thomas Aquinas: P h i l o s o p h i c a l Texts (New York: 1960), p. 132. 3 A s c i t e d i n P r i o r , A., Past, Present, and Future (Oxford: 1967), p. 140. * I n t h i s connection see God and the Soul (New York: 1968), pp. 83-4, where Geach attempts to d i s t i n g u i s h transformations from absolute c r e a t i o n s . 9? not know what He was about to c r e a t e . R e c a l l i n g that on Parmenides's reason-in g discourse about the nonexistent appears impossible because the nonexis-t e n t i s assumed t o have no nature, we see t h a t C h r i s t i a n s are committed t o adopting a r a d i c a l l y non-Parmenidean a n a l y s i s of the r e l a t i o n between the e x i s t e n t i a l and p r e d i c a t i o n a l uses of 'to be'. For the purposes of elementary e x p o s i t i o n , I have permitted myself to d i s t i n g u i s h the Greek and C h r i s t i a n outlooks w i t h reference to the C h r i s t i a n c r e a t i o n myth, where God a c t s of c r e a t i o n appear i n a temporal order. Our problem was: How can God i d e n t i f y the as yet uncreated Adam? This was, I t h i n k , a good way of launching our d i s c u s s i o n , and not without i n t e r e s t . i n i t s own r i g h t . But we must now n o t i c e t h a t t h i s approach (a) i n v o l v e s us i n the s p e c i a l problems concerning the r e l a t i o n s h i p of an a l l e g e d l y atemporal being to h i s temporal works, w h i l e i t (b) avoids the very problems with which we are p r i m a r i l y concerned j u s t because i t centers our a t t e n t i o n upon f a i l u r e of reference i n temporal c o n t e x t s . To set matters r i g h t , we w i l l now consider the C h r i s t i a n concept of s i n . In the Apology (26a-b) and elsewhere Socrates argues t h a t no man would cons-c i o u s l y choose to do e v i l . A dominent theme i n Greek e t h i c s i s to equate e v i l - d o i n g w i t h ignorance. C h r i s t i a n s f o r the most part are of a d i f f e r e n t o p i n i o n . According to S a i n t Augustine, s i n i s the conscious choice of e v i l as e v i l ; i t i s something we do f r e e l y (and o f t e n ) . Free w i l l i s thus at the crux of s i n , and f r e e w i l l r e q u i r e s contingency. We should t h e r e f o r e expect to see C h r i s t i a n philosophers devoting a good deal of a t t e n t i o n to the t o p i c of contingency, and i n f a c t we do. Parmenides held that 'the same t h i n g can be thought as can be*, which I understand to mean: 'something i s p o s s i b l e i f and only i f i t e x i s t s ' . I f 98 we may i n t e r p r e t *G' i n (3') (Vx)(Gx - Ex) as ' p o s s i b l y e x i s t e n t * , then 'something i s p o s s i b l e i f and only i f i t e x i s t s ' emerges as a v a l i d consequence of the Parmenidean premise (2) (Vx)Ex, given the apparent tautology t h a t , i f something does e x i s t , i t i s p o s s i b l y e x i s t e n t . * Generally speaking, Greeks rather c h e e r f u l l y accepted the view t h a t every p o s s i b i l i t y i s r e a l i z e d . In h i s famous (now l o s t ) Waster Argument 2 Diodorus i s s a i d to have argued: The "master argument" appears to have been propounded on some such b a s i s as t h i s . There are three p r o p o s i t i o n s which are at variance with one a n o t h e r — i ^ i s . , any two with the t h i r d — n a m e l y , these: (1) everything as an event i n the past i s necessary; (2) the impossible does not f o l l o w from the p o s s i b l e ; (3) what n e i t h e r i s true nor w i l l be i s yet p o s s i b l e . Dio-dorus, n o t i c i n g t h i s c o n f l i c t of statements, used the p r o b a b i l i t y of the f i r s t two to;prove the c o n c l u s i o n , "Nothing i s p o s s i b l e which n e i t h e r i s nor w i l l be t r u e " . Boethius says t h a t 'Diodorus defi n e s the p o s s i b l e as that which e i t h e r i s or 3 w i l l be'. Though there are passages i n A r i s t o t l e r e m i n i s c i e n t of Diodorus (who was A r i s t o t l e ' s younger contemporary), t h i s d e f i n i t i o n of ' p o s s i b l e ' — and indeed the Waster Argument i t s e l f , whatever i t was*—would have been ^-'Possibly e x i s t e n t ' i s undoubtedly an i l l e g i t i m a t e p r e d i c a t e , and we w i l l see why i h the next chapter; but, given c e r t a i n p l a u s i b l e assumptions about generating 'QG' from 'G' and the employment of 'E* as a p r e d i c a t e , i t seems p e r m i s s i b l e t o use '<}E' as a p r e d i c a t e . 2 E p i c t e t u s , D i s s e r t a t i o n e , bk I I , ch 19. 3As c i t e d i n Kneale, W. and W., The Development of L o g i c , p. 117. *No one has been able to r e c o n s t r u c t t h i s l o s t argument. 99 anathema to C h r i s t i a n t h i n k e r s ; thus, we f i n d John Buridan, e_.£., saying: 'This p r o p o s i t i o n i s t r u e : "Something which w i l l not be, can be".' Buridan i s denying the v i e w — i m p l i c i t i n Parmenides, e x p l i c i t i n D i o d o r u s — t h a t every p o s s i b i l i t y i s r e a l i z e d . What i s at issue between the Greeks and C h r i s t i a n s 2 i s w e l l brought out by L e i b n i z , as f o l l o w s : One of the o l d e s t doubts of mankind concerns the ques-t i o n of how freedom and contingency are compatible with the chain of causes and w i t h providence. And C h r i s t i a n i n v e s t i g a t i o n s of the j u s t i c e of God i n accomplishing man's s a l v a t i o n have merely increased the d i f f i c u l t y of the matter. When I considered that nothing occurs by chance or by ac-c i d e n t unless we r e s o r t to c e r t a i n p a r t i c u l a r substances, t h a t fortune apart from f a t e i s an empty word, and that nothing e x i s t s unless c e r t a i n c o n d i t i o n s are f u l f i l l e d I found myself very c l o s e to the opinions of those who hold everything to be a b s o l u t e l y necessary; b e l i e v i n g that when t h i n g s are not subject to c o e r c i o n even though they are to n e c e s s i t y , there i s freedom, and not d i s t i n -g u i shing between the i n f a l l i b l e , or what i s known with c e r t a i n t y to be t r u e , and the necessary. But I was p u l l e d back from t h i s p r e c i p i c e by c o n s i d e r -ing those p o s s i b l e things which n e i t h e r are nor w i l l be nor have been. For i f c e r t a i n p o s s i b l e t h i n g s never e x i s t , e x i s t i n g things cannot always be necessary; other-wise i t would be impossible f o r other t h i n g s to e x i s t i n t h e i r p l a c e , and whatever never e x i s t s would t h e r e f o r e be impossible. For i t cannot be denied that many s t o r i e s , e s p e c i a l l y those we c a l l n o v e l s , may be regarded as pos-s i b l e , even i f they do not a c t u a l l y take place i n t h i s p a r t i c u l a r sequence of the universe which God has c h o s e n — unless someone imagines that there are c e r t a i n p o e t i c regions i n the i n f i n i t e extent of space and time where we might see wandering over the e a r t h King Arthur of Great B r i t a i n , Amadis of Gaul, and the fabulous D i e t r i c h von Bern invented by the Germans. •••As c i t e d i n Woody, E., Truth and Consequence i n Wediaval Logic (Amster-dam: 1953), p. 58. •On Freedom', as contained In: Loemker, L., ed., G o t t f r i e d Wilhelro  L e i b n i z : P h i l o s o p h i c a l Papers and L e t t e r s ( H o l l a n d : 1969), p. 263. 100 To the view that every p o s s i b i l i t y i s r e a l i z e d , L e i b n i z objects as f o l -lows: many t h i n g s , though p o s s i b l e i n themselves, are incompatible w i t h what does i n f a c t e x i s t ; hence, not every p o s s i b i l i t y i s r e a l i z e d — i..e_., some pos-s i b i l i t i e s are u n r e a l i z e d . By t h i s , L e i b n i z does not mean th a t u n r e a l i z e d p o s s i b i l i t i e s e x i s t ; on the c o n t r a r y , we w i l l see th a t he does not a t t r i b u t e e x i s t e n t i a l import to the p a r t i c u l a r q u a n t i f i e r 'some'. Thus, he does not f a l l i n t o the e r r o r of assuming t h a t the nonexistent i n some cu r i o u s way e x i s t s . Contrary to Parmenides, L e i b n i z holds that some p r o p o s i t i o n s of the form a i s 8 are true even i f a r e f e r s to nothing which e x i s t s . The p r o p o s i t i o n 'King Ar-thur i s p o s s i b l e * , e.g., i s true and yet does not imply the exi s t e n c e of King A r t h u r . To Arnauld, who objects t h a t L e i b n i z t r e a t s mere p o s s i b l e s as though they were r e a l , L e i b n i z answers:* Everything that i s a c t u a l can be conceived as p o s s i b l e , and i f the a c t u a l Adam w i l l have a c e r t a i n f p o s t e r i t y i n the course of time, one cannot deny t h i s same predicate t o t h i s Adam thought of as p o s s i b l e , e s p e c i a l l y s i n c e you agree t h a t God envisages i n him a l l h i s a t t r i b u t e s when he decides to create him. So these a t t r i b u t e s per-t a i n to him, and I do not see th a t what you say about the r e a l i t y of p o s s i b i l i t i e s i s contrary to t h i s . In or-der to c a l l something p o s s i b l e , i t i s enough merely to be able to form a concept of i t when i t i s only i n the d i v i n e understanding, which i s , so to speak, the realm of p o s s i b l e r e a l i t i e s . As concerns p o s s i b l e s , I am thus content that one can form true p r o p o s i t i o n s from them; thus one can judge, f o r example, that a p e r f e c t square i m p l i e s no c o n t r a d i c t i o n , even i f there has never been a p e r f e c t square i n the world. If we wished a b s o l u t e l y t o r e j e c t such pure p o s s i b l e s , we should destroy c o n t i n -gency and freedom, f o r i f nothing i s p o s s i b l e except what God has a c t u a l l y c r e a t e d , whatever God has created would be necessary, and i n w i l l i n g t o create something, God could create only that t h i n g alone, without any f r e e -dom of choi c e . •The L e i b n i z - A r n a u l d Correspondence';, as contained i n Loemker, p. 336.-101 Thus, L e i b n i z does not commit himself to there being nonexistent t h i n g s , such as King Arthur; he i s r a t h e r saying t h a t we can frame true p r o p o s i t i o n s about what does not e x i s t . N o t i c e , moreover, t h a t he i s not merely saying t h a t such comparatively unusual p r e d i c a t e s as ' i s p o s s i b l e ' apply d i r e c t l y to the nonexistent, but even ordinary ones such as 'has a p o s t e r i t y ' . L e i b n i z i s indeed committed to the view that a great many pr e d i c a t e s apply t o th i n g s independently of t h e i r e x i s t e n c e . For independently of Cod's d e c i s i o n t o cr e a t e something^He has a complete concept of every p o s s i b l e i n -d i v i d u a l which 'contains once and f o r a l l everything t h a t w i l l ever happen to him*, 1 I f God cou l d not know the nature of things independently of His ac t s of c r e a t i o n (i,.e_., independently of t h e i r a c t u a l e x i s t e n c e ) , then His knowledge of the world would have to be a p o s t e r i o r i and He would not be i n a p o s i t i o n to make r a t i o n a l choices amongst p o s s i b i l i t i e s , we may say that i n L e i b n i z ' s view any pred i c a t e necessary to the i n d i v i d u a t i o n of something a p p l i e s independently of i t s e x i s t e n c e . In a very strong sense, t h e r e f o r e , L e i b n i z i s committed t o the independence of the p r e d i c a t i o n a l use of 'to be* from i t s e x i s t e n t i a l use. Arnauld objected to L e i b n i z ' s i-complete-concepts' on the grounds t h a t they subjected the human race to 'a more than f a t a l n e c e s s i t y ' . To t h i s charge, i f I have understood him c o r r e c t l y , L e i b n i z r e p l i e d t h a t , although the concept of s i n i s contained i n the complete concept of Adam, e.g., the p r o p o s i t i o n 'Adam sinned' i s nonetheless contingent because God might not have created Adam at a l l , and i n that event 'Adam sinned' would i n f a c t have Lucas, P. and G r i n t , L., t r s , L e i b n i z ' s Discourse on Metaphysics (Man-c h e s t e r : 1968), pp. 18-9, number X I I I . 2Mason, H., t r , The Le i b n i z - A r n a u l d Correspondence (Manchester: 1967), p. 9. 102 been f a l s e . A In the New Essays he w r i t e s : c The s c h o l a s t i c s h o t l y debated de c o n s t a n t i a s u b j e c t ! , as they c a l l e d i t ; that i s , how a s u b j e c t - p r e d i c a t e propo-s i t i o n can have a r e a l t r u t h when the subject does not e x i s t . The answer i s that i t s t r u t h i s merely c o n d i t i -o n a l , i n t h a t that i f the s u b j e c t ever does e x i s t i t w i l l be found to be thus and so. I t i s d i f f i c u l t to see i n L e i b n i z ' s views a c r e d i b l e answer to Arnauld. I f the only c o n d i t i o n which must be s a t i s f i e d f o r Judas t o s i n , e.£., i s that he e x i s t , then, because i t i s not w i t h i n h i s power never to have e x i s t e d , Judas i s under the yoke of 'a more than f a t a l n e c e s s i t y ' , as Arnauld puts i t . L e i b n i z ' s f u r t h e r e l u c i d a t i o n s i n t h i s regard serve merely to render the a b s u r d i t y of h i s p o s i t i o n more evident. L e i b n i z o f t e n says t h a t neces-sary p r o p o s i t i o n s are r e d u c i b l e to i d e n t i t y statements i n a f i n i t e number of s t e p s , whereas contingent p r o p o s i t i o n s are not so r e d u c i b l e . For they are rooted i n the complete concepts of t h e i r s u b j e c t s , and such concepts are i n -f i n i t e — jL.e,, i n d i v i d u a l substances possess an i n f i n i t e number of p r i m i t i v e p r o p e r t i e s necessary t o t h e i r i n d i v i d u a t i o n . But, he adds, contingent pro-p o s i t i o n s nevertheless have t h e i r proofs a p r i o r i — i . e . , they are a n a l y t i c i n the sense defined by Kant. Cod, who alone can conduct demonstrations i n v o l v i n g an i n f i n i t e a n a l y s i s , sees the proofs a p r i o r i even of contingent p r o p o s i t i o n s . In t h i s way the d i v i n e foreknowledge necessary f o r God to '' 1 See Lucas and G r i n t , pp. 19-22; and Mason, pp. 11-7 and 39-66. (The reader may n o t i c e . t h a t t h i s defense of contingency and the q u o t a t i o n I am about to give from the New Essays Is i n c o n s i s t e n t with the a n a l y s i s of e x i s -tence t o which L e i b n i z i s committed;,: I w i l l deal w i t h t h i s p o i n t s h o r t l y . ) 2 New Essays concerning Human Understanding, bk i v , ch x i sec 13; t r a n s -l a t e d by J . Bennett and P. Remnant. 3see Parkinson, G., ed., L e i b n i z : L o g i c a l Papers (Oxford: 1966), pp. 60-4 and 76-8. 103 choose the o b j e c t s of h i s c r e a t i o n i s supposedly explained i n terms which do not commit b e l i e v e r s t o a k i n d of l o g i c a l determinism which i s i n c o n s i s -t e n t w i t h the contingency r e q u i r e d f o r s i n . From Augustine onwards, C h r i s -t i a n a p o l o g i s t s have spent much useless thought on the problem of d i v i n e foreknowledge and f r e e w i l l . But L e i b n i z i s perhaps alone i n h i s b e l i e f t h a t the problem' of l o g i c a l determinism f o r supposedly contingent p r o p o s i -t i o n s can be e l i m i n a t e d merely by making the demonstrations of such p r o p o s i -t i o n s very lengthy. Our concern, of course, Is not with the problem of f a t a l i s m , but we should nevertheless n o t i c e c e r t a i n l o g i c a l d i f f i c u l t i e s i n L e i b n i z ' s defence of f r e e w i l l } he w r i t e s : * But can i t be that i t i s assured from a l l e t e r n i t y that I s h a l l s i n ? Answer t h i s f o r yourselves} per-haps i t i s not. So i n s t e a d of musing on what you cannot know and what cannot give you any l i g h t , act according t o the duty which you know. But someone e l s e may say, how does i t come that t h i s man w i l l c e r -t a i n l y commit t h i s s i n ? The r e p l y i s easy; i t i s that otherwise he would not be t h i s man. For God foresees from a l l time that there w i l l be a c e r t a i n Judas, whose idea or concept which God has c o n t a i n s t h i s f u t u r e f r e e a c t . There remains then only t h i s question: Why does such a Judas, a t r a i t o r , who i s merely p o s s i b l e i n the Idea of God, a c t u a l l y e x i s t ? But to t h i s question no answer can be expected here on e a r t h , except the gen-e r a l one that s i n c e God has found i t good that he should e x i s t i n s p i t e of the s i n which God foresaw, t h i s e v i l must be compensated f o r with i n t e r e s t i n the universe and that God w i l l draw a greater good from i t and that i t w i l l t u rn out f i n a l l y that t h i s sequence of events, i n c l u d i n g the existence of t h i s s i n n e r , i s the most p e r f e c t among a l l other p o s s i b l e k i n d s . I m p l i c i t i n t h i s s u b t l e passage i s the view,that God has power over the Leemker, p. 32Z. [Discourse -on"Metaphysics, prop. 30] 1G4 e x i s t e n c e of t h i n g s , but not over t h e i r essences. I t mould seem that ' e x i s t s ' i s the only p r e d i c a t e which God i s at l i b e r t y to confer upon His c r e a t u r e s or w i t h h o l d from them. But, as we have seen, to save f r e e w i l l L e i b n i z a l s o holds that (A)-'Adam sinned* would have been f a l s e had God not created Adam; i t i s t h i s assumption which makes 'Adam sinned' a contingent p r o p o s i t i o n . But how can L e i b