UBC Theses and Dissertations

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UBC Theses and Dissertations

Particles and motion in Spinoza's physics Boulogne, Jack 1969

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PARTICLES AND MOTION IN SPINOZA'S PHYSICS by Jac o b Boulogne B.A., U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1960 A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A. i n the Department o f PHILOSOPHY We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e qu i r e d/st^inda r d THE UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER, 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h C olumbia, I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and Study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date ABSTRACT The c e n t r a l aim o f my t h e s i s i s t o e n q u i r e i n t o S p i n o z a ' s t h e o r y of the s t r u c t u r e of the p h y s i c a l u n i v e r s e . I t i s g e n e r a l l y a c c e p t e d t h a t f r o m a s c i e n t i f i c p o i n t o f v i e w S p i n o z a r e g a r d e d the u n i v e r s e as c o n s i s t i n g o f p a r t i c l e s i n m o t i o n . My major c o n c e r n i s w i t h the n a t u r e o f t h e s e p a r t i c l e s and what r o l e t h e y p l a y i n h i s cosmology. My b a s i c method of e n q u i r y i s t o c o n s i d e r , as f a r as t h i s i s p o s s i b l e , S p i n o z a ' s s t a t e m e n t s about the s t r u c t u r e o f m a t t e r as a s c i e n t i f i c t h e o r y , a system of p h y s i c s . C h a p t e r Two i s a b r i e f s u r v e y o f S p i n o z a ' s s c i e n t i f i c a c t i v i t i e s , by way o f p r o v i d i n g background. I n C h a p t e r Three I e x p l o r e the p h y s i c a l t h e o r y p r e s e n t e d i n P a r t Two o f the P r i n c i p l e s o f C a r t e s i a n P h i l o s o p h y w i t h p a r t i c u l a r emphasis on the b a s i c p r e m i s s e s o f t h a t t h e o r y , and t h e problems a r i s i n g f r o m t h o s e b a s i c p r e m i s s e s . I n C h a p t e r s F o u r , F i v e , and S i x , the p h y s i c a l t h e o r y o f the E t h i c s i s d i s c u s s e d , w i t h p a r t i c u l a r a t t e n t i o n to S p i n o z a ' s t h e o r y o f i n d i v i d u a l s and h i s i d e a s on m o t i o n . C h a p t e r Seven i s a f a i r l y d e t a i l e d d i s c u s s i o n o f t h e n a t u r e o f the s i m p l e s t b o d i e s i n S p i n o z a ' s system. C h a p t e r E i g h t i s a d i s c u s s i o n o f S p i n o z a ' s c o n c e p t of t h e u n i v e r s e as a system composed i i i o f p a r t i c l e s i n m o t i o n , w i t h p a r t i c u l a r emphasis on h i s i d e a s on t h e continuum. My major c o n c l u s i o n i s t h a t as f a r as s c i e n t i f i c e x p l a n a t i o n i s co n c e r n e d , t h e S p i n o -z i s t i c p h y s i c s i s v e r y s i m i l a r t o t h e C a r t e s i a n p h y s i c s as p r e s e n t e d i n t h e P r i n c i p l e s o f C a r t e s i a n P h i l o s o p h y . T h i s c o n c l u s i o n i s based on f i v e c o n s i d e r a t i o n : (1) the g e n e r a l c h a r a c t e r o f t h e p h y s i c s o f t h e E t h i c s i s q u i t e c o m p a t i b l e w i t h t h e C a r t e s i a n p h y s i c s w i t h one apparent e x c e p t i o n : I g i v e an e x p l a n a t i o n o f t h i s a pparent d i s -c r e p a n c y ; (2) S p i n o z a ' s deep c o n c e r n w i t h t h e problems o f t h e continuum can o n l y be e x p l a i n e d i f t h e b a s i c p r e m i s s e s o f h i s p h y s i c s a re t h e same as t h a t o f t h e C a r t e s i a n p h y s i c s ; (3) the same a p p l i e s t o h i s d e n i a l o f t h e e x i s t e n c e o f the vacuum; (4) t h e r e i s n o t h i n g t h a t i n d i c a t e s t h a t S p i n o z a ' s s c i e n t i f i c method i f r a d i c a l l y d i f f e r e n t from t h a t u n d e r l y i n g t h e P r i n c i p l e s  o f C a r t e s i a n P h i l o s o p h y ; (5) the one i n s t a n c e o f S p i n o z a ' s o u t r i g h t l y condemning t h e C a r t e s i a n p h y s i c s i s based on a fundamental m e t a p h y s i c a l i s s u e and has no d i r e c t b e a r i n g on t h a t p h y s i c s qua p h y s i c s . The major i m p l i c a t i o n o f my c o n c l u s i o n i s t h a t many o f S p i n o z a ' s p o i n t s o f d o c t r i n e cannot be f u l l y u n d e r s t o o d u n l e s s t h e y a r e i n t e r p r e t e d i n the c o n t e x t o f t h e C a r t e s i a n cosmology. i v TABLE OF CONTENTS ABSTRACT TABLE OF CONTENTS ACKNOWLEDGEMENT CHAPTER I : CHAPTER I I : CHAPTER I I I : CHAPTER IV: CHAPTER V: CHAPTER V I : CHAPTER V I I : CHAPTER V I I I : BIBLIOGRAPHY APPENDIX A: APPENDIX B: APPENDIX C: INTRODUCTION SPINOZA'S SCIENTIFIC ACTIVITIES THE CARTESIAN PHYSICS THE PHYSICS OF THE ETHICS THE THEORY OF INDIVIDUALS MOTION IN SPINOZA'S PHYSICS THE CORPORA SIMPLICISSIMA MOTION AND PARTICLES SPINOZA'S LIBRARY THE HYDROSTATIC EXPERIMENT THE SIXTH RULE OF MOTION V ACKNOWLEDGEMENT I am g r a t e f u l t o P r o f e s s o r Remnant f o r h i s s u g g e s t i o n s and c r i t i c i s m s , and t o the U n i v e r s i t y o f B r i t i s h Columbia f o r t h e f i n a n c i a l a s s i s t a n c e w h i c h made my s t u d i e s p o s s i b l e . I e s p e c i a l l y w i s h t o thank my w i f e , J e a n , f o r h e r h e l p and encouragement. CHAPTER I INTRODUCTION The b a s i c purpose o f t h i s t h e s i s i s t o e x p l o r e t h e c h a r a c t e r o f t h e p r i m a r y p a r t i c l e s and o f m o t i o n i n S p i n o z a ' s system, and the r o l e t h e y p l a y i n h i s cosmology. As f a r as I have been a b l e t o d i s c o v e r , t h i s p a r t o f S p i n o z a ' s t h e o r y has not r e c e i v e d a v e r y c l o s e s c r u t i n y , and y e t , as I w i l l show, a number o f i n t e r e s t i n g f a c e t s o f S p i n o z a ' s t h o u g h t a r e r e v e a l e d when h i s i d e a s on the f o u n d a t i o n s o f p h y s i c a l s c i e n c e a r e e x p l o r e d . A l a r g e q u a n t i t y o f commentary i s a v a i l a b l e on S p i n o z a ' s p h y s i c s from a m e t a p h y s i c a l p o i n t o f v i e w , t h a t i s , as a v e r y g e n e r a l scheme f o r l o o k i n g a t r e a l i t y ; b u t h i s p h y s i c s as a d e t a i l e d e x p l a n a t i o n o f the p h y s i c a l phenomena does not seem t o have had t h e b e n e f i t o f a c l o s e e x a m i n a t i o n . T h i s c o n c e r n s p a r t i c u l a r l y t h e n a t u r e o f t h e s i m p l e s t b o d i e s and m o t i o n i n h i s system; t h a t S p i n o z a v i e w e d t h e p h y s i c a l w o r l d i n terms o f p a r t i c l e s i n m o t i o n seems t o be g e n e r a l l y a g r e e d on, b u t e x a c t l y how h i s scheme works i n d e t a i l , and p r e c i s e l y what t h e n a t u r e o f t h e s e p a r t i c l e s i s , remains o b s c u r e . My r e a d -i n g o f S p i n o z a ' s w r i t i n g s , e s p e c i a l l y h i s cor r e s p o n d e n c e , has c o n v i n c e d me t h a t he had always i n mind t h e i n t e n t i o n t o s e t up a d e t a i l e d s c i e n c e o f mechanics, o r a t l e a s t t o l a y a s o l i d f o u n d a t i o n on w h i c h s u c h a s c i e n c e i s t o be based. My emphasis, t h e r e f o r e , w i l l be on t r e a t i n g h i s i d e a s i n t h a t l i g h t , t o c o n s i d e r h i s scheme, as a program f o r p h y s i c a l s c i e n c e . A f o r m i d a b l e o b s t a c l e i n t h e way o f t h i s k i n d o f p r o j e c t i s t h e p a u c i t y o f a v a i l a b l e m a t e r i a l . The t h r e e p r i n c i p a l s o u r c e s a r e t h e P r i n c i p l e s o f C a r t e s i a n  P h i l o s o p h y ( h e r e a f t e r t o be a b b r e v i a t e d as " P r i n c i p l e s " ) , a few l e t t e r s and a few pages i n t h e E t h i c s . The P r i n c i p l e s p u b l i s h e d i n 1663, has t h e s e r i o u s d i s a d v a n t a g e as a s o u r c e , i n t h a t i t p u r p o r t s t o be m e r e l y an e x p o s i t i o n o f D e s c a r t e s ' p h i l o s o p h y , and s u p p o s e d l y does not r e p r e s e n t S p i n o z a ' s own i d e a s . The E t h i c s , w h i c h can be t a k e n as r e p r e s e n t i n g h i s i d e a s i n t h e i r most complete and f u l l y d e v e l o p e d form, l a m e n t a b l y i s w r i t t e n i n a h i g h l y condensed form, and c o n t a i n s v e r y l i t t l e i n t h e way o f d i s c u s s i o n , comment o r e x p l a n a t i o n . The e a r l i e r l e t t e r s , e s p e c i a l l y t h o s e ad-d r e s s e d t o Oldenburg and w r i t t e n i n A p r i l 1662, A p r i l 1663, and June 1663, c o n t a i n e x t e n s i v e d i s c u s s i o n s , b u t t h e i r v a l u e i s somewhat l i m i t e d w i t h r e s p e c t t o S p i n o z a ' s l a t e r i d e a s . The l a t e r l e t t e r s c o n t a i n o n l y a sentence here and t h e r e , w h i c h a r e u s e f u l as c l u e s , b u t p r o v i d e l i t t l e c o n c r e t e i n f o r m a t i o n . Hence I have t a k e n t h e p h y s i c a l t h e o r y o f t h e E t h i c s as t h e k e y s o u r c e o f i n f o r m a t i o n , and the f i n a l a r b i t e r on what S p i n o z a ' s l a t e s t and most f u l l y d e v e l o p e d v i e w s a r e . However, I have d e v o t e d a c o n s i d e r a b l e amount o f a t t e n t i o n t o the p h y s i c s o f t h e P r i n c i p l e s , t h e reasons f o r w h i c h I have o u t l i n e d i n t h e t h i r d c h a p t e r , w h i c h c o n t a i n s a d i s c u s s i o n o f t h a t p h y s i c s . T h i s t h e s i s i s n e c e s s a r i l y l i m i t e d i n s e v e r a l ways. F o r i n s t a n c e , I have l a r g e l y b y p a s s e d a d i s c u s s i o n o f S p i n o z a ' s t h e o r y o f s c i e n t i f i c method, w h i c h o f c o u r s e i s r a t h e r i m p o r t a n t i n i t s own r i g h t , b u t w h i c h d e s e r v e s a more tho r o u g h d i s c u s s i o n t h a n I c o u l d p o s s i b l y g i v e i t h e r e . A f u l l t r e a t m e n t o f t h i s t o p i c can be f o u n d i n R i c h a r d McKeon's^ book, w h i c h I have f o u n d t o be an i n -v a l u a b l e s o u r c e o f i d e a s ; t h e c h a p t e r on D e s c a r t e s and S p i n o z a and t h e c h a p t e r on e x p e r i m e n t a l s c i e n c e a r e e s p e c i a l l y u s e f u l . McKeon bases h i s d i s c u s s i o n o f S p i n o z a ' s s c i e n t i f i c method l a r g e l y on the d i s p u t e between Robert B o y l e and S p i n o z a on t h e n a t u r e o f n i t r e and t h e c h a r a c t e r o f h a r d n e s s , s o f t n e s s and f l u i d i t y . T h i s d i s p u t e , w h i c h i s f o u n d , i n t h e c orrespondence w i t h Henry Oldenburg, has not been a n a l y z e d i n d e t a i l i n t h i s t h e s i s , f o r s e v e r a l reasons; one i s t h a t i t i s r a t h e r i n v o l v e d , e s p e c i a l l y because o f Oldenburg's r o l e as an i n t e r m e d i a r y i n the d i s p u t e . Second, th e d i s p u t e d a t e s from the same p e r i o d as the w r i t i n g o f t h e P r i n c i p l e s , and hence i t s u s e f u l n e s s as i n f o r m a t i o n on S p i n o z a ' s l a t e r i d e a s i s somewhat l i m i t e d . 4 T h i r d , i t s c h i e f u s e f u l n e s s i s i n the a r e a o f s c i e n t i f i c method, w h i c h i s o u t s i d e t h e scope o f t h i s t h e s i s , a l t h o u g h t h e s u b j e c t cannot be a v o i d e d a l t o g e t h e r . A n o t h e r l i m i t a t i o n w h i c h I have had t o s e t my-s e l f i n t h e w r i t i n g o f t h i s t h e s i s c o n s i s t s o f a v o i d i n g a d i s c u s s i o n o f S p i n o z a ' s p h i l o s o p h y i n b r o a d e r terms. P l e n t y o f commentary on t h a t s u b j e c t e x i s t s a l r e a d y , and, b e s i d e s , my purpose i s t o e x p l o r e S p i n o z a ' s p h y s i c s i n o r d e r t o shed l i g h t on h i s l a r g e r scheme, and not v i c e v e r s a . N o n e t h e l e s s , I have had t o t a k e c e r t a i n p a r t s o f h i s d o c t r i n e f o r g r a n t e d as common knowledge. F o r i n s t a n c e , I have t a k e n f o r g r a n t e d h i s p o i n t s o f d o c t r i n e t h a t t h e r e i s no p l u r a l i t y o f s u b s t a n c e s , t h a t t h e r e i s a p e r f e c t p a r a l l e l i s m between the a t t r i b u t e s o f Thought and o f E x t e n s i o n , and t h a t t h e r e i s no c r e a t o r o u t s i d e o f sub-s t a n c e . A r e f e r e n c e t o S p i n o z a ' s g e n e r a l p h i l o s o p h i c a l system i s o f t e n n e c e s s a r y t o c l a r i f y some o f t h e t h i n g s he s a y s , e s p e c i a l l y what he says i n the E t h i c s , b u t I have t r i e d t o a v o i d m i s r e p r e s e n t i n g h i s d o c t r i n e , and p u t t i n g t o o much w e i g h t on s p e c i f i c p o i n t s o f d o c t r i n e . I have t a k e n c a r e t o a v o i d becoming e n t a n g l e d i n the p h i l o s o p h i c a l d i s a g r e e m e n t s between D e s c a r t e s and S p i n o z a . Throughout t h i s work, r e f e r e n c e s t o D e s c a r t e s a r e a l m o s t e x c l u s i v e l y l i m i t e d t o the m a t e r i a l o f t h e P r i n c i p l e s ; when I have o c c a s i o n t o r e f e r t o t h e C a r t e s i a n p h y s i c s , I s h a l l be 5 r e f e r r i n g t o t h e p h y s i c s o f t h e P r i n c i p l e s , l e a v i n g i t d e l i b e r a t e l y u n s p e c i f i e d t o what e x t e n t t h a t p h y s i c a l t h e o r y r e p r e s e n t s D e s c a r t e s ' s i d e a s . My aim i s t o d i s c u s s S p i n o z a ' s i d e a s , not tho s e o f D e s c a r t e s ' s . x S e e McKeon, pages 137-157. ( A l l r e f e r e n c e s are t o the appended l i s t o f w o r k s ) . 6 CHAPTER I I SPINOZA'S SCIENTIFIC ACTIVITIES S p i n o z a was u n d o u b t e d l y a w e l l e d u c a t e d man i n s c i e n t i f i c m a t t e r s . The l i s t o f books l e f t by him i n h i s l i b r a r y a t h i s d e a t h i s good e v i d e n c e o f t h i s ( I have appended t h i s l i s t , t o g e t h e r w i t h some comments). He was a c q u a i n t e d w i t h almost a l l o f t h e s c i e n t i f i c developments of h i s t i m e , and he was always a s k i n g h i s c o r r e s p o n d e n t s f o r i n f o r m a t i o n about the l a t e s t e x p e r i m e n t s and d i s c o v e r i e s . He was t h o r o u g h l y f a m i l i a r w i t h t h e s c i e n t i f i c i d e a s o f D e s c a r t e s , whose t h e o r i e s were v e r y much a p a r t o f t h e mainstream o f t h e s c i e n t i f i c t h o u g h t o f t h a t age. H i s d i s p u t e w i t h Robert B o y l e on the t o p i c o f t h e r e d i n t e g r a t i o n o f n i t r e shows us a man who had a good u n d e r s t a n d i n g o f t h e n a t u r e o f B o y l e ' s s c i e n t i f i c work; h i s c r i t i c i s m s o f B o y l e , a l t h o u g h not c o m p l e t e l y w i t h o u t f l a w s , were w e l l founded and q u i t e s o p h i s t i c a t e d . ^ A s i d e f r o m a g e n e r a l i n t e r e s t i n the s c i e n c e o f h i s t i m e , S p i n o z a was a l s o t o some e x t e n t more d i r e c t l y i n v o l v e d . S u p r i s i n g l y , f o r a man who i s l a b e l e d a r a t i o n -a l i s t p h i l o s o p h e r 2 , he c a r r i e d out a s m a l l amount o f e x p e r i m e n t a l work. There i s f i r s t o f a l l the h y d r o s t a t i c e x p e r i m e n t d e s c r i b e d i n t h e l e t t e r t o J a r i g J e l l e s o f September 1669, w h i c h i s f a i r l y e l a b o r a t e and c a r e f u l l y 7 s e t up. The f i r s t p a r t o f t h e e x p e r i m e n t i s d e s i g n e d t o show t h a t w a t e r i n a s e r i e s o f i n t e r c o n n e c t e d tubes w i l l r e a c h t h e same l e v e l i n t h o s e t u b e s . The second h a l f o f the e x p e r i m e n t i s b e t t e r d e s c r i b e d as a hydrodynamic e x p e r i m e n t , because i t d e a l s w i t h r a t e s o f f l o w o f w a t e r . The second p a r t o f t h e e x p e r i m e n t i s r a t h e r i n t e r e s t i n g i n t h a t t h e e x p e r i m e n t a l a p p a r a t u s used by S p i n o z a i s q u i t e s u i t a b l e f o r the i n v e s t i g a t i o n o f momentum, v e l o c i t y and a c c e l e r a t i o n . As a p o i n t o f g e n e r a l i n t e r e s t I have appended a more d e t a i l e d d i s c u s s i o n o f t h e e x p e r i m e n t (see Appendix B ) . A n o t h e r s e t o f e x p e r i m e n t s i s c o n n e c t e d w i t h the n i t r e d i s p u t e ; t h e d e s c r i p t i o n o f t h e s e i s f o u n d i n the l e t t e r o f A p r i l 1662 t o Oldenburg. These e x p e r i m e n t s a r e u n d e r t a k e n by S p i n o z a not so much out o f what we might c a l l s h e e r s c i e n t i f i c c u r i o s i t y , b u t t o p r o v e a c e r t a i n p o i n t , t h e p o i n t b e i n g t h a t h i s e x p l a n a t i o n s o f the c h a r a c t e r o f n i t r e a re a t l e a s t as p l a u s i b l e as t h o s e o f B o y l e ' s , and t h a t o n l y v e r y s i m p l e e x p e r i m e n t s a r e needed, r a t h e r t h a n the e l a b o r a t e ones t h a t B o y l e has p e r f o r m e d . A c c o r d i n g l y , S p i n o z a ' s e x p e r i m e n t s are r a t h e r s i m p l e . A n o t h e r e x p e r i m e n t w h i c h S p i n o z a d e s c r i b e s , but does not p e r f o r m , i s mentioned i n t h e l e t t e r o f A p r i l 1662 t o Oldenburg. I t s purpose i s t o compare a t m o s p h e r i c 8 p r e s s u r e i n a h o r i z o n t a l p l a n e w i t h t h a t i n a v e r t i c a l p l a n e , w h i c h i s done by t a k i n g measurements o f t h e f o r c e r e q u i r e d t o p u l l a p a r t two smoothly p o l i s h e d p i e c e s o f mar b l e . T h i s e x p e r i m e n t may n o t be o r i g i n a l w i t h S p i n o z a , 3 sxnce mentxon i s made o f i t by D e s c a r t e s and o t h e r s ; the p o i n t o f i n t e r e s t i s t h a t he does not f e e l s u f f i c i e n t l y c u r i o u s about t h e r e s u l t o f such an e x p e r i m e n t t o e x e c u t e i t , i t seems. T h i s apparent l a c k o f c u r i o s i t y i s e v i d e n t i n t h e o t h e r e x p e r i m e n t s as w e l l ; as soon as some p o i n t i s s u f f i c i e n t l y w e l l e s t a b l i s h e d , i n h i s o p i n i o n , S p i n o z a l o s e s i n t e r e s t . What s t a n d s out c l e a r l y f r o m S p i n o z a ' s e x p e r i m e n t a l a c t i v i t i e s , i s t h a t as f a r as h i s own l i f e and work i s concerned, he does not a t t a c h a g r e a t d e a l o f imp o r t a n c e t o e x p e r i m e n t a t i o n . On t h e o t h e r hand, whether he t h o u g h t t h a t e x p e r i m e n t a t i o n and o b s e r v a t i o n were an e s s e n t i a l element o f s c i e n t i f i c a c t i v i t y i s out o f t h e scope o f t h i s t h e s i s t o de t e r m i n e . He may have thought t h a t e x p e r i m e n t s were v e r y i m p o r t a n t w h i l e b e i n g c o n t e n t t o l e t o t h e r s c a r r y them o u t , o r he may have thought t h a t e x p e r i m e n t s were i n c i d e n t a l and s e r v e d m e r e l y as an a i d t o t h o u g h t . The e v i d e n c e i s somewhat c o n t r a d i c t o r y on t h i s p o i n t . The major p o r t i o n o f S p i n o z a ' s s c i e n t i f i c work was i n the f i e l d o f g e o m e t r i c a l o p t i c s . H i s r e p u t a t i o n i n t h i s a r e a was w e l l e s t a b l i s h e d and wide s p r e a d . L e i b n i z , 9 i n a l e t t e r w r i t t e n i n O c t o b e r 1671, s a ys t o him: "Among the o t h e r p r a i s e s o f you w h i c h fame has b r u i t e d abroad, I u n d e r s t a n d i s y o u r g r e a t s k i l l i n o p t i c s . " L e i b n i z sends a l o n g a t e c h n i c a l paper f o r comment, and t h e y d i s c u s s t h e p r o b l e m o f s p h e r i c a l a b e r r a t i o n i n l e n s systems. There a r e numerous o t h e r i t e m s w h i c h a t t e s t t o S p i n o z a ' s h i g h l e v e l o f competence i n o p t i c a l s c i e n c e . I n a l e t t e r t o J a r i g J e l l e s , d a t e d March 25, 1667, he d i s c u s s e s , geo-m e t r i c a l l y and i n d e t a i l , how the eye sees an image p r o -duced by a t e l e s c o p e . I n a l e t t e r t o John Hudde, June 1666, he d e s c r i b e s and compares t h e o p t i c a l p r o p e r t i e s o f v a r i o u s l e n s shapes. There are a l s o a number o f i t e m s d e a l i n g w i t h p r a c t i c a l problems of l e n s g r i n d i n g , one of w h i c h s h o u l d be r e p o r t e d i f o n l y because i t i s amusing. Huygens has c o n s t r u c t e d a l e n s p o l i s h i n g machine 4*, but S p i n o z a i s opposed t o a u t o m a t i o n , and b e l i e v e s t h a t , a l t h o u g h he i s not a c q u a i n t e d w i t h such a machine, manual methods a r e p r e f e r a b l e , because "... e x p e r i e n c e has t a u g h t me s u f f i c i e n t l y t h a t i n s p h e r i c a l t o o l s i t i s s a f e r and b e t t e r f o r g l a s s e s t o be p o l i s h e d w i t h a f r e e hand t h a n by any machine". S p i n o z a ' s o n l y major work i n o p t i c a l s c i e n c e i s h i s T r e a t i s e on t h e Rainbow^, w h i c h i s a d e t a i l e d and c a r e f u l l y worked o u t m a t h e m a t i c a l d e r i v a t i o n o f the a n g u l a r s i z e s o f b o t h p r i m a r y and s econdary r a i n b o w s . I t i s r e a l l y more an e x e r c i s e i n geometry and t r i g o n o m e t r y , t h a n a work of p h y s i c a l s c i e n c e , and i n d e e d , t h e work i s p r e -s e n t e d t o the r e a d e r as a means o f t e s t i n g and i m p r o v i n g h i s m a t h e m a t i c a l a b i l i t y , a l t h o u g h i t a l s o c o n t a i n s a b r i e f e x p l a n a t i o n of t h e cause o f t h e c o l o u r s o f t h e r a i n b o w . The e x p l a n a t i o n , w h i c h S p i n o z a a t t r i b u t e s t o D e s c a r t e s , i s i n terms o f t h e d i f f e r e n t degrees o f s t r e n g t h o f c o l o u r s , r e d b e i n g t h e s t r o n g e s t , and v i o l e t , on the o t h e r end o f the spectrum, the weakest. Of t h e s e r a y s o f l i g h t w h i c h have t o t r a v e l t h r o u g h t h e g r e a t e s t t h i c k n e s s o f w a t e r , the weaker c o l o u r s are s o r t e d o u t , and o n l y t h e s t r o n g e r get t h r o u g h . Rays w h i c h t r a v e l t h r o u g h a s h o r t e r d i s t a n c e i n w a t e r show the o t h e r c o l o u r s more s t r o n g l y . The t h e o r y as i t i s p r e s e n t e d i n t h e t r e a t i s e i s somewhat vague and i s n o t d e v e l o p e d i n d e t a i l , b u t i t i s a f a i r l y p l a u s i b l e e x p l a n a t i o n o f c o l o u r d i s p e r s i o n . Newton, a few y e a r s l a t e r , gave t h e c o r r e c t e x p l a n a t i o n , namely t h a t w h i t e l i g h t i s composed o f , o r can be r e s o l v e d i n t o , l i g h t o f d i f f e r e n t c o l o u r s , e a c h c o l o u r h a v i n g a s l i g h t l y d i f f e r e n t i n d e x o f r e f r a c t i o n . I n r e t r o s p e c t i t seems t h a t S p i n o z a , p o s s e s s i n g a sound s c i e n t i f i c background and undoubted m a t h e m a t i c a l competence, was i n a good p o s i t i o n t o have made t h i s d i s c o v e r y h i m s e l f , b u t l i k e l y he f e l t t h a t the o t h e r e x p l a n a t i o n was q u i t e adequate, e s p e c i a l l y s i n c e he p r a i s e s D e s c a r t e s i n t h e T r e a t i s e f o r h a v i n g g i v e n i t . A p a r t from th e q u e s t i o n o f c o l o u r d i s p e r s i o n , t h e T r e a t i s e says n o t h i n g about th e n a t u r e o f l i g h t , a l t h o u g h we may assume t h a t S p i n o z a ' s t h e o r y o f l i g h t was much the same as t h a t o f D e s c a r t e s ' s ^ . The s i g n i f i c a n c e o f S p i n o z a ' s work on o p t i c s l i e s i n the f a c t t h a t g e o m e t r i c a l o p t i c s i s a d e d u c t i v e s c i e n c e p a r e x c e l l e n c e . From two s i m p l e , b a s i c e l e m e n t s , the law o f r e f l e c t i o n , and t h e r u l e s o f r e f r a c t i o n , and u s i n g o n l y g e o m e t r i c a l methods, i t i s p o s s i b l e t o deduce a l a r g e number o f complex r e l a t i o n s h i p s about t e l e s c o p e s , r a i n b o w s , and bent s t i c k s i n w a t e r . I t i s the s c i e n c e f o r w h i c h D e s c a r t e s ' s famous i d e n t i f i c a t i o n o f p h y s i c s w i t h geometry i s c l o s e s t t o b e i n g t r u e . I t i s a p l a u s i b l e c o n j e c t u r e t h a t S p i n o z a v i s u a l i z e d a p h y s i c a l s c i e n c e w i t h the same e l e g a n c e and p r e c i s i o n t h a t i s c h a r a c t e r i s t i c o f o p t i c s , a s c i e n c e based on a few axioms and d e f i n i t i o n s f r o m w h i c h a l l t h e complex phenomena can be deduced. A l l i n a l l , S p i n o z a was r i g h t i n t h e m i d s t of t h i n g s s c i e n t i f i c , and i n v i e w o f h i s i n v o l v e m e n t w i t h t h e s c i e n c e o f h i s day and h i s m a t h e m a t i c a l competence, as t h e T r e a t i s e on the Rainbow makes c l e a r , i t i s r a t h e r s u r p r i s i n g t h a t h i s work d i d not have the scope and i m p a c t of the work o f such men as G a l i l e o , D e s c a r t e s o r Huygens. But t h e r e a s o n i s not h a r d t o f i n d ; f o r S p i n o z a s c i e n c e p l a y e d o n l y a s u b o r d i n a t e r o l e ; h i s c h i e f aim was t h e 12 improvement o f the u n d e r s t a n d i n g i n the most g e n e r a l sense and i n h i s a m b i t i o u s program s c i e n t i f i c knowledge was c o n s i d e r e d as a means t o an end o n l y . We have a v e r y good statement o f t h i s i n h i s own words as found i n The Improvement of t h e U n d e r s t a n d i n g : Thus i t i s a p p a r e n t t o e v e r y one t h a t I w i s h t o d i r e c t a l l s c i e n c e s t o one end and aim, so t h a t we may a t t a i n t o the supreme human p e r f e c t i o n w h i c h I have named? and, t h e r e f o r e , w h a t s o e v e r i n t h e s c i e n c e s does not s e r v e t o promote o u r o b j e c t w i l l have t o be r e j e c t e d as u s e l e s s . A l t h o u g h i n h i s t i m e t h e r e was no s h a r p d i s t i n c t i o n made between the work o f a p h i l o s o p h e r and t h a t o f a s c i e n t i s t , i t i s s a f e t o say, i n r e t r o s p e c t , t h a t S p i n o z a was f i r s t and f o r e m o s t a p h i l o s o p h e r and o n l y i n c i d e n t a l l y , a man o f s c i e n c e . H i s e n t e r p r i s e was t o c o n s t r u c t a scheme i n w h i c h e v e r y t h i n g was e x p l a i n a b l e , and the p a t i e n t f e r r e t i n g out o f " l i t t l e " t r u t h s about th e n a t u r e o f t h i n g s , perhaps b e s t e x e m p l i f i e d by t h e work o f B o y l e , was f o r him o f s e c o n d a r y i m p o r t a n c e , a l t h o u g h he was always an i n t e r -e s t e d s p e c t a t o r o f the a c t i v i t i e s o f o t h e r s i n s c i e n c e . Making a d i s t i n c t i o n between t h e work o f a s c i e n t i s t and t h a t o f a p h i l o s o p h e r i s somewhat a r t i f i c i a l , e s p e c i a l l y as a p p l y i n g t o t h e s e v e n t e e n t h c e n t u r y . S p i n o z a ' s own work s e r v e s as a case i n p o i n t : even though h i s o v e r -r i d i n g c o n c e r n was f o r the l a r g e r more a b s t r a c t i s s u e s , h i s i n t e r s t s c o v e r a wide spectrum, from t h e p r o p e r t i e s o f n i t r e t o the n a t u r e o f God. N e v e r t h e l e s s h i s work r e v e a l s an o u t l o o k and temperament q u i t e d i f f e r e n t from t h a t o f such men as B o y l e and Huygens. Hence, what i s i n t e r e s t i n g about h i s s c i e n t i f i c i d e a s does not l i e so much i n t h e g e n e r a l s c i e n t i f i c a c t i v i t i e s r e f e r r e d t o above, b u t i n t h e more t h e o r e t i c a l a s p e c t s o f p h y s i c a l s c i e n c e , such as t h e s t r u c t u r e o f m a t t e r , the b a s i c components o f t h e p h y s i c a l u n i v e r s e , the fundamental elements o f s c i e n t i f i c e x p l a n a t i o n . I n t h i s c o n n e c t i o n , i t i s t h i s t h e o r y o f p a r t i c l e s and m o t i o n w h i c h i s o f g r e a t i n t e r e s t , and i t i s t h i s t h e o r y w h i c h i s the main c o n c e r n o f t h i s t h e s i s . •^See McKeon, page 156. 2 The same i s t r u e o f a n o t h e r r a t i o n a l i s t , D e s c a r t e s , who made o b s e r v a t i o n s on the passage o f l i g h t r a y s t h r o u g h g l a s s spheres i n c o n n e c t i o n w i t h t h i s t h e o r y o f t h e rainbow. See S c o t t , page 74. JSee S c o t t , page 12. 4 S e e W o l f , pages 423-425. ^F o r comments on the a u t h e n t i c i t y o f t h i s work, see Gebhardt, pages 431-434. 6 S e e S c o t t , pages 28-63. 1 14 CHAPTER I I I THE CARTESIAN PHYSICS Three c o n s i d e r a t i o n s make the d i s c u s s i o n o f t h e C a r t e s i a n p h y s i c s r e l e v a n t t o t h e t o p i c o f t h i s t h e s i s : (a) The C a r t e s i a n p h y s i c s i s i n some way a l s o S p i n o z a ' s p h y s i c s . S p i n o z a s t u d i e d D e s c a r t e s ' s t h e o r i e s v e r y c l o s e l y , and p a i d t r i b u t e t o D e s c a r t e s * s i n t e l l i g e n c e and h i s keen mind^. The v e r y f a c t t h a t S p i n o z a w r o t e t h e P r i n c i p l e s a t t e s t s t o h i s i n v o l v e m e n t w i t h the C a r t e s i a n i d e a s , and w h i l e t h a t work i s supposed t o r e p r e s e n t D e s c a r t e s ' s t h o u g h t , and n o t S p i n o z a ' s , i t i s u n c e r t a i n t o what e x t e n t and how S p i n o z a ' s p h y s i c a l t h e o r i e s d i f f e r e d from t h o s e o f D e s c a r t e s . When the i n t r o d u c t i o n t o t h e P r i n c i p l e s , w r i t t e n b y Ludwig Meyer, i s examined, we f i n d t h a t Meyer mentions the w i l l , the i n t e l l e c t , t h e e x i s t e n c e o f t h i n k i n g s u b s t a n c e , t h e l i m i t s o f human knowledge as t o p i c s on w h i c h S p i n o z a d i s a g r e e s w i t h D e s c a r t e s . There i s no m e n t i o n o f a d i v e r g e n c e on such t h i n g s as t h e n a t u r e o f m o t i o n , the c h a r a c t e r o f p a r t i c l e s , s c i e n t i f i c method, laws o f m o t i o n , e t c . . I n t h e l e t t e r t o Oldenburg, w r i t t e n i n November 1665 (two y e a r s a f t e r t h e p u b l i c a t i o n o f the P r i n c i p l e s } , S p i n o z a s a y s : As t o y o u r n e x t remark, t h a t I h i n t e d t h a t the C a r t e s i a n laws o f m o t i o n a r e n e a r l y a l l f a l s e , i f I remember r i g h t l y , I s a i d t h a t Mr. Huygens t h i n k s s o . Nor d i d I say t h a t any law i s f a l s e e x c e p t the s i x t h law o f D e s c a r t e s , and even about t h a t I s a i d Huygens t o o i s m i s t a k e n . There are no c l u e s anywhere i n S p i n o z a ' s w r i t i n g s as t o t h e e x a c t p o i n t o f d i s p u t e w i t h r e g a r d t o t h e s e laws o f m o t i o n , w i t h one e x c e p t i o n , p e r h a p s : i n the P r i n c i p l e s S p i n o z a i s seen t o amend D e s c a r t e s ' s s i x t h r u l e o f m o t i o n s l i g h t l y . However, whether S p i n o z a r e g a r d s t h e m o d i f i e d s i x t h law as t r u e o r not i s i m p o s s i b l e t o d e t e r m i n e , and hence, from t h i s remark a l o n e i t must remain u n d e c i d e d e x a c t l y how S p i n o z a f e l t about t h e C a r t e s i a n p h y s i c s . (b) S p i n o z a ' s p h y s i c s may w e l l be r e g a r d e d as a m o d i f i c a t i o n o f t h e e a r l i e r p h y s i c s . From t h e v e r y f a c t t h a t t h e s e two p h i l o s o p h e r s were so c l o s e t o g e t h e r i n t i me and t h a t S p i n o z a was t h o r o u g h l y v e r s e d i n D e s c a r t e s ' t h e o r i e s , i t i s o n l y n a t u r a l t o e x p e c t t h a t S p i n o z a began where D e s c a r t e s l e f t o f f . S t u d y i n g t h e r a m i f i c a t i o n s o f t h e C a r t e s i a n p h y s i c s s h o u l d b e , u s e f u l f o r t h e u n d e r s t a n d -i n g o f S p i n o z a ' s p h y s i c s . B e s i d e s , t h e r e a re a number o f i t e m s w h i c h a r e common t o b o t h t h e o r i e s . F o r i n s t a n c e , S p i n o z a ' s t r e a t m e n t o f h a r d n e s s , s o f t n e s s , and f l u i d i t y i n t h e E t h i c s f i t s i n q u i t e w e l l w i t h the p h y s i c s o f t h e P r i n c i p l e s ; i n t h e d i s p u t e w i t h B o y l e , S p i n o z a g i v e s t h e o r e t i c a l e x p l a n a t i o n s which, a r e e s s e n t i a l l y C a r t e s i a n i n c h a r a c t e r . A l s o , w i t h r e g a r d t o the e x i s t a n c e o f a 16 vacuum, and t h e n a t u r e o f s c i e n t i f i c method, t h e r e seems t o be a g r e a t d e a l i n common i n t h e i r i d e a s . (c) The C a r t e s i a n p h y s i c s forms a u s e f u l frame o f r e f e r e n c e f o r t h e d i s c u s s i o n o f S p i n o z a ' s i d e a s . D e s c a r t e s * s cosmology and t h e o r i e s o f m a t t e r were dominant at t h a t t ime and had a p o w e r f u l i n f l u e n c e o v e r men l i k e C h r i s t i a n Huygens, t o name one example; h i s v o r t e x t h e o r y o f p l a n e t a r y m o t i o n h e l d sway f o r a l o n g t i m e , even a f t e r the appearance o f Newton's t h e o r i e s . The C a r t e s i a n p h y s i c s , t h e n , i s v e r y much r e p r e s e n t a t i v e o f t h e s c i e n t i f i c i d e a s o f t h a t age, and as such i s q u i t e r e l e v a n t t o S p i n o z a ' s p h y s i c s . Because t h e s c i e n t i f i c i d e a s o f D e s c a r t e s a r e not the c e n t r a l t o p i c o f t h i s t h e s i s , the d i s c u s s i o n w i l l n a t u r a l l y have t o be somewhat l i m i t e d . The most a p p r o p r i a t e way o f d o i n g t h i s i s t o r e s t r i c t t h e d i s c u s s i o n t o t h e second and t h i r d p a r t s o f the P r i n c i p l e s . F u r t h e r m o r e , I w i l l d i s c u s s o n l y t h o s e a s p e c t s o f t h e P r i n c i p l e s w h i c h have some b e a r i n g on the main t o p i c o f t h i s t h e s i s , namely the c h a r a c t e r o f the p a r t i c l e s and o f m o t i o n i n S p i n o z a ' s system. Of c o u r s e i n a sense a l l o f t h e P r i n c i p l e s i s r e l e v a n t t o t h i s t o p i c , because S p i n o z a , even though he d i s a g r e e s w i t h D e s c a r t e s on a number o f t h i n g s , i n t h a t work does not m e r e l y r e p e a t D e s c a r t e s , but works o u t t h e whole scheme i n h i s own words. I t i s o b v i o u s t h a t he 17 t a k e s D e s c a r t e s ' s p h y s i c s q u i t e s e r i o u s l y , and i t i s a l s o c l e a r t h a t he doesn't i n t e n t i o n a l l y i n c l u d e p r o o f s t h a t a r e l o g i c a l l y unsound, so t h a t even i f t h e p r o p o s i t i o n s are f a l s e i n h i s o p i n i o n , the r e a s o n i n g w o u l d s t i l l be o f i n t e r e s t . However, i n t h e main, th e P r i n c i p l e s i s s t i l l a work on D e s c a r t e s 's p h y s i c s , and t h e r e f o r e a d i s c u s s i o n o f c e r t a i n problems w o u l d n a t u r a l l y t e n d t o be m e r e l y a d i s c u s s i o n o f D e s c a r t e s ' s i d e a s and would b r i n g us no c l o s e r t o u n d e r s t a n d i n g what S p i n o z a ' s i d e a s were. T h e r e -f o r e I have s e l e c t e d t h o s e problems f o r d i s c u s s i o n w h i c h I t h i n k a r e r e l e v a n t t o t h e p h y s i c s o f the E t h i c s . Because i t i s u n c e r t a i n t o what degree t h e p h y s i c s of t h e P r i n c i p l e s r e p r e s e n t s S p i n o z a ' s t h e o r y , I w i l l r e f e r t o t h a t p h y s i c s s i m p l y as t h e " C a r t e s i a n p h y s i c s " , l e a v i n g i t d e l i b e r a t e l y u n s p e c i f i e d t o what e x t e n t the " C a r t e s i a n p h y s i c s " i s a l s o S p i n o z a ' s p h y s i c s . By the t e r m I s h a l l not be r e f e r r i n g t o the whole of D e s c a r t e s ' s t h e o r i e s o f t h e p h y s i c a l w o r l d , w h i c h i n c l u d e s a l a r g e number o f i t e m s n o t d i s c u s s e d i n t h e P r i n c i p l e s , s u c h as the v o r t i c a l t h e o r y o f t h e s o l a r system, th e n a t u r e o f h e a t and l i g h t , t h e t h r e e k i n d s o f m a t t e r , g r a v i t y , e t c . . The P r i n c i p l e s , n o t c o u n t i n g t h e C o g i t a t a M e t a p h y s i c a , w h i c h i s an a p p e n d i x , i s c a s t i n the g e o m e t r i c form. P a r t Two b e g i n s w i t h a s t atement o f n i n e d e f i n i t i o n s and t w e n t y -one axioms; from t h e s e , w i t h an o c c a s i o n a l r e f e r e n c e t o P a r t One, a number o f p r o p o s i t i o n s are e s t a b l i s h e d . The 2 . b a s i c a s s u m p t i o n , axiom, o r p o s t u l a t e i s t h a t p h y s i c a l s u b s t a n c e i s e x t e n s i o n . A l l t h e p r o p e r t i e s of b o d i e s s u c h as c o l o u r , h a r d n e s s , w e i g h t , t a s t e , warmth and c o l d -n e s s , e t c . , are s e c o n d a r y p r o p e r t i e s , dependent on t h e s e n s e s . P r o p o s i t i o n 2 s t a t e s : "The n a t u r e o f body o r m a t t e r c o n s i s t s i n e x t e n s i o n a l o n e " . The C o r o l l a r y t o t h i s p r o p o s i t i o n sums up n i c e l y the fundamental f e a t u r e of the C a r t e s i a n p h y s i c s ; i t s t a t e s : "Space and Body are the same". What makes the C a r t e s i a n p h y s i c s so r a d i c a l l y d i f f e r e n t f rom the Newtonian^ system, i s the . t r e a t m e n t of t h e c oncept o f mass. I n t h e Newtonian system two d i s t i n c t q u a n t i t i e s a p p l y t o b o d i e s , t h e i r volume and t h e i r mass o r q u a n t i t y o f m a t t e r , so t h a t s o l i d b o d i e s can have the same s i z e b u t d i f f e r e n t w e i g h t and mass, or v i c e v e r s a , and a g i v e n body can change i t s volume w i t h o u t c h a n g i n g i t s mass o r w e i g h t , i . e . can change i t s d e n s i t y . I n t h e C a r t e s i a n system, o n l y one q u a n t i t y a p p l i e s t o s o l i d body. T h i s i s c l e a r l y e x p r e s s e d i n t h e C o r o l l a r y t o P r o p o s i t i o n 4: B o d i e s w h i c h occupy an e q u a l amount o f s pace, as f o r example some g o l d and b r a s s , have an e q u a l amount o f m a t t e r o r o f c o r p o r e a l s u b s t a n c e . The mass o f a body i s the same as i t s t r u e s i z e , t h e volume 19 i t w o uld occupy i f the m a t e r i a l o f t h e body were r e d i s -t r i b u t e d so t h a t t h e r e were no p o r e s o r i n t e r s t i c e s l e f t . To e x p l a i n the commonly o b s e r v e d phenomenon o f conden-s a t i o n and r a r e f a c t i o n , the example o f a sponge i s used i n the d e m o n s t r a t i o n t o Lemma 2. When a body i s seen t o change i t s volume, i t i s a c t u a l l y o n l y c h a n g i n g i t s e x t e r i o r d i m e n s i o n s , w h i l e the i n t e r s t i c e s between the p a r t s o f t h e body become l a r g e r o r s m a l l e r . The i d e n t i f i c a t i o n o f space w i t h body has t h e immediate consequence t h a t a vacuum does not e x i s t . A vacuum i s d e f i n e d as space w i t h o u t body, and s i n c e space i s body, t h i s i s s e l f - c o n t r a d i c t o r y . I t i s i m p o r t a n t t o note t h a t the n o n - e x i s t e n c e o f a vacuum i s n o t m e r e l y a c o n t i n g e n t f a c t about n a t u r e , i t i s a l o g i c a l t r u t h d e r i v e d f r o m the meaning o f t h e b a s i c t e r m s . The vacua p r o d u c e d e x p e r i m e n t a l l y by such p e o p l e as Von G u e r i c k e and R o b e r t B o y l e a r e o n l y apparent v a c u a . D e s c a r t e s , i n h i s P r i n c i p l e s  o f P h i l o s o p h y , (not t o be c o n f u s e d w i t h S p i n o z a ' s P r i n c i p l e s  o f C a r t e s i a n P h i l o s o p h y ) , P r i n c i p l e X I I , d i s t i n g u i s h e d between o r d i n a r y v a c u a , w h i c h o c c u r when we do not f i n d the t h i n g s we o r d i n a r i l y e x p e c t t o f i n d i n some c o n t a i n e r , and a b s o l u t e v a c u a , w h i c h a r e p l a c e s c o m p l e t e l y d e v o i d o f m a t t e r . When someone removes a i r f rom a c o n t a i n e r , something e l s e must f l o w i n , some e x c e e d i n g l y f i n e m a t e r i a l w h i c h can f l o w t h r o u g h the w a l l s o f the c o n t a i n e r 4 . I n s o f a r as 20 t h e r e i s no e v i d e n c e t o t h e c o n t r a r y , i t i s r e a s o n a b l e t o assume t h a t S p i n o z a ' s i d e a s on t h i s p o i n t were t h e same. A n o t h e r major f e a t u r e o f t h e C a r t e s i a n p h y s i c s i s t h a t atoms, i . e . i n d i v i s i b l e b i t s o f m a t t e r , do n o t e x i s t . I t i s p a r t o f the concept o f e x t e n s i o n t h a t e x t e n s i o n i s always d i v i s i b l e . Axiom 9 s a y s : " A l l e x t e n s i o n can be d i v i d e d , a t l e a s t , i n t h o u g h t . " . A g r e a t d e a l h i n g e s on the p h r a s e "at l e a s t i n t h o u g h t " , as I w i l l e l a b o r a t e s h o r t l y . A l t h o u g h atoms as i n d i v i s i b l e b i t s o f m a t t e r are not p a r t o f the C a r t e s i a n p h y s i c s , t h e system i s n e v e r -t h e l e s s b ased on p a r t i c l e s . To e v a l u a t e the c h a r a c t e r o f t h e C a r t e s i a n p a r t i c l e s and t h e g e n e r a l C a r t e s i a n cosmology, we t u r n t o t h e account o f the c r e a t i o n o f the u n i v e r s e as g i v e n i n P a r t Three: . . . i n the b e g i n n i n g , a l l m a t t e r of w h i c h the v i s i b l e w o r l d i s composed was d i v i d e d by God i n t o p a r t i c l e s as n e a r l y as p o s s i b l e e q u a l t o one a n o t h e r . These p a r t i c l e s , however, from w h i c h now the heavens and t h e s t a r s a r e composed were not s p h e r i c a l , f o r a number o f spheres j o i n e d t o g e t h e r do not f i l l up t h e space t h e y occupy; but t h e y , s m a l l i n s i z e , were f a s h i o n e d i n some o t h e r way. These p a r t i c l e s had i n them j u s t as much m o t i o n as t h e r e i s i n the w o r l d t o d a y and t h e y were a l l moving w i t h an e q u a l v e l o c i t y . S i n c e t h e c r e a t i o n o f t h e u n i v e r s e p a r t i c l e s o f a l l s o r t s o f s i z e s and shapes d e v e l o p e d and assumed v a r i o u s c o n f i g u r -a t i o n s w h i c h c o n s t i t u t e t h e w o r l d we see t o d a y . A l l s c i e n t i f i c e x p l a n a t i o n i s i n terms of p a r t i c l e s 21 i n m o t i o n . To g i v e d e t a i l e d d e s c r i p t i o n s and c a u s a l e x p l a n a t i o n s , a t h e o r y o f the b e h a v i o u r o f p a r t i c l e s i s needed. T h i s t h e o r y i s s t a t e d i n P r o p o s i t i o n 14 t o 37, i n c l u s i v e . T h i s t h e o r y c a n be d i v i d e d i n two p a r t s : (a) p e r t a i n i n g t o b o d i e s i n i s o l a t i o n , (b) p e r t a i n i n g t o b o d i e s i n c o l l i s i o n . A body i n motion tends t o c o n t i n u e i n s t r a i g h t l i n e m o t i o n , i . e . i t w i l l c o n t i n u e i n a s t r a i g h t l i n e w i t h u n d i m i n i s h e d v e l o c i t y u n l e s s i t i n t e r -a c t s w i t h o t h e r b o d i e s (see C o r o l l a r y t o P r o p o s i t i o n 14, P r o s i t i o n 15, 16 and 1 7 ) . There i s no c o r r e s p o n d i n g r u l e o r law f o r b o d i e s a t r e s t ; t h i s i s i m p o r t a n t , as wa s h a l l s ee. As r e g a r d s b o d i e s i n c o l l i s i o n the f i r s t r u l e o r law i s t h a t i n an impact t h e r e i s no l o s s o f m o t i o n (see P r o p o s i t i o n s 18, 20, 21, 2 2 ) . Note a t t h i s p o i n t t h a t m o t i o n i s n o t m e r e l y v e l o c i t y i n t h e C a r t e s i a n p h y s i c s , t h e amount of m o t i o n t h a t a body p o s s e s s e s i s dependent on b o t h t h e s i z e and the v e l o c i t y of the body. A l t h o u g h t h i s i s not s t a t e d e x p l i c i t l y , t he q u a n t i t y ^ o f m o t i o n o f a body i s a c t u a l l y j u s t the p r o d u c t o f i t s s i z e and v e l o c i t y . I n any c o l l i s i o n between two b o d i e s , the t o t a l q u a n t i t y i f c o n s e r v e d . F o l l o w i n g t h e statement o f t h i s l a w t h e r e a r e g i v e n a number o f p r o p o s i t i o n s d e a l i n g w i t h c o l l i s i o n s i n more d e t a i l . I n D e s c a r t e s ' s P r i n c i p l e s o f P h i l o s o p h y (paragraphs 46 t o 52 i n c l u s i v e ) a r e f o u n d h i s well-known seven r u l e s o f m o t i o n . S p i n o z a s t a t e s t h e s e r u l e s w i t h some r e l a t i v e l y minor and not o b v i o u s l y s i g n i f i c a n t m o d i f i c a t i o n s ( o f w h i c h I have a l r e a d y mentioned the s i x t h r u l e ) . He a l s o adds one e x t r a p r o p o s i t i o n t o t h e s e r i e s , o s t e n s i b l y t o f i l l a gap. These p r o p o s i t i o n s are g i v e n below; f o r t h e sake o f c l a r i t y , I have g i v e n them i n my own words: P r o p o s i t i o n 24 ( R u l e #1): I f two b o d i e s o f e q u a l s i z e and e q u a l v e l o c i t y c o l l i d e , e a c h w i l l r e t u r n i n t h e o p p o s i t e d i r e c t i o n w i t h o u t any change o f v e l o c i t y . P r o p o s i t i o n 25 (Rule #2): I f two b o d i e s w i t h d i f f e r e n t s i z e s , b u t e q u a l v e l o c i t i e s , c o l l i d e , t h e s m a l l e r one w i l l be r e f l e c t e d i n t h e o p p o s i t e d i r e c t i o n w i t h i t s o r i g i n a l v e l o c i t y , w h i l e the l a r g e r one r e t a i n s b o t h i t s o r i g i n a l d i r e c t i o n and v e l o c i t y . P r o p o s i t i o n 26: I f two b o d i e s have b o t h d i f -f e r e n t s i z e and v e l o c i t y , b u t t h e p r o d u c t o f v e l o c i t y and s i z e i s t h e same f o r b o t h , t h e n upon c o l l i s i o n b o t h b o d i e s w i l l rebound w i t h t h e i r o r i g i n a l v e l o c i t i e s . P r o p o s i t i o n 27 (R u l e #3): I f two b o d i e s o f e q u a l s i z e b u t w i t h d i f f e r e n t v e l o c i t i e s c o l l i d e , the f a s t e r body w i l l g i v e h a l f o f i t s e x c e s s v e l o c i t y t o t h e s l o w e r body and t h e y w i l l b o t h move on t o g e t h e r i n t h e d i r e c t i o n o f the f a s t e r body. 23 P r o p o s i t i o n 28 ( R u l e #4): I f a body a t r e s t i s s t r u c k by a s m a l l e r body, t h e n , no m a t t e r how g r e a t t h e v e l o c i t y o f t h e s m a l l e r body, t h e l a r g e r body w i l l r e m a i n a t r e s t , w h i l e t h e s m a l l e r i s d e f l e c t e d a t an a n g l e , r e t a i n i n g i t s o r i g i n a l v e l o c i t y . P r o p o s i t i o n 29 ( R u l e #5): I f the body a t r e s t i s s m a l l e r t h a n t h e i m p i n g i n g body, t h e n no m a t t e r how s l o w l y t h e i m p i n g i n g body moves, i t w i l l g i v e up p a r t o f i t s v e l o c i t y t o t h e body a t r e s t so t h a t t h e y b o t h move on t o g e t h e r . P r o p o s i t i o n 30 (R u l e #6): I f t h e body a t r e s t i s s t r u c k by a body o f e q u a l s i z e , t he f i r s t body w i l l be i m p e l l e d and t h e second body w i l l be r e p e l l e d . P r o p o s i t i o n 31 ( R u l e #7): I f a body, A, i s moving f a s t e r t h a n , b u t i n the same d i r e c t i o n as a n o t h e r body, B, t h e n e i t h e r (a) the p r o d u c t o f s i z e and v e l o c i t y o f A i s l a r g e r t h a n t h e c o r r e s p o n d i n g p r o d u c t f o r B, i n w h i c h case A w i l l g i v e up p a r t o f i t s v e l o c i t y t o B and t h e y w i l l b o t h move on t o g e t h e r , o r , (b) t h e p r o d u c t o f s i z e and v e l o c i t y o f A i s s m a l l e r t h a n t h a t o f B, i n w h i c h case A w i l l be r e f l e c t e d back w h i l e B moves on, each w i t h i t s o r i g i n a l v e l o c i t y . Two a s p e c t s o f t h e s e seven laws o f m o t i o n s t a n d out i m m e d i a t e l y . The f i r s t i s t h a t t h e y seem p l a i n l y c o n t r a r y t o e x p e r i e n c e , and t h e y have been c r i t i c i z e d on t h i s count by many. S c o t t 0 mentions one contemporary c r i t i c i s m . d i r e c t e d a t the f o u r t h r u l e . I t i s a common e x p e r i e n c e t h a t a v e r y s m a l l o b j e c t , such as a b u l l e t , s t r i k i n g a l a r g e s t a t i o n a r y one, say a c a n n o n b a l l , w i t h h i g h v e l o c i t y , w i l l cause some movement i n the l a r g e o b j e c t , c o n t r a r y t o t h e f o u r t h r u l e , w h i c h s t a t e s t h a t t h e s m a l l e r body w i l l bounce back, w h i l e the l a r g e r body remains a t r e s t . An example o f a l a t e r c r i t i c i s m i s t h a t 7 o f C. D. Br o a d who s t a t e s t h a t ...some laws h o l d o n l y when b o d i e s a r e p e r f e c t l y e l a s t i c , o t h e r s o n l y when th e y are p e r f e c t l y i n e l a s t i c and o t h e r s under no c o n d i t i o n s w hatever. Two c o n s i d e r a t i o n s make t h i s judgment a l i t t l e m i s l e a d i n g . F i r s t , i t i s t r u e o n l y i f a c e r t a i n a s s u m p t i o n i s made r e g a r d i n g the mass of b o d i e s . I n the C a r t e s i a n scheme, two b o d i e s e q u a l i n volume p o s s e s s an e q u a l amount o f c o r p o r e a l m a t t e r , even though t h e y may be d i f f e r e n t m a t e r i a l s , such as b r a s s and g o l d . I n the Newtonian scheme, two such b o d i e s would have d i f f e r e n t masses, even i f t h e y o c c u p i e d the same amount o f space: t h a t the d i f -f e r e n t c o n c e p t i o n s o f mass i n t h e C a r t e s i a n and t h e New-t o n i a n scheme make a judgment of the C a r t e s i a n system i n Newtonian terms a l i t t l e m i s l e a d i n g i s f a i r l y o b v i o u s , and does not need t o be s p e l l e d o u t . A second p o i n t o v e r l o o k e d by Broad i s t h a t t h e c o l l i s i o n s w i t h w h i c h t h e seven r u l e s d e a l a r e c o l l i s i o n s i n i s o l a t i o n . Now 25 s i n c e the u n i v e r s e i s a plenum, t h e r e i s never a c t u a l l y any i s o l a t e d c o l l i s i o n , s o t h a t t h e s e laws do not a p p l y d i r e c t l y t o t h e w o r l d o f e x p e r i e n c e . I n t h e S c h o l i u m t o P r o p o s i t i o n 31 S p i n o z a s t a t e s : F o r e x p l a i n i n g t h e changes o f b o d i e s w h i c h are m u t u a l l y i m p e l l e d we have s o f a r c o n s i d e r e d two b o d i e s as though s e p a r a t e d from a l l o t h e r s , no account b e i n g t a k e n o f o t h e r i m p i n g i n g b o d i e s . That i s , the seven laws are what we might c a l l p r i m a r y l a w s , and f o r s c i e n t i f i c e x p l a n a t i o n s we need a s e t o f secondary l a w s , d e r i v e d from the p r i m a r y l a w s , w h i c h do a p p l y t o t h e o b s e r v a b l e phenomena. I n the l a s t s i x p r o p o s i t i o n s o f P a r t Two, a s t a r t i s made i n g i v i n g t h e s e secondary l a w s , but t h e t a s k i s not p u r s u e d t o any g r e a t e x t e n t . The second n o t a b l e a s p e c t o f t h e seven laws i s t h a t a sh a r p d i s t i n c t i o n i s made between b o d i e s a t r e s t , and b o d i e s i n mo t i o n , no m a t t e r how s l o w l y . To g i v e n an example, l e t us l o o k a t R u l e s #4 and #7. C o n s i d e r a s m a l l body, say a b u l l e t , s t r i k i n g a l a r g e r o b j e c t , a c a n n o n b a l l , a t r e s t . Rule #4 s t a t e s t h a t t h e b u l l e t w i l l bounce back w h i l e t h e c a n n o n b a l l remains a t r e s t . Now imagine the. c a n n o n b a l l t o move i n the same d i r e c t i o n as th e b u l l e t b u t w i t h an e x c e e d i n g l y s m a l l v e l o c i t y , such t h a t t h e q u a n t i t y o f m o t i o n ( s i z e t i m e s v e l o c i t y ) o f t h e b u l l e t i s l a r g e r t h a n t h a t o f t h e c a n n o n b a l l . T h i s b r i n g s t h e example under t h e c o n s i d e r a t i o n o f the f i r s t ease o f the s e v e n t h r u l e , w h i c h says t h a t t h e c a n n o n b a l l arid the b u l l e t w i l l move on t o g e t h e r , w h i c h i s r a d i c a l l y d i f f e r e n t f r om the case o f t h e c a n n o n b a l l a t r e s t . Ttfhat i n t h e Newtonian system w o u l d count as an e x t r e m e l y s m a l l change, namely a . s l i g h t change o f v e l o c i t y i n the c a n n o n b a l l , w h i c h c o r r e s p o n d i n g l y p roduces a s m a l l change i n the e f f e c t produced, i n t h e C a r t e s i a n system produces a d r a s t i c a l l y d i f f e r e n t s i t u a t i o n . S e v e r a l such cases o f a r a d i c a l d i f f e r e n c e produced by a s m a l l change i n the i n i t i a l c o n d i t i o n s , can be d i s c o v e r e d by e x a m i n i n g t h e s e s even r u l e s . The example I have c o n s i d e r e d i s o f p a r t i c u l a r s i g n i f i c a n c e i n t h a t i t makes c l e a r t h a t the state:-of r e s t does have a s p e c i a l s t a t u s i n t h e C a r t e s i a n scheme. A l s o what i t b r i n g s out c l e a r l y i s an i m p o r t a n t d i f f e r e n c e between t h e Newtonian and C a r t e s i a n schemes w i t h r e s p e c t t o moving frames o f r e f e r e n c e . To g i v e a homely example, l e t us imagine o u r s e l v e s s i t t i n g i n a r a i l r o a d c a r and o b s e r v i n g the c o l l i s i o n s o f b o d i e s . I n t h e Newtonian case i t would be i m p o s s i b l e t o t e l l from the o b s e r v e d c o l l i s i o n s o f b o d i e s whether the r a i l r o a d c a r were moving o r n o t . I n t h e C a r t e s i a n scheme, w i t h i t s s p e c i a l laws f o r b o d i e s a t r e s t , we w o u l d be a b l e t o d e t e r m i n e whether the r a i l r o a d c a r was moving o r n o t . T h i s i s an i m p o r t a n t b e a r i n g on t h e q u e s t i o n o f t h e " r e l a t i v i t y " o f the C a r t e s i a n space, a t o p i c I w i l l r e t u r n t o s h o r t l y . The r e a s o n i n g by w h i c h these r u l e s o f m o t i o n are e s t a b l i s h e d i s i n t e r e s t i n g and w o r t h e x p l o r i n g . Each p r o p o s i t i o n i s argued s e p a r a t e l y , b u t the whole s e t o f r u l e s i n v o l v e s b a s i c a l l y f o u r p r i n c i p l e s : (a) The p r i n c i p l e o f c o n s e r v a t i o n o f m o t i o n (as I c a l l i t ) i s the b a s i c r u l e t h a t a p p l i e s t o a l l c a ses o f c o l l i s i o n between two b o d i e s . However, w h i l e none o f t h e r u l e s v i o l a t e s t h i s p r i n c i p l e , not a l l r u l e s are s p e c i f i c enough t o e x c l u d e th e p o s s i b i l i t y o f v i o l a -t i o n . When th e y a r e examined, the r u l e s can be seen t o f a l l i n t o two c l a s s e s . I n the one c l a s s , w h i c h i n c l u d e s R u l e s #1, 2, 3, 4 and p a r t (b) o f #7, and a l s o P r o p o s i t i o n .26, t h e f i n a l v e l o c i t i e s a r e d e f i n i t e l y s p e c i f i e d , w h i l e t h e o t h e r c l a s s , w h i c h c o n s i s t s o f R u l e s #5, 6 and 7 ( a ) , the r e s u l t a n t v e l o c i t i e s a r e l e f t undetermined. I n t h e former c a s e , g i v e n t h e s i z e s and i n i t i a l v e l o c i t i e s , i t i s p o s s i b l e t o c a l c u l a t e the f i n a l v e l o c i t i e s , w h i l e i n t h e l a t t e r t h i s i s n o t p o s s i b l e on t h e b a s i s o f t h e r u l e s . The l a t t e r r u l e s , t h e r e f o r e , are i n c o m p l e t e i n t h a t t h e y do not guarantee th e c o n s e r v a t i o n o f m o t i o n i n the u n i v e r s e . T h i s i s s i g n i f i c a n t because the c o n s t a n c y o f t h e u n i v e r s e i s an i m p o r t a n t i s s u e i n b o t h D e s c a r t e s ' s and S p i n o z a ' s p h i l o s o p h i e s , and i t i n d i c a t e s t h a t t h e p h y s i c s o f the P r i n c i p l e s s h o u l d not be r e g a r d e d as a c l o s e d , f i n i s h e d , system, b u t r a t h e r as a p r o t o t y p e o r b l u e p r i n t f o r a f u l l y d e v e l o p e d p h y s i c s . The s e t o f r u l e s i s a l s o i n c o m p l e t e i n a n o t h e r way. A l l the p o s s i b l e c o m b i n a t i o n s o f s i z e s and v e l o c i t i e s a re c o v e r e d w i t h one e x c e p t i o n , namely t h e case i n w h i c h two b o d i e s w i t h d i f f e r e n t s i z e and v e l o c i t y meet each o t h e r head on. What i s m i s s i n g i s a r u l e l i k e #7, b u t f o r b o d i e s moving i n o p p o s i t e d i r e c t i o n s . T h i s o m i s s i o n may be s i g n i f i c a n t i n v a r i o u s ways, b u t f o r l a c k o f c l u e s t h e e x p l o r a t i o n o f i t s meaning w i l l n e c e s s a r i l y be h i g h l y s p e c u l a t i v e ; s i n c e i t does not seem t o be p e r t i n e n t t o the main t o p i c o f t h i s t h e s i s I w i l l f o r e g o the d i s c u s s i o n o f t h i s p o i n t . F o r my purpose a l l t h a t i s r e l e v a n t i s t h a t the laws o f m o t i o n are not d e v e l o p e d t o the f u l l e x t e n t w h i c h i s p o s s i b l e w i t h i n the t h e o r e t i c a l frame-work o f t h e P r i n c i p l e s . (b) The c o n t e s t - o f - s t r e n g t h p r i n c i p l e (as I c a l l i t ) i s one t h a t a p p l i e s t o a l l r u l e s . I t s t a t e s t h a t i n any c o l l i s i o n t h e s t r o n g e r body s h a l l s u f f e r the l e a s t p o s s i b l e change, and t h e weaker body undergoes as much as i s r e q u i r e d ; r e l a t i v e s t r e n g t h i s d e t e r m i n e d d i f f e r e n t l y i n c a s e s where body b o d i e s are i n m o t i o n , and t h o s e cases where one body i s a t r e s t . I n the f o r m e r case t h e s t r o n g e r body i s the one w i t h the l a r g e r q u a n t i t y o f m o t i o n , w h i l e i n t h e l a t t e r case s i z e a l o n e d e t e r m i n e s s u p e r i o r i t y . The c r u c i a l axiom i n c o n n e c t i o n w i t h t h i s p r i n c i p l e i s Axiom 20: " V a r i a t i o n i n any o b j e c t p r o c e e d s from a s t r o n g e r f o r c e . " . I t i s n o t e x p l a i n e d anywhere why s t r e n g t h s h o u l d be d e t e r m i n e d i n the way I have d e s c r i b e d . I t j u s t seems t o be t a k e n f o r g r a n t e d . The f a c t t h a t s t r e n g t h i s de t e r m i n e d d i f f e r e n t l y i n the case o f r e s t and i n t h e case o f m o t i o n i s r a t h e r i m p o r t a n t , i n c o n n e c t i o n w i t h the concept o f q u a n t i t y o f r e s t , and I w i l l r e t u r n t o i t s h o r t l y . (c) The p r i n c i p l e o f symmetry (as I c a l l i t ) a p p l i e s t o R u l e s #1 and #6 and t o P r o p o s i t i o n 26. I t says t h a t when two b o d i e s are e q u a l i n s t r e n g t h , the r e s u l t o f a c o l l i s i o n w i l l be s y m m e t r i c a l w i t h r e s p e c t t o t h o s e b o d i e s . What i s i n t e r e s t i n g about t h i s p r i n c i p l e i s t h a t i t b e a r s a k i n s h i p t o L e i b n i z ' s law o f s u f f i c i e n t r e a s o n . I n the case o f t h e f i r s t r u l e , t h e r e i s j u s t no c o n c e i v a b l e r e a s o n why what happens t o one body s h o u l d be any d i f f e r e n t from what happens t o the o t h e r ; e r g o , the r e s u l t s must be t h e same f o r t h o s e b o d i e s . The p r i n c i p l e does n o t a p p l y so c l e a r l y t o P r o p o s i t i o n 26, where t h e two b o d i e s are not c o m p l e t e l y s y m m e t r i c a l and o n l y e q u a l i n one r e s p e c t , namely t h e q u a n t i t y o f m o t i o n . A s i m i l a r case i s the s i x t h r u l e , where the b o d i e s are e q u a l i n s i z e , b u t d i f f e r i n v e l o c i t y . F o r a more 30 d e t a i l e d d i s c u s s i o n o f t h e p r i n c i p l e o f symmetry as i t a p p l i e s t o the s i x t h law, see "Appendix C. (d) The p r i n c i p l e of economy (as I c a l l i t ) s t a t e s t h a t t h e changes due t o a c o l l i s i o n s h a l l be t h e minimum p o s s i b l e . T h i s p r i n c i p l e i s i n t e r e s t i n g i n t h a t i t has the c h a r a c t e r o f a p r i n c i p l e o f l e a s t a c t i o n . I t s a p p l i c a t i o n i n the p r o o f s i s obscure and because o f t h i s , and a l s o because i t has no r e l e v a n c e t o S p i n o z a ' s l a t e r w r i t i n g s , I w i l l n o t d e l v e i n t o i t . The o n l y d i r e c t l y r e l e v a n t a s p e c t o f t h i s p r i n c i p l e i s i n t h e way change i s c a l c u l a t e d ; f o r t h e purpose o f d e c i d i n g how much change a p a r t i c u l a r c o l l i s i o n i n v o l v e s , change i n motion and change i n d i r e c t i o n a r e c o u n t e d q u i t e s e p a r a t e l y . F o r example, i n t h e case o f R u l e #1, each body undergoes no change i n v e l o c i t y , o n l y i n d i r e c t i o n . How changes i n d i r e c t i o n a re t o weigh a g a i n s t changes i n v e l o c i t y i s u n c e r t a i n , but the i m p o r t a n t p o i n t i s t h a t m o t i o n i n the C a r t e s i a n p h y s i c s i s not a v e c t o r q u a n t i t y as are v e l o c i t y and momentum i n the Newtonian p h y s i c s . F o r example, l e t us c o n s i d e r a body whose v e l o c i t y i s 10 u n i t s and l e t us say i t s u d d e n l y r e v e r s e s i t s d i r e c t i o n o f m o t i o n c o m p l e t e l y . I n the Newtonian system the body has undergone a change o f 20 u n i t s , w h i l e i n t h e C a r t e s i a n system t h e r e has been o n l y a change o f d i r e c t i o n . T h i s example s h o u l d s e r v e t o emphasize t h e r a t h e r d i f f e r e n t c h a r a c t e r o f m o t i o n 31 i n the C a r t e s i a n s y s t e m and the d i f f i c u l t y o f making judgments o f t h a t system i n Newtonian t e r m s . I have not t a k e n t h e time o r space t o examine i n d e t a i l the arguments f o r t h e r u l e s o f m o t i o n , and I do not t h i n k t h i s i s n e c e s s a r y . On the whole t h e system i s c a r e f u l l y worked out and t h e r e a r e no o b v i o u s f l a w s i n the l o g i c by w h i c h t h e y are d e r i v e d , a l t h o u g h t h e r e are s e v e r a l o b s c u r i t i e s , e s p e c i a l l y w i t h r e g a r d t o the p r i n c i p l e o f symmetry and t h e n o t i o n o f q u a n t i t y o f r e s t . As I have t r i e d t o show, th e o b v i o u s i m p l a u s i b i l i t y o f the laws o f m o t i o n i s not so o b v i o u s when t h e i r d e r i v a t i o n and a p p l i c a t i o n i s examined more c l o s e l y . D e s p i t e t h e o b s c u r i t i e s , anyone who reads t h e P r i n c i p l e s a t t e n t i v e l y w i l l see t h a t t h e t h e o r y p r e s e n t e d t h e r e r e p r e s e n t s an attempt t o come t o g r i p s w i t h t h e b a s i c p h y s i c a l c o n c e p t s ; one can sense a g r o p i n g towards a f u l l y d e v e l o p e d m a t h e m a t i c a l s c i e n c e o f mechanics, an e f f o r t t o f o r m a l i z e the c o n c e p t s o f mass, v e l o c i t y , momentum, i n e r t i a , f o r c e , c o n c e p t s w h i c h were f u l l y f o r m a l i z e d by I s a a c Newton. I n p a r t i c u l a r I want t o m e n t i o n t h e i n e r t i a o f b o d i e s a t r e s t , w h i c h i s connected w i t h the n o t i o n o f q u a n t i t y o f r e s t . To e x p l o r e t h i s n o t i o n f u r t h e r we w i l l f i r s t c o n s i d e r t h e more g e n e r a l q u e s t i o n o f the d e f i n i t i o n o f m o t i o n i n the C a r t e s i a n system. F o r t h a t we w i l l t u r n t o D e f i n i t i o n 8 w h i c h r e a d s as f o l l o w s : 32 L o c a l m otion i s t h e t r a n s f e r e n c e o f a p a r t i c l e o f m a t t e r o r o f a body from t h e v i c i n i t y o f o t h e r c o n t i g u o u s b o d i e s c o n s i d e r e d as i n a s t a t e d o f r e s t , t o the v i c i n i t y o f o t h e r s . T o g e t h e r w i t h t h i s d e f i n i t i o n t h e r e i s a l o n g d i s c u s s i o n c o n s i s t i n g o f f i v e p o i n t s ; I have p a r a p h r a s e d and a b b r e v i a t e d t h e s e : 1. A p a r t i c l e o f m a t t e r i s t o be u n d e r s t o o d as a l l t h a t w h i c h i s t r a n s f e r r e d a t t h e same t i m e , a l t h o u g h i t may i t s e l f be composed o f many p a r t s . 2. T r a n s f e r e n c e i s not t o be c o n f u s e d w i t h f o r c e o r a c t i o n w h i c h t r a n s f e r s . T h i s f o r c e o r a c t i o n , a s i s g e n e r a l l y b e l i e v e d , i s r e q u i r e d o n l y f o r mo t i o n , and n o t f o r r e s t , w h i c h i s p l a i n l y wrong. That i t r e q u i r e s j u s t as much f o r c e t o p u t a body i n t o m o t i o n as i t does t o b r i n g i t t o r e s t , i s s e l f - e v i d e n t , and i t i s a l s o p r o v e d by e x p e r i e n c e ; a s h i p r e q u i r e s about t h e same f o r c e t o be p u t i n m o t i o n as i t r e q u i r e s t o be s t o p p e d , and t h i s would be e x a c t l y the same i f we i g n o r e d the w e i g h t and v i s c o s i t y o f t h e w a t e r . 3. T r a n s f e r e n c e i s n o t made from one p l a c e t o a n o t h e r , b u t r a t h e r f r om t h e c o n t i g u i t y o f one body t o the c o n t i g u i t y o f a n o t h e r . P l a c e i s not something t h a t b e l o n g s t o an o b j e c t , but i t depends on o u r t h o u g h t . 4. When we c o n s i d e r two b o d i e s , i t i s ap p a r e n t t h a t the m o t i o n o f one w i t h r e s p e c t t o t h e o t h e r i s r e c i p r o c a l . When we push a b o a t out o f the sand we push the b o a t and t h e sand w i t h e q u a l f o r c e . The a c t i o n and t h e r e a c t i o n are e q u a l . So the b o a t moves w i t h r e s p e c t t o the sand as much as t h e sand moves w i t h r e s p e c t t o t h e b o a t . But the l a t t e r p h r a s e i s t o o much a t v a r i a n c e w i t h t h e common way of s p e a k i n g , w h i c h i s t o a t t r i b u t e o n l y t o t h e boat a m o t i o n . 5. E v e r y body has i t s own one p r o p e r m o t i o n , because m o t i o n i s d e f i n e d as t r a n s f e r e n c e f r o m b o d i e s a t r e s t . As r e g a r d s the r e l a t i v i t y o f m o t i o n t h e r e seems t o be a m a n i f e s t c o n t r a d i c t i o n between p o i n t s 4 and 5. P o i n t 4 c o n s i d e r e d by i t s e l f seems t o i m p l y t h a t m o t i o n i s a r e l a t i o n between two o b j e c t s , whereas p o i n t 5 s t a t e s b l u n t l y t h a t e a c h body has i t s one p r o p e r m o t i o n . From the s h a r p d i s t i n c t i o n t h a t i s made by t h e laws o f m o t i o n between b o d i e s a t r e s t and t h o s e i n m o t i o n , i t i s c l e a r t h a t p o i n t 5 means what i t s a y s . B o t h r e l a t i v e and a b s o l u t e m o t i o n p l a y a p a r t i n t h e C a r t e s i a n scheme. A d e f i n i t i o n o f a b s o l u t e m o t i o n would r e a d : "motion i s t r a n s f e r e n c e from b o d i e s a t r e s t " w h i l e t h e d e f i n i t i o n o f r e l a t i v e m o t i o n would r e a d : "motion i s t r a n s f e r e n c e f rom b o d i e s c o n s i d e r e d a t r e s t " . T h i s , however, s t i l l l e a v e s a q u e s t i o n about the d e f i n i t i o n o f m o t i o n i n terms o f r e s t : how i s r e s t d e f i n e d ? I f r e s t were d e f i n e d i n terms o f motion we would u n a v o i d a b l y r u n i n t o a c i r c u l a r i t y . As a m a t t e r o f f a c t r e s t i s n o t d e f i n e d a t a l l , e x c e p t i n d i r e c t l y . T h i s b r i n g s us back t o t h e n o t i o n o f r e s t as a q u a n t i t y (see page 2 9 ) . T h i s n o t i o n i s t h a t t h e r e i s a p e r f e c t symmetry between m o t i o n and r e s t ; the f a s t e r a body moves t h e more i t p a r t a k e s of m o t i o n and the g r e a t e r i t s q u a n t i t y o f m o t i o n i s ; the s l o w e r a body moves, the more i t p a r t a k e s o f r e s t , and the g r e a t e r i s i t s q u a n t i t y o f r e s t . P r o p o s i t i o n 18, w h i c h s t a t e s t h a t i f , i n a c o l l i s i o n , one body a c q u i r e s no m o t i o n from t h e c o l l i s i o n t h e n the o t h e r p a r t y t o t h e c o l l i s i o n l o s e s no m o t i o n , has t h e f o l l o w i n g d e m o n s t r a t i o n : I f you deny i t , l e t i t be supposed t h a t A has l o s t some o f i t s m o t i o n b u t has not t r a n s f e r r e d i t t o a n o t h e r body, a s , f o r example B. I f t h i s happens t h e r e w i l l be l e s s m o t i o n i n Nature t h a n b e f o r e w h i c h i s a b s u r d , (see Prop. 1 3 ) . The d e m o n s t r a t i o n i n r e s p e c t t o r e s t i n B i s t h e same. T h e r e f o r e i f no m o t i o n i s t r a n s f e r r e d B w i l l be i n the same s t a t e o f r e s t and A w i l l r e t a i n the same amount o f m o t i o n . Q.E.D. The i m p o r t a n t p h r a s e i s "the d e m o n s t r a t i o n i n r e s p e c t t o the r e s t i n B i s the same"; here i s one example o f an attempt t o f o r m u l a t e r e s t as t h e o p p o s i t e o f m o t i o n . The C o r o l l a r y t o P r o p o s i t i o n 19 s t a t e s : "Hence i t f o l l o w s t h a t m o t i o n i s n o t t h e o p p o s i t e o f m o t i o n " I n d i r e c t l y t h i s i m p l i e s t h a t r e s t i s t h e o p p o s i t e o f m o t i o n , the g e n e r a l i d e a b e i n g t h a t a l o s s o f m o t i o n i s a g a i n o f r e s t , and a g a i n i n m o t i o n i s a l o s s o f r e s t , and v i c e v e r s a . I n t h e d e m o n s t r a t i o n t o P r o p o s i t i o n 22 t h e r e o c c u r s a n o t h e r s i g n i f i c a n t passage: T h e r e f o r e t h o s e moving more s w i f t l y have more moti o n ( p e r Def. 8 ) . I n b o d i e s a t r e s t by f o r c e o f r e s i s t a n c e we u n d e r s t a n d t h e q u a n t i t y o f r e s t . From w h i c h f o l l o w : C o r o l l a r y I . The more s l o w l y b o d i e s move, t h e more t h e y p a r t a k e o f r e s t , f o r b o d i e s h a v i n g a g r e a t e r v e l o c i t y m e e t i n g t h o s e w h i c h have l e s s f o r c e , r e s i s t more and are n o t s e p a r a t e d so f a r from b o d i e s i m m e d i a t e l y c o n -t i g u o u s t o them. The i m p o r t a n t sentence here i s "the more s l o w l y b o d i e s move, t h e more t h e y p a r t a k e o f r e s t " . The q u e s t i o n i s , how i s q u a n t i t y o f r e s t f o r m u l a t e d , and how i s i t used? B e f o r e we d e a l w i t h t h i s q u e s t i o n , we might f i r s t ask a n o t h e r q u e s t i o n : why i s r e s t as a q u a n t i t y needed, what does i t e x p l a i n ? The answer t o t h e l a t t e r q u e s t i o n can be f o u n d i n P o i n t 2 o f D e f i n i t i o n 8. The k e y sent e n c e t h e r e i s : "This f o r c e o r a c t i o n , as i s g e n e r a l l y b e l i e v e d , i s r e q u i r e d o n l y f o r mo t i o n , and not f o r r e s t , w h i c h i s p l a i n l y wrong.". The r e a s o n i n g i n v o l v e d i s something l i k e t h e f o l l o w i n g : s i n c e j u s t as much f o r c e i s r e q u i r e d t o speed t h i n g s up as i s r e q u i r e d t o slow them down, mot i o n and r e s t , speed and s l o w n e s s , are s y m m e t r i c a l o p p o s i t e s . T h e r e f o r e , t h e f a s t e r t h i n g s move, the more t h e y p a r t a k e o f m o t i o n , the g r e a t e r t h e i r q u a n t i t y o f m o t i o n ; c o n -v e r s e l y , t h e s l o w e r t h i n g s move, t h e more t h e y p a r t a k e o f r e s t , t h e g r e a t e r t h e i r q u a n t i t y o f r e s t . J u s t as t h e f o r c e o f i m p u l s e o f m o t i o n depends on q u a n t i t y o f m o t i o n , 36 so the f o r c e o f r e s i s t a n c e o f r e s t depends on t h e q u a n t i t y o f r e s t . What i s i n v o l v e d here i s t h e concept o f i n e r t i a f o r b o d i e s a t r e s t . I n the Newtonian system t h e r e are two s e p a r a t e laws i n the p r i n c i p l e o f i n e r t i a : (a) b o d i e s i n m o t i o n s t a y i n m o t i o n , (b) b o d i e s a t r e s t s t a y a t r e s t . As I have a l r e a d y mentioned (see page 21), i n the C a r t e s i a n system t h e r e i s a c l e a r statement o f o n l y the second p a r t o f t h i s p r i n c i p l e . The q u e s t i o n o f why t h e r e i s no s t a t e m e n t f o r t h e f i r s t p a r t i s connected w i t h t h i s n o t i o n of r e s t n o t as a s t a t e o f z e r o m o t i o n , b u t as something opposed t o m o t i o n . I t i s not o n l y d i f f i c u l t t o s t a t e a p r i n c i p l e o f i n e r t i a f o r r e s t , d e f i n e d i n t h i s manner, i t i s a l s o d i f f i c u l t t o g i v e a m a t h e m a t i c a l f o r -m u l a t i o n o f t h e n o t i o n o f q u a n t i t y o f r e s t : t h e q u a n t i t y o f m o t i o n i s t h e p r o d u c t o f s i z e and v e l o c i t y , but. how s h a l l q u a n t i t y o f r e s t be f o r m u l a t e d ? I f we c o n s i d e r how t h e p r i n c i p l e o f c o n t e s t - o f - s t r e n g t h i s a p p l i e d t o the laws o f m o t i o n , t h e n we w i l l see t h a t the e f f e c t i v e , o r a c t u a l f o r m u l a t i o n o f q u a n t i t y o f r e s t u s e d i s the f o l l o w i n g : the q u a n t i t y o f r e s t o f a body a t r e s t i s p r o p o r t i o n a l t o t h e s i z e o f the body - the q u a n t i t y o f r e s t f o r b o d i e s i n m o t i o n i s z e r o . I n e f f e c t t h e n , the n o t i o n o f r e s t as s l o w n e s s , as r e l a t i v e absence o f m o t i o n , a p p a r e n t l y i s not even a p p l i e d i n the r u l e s o f m o t i o n . I f i t were a p p l i e d , t h e n i t i s v e r y d i f f i c u l t t o see how. On t h i s p o i n t t h e r e i s somewhat o f an i n c o n s i s t e n c y i n t h e p h y s i c s o f t h e P r i n c i p l e s . T h i s n o t i o n o f q u a n t i t y o f r e s t , and r e s t as t h e o p p o s i t e o f m o t i o n , i s r a t h e r h a r d t o g r a s p , and t h e e f f o r t t o r e c o n s t r u c t the thought p r o c e s s e s i n v o l v e d i s n e c e s s a r i l y somewhat s p e c u l a t i v e i n c h a r a c t e r . What does s t a n d o u t c l e a r l y i s t h a t i n the P r i n c i p l e s t h e r e i s an e f f o r t t o come t o g r i p s w i t h t h e c oncept o f i n e r t i a l mass, and t h a t t h i s e f f o r t l e a d s t o a c o n c e p t o f r e s t as something opposed t o , b u t sym-m e t r i c a l w i t h m o t i o n . T h i s p o i n t i s c r u c i a l f o r under-s t a n d i n g what S p i n o z a says i n t h e E t h i c s about m o t i o n . B e s i d e s t h e d i f f i c u l t i e s a s s o c i a t e d w i t h f o r m u l a t i n g m o t i o n , a number o f o t h e r problems a r i s e from the d e f i n i t i o n o f c o r p o r e a l m a t t e r as e x t e n s i o n . These problems are o f p a r t i c u l a r c o n c e r n t o t h e p h y s i c s o f t h e E t h i c s , and a r e , i n my o p i n i o n , c r u c i a l t o the u n d e r s t a n d i n g o f what S p i n o z a says about p h y s i c a l s u b s t a n c e i n h i s o t h e r w r i t i n g s . P h y s i c a l s u b s t a n c e and e x t e n s i o n a r e one and t h e same t h i n g , i n the p h y s i c s o f t h e P r i n c i p l e s ; l e t us e x p l o r e the consequences o f t h i s f u n d amental axiom, a s s u m p t i o n , p o s t u l a t e o r h y p o t h e s i s , whatever one w i s h e s t o c a l l i t . The d e f i n i t i o n o f e x t e n s i o n i s D e f i n i t i o n 1: E x t e n s i o n i s t h a t w h i c h c o n s i s t s o f t h r e e d i m e n s i o n s . 38 We do not u n d e r s t a n d by the term the a c t o f e x t e n d i n g o r a n y t h i n g e l s e d i s t i n c t from q u a n t i t y . E x t e n s i o n i s p e r f e c t l y homogeneous, one p a r t o f i t i s no d i f f e r e n t f r om any o t h e r ; i t i s i n f i n i t e l y d i v i s i b l e : any p a r t o f i t can always be seen as c o n s i s t i n g o f y e t s m a l l e r p a r t s . I t i s not o n l y i n f i n i t e l y d i v i s i b l e b u t a l s o i n f i n i t e i n e x t e n t ; i t makes no sense t o t h i n k o f a n y t h i n g " o u t s i d e " o f e x t e n s i o n (see Axiom 1 0 ) , nor f o r t h a t m a t t e r something " i n s i d e " e x t e n s i o n and y e t not p a r t o f i t , s uch as t h e vacuum (see P r o p o s i t i o n 3 ) . E x t e n s i o n by i t s e l f i s not s u f f i c i e n t t o e x p l a i n t h e v a r i e t y o f o b s e r v e d o b j e c t s and phenomena; f o r t h a t m o t i o n - a n d - r e s t i s needed. M o t i o n - a n d - r e s t "breaks up" e x t e n s i o n i n t o a m y r i a d fragments w h i c h t o g e t h e r c o n s t i t u t e the w o r l d o f v a r i e t y and change. I t i s t h i s p i c t u r e o f the u n i v e r s e t o w h i c h D e s c a r t e s " s famous i d e n t i f i c a t i o n o f p h y s i c s w i t h geometry i s a p p l i c a b l e . D e s c a r t e s s a i d : "Qu'on me donne l ' e t e n d u e e t l e mouvement, e t j e v a i s r e f a i r e l e monde", and, " L ' u n i v e r s e e n t i e r e s t un machine ou t o u t se f a i t p a r f i g u r e e t mouvement.". One c o n c e p t u a l d i f f i c u l t y i n h e r e n t i n t h i s p i c t u r e c o n c e r n s t h e s e p a r a t e e x i s t e n c e o f p a r t i c l e s . I f we imagine a composite body c o n s i s t i n g o f a number o f p a r t i c l e s a t r e s t w i t h r e s p e c t t o e a c h o t h e r , the q u e s t i o n t h a t i m m e d i a t e l y a r i s e s i s , i n what sense i s such a body composite a t a l l ? And i f i t i s c o m p o s i t e , why must i t c o n s i s t o f a p a r t i c u l a r s e t o f p a r t i c l e s , s i n c e i t can a l s o be c o n c e i v e d as c o n s i s t i n g o f a q u i t e d i f f e r e n t s e t o f p a r t i c l e s . There i s a p r o f o u n d d i f f i c u l t y i n t h e p h r a s e o c c u r r i n g i n Axiom 9: " A l l e x t e n s i o n can be d i v i d e d , a t l e a s t , i n t h o u g h t . " . I t i s d i f f i c u l t t o c o n c e i v e how t h e e x i s t e n c e o f s e p a r a t e p a r t i c l e s i s c o m p a t i b l e w i t h e x t e n s i o n as g e o m e t r i c a l s p a c e . T h i s d i f f i c u l t y does n o t , a t f i r s t s i g h t , o c c u r i n c o n n e c t i o n w i t h p a r t i c l e s w h i c h a r e i n m o t i o n w i t h r e s p e c t t o e a c h o t h e r . Axiom 16 s a y s : " M a t t e r w h i c h i s moved i n d i f f e r e n t ways has a t l e a s t as many d i v i d e d p a r t s as t h e r e were degrees o f s w i f t n e s s o b s e r v e d a t any g i v e n t i m e . " . I f the "at l e a s t " i s i g n o r e d o r d e l e t e d t h e n we seem t o have an a c c e p t a b l e p r a g m a t i c d e f i n i t i o n o f a p a r t i c l e . But t h e same d i f f i c u l t y c r o p s up a g a i n . S i n c e a l l p a r t i c l e s a r e a t a l l t i m e s i n c o n t a c t w i t h t h e i r n e i g h b o u r s , i t i s c l e a r t h a t any r e l a t i v e m o t i o n between a d j a c e n t p a r t i c l e s must always be s l i d i n g m o t i o n . Now, i f we imagine two p a r t i c l e s s l i d i n g p a s t each o t h e r , we can ask t h e same q u e s t i o n as above, namely, a t t h e c o n t r a c t i n g s u r f a c e s what p r e c i s e l y i s i t t h a t marks the b o u n d a r i e s between th e two p a r t i c l e s ; and i f t h e r e i s n o t h i n g , t h e n the two p a r t i c l e s are i n e f f e c t one l a r g e r one w h i c h i s c h a n g i n g i t s shape, and i t f o l l o w s t h e r e f o r e a l l t h e p a r t i c l e s i n the u n i v e r s e are i n s e p a r a b l y f u s e d t o g e t h e r , and i t i s i m p o s s i b l e f o r m o t i o n t o " c r a c k " e x t e n s i o n . T h i s k i n d o f c o n c e p t u a l d i f f i c u l t y i s a d m i t t e d l y an i n t u i t i v e one, b u t i t i s t h e g r e a t e s t i m p o r t a n c e f o r u n d e r s t a n d i n g many o f S p i n o z a ' s u t t e r a n c e s , so I w i l l t r y t o e x p l a i n i t a l i t t l e f u r t h e r . The space = body p o s t u l a t e (as I c a l l i t ) o f f e r s no c o n c e p t u a l d i f f i c u l t i e s as l o n g as one has i n mind t h e f o l l o w i n g p i c t u r e : the u n i v e r s e i s space f i l l e d w i t h some s o r t o f t r a n s p a r e n t s u b s t a n c e whose o n l y p h y s i c a l p r o p e r t y i s t h a t i t i s e x t e n d e d . M o t i o n i s b r o u g h t i n t o t h i s g l a s s y m a t e r i a l , and b r e a k s i t up i n t o f ragments w h i c h from t h e n on never cease moving about. T h i s p i c t u r e i s e a s i l y u n d e r s t o o d and i t i s t o t h i s p i c t u r e t h a t t h e word "plenum", a space f u l l o f body, i s a p p r o p r i a t e l y a p p l i e d . However, t h e C a r t e s i a n u n i v e r s e does n o t a c t u a l l y f i t the plenum p i c t u r e o f the u n i v e r s e , because a d i f f e r e n t c l a i m i s made, namely not t h a t space i s f i l l e d w i t h body, bu t r a t h e r t h a t space and body a r e one and the same. That t h i s i s so i s c l e a r , amongst o t h e r t h i n g s , f rom what th e P r i n c i p l e s says about t h e vacuum. I t says t h a t the v e r y i d e a o f a vacuum i s s e l f - c o n t r a d i c t o r y , whereas i n the plenum u n i v e r s e the e x i s t e n c e o f the vacuum i s a c o n t i n g e n t m a t t e r : i t i s q u i t e p o s s i b l e t o t h i n k o f a b i t o f space not c o n t a i n i n g any c o r p o r e a l m a t t e r . There a r e s e v e r a l d i f f i c u l t i e s i n h e r e n t i n the C a r t e s i a n i d e n t i f i c a t i o n o f c o r p o r e a l m a t t e r w i t h e x t e n s i o n . F i r s t , i t l e a d s one t o s p e a k i n g , i n e f f e c t , o f a r e g i o n o f space moving i n the p l a c e o f some o t h e r r e g i o n o f space, w h i c h i s q u i t e odd. A n o t h e r i s t h a t i t g i v e s t h e e i g h t laws o f m o t i o n a v e r y p e c u l i a r s t a t u s : t o s t a t e , as a h y p o t h e s i s , t h a t two b o d i e s c o l l i d e i n i s o l a t i o n , i s t o b e g i n an argument w i t h t h e l o g i c a l l y i m p o s s i b l e p r e m i s s : a n y t h i n g a t a l l f o l l o w s from a c o n t r a d i c t i o n . From the p o i n t o f v i e w o f t h i s t h e s i s , the above mentioned problems are not i m p o r t a n t , s i n c e nowhere does S p i n o z a devote any a t t e n t i o n t o them, b u t t h e r e i s a t h i r d k i n d o f d i f f i c u l t y w h i c h i s e x t r e m e l y s i g n i f i c a n t , and t h i s i s the d i f f i c u l t y o f r e c o n c i l i n g t h e s e p a r a t e e x i s t e n c e o f p a r t i c l e s w i t h the c o n t i n u o u s c h a r a c t e r o f e x t e n s i o n . How s e r i o u s l y the i d e n t i f i c a t i o n o f m a t t e r and g e o m e t r i c a l space i s t a k e n can be seen f r o m Axiom 9: A l l e x t e n s i o n can be d i v i d e d , a t l e a s t , i n thought. C o n c e r n i n g t h e t r u t h o f t h i s axiom no one can doubt who has l e a r n e d even th e lements of mathematics. F o r t h e space between a g i v e n c i r c l e and i t s t a n g e n t can always be d i v i d e d by an i n f i n i t e number of g r e a t e r c i r c l e s . Which i s a l s o t r u e as r e g a r d s t h e asymptote o f the h y p e r b o l e . The c r u c i a l p o i n t i s t h a t the P r i n c i p l e s r e c o g n i z e s two t y p e s o f d i v i s i o n i n e x t e n s i o n : (a) d i v i s i o n i n t h o u g h t ; g e o m e t r i c a l e x t e n s i o n i s p e r f e c t l y c o n t i n u o u s : we can always t h i n k o f a p a r t i c u l a r shape as b e i n g s p l i t i n t o two p a r t s by a p l a n e , a p l a n e f i g u r e b e i n g s p l i t up by a l i n e , a l i n e d i v i d e d by a p o i n t ; anywhere i n t h e t h r e e d i m e n s i o n a l continuum we can m e n t a l l y c o n s t r u c t a shape, and on p a per we can r e p r e s e n t t h i s shape by p e n c i l l i n e s w h i c h r e p r e s e n t g e o m e t r i c a l s u r f a c e s o r l i n e s . T h i s i s t h e f o r c e of t h e p h r a s e " i n t h o u g h t " . (b) a c t u a l d i v i s i o n ; t h r o u g h the agency of God the g e o m e t r i c a l continuum has a c t u a l l y come t o be d i v i d e d i n p a r t s , whose motions and c o n f i g u r a t i o n s account f o r the d a i l y p h y s i c a l e v e n t s i n the w o r l d o f e x p e r i e n c e . W i t h o u t f u r t h e r d i s c u s s i o n I t h i n k one can see how the C a r t e s i a n p h y s i c s i s caught between two c o n t r a d i c t o r y d e s i d e r a t a . On t h e one hand i t wants t o r e t a i n the p u r i t y o f g e o m e t r i c a l e x t e n s i o n w h i c h i s c o n t i n u o u s and can be t h o u g h t of as c o n s i s t i n g o f p a r t s w i t h o u t d e s t r o y i n g i t s e s s e n t i a l u n i t y , and a t the same ti m e i t wants t o i m p o r t i n t o t h i s r e a l m t h e a c t u a l i t y 8 o f m o t i o n , w h i c h can a c c o u n t f o r t h e w o r l d o f change . I t s h o u l d be s t r e s s e d , a t t h i s p o i n t , t h a t I do not presume t o have g i v e n t h e d i f f i c u l t i s s u e o f how t o r e c o n c i l e t h e i n d i v i s i b i l i t y o f t h e continuum w i t h the w o r l d o f p a r t i c u l a r s a n y t h i n g l i k e a f u l l t r e a t m e n t ; my e f f o r t has been d i r e c t e d toward showing t h a t t h i s k i n d o f c o n c e p t u a l p r o b l e m does a r i s e f r o m t h e space = body p o s t u l a t e . L a t e r I i n t e n d t o show t h a t S p i n o z a d i d i n d e e d have an i n t e n s e c o n c e r n f o r t h i s type o f problem, and t h a t i s why I have i n t r o d u c e d t h i s t o p i c i n t h e P r i n c i p l e s . L o o k i n g a t P a r t Two o f t h e P r i n c i p l e s as a whole, i t i s p l a i n t h a t as a p h y s i c a l t h e o r y i t i s a f a i l u r e . There a r e p r o f o u n d c o n t r a d i c t i o n s i n the b a s i c p r e m i s s e s , and t h e r e a r e f l a w s i n t h e r u l e s of m o t i o n , a l t h o u g h t h e s e f l a w s are not as o b v i o u s as some have thought. But, i n a way, i t i s a m a g n i f i c e n t f a i l u r e : t h e r e i s an a t t e m p t , i n one s h o r t work, t o l a y , once and f o r a l l , the f o u n d a t i o n s f o r a l l p h y s i c a l s c i e n c e . Not o n l y i s t h e scope a m b i t i o u s , b u t t h e method i s a p p e a l i n g . By s t a r t i n g from what were t h o u g h t t o be e m i n e n t l y c l e a r c o n c e p t s , e x t e n s i o n and m o t i o n as the s o l e p r i m a r y q u a l i t i e s o f m a t t e r , and p r o c e e d i n g by a c a r e f u l d e d u c t i v e method, the t r u t h s a r r i v e d a t would have a m a t h e m a t i c a l c e r t a i n t y about them. B e s i d e s , i t h e l d out t h e promise o f e x p l a i n i n g a g r e a t number o f p h y s i c a l phenomena w i t h -out h a v i n g t o r e s o r t t o such m y s t e r i e s as g r a v i t y , a f o r c e t h a t a c t s a t a d i s t a n c e , t h e vacuum, something t h a t i s and y e t i s n o t h i n g , atoms, w h i c h are e x t e n d e d and are 44 a t the same time i n d i v i s i b l e . A l l t h i s makes the P r i n c i p l e s an i n t e r e s t i n g document i n the h i s t o r y o f s c i e n c e , and a w o r t h w h i l e s u b j e c t f o r s t u d y i n i t s own r i g h t . See, f o r i n s t a n c e , the T r e a t i s e on the Rainbow. 2 On what p h i l o s o p h i c a l grounds the i d e n t i f i c a t i o n of p h y s i c a l s u b s t a n c e w i t h e x t e n s i o n i s made, and c o r -r e s p o n d i n g l y what l o g i c a l s t a t u s t h i s i d e n t i f i c a t i o n has i n the system o f t h e P r i n c i p l e s , i s a q u e s t i o n I do n o t d e a l v / i t h , because, f o r one t h i n g , i t would i n v o l v e us t o o f a r i n D e s c a r t e s ' s m e t a p h y s i c a l t h e o r i e s . 3 Throughout t h i s t h e s i s I use t h e term "Newtonian" t o denote what i s now l a b e l e d " c l a s s i c a l mechanics", w i t h -out making any i m p l i c a t i o n s about I s a a c Newton's thought p r o c e s s e s . 4 F o r comments on B o y l e ' s e x p e r i m e n t s t o t e s t t h e P l e n i s t h y p o t h e s i s , see Conant, pages 34-38. 5 Throughout the P r i n c i p l e s , "motion" and " q u a n t i t y o f m o t i o n " are synonymous t e r m s , so t h a t t h e word " q u a n t i t y " i s g e n e r a l l y s u p e r f l u o u s . ^ S c o t t , page 163. 7 Broad, page 165. 8 I t might a l s o be n o t e d t h a t by t h e i n t r o d u c t i o n t h e a c t u a l d i v i s i o n i n t o the g e o m e t r i c a l continuum, t h e r e has a l s o been i n t r o d u c e d a c o n t i n g e n t f a c t o r i n t o the s u b j e c t o f geometry, so t h a t the t r u t h s about t h e p h y s i c a l w o r l d do not p o s s e s s t h e same a p o d e i c t i c c h a r a c t e r t h a t we a t t r i b u t e t o m a t h e m a t i c a l t r u t h s . I t seems t o me t h i s has some b e a r i n g on S p i n o z a ' s d o c t r i n e o f n e c e s s i t y , but I w o u l d l i k e t o a v o i d t h a t s u b j e c t i f I can. 45 CHAPTER I V THE PHYSICS OF THE ETHICS The main body o f S p i n o z a ' s p h y s i c s i n t h e E t h i c s i s f o u n d i n the S c h o l i u m a f t e r P r o p o s i t i o n 13 o f P a r t Two. T h i s p r o p o s i t i o n r e a d s as f o l l o w s : "The o b j e c t o f the i d e a c o n s t i t u t i n g t h e human mind i s a body, o r a c e r t a i n mode o f e x t e n s i o n a c t u a l l y e x i s t i n g and n o t h i n g e l s e . " . I t i s i n t e r e s t i n g t o note how the p h y s i c a l t h e o r y i s h i d d e n , we might almost say, i n a s c h o l i u m on a p r o p o s i t i o n w h i c h d e a l s w i t h the c o n n e c t i o n o f body and mind. T h i s i s i n d i c a t i v e o f how minor a r o l e p h y s i c s as such p l a y s i n S p i n o z a ' s grand scheme; he mentions t h e s u b j e c t o n l y i n o r d e r t o r e i n f o r c e c e r t a i n p o i n t s o f m e t a p h y s i c a l d o c t r i n e . Because the pur p o s e s f o r w h i c h S p i n o z a i n t r o d u c e s h i s p h y s i c a l t h e o r y are a good d e a l c l e a r e r t h a n t h e t h e o r y i t s e l f , we might w e l l b e g i n by o u t l i n i n g t h e s e p u r p o s e s . One o f t h e s e p u r p o s e s i s t o e x p l a i n t h e i n t e r -c o n n e c t i o n between body and mind, t o make sense o f the n o t i o n t h a t the mind i s t h e i d e a o f the body. The S c h o l i u m s t a r t s out as f o l l o w s : Hence we see not o n l y t h a t the human mind i s u n i t e d t o t h e body, b u t a l s o what i s t o be u n d e r s t o o d by the u n i o n o f mind and body. But no one can under-s t a n d i t a d e q u a t e l y o r d i s t i n c t l y w i t h o u t knowing a d e q u a t e l y b e f o r e h a n d t h e n a t u r e o f our body; f o r those t h i n g s w h i c h we have p r o v e d h i t h e r t o are a l t o g e t h e r g e n e r a l , n or do t h e y r e f e r more t o man th a n t o o t h e r i n d i v i d u a l s , a l l o f w h i c h are animate, a l t h o u g h i n d i f f e r e n t d e g r e e s . S p i n o z a e x p l a i n s t h e s p e c i a l s t a t u s o f t h e human mind i n terms o f t h e o r g a n i z e d c o m p l e x i t y of the human body; a l t h o u g h a l l b o d i e s a re animated, t h e r e are degrees o f a n i m a t i o n , c o r r e s p o n d i n g t o degrees o f o r g a n i z e d c o m p l e x i t y . S t i c k s and s t o n e s , w h i c h a re a t the bottom o f the s c a l e , have a v e r y low l e v e l o f s t r u c t u r a l i n t e g r i t y ; human b e i n g s , a t the t o p o f the s c a l e , have a body w h i c h i s h i g h l y i n t e g r a t e d and hence t h e i r minds a r e g r e a t l y s u p e r i o r t o the "minds" o f s t i c k s and s t o n e s . B e s i d e s e x p l a i n i n g how some b o d i e s can be s a i d t o be animated t o a h i g h e r degree t h a n o t h e r s , S p i n o z a ' s p h y s i c a l t h e o r y s e r v e s a n o t h e r purpose, namely how we have knowledge o f t h e o u t s i d e w o r l d . From the f a c t t h a t a mind i s the i d e a o f a body, i t would seem t o f o l l o w t h a t minds can o n l y know the b o d i e s w i t h w h i c h t h e y a re a s s o c i a t e d . S p i n o z a ' s s o l u t i o n t o t h i s i s t o show t h a t b o d i e s a r e a f f e c t e d by b o d i e s e x t e r n a l t o them. How t h i s i s worked o ut we can see from P o s t u l a t e 5: When a f l u i d p a r t o f the human body i s dete r m i n e d by an e x t e r n a l body, so t h a t i t o f t e n s t r i k e s upon an o t h e r w h i c h i s s o f t , t h e f l u i d p a r t changes the p l a n e o f the s o f t p a r t , and l e a v e s upon i t , as i t were some t r a c e s o f the i m p e l l i n g e x t e r n a l body. We f i n d h e r e a s o r t o f c a u s a l t h e o r y o f p e r c e p t i o n we p e r c e i v e t h e e x t e r n a l w o r l d because i t a f f e c t s o u r b o d i e s . T h i s t h e o r y o f i n t e r a c t i o n amongst b o d i e s i s t h e apparent purpose f o r t h e i n t r o d u c t i o n o f the d e f i n i t i o n o f h a r d n e s s , s o f t n e s s and f l u i d i t y , and i t e x p l a i n s the p r e s e n c e of t h i s b i t o f p h y s i c a l t h e o r y i n the E t h i c s . A t h i r d purpose o f t h e E t h i c s i s t o p r o v i d e a way o f e x p l a i n i n g how the u n i v e r s e as a whole i s c h a n g e l e s s , even though a l l s o r t s o f changes t a k e p l a c e w i t h i n i t . To see how t h i s i s done, we need t o l o o k a l i t t l e c l o s e r a t S p i n o z a ' s t h e o r y o f i n d i v i d u a l s . B e f o r e we do t h i s , however, i t might be b e t t e r , f i r s t , t o d i s c u s s some o f the more g e n e r a l f e a t u r e s of t h e p h y s i c s o f t h e E t h i c s . One major, and d e p l o r a b l e , f e a t u r e o f the p h y s i c s o f t h e E t h i c s i s i t s b r e v i t y . A t f i r s t s i g h t the i m p r e s s i o n i s t h a t i t i s j u s t a b i t o f i n c i d e n t a l m a t e r i a l s t u c k away i n a c o r n e r ; f o r example the f o u r t h axiom (see page 49) does not seem t o f i t i n w i t h what S p i n o z a says b e f o r e o r a f t e r . The t h e o r y p r e s e n t e d seems so s k e t c h y t h a t i t h a r d l y d e s e r v e s the t i t l e " p h y s i c s " . Y e t when we l o o k a l i t t l e c l o s e r , we w i l l f i n d t h a t i t a l l hangs t o g e t h e r , and f u r t h e r m o r e , t h a t almost a l l the b a s i c elements t h a t are n e c e s s a r y t o l a y down the f o u n d a t i o n s o f p h y s i c a l s c i e n c e are t h e r e . I w i l l t a k e advantage o f t h e b r e v i t y o f the t h e o r y p r e s e n t e d by s t a t i n g a l l the axioms, d e f i n i t i o n s , and lemmas o f t h e S c h o l i u m t o P r o p o s i t i o n 13, P a r t Two, i n the o r d e r i n w h i c h t h e y o c c u r . T h i s by i t s e l f w i l l g i v e a good i d e a o f the form and s t y l e o f t h e p h y s i c s o f t h e E t h i c s . B e s i d e s , I s h a l l be r e f e r r i n g t o alm o s t a l l o f t h e s e sooner o r l a t e r , so t h a t i t i s c o n v e n i e n t t o s t a t e them here and now. I have o m i t t e d the s i x p o s t u l a t e s w h i c h come as a body a t t h e end. These p o s t u l a t e s are c l e a r and u n c o n t r o v e r s i a l , so t h a t t h e y c a n s a f e l y be p a r a p h r a s e d . What t h e y s t a t e i s t h a t human b o d i e s a re composite t o a h i g h degree, t h a t p a r t s o f t h e human body are e i t h e r s o f t , h a r d o r f l u i d , t h a t human b o d i e s a r e a f f e c t e d by and c a n a f f e c t the e x t e r n a l w o r l d i n many ways, t h a t t h e y r e g e n e r a t e themselves c o n t i n u o u s l y from o u t s i d e m a t e r i a l , and t h a t e x t e r n a l b o d i e s a t tim e s l e a v e l a s t i n g e f f e c t s on t h e human body. Axiom 1; A l l b o d i e s are e i t h e r i n a s t a t e o f moti o n o r r e s t . Axiom 2: E v e r y body moves, sometimes s l o w l y , sometimes q u i c k l y . Lemma 1: B o d i e s a r e d i s t i n g u i s h e d from one anot h e r i n r e s p e c t o f mo t i o n and r e s t , q u i c k n e s s and s l o w n e s s , and not i n r e s p e c t o f s u b s t a n c e . Lemma 2: A l l b o d i e s agree i n some r e s p e c t s . Lemma 3: A body i n mo t i o n o r a t r e s t must be de t e r m i n e d t o mo t i o n o r r e s t by ano t h e r body, w h i c h was a l s o d e t e r m i n e d t o mot i o n and r e s t by a n o t h e r , and t h a t i n i t s t u r n by a n o t h e r , and so on ad i n f i n i t u m . 49 C o r o l l a r y t o Lemma 3; Hence i t f o l l o w s t h a t a body i n mot i o n w i l l c o n t i n u e i n m o t i o n u n t i l i t be de t e r m i n e d t o a s t a t e o f r e s t by a n o t h e r body, and t h a t a body a t r e s t w i l l c o n t i n u e a t r e s t u n t i l i t be d e t e r m i n e d t o a s t a t e o f m o t i o n by a n o t h e r body. Axiom 3:^ A l l the modes by w h i c h one body i s a f f e c t e d by a n o t h e r f o l l o w f rom the n a t u r e o f t h e body a f f e c t e d , and a t t h e same ti m e from t h e n a t u r e o f t h e a f f e c t i n g body, so t h a t one and t h e same body may be moved i n d i f f e r e n t ways a c c o r d i n g t o the d i v e r s i t y o f t h e n a t u r e o f t h e moving b o d i e s , and, on the o t h e r hand, d i f f e r e n t b o d i e s may be moved i n d i f f e r e n t ways by one and the same body. Axiom 4: "When a body i n m o t i o n s t r i k e s a g a i n s t a n o t h e r w h i c h i s a t r e s t and immovable, i t i s r e f l e c t e d i n o r d e r t h a t i t may c o n t i n u e i t s m o t i o n , and t h e a n g l e o f the l i n e o f r e f l e c t e d m o t i o n w i t h the p l a n e o f t h e body a t r e s t a g a i n s t w h i c h i t s t r u c k w i l l be e q u a l t o t h e ang l e w h i c h the l i n e o f m o t i o n o f i n c i d e n c e makes w i t h the same p l a n e . D e f i n i t i o n : When a number o f b o d i e s o f t h e same o r d i f f e r e n t magnitude are p r e s s e d t o g e t h e r by o t h e r s , so t h a t t h e y l i e one upon the o t h e r , o r i f t h e y are i n m o t i o n w i t h t h e same o r d i f f e r e n t degrees o f speed, so t h a t t h e y communicate t h e i r m otion t o one ano t h e r i n a c e r t a i n f i x e d p r o p o r t i o n , t h e s e b o d i e s are s a i d t o be m u t u a l l y u n i t e d , and t a k e n a l t o g e t h e r t h e y a r e s a i d t o compose one body o r i n d i v i d u a l , w h i c h i s d i s t i n g u i s h e d from o t h e r b o d i e s by t h i s u n i o n o f b o d i e s . Axiom 5: Whether i t i s e a s y o r d i f f i c u l t t o f o r c e t h e p a r t s composing an i n d i v i d u a l t o change t h e i r s i t u a t i o n , and c o n s e q u e n t l y whether i t i s e a s y o r d i f -f i c u l t f o r t h e i n d i v i d u a l t o change i t s shape, depends upon whether t h e p a r t s o f the i n d i v i d u a l o r compound body l i e w i t h l e s s o r whether w i t h g r e a t e r s u r f a c e s upon one a n o t h e r . Hence b o d i e s whose p a r t s l i e upon e a c h o t h e r w i t h g r e a t e r s u r f a c e s I w i l l c a l l h a r d ; those s o f t , whose p a r t s l i e on one a n o t h e r w i t h s m a l l e r s u r f a c e s ; and those f l u i d , whose p a r t s move amongst each o t h e r . Lemma 4: I f a c e r t a i n number o f b o d i e s be s e p a r a t e d from the body o r i n d i v i d u a l w h i c h i s composed of a number o f b o d i e s , and i f t h e i r p l a c e be s u p p l i e d by the same number o f o t h e r b o d i e s o f t h e same n a t u r e , t h e i n d i v i d u a l w i l l r e t a i n t he n a t u r e w h i c h i t had b e f o r e 50 w i t h o u t any change o f form. Lemma 5; I f the p a r t s composing an i n d i v i d u a l become g r e a t e r o r l e s s p r o p o r t i o n a l l y , so t h a t t h e y p r e s e r v e t o one a n o t h e r t h e same k i n d o f m o t i o n and r e s t , the i n d i v i d u a l w i l l a l s o r e t a i n the n a t u r e w h i c h i t had b e f o r e w i t h o u t any change o f form. Lemma 6; I f any number o f b o d i e s composing an i n d i v i d u a l a r e c o m p e l l e d t o d i v e r t i n t o one d i r e c t i o n t h e m o t i o n t h e y p r e v i o u s l y had i n a n o t h e r , b u t are n e v e r t h e l e s s a b l e t o c o n t i n u e and r e c i p r o c a l l y com-municate t h e i r motions i n the same manner as b e f o r e , t h e i n d i v i d u a l w i l l t h e n r e t a i n i t s n a t u r e w i t h o u t any change o f form. Lemma 7: The i n d i v i d u a l t h u s composed w i l l , moreoever, r e t a i n i t s n a t u r e whether i t move as a whole or be a t r e s t , o r whether i t move i n t h i s o r t h a t d i r e c t i o n , p r o v i d e d t h a t each p a r t r e t a i n i t s m o t i o n and communicates i t as b e f o r e t o t h e r e s t . The o u t s t a n d i n g d i f f e r e n c e between t h e p h y s i c s o f t h e E t h i c s and t h a t o f the P r i n c i p l e s i s t h a t the former c o n t a i n s a much more s o p h i s t i c a t e d and p o w e r f u l t h e o r y o f composite body, namely the t h e o r y o f i n d i v i d u a l s . There i s no e v i d e n c e t h a t t h i s t h e o r y i s n o t c o m p l e t e l y o r i g i n a l w i t h S p i n o z a ; a t l e a s t t h e r e i s no h i n t o f i t i n t h e P r i n c i p l e s , so t h a t t h i s p a r t o f t h e p h y s i c a l t h e o r y can p r o p e r l y be l a b e l l e d " Spinoza's p h y s i c s " . A l t h o u g h the t h e o r y o f i n d i v i d u a l s has f a r r e a c h i n g and complex r a m i f i c a t i o n s , i t i s r a t h e r s i m p l e i n o u t l i n e : the u n i v e r s e i s a h i e r a r c h y o f d i f f e r e n t k i n d s o f i n d i v i d u a l s ; a t t h e bottom o f the s c a l e t h e r e are the i n d i v i d u a l s o f t h e s i m p l e s t k i n d , whose component p a r t s a r e t h e s i m p l e s t b o d i e s , the c o r p o r a s i m p l i c i s s i m a ; t h e s e l o w e s t l e v e l s combine t o form i n d i v i d u a l s o f t h e second o r d e r , and t h e s e a g a i n t o f o r m i n d i v i d u a l s o f the t h i r d o r d e r , and so on. A t the h i g h e s t l e v e l t h e r e i s o n l y one i n d i v i d u a l , the u n i v e r s e i t s e l f . The p i c t u r e o f t h e u n i v e r s e as a h i e r a r c h y o f composite b o d i e s w i t h t h e u n i v e r s e a t t h e t o p , and t h e p a r t i c l e s a t the bottom, i s n o t h a r d t o u n d e r s t a n d and i s on t h e f a c e o f i t q u i t e a p p e a l i n g . What i s more d i f f i c u l t t o u n d e r s t a n d i s how a number o f elements combine t o form a l a r g e r u n i t , i . e . what b i n d s the e lements t o -g e t h e r and i n what way can a number o f s i m p l e r u n i t s be p a r t o f a more complex u n i t , what does th e s t r u c t u r a l i n t e g r i t y o f a p a r t i c u l a r i n d i v i d u a l c o n s i s t o f . Answers t o t h e s e q u e s t i o n s are not r e a d i l y a v a i l a b l e because o f t h e c o n c i s e n e s s and almost e n i g m a t i c c h a r a c t e r o f t h e p h y s i c s o f ' t h e E t h i c s . That somehow t h e concept o f o r g a n i z e d c o m p l e x i t y i n v o l v e s t h e motions o f p a r t i c l e s i s f a i r l y c l e a r from the D e f i n i t i o n , b u t what the p r o p -e r t i e s o f t h e s e p a r t i c l e s o r s i m p l e s t b o d i e s a r e , and what t h e c h a r a c t e r o f m o t i o n i s , i s j u s t as d i f f i c u l t t o determine as the n a t u r e o f o r g a n i z e d c o m p l e x i t y o f t h e i n d i v i d u a l s , and o b v i o u s l y t h e s e q u e s t i o n s are i n t e r -r e l a t e d . I n the n e x t two c h a p t e r s I w i l l examine t h e s e q u e s t i o n s more c l o s e l y . A t t h i s p o i n t i t might be u s e f u l t o compare t h e p h y s i c s o f t h e E t h i c s w i t h t h a t o f the P r i n c i p l e s , f o r t h e purpose o f c o n s i d e r i n g some o f t h e o b v i o u s d i f f e r e n c e s and s i m i l a r i t i e s . O u t s i d e o f , p e r h a p s , the t h e o r y o f i n d i v i d u a l s , t h e r e seems t o be l i t t l e i n t h e p h y s i c s o f t h e E t h i c s t h a t w o u l d mark i t as something r a d i c a l l y d i f f e r e n t f rom t h e p h y s i c s o f t h e P r i n c i p l e s . F o r i n s t a n c e , t h e f o u r t h axiom i s q u i t e s i m i l a r t o the f o u r t h r u l e o f m o t i o n ( P r o p o s i t i o n 28) o f the P r i n c i p l e s and the f o r m e r might w e l l a t f i r s t s i g h t be r e g a r d e d as a r e f o r m u l a t i o n o f t h e l a t t e r . I t i s t r u e t h a t t h e r e are no c o r r e s p o n d i n g axioms f o r the o t h e r r u l e s o f m o t i o n , b u t t h i s has a ready e x p l a n a t i o n i n t h a t , a f t e r a l l , the E t h i c s i s n o t p r i m a r i l y a work on p h y s i c a l s c i e n c e , so t h a t o t h e r laws o f m o t i o n would not be p e r t i n e n t t o i t s purpose. Why S p i n o z a i n c l u d e s t h i s law and not o t h e r s may be q u i t e i n s i g n i f i c a n t . The p h y s i c a l t h e o r y o f t h e s e two works i s s i m i l a r i n o t h e r r e s p e c t s as w e l l . F o r i n s t a n c e , i n b o t h c a s e s the f u n damental elements o f s c i e n t i f i c e x -p l a n a t i o n a r e m o t i o n and p a r t i c l e s . The b a s i c method o r p r o c e d u r e i s , s u p e r f i c i a l l y a t l e a s t , the same. Not a s i n g l e r e f e r e n c e i s made i n the p h y s i c s o f t h e E t h i c s t o a n y t h i n g l i k e e x p e r i m e n t a l e v i d e n c e o r o b s e r v a t i o n a l d a t a 2 . There i s no m e n t i o n o f a c t i o n a t a d i s t a n c e ; t h e f o u r t h axiom, t h e o n l y i t e m t h a t d e a l s w i t h t h e i n t e r a c t i o n o f b o d i e s , s u g g e s t s t h a t b o d i e s can i n t e r a c t by c o n t a c t a l o n e , j u s t as i n the P r i n c i p l e s . On the q u e s t i o n o f the vacuum t h e r e seems t o be agreement as w a l l ; i n t h e S c h o l i u m t o P r o p o s i t i o n 15, P a r t One o f the E t h i c s , S p i n o z a s t a t e s : Everyone who knows t h a t c l e a r r e a s o n i s i n f a l l i b l e ought t o admit t h i s , and e s p e c i a l l y t h o s e who deny t h a t t h e vacuum can e x i s t . A l l i n a l l , enough s i m i l a r i t i e s e x i s t t o j u s t i f y t he t e n t a t i v e a s s u m p t i o n t h a t S p i n o z a ' s i d e a s about t h e s t r u c t u r e of t h e p h y s i c a l u n i v e r s e are w e l l r e p r e s e n t e d by P a r t Two o f t h e P r i n c i p l e s . What might argue a g a i n s t t h i s a s sumption i s t h a t on s e v e r a l major p o i n t s o f p h i l o s o p h i c a l d o c t r i n e S p i n o z a ' s p o s i t i o n i s a n t i t h e t i c a l t o t h a t o f D e s c a r t e s ; some o f t h e s e w i l l be d i s c u s s e d l a t e r . A l s o , t h e r e i s one i n s t a n c e o f S p i n o z a ' s o u t -r i g h t l y condemning D e s c a r t e s ' s " p r i n c i p l e s o f n a t u r a l t h i n g s " i n no u n c e r t a i n terms ( l e t t e r t o T s c h i r n h a u s , May 1676); I w i l l r e t u r n t o t h i s p o i n t i n a l a t e r c h a p t e r . i s p i n o z a l a b e l s t h i s axiom and t h e f o l l o w i n g two axioms as Axiom 1, 2 and 3 r e s p e c t i v e l y , b u t f o r convenience sake I w i l l c a l l t h e s e Axiom 3, 4 and 5 r e s p e c t i v e l y . 2 I n the P r i n c i p l e s t h e r e i s a r e f e r e n c e here and t h e r e t o p r a c t i c a l c a s e s , b u t t h e s e a re m a i n l y used as examples t o s t r e n g t h e n the argument. CHAPTER V THE THEORY OF INDIVIDUALS The t h e o r y o f i n d i v i d u a l s has o b v i o u s l y a v e r y i m p o r t a n t r o l e t o p l a y i n S p i n o z a ' s grand scheme; i t i s n o t m e r e l y a t h e o r y o f composite body b u t a l s o , a way o f e x p l a i n i n g the i n t e r a c t i o n o f mind and body. From the p o i n t o f v i e w o f t h i s t h e s i s the d i s c u s s i o n o f t h i s t h e o r y w i l l o f n e c e s s i t y be q u i t e l i m i t e d ; i t w i l l be l i m i t e d t o c o n s i d e r i n g the t h e o r y as a p h y s i c a l t h e o r y , namely a t h e o r y o f composite body. Whatever e l s e i s obscure about the t h e o r y o f i n d i v i d u a l s , t h i s much i s c e r t a i n : S p i n o z a d i s t i n g u i s h e s c l e a r l y between two k i n d s o f b o d i e s , t h e s i m p l e s t b o d i e s and t h e i n d i v i d u a l s . The f i r s t f o u r axioms and t h e f i r s t t h r e e lemmas a p p l y s p e c i f i c a l l y t o t h e c o r p o r a s i m p l i c i s s i m a ( I w i l l t a k e the l i b e r t y o f a b b r e v i a t i n g i t as c o r p . s i m p . ) . T h i s i s e v i d e n t f rom the statement i m m e d i a t e l y f o l l o w i n g Axiom 4: "Thus much f o r s i m p l e s t b o d i e s w h i c h a re d i s t i n g u i s h e d f rom one a n o t h e r by motion and r e s t , speed and slowness a l o n e ; l e t us now advance t o composite b o d i e s . " . He t h e n p r o c e e d s t o g i v e t h e d e f i n i t i o n o f an i n d i v i d u a l . The f i r s t q u e s t i o n we might ask i s how t h e c o n s t i t u e n t p a r t s o f any p a r t i c u l a r i n d i v i d u a l a r e bound t o g e t h e r , i n what way t h e y combine t o form a l a r g e r u n i t . L o o k i n g a t t h e d e f i n i t i o n , we see t h a t t h e r e are b a s i c a l l y two ways i n w h i c h t h i s i s done: (a) a number o f b o d i e s a r e a t r e s t w i t h r e s p e c t t o e a c h o t h e r , o r , (b) a number o f b o d i e s e x h i b i t c e r t a i n r e g u l a r i t i e s i n t h e i r motions w i t h r e s p e c t t o e a c h o t h e r . Case (a) can be u n d e r s t o o d by t h i n k i n g o f a house b u i l t o u t o f b r i c k s w h i l e (b) i s perhaps r e p r e s e n t e d by a wheel r o t a t i n g about a f i x e d a x l e , o r a watch, whose p a r t s e x h i b i t c e r t a i n d e f i n i t e r e l a t i o n s o f m o t i o n . I f we c o n s i d e r r e l a t i v e r e s t as a s p e c i a l k i n d o f r e g u l a r i t y , t h e n (a) i s a c t u a l l y o n l y a s p e c i a l case o f ( b ) : we can say th e n t h a t the " s t r u c t u r a l i n t e g r i t y o f an i n d i v i d u a l l i e s s i m p l y i n t h e r e g u l a r i t y o f t h e motions o f the p a r t s o f t h e i n d i v i d u a l . One has t o be somewhat c a r e f u l i n the use o f these examples. S p i n o z a g i v e s no s i m p l e examples; the o n l y example he does g i v e i s t h e human body, w h i c h , as we can see from P o s t u l a t e 1, i s h i g h l y complex i n t h a t the c o n s t i t u e n t p a r t s o f human b o d i e s a r e the m s e l v e s composite t o a h i g h degree. Hence we a r e somewhat a t a l o s s when we t r y t o imagine how a l l the d e t a i l s are supposed t o be worked o u t , nor i s t h e r e any e v i d e n c e t h a t S p i n o z a had worked t h e s e d e t a i l s o u t . So t h e t a l k about watches, wheels o r houses i s somewhat s p e c u l a t i v e i n n a t u r e . What i s f a i r l y c l e a r , however, i s the concept o f an i n d i v i d u a l as something more t h a n the sum o f i t s p a r t s . J u s t as i n t h e case w i t h the modern n o t i o n o f the atom, w h i c h i s more t h a n a mere c o l l e c t i o n o f p r o t o n s , n e u t r o n s and e l e c t r o n s , the i n d i v i d u a l i s more t h a n a c o l l e c t i o n o f p a r t s , i t i s a "union o f b o d i e s " , an o r g a n i z a t i o n o f p a r t s . S p i n o z a c o n c e i v e s o f the u n i v e r s e as a whole as a super i n d i v i d u a l (see S c h o l i u m t o Lemma 7) and t h i s i n d i c a t e s a cosmology somewhat d i f f e r e n t f r o m t h a t o f t h e C a r t e s i a n p h y s i c s . The p i c t u r e o f t h e C a r t e s i a n u n i v e r s e i s t h a t o f a g i a n t c o n g l o m e r a t i o n o f a l l s o r t s o f p a r t i c l e s i n m o t i o n w i t h no e s s e n t i a l u n i f y i n g f a c t o r 1 . I n t h e C a r t e s i a n p h y s i c s a composite body has s t r u c t u r e o n l y i n s o f a r as t h e p a r t s o f t h e body happen t o be c l o s e t o g e t h e r f o r a c e r t a i n p e r i o d o f t i m e , w h i l e i n t h e E t h i c s a composite body has d e f i -n i t e o r g a n i z e d c o m p l e x i t y . On the o t h e r hand, the E t h i c s and the P r i n c i p l e s have i n common t h a t i n n e i t h e r a re t h e r e mentioned any a t t r a c t i v e f o r c e s , o r any p h y s i c a l e n t i t y t h a t b i n d s p a r t i c l e s t o g e t h e r . I n the d e f i n i t i o n the p h r a s e " p r e s s e d t o g e t h e r " o c c u r s , and t h i s i s the o n l y p h r a s e t h a t s u g g e s t s f o r c e i n any fo r m o r way. T h i s p h rase i s w e l l i n a c c o r d w i t h the p i c t u r e o f t h e u n i v e r s e as p r e s e n t e d i n the P r i n c i p l e s , namely as a plenum, a space c o m p l e t e l y f i l l e d w i t h p a r t i c l e s , and where the mot i o n 57 o f any p a r t i c l e must i n v o l v e the motions o f one or more o f i t s n e i g h b o u r s . T h i s n o t i o n o f o r g a n i z e d c o m p l e x i t y , t h a t t h e composite body i s more t h a n the sum o f i t s p a r t s , ; i s , v e r y i m p o r t a n t t o S p i n o z a ' s m e t a p h y s i c a l scheme; t h e u n i v e r s e i s t h e body o f God, and hence i n some way i t must be a u n i t , an o r g a n i z e d whole and somehow i t must be c h a n g e l e s s . That t h e u n i v e r s e as a whole, b e i n g an i n d i v i d u a l , i s a u n i t , i s n o t so p r o b l e m a t i c , b u t i n what way t h e u n i v e r s e i s c h a n g e l e s s i s more d i f f i c u l t t o u n d e r s t a n d . T h i s i s b u t p a r t o f a more g e n e r a l problem, namely i n what way are i n d i v i d u a l s i n g e n e r a l s a i d t o be u n d e r g o i n g change, what c o n s t i t u t e s a change i n an i n d i v i d u a l . Lemmas 4, 5, 6, and 7 t e l l us what does n o t c o n s t i t u t e change i n an i n d i v i d u a l : (1) i f c e r t a i n p a r t s o f an i n d i v i d u a l a r e r e p l a c e d by o t h e r s o f t h e same n a t u r e , (2) i f a l l the p a r t s o f an i n d i v i d u a l become p r o p o r t i o n a t e l y l a r g e r o r s m a l l e r , ( 3 ) i f some p a r t s o f an i n d i v i d u a l change t h e d i r e c t i o n o f t h e i r m o t i o n b u t somehow p r e s e r v e t h e i r r e l a t i o n w i t h o t h e r p a r t s , (4) i f t h e i n d i v i d u a l as a whole comes t o r e s t , t h e n t h e r e i s i m p l i e d no change i n t h e i n d i v i d u a l as a whole. What S p i n o z a has i n mind w i t h t h e s e lemmas can be seen more c l e a r l y by c o n s i d e r i n g the s i x p o s t u l a t e s . w h i c h r e f e r s p e c i f i c a l l y t o human b o d i e s : (1) human b o d i e s s t a y the same even though new m a t e r i a l i s i n g e s t e d and o l d m a t e r i a l i s e x c r e t e d ; (2) human b o d i e s r e t a i n much the same shape and c o n s t i t u t i o n even though t h e y i n c r e a s e s e v e r a l f o l d i n s i z e o v e r t h e p e r i o d o f a l i f e -t i m e ; (3) human b o d i e s have a c o n s i d e r a b l e amount o f freedom o f movement i n the i n d i v i d u a l members, w i t h o u t t h i s c o n s t i t u t i n g an e s s e n t i a l change o f t h e i n d i v i d u a l ; (4) human b o d i e s r e t a i n t h e i r i d e n t i t y r e g a r d l e s s o f whether t h e y move around o r are a t r e s t . The two i m p o r t a n t d i f f e r e n c e s between human b o d i e s as i n d i v i d u a l s and t h e u n i v e r s e as an i n d i v i d u a l , i s t h a t human b o d i e s have n e i g h b o u r s , so t o speak, and t h a t human b o d i e s a r e c o n s t a n t l y s u b j e c t t o change, w h i l e the u n i v e r s e , by d e f i n i t i o n , i s a l o n e and i s c h a n g e l e s s . I n the S c h o l i u m t o Lemma 7, S p i n o z a s t a t e s : Thus, i f we advance ad i n f i n i t u m , we may e a s i l y c o n c e i v e t h e whole of n a t u r e t o be one i n d i v i d u a l , whose p a r t s , t h a t i s t o say, a l l b o d i e s , d i f f e r i n i n f i n i t e ways w i t h o u t any change i n the whole i n d i v i d u a l . A l t h o u g h i t i s not s p e c i f i c a l l y s t a t e d , t h e p r o o f o f the c h a n g e l e s s n e s s o f t h e u n i v e r s e depends on the f o l l o w i n g p r o p o s i t i o n : any change i n an i n d i v i d u a l must come f r o m o u t s i d e t h e i n d i v i d u a l ; t h e r e i s no spontaneous change. I t i s an e s s e n t i a l p a r t o f S p i n o z a ' s scheme t h a t a l l b o d i e s b e i n g f i n i t e and d e t e r m i n a t e . have the cause o f t h e i r e x i s t e n c e and a c t i v i t y i n o t h e r f i n i t e and d e t e r m i n a t e e n t i t i e s (see P r o p o s i t i o n 25, P a r t One). I n o t h e r words, t o e x p l a i n what happens t o one body, we must always l o o k f o r i t s i n t e r a c t i o n s w i t h o t h e r b o d i e s . Now, f o r s i m p l e s t b o d i e s , how t h i s works out i s c l e a r l y e x p l a i n e d i n the p h y s i c s o f t h e E t h i c s . S i m p l e s t b o d i e s have o n l y one p r o p e r t y t h a t can change, namely t h e i r m o t i o n . A change from m o t i o n t o r e s t o r v i c e -v e r s a i s b r o u g h t about o n l y by i n t e r a c t i o n , i . e . c o l l i s i o n , w i t h o t h e r b o d i e s , so t h a t i n o r d e r t o e x p l a i n why a p a r t i c u l a r s i m p l e body has a c e r t a i n s t a t e o f m o t i o n o r r e s t , we have t o r e f e r t o a h i s t o r y o f c o l l i s i o n s . But t h e case w i t h i n d i v i d u a l s i s o b v i o u s l y d i f f e r e n t , because b e s i d e s the m o t i o n t h e y p o s s e s s as a whole, t h e r e i s a n o t h e r p r o p e r t y t h a t i n d i v i d u a l s p o s s e s s , namely t h e i r i n t e r n a l c o n s t i t u t i o n . I t i s t h e r e g u l a r i t y o f t h e m o t ions o f the p a r t s t h a t c o n s t i t u t e s the f o r m o r n a t u r e o f an i n d i v i d u a l , t o use S p i n o z a ' s t e r m i n o l o g y . T h i s i m p l i e s t h a t t h e i n d i v i d u a l i s r a t h e r a d i f f e r e n t s o r t o f e n t i t y f r om the c o r p . simp. The i n d i v i d u a l i s s a i d t o change o n l y i n s o f a r as i t s i n t e r n a l c o n s t i t u t i o n changes, w h i l e t h e c o r p . simp, change o n l y w i t h r e s p e c t t o m o t i o n and r e s t . The p o i n t i n a l l t h i s i s t h a t S p i n o z a does not show i n any way why i n d i v i d u a l s do not change u n l e s s t h e y i n t e r a c t w i t h o t h e r i n d i v i d u a l s . On the b a s i s o f what he says about th e c o r p . simp., i t i s q u i t e c o n -c e i v a b l e t h a t i n d i v i d u a l s are u n d e r g o i n g c o n t i n u o u s i n t e r n a l change owing t o t h e c o l l i s i o n s o f t h e p a r t s , w i t h o u t i n t e r a c t i o n amongst i n d i v i d u a l s . But t h i s de-pends on what i s t o count as change i n an i n d i v i d u a l . One p o s s i b i l i t y i s t h a t an i n d i v i d u a l i s unchanged as l o n g as t h e t o t a l m o t i o n of t h e p a r t s o f t h e i n d i v i d u a l remains c o n s t a n t . There i s e v i d e n c e t h a t S p i n o z a d i d have something l i k e t h i s i n mind. I n the l e t t e r t o Oldenburg, November 1665, S p i n o z a d i s c u s s e s a t l e n g t h on the r e l a t i o n o f t h e p a r t s of n a t u r e t o the whole o f n a t u r e . He s a y s : Now, a l l the b o d i e s o f n a t u r e can and s h o u l d be c o n c e i v e d i n the same way as we have here c o n c e i v e d t h e b l o o d : f o r a l l b o d i e s a r e s u r r o u n d e d by o t h e r s , and are m u t u a l l y d e t e r m i n e d t o e x i s t i n a d e f i n i t e and d e t e r m i n a t e manner, w h i l e t h e r e i s p r e s e r v e d i n a l l t o g e t h e r , t h a t i s , i n t h e whole u n i v e r s e , t h e same p r o p o r t i o n o f m o t i o n and r e s t . T h i s q u o t a t i o n would i n d i c a t e t h a t f o r S p i n o z a t h e c h a n g e l e s s n e s s o f the u n i v e r s e c o n s i s t s s o l e l y i n t h e f a c t t h a t the t o t a l q u a n t i t y of m o t i o n i n t h e u n i v e r s e i s c o n s t a n t , and by i m p l i c a t i o n , t h a t e a ch i n d i v i d u a l i s changed o n l y i n s o f a r as the sum t o t a l o f t h e motions o f p a r t s i s changed. T h i s i n t e r p r e t a t i o n has the d e f i n i t e advantage t h a t i t makes f o r c o n s i s t e n c y : as l o n g as we can show t h a t m o t i o n i s p r e s e r v e d i n i n d i v i d u a l c o l l i s i o n s , t h e n i t f o l l o w s t h a t the t o t a l q u a n t i t y o f m o t i o n o f an i n d i v i d u a l w i l l remain c o n s t a n t as l o n g as the i n d i v i d u a l does not i n t e r a c t w i t h o t h e r b o d i e s , and o f c o u r s e , i t a l s o f o l l o w s t h a t t h e t o t a l q u a n t i t y o f mo t i o n i n the u n i v e r s e i s c o n s t a n t . On the o t h e r hand, i t a l s o w o u l d seem t o f o l l o w t h a t two i n d i v i d u a l s are t h e same, j u s t i n case the t o t a l q u a n t i t y o f m o t i o n i n each i s t h e same, and t h i s l e a d s t o s t r a n g e consequences. A t r e e would be t h e i d e n t i c a l i n d i v i d u a l as an e l e p h a n t , as l o n g as t h e t o t a l q u a n t i t y o f m o t i o n o f a t r e e and an e l e p h a n t a re the same. A l l watches i n t h e w o r l d w o u l d be i d e n t i c a l p r o v i d e d t h a t t h e sum o f t h e motions o f t h e p a r t s o f each watch would be the same. I t i s e v i d e n t from t h e d e f i n i t i o n and t h e l a s t f o u r lemmas t h a t the form and n a t u r e o f an i n d i v i d u a l i s more t h a n t h e t o t a l sum o f the motions o f t h e p a r t s ; i t has t o do w i t h c e r t a i n r e g u l a r i t i e s o f t h e motions o f t h e p a r t s , a d e f i n i t e i n t e r n a l s t r u c t u r e . What b i n d s t h e p a r t s o f an i n d i v i d u a l t o g e t h e r i s more t h a n the mere f a c t t h a t o v er a g i v e n p e r i o d o f time t h e t o t a l sum o f t h e i r motions i s r e l a t i v e l y c o n s t a n t . I n some way t h e r e i s o r g a n i z e d c o m p l e x i t y , and i n some way the u n i v e r s e i s a s t r u c t u r e d whole. From t h e p o i n t o f v i e w o f t h i s t h e s i s t h e f o l l o w i n g q u e s t i o n about S p i n o z a ' s t h e o r y o f i n d i v i d u a l s i s c r u c i a l : does t h e t h e o r y o f i n d i v i d u a l s i n d i c a t e a p h y s i c a l t h e o r y t h a t i s s i g n i f i c a n t l y d i f f e r e n t f rom the p h y s i c s o f the P r i n c i p l e s ? My c l a i m i s t h a t i t does n o t . The t h e o r y i s e s s e n t i a l l y an e x t e n s i o n o f the C a r t e s i a n p h y s i c s , and stems from an e f f o r t on S p i n o z a ' s p a r t t o remedy a d e f e c t o f t h e C a r t e s i a n p h y s i c s . The d e f e c t o f t h e C a r t e s i a n p h y s i c s i s t h a t the C a r t e s i a n u n i v e r s e i s e s s e n t i a l l y an u n o r g a n i z e d c o n g l o m e r a t i o n , a mad m i l l i n g about o f a l a r g e number of p a r t i c l e s ; i n s h o r t , i t i s c h a o t i c . F o r D e s c a r t e s ' s m e t a p h y s i c s t h i s was no o b s t a c l e , b u t f o r S p i n o z a ' s scheme the C a r t e s i a n cosmos i s u n s a t i s f a c t o r y i n a t l e a s t two ways: (a) the u n i v e r s e i s t h e body o f God and t o see t h e body o f God as a l o o s e c o n g l o m e r a t i o n o f p a r t i c l e i s a b s u r d , o r a t l e a s t repugnant. (b) the human mind i s t h e i d e a o f t h e human body, and s u p e r i o r minds must "be l o n g " t o s u p e r i o r b o d i e s hence t h e r e must be v a r y i n g degrees of a n i m a t i o n w i t h c o r r e s p o n d i n g v a r y i n g degrees o f o r g a n i z e d c o m p l e x i t y . What i s s e r i o u s l y l a c k i n g i n t h e C a r t e s i a n p h y s i c s , f rom S p i n o z a ' s p o i n t o f v i e w , i s a t h e o r y o f c omposite body. I n the C a r t e s i a n p h y s i c s a composite body i s b a s i c a l l y a number o f p a r t i c l e s a t r e s t w i t h r e s p e c t t o . e a c h o t h e r and " p r e s s e d t o g e t h e r " i n the p h r a s e o l o g y o f the d e f i n i t i o n . T h i s i m p l i e s t h a t a human body and a stone are not v e r y much d i f f e r e n t . The f i r s t h a l f o f the d e f i n i t i o n (see case (a) on page 55) i s not adequate. There o b v i o u s l y are composite b o d i e s , such as a watch, o r a human body, whose p a r t s a r e i n m o t i o n r e l a t i v e t o each o t h e r , and y e t have a d e f i n i t e s t r u c t u r e w h i c h remains r e l a t i v e l y s t a b l e o v e r a g i v e n p e r i o d o f t i m e . Hence S p i n o z a ' s d e f i n i t i o n can be t a k e n as an e x t r a p o l a t i o n o r an e x t e n s i o n o f the C a r t e s i a n t h e o r y o f composite body. A l l t h i s l e a v e s a number of q u e s t i o n s unanswered; f o r i n s t a n c e , p r e c i s e l y what are t h e s e r e g u l a r i t i e s o f m o t i o n , and what i s t o count as change i n an i n d i v i d u a l ; i n what sense i s the u n i v e r s e c h a n g e l e s s ? No re a d y answers are t o be f o u n d t o t h e s e q u e s t i o n s , and i t i s d o u b t f u l t h a t S p i n o z a had worked out the f u l l i m p l i c a t i o n s o f h i s t h e o r y . I n h i s own words, a t t h e end o f the S c h o l i u m t o Lemma 7: I f i t had been my o b j e c t t o c o n s i d e r s p e c i a l l y t h e q u e s t i o n o f a body, I s h o u l d have had t o e x p l a i n and demonstrate t h e s e t h i n g s more f u l l y . But, as I have a l r e a d y s a i d , I have a n o t h e r end i n v i e w , and I have n o t i c e d them o n l y because I can e a s i l y deduce from them t h o s e t h i n g s w h i c h I have p r o p o s e d t o demonstrate. On the whole, i t can be s a i d t h a t S p i n o z a ' s purposes f o r i n t r o d u c i n g t h e t h e o r y o f i n d i v i d u a l s are a good d e a l c l e a r e r t h a n t h e t h e o r y i t s e l f ; hence t h e r e a r e a c e r t a i n number o f it e m s on w h i c h e n l i g h t e n m e n t i s s i m p l y n o t t o be had. The major p o i n t i s t h a t the t h e o r y o f i n d i v i d u a l s does, n o t n e c e s s a r i l y , mean a system r a d i c a l l y d i f f e r e n t from t h a t o f the P r i n c i p l e s , but on the c o n t r a r y , i t can be seen as an e x t e n s i o n o f the C a r t e s i a n p h y s i c s , an added element t o f i l l a c e r t a i n gap, o r a s l i g h t m o d i f i c a t i o n t o make i t c o n s i s t e n t w i t h t h e c e n t r a l p o i n t s o f S p i n o z i s t i c dogma. •^Note t h a t I am u s i n g t h e word " C a r t e s i a n " i n the way I have d e f i n e d i t i n Chapter I I I . 65 CHAPTER V I MOTION I N SPINOZA'S PHYSICS A l t h o u g h b o t h the P r i n c i p l e s and the E t h i c s a r e w r i t t e n i n the g e o m e t r i c a l form, t h e former i s much more e a s i l y u n d e r s t o o d t h a n the l a t t e r . I t seems al m o s t as i f the p h y s i c s o f t h e E t h i c s i s a c o n d e n s a t i o n o f t h e P r i n c i p l e s , and the P r i n c i p l e s i s a l r e a d y a work o f g r e a t c o n c i s e n e s s . I n the E t h i c s S p i n o z a does n ot b o t h e r t o d i s c u s s h i s t h e o r y i n d e t a i l o r e l u c i d a t e i t b y means of examples. F u r t h e r m o r e , and t h i s i s e s p e c i a l l y t r u e on the s u b j e c t o f m o t i o n , h i s t e r m i n o l o g y i s u n f a m i l i a r and a l m o s t i n c o m p r e h e n s i b l e a t t i m e s . My main t a s k , t h e r e f o r e , i s t o t r y t o make some sense out o f t h e s t a t e -ments d e a l i n g w i t h m o t i o n , and t o t r y t o t r a c e a c o n n e c t i o n between them and c o r r e s p o n d i n g p a r t s o f the P r i n c i p l e s . Whatever e l s e i s u n c l e a r , i t i s c l e a r t h a t the laws o r p r i n c i p l e s o f mot i o n f a l l i n t o two c a t e g o r i e s : (a) those g o v e r n i n g b o d i e s c o n s i d e r e d i n i s o l a t i o n , and, (b) t h o s e g o v e r n i n g t h e i n t e r a c t i o n o f b o d i e s . C a t e g o r y (a) i s f i l l e d b y the C o r o l l a r y t o Lemma 3 (see page 49) w h i l e t h e f o u r t h axiom (see page 49) i s t h e s o l e r e p r e s e n t -a t i v e o f c a t e g o r y ( b ) . The C o r o l l a r y t o Lemma 3 i s Sp i n o z a ' s p r i n c i p l e o f i n e r t i a : b o d i e s i n m o t i o n t e n d t o remain i n mo t i o n , w h i l e b o d i e s a t r e s t t e n d t o remain i n t h a t s t a t e . T h i s p r i n c i p l e i s not s t a t e d as a b a s i c p o s t u l a t e about n a t u r e , b u t r a t h e r i t i s dependent on st a t e m e n t s e s t a b l i s h e d b e f o r e . The p r e c e e d i n g lemma s t a t e s t h a t a change from m o t i o n t o r e s t o r v i c e v e r s a can come o n l y f rom i n t e r a c t i o n w i t h o t h e r b o d i e s ; t h i s lemma i n t u r n depends on P r o p o s i t i o n 28 o f P a r t One, w h i c h s t a t e s t h a t t h e cause o f t h e a c t i v i t y and e x i s t e n c e o f one p a r t i c u l a r f i n i t e t h i n g must be sought i n the e x i s t e n c e and a c t i v i t y o f o t h e r f i n i t e t h i n g s . The d e r i v a t i o n i s f u r t h e r augmented by t h e d i s c u s s i o n t h a t f o l l o w s t h e C o r o l l a r y : T h i s i n d e e d i s s e l f - e v i d e n t . F o r i f I suppose t h a t a body A, f o r example, i s a t r e s t , i f I pay no r e g a r d t o o t h e r b o d i e s i n m o t i o n , I can say n o t h i n g about t h e body A e x c e p t t h a t i t i s a t r e s t . I f i t s h o u l d a f t e r w a r d s happen t h a t t h e body A s h o u l d move, i t s m o t i o n c o u l d not c e r t a i n l y be a r e s u l t o f i t s former r e s t , f o r from i t s r e s t n o t h i n g c o u l d f o l l o w t h a n t h a t the body A s h o u l d remain a t r e s t . The second h a l f o f t h e p r o o f i s the e x a c t c o n v e r s e o f the above. What i s c l e a r from t h i s p r o o f i s S p i n o z a ' s c o n c e p t i o n o f motion as a q u a l i t y o f a body: a body i s not u n d e r g o i n g any change as l o n g as i t c o n -t i n u e s i n i t s m o t i o n , and t h e r e i s no c a u s a l e x p l a n a t i o n r e q u i r e d f o r t h i s c o n t i n u a t i o n o f m o t i o n . T h i s can be c o n t r a s t e d w i t h the A r i s t o t e l i a n c o n c e p t o f m o t i o n , where i n o r d e r t o keep an o b j e c t i n m o t i o n , a mover i s needed, and a body w i l l come t o r e s t when n o t h i n g causes i t t o 67 move. I n a sense t h e body i s u n d e r g o i n g change when i t i s moving. I n t h i s r e s p e c t , S p i n o z a ' s p r i n c i p l e o f i n e r t i a i s no d i f f e r e n t from the e q u i v a l e n t s t a t e m e n t s i n the P r i n c i p l e s , where m o t i o n i s spoken o f as an unchanging q u a l i t y (see P r o p o s i t i o n 14, P a r t Two). But t h e r e i s an i m p o r t a n t d i f f e r e n c e w i t h r e s p e c t t o the t w o - s i d e d c h a r a c t e r o f t h e p r i n c i p l e o f i n e r t i a : i n t h e P r i n c i p l e s i t i s s t a t e d c l e a r l y o n l y i n r e s p e c t t o m o t i o n , and not f o r r e s t 1 . T h i s d i f f e r e n c e i s s i g n i f i c a n t and s h o u l d be e x p l a i n e d a l i t t l e f u r t h e r . I f we r e t u r n f o r a moment t o S p i n o z a ' s p r o o f o f the p r i n c i p l e o f i n e r t i a j u s t g i v e n above, we w i l l n o t i c e a c e r t a i n p e c u l i a r i t y i n t h a t t h e p r o o f depends on a dichotomous t r e a t m e n t o f mo t i o n o r r e s t : b o d i e s a r e e i t h e r i n m o t i o n o r a t r e s t . What i s n o t t a k e n i n t o a c c o u n t i s the p o s s i b i l i t y t h a t b o d i e s might speed up o r s l o w down, and what i s m a n i f e s t l y l a c k i n g i n S p i n o z a ' s p r i n c i p l e o f i n e r t i a i s t h e phase " w i t h u n d i m i n i s h e d v e l o c i t y " o r i t s e q u i v a l e n t . Both the statement o f t h e p r i n c i p l e and the method o f p r o o f i n v o l v e a " t w o - s t a t e " c o n c e p t i o n o f m o t i o n . The o b v i o u s p r o b l e m w i t h t h i s i s how t o d e a l w i t h v a r i o u s degrees o f v e l o c i t y , and i t i s h a r d t o t a k e t h i s s e r i o u s l y as p h y s i c a l t h e o r y . But t h e f a c t remains t h a t S p i n o z a does employ t h i s t e r m i n o l o g y and t h a t h i s p r o o f o f t h e p r i n c i p l e o f i n e r t i a depends on i t . T h i s p e c u l i a r t e r m i n o l o g y o f S p i n o z a ' s does not a p p l y o n l y t o the p r i n c i p l e o f i n e r t i a ; i f we t a k e a c l o s e r l o o k a t t h e f i r s t two axioms, we see i t i n e f f e c t t h e r e as w e l l . Axiom 1 s t a t e s t h a t a l l b o d i e s are e i t h e r i n m o t i o n o r a t r e s t . Axiom 2 s t a t e s t h a t a l l b o d i e s move. I f we take Axiom 2 t o s t a t e t h a t a l l b o d i e s a r e i n m o t i o n , t h e n i t f o l l o w s from t h e c o n j u n c t i o n o f t h e two axioms t h a t no b o d i e s are a t r e s t , and t h i s makes the p r i n c i p l e o f i n e r t i a t r i v i a l : i f a l l b o d i e s a r e i n mo t i o n , t h e n i t i s t r i v i a l l y t r u e t h a t b o d i e s i n m o t i o n remain i n m o t i o n and a l l b o d i e s a t r e s t r e m a i n a t r e s t . C o n s e q u e n t l y the e q u a t i o n o f "moves" w i t h " i n m o t i o n " i s n o t c o r r e c t . The r e l a t i o n between m o t i o n and r e s t i n S p i n o z a ' s p h y s i c s i s n o t a t a l l a s t r a i g h t f o r w a r d m a t t e r . Two t h i n g s a re commonly s a i d o f t h i s r e l a t i o n : (a) r e s t i s i n f i n i t e l y s l o w m o t i o n ; i . e . the s t a t e o f r e s t i s t h e l i m i t o f a s e r i e s o f s t a t e s o f m o t i o n , each s l o w e r t h a n t h e p r e v i o u s one, so t h a t b o d i e s approach a s t a t e o f r e s t b u t never a c t u a l l y r e a c h i t . (b) r e s t i s a s p e c i a l case o f motion, i . e . r e s t i s z e r o v e l o c i t y . N e i t h e r o f t h e s e i n t e r p r e t a t i o n s i s q u i t e 69 adequate. I n t e r p r e t a t i o n (a) seems t o be f l a t l y c o n t r a -d i c t e d by Axiom 1, w h i l e (b) r u n s c o n t r a r y t o Axiom 2. To e x p l a i n what I t h i n k S p i n o z a has i n mind, I o f f e r a t h i r d i n t e r p r e t a t i o n , w h i c h a d m i t t e d l y i s not w i t h o u t problems of i t s own, b u t w h i c h , I f e e l , n o n e t h e l e s s r e p r e s e n t s S p i n o z a ' s i d e a s b e t t e r t h a n the o t h e r two. C o n s i d e r t h e f o l l o w i n g p i c t u r e : f a s t e r r e s t f a s t e r -> s l o w e r s l o w e r n e g a t i v e motion p o s i t i v e m o t i o n (2) ^ r e s t m otion > s l o w e r f a s t e r I n t h i s p i c t u r e , (1) can be t a k e n t o r e p r e s e n t the Newtonian i d e a o f v e l o c i t y as a v e c t o r q u a n t i t y , w h i l e (2) r e p r e s e n t s what I t h i n k S p i n o z a had i n mind. I t s h o u l d be n o t e d t h a t (2) r e p r e s e n t s the i d e a o f r e s t as i n f i n i t e l y s l o w m o t i o n but i n q u i t e a d i f f e r e n t sense from (a) above. I n defense o f t h i s i n t e r p r e t a t i o n o f t h e c o n n e c t i o n between m o t i o n and r e s t i n S p i n o z a ' s t h o u g h t , I f i r s t draw a t t e n t i o n t o t h e f a c t t h a t i n the E t h i c s he c o n s i s t e n t l y p a i r s up "motion" w i t h " q u i c k n e s s " , and " r e s t " w i t h "slowness", and i t i s r e a l l y t h e most p l a u s i b l e way o f l o o k i n g a t Axioms 1 and 2. Axiom 1 s t a t e s t h a t any p a r t i c u l a r ' body i s i n e i t h e r one o f two p o s s i b l e s t a t e s w h i l e Axiom 2 a s s e r t s t h a t a l l b o d i e s a r e s u b j e c t t o t h e one i n f i n i t e mode under the a t t r i b u t e E x t e n s i o n , m o t i o n -a n d - r e s t . I f we ask why S p i n o z a a r r i v e d a t s uch a s t r a n g e and unmanageable c o n c e p t i o n , t h e n I t h i n k we can f i n d the answer i n the P r i n c i p l e s , and i n p a r t i c u l a r we can t r a c e a c o n n e c t i o n t o t h e n o t i o n o f q u a n t i t y of r e s t (see pages 31 t o 3 7 ) . As I have a l r e a d y d i s c u s s e d i n C h a p t e r I I I , i n the P r i n c i p l e s t h e r e i s an attempt t o f o r m u l a t e t h e n o t i o n o f q u a n t i t y o f r e s t . There was somewhat of a c o n t r a d i c t i o n between q u a n t i t y o f r e s t as f o r m u l a t e d by C o r o l l a r y 1 t o P r o p o s i t i o n 22, w h i c h s t a t e d t h a t t h e s l o w e r b o d i e s move the g r e a t e r t h e i r q u a n t i t y of r e s t , and the e f f e c t i v e d e f i n i t i o n o f q u a n t i t y of r e s t as u sed i n t h e r u l e s o f m o t i o n : q u a n t i t y o f r e s t i s p r o p o r t i o n a l t o the s i z e o f b o d i e s a t r e s t , and z e r o f o r b o d i e s i n m o t i o n , no m a t t e r how s l o w l y (see page 3 7 ) . A l s o he may have n o t e d th e absence i n t h e P r i n c i p l e s o f the one h a l f o f t h e p r i n c i p l e o f i n e r t i a t h a t d e a l s w i t h b o d i e s a t r e s t . By t a k i n g r e s t as t h e o p p o s i t e o f m o t i o n , r a t h e r t h a n a s p e c i a l case o f m o t i o n , he was a b l e t o f o r m u l a t e a complete p r i n c i p l e o f i n e r t i a and a t t h e same time g i v e an e l e g a n t p r o o f o f i t , one t h a t f i t t e d i n w i t h h i s i d e a s on the s e l f - e v i d e n t n a t u r e of p h y s i c a l t r u t h . 71 T h i s i s i n c i d e n t a l t o my main theme, and somewhat s p e c u l a t i v e , b u t I t h i n k we can see an i n t e r e s t i n g development o f the p r i n c i p l e o f i n e r t i a from D e s c a r t e s t o Newton. I n t h e P r i n c i p l e s t h e r e i s a c l e a r statement o f t h e p r i n c i p l e o f i n e r t i a as p e r t a i n i n g t o u n i f o r m motion i n a s t r a i g h t l i n e , b u t i t i s w i t h the o t h e r h a l f o f t h e p r i n c i p l e t h a t p r o f o u n d d i f f i c u l t i e s a r o s e . These d i f -f i c u l t i e s have t h e i r s o u r c e i n t h e d e f i n i t i o n o f r e s t . Newton was a b l e t o f o r m u l a t e a complete p r i n c i p l e o f i n e r t i a by t a k i n g r e s t as z e r o m o t i o n and by making m o t i o n i n t o a d i r e c t e d q u a n t i t y , however, he c o u l d do so o n l y by i n t r o d u c i n g the n o t i o n of space as something s e p a r a t e from body. But i n the C a r t e s i a n u n i v e r s e space and body were the same, so t h a t m o t i o n n e c e s s a r i l y had t o be c o n c e i v e d as a q u a l i t y o f a body, o r a s t a t e i n w h i c h i t i s f o u n d . S p i n o z a was committed t o t h e i d e n t i t y o f c o r p o r e a l s u b s t a n c e and e x t e n s i o n , as I s h a l l argue i n C h a p t e r E i g h t , and he i s t h e r e f o r e l e d t o a c o n c e p t i o n o f m o t i o n and r e s t as c o r r e l a t i v e c o n c e p t s , o f m o t i o n and r e s t as s y m m e t r i c a l o p p o s i t e s . That he was u n a b l e t o a c h i e v e a s a t i s f a c t o r y f o r m u l a t i o n i s not s u r p r i s i n g , b u t i t s h o u l d a l s o be remembered t h a t Newton's s o l u t i o n t o the p r o b l e m o f the p r i n c i p l e o f i n e r t i a c r e a t e d p u z z l e s of i t s own. Thus f a r I have been d e a l i n g w i t h the f i r s t c a t e g o r y o f laws o f m o t i o n , namely tho s e d e a l i n g w i t h b o d i e i n i s o l a t i o n . Of laws d e a l i n g w i t h t h e c o l l i s i o n o f b o d i e s t h e r e i s i n t h e E t h i c s o n l y one sample, th e f o u r t h axiom. A t f i r s t s i g h t the f o u r t h axiom seems t o p l a y no p a r t i c u l a r r o l e i n the p h y s i c s o f the E t h i c s : n o t h i n g l e a d s up t o i t and n o t h i n g f o l l o w s from i t . The most p l a u s i b l e way o f l o o k i n g ^at t h e f o u r t h axiom i s t o c o n s i d e r i t as some-t h i n g n e c e s s a r y t o make t h e p h y s i c s o f t h e E t h i c s complete. To g i v e a c a u s a l e x p l a n a t i o n o f any p h y s i c a l e v e n t , i t i s o n l y n e c e s s a r y t o g i v e a h i s t o r y o f t h e m o tions o f p a r t i c l e s and f o r t h i s a law t h a t , d e a l s w i t h t h e i n t e r -a c t i o n o f b o d i e s i s e s s e n t i a l . But t h e n , the q u e s t i o n t h a t comes t o mind i s whether the f o u r t h axiom 1 was i n t e n d e d as a p e r f e c t l y g e n e r a l law c o v e r i n g a l l k i n d s o f c o l l i s i o n s , o r whether i t was i n t e n d e d o n l y t o d e a l w i t h a c e r t a i n type o f c o l l i s i o n , i n which case we s h o u l d c o n s i d e r i t i s a p r o t o t y p e , o r sample o f o t h e r , s i m i l a r l a w s . To t r y t o answer t h i s q u e s t i o n , we s h o u l d l o o k a t i t a l i t t l e more c l o s e l y , t o see j u s t what i t i s t h a t i s b e i n g a s s e r t e d by t h e axiom. The most co n -t r o v e r s i a l word i n t h e axiom i s t h e word "immovable". I t might mean " p r a c t i c a l l y immovable" such as i n the case o f a v e r y l a r g e s t a t i o n a r y o b j e c t b e i n g s t r u c k by a much s m a l l e r one, w h i c h w o u l d mean t h a t the axiom a p p l i e s o n l y t o s p e c i a l c a s e s . "Immovable" might a l s o mean t h a t the o b j e c t b e i n g s t r u c k i s n o t g o i n g t o be d i s p l a c e d , i n v i r t u e o f i t s s i z e , as i n t h e case o f t h e f o u r t h r u l e o f mo t i o n i n t h e P r i n c i p l e s ; i n t h i s c a s e , a g a i n , t h e axiom i s not a g e n e r a l l a w of c o l l i s i o n . The o n l y way i n w h i c h t h e axiom might be c o n s i d e r e d as a p e r f e c t l y g e n e r a l law, i s t o r e a d "immovable" as " c o n s i d e r e d immovable". What i t might mean i s t h a t i n a c o l l i s i o n we c o n s i d e r o n l y t h e r e l a t i v e m o t i o n o f the two b o d i e s i n v o l v e d , and f o r the purpose o f c a l c u l a t i n g the r e s u l t a n t v e l o c i t i e s , we t a k e t e m p o r a r i l y e i t h e r of t h e b o d i e s t o be a t r e s t ; t h i s i s e q u i v a l e n t t o t a k i n g a moving frame o f r e f e r e n c e i n Newtonian p h y s i c s . However, t h i s l i n e o f approach i n t r o d u c e s a l l s o r t s o f c o m p l i c a t i o n s , and s i n c e t h e r e i s n o t h i n g t o s u p p o r t the c o n t e n t i o n t h a t S p i n o z a was t h i n k i n g i n terms o f frames o f r e f e r e n c e , i t seems v e r y u n l i k e l y t h a t t h i s i n t e r p r e t a t i o n o f the axiom i s c o r r e c t . There i s a problem h e r e . On the one hand, the f o u r t h axiom, s i n c e i t i s t h e o n l y law o f c o l l i s i o n p r e s e n t e d , might be e x p e c t e d t o be p e r f e c t l y g e n e r a l i n c h a r a c t e r , w h i l e on t h e o t h e r hand, t h e r e seems t o be no f e a s i b l e i n t e r p r e t a t i o n t h a t makes sense o f t h e axiom: as a g e n e r a l law. S i n c e t h e r e i s no d i r e c t t e x t u a l e v i d e n c e on t h i s p o i n t , I can o n l y o f f e r a c o n j e c t u r e , w h i c h i s t h a t the f o u r t h axiom i s b u t one member o f a group o r system o f laws o f m o t i o n . As t o why S p i n o z a might have s e l e c t e d t h i s p a r t i c u l a r l a w as r e p r e s e n t a t i v e t h e r e are two c l u e s : (a) The s c i e n c e o f o p t i c s was t h e most h i g h l y d e v e l o p e d of the s c i e n c e s o f t h a t day. I t i s c e r t a i n t h a t S p i n o z a , as w e l l as o t h e r s , was g r e a t l y i m p r e s s e d by the power and p r e c i s i o n o f o p t i c a l s c i e n c e , and q u i t e l i k e l y saw i n o p t i c s a model f o r a l l o f s c i e n c e . Geo-m e t r i c a l o p t i c s has two b a s i c laws, the law o f r e f l e c t i o n and the law o f r e f r a c t i o n . My c o n j e c t u r e i s t h a t S p i n o z a saw i n the law o f r e f l e c t i o n , w i t h i t s o b v i o u s c o n n e c t i o n w i t h t h e b e h a v i o u r o f s m a l l b o d i e s r e b o u n d i n g o f f l a r g e r ones, as one o f t h e most fundamental laws o f n a t u r e , and' f o r t h a t r e a s o n i n c l u d e d i t i n the E t h i c s . (b) I n the P r i n c i p l e s S p i n o z a i s seen t o amend th e f o u r t h r u l e o f m o t i o n . D e s c a r t e s ' s v e r s i o n s a ys n o t h i n g about c o l l i s i o n s a t an a n g l e , and S p i n o z a d e v o t e s c o n s i d e r a b l e space and e f f o r t t o p u t h i s m o d i f i e d v e r s i o n on sound f o o t i n g . The s u p p o s i t i o n , h e r e , t h e n , i s t h a t he f e l t q u i t e c o n f i d e n t about t h e soundness o f t h i s r u l e o f m o t i o n , c o n f i d e n t enought, a t any r a t e , t o i n c l u d e i t i n h i s magnum opus. An o t h e r i n t e r e s t i n g f e a t u r e o f the f o u r t h axiom i s i t s vagueness on the s u b j e c t o f t h e c o n s e r v a t i o n o f m o t i o n . The p h r a s e " i n o r d e r t h a t i t may c o n t i n u e i t s m o t i o n " i s not s p e c i f i c enough t o make t h e axiom i n t o a p r i n c i p l e o f c o n s e r v a t i o n o f motion i n c o l l i s i o n s , o f t o guarantee t h a t motion i s c o n s e r v e d i n the p a r t i c u l a r k i n d o f i n t e r a c t i o n between b o d i e s t h a t the axiom i s supposed t o be d e a l i n g w i t h . T h i s i s somewhat p u z z l i n g ; i f on t h e one hand, S p i n o z a i n t e n d e d t h e axiom t o a s s e r t t h a t m o t i o n i s c o n s e r v e d i n t h i s o r any k i n d o f c o l l i s i o n , why t h e n does he not make i t more s p e c i f i c ? I f , on the o t h e r hand, he does not i n t e n d t h e axiom t o say a n y t h i n g about c o n s e r v a t i o n o f m o t i o n , how do we e x p l a i n h i s f a i l u r e t o d e a l w i t h t h i s s u b j e c t ? One might argue t h a t s i n c e the E t h i c s i s not p r i m a r i l y a t r e a t i s e on p h y s i c a l s c i e n c e , S p i n o z a was not g r e a t l y c o n cerned about c o n s e r v a t i o n o f m o t i o n , b u t I f i n d i t h a r d t o b e l i e v e t h a t S p i n o z a would be so hap-h a z a r d i n t h i s m a t t e r . And i n any case t h e r e i s some e v i d e n c e t h a t he d i d c o n s i d e r the t o p i c i m p o r t a n t . I n the l e t t e r t o Oldenburg a l r e a d y mentioned i n t h e p r e v i o u s c h a p t e r (see page 6 0 ) , he d e s c r i b e s t h e u n i v e r s e as a whole i n w h i c h "the same p r o p o r t i o n o f mo t i o n and r e s t " i s c o n s e r v e d . I f c o n s e r v a t i o n o f m o t i o n i s not g u a r a n t e e d i n i n d i v i d u a l c o l l i s i o n s , t h e n t h e r e i s no guarantee t h a t the whole u n i v e r s e w i l l n o t r u n down, so t o speak. S i n c e , i n S p i n o z a ' s t h o u g h t , the u n i v e r s e i s a system t h a t m a i n t a i n s i t s e l f w i t h o u t any o u t s i d e i n t e r v e n t i o n , such 76 a guarantee i s needed. There remains t h e n the t a s k o f e x p l a i n i n g how the p h r a s e " i n o r d e r t h a t i t may c o n t i n u e i t s m o t i o n " can be c o n s t r u e d as a s s e r t i n g t h a t m o t i o n i s c o n s e r v e d . To do t h i s we s h o u l d r e t u r n t o the d i s c u s s i o n o f the p r i n c i p l e o f i n e r t i a and note t h a t what i s m i s s i n g i n b o t h t h e p r i n c i p l e and t h e f o u r t h axiom i s t h e p h r a s e " w i t h u n d i m i n i s h e d v e l o c i t y " , and I t h i n k i n b o t h i n s t a n c e s t h i s o m i s s i o n f i n d s i t s cause i n t h e f a c t t h a t S p i n o z a w o u l d have c o n s i d e r e d t h i s p h r a s e redundant. That means, t h e n , t h a t t h e p h r a s e "may c o n t i n u e i t s m o t i o n " s h o u l d be t a k e n t o r e a d " m a i n t a i n s i t s v e l o c i t y " , and we can c o n c l u d e w i t h a r e a s o n a b l e degree o f c e r t a i n t y t h a t S p i n o z a d i d i n t e n d the f o u r t h axiom t o say t h a t m o t i o n i s c o n s e r v e d . My major c o n c e r n i n t h i s c h a p t e r has been t o d i s c u s s whether S p i n o z a ' s t h e o r y o f m o t i o n marks the p h y s i c s o f t h e E t h i c s as something f u n d a m e n t a l l y d i f -f e r e n t from t h e C a r t e s i a n p h y s i c s , and my major con-c l u s i o n i s t h a t i t does n o t . On the c o n t r a r y , t h e r e i s good e v i d e n c e t h a t i n the E t h i c s he i s d e a l i n g w i t h e s s e n t i a l l y the same k i n d o f problems as c r o p up i n the P r i n c i p l e s . F o r i n s t a n c e , h i s amendment o f t h e p r i n c i p l e o f i n e r t i a t o i n c l u d e a c l e a r statement f o r b o d i e s a t r e s t , can be t a k e n as an e f f o r t t o improve on the 77 C a r t e s i a n p h y s i c s . H i s c o n c e p t i o n o f mo t i o n and r e s t as s y m m e t r i c a l o p p o s i t e s can be t r a c e d f a i r l y c o n c l u s i v e l y t o the d i f f i c u l t i e s i n h e r e n t i n the attempt t o f o r m u l a t e q u a n t i t y o f r e s t i n the P r i n c i p l e s . The f o u r t h axiom b e a r s a c l o s e k i n s h i p t o the f o u r t h r u l e o f m o t i o n , w h i c h he, i n t h e P r i n c i p l e s , i s a l r e a d y s u b j e c t i n g t o c o n s i d e r -a b l e a l t e r a t i o n . W h i l e i t i s t r u e t h a t he does not ta k e o v e r from the P r i n c i p l e s the whole s e t o f laws o f m o t i o n , the main r e a s o n may have s i m p l y been h i s d e s i r e t o keep t h e amount o f p h y s i c a l t h e o r y t o a bare minimum, and even i f he d i d have qualms c o n c e r n i n g the v a l i d i t y o f some o f the r u l e s o f m o t i o n , t h e r e i s not a s h r e d o f e v i d e n c e t o j u s t i f y t h e p o s i t i o n t h a t he c o n s i d e r e d t h a t k i n d o f law t o be i n v a l i d . On the w h o l e , the p h y s i c s o f the E t h i c s s h o u l d be l o o k e d on as a c o n t i n u a t i o n o f t h a t o f the P r i n c i p l e s ; the f o r m e r i s b a s i c a l l y a c o n d e n s a t i o n o f t h e l a t t e r , w i t h some amendments, some d e l e t i o n s , and some e x t e n s i o n s . S p i n o z a ' s w r i t i n g o f t h e P r i n c i p l e s i s o f t e n d i s m i s s e d as a mere commentary on D e s c a r t e s , p e r f o r m e d m a i n l y as p r a c t i c e i n t h e use o f t h e g e o m e t r i c a l s t y l e o f w r i t i n g . I c o n s i d e r t h i s a s e r i o u s m i s t a k e , s i n c e t o a g r e a t e x t e n t t h e i d e a s p r e s e n t e d i n the P r i n c i p l e s a re r e p r e -s e n t a t i v e o f S p i n o z a ' s t h o u g h t . A f u r t h e r d i f f e r e n c e i s a l s o t h a t i n t h e P r i n c i p l e s the p r i n c i p l e o f i n e r t i a s p e c i f i e d m o t i o n i n a s t r a i g h t l i n e ; t h i s i s o m i t t e d i n the E t h i c s , but f o r p r e c i s e l y what r e a s o n i s not o b v i o u s . 79 CHAPTER V I I THE CORPORA SIMPLICISSIMA The c e n t r a l i d e a i n the t h e o r y o f i n d i v i d u a l s i s t h a t o f o r g a n i z e d c o m p l e x i t y , and t h e v e r y n o t i o n o f an o r g a n i z e d whole i m p l i e s o r presupposes the e x i s t e n c e o f s i m p l e s t e l e m e n t s , o r a l t e r n a t i v e l y , an i n f i n i t e h i e r a r c h y o f c o m p l e x i t y , i n w h i c h any body can always i n p r i n c i p l e be a n a l y z e d i n y e t s i m p l e r e l e m e n t s . S p i n o z a d e f i n e s t h e s i m p l e s t b o d i e s i n an o f f - h a n d manner j u s t a f t e r Axiom 4, b u t a f t e r t h a t says v e r y l i t t l e more about them s p e c i f i c a l l y . He says n o t h i n g , d i r e c t l y , about t h e i r s i z e o r shape, t h e i r o r i g i n o r t h e i r b e h a v i o u r , and worse, he f a i l s t o make c l e a r whether t h e r e even a r e such t h i n g s as s i m p l e s t p a r t i c l e s ; i n o t h e r words we are not even sure whether t h e r e a c t u a l l y e x i s t s i m p l e s t p a r t i c l e s , o r whether each body s h o u l d always be thought o f as a n a l y z a b l e i n t o s i m p l e r e l e m e n t s . The g e n e r a l l i t e r a t u r e on the s u b j e c t o f t h e c o r p . simp, i s l i m i t e d and not a g r e a t d e a l o f a t t e n t i o n seems t o have been d i r e c t e d toward d i s c o v e r i n g e x a c t l y what S p i n o z a had i n mind when he t a l k s about s i m p l e s t b o d i e s . As an example, t h e r e i s S t u a r t Hampshire's commentary on t h i s t o p i c 1 : I t was not u n t i l t h e end o f t h e l a s t c e n t u r y t h a t 80 h i s t h r e e c o n c e p t i o n s (a) o f m o t i o n - a n d - r e s t as the e s s e n t i a l and u n i v e r s a l f e a t u r e o f the ex t e n d e d w o r l d , and, (b) o f u l t i m a t e p a r t i c l e s as c e n t r e s o f energy,.and, (c) o f c o n f i g u r a t i o n s o f t h e s e u l t i m a t e p a r t i c l e s - f o r m i n g r e l a t i v e l y s e l f - m a i n t a i n i n g systems were seen t o c o r r e s p o n d w i t h a c t u a l l y used s c i e n t i f i c c o n c e p t s . More s p e c i f i c a l l y about the p a r t i c l e s , Hampshire s a y s : Q u a l i t a t i v e changes i n medium-sized o b j e c t , as t h e s e a r e d e s c r i b e d i n common-sensed knowledge, ar e r e p r e s e n t e d i n t h e l i g h t o f s y s t e m a t i c knowledge s o l e l y as measurable changes i n the v e l o c i t y and c o n f i g u r a t i o n o f q u a l i t a t i v e l y u n d i f f e r e n t i a t e d p a r t i c l e s . Hampshire's book has been v e r y h e l p f u l on t h e s u b j e c t o f S p i n o z a ' s s c i e n t i f i c i d e a s , and y e t what he says l e a v e s a g r e a t d e a l t o be a s k e d . F o r i n s t a n c e , does " q u a l i t a t i v e l y u n d i f f e r e n t i a t e d " mean t h a t a l l the u l t i m a t e p a r t i c l e s a re o f t h e same s i z e o r the same shape? Or, f o r t h a t m a t t e r , i n what way a r e t h e u l t i m a t e p a r t i c l e s u l t i m a t e ? Does " u l t i m a t e " mean " i n d i v i s i b l e " ? Or even, i n what sense are the c o r p . simp, p a r t i c l e s a t a l l ? Perhaps we s h o u l d l o o k upon them as a b s t r a c t e n t i t i e s l i k e t he monads o f L e i b n i t z , n o t r e a l l y m a t e r i a l , b u t w h i c h somehow account f o r the phenomena o f t h e m a t e r i a l w o r l d . A l l t h e s e q u e s t i o n s have no r e a d y answer on t h e b a s i s o f a s u p e r f i c i a l s c r u t i n y o f what S p i n o z a s a y s i n the E t h i c s . To o b t a i n c l a r i f i c a t i o n on the n a t u r e o f t h e c o r p . simp., we s h o u l d d i r e c t our a t t e n t i o n t o t h e f o l l o w -i n g q u e s t i o n : ' are t h e c o r p . simp, extended, l i k e the C a r t e s i a n p a r t i c l e s , o r are t h e y n o t ? F o r b o t h the n e g a t i v e and the a f f i r m a t i v e answers t h e r e i s good e v i d e n c e ; t h i s e v i d e n c e i s as f o l l o w s : 1. P r o e x t e n d e d p a r t i c l e s : (a) Axiom 4, the o n l y l a w o f c o l l i s i o n i n t h e E t h i c s , speaks o f a body s t r i k i n g the p l a n e o f a n o t h e r body. T h i s c l e a r l y i n d i c a t e s t h a t a t l e a s t one o f t h e p a r t i e s t o t h e c o l l i s i o n i s extended. The q u e s t i o n t h e n , i s , does the axiom d e a l w i t h s i m p l e b o d i e s o r w i t h complex ones. That the f i r s t a l t e r n a t i v e i s t h e c o r r e c t , o n e i s shown by the sentence d i r e c t l y f o l l o w i n g t h e s t a t e m e n t o f t h e axiom: Thus much f o r t h e s i m p l e s t b o d i e s w h i c h are d i s t i n g u i s h e d from one a n o t h e r by m o t i o n and r e s t , speed and slowness a l o n e ; l e t us now advance t o composite b o d i e s . (b) The d e f i n i t i o n o f an i n d i v i d u a l , w h i c h f o l l o w s t h e sentence j u s t r e f e r r e d t o , c o n t a i n s t h e p h r a s e : "When a number o f b o d i e s of t h e same o r d i f -f e r e n t magnitudes are p r e s s e d t o g e t h e r " . F o r t h i s d e f i n i t i o n t o be a p p l i c a b l e t o any i n d i v i d u a l , i t must a l s o a p p l y t o t h e l o w e s t l e v e l i n d i v i d u a l s , namely tho s e whose c o n s t i t u e n t s a r e c o r p . simp.. I t f o l l o w s t h a t t h e c o r p . simp, have magnitude; t h i s , t o g e t h e r w i t h the 82 ph r a s e " p r e s s e d t o g e t h e r " , s u g g e s t s extended p a r t i c l e s . (c) Axiom 5, a d e f i n i t i o n o f h a r d n e s s , s o f t -ness and f l u i d i t y , d e f i n e s t h e s e i n terms o f t h e s u r f a c e s o f c o n t a c t between the c o n s t i t u e n t s o f a body. I n the absence o f e v i d e n c e t o t h e c o n t r a r y , i t i s a l e g i t i m a t e s u p p o s i t i o n t h a t t h e l o w e s t l e v e l i n d i v i d u a l s may a l s o be h a r d , s o f t o r f l u i d , w h i c h makes t h e c o r p . simp, out as extended p a r t i c l e s . (d) Lemma 5 s t a t e s t h a t i f "the p a r t s composing an i n d i v i d u a l become g r e a t e r o r l e s s p r o p o r t i o n a t e l y . . . " the o t h e r c o n d i t i o n s r e m a i n i n g the same, then the i n d i -v i d u a l w i l l " r e t a i n t h e n a t u r e i t had b e f o r e " . The same p o i n t as made i n (b) and (c) above a p p l i e s h e r e . 2. C o n t r a extended p a r t i c l e s : (a) The st a t e m e n t f o l l o w i n g Axiom 2 d e s c r i b e s the c o r p . simp, as those b o d i e s "which a r e d i s t i n g u i s h e d f r o m one a n o t h e r by mot i o n and r e s t , speed and slow n e s s a l o n e " . T h i s appears t o e x c l u d e u n e q u i v o c a l l y the p o s s i b i l i t y t h a t t h e c o r p . simp, v a r y as t o s i z e and shape. (b) Lemma 1 s t a t e s t h a t b o d i e s a r e d i s -t i n g u i s h e d not i n s u b s t a n c e , b u t " i n r e s p e c t t o motion and r e s t " . A l s o , i n the S c h o l i u m a f t e r Lemma 7, S p i n o z a s a y s : 83 Up t o t h i s p o i n t we have c o n c e i v e d an i n d i v i d u a l t o be composed m e r e l y o f b o d i e s w h i c h a r e d i s -t i n g u i s h e d from one a n o t h e r s o l e l y by m o t i o n and r e s t , speed and s l o w n e s s , t h a t i s t o say, t o be composed o f the most s i m p l e b o d i e s . B o t h t h e s e q u o t a t i o n s s e r v e t o r e i n f o r c e t h e p o i n t made i n 2(a) . The c r u c i a l i s s u e i s : how can S p i n o z a say t h a t t h e c o r p . simp, are d i f f e r e n t i a t e d s o l e l y i n terms o f m o t i o n and r e s t , and y e t speak o f shape, s u r f a c e , and magnitude as p e r t a i n i n g t o them? On t h e b a s i s o f t h e e v i d e n c e o u t l i n e d above, an o b v i o u s p o s s i b i l i t y i s t h a t the p a r t i c l e s a r e e x t e n d e d , but a r e a l l o f t h e same s i z e and shape. But t h i s makes S p i n o z a i n t o an a t o m i s t , and I have not found one i o t a o f e v i d e n c e t h a t might s u p p o r t t h i s c o n t e n t i o n : as a m a t t e r o f f a c t t h e r e i s a g r e a t d e a l o f e v i d e n c e a g a i n s t i t , e s p e c i a l l y i n the n i t r e d i s p u t e w i t h Robert B o y l e . F u r t h e r m o r e , the a t o m i s t h y p o t h e s i s i s a l m o s t c e r t a i n l y i r r e c o n c i l a b l e w i t h t h e d e n i a l o f t h e e x i s t e n c e of a vacuum. R a t h e r t h a n d e l v i n g f u r t h e r i n t o t h i s q u e s t i o n , we s h o u l d r e t r e a t somewhat, and s c r u t i n i z e t h e phrase " d i s t i n g u i s h e d i n r e s p e c t t o m o t i o n and r e s t " a l i t t l e more t h o r o u g h l y . The e x p l a n -a t i o n t h a t comes most r e a d i l y t o mind i s t h a t the p h r a s e means t h a t b o d i e s d i f f e r i n t h e i r v e l o c i t i e s , b u t t h e r e i s a n o t h e r way o f l o o k i n g a t i t . I f we t h i n k back t o the C a r t e s i a n scheme f o r a moment, i t w i l l be remembered t h a t i t was the a d d i t i o n of mo t i o n t o e x t e n s i o n w h i c h c r e a t e d the p a r t i c l e s , so t h a t i n f a c t t h e shapes and s i z e s o f p a r t i c l e s depend d i r e c t l y on o n l y one v a r i a b l e , namely t h e d i s t r i b u t i o n o f m o t i o n i n e x t e n s i o n . I t i s c o r r e c t t o say of t h e C a r t e s i a n p a r t i c l e s , t h e n , t h a t t h e y a re d i f f e r e n t i a t e d by mo t i o n and r e s t a l o n e . I t f o l l o w s from t h i s t h a t t o say t h a t t h e c o r p . simp, are d i s t i n g u i s h e d s o l e l y by mo t i o n and r e s t i s not n e c e s s a r i l y c o n t r a d i c t o r y t o s a y i n g t h a t t h e y have v a r i o u s shapes and s i z e s , as l o n g as we t h i n k o f them i n terms o f t h e C a r t e s i a n p h y s i c s . To s u p p o r t the c o n t e n t i o n t h a t t h e c o r p . simp, are v e r y s i m i l a r t o the C a r t e s i a n p a r t i c l e s , t h e r e are t h e f o l l o w i n g c o n s i d e r a t i o n s : (a) The d e m o n s t r a t i o n t o Lemma 1 s u g g e s t s v e r y s t r o n g l y t h a t t h e lemma does not a p p l y o n l y t o the c o r p . simp., b u t t o the i n d i v i d u a l s as w e l l . The lemmas a s s e r t s t h a t a l l b o d i e s d i f f e r i n r e s p e c t t o m o t i o n and r e s t , and not w i t h r e s p e c t t o s u b s t a n c e . Now i t i s o b v i o u s t h a t a l l b o d i e s , s uch as p e o p l e , a p p l e s , o r s t o n e s , can be s a i d t o d i f f e r i n a g r e a t many ways, w h i c h i n c l u d e s s i z e and shape. The r e a s o n why S p i n o z a does not mention t h e s e i s t h a t he i s m a i n l y i n t e r e s t e d i n making c l e a r t h a t b o d i e s do not d i f f e r w i t h r e s p e c t t o s u b s t a n c e , whatever e l s e t h e y may d i f f e r i n . Hence the f a c t t h a t i n the d e f i n i t i o n o f a s i m p l e s t body he does not mention s i z e o r shape, i s not as i m p o r t a n t as i t seems a t f i r s t s i g h t . A l s o , by comparing Lemma 1 and t h e d e f i n i t i o n o f a c o r p . simp, we b e g i n t o see more c l e a r l y what S p i n o z a has i n mind. He wants t o d i s t i n g u i s h c l e a r l y between the i n d i v i d u a l s w h i c h d i f f e r from e a c h o t h e r by v i r t u e o f t h e i r c o n s t i t u t i o n , and t h e c o r p . simp., w h i c h , s i n c e t h e y a r e not composite, cannot be s a i d t o d i f f e r i n t h e i r c o n s t i t u t i o n . (b) A p o s s i b l e o b j e c t i o n t o comparing th e c o r p . simp, t o the C a r t e s i a n p a r t i c l e s i s t h a t i n the P r i n c i p l e s a d e f i n i t e a c c o u n t i s g i v e n o f t h e o r i g i n a t i o n o f t h e p a r t i c l e s , w h i l e i n t h e E t h i c s t h e r e i s n o t h i n g t o s u g g e s t t h a t the c o r p . simp, are t o be thought o f as r e l a t i v e l y s t a b l e p a r t i c l e s . The answer i s t h a t i n the p h y s i c s o f t h e E t h i c s the c r e a t i o n of p a r t i c l e s s h o u l d be thought o f as a c o n t i n u o u s p r o c e s s , something t h a t has always gone on, and w i l l always go on. I t s h o u l d a l s o be n o t e d t h a t t h e c r e a t i o n o f p a r t i c l e s a t a d e f i n i t e t i m e i s i n t h e P r i n c i p l e s p r e s e n t e d as a h y p o t h e s i s , as something t h a t might be r e a s o n a b l y supposed t o have t a k e n p l a c e , and t h u s i s not a p a r t o f t h e l o g i c a l s t r u c t u r e o f P a r t Two o f t h e P r i n c i p l e s : some o t h e r way of e x p l a i n i n g how the p r e s e n t s t a t e o f a f f a i r s came t o be might be e q u a l l y a c c e p t a b l e . I n any c a s e , t o S p i n o z a the c r e a t i o n o f a l l the p a r t i c l e s a t a d e f i n i t e p o i n t i n time i s q u i t e u n a c c e p t a b l e , so t h a t i n h i s scheme i t i s n ot so e a s y t o c o n c e i v e o f t h e p a r t i c l e s as r e l a t i v e l y e n d u r i n g e n t i t i e s ; b u t a t t h e same time t h i s does not n e c e s s a r i l y i m p l y a r a d i c a l s h i f t f r o m t h e C a r t e s i a n p h y s i c s . I n b o t h c a s e s t h e d e t a i l e d e x p l a n a t i o n o f p h y s i c a l phenomena c o n s i s t s o f d e s c r i b i n g the motions of p a r t i c l e s o f v a r i o u s s i z e s and shapes. (c) I n the d i s p u t e w i t h Robert B o y l e o v e r the r e d i n t e g r a t i o n o f n i t r e , S p i n o z a ' s arguments are con-v i n c i n g p r o o f o f h i s a c c e p t a n c e of t h e p r a c t i c a l a s p e c t s o f t h e C a r t e s i a n p h y s i c s . S p i n o z a c o n s i d e r s B o y l e ' s e x p e r i m e n t s f a r from adequate f o r p r o v i n g t h a t n i t r e i s heterogeneous i n c h a r a c t e r . H i s own e x p l a n a t i o n s are c o m p l e t e l y i n a c c o r d w i t h t h e p h y s i c s o f the P r i n c i p l e s . He s u g g e s t s t h a t the main d i f f e r e n c e between s p i r i t o f n i t r e and n i t r e i s " t h a t t h e p a r t i c l e s o f the l a t t e r are i n a s t a t e o f r e s t , w h i l e t h o s e of the f o r m e r a g i t a t e e a c h o t h e r w i t h no l i t t l e vehemence". The s a l t o f n i t r e , i n h i s o p i n i o n , c o n s i s t s of p a r t i c l e s w h i c h have h o l e s o r p o r e s i n them, i n which t h e p a r t i c l e s o f n i t r e are lodged. The t a s t e o f n i t r e he a t t r i b u t e s t o t h e f a c t t h a t the s h a r p p o i n t s o f t h e n i t r e p a r t i c l e s t o u c h the tongue. These are b u t a few examples o f h i s arguments i n t h e n i t r e d i s p u t e , arguments w h i c h i n e f f e c t a r e a s p i r i t e d 87 defense o f t h e C a r t e s i a n p h y s i c s . P o i n t s ( a ) , (b) and (c) d i s c u s s e d above a r e s u p p o r t i n g e v i d e n c e f o r the main c o n c l u s i o n : t h a t the c o r p . simp, o f the E t h i c s are v e r y s i m i l a r t o t h e p a r t i c l e s o f the C a r t e s i a n p h y s i c s . To sum up my argument, t h e r e i s a g r e a t d e a l o f m a t e r i a l t h a t p o i n t s t o t h e c o r r e c t -ness of t h i s c o n c l u s i o n , w h i l e t h e r e i s i n e f f e c t o n l y one s t a t e m e n t i n the E t h i c s t h a t c a s t s doubt on i t . As I have shown, t h e r e i s a p l a u s i b l e i n t e r p r e t a t i o n o f t h a t s t a t e m e n t w h i c h removes t h a t d i f f i c u l t y . The most immediate i m p l i c a t i o n o f t h i s con-c l u s i o n i s t h a t i f we w i s h t o s t u d y S p i n o z a ' s t h e o r i e s o f t h e p h y s i c a l u n i v e r s e , we are not l i m i t e d t o the m a t e r i a l o f t h e E t h i c s , b u t we can use t h e P r i n c i p l e s t o c l a r i f y some of the o b s c u r i t i e s o f t h e E t h i c s . There are i n the P r i n c i p l e s u n d o u b t e d l y many items t h a t S p i n o z a had s e r i o u s qualms about. One concerns the o r i g i n a l c r e a t i o n o f p a r t i c l e s , and t h e r e i s a l s o t h e case o f the s i x t h r u l e o f m o t i o n ; t h e s e are t h e o n l y two f o r w h i c h d i r e c t t e x t u a l c o n f i r m a t i o n i s a v a i l a b l e . But on the o t h e r hand, t h e r e i s no s o l i d e v i d e n c e t h a t he had any o b j e c t i o n s t o t h e b a s i c f e a t u r e s o f t h e C a r t e s i a n p h y s i c s , i t s b a s i c p r e m i s s e s and i t s method. A more f a r r e a c h i n g i m p l i c a t i o n o f t h e s i m i -l a r i t y of the c o r p . simp, t o t h e C a r t e s i a n p a r t i c l e s 88 i s t h a t i t c a s t s a new l i g h t on t h e more fundamental a s p e c t s o f S p i n o z a ' s cosmology. I t l e a d s t o a somewhat d i f f e r e n t i n t e r p r e t a t i o n o f h i s d o c t r i n e o f Substance, A t t r i b u t e and Mode, t o t h e one t h a t i s g e n e r a l l y a c c e p t e d . I w i l l d e a l w i t h t h i s f u r t h e r i n the nex t c h a p t e r . I t may seem t h a t S p i n o z a ' s agreement w i t h the b a s i c f e a t u r e s o f t h e C a r t e s i a n p h y s i c s makes him o f l e s s e r i m p o r t a n c e as an o r i g i n a l t h i n k e r and more o f an e x p o s i t o r o f t h e i d e a s o f D e s c a r t e s , a t l e a s t i n t h e r e a l m o f p h y s i c a l s c i e n c e , but I f e e l t h i s i m p r e s s i o n i s f a l s e . I n s t e a d o f m e r e l y expounding D e s c a r t e s ' s v i e w s , he i s engaged i n t h e t a s k o f s o r t i n g out the more fundamental a s p e c t s o f t h e C a r t e s i a n p h y s i c s i n o r d e r t o p u t i t on a sounder f o o t i n g , and he i s g r a p p l i n g w i t h the p r o f o u n d c o n t r a d i c t i o n s i n h e r e n t i n the system. I n t h i s t h e s i s I have l a r g e l y a v o i d e d t h e t o p i c o f t h e m o d e r n i t y of S p i n o z a ' s i d e a s . One r e a s o n i s my f e e l i n g t h a t any p a r a l l e l between S p i n o z a ' s i d e a s on t h e s t r u c t u r e o f t h e p h y s i c a l u n i v e r s e and modern p h i l o s o p h i e s o f s c i e n c e a r e a t t h e b e s t v e r y t e n u o u s . B e s i d e s , I am c e r t a i n t h a t S p i n o z a ' s p h y s i c a l t h e o r i e s do n o t need any a p o l o g y , any e f f o r t t o p u t them i n a b e t t e r l i g h t . A c u r s o r y r e a d i n g o f t h e P r i n c i p l e s perhaps c r e a t e s an i m p r e s s i o n t h a t t h e p h y s i c a l t h e o r y i t p r e s e n t s i s a b i t n a i v e ; a c l o s e r e x a m i n a t i o n r e v e a l s t h a t i t i s d e f i n i t e l y more t h a n a c o l l e c t i o n o f i m p l a u s i b l e laws o f m o t i o n , t h a t i t d e a l s w i t h the e x t r e m e l y a b s t r u s e i s s u e o f t h e m e t a p h y s i c a l f o u n d a t i o n s of s c i e n c e . See Hampshire, page 79. 90 CHAPTER V I I I MOTION AND PARTICLES i My c o n t e n t i o n i s t h a t S p i n o z a ' s c o n c e p t i o n o f t h e s t r u c t u r e o f the p h y s i c a l u n i v e r s e i s b a s i c a l l y the same as t h e C a r t e s i a n one; t h a t i s , the u n i v e r s e i s a plenum, f i l l e d w i t h p a r t i c l e s o f v a r i o u s s i z e s and shapes w h i c h f i t t o g e t h e r so t h a t t h e r e i s no vacuum, and s c i e n t i f i c e x p l a n a t i o n i s i n terms o f the i n t e r -a c t i o n , by c o n t a c t a l o n e , of t h e b a s i c p a r t i c l e s . The e v i d e n c e f o r t h i s c o n t e n t i o n f a l l s i n t o c e r t a i n major c a t e g o r i e s w h i c h I w i l l d i s c u s s more o r l e s s s y s t e m a t i c a l l y . 1. I n t h e p h y s i c s o f t h e E t h i c s t h e r e i s r e a l l y o n l y one statement t h a t does not f i t i n w i t h the i n t e r p r e t a t i o n o f t h e c o r p . simp, as e x t e n d e d p a r t i c l e s o f v a r i o u s s i z e s and shapes, namely t h a t the s i m p l e s t b o d i e s a r e d i s t i n g u i s h e d by m o t i o n and r e s t a l o n e . T h i s s t a t e m e n t , as I have d i s c u s s e d i n the p r e v i o u s c h a p t e r , seems t o i m p l y t h a t t h e s i m p l e s t b o d i e s are not d i f f e r e n t i n s i z e and shape, w h i c h i s i n c o n t r a d i c t i o n w i t h t h e C a r t e s i a n scheme. However, as I have mentioned, t h e r e i s a p l a u s i b l e e x p l a n a t i o n f o r t h i s d i s c r e p a n c y * i n t h a t i n the C a r t e s i a n scheme, i t was the a d d i t i o n o f m o t i o n t o e x t e n s i o n w h i c h c r e a t e d t h e p a r t i c l e s so t h a t the shapes and s i z e s o f t h e p a r t i c l e s depend d i r e c t l y 91 on o n l y one v a r i a b l e , namely t h e d i s t r i b u t i o n o f m o t i o n i n e x t e n s i o n . T h e r e f o r e , i n a s t r o n g sense, i t i s t r u e o f t h e C a r t e s i a n p a r t i c l e s a l s o , t h a t t h e y are d i f f e r -e n t i a t e d by m o t i o n and r e s t a l o n e . 2. Throughout h i s w r i t i n g s , S p i n o z a shows a deep c o n c e r n f o r t h e problems o f t h e continuum; h i s u n d o u b t e d l y s t r o n g i n t e r e s t i n t h e s e problems i s most r e a d i l y e x p l a i n e d i f h i s concept of t h e s t r u c t u r e o f t h e p h y s i c a l u n i v e r s e i s b a s e d on t h e same b a s i c p r e m i s s e s as t h o s e o f the C a r t e s i a n p h y s i c s , the main p r e m i s s b e i n g t h a t c o r p o r e a l substance and e x t e n s i o n a r e one and t h e same. A l r e a d y i n the P r i n c i p l e s we f i n d a c o n c e r n w i t h t h e problems o f t h e continuum. I n t h e S c h o l i u m t o P r o p o s i t i o n 6, P a r t Two, t h e r e i s a d i s c u s s i o n o f some o f t h e p aradoxes of Zeno; the paradoxes are d es-c r i b e d as a r i s i n g f r om the i l l e g i t i m a t e d i v i s i o n o f t h e continuum i n t o p a r t s , time i n t o moments and m o t i o n i n t o u n i t s o f v e l o c i t y . I n the l e t t e r t o Mayer, A p r i l 1663, w h i c h i s g r e a t l y s i g n i f i c a n t w i t h r e s p e c t t o t h i s t o p i c , S p i n o z a d e a l s e x t e n s i v e l y w i t h t h e t o p i c s o f t i m e , d u r a t i o n and e x t e n s i o n i n terms o f t h e continuum. F o r example, he a s s e r t s t h a t i f i t i s assumed t h a t time i s composed of moments, i t w o u l d not be p o s s i b l e t o u n d e r s t a n d how an hour c o u l d p a s s : 92 F o r i n o r d e r t h a t t h e hour may pass i t w i l l be n e c e s s a r y f o r the h a l f o f i t t o pass f i r s t , and t h e n a h a l f o f what remains o f the remainder; and i f you thus go on i n d e f i n i t e l y , s u b t r a c t i n g the h a l f o f what i s l e f t , you w i l l never be a b l e t o r e a c h the end o f t h e ho u r . T h e r e f o r e , many who have not got used t o d i s t i n g u i s h i n g the t h i n g s o f r e a s o n from r e a l t h i n g s , have dared t o d e c l a r e t h a t D u r a t i o n i s composed o f moments. I t s h o u l d be n o t e d t h a t h e r e , as w e l l as i n o t h e r o f S p i n o z a ' s d i s c u s s i o n s , he a t t e m p t s t o s o l v e the paradoxes by means o f h i s t h e o r y o f knowledge. Here he c o n t r a s t s " t h i n g s o f r e a s o n " w i t h " r e a l t h i n g s " , w h i l e i n o t h e r i n s t a n c e s he emphasizes the d i s t i n c t i o n between the i n t e l l e c t and the i m a g i n a t i o n . Whether the d i s -t i n c t i o n between " t h i n g s o f r e a s o n " and " r e a l t h i n g s " i s the same as the d i s t i n c t i o n between t h e i n t e l l e c t and the i m a g i n a t i o n i s one problem; more g e n e r a l l y , how S p i n o z a a t t e m p t s t o r e s o l v e the paradoxes o f the con-tinuum i n v o l v e s a t h o r o u g h e x a m i n a t i o n o f h i s t h e o r y o f knowledge, w h i c h i s d e f i n i t e l y beyond the scope o f t h i s t h e s i s . The main p o i n t i s t h a t he devotes c o n s i d e r a b l e a t t e n t i o n t o t h e paradoxes o f t h e continuum and t h a t t h e s e a re v e r y much a t t h e c e n t r e o f h i s t h o u g h t . From S p i n o z a ' s d i s c u s s i o n o f the paradoxes o f Zeno I t h i n k h i s i n t e n s e i n t e r e s t i n the problems of the continuum i s a b u n d a n t l y c l e a r , but so f a r we have seen no c l e a r c o n n e c t i o n between the paradoxes o f Zeno and the problems o f t h e continuum g e n e r a t e d by the 93 i d e n t i f i c a t i o n o f p h y s i c a l s u b s t a n c e w i t h g e o m e t r i c a l space i n t h e C a r t e s i a n p h y s i c s . That t h e s e two a r e i n d e e d connected, we can see f r o m th e l o n g S c h o l i u m t o P r o p o s i t i o n 15, P a r t One o f the E t h i c s . I n t h a t S c h o l i u m S p i n o z a defends the p o s i t i o n t h a t God can be a c o r p o r e a l b e i n g and a t the same t i m e be b o t h i n f i n i t e and s i m p l e , i . e . not d i v i s i b l e o r c o n s i s t i n g of p a r t s . He does so by a t t a c k i n g the arguments o f those who b e l i e v e t h a t God cannot be an e x t e n d e d b e i n g because p h y s i c a l s u b s t a n c e i s n e c e s s a r i l y f i n i t e and hence cannot p r o p e r l y p e r t a i n t o God who i s a p e r f e c t b e i n g . He r e p r e s e n t s some o f the arguments o f h i s opponents as f o l l o w s : I f c o r p o r e a l s u b s t a n c e , t h e y say, be i n f i n i t e , l e t us c o n s i d e r i t t o be d i v i d e d i n t o two p a r t s ; e a ch p a r t , t h e r e f o r e w i l l be e i t h e r f i n i t e of i n f i n i t e 1 . I f e a c h p a r t be f i n i t e , t h e n the i n f i n i t e i s composed o f two f i n i t e p a r t s , w h i c h i s a b s u r d . I f each p a r t be i n f i n i t e , t h e r e i s an i n f i n i t e t w i c e as g r e a t as a n o t h e r i n f i n i t e , w h i c h i s a l s o a b s u r d . A g a i n , i f i n f i n i t e q u a n t i t y 2 be measured by e q u a l p a r t s o f a f o o t each, i t must c o n t a i n an i n f i n i t e number o f such p a r t s , and s i m i l a r l y i f i t be measured by e q u a l p a r t s o f an i n c h each; and t h e r e f o r e one i n f i n i t e number w i l l be t w e l v e t i m e s g r e a t e r t h a n a n o t h e r i n f i n i t e number. S p i n o z a s t a t e s t h a t t h e f a l l a c y o f h i s opponents' argument l i e s i n t h e i r " . . . s u p p o s t i o n t h a t b o d i l y s u b s t a n c e c o n s i s t s o f p a r t s " , a s u p p o s i t i o n w h i c h he c o n s i d e r s t o be a b s u r d . He s a y s : And i n d e e d i t i s not l e s s a b s u r d t o suppose t h a t c o r p o r e a l s u b s t a n c e i s composed o f b o d i e s o r p a r t s t h a n t o suppose t h a t a body i s composed o f 94 s u r f a c e s , s u r f a c e s o f l i n e s , and t h a t l i n e s , f i n a l l y , a r e composed o f p o i n t s . E v e r y one who knows t h a t c l e a r r e a s o n i s i n f a l l i b l e ought t o admit t h i s , and e s p e c i a l l y t h o s e who deny t h a t a vacuum can e x i s t . So f a r S p i n o z a ' s arguments c o n s i s t m a i n l y o f a c c u s i n g h i s opponents o f a b s u r d i t i e s ; we would n a t u r a l l y l i k e t o know how h§_ r e s o l v e s the problems t h a t a r i s e f r om the s u p p o s i t i o n t h a t c o r p o r e a l s u b s t a n c e i s i n f i n i t e . H i s s o l u t i o n i s b e s t e x p r e s s e d by the f o l l o w i n g passage i n t h e same S c h o l i u m : I f , n e v e r t h e l e s s , any one s h o u l d ask why t h e r e i s a n a t u r a l tendency t o c o n s i d e r q u a n t i t y as c a p a b l e o f d i v i s i o n , I r e p l y t h a t q u a n t i t y i s c o n c e i v e d by us i n two ways: e i t h e r a b s t r a c t l y o r s u p e r f i c i a l l y ; t h a t i s t o say, as we imagine i t , o r e l s e as s u b s t a n c e , i n w h i c h way i t i s c o n c e i v e d by the i n t e l l e c t a l o n e . I f , t h e r e f o r e , we r e g a r d q u a n t i t y (as we do o f t e n and e a s i l y ) as i t e x i s t s i n t h e - i m a g i n a t i o n , we f i n d i t t o be f i n i t e , d i v i s i b l e , and composed o f p a r t s ; b u t i f we r e g a r d i t as i t e x i s t s i n the i n t e l l e c t , and c o n c e i v e i t i n so f a r as i t i s s u b s t a n c e , we f i n d i t t o be i n f i n i t e , one and i n d i v i s i b l e . I n the l e t t e r t o Meyer, S p i n o z a sees t h e paradox a r i s i n g out o f t h e f a i l u r e t o d i s t i n g u i s h between t h i n g s o f r e a s o n and r e a l t h i n g s ; here he g i v e s h i s s o l u t i o n t o the p r o b l e m o f d i v i s i b i l i t y o f subst a n c e i n terms o f the i n t e l l e c t and the i m a g i n a t i o n . T h i s same theme i s e v i d e n t i n Chapter Two of the S h o r t T r e a t i s e , where he d i s c u s s e s the same t o p i c , the d i v i s i b i l i t y o f c o r p o r e a l m a t t e r and the s i m p l i c i t y o f God. There he says " P a r t and whole a r e not t r u e o r r e a l e n t i t i e s , but o n l y t h i n g s 95 o f r e a s o n " . I n a l l t h e s e v a r i o u s i n s t a n c e s o f S p i n o z a ' s i n v o l v e m e n t w i t h the pr o b l e m o f t h e i n f i n i t e , i t i s obviou s t h a t t h e r e i s something v e r y i m p o r t a n t a t s t a k e f o r h i s system, and what I t h i n k i s a t s t a k e i s t h e v i a b i l i t y o f t h e C a r t e s i a n p h y s i c s as a cosmology, i n Ch a p t e r Three I have mentioned some o f t h e c o n c e p t u a l p u z z l e s t h a t a r i s e n a t u r a l l y o u t of t h e i d e n t i f i c a t i o n of c o r p o r e a l s u b s t a n c e w i t h e x t e n s i o n . The f a c t i s t h a t t h e r e i s a b a s i c c o n t r a d i c t i o n i n p i c t u r e o f the u n i v e r s e as e x t e n s i o n w h i c h i s c r a c k e d by mo t i o n t o c r e a t e the w o r l d o f v a r i e t y and change. As l o n g as we t h i n k o f e x t e n s i o n as some s o r t o f g l a s s y s u b s t a n c e 3 , p e r f e c t l y homogeneous and e x t e n d i n g i n d e f i n i t e l y i n a l l d i r e c t i o n s , t h e n we c a n e a s i l y v i s u a l i z e i t b r e a k i n g up i n t o m y r i a d s o f fragments and t h i s p i c t u r e seems q u i t e p l a u s i b l e . However, i n t h e C a r t e s i a n p h y s i c s t h i s g l a s s y s u b s t a n c e i s n o t s u b s t a n c e o r m a t e r i a l of any k i n d , i t i s p u r e e x t e n s i o n , g e o m e t r i c a l space. The b a s i c c o n t r a d i c t i o n i s between t h i n k i n g of c o r p o r e a l s u b s t a n c e as b e i n g p e r f e c t l y homogeneous, a continuum, and y e t a t the same time t h i n k i n g o f i t as c o n s i s t i n g o f p a r t s , t h e same c o n t r a d i c t i o n t h a t , i n S p i n o z a ' s v i e w , l e a d s t o the paradoxes o f Zeno. 3. S p i n o z a ' s v i e w s on the vacuum r e i n f o r c e the p o i n t s d i s c u s s e d above. B o t h i n the S c h o l i u m t o P r o p o s i t i o n 15, P a r t Two o f t h e E t h i c s and i n Ch a p t e r Two o f the S h o r t T r e a t i s e S p i n o z a ' s d i s c u s s i o n o f the u n i t y o f p h y s i c a l s u b s t a n c e i s c o u p l e d w i t h a d e n i a l o f t h e e x i s t e n c e o f t h e vacuum. S p i n o z a ' s argument i s e x a c t l y the same as t h a t o f the P r i n c i p l e s . The vacuum i s a l o g i c a l a b s u r d i t y , "something p o s i t i v e and y e t no body", as he p u t s i t i n the S h o r t T r e a t i s e . I n the S c h o l i u m j u s t mentioned, S p i n o z a makes a c l o s e c o n n e c t i o n between the u n i t y o f p h y s i c a l s u b s t a n c e and t h e e x i s t e n c e o f a vacuum: F o r i f c o r p o r e a l s u b s t a n c e c o u l d be so d i v i d e d t h a t i t s p a r t s c o u l d r e a l l y be d i s t i n c t , why c o u l d n o t one p a r t be a n n i h i l a t e d , the r e s t r e m a i n i n g , as b e f o r e , c o n n e c t e d w i t h one a n o t h e r ? And why must a l l be so f i t t e d t o g e t h e r t h a t t h e r e can be no vacuum. S p i n o z a c o n s i d e r s t h a t a gap i n the continuum i s c o n t r a d i c t o r y t o t h e v e r y n o t i o n o f a continuum. The above passage i n d i c a t e s p r e t t y c l e a r l y t h a t S p i n o z a thought o f t h e u n i t y o f p h y s i c a l s u b s t a n c e not on some a b s t r a c t m e t a p h y s i c a l p l a n e , b u t i n r a t h e r c o n c r e t e , d own-to-earth terms, u n l e s s , o f c o u r s e , he was not s p e a k i n g about the same k i n d o f vacuum wh i c h was b e i n g i n v e s t i g a t e d e x p e r i m e n t a l l y b y B o y l e and Von G u e r i c h e , w h i c h seems h i g h l y u n l i k e l y 4 . H i s arguments a r e most e a s i l y u n d e r s t o o d i n the framework o f t h e C a r t e s i a n p h y s i c s . 97 4. S p i n o z a ' s i d e a s on the n a t u r e o f s c i e n t i f i c method a r e s u b t l e and not e a s i l y c a t e g o r i z e d , b u t a t the same t i m e i n the s t y l e o f h i s arguments and the c h a r a c t e r o f h i s w r i t i n g t h e r e i s a g r e a t d e a l o f s i m i l a r i t y t o the b a s i c method of the P r i n c i p l e s . The P r i n c i p l e s has as o p e n i n g statement the f o l l o w i n g : I t i s o n l y asked here t h a t e a c h one a t t e n d as a c c u r a t e l y as p o s s i b l e t o h i s concepts i n o r d e r t o be a b l e t o d i s t i n g u i s h t h e c l e a r from the o b s c u r e . T h i s s t a t e m e n t a p p l i e s t o the method of mathematics and e s p e c i a l l y t o geometry. That S p i n o z a had g r e a t f a i t h i n t h e method o f geometry w h i c h proceeds from s e l f - e v i d e n t t r u t h s t o l e s s o b v i o u s b u t l o g i c a l l y i n d i s p u t a b l e t r u t h s i s e v i d e n c e d by h i s s e l e c t i o n o f the g e o m e t r i c a l s t y l e o f w r i t i n g i n b o t h t h e P r i n c i p l e s and the E t h i c s . I n t h e l e t t e r t o Oldenburg o f A p r i l 1662, S p i n o z a c r i t i c i z e s B o y l e ' s attempt t o p r o v e the p a r t i c u l a t e n a t u r e o f m a t t e r by e x p e r i m e n t s : One w i l l never be a b l e t o p r o v e t h i s by c h e m i c a l o r by o t h e r e x p e r i m e n t s , b u t o n l y by r e a s o n i n g and c a l c u l a t i o n . F o r by r e a s o n and c a l c u l a t i o n we d i v i d e b o d i e s i n f i n i t e l y ; . . . I n the E t h i c s he p r e s e n t s h i s p r i n c i p l e o f i n e r t i a not as a p r o p e r t y of m a t t e r or as a h y p o t h e s i s about n a t u r e , but as something w h i c h " i s i n d e e d s e l f -e v i d e n t " . Hardness, s o f t n e s s and f l u i d i t y a re n o t d e s c r i b e d as g r o s s p r o p e r t i e s o f m a t t e r w h i c h we must 98 t r y t o account f o r , b u t r a t h e r are d e f i n e d as depending on c e r t a i n p r o p e r t i e s o f p a r t i c l e s . A l l i n a l l he e x h i b i t s c o n s i d e r a b l e c o n f i d e n c e i n the p o s s i b i l i t y o f a r r i v i n g a t t h e b a s i c p h y s i c a l t r u t h s by t h e p r o c e s s of a r g u i n g from the n a t u r e o f the c o n c e p t s t h e m s e l v e s , c o n c e p t s such as s u b s t a n c e , body, e x t e n s i o n , and m o t i o n . 5. There are a g r e a t many m e t a p h y s i c a l i s s u e s on w h i c h D e s c a r t e s and S p i n o z a a r e c o n s i d e r e d t o h o l d d i a m e t r i c a l l y opposed v i e w s , and i t may t h e r e f o r e be t h o u g h t t o be s u r p r i s i n g t h a t t h e i r c o s m o l o g i e s a r e so s i m i l a r , as I have s u g g e s t e d . Of c o u r s e , i t i s not f e a s i b l e t o d i s c u s s a l l t h e s e i s s u e s t o show t h a t t h e d i f f e r e n t p h i l o s o p h i e s are not r e f l e c t e d i n t h e i r c o s m o l o g i e s , but t h e r e i s one i t e m t h a t s h o u l d be examined more c l o s e l y , e s p e c i a l l y s i n c e i t i s i n c o n n e c t i o n w i t h t h a t i t e m t h a t S p i n o z a o u t r i g h t l y condemns the whole C a r t e s i a n p h y s i c s . I n t h e l e t t e r o f May 1676, t o T s c h i r n h a u s , S p i n o z a s a y s : From e x t e n s i o n as D e s c a r t e s c o n c e i v e s i t , t h a t i s , as a q u i e s c e n t mass, i t i s not o n l y , as you say, d i f f i c u l t t o p r o ve t h e e x i s t e n c e o f b o d i e s , but a b s o l u t e l y i m p o s s i b l e . F o r m a t t e r a t r e s t w i l l c o n t i n u e a t r e s t as much as p o s s i b l e , and w i l l n o t be s e t i n m o t i o n e x c e p t by some s t r o n g e r e x t e r n a l c a u s e . F o r t h i s r e a s o n I d i d not h e s i t a t e t o say once t h a t D e s c a r t e s * s p r i n c i p l e s o f n a t u r a l t h i n g s a r e u s e l e s s , not t o s a y a b s u r d . About t h i s passage Wolf^ says the f o l l o w i n g : 99 The use o f the same term E x t e n s i o n by S p i n o z a and D e s c a r t e s has u n f o r t u n a t e l y o b s c u r e d f o r most p e o p l e the enormous d i f f e r e n c e between the C a r t e s i a n and S p i n o z i s t i c c o n c e p t i o n o f t h e u l t i m a t e n a t u r e o f m a t t e r . F o r S p i n o z a , E x t e n s i o n o r M a t t e r i s e s s e n t i a l l y p h y s i c a l energy. I t e x p r e s s e s i t s e l f i n the i n f i n i t e mode o f motion-and r e s t , w h i c h c o n s e q u e n t l y need not be i n t r o d u c e d m i r a c u l o u s l y f r om the o u t s i d e , as was the case i n D e s c a r t e s ' s , scheme o f t h i n g s . That t h e r e i s a g r e a t d i f f e r e n c e between S p i n o z a ' s and D e s c a r t e s ' s scheme o f t h i n g s i s a comment f r e q u e n t l y made^, but what p r e c i s e l y i s t h i s d i f f e r e n c e ? What i s a t s t a k e i s whether m o t i o n i s something s e p a r a t e f rom p h y s i c a l s u b s t a n c e o r an i n h e r e n t p a r t o f p h y s i c a l sub-s t a n c e . I n the P r i n c i p l e s t h e c r e a t i o n of p a r t i c l e s by mot i o n was d e s c r i b e d as h a v i n g t a k e n p l a c e i n t h e be-g i n n i n g , when God c r e a t e d the v i s i b l e w o r l d ; a l l t h e o r i g i n a l p a r t i c l e s were produced i n one f e l l swoop. I n S p i n o z a ' s p h i l o s o p h y t h i s "one-shot" c r e a t i o n o f t h e p a r t i c l e s i s a b s u r d ; c o n s e q u e n t l y t h i s c r e a t i o n o f p a r t i c l e s i n S p i n o z a ' s p h y s i c s i s more o f a c o n t i n u o u s p r o c e s s , something t h a t has always gone on and w i l l go on f o r e v e r . S u p e r f i c i a l l y , i t does n o t make a g r e a t d e a l o f d i f f e r e n c e how o r when mo t i o n came i n t o t h e w o r l d , as l o n g as t h e p r e s e n t d e s c r i p t i o n o f t h e u n i v e r s e i s u n a f f e c t e d . How-eve r , t h e r e i s a s u b t l e b u t f a r - r e a c h i n g d i f f e r e n c e i n emphasis: i n the C a r t e s i a n p h y s i c s the emphasis i s on p a r t i c l e s , w h i c h a r e t o be c o n s i d e r e d as e n d u r i n g e n t i t i e s , 100 on the whole, even though t h e y f r a c t u r e o r f u s e o c c a s i o n a l l y (how, when o r why i s l a r g e l y a m y s t e r y ) . I n the S p i n o -z i s t i c p i c t u r e the i d e a t h a t m otion i s t h e cause o f t h e c h a r a c t e r and the e x i s t e n c e of t h e p a r t i c l e s i s t a k e n much more s e r i o u s l y and c o n s e q u e n t l y t h e p a r t i c l e s a r e t o a l e s s e r e x t e n t r e a l o r c o n c r e t e e x i s t e n t s . To p u t i t a l i t t l e d i f f e r e n t l y , i n the C a r t e s i a n p h y s i c s s c i e n t i f i c e x p l a n a t i o n s d e a l e s s e n t i a l l y w i t h the motions and i n t e r a c t i o n s of p a r t i c l e s , w h i l e i n S p i n o z a ' s p h y s i c s t h e s c i e n t i f i c account b a s i c a l l y c o n c e r n s i t s e l f w i t h the d i s t r i b u t i o n o f m o t i o n - a n d - r e s t i n t h e u n i v e r s e . The g e n e r a l p i c t u r e o f the cosmos as one i n w h i c h the fundamental v a r i a b l e i s the d i s t r i b u t i o n o f m o t i o n and r e s t i s d i f f i c u l t t o v i s u a l i z e and even h a r d e r t o d e s c r i b e . The p h y s i c a l u n i v e r s e i s space, o r e m p t i n e s s , w h i c h i s "shot t h r o u g h " , so t o speak, w i t h m otion and r e s t . S u p e r f i c i a l l y , t h e C a r t e s i a n and S p i n o -z i s t i c s c i e n t i f i c schemes a r e t h e same: b o t h d e a l i n terms o f p a r t i c l e s i n m o t i o n , but the emphasis i s q u i t e d i f f e r e n t . I n the C a r t e s i a n system a composite body i s a c o n g l o m e r a t i o n o f p a r t i c l e s , w h i l e i n S p i n o z a ' s system i t i s a p p r o p r i a t e t o say t h a t "the human body, t h e r e f o r e , i s n o t h i n g e l s e t h a n a c e r t a i n p r o p o r t i o n o f motion and r e s t " (Appendix Two, S h o r t T r e a t i s e ) . The arguments I have p r e s e n t e d i n the above 101 f i v e p o i n t s demonstrate c l e a r l y , I s u b m i t , t h a t S p i n o z a was s a t i s f i e d i n t h e main, w i t h the k i n d o f p h y s i c a l t h e o r y p r e s e n t e d i n t h e P r i n c i p l e s , and t h a t h i s c r i t i c i s m s o f D e s c a r t e s a r e d i r e c t e d n o t so much a t the C a r t e s i a n p h y s i c s , as a t t h e m e t a p h y s i c a l f o u n d a t i o n s o f t h a t system o f p h y s i c s . I t e x p l a i n s why S p i n o z a p r e s e n t e d so l i t t l e p h y s i c a l t h e o r y o f h i s own, and why the g e n e r a l c h a r a c t e r o f t h e p h y s i c s o f t h e E t h i c s i s q u i t e c o m p a t i b l e w i t h t h a t o f t h e P r i n c i p l e s . A t t h e same t i m e we s h o u l d n o t e , however, t h a t he g i v e s t h e C a r t e s i a n p h y s i c s , by f i t t i n g i t i n t o h i s own m e t a p h y s i c a l scheme, a d i s t i n c t l y d i f f e r e n t f l a v o u r , so t o speak. Or, p u t t i n g i t a l i t t l e more s t r o n g l y , i t i s p o s s i b l e t o l o o k upon h i s m e t a p h y s i c s as a development o f t h e C a r t e s i a n p h y s i c s , a r e s u l t o f the e f f o r t s t o d e a l w i t h t h e p u z z l e s c r e a t e d by the C a r t e s i a n scheme. H i s d o c t r i n e o f s u b s t a n c e , a t t r i b u t e , and mode, can be seen as a r i s i n g f r o m the e f f o r t t o c o n s t r u c t a scheme t o e x p l a i n t h e r e l a t i o n s between e x t e n s i o n and motion . H i s d i s t i n c t i o n between i n f i n i t e , o r mediate modes and f i n i t e modes can be i n t e r p r e t e d i n terms o f m o t i o n b r e a k i n g up c o n t i n u o u s space i n t o t h e w o r l d o f p a r t i c u l a r s . The t h e o r y o f i n d i v i d u a l s c o u l d be c o n s i d e r e d as an e f f o r t t o found a t h e o r y o f o r g a n i z e d c o m p l e x i t y i n o r d e r t o e x p l a i n the i n t e r c o n n e c t i o n o f mind and body; i n t h e C a r t e s i a n system t h i s i s not needed s i n c e mind and body are s e p a r a t e s u b s t a n c e s . S p i n o z a ' s t h r e e k i n d s o f knowledge can be seen as d i r e c t l y r e l a t e d t o the t h r e e d i f f e r e n t ways of l o o k i n g a t the u n i v e r s e : w i t h I m a g i n a t i o we see t h e w o r l d of s i g h t s , sounds, s m e l l s , e t c . ; w i t h R a t i o we see the w o r l d a s made up o f p a r t i c l e s i n m o t i o n , w h i l e w i t h S c i e n t i a I n t u i t i v a we see c o r p o r e a l s u b s t a n c e as e x t e n s i o n , c o n t i n u o u s and i n d i v i s i b l e . H i s d i s t i n c t i o n between R a t i o and S c i e n t i a I n t u i t i v a can be seen as an e f f o r t t o s o l v e the p a r a d o x e s of the i n f i n i t e , w h i l e h i s p r o o f s o f t h e u n i t y o f p h y s i c a l s u b s t a n c e a p p l y d i r e c t l y t o t h e C a r t e s i a n cosmology. A l l t h i s i s somewhat s p e c u l a t i v e and goes w e l l beyond t h e scope of t h i s t h e s i s , b u t i t s e r v e s t o emphasize the n e c e s s i t y o f p a y i n g c l o s e a t t e n t i o n t o S p i n o z a ' s p h y s i c s . H i s w r i t i n g o f the P r i n c i p l e s i s u s u a l l y d i s -m i s s e d as something of i n c i d e n t a l i n t e r e s t , w h i l e the p h y s i c a l t h e o r y c o n t a i n e d i n t h e E t h i c s has n o t had the b e n e f i t o f a d e t a i l e d a n a l y s i s . H i s v i e w s on the vacuum are i g n o r e d by and l a r g e , and h i s c o n c e r n w i t h the p a r a d o x e s o f Zeno has not been c o n s i d e r e d v e r y s i g n i f i c a n t w i t h r e s p e c t t o h i s major d o c t r i n e s . My e f f o r t has been t o show t h a t a l l t h e s e t o p i c s , w h i c h a t f i r s t s i g h t a r e q u i t e unconnected, do hang t o g e t h e r , and t h a t t o g e t h e r t h e y i n d i c a t e t h a t S p i n o z a ' s i d e a s on the n a t u r e and s t r u c t u r e o f m a t t e r are not r a d i c a l l y d i f f e r e n t from. 103 o r t o t a l l y unconnected w i t h t h o s e o f Rene D e s c a r t e s ; t h a t i n s p i t e o f m e t a p h y s i c a l d i s a g r e e m e n t s , S p i n o z a ' s and D e s c a r t e s ' s s c i e n t i f i c t h e o r i e s a r e q u i t e s i m i l a r . The c e n t r a l i s s u e t o w h i c h I have dev o t e d my a t t e n t i o n i s t h e n a t u r e o f the c o r p o r a s i m p l i c i s s i m a i n S p i n o z a ' s system and what r o l e they p l a y i n h i s c o n c e p t i o n o f the p h y s i c a l u n i v e r s e as c o n s i s t i n g o f p a r t i c l e s i n m o t i o n . My c o n c l u s i o n , t h a t t h e c o r p o r a s i m p l i c i s s i m a are e x t e n d e d p a r t i c l e s v e r y s i m i l a r t o those o f t h e C a r t e s i a n p h y s i c s , has not o n l y a d e f i n i t e b e a r i n g on S p i n o z a ' s s c i e n t i f i c t h e o r i e s , b u t has i m p o r t a n t i m p l i c a t i o n s f o r the i n t e r -p r e t a t i o n o f h i s p h i l o s o p h y as a w h o l e . •^What i s a t s t a k e here i s t h e f a c t t h a t an i n f i n i t e s e t can be p u t i n t o a one-to-one correspondence w i t h a p r o p e r s u b s e t o f t h a t s e t . ^ S p i n o z a f r e q u e n t l y seems t o i d e n t i f y p h y s i c a l s u b s t a n c e w i t h q u a n t i t y . T h i s i s a l s o done i n t h e P r i n c i p l e s ; see, f o r i n s t a n c e , the d e f i n i t i o n o f e x t e n s i o n ( D e f i n i t i o n 1, P a r t Two). ^There i s an i n v i t i n g p a r a l l e l between t h e n o t i o n o f t h e u n i v e r s e as i n f i n i t e e x t e n s i o n , p e r f e c t l y homogeneous and c h a n g e l e s s and Parmenides's i d e a o f the u n i v e r s e as a homogeneous s p h e r e . W i t h b o t h Parmenides and S p i n o z a t h e r e i s the problem o f r e c o n c i l i n g a t i m e l e s s , change-l e s s whole, w i t h t h e p e r c e i v e d w o r l d , w h i c h i s f u l l of v a r i e t y and change. 4 S e e , f o r example, t h e l e t t e r t o Oldenburg, J u l y , 1663. 5 S e e Wolf, page 62. D S e e , f o r i n s t a n c e , Hampshire, pages 70-71. 104 BIBLIOGRAPHY B e l l , A r t h u r E r n e s t , C h r i s t i a n Huygens and t h e Development  of S c i e n c e i n the S e v e n t e e n t h C e n t u r y , London, E. A r n o l d and Company, 1947. B i r c h , Thomas ( e d i t o r ) , The C o l l e c t e d Works o f t h e Honourable  R o b e r t B o y l e , w i t h an i n t r o d u c t i o n by Douglas M c K i e , H i l d e s h e i m , G. Olms, 1965-1966. B l u h , O., "Newton and S p i n o z a " , N a t u r e : 135 ( A p r i l 27, 1955), pp. 658-659. . • Broad, C. D., E t h i c s and t h e H i s t o r y o f P h i l o s o p h y , London, Routledge and Kegan- P a u l , 19 52. B u t t e r f i e l d , H e r b e r t , The O r i g i n s o f Modern S c i e n c e 1300 - 1800, New York, F r e e P r e s s , 1966. ' Camerer, Theodor, D i e Lehre S p i n o z a ' s , Z w e i t e A u f l a g e , . S t u t t g a r t und B e r l i n , 1914. Conant, James Bry a n ( e d i t o r ) , H a r v a r d Case H i s t o r i e s i n  E x p e r i m e n t a l S c i e n c e , Case One R o b e r t B o y l e ' s  E x p e r i m e n t s i n Pneumatics, H a r v a r d U n i v e r s i t y P r e s s , 1961. D i j k s t e r h u i s , E. J . , The M e c h a n i z a t i o n o f the World P i c t u r e , t r a n s l a t o r C. D i k s h o o r n , O x f o r d , 1961. Dutch C l a s s i c s on H i s t o r y o f S c i e n c e V, B e n e d i c t u s de S p i n o z a , A l g e b r a i c C a l c u l a t i o n o f t h e Rainbow, 1687, w i t h an i n t r o d u c t i o n by G. Ten D o e s s c h a t e , Niewkoop and B. De G r a a f , 1963.. E a t o n , R a l p h M. ( e d i t o r ) , D e s c a r t e s S e l e c t i o n s , C h a r l e s S c r i b n e r ' s Sons,-1927. F r e u d e n t h a l , J . , D i e L e b e n s g e s c h i c h t e S p i n o z a s , L e i p z i g V e r l a g Von V e i t and Co., 1899. Gebhardt, C a r l , S p i n o z a Opera, V o l . IV, H e i d e l b e r g , C a r l W i n t e r s , 19 24. H a l l , A.R., B a l l i s t i c s i n the S e v e n t e e n t h C e n t u r y , Cambridge U n i v e r s i t y P r e s s , 1952. , The S c i e n t i f i c R e v o l u t i o n 1500 - 1800, London, Longmans, Green and Co., 1954. 105 H a l l , M a r i e Boas, "Robert B o y l e " , S c i e n t i f i c A merican, Volume 217, Number 2 (August 1967). Hampshire, S t u a r t , S p i n o z a , Penguin Books I n c . , 1962. Joachim, H a r o l d H., A S t udy o f the E t h i c s o f S p i n o z a , R u s s e l l and R u s s e l l I n c . , New York, 1964. L e i b n i z , G o t t f r i e d W i l h e l m Von, Monadology and Other P h i l o - s o p h i c a l E s s a y s , t r a n s l a t e d by P a u l S c h r e c k e r and Anne M a r t i n S c h r e c k e r , New York, B o b b s - M e r r i l Co. L t d . , 1965. M a r t i n a u , James, A S tudy o f S p i n o z a , M a c M i l l a n and Co., 1883. McKeon, R i c h a r d , The P h i l o s o p h y of S p i n o z a , New Y o r k , Longmans, Green and Co., 19 28. P a r k i n s o n , G. H. R., S p i n o z a ' s Theory o f Knowledge, O x f o r d U n i v e r s i t y P r e s s , 1953. P o l l o c k , F r e d e r i c k , S p i n o z a , H i s L i f e and P h i l o s o p h y , London, Kegan P a u l and Co., 1880. R i v a u d - P o i t i e r s , A l b e r t , "La P h y s i q u e de S p i n o z a " , Tomus  Quartus C h r o n i c o n Spinozanum, pages 24-57, Hagae C o m i t i s C u r i s S o c i e t a t i s S pinozanae, MCMXXIV/MCMXXV/MCMXXVI. Roth, Leon, S p i n o z a , London, E r n e s t Benn L t d . , 1929. R u s s e l l , B e r t r a n d , A C r i t i c a l E x p o s i t i o n o f the P h i l o s o p h y  o f L e i b n i z , , C a m b r i d g e U n i v e r s i t y P r e s s , 1900. S c o t t , J . F., The S c i e n t i f i c Work of Rene D e s c a r t e s 1596 -1650, London, T a y l o r and F r a n c i s , 1952. S p i n o z a , B a r u c h , E a r l i e r P h i l o s o p h i c a l W r i t i n g s . The C a r t e s i a n P r i n c i p l e s and Thoughts on M e t a p h y s i c s , t r a n s l a t e d by F r a n k A. Hayes w i t h an i n t r o d u c t i o n by D a v i d B i d n e y , The B o b b s - M e r r i l Co. I n c . , L i b r a r y o f L i b e r a l A r t s , 1963. , P r i n c i p l e s o f C a r t e s i a n P h i l o s o p h y , from L a t i n by. H a r r y E. Wedeck. P r e f a c e by Dagobert D.-Runes, New Y o r k , P h i l o s o p h i c a l L i b r a r y , 1961. 106 S p i n o z a , Baruch, The P r i n c i p l e s o f D e s c a r t e s ' s P h i l o s o p h y , H a l b e r t B r i t a n T r a n s l a t i o n , Open C o u r t , 1961. (Note: A l l q u o t a t i o n s a re from t h i s e d i t i o n ) . Wiener, P h i l i p P., ( e d i t o r ) , L e i b n i z S e l e c t i o n s , New York, C h a r l e s S c r i b n e r ' s Sons, 1951. W i l d , John ( e d i t o r ) , S p i n o z a S e l e c t i o n s , New Y o r k , C h a r l e s S c r i b n e r ' s Sons, 1958. Wo l f , A r n o l d , The Correspondence o f S p i n o z a , London, Frank Cass and Co., L t d . , 1966. . Wo l f s o n , H a r r y A u s t r y n , "Spinoza on t h e I n f i n i t y o f C o r p o r e a l S u b s t a n c e " , Tomus Quartus C h r o n i c o n  Spinozanum, pages 7 9-103, Hagae C o m i t i s C u r i s S o c i e t a t i s S p i n o z a n a e , MCMXXIV/MCMXXV/MCMXXVI. 107 APPENDIX A SPINOZA'S LIBRARY I have i n c l u d e d t h i s i t e m because i t c a s t s a l i g h t on S p i n o z a ' s i n t e r e s t i n s c i e n c e , and a l s o because the l i s t i s h a r d t o f i n d , e s p e c i a l l y i n E n g l i s h works. T h i s s e l e c t i o n i s t a k e n from the l i s t i n F r e u d e n t h a l 1 s D i e L e b e n s g e s c h i c h t e S p i n o z a s w h i c h c o n t a i n s 161 i t e m s . I t i n c l u d e s works w r i t t e n i n L a t i n , Hebrew, S p a n i s h and Dutch. Most o f t h e books r e l a t e t o S p i n o z a ' s p h i l o s o p h -i c a l , t h e o l o g i c a l and p o l i t i c a l s t u d i e s , b u t the s e l e c t i o n I have made d e a l s m o s t l y w i t h astronomy, m e d i c i n e , p h y s i c s and mathematics. F r e u d e n t h a l ' s l i s t i s b e l i e v e d t o be i n c o m p l e t e , the more v a l u a b l e books h a v i n g been removed b e f o r e the i n v e n t o r y was made. I t i s .unfortunate t h a t the a u d i t o r used a b b r e v i a t i o n s o r s h o r t t i t l e s . I have t r a n s l a t e d the Dutch t i t l e s i n b r a c k e t s a f t e r the o r i g i n a l t i t l e . - Longomontani A s t r o n o m i a d a n i c a cum appendice de s t e l l i s N o v i s e t Come t i s . 1640. A m s t e l . - D i o p h a n t i A l e x a n d r i n i A r i t h m e t i c o r u m L i b r i 6 P a r i s . 1621. Gr. L a t . - V i e t a e o p e r a Mathematica. Lugd. 1646. - H u g e n i i Z u l i c h e m i i H o r o l o g i u m O s c i l l a t o r i u m . P a r i s . 1673. 108 V e s l i n g i i Syntagma Anatomicum. P a t a v i i . 1647. R i o l a n i A n atomica. P a r i s . 1626. D e s c a r t e s B r i e v e n . ( L e t t e r s o f D e s c a r t e s ) K e r c k r i n g i i S p e c i l e g i u m (!) anatomicum. 1670. D e s c a r t e s Proeven. ( D e s c a r t e s ' s p r o o f s ) Renatus D e s c a r t e s de p r i m a P h i l o s o p h i a . Renatus D e s c a r t e s de G e o m e t r i a . Renatus D e s c a r t e s de P h i l o s o p h i a p r i m a . D e s c a r t e s opera P h i l o s o p h i c a . 1650. D e s c a r t e s de homine. a Schooten E x e r c i t a t i o n e s Mathematicae. Een Rabbinsch Mathematisch boeck. (a r a b b i n i c a l m a t h e m a t i c a l book) S n e l l i i T i p h y s B a t a v u s . G r e g o r i i O p t i c a Promota Lond. 1663. a Schooten P r i n c i p i a Matheseos U n i v e r s . 1651. L a n s b e r g i i Comm. i n Motum T e r r a e . M i d d e l b . 1630. L a n s b e r g i i C y c l o m e t r i a nova. A l g e b r a door K i n c k h u y s e n . ( A l g e b r a by Kinckhuysen) Gront der Meetkunst door K i n c k h u y s e n . ( F o u n d a t i o n s o f geometry) De Meetkunst door K i n c k h u y s e n . (Geometry by Kinckhuysen) L a n s b e r g i i Progymnasmata a s t r o n . R e s t i t u t a . Wouter V e r s t a p . a r i t h m e t i c a . B a r t h o l i n i anatomia. 1651. 109 M e t i i A l c m a r i a n i I n s t i t . a s t r o n . L i b r i 3. T u l p i i O b s e r v a t i o n e s Med. 1672. B o y l e de E l e a t e r e e t g r a v i t a t e a e r i s . 1663. Lond. Kekkermanni L o g i c a . M e t i i A s t r o l a b i u m . de G r a e f s d r i e h o e k s m e t i n g . ( t r i g o n o m e t r y ) K l a u b e r g h s u y t b r e i d i n g v a n D e s c a r t e s . ( K l a u b e r g h ' s commentary on D e s c a r t e s ) Hobbes Elementa P h i l o s o p h i c a . B o y l e Paradoxa H y d r o s t a t i c a . E u c l i d e s . S t e n o n i s Observ. a n a t . Pharmacopaea A m s t e l r e d . Elementa P h y s i c a . 110 APPENDIX B THE HYDROSTATIC EXPERIMENT The d e s c r i p t i o n o f t h i s e x p e r i m e n t o f S p i n o z a ' s i s f o u n d i n h i s l e t t e r t o J a r i g J e l l e s o f September, 1669. The e x p e r i m e n t a l a p p a r a t u s employed by S p i n o z a i s f a i r l y s i m p l e and h i s d r a w i n g , w h i c h I have rep r o d u c e d below, i s a l most s e l f - e x p l a n a t o r y . 1 and 2/3 i n c h e s . We may assume t h a t t h e o t h e r tubes are drawn r o u g h l y t o s c a l e . The l e t t e r "A" d e s i g n a t e s a k i n d o f gate o r v a l v e , w h i l e S p i n o z a a l s o had a way o f b l o c k i n g o f f tube B, not shown i n h i s diagram. The f i r s t p a r t o f t h e e x p e r i m e n t need not d e t a i n us f o r l o n g ; i t s purpose i s t o determine t o what h e i g h t the w a t e r w i l l r i s e i n s m a l l tube C w i t h gate A c l o s e d o f f and t o compare t h i s w i t h the h e i g h t the w a t e r r e a c h e s i n C and D w i t h A open. S p i n o z a ' s c o n c l u s i o n i s t h a t t h e f a c t t h a t E i s f a r t h e r removed from G t h a n B has no e f f e c t on the l e v e l t o w h i c h w a t e r r i s e s i n C and D, and more g e n e r a l l y t h a t F c D The t u b e , M, i s 10 f e e t l o n g and has a bore o f I l l t h e l e n g t h o f tube M i s not a r e l e v a n t f a c t o r . The second p a r t o f t h e e x p e r i m e n t i s more a hydrodynamic e x p e r i m e n t t h a n a h y d r o s t a t i c one, because S p i n o z a p r o c e e d s . t o compare the r a t e s o f w a t e r f l o w through tubes B and E (the s m a l l b o r e tubes C and D are removed f o r t h i s e x p e r i m e n t ) . I n o r d e r t o do t h a t he measures the time t a k e n t o f i l l a v e s s e l o f one c u b i c f o o t c a p a c i t y by w a t e r f l o w i n g out o f tubes B and E r e s p e c t i v e l y . R e l -a t i v e t i m e s are measured by w e i g h i n g the amount of w a t e r s i p h o n e d from one v e s s e l t o a n o t h e r a t a l o w e r l e v e l t h r o u g h a narrow g l a s s tube i n t h e shape o f t h e l e t t e r J . S p i n o z a ' s r e a s o n f o r u s i n g what i s a c c u r a t e l y d e s c r i b e d as a w a t e r c l o c k i s s i m p l y t h a t he does not have a pendulum c l o c k a v a i l a b l e ; i n any case the w a t e r c l o c k i s p r o b a b l y a c c u r a t e enough f o r h i s p u r p o s e s . S p i n o z a o b s e r v e s t h a t the o n l y time t h a t t h e r e i s a s i g n i f i c a n t d i f f e r e n c e i n the r a t e s o f f l o w t h r o u g h B and E i s a t t h e b e g i n n i n g , when E i s s l o w e r . O t h e r -w i s e , he c o n c l u d e s , i t would make no d i f f e r e n c e whether M i s 10 f e e t l o n g o r 40,000 f e e t l o n g ; t h a t i s , he c o n -c l u d e s t h a t t h e t e r m i n a l r a t e o f f l o w i s independent o f the l e n g t h o f tube M, but depends o n l y on the l e v e l o f w a t e r i n the c o n t a i n e r F. T h i s c o n c l u s i o n i s c o r r e c t p r o v i d e d t h a t f r i c t i o n and v i s c o s i t y e f f e c t s are i g n o r e d . I n h i s e f f o r t s t o e x p l a i n why t h e w a t e r f l o w 112 i s s m a l l e r i n E a t t h e b e g i n n i n g S p i n o z a g i v e s a f o r m u l a t h a t i s supposed t o gover n the r a t e of a c c e l e r a t i o n o c c u r r i n g i n t h e w a t e r : F o r i t i s c e r t a i n t h a t i f t h e w a t e r i n the tube G i m p a r t s t o t h e wa t e r i n t h e tube M one degree o f speed i n the f i r s t moment, th e n i n the second moment, i t i f r e t a i n s i t s o r i g i n a l f o r c e , as i t i s supposed t o , i t w i l l communicate f o u r degrees o f speed t o the w a t e r , and so f o r t h . U n t i l t h e wa t e r i n the l o n g tube M has r e c e i v e d j u s t as much v e l o c i t y as the g r a v i t a t i o n a l f o r c e can g i v e the h i g h e r w a t e r , c o n t a i n e d i n the tube G. The m y s t e r y about t h i s s tatement i s where S p i n o z a got i f from. I t c e r t a i n l y does not f o l l o w from any e x p e r i -m e ntal o b s e r v a t i o n s nor does he say t h a t i t i s supposed t o . What S p i n o z a i s a s s e r t i n g i s t h a t t h e v e l o c i t y i s p r o p o r t i o n a l t o t h e square o f t h e e l a p s e d t i m e : V = a t 2 . About t h i s . W o l f 1 , says t h e f o l l o w i n g : S p i n o z a must be t h i n k i n g o f t h e d i s t a n c e t r a v e r s e d . T h i s i s p r o p o r t i o n a l t o t h e square o f t h e t i m e . The a c t u a l v e l o c i t y d e v e l o p e d by a body under the a c t i o n o f a c o n s t a n t f o r c e i s s i m p l y p r o p o r t i o n a l t o the t i m e . Wolf i s r i g h t about b o d i e s moving under the i n f l u e n c e o f a c o n s t a n t f o r c e ; t h i s i s j u s t t h e r e l a t i o n v=at. T h i s p r o p o r t i o n a l i t y o f v e l o c i t y and time was a l r e a d y d i s c o v e r e d by G a l i l e o i n 1609 from h i s o b s e r v a t i o n s o f b a l l s r o l l i n g down i n c l i n e s . But i n t h i s p a r t i c u l a r case b o t h Wolf and S p i n o z a a r e wrong, because the a c c e l e r a t i o n i s not c o n s t a n t ; i t i s g r e a t e s t when the w a t e r s t a r t s f l o w i n g and d e c r e a s e s l i n e a r l y u n t i l i t rea c h e s z e r o when the 113 w a t e r reaches t e r m i n a l v e l o c i t y , so t h a t the r e l a t i o n between time, and v e l o c i t y i s much more c o m p l i c a t e d . Q u i t e a s i d e from whether S p i n o z a was r i g h t o r wrong i n making t h i s s t a t e m e n t , t h e r e i s s t i l l t he q u e s t i o n on what b a s i s he makes t h i s s t a t e m e n t . The l e t t e r t o J e l l e s i s the o n l y o c c a s i o n on w h i c h S p i n o z a even mentions a c c e l e r a t i o n , so t h a t i t i s i m p o s s i b l e t o make com p a r i s o n s . We might suppose t h a t S p i n o z a was a c q u a i n t e d w i t h the work o f G a l i l e o , even though no works of G a l i l e o were found i n h i s l i b r a r y , and t h a t he made a l i t t l e s l i p h e r e , as Wolf s u g g e s t s . But a l l t h i s i s h i g h l y c o n j e c t u r a l . The c h i e f p o i n t o f i n t e r e s t i n the h y d r o s t a t i c e x p e r i m e n t i s t h a t i t shows t h a t S p i n o z a , when he was so i n c l i n e d , was q u i t e capable o f c o n d u c t i n g f a i r l y e l a b o r a t e e x p e r i m e n t s . I t may be s a i d t h a t t h e h y d r o -s t a t i c e x p e r i m e n t i s a f a i r l y s i m p l e and s t r a i g h t f o r w a r d e x p e r i m e n t , and i n d e e d , i t p a l e s i n comparison w i t h the e x t e n s i v e and t h o r o u g h e x p e r i m e n t a l work of a man l i k e R o bert B o y l e , b u t we s h o u l d l o o k on i t as a sample o f what S p i n o z a might have done, had he been more i n t e r e s t e d . A l s o , from th e d e s c r i p t i o n t h a t S p i n o z a g i v e s o f t h e e x p e r i m e n t , even though i t i s v e r y c o n c i s e , i t can s a f e l y be s a i d t h a t he shows a t l e a s t some competence as an e x p e r i m e n t a l s c i e n t i s t . He seems t o be aware of t h e n e c e s s i t y o f c o n t r o l l i n g t h e r e l e v a n t v a r i a b l e s i n the e x p e r i m e n t , and h i s o b s e r v a t i o n s are made c a r e f u l l y . He t a k e s note o f the p o s s i b l e s o u r c e s o f e r r o r and h i s major c o n c l u s i o n s are s o u n d l y based on the o b s e r v a t i o n a l e v i d e n c e . See W o l f , page 435. 115 APPENDIX C THE SIXTH RULE OF MOTION I t i s o f some i n t e r e s t t o e x p l o r e what reasons S p i n o z a m i g h t have had f o r c h a n g i n g D e s c a r t e s ' s s i x t h r u l e o f m o t i o n . D e s c a r t e s ' s v e r s i o n , w h i c h i s found i n p a r a g r a p h 51 o f P a r t Two o f h i s P r i n c i p l e s o f P h i l o s o p h y reads as f o l l o w s : I f C, a t r e s t , i s e q u a l t o B w h i c h approaches i t , the l a t t e r must t r a n s f e r some of i t s m o t i o n t o the f o r m e r , and rebound w i t h the r e s t ; f o r example, i f B approach C w i t h f o u r degrees o f speed, i t w i l l t r a n s f e r one and w i t h the o t h e r t h r e e r e t u r n t o t h e s i d e whence i t came. D e s c a r t e s ' s r e a s o n i n g i n v o l v e s c o n s i d e r i n g t h r e e c a s e s : (a) B and C move a l o n g t o g e t h e r w i t h two u n i t s o f v e l o c i t y , so t h a t B l o s e s two u n i t s and C g a i n s two u n i t s o f v e l o c i t y , (b) B i s r e f l e c t e d w i t h f o u r degrees o f v e l o c i t y w h i l e C remains a t r e s t , (c) B i s r e f l e c t e d w i t h l e s s t h a n i t s o r i g i n a l v e l o c i t y w h i l e C g a i n s w h a t e v e r B l o s e s . I n a l l t h r e e c a s e s , i t w i l l be n o t e d , q u a n t i t y o f m o t i o n i s c o n s e r v e d . Case (a) i s r e j e c t e d because i t i n v o l v e s c h a n g i n g C from r e s t t o m o t i o n , w h i l e B i s not r e f l e c t e d ; somehow t h i s i s not c o n s i d e r e d p e r f e c t l y e q u a l " t r e a t m e n t " . B and C a r e e q u a l i n s i z e and hence are e q u a l l y " s t r o n g " , so t h a t the r e s u l t s s h o u l d be e q u a l f o r them. Case (b) i s r e j e c t e d because 116 i t " f a v o u r s " C o v e r B. Hence (c) i s t h e c o r r e c t r e s u l t . I n case ( a ) , w h i c h f a v o u r s B, B l o s e s 2 u n i t s o f v e l o c i t y . I n case ( b ) , w h i c h f a v o u r s C, B l o s e s z e r o u n i t s . S i n c e n e i t h e r B nor C i s t o be f a v o u r e d , t h e r e s u l t must be h a l f - w a y between case (a) and case ( b ) , w h i c h means B w i l l l o s e one u n i t o f v e l o c i t y and C g a i n s one u n i t o f v e l o c i t y . Q.E.D. T h i s whole l i n e o f r e a s o n i n g i s obscure and p e c u l i a r . F o r i n s t a n c e , i t i s not a t a l l c l e a r why c e r t a i n o t h e r p o s s i b i l i t i e s a r e e x c l u d e d ; c o n s i d e r t h e f o l l o w i n g : B s t o p s dead and C c a r r i e s on w i t h f o u r u n i t s o f v e l o c i t y , o r t h e f o l l o w i n g : B rebounds w i t h two u n i t s o f v e l o c i t y and C i s i m p e l l e d w i t h two u n i t s o f v e l o c i t y . B o t h these p o s s i b i l i t i e s obey the l a w o f c o n s e r v a t i o n o f m o t i o n and seem " f a i r " t o B and C. S p i n o z a ' s argument has t h e same c h a r a c t e r as t h a t o f D e s c a r t e s ' s . He a l s o poses t h r e e p o s s i b i l i t i e s and r e j e c t s two of them as c o u n t e r t o t h e h y p o t h e s i s , w h i c h i s t h a t A and B are e q u a l . The major d i f f e r e n c e i s t h a t S p i n o z a does not c a r r y the argument from symmetry as f a r as D e s c a r t e s does, and t h e r e f o r e s t o p s s h o r t o f s p e c i f y i n g the r e s u l t a n t v e l o c i t i e s . E x a c t l y why he does so i s d i f f i c u l t t o d i s c o v e r , however. He may have f o u n d something repugnant about " s p l i t t i n g t he d i f f e r e n c e " between two cases b o t h o f w h i c h are c o n t r a r y t o t h e h y p o t h e s i s . He may have f o u n d something wrong w i t h e q u a t i n g a change from f o u r t o t h r e e u n i t s o f v e l o c i t y w i t h a change from r e s t t o one u n i t o f v e l o c i t y . Or he may have c o n s i d e r e d D e s c a r t e s * s whole l i n e o f argument r a t h e r shaky and f e l t i t was s a f e r t o r e s t r i c t h i m s e l f t o a more l i m i t e d c o n c l u s i o n . F o r l a c k o f e v i d e n c e as t o e x a c t l y what S p i n o z a c o n s i d e r e d wrong i n D e s c a r t e s ' s argument, we can o n l y c o n c l u d e t h a t he p r o b a b l y t h o u g h t i t was f a l l a c i o u s i n one way o r a n o t h e r . T h i s i n d i c a t e s t h a t S p i n o z a ' s arguments i n t h e P r i n c i p l e s are n o t m e r e l y f a i t h f u l c o p i e s o f D e s c a r t e s ' s r e a s o n i n g s , b u t t h a t t h e arguments a r e t h o u g h t t h r o u g h c a r e f u l l y and s t a t e d . i n h i s own terms. T h i s means, t h e n , t h a t i f we a r e t r y i n g t o d e c i d e how S p i n o z a f e l t about t h e C a r t e s i a n . p h y s i c s , we must l o o k f o r c l u e s i n the b a s i c p r e m i s s e s o f t h a t system, and not so much i n i t s d e t a i l s . 

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