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 I N SPINOZA'S PHYSICS by Jacob  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 P A R T I A L FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A. i n t h e Department of PHILOSOPHY  We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e qu i r e d / s t ^ i n d a r d  THE UNIVERSITY OF B R I T I S H COLUMBIA SEPTEMBER, 1969  In p r e s e n t i n g an  this  thesis  advanced degree at  the  Library  I further for  shall  the  his  of  this  agree that  written  University  of  permission  representatives. thesis  f u l f i l m e n t of  make i t f r e e l y  s c h o l a r l y p u r p o s e s may  by  in p a r t i a l  be  available for for extensive  g r a n t e d by  gain  permission.  Department  Date  the  It i s understood  for financial  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  British  Columbia  shall  requirements  Columbia,  Head o f my  be  I agree  r e f e r e n c e and copying of  that  not  the  that  Study.  this  thesis  Department  copying or  for  or  publication  allowed without  my  ABSTRACT  The  c e n t r a l a i m o f my  thesis i s to enquire  i n t o Spinoza's t h e o r y of the s t r u c t u r e of the universe.  physical  I t i s g e n e r a l l y accepted that from a  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 t h e u n i v e r s e as of p a r t i c l e s i n motion.  My m a j o r  scientific consisting  concern 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 his  cosmology.  as f a r a s t h i s  My b a s i c method o f e n q u i r y i s t o c o n s i d e r , i s p o s s i b l e , Spinoza's statements  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  about  theory, a  system  of p h y s i c s . C h a p t e r Two scientific  activities,  I n C h a p t e r Three i n P a r t Two  i s a b r i e f survey of b y way  of p r o v i d i n g  Spinoza's background.  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  of 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 e o r y , and t h e p r o b l e m s premisses.  a r i s i n g from those  I n Chapters Four, F i v e ,  that  basic  and S i x , t h e p h y s i c a l  theory of 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 .  Chapter Seven i s a f a i r l y  detailed  d i s c u s s i o n of the nature of the s i m p l e s t bodies i n Spinoza's system.  Chapter E i g h t i s a d i s c u s s i o n  S p i n o z a ' s concept of the u n i v e r s e as a system  of  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 e m p h a s i s on h i s i d e a s on t h e continuum. far  My m a j o r c o n c l u s i o n i s t h a t a s  as s c i e n t i f i c e x p l a n a t i o n i s concerned, t h e Spino-  z i s t i c physics as p r e s e n t e d  i s very s i m i l a r t o the Cartesian  i n the Principles of Cartesian  Philosophy.  This 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 : general  physics  (1)the  character of the physics of the Ethics i s quite  compatible exception: crepancy;  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 a p p a r e n t I give an e x p l a n a t i o n o f t h i s apparent (2)  dis-  S p i n o z a ' s deep c o n c e r n w i t h t h e p r o b l e m s  o f t h e c o n t i n u u m c a n 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 r e t h e same a s t h a t o f t h e Cartesian physics;  (3)  t h e 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 t h e vacuum;  (4)  there i s nothing  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 of C a r t e s i a n Philosophy;  (5)  t h e 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 i s based on a fundamental m e t a p h y s i c a l  physics  i s s u e a n d h a s 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  m a j o r 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 c a n n o t be f u l l y understood unless they are i n t e r p r e t e d i n the context of t h e C a r t e s i a n  cosmology.  iv  TABLE OF CONTENTS  ABSTRACT TABLE OF CONTENTS ACKNOWLEDGEMENT CHAPTER I :  INTRODUCTION  CHAPTER I I :  SPINOZA'S S C I E N T I F I C A C T I V I T I E S  CHAPTER  THE CARTESIAN PHYSICS  III:  CHAPTER I V :  THE PHYSICS OF THE ETHICS  CHAPTER V:  THE THEORY OF INDIVIDUALS  CHAPTER V I :  MOTION I N SPINOZA'S PHYSICS  CHAPTER V I I :  THE CORPORA S I M P L I C I S S I M A  CHAPTER V I I I :  MOTION AND PARTICLES  BIBLIOGRAPHY APPENDIX A:  SPINOZA'S LIBRARY  APPENDIX B:  THE HYDROSTATIC EXPERIMENT  APPENDIX C:  THE S I X T H 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 suggestions and c r i t i c i s m s ,  and t o t h e 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 made my s t u d i e s p o s s i b l e . my w i f e , J e a n , f o r h e r h e l p  Remnant f o r h i s  assistance  which  I e s p e c i a l l y wish t o thank and encouragement.  CHAPTER I INTRODUCTION  The b a s i c p u r p o s e o f t h i s t h e s i s i s t o e x p l o r e the c h a r a c t e r o f t h e primary p a r t i c l e s and o f motion i n Spinoza's As  s y s t e m , and t h e r o l e t h e y p l a y i n h i s cosmology.  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  Spinoza's  t h e o r y has n o t r e c e i v e d a v e r y c l o s e  and y e t , a s I w i l l of Spinoza's  scrutiny,  show, a number o f i n t e r e s t i n g f a c e t s  thought  a r e r e v e a l e d when h i s i d e a s o n t h e  foundations of p h y s i c a l science are explored. 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 Spinoza's is,  on  p h y s i c s from a metaphysical p o i n t o f view,  that  a s 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 ;  but  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 d o e s n o t seem t o h a v e h a d t h e b e n e f i t o f a close examination.  This concerns  of the simplest bodies  p a r t i c u l a r l y the nature  and m o t i o n i n h i s system;  that  Spinoza viewed 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 b e g e n e r a l l y a g r e e d how h i s scheme w o r k s i n d e t a i l ,  on, b u t e x a c t l y  and p r e c i s e l y what t h e  nature o f these p a r t i c l e s i s , remains obscure. ing of Spinoza's has  writings, especially his  My  read-  correspondence,  c o n v i n c e d me t h a t h e h a d a l w a y s i n m i n d 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 m e c h a n i c s , o r a t l e a s t  to l a y a s o l i d foundation be his  based.  My  on w h i c h s u c h a s c i e n c e  e m p h a s i s , t h e r e f o r e , w i l l be  ideas i n that l i g h t ,  program f o r p h y s i c a l  on  treating  t o c o n s i d e r h i s scheme, a s  obstacle  i n t h e way  of t h i s  of p r o j e c t i s the p a u c i t y of a v a i l a b l e m a t e r i a l . three p r i n c i p a l sources are the P r i n c i p l e s of  a few  published in  ( h e r e a f t e r t o be  l e t t e r s and  abbreviated  as  has  that i t purports  The  Cartesian  The  t o be m e r e l y an e x p o s i t i o n o f  and  s u p p o s e d l y does not  own  ideas.  The  E t h i c s , w h i c h can  his  ideas  represent be  i n t h e i r m o s t c o m p l e t e and  t a k e n as  explanation.  The  dressed and  representing  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 those  contain extensive  1662,  theory  ad-  April  d i s c u s s i o n s , but  later  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  information.  little  Hence I have t a k e n t h e p h y s i c a l  o f the E t h i c s as t h e key  source of  1663,  their  to Spinoza's  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 concrete  and  o f d i s c u s s i o n , comment o r  i s somewhat l i m i t e d w i t h r e s p e c t  ideas.  Descartes'  f u l l y developed form,  t o O l d e n b u r g and w r i t t e n i n A p r i l  J u n e 1663,  value  i n t h e way  source,  Spinoza's  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, little  Principles  t h e s e r i o u s d i s a d v a n t a g e as a  philosophy,  contains very  kind  "Principles"),  a few p a g e s i n t h e E t h i c s .  i n 1663,  a  science.  A formidable  Philosophy  i s to  information,  and  and  the  f i n a l a r b i t e r on w h a t S p i n o z a ' s l a t e s t a n d  f u l l y developed views are. considerable  most  However, I have d e v o t e d  amount o f a t t e n t i o n t o t h e p h y s i c s o f  P r i n c i p l e s , the t h i r d chapter,  a the  reasons f o r w h i c h I have o u t l i n e d i n the which contains a d i s c u s s i o n of that physics.  This thesis i s necessarily l i m i t e d i n several ways.  For  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 i s rather important  i n i t s own  r i g h t , but which  course  deserves  a more t h o 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 here.  A full  treatment  o f t h i s t o p i c c a n be  found i n  R i c h a r d M c K e o n ' s ^ b o o k , w h i c h I h a v e f o u n d t o be v a l u a b l e source Spinoza  and  of ideas;  the chapter  especially useful.  the chapter  on e x p e r i m e n t a l  an i n -  on D e s c a r t e s science  and  are  McKeon b a s e s h i s d i s c u s s i o n o f  Spinoza's  s c i e n t i f i c m e t h o d l a r g e l y on t h e d i s p u t e b e t w e e n R o b e r t Boyle  and  Spinoza  on t h e n a t u r e  o f h a r d n e s s , s o f t n e s s and  o f n i t r e and  fluidity.  the  character  This dispute, which  i s f o u n d , i n the correspondence w i t h Henry Oldenburg, not been a n a l y z e d reasons;  one  has  i n detail i n this thesis, for several  i s that i t i s rather involved, e s p e c i a l l y  because o f O l d e n b u r g ' s r o l e as an i n t e r m e d i a r y i n the dispute.  Second, the d i s p u t e dates from the  same p e r i o d  as t h e w r i t i n g o f t h e P r i n c i p l e s , a n d h e n c e 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  Third, i t schief usefulness method, w h i c h i s o u t s i d e the  i s i n the area  of s c i e n t i f i c  t h e scope o f t h i s t h e s i s ,  s u b j e c t c a n n o t be a v o i d e d  although  altogether.  A n o t h e r l i m i t a t i o n w h i c h I h a v e h a d t o s e t mys e l f i n the w r i t i n g of t h i s thesis consists of avoiding a d i s c u s s i o n of Spinoza's philosophy  i n broader terms.  P l e n t y o f commentary o n t h a t s u b j e c t e x i s t s a l r e a d y , a n d , besides, order  my p u r p o s e i s t o e x p l o r e  Spinoza's physics i n  t o s h e d l i g h t o n h i s l a r g e r scheme, a n d n o t v i c e  versa.  N o n e t h e l e s s , I have h a d t o t a k e  certain parts of  h i s doctrine f o r granted  a s common k n o w l e d g e .  I have t a k e n f o r g r a n t e d  h i s points of doctrine that  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  For instance, there  i s a perfect  p a r a l l e l i s m between t h e a t t r i b u t e s o f Thought and o f Extension, stance.  and t h a t there  A reference  i s no c r e a t o r o u t s i d e o f sub-  t o Spinoza's general p h i l o s o p h i c a l  s y s t e m 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 w h a t he s a y s i n t h e E t h i c s , b u t I h a v e t r i e d t o avoid misrepresenting  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 o n s p e c i f i c p o i n t s o f d o c t r i n e . taken care  t o a v o i d becoming entangled  i n the p h i l o s o p h i c a l  disagreements between D e s c a r t e s and S p i n o z a . t h i s work, r e f e r e n c e s  Throughout  t o Descartes are almost e x c l u s i v e l y  l i m i t e d t o the material of the P r i n c i p l e s ; occasion  I have  when I h a v e  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 the physics of the P r i n c i p l e s , leaving 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 theory represents Descartes's Spinoza's i d e a s , not those  ideas.  of Descartes's.  S e e McKeon, p a g e s 1 3 7 - 1 5 7 . t o t h e appended l i s t o f w o r k s ) . x  My a i m i s t o d i s c u s s  ( A l l references are  6 CHAPTER I I SPINOZA'S S C I E N T I F I C A C T I V I T I E S  S p i n o z a was  undoubtedly  i n s c i e n t i f i c matters.  The  list  a w e l l educated  man  o f b o o k s 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 have appended t h i s l i s t , He was  a l l of the  d e v e l o p m e n t s o f h i s t i m e , a n d he was  and  scientific  always a s k i n g h i s  f o r i n f o r m a t i o n about the l a t e s t  d i s c o v e r i e s . He was  experiments  thoroughly f a m i l i a r with  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 w e r e much a p a r t o f t h e m a i n s t r e a m o f t h e o f t h a t age.  H i s d i s p u t e w i t h Robert  scientific  work; without  of the nature of Boyle's  the very  thought  Boyle on the  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 good u n d e r s t a n d i n g  (I  t o g e t h e r w i t h some c o m m e n t s ) .  acquainted w i t h almost  correspondents  of t h i s  who  topic had  a  scientific  h i s c r i t i c i s m s of Boyle, although not  completely  f l a w s , were w e l l f o u n d e d and q u i t e s o p h i s t i c a t e d . ^ Aside from 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  his  t i m e , S p i n o z a was  involved.  S u p r i s i n g l y , f o r a man  a l i s t p h i l o s o p h e r , he 2  experimental work. experiment  a l s o t o some e x t e n t more who  directly  i s labeled a  ration-  c a r r i e d o u t a s m a l l amount o f  There i s f i r s t of a l l the h y d r o s t a t i c  d e s c r i b e d i n the l e t t e r t o J a r i g J e l l e s  S e p t e m b e r 1669,  of  w h i c h i s f a i r l y e l a b o r a t e and  of  carefully  7 set  up.  The  f i r s t p a r t of the experiment i s designed 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 t u b e s 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  The  will  second h a l f  of  experiment i s b e t t e r d e s c r i b e d as a hydrodynamic  experiment, because i t d e a l s w i t h r a t e s of f l o w of water. The  second p a r t o f the experiment i s r a t h e r  interesting  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 u s e d 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 t h e 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 h a v e  a p p e n d e d 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).  Another set of experiments i s connected w i t h the  nitre dispute;  the  l e t t e r o f A p r i l 1662  are  u n d e r t a k e n b y S p i n o z a n o t s o much o u t o f w h a t  might c a l l  the d e s c r i p t i o n of these i s found i n t o Oldenburg.  sheer s c i e n t i f i c  These e x p e r i m e n t s we  c u r i o s i t y , but t o prove  a  c e r t a i n p o i n t , the point being that h i s explanations of the of  c h a r a c t e r o f n i t r e a r e a t l e a s t as p l a u s i b l e a s t h o s e 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 t h e e l a b o r a t e ones t h a t B o y l e performed.  has  A c c o r d i n g l y , Spinoza's experiments are  rather simple. Another experiment which Spinoza describes, does n o t p e r f o r m , i s m e n t i o n e d 1662  t o Oldenburg.  but  i n the l e t t e r of A p r i l  I t s p u r p o s e i s t o compare a t m o s p h e r i c  8  pressure i n a h o r i z o n t a l plane with that i n a v e r t i c a l p l a n e , w h i c h i s done b y t a k i n g m e a s u r e m e n t s 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 s m o o t h l y p o l i s h e d p i e c e s o f marble.  This experiment  may n o t b e o r i g i n a l w i t h  Spinoza, 3  s x n c e m e n t x o n i s made o f i t b y D e s c a r t e s  and others ;  t h e p o i n t o f i n t e r e s t i s t h a t he d o e s n o t f e e l  sufficiently  c u r i o u s about t h e r e s u l t o f such an experiment it,  i t seems.  T h i s apparent  i n t h e other experiments is  t o execute  lack of c u r i o s i t y i s evident  as w e l l ;  a s s o o n a s some p o i n t  sufficiently well established, i n h i sopinion,  loses interest.  What s t a n d s  experimental a c t i v i t i e s , and w o r k i s c o n c e r n e d ,  out c l e a r l y from  Spinoza  Spinoza's  i s t h a t a s f a r a s h i s own  life  he d o e s n o t a t t a c h a g r e a t d e a l o f  importance  t o experimentation.  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 a n  e s s e n t i a l element o f s c i e n t i f i c  On t h e o t h e r h a n d , w h e t h e r  a c t i v i t y i s out of the  scope o f t h i s t h e s i s t o d e t e r m i n e . that experiments  He may h a v e  were v e r y i m p o r t a n t w h i l e b e i n g  thought content  t o l e t o t h e r s c a r r y them o u t , o r he may h a v e t h o u g h t experiments t o thought.  were i n c i d e n t a l and s e r v e d m e r e l y The e v i d e n c e  that  as an a i d  i s somewhat c o n t r a d i c t o r y o n  this point. The m a j o r p o r t i o n o f S p i n o z a ' s was i n t h e f i e l d o f g e o m e t r i c a l o p t i c s .  s c i e n t i f i c work His reputation  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 a n d w i d e s p r e a d .  Leibniz,  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 y s t o him:  t h e o t h e r p r a i s e s o f y o u w h i c h fame has I understand i s your great sends a l o n g  skill  "Among  b r u i t e d abroad,  in optics."  Leibniz  a t e c h n i c a l p a p e r f o r comment, and  they  discuss the problem of s p h e r i c a l a b e r r a t i o n i n lens There are high  numerous o t h e r  items which a t t e s t t o  l e v e l o f competence i n o p t i c a l s c i e n c e .  t o J a r i g J e l l e s , d a t e d M a r c h 25, m e t r i c a l l y and  i n d e t a i l , how  1667,  the eye  he  systems.  Spinoza's In a  letter  discusses,  geo-  s e e s a n image  pro-  duced by  a telescope.  I n a l e t t e r t o J o h n Hudde, J u n e  1666,  describes  compares t h e o p t i c a l  he  of various  and  l e n s shapes.  properties  T h e r e a r e a l s o a number o f  items  d e a l i n g w i t h p r a c t i c a l p r o b l e m s o f l e n s g r i n d i n g , one w h i c h s h o u l d be Huygens h a s  reported  constructed  i f o n l y because i t i s amusing. a l e n s p o l i s h i n g machine *, 4  S p i n o z a i s opposed t o a u t o m a t i o n , and although  he  i s not a c q u a i n t e d  believes that,  "...  experience  has  taught  s u f f i c i e n t l y that i n spherical tools i t i s safer  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 h a n d by  but  w i t h such a machine, manual  methods a r e p r e f e r a b l e , because me  any  of  and than  machine". S p i n o z a ' s o n l y m a j o r work i n o p t i c a l  science  i s h i s T r e a t i s e on t h e R a i n b o w ^ , w h i c h i s a d e t a i l e d c a r e f u l l y worked out 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 s i z e s of b o t h p r i m a r y and  secondary rainbows.  It is  and angular really  more a n e x e r c i s e i n g e o m e t r y a n d work of p h y s i c a l s c i e n c e , sented  t o the reader  b r i e f e x p l a n a t i o n of the The  Descartes,  although  the work i s p r e improving  i t also contains  cause of the  colours of  i s i n terms of the  of the  the  strongest,  and  spectrum, the weakest.  o f w a t e r , the weaker c o l o u r s are stronger  get through.  distance  i n w a t e r show t h e o t h e r  theory  vague and  i s not  years l a t e r ,  s o r t e d out,  only  i t is a  shorter  fairly  Newton, a  gave t h e c o r r e c t e x p l a n a t i o n ,  possessing  the  i n t h e t r e a t i s e i s somewhat  developed i n d e t a i l , but  of r e f r a c t i o n .  of  c o l o u r s more s t r o n g l y .  namely  resolved a  into,  slightly  I n r e t r o s p e c t i t seems  a sound s c i e n t i f i c  u n d o u b t e d m a t h e m a t i c a l c o m p e t e n c e , was  background i n a good  p o s i t i o n t o h a v e made t h i s d i s c o v e r y h i m s e l f , b u t he  the  thickness  and  l i g h t of d i f f e r e n t c o l o u r s , each c o l o u r having  and  on  Of t h e s e r a y s  t h a t w h i t e l i g h t i s composed o f , o r c a n be  d i f f e r e n t index  to strength  Rays w h i c h t r a v e l t h r o u g h a  as i t i s p r e s e n t e d  that Spinoza,  the  violet,  plausible explanation of colour dispersion. few  a  d i f f e r e n t degrees of  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  The  a  explanation, which Spinoza a t t r i b u t e s  of c o l o u r s , red being o t h e r end  indeed,  than  a s a means o f t e s t i n g a n d  h i s mathematical a b i l i t y ,  rainbow.  and  trigonometry,  f e l t t h a t t h e o t h e r e x p l a n a t i o n was  quite  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  likely  adequate, Treatise  f o r having  given i t .  Apart from the  question  d i s p e r s i o n , the T r e a t i s e says n o t h i n g of l i g h t ,  although  o f l i g h t was  may  much t h e  The l i e s i n the  we  nature  assume t h a t S p i n o z a ' s  theory  Descartes's^.  s i g n i f i c a n c e o f S p i n o z a ' s work on  f a c t that geometrical F r o m two  the l a w o f r e f l e c t i o n , and using only geometrical  deductive  simple, basic  elements,  the r u l e s of r e f r a c t i o n ,  and  methods, i t i s p o s s i b l e t o deduce  rainbows, and bent s t i c k s i n water.  telescopes,  I t i s the  science  famous i d e n t i f i c a t i o n o f  physics  w i t h geometry i s c l o s e s t t o b e i n g  the  optics  optics i s a  a l a r g e number o f c o m p l e x r e l a t i o n s h i p s a b o u t  f o r which Descartes's  colour  about the  same as t h a t o f  science par excellence.  conjecture  of  true.  I t i s a plausible  that Spinoza v i s u a l i z e d a p h y s i c a l science  same e l e g a n c e a n d p r e c i s i o n t h a t i s  of o p t i c s , a science  b a s e d on  a few  characteristic  axioms and  f r o m w h i c h a l l t h e c o m p l e x phenomena c a n be All  in all,  S p i n o z a was  definitions  deduced.  r i g h t i n the midst  t h i n g s s c i e n t i f i c , and  i n view of h i s involvement  the  and  science  o f h i s day  with  of  with  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 t h e R a i n b o w 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 o f t h e w o r k o f s u c h men But  the reason i s not  played  scope and  impact  as G a l i l e o , D e s c a r t e s o r H u y g e n s .  hard to f i n d ;  only a subordinate  role;  f o r Spinoza  science  h i s c h i e f a i m was  the  12 improvement o f the u n d e r s t a n d i n g and  i n h i s ambitious  considered  i n t h e most g e n e r a l  program s c i e n t i f i c knowledge  as a means t o a n e n d  only.  g o o d s t a t e m e n t o f t h i s i n h i s own The  Improvement of the  We  have a  w o r d s as  sense  was very  found i n  Understanding:  T h u s 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 e n d and a i m , s o t h a t we may a t t a i n t o t h e supreme human p e r f e c t i o n w h i c h I h a v e named? a n d , 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 serve t o promote our o b j e c t w i l l h a v e 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 of a p h i l o s o p h e r it and  i s s a f e t o say,  out  and  only incidentally,  H i s e n t e r p r i s e was  i n w h i c h e v e r y t h i n g was ferreting  of  scientist,  i n r e t r o s p e c t , t h a t S p i n o z a was  foremost a philosopher  of science.  and t h a t o f a  a  the  patient  t r u t h s about the nature  perhaps b e s t e x e m p l i f i e d by  of  t h e w o r k o f B o y l e , was  of secondary importance, although  he was  a l w a y s an  e s t e d s p e c t a t o r of the a c t i v i t i e s of others  in  t h a t of a p h i l o s o p h e r  e s p e c i a l l y as a p p l y i n g t o the own  work serves  his  intersts  f o r the  for  a  artificial,  even though h i s  Spinoza's over-  l a r g e r more a b s t r a c t i s s u e s ,  cover a wide spectrum, from the  him  inter-  seventeenth century.  as a c a s e i n p o i n t :  r i d i n g c o n c e r n was  i s somewhat  things,  science.  Making a d i s t i n c t i o n between the work of s c i e n t i s t and  man  t o c o n s t r u c t a scheme  e x p l a i n a b l e , and  "little"  first  properties  o f n i t r e t o t h e 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 a n d t e m p e r a m e n t q u i t e d i f f e r e n t t h a t o f s u c h men a s B o y l e a n d H u y g e n 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  from  Hence, what i s  i d e a s does n o t 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  referred to  a b o v e , 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 matter,  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 , t h e f u n d a m e n t a l e l e m e n t s of s c i e n t i f i c explanation.  I n t h i s connection, 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 and  i t i s t h i s t h e o r y which i s the main concern  interest, of this  thesis.  •^See McKeon, page 1 5 6 . 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 t h e p a s s a g e 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 connection w i t h t h i s theory o f the rainbow. See S c o t t , p a g e 74. J  S e e S c o t t , page 12.  4  S e e Wolf, pages 423-425.  ^ F o r comments o n t h e a u t h e n t i c i t y o f t h i s w o r k , see G e b h a r d t , p a g e s 4 3 1 - 4 3 4 . 6  S e e S c o t t , pages 28-63.  1  14 CHAPTER I I I THE CARTESIAN PHYSICS  T h r e e c o n s i d e r a t i o n s make t h e d i s c u s s i o n o f the Cartesian physics  relevant t o the topic of this  thesis: (a)  The C a r t e s i a n p h y s i c s  Spinoza's physics. very  i s i n some way a l s o  Spinoza studied Descartes's  theories  c l o s e l y , and p a i d t r i b u t e t o Descartes*s  and h i s k e e n mind^.  intelligence  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 involvement w i t h the Cartesian i d e a s , and w h i l e Descartes's  t h a t work i s supposed t o represent  thought, and n o t Spinoza's,  t o what e x t e n t  i t i s uncertain  a n d 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 those o f Descartes.  When t h e 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 M e y e r m e n t i o n s t h e w i l l , existence  the i n t e l l e c t , the  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 Descartes.  with  There i s no m e n t i o n o f a d i v e r g e n c e  t h i n g s as t h e n a t u r e  o f motion, the character  s c i e n t i f i c method, laws o f m o t i o n , e t c . .  on s u c h  of particles,  I n the l e t t e r t o  O l d e n b u r g , w r i t t e n i n November 1665 ( t w o y e a r s a f t e r t h e p u b l i c a t i o n of the P r i n c i p l e s } , Spinoza As  says:  t o your next remark, t h a t I h i n t e d t h a t t h e  C a r t e s i a n laws o f motion 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 M r . H u y g e n s t h i n k s so. Nor d i d I s a y t h a t any l a w i s f a l s e e x c e p t t h e 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 a r e 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 the exact p o i n t of dispute w i t h regard m o t i o n , w i t h one e x c e p t i o n ,  perhaps:  S p i n o z a i s s e e n t o amend D e s c a r t e s ' s slightly.  t o these laws o f i n the P r i n c i p l e s  s i x t h rule o f motion  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  h e n c e , f r o m t h i s r e m a r k a l o n e i t must r e m a i n 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 a b o u t t h e C a r t e s i a n (b)  physics.  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 a s  a modification of the e a r l i e r physics. 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  From t h e v e r y  were s o c l o s e  i n t i m e a n d t h a t S p i n o z a was t h o r o u g h l y  versed  together i n Descartes'  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 Spinoza began where D e s c a r t e s l e f t o f f . the Cartesian physics ing  Studying  the ramifications of  should be,useful  of Spinoza's physics.  Besides,  f o r the understand-  there  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 .  a r e a number o f For instance,  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 i n the Ethics f i t s Principles;  i n q u i t e w e l l w i t h the physics  i n the dispute with Boyle,  theoretical explanations i n character.  fluidity  Spinoza  which, a r e e s s e n t i a l l y  Also, with regard  of the gives  Cartesian  t o the existance  of a  16 vacuum, and t o be  the nature  a great (c)  of reference Descartes*s  o f s c i e n t i f i c method, t h e r e  d e a l i n common i n t h e i r The  Cartesian physics  f o r the  at t h a t time and  had  ideas. forms a u s e f u l frame  discussion of Spinoza's  c o s m o l o g y and  ideas.  t h e o r i e s o f m a t t e r were dominant  a powerful  C h r i s t i a n H u y g e n s , t o name one  i n f l u e n c e o v e r men example;  a p p e a r a n c e o f Newton's t h e o r i e s .  then,  The  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  o f t h a t age,  and as  like  h i s vortex  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 , the  seems  theory  even a f t e r  Cartesian  physics,  scientific  such i s q u i t e r e l e v a n t t o  ideas  Spinoza's  physics. Because the s c i e n t i f i c i d e a s of D e s c a r t e s not  the  c e n t r a l t o p i c of t h i s t h e s i s , the  n a t u r a l l y h a v e t o be way  of doing  s e c o n d and I will  somewhat l i m i t e d .  h a v e some b e a r i n g the c h a r a c t e r Of  The  Principles.  discuss only those aspects  system.  most  on  will  appropriate the  Furthermore,  o f the P r i n c i p l e s which  the main t o p i c o f t h i s t h e s i s , namely  o f the p a r t i c l e s and  of motion i n Spinoza's  course i n a sense a l l o f the 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 Spinoza, disagrees  discussion  t h i s i s to r e s t r i c t the d i s c u s s i o n t o  t h i r d p a r t s of the  are  even though  he  w i t h D e s c a r t e s o n 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 w h o l e scheme i n h i s own  Descartes,  words.  but works out  I t i s obvious that  he  the  17  takes  Descartes's  a l s o c l e a r t h a t he  physics  q u i t e s e r i o u s l y , and  i t is  doesn't i n t e n t i o n a l l y include  proofs  t h a t a r e l o g i c a l l y unsound, so t h a t e v e n i f t h e are  false  i n h i s o p i n i o n , the  interest.  reasoning  propositions  would s t i l l  be  However, i n t h e m a i n , t h e P r i n c i p l e s i s  a w o r k o n D e s c a r t e s 's p h y s i c s , and  therefore  of c e r t a i n problems would n a t u r a l l y tend discussion of Descartes's closer to understanding  ideas  of  still  a discussion  t o be  merely a  a n d w o u l d b r i n g us  no  what S p i n o z a ' s i d e a s were.  There-  f o r e I have s e l e c t e d t h o s e p r o b l e m s f o r d i s c u s s i o n w h i c h I t h i n k are r e l e v a n t to the 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 physics I will  of the P r i n c i p l e s r e p r e s e n t s refer to that physics  simply  Spinoza's as the  the  theory,  "Cartesian  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 extent By  the  "Cartesian physics" i s a l s o Spinoza's  t h e t e r m I s h a l l n o t be  Descartes's  r e f e r r i n g to the whole  t h e o r i e s of the p h y s i c a l world, which  of includes  a l a r g e number o f i t e m s n o t  discussed  s u c h as the v o r t i c a l t h e o r y  o f the s o l a r system, the  o f h e a t and  light,  i n the  physics.  Principles, nature  the three kinds of matter, g r a v i t y ,  etc.. The  P r i n c i p l e s , not counting  w h i c h i s an a p p e n d i x , i s c a s t i n t h e  the C o g i t a t a  geometric form.  Metaphysica, Part  Two  b e g i n s w i t h a s t a t e m e n t o f n i n e d e f i n i t i o n s and  one  axioms;  P a r t One,  twenty-  f r o m 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  a number o f p r o p o s i t i o n s a r e e s t a b l i s h e d .  b a s i c assumption, axiom, o r p o s t u l a t e substance i s extension.  2  The  . i s that physical  A l l the p r o p e r t i e s of  bodies  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 , w a r m t h and ness, e t c . , are senses.  s e c o n d a r y p r o p e r t i e s , d e p e n d e n t on  Proposition 2 states:  matter consists i n extension  "The  of the C a r t e s i a n p h y s i c s ; same".  nature  alone".  t h i s p r o p o s i t i o n sums up n i c e l y t h e  are the  to  The  the  of body  or  Corollary to  fundamental  i t states:  cold-  feature  "Space and  What makes t h e C a r t e s i a n p h y s i c s  Body so  r a d i c a l l y d i f f e r e n t from the Newtonian^ system, i s the treatment of the two  c o n c e p t o f mass.  I n the Newtonian system  d i s t i n c t q u a n t i t i e s apply to bodies,  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 , s o t h a t s o l i d b o d i e s have the versa,  same s i z e b u t  and  d i f f e r e n t w e i g h t and  a g i v e n body can  c h a n g i n g i t s mass o r w e i g h t , i . e . c a n  body.  This  Proposition  can  mass, o r v i c e  change i t s v o l u m e  I n t h e C a r t e s i a n s y s t e m , o n l y one  .  without  change i t s d e n s i t y .  quantity applies to  solid  i s c l e a r l y expressed i n the C o r o l l a r y to 4:  B o d i e s w h i c h o c c u p y a n e q u a l amount o f s p a c e , a s f o r example some g o l d and b r a s s , h a v e an e q u a l amount o f matter or of c o r p o r e a l substance. The  mass o f a b o d y i s t h e  same as i t s t r u e s i z e , t h e  volume  19  i t w o u l d o c c u p y i f t h e m a t e r i a l o f t h e body were  redis-  t r i b u t e d s o t h a t t h e r e w e r e no p o r e s o r i n t e r s t i c e s  left.  To e x p l a i n t h e commonly o b s e r v e d phenomenon o f c o n d e n s a t i o n a n d r a r e f a c t i o n , t h e example o f a sponge i s u s e d i n the demonstration  t o Lemma 2.  When a b o d y i s s e e n t o  change i t s v o l u m e , 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 dimensions, while  t h e i n t e r s t i c e s between t h e p a r t s o f t h e  b o d y 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 h a s t h e  i m m e d i a t e c o n s e q u e n c e t h a t a vacuum d o e s n o t e x i s t . vacuum i s d e f i n e d a s s p a c e 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 . note t h a t the non-existence contingent  I t i s important t o  o f a vacuum i s n o t m e r e l y a  f a c t about nature,  i t i sa logical truth  f r o m t h e meaning o f t h e b a s i c terms.  a r e o n l y apparent vacua.  of Philosophy,  Descartes,  ( n o t t o be c o n f u s e d  derived  The v a c u a p r o d u c e d  e x p e r i m e n t a l l y by such people as Von Guericke Boyle  A  and Robert  i nhis  Principles  with Spinoza's  Principles  of Cartesian Philosophy), 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 b e t w e e n 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 n o t f i n d t h e 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  absolute  matter.  vacua, which a r eplaces  devoid o f  When someone r e m o v e s a i r f r o m a c o n t a i n e r ,  e l s e m u s t f l o w i n , some e x c e e d i n g l y can  completely  something  f i n e m a t e r i a l which  flow through the w a l l s o f the c o n t a i n e r . 4  Insofar as  20  t h e r e i s no e v i d e n c e assume t h a t S p i n o z a ' s  to the contrary, i t i s reasonable i d e a s on  t h i s p o i n t were t h e  to  same.  Another major f e a t u r e o f the 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 , exist.  I t i s p a r t o f the  i s always d i v i s i b l e . be  do  not  concept of extension t h a t  Axiom 9 says:  d i v i d e d , at l e a s t , i n thought.".  " A l lextension A great deal  on t h e p h r a s e " a t l e a s t i n t h o u g h t " ,  as I w i l l  extension can  hinges  elaborate  shortly. Although  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  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 t h e l e s s b a s e d on p a r t i c l e s .  To e v a l u a t e  o f t h e C a r t e s i a n p a r t i c l e s and c o s m o l o g y , we  the  the general  are  never-  character  Cartesian  t u r n t o the 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 b y God i n t o p a r t i c l e s a s n e a r l y a s 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 , h o w e v e r , f r o m w h i c h now t h e h e a v e n s a n d t h e s t a r s a r e composed w e r e n o t s p h e r i c a l , f o r a number o f s p h e r e s j o i n e d t o g e t h e r do n o t 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 a s much m o t i o n a s t h e r e i s i n t h e w o r l d t o d a y and t h e y w e r e a l l m o v i n g w i t h an e q u a l v e l o c i t y . Since the c r e a t i o n of the u n i v e r s e p a r t i c l e s of a l l s o r t s o f s i z e s and  shapes developed  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 All  see  today.  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  particles  21 i n motion.  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 a n d c a u s a l  explanations,  a theory  needed.  theory  This  inclusive.  This  of the behaviour o f p a r t i c l e s i s  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,  theory  c a n be d i v i d e d i n two p a r t s :  pertaining t o bodies i n i s o l a t i o n , bodies i n c o l l i s i o n . in  (b)  pertaining to  A body i n motion tends t o  s t r a i g h t l i n e motion, i . e . i t w i l l  continue  continue  i n a  s t r a i g h t l i n e with undiminished v e l o c i t y unless acts w i t h other bodies  (a)  i t inter-  (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 1 5 , 16 a n d 1 7 ) . or law f o r bodies a t r e s t ;  T h e r e i s no c o r r e s p o n d i n g t h i s i s important,  rule  a s wa  s h a l l see. As  regards bodies i n c o l l i s i o n the f i r s t  o r l a w i s t h a t i n an impact t h e r e (see  Propositions  i s no l o s s o f m o t i o n  18, 20, 21, 2 2 ) .  Note a t t h i s  point  that motion i s not merely v e l o c i t y i n the Cartesian the  rule  physics,  amount o f m o t i o n t h a t a b o d y p o s s e s s e s i s d e p e n d e n t  on b o t h t h e s i z e and t h e v e l o c i t y o f t h e body. this  i s not stated e x p l i c i t l y ,  Although  the quantity^ o f motion  o f a body i s a c t u a l l y j u s t t h e p r o d u c t o f i t s s i z e and velocity.  I n a n y c o l l i s i o n b e t w e e n two b o d i e s ,  the t o t a l  q u a n t i t y i f conserved. Following given  the statement o f t h i s law there are  a number o f p r o p o s i t i o n s  more d e t a i l .  dealing with  I n Descartes's P r i n c i p l e s of  collisions i n Philosophy  ( p a r a g r a p h s 46 t o 52 i n c l u s i v e ) seven r u l e s  o f motion.  are found h i s  Spinoza states  some r e l a t i v e l y m i n o r a n d n o t o b v i o u s l y  well-known  these rules  with  significant  modifications  ( o f w h i c h I have a l r e a d y mentioned t h e  sixth rule).  He a l s o  series, are  ostensibly  g i v e n below;  a d d s one e x t r a  to f i l l  a gap.  proposition  t o the  These p r o p o s i t i o n s  f o r t h e sake o f c l a r i t y ,  I have  given  them i n my own w o r d s : Proposition  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 , each w i l l the  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 . Proposition  different one  return i n  will  25 ( R u l e # 2 ) :  I f two b o d i e s w i t h  s i z e s , but equal v e l o c i t i e s , c o l l i d e , the smaller be r e f l e c t e d  i n the opposite d i r e c t i o n with i t s  o r i g i n a l v e l o c i t y , while the larger  one r e t a i n s  both 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 . Proposition ferent size  26:  I f two b o d i e s have b o t h  dif-  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  i s t h e same f o r b o t h , t h e n u p o n c o l l i s i o n  bodies w i l l  both  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 .  Proposition  27 ( R u l e # 3 ) :  I f two b o d i e s o f  equal size but with 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  give half  slower body and they w i l l d i r e c t i o n of the faster  o f i t s excess v e l o c i t y t o the b o t h move o n t o g e t h e r i n t h e  body.  23 P r o p o s i t i o n 28 ( R u l e # 4 ) : is  I f a body a t r e s t  s t r u c k b y a s m a l l e r b o d y , t h e n , n o m a t t e r how g r e a t  the 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  will  remain a t r e s t , w h i l e the s m a l l e r i s d e f l e c t e d a t an angle, r e t a i n i n g i t s o r i g i n a l  velocity.  P r o p o s i t i o n 29 ( R u l e # 5 ) : is  I f t h e body a t r e s t  s m a l l e r t h a n t h e i m p i n g i n g b o d y , 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 b o d y moves, i t w i l l of  g i v e up p a r t  i t s v e l o c i t y t o t h e b o d y a t r e s t s o 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 b y a body o f e q u a l s i z e , t h e f i r s t body  will  be i m p e l l e d a n d t h e s e c o n d b o d y w i l l b e 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 b o d y , A, i s  m o v i n g f a s t e r t h a n , b u t i n t h e same d i r e c t i o n a s a n o t h e r b o d y , B, t h e n e i t h e r of  (a) 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  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  which case A w i l l they 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 a n d  b o t h move o n 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 a n d 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 its original  be r e f l e c t e d b a c k w h i l e B moves o n , e a c h w i t h velocity.  Two a s p e c t s o f t h e s e s e v e n l a w s o f m o t i o n out immediately.  stand  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  criticized  on  t h i s c o u n t b y many.  Scott  0  m e n t i o n s one c o n t e m p o r a r y  c r i t i c i s m . d i r e c t e d at the fourth rule. experience  that a very  I t i s a common  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, s a y a c a n n o n b a l l , high velocity, w i l l object, the  c a u s e some movement i n t h e l a r g e  contrary t o the fourth rule, which states  s m a l l e r body w i l l bounce back, w h i l e  remains a t r e s t .  with  that  the l a r g e r body  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. B r o a d  who s t a t e s  that  ...some l a w s 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 t h e y a r e p e r f e c t l y i n e l a s t i c a n d o t h e r s u n d e r no c o n d i t i o n s w h a t e v e r . Two c o n s i d e r a t i o n s make t h i s First,  misleading.  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  regarding two  judgment a l i t t l e  t h e mass o f b o d i e s .  bodies equal  I n the Cartesian  i n volume p o s s e s s a n e q u a l  scheme,  amount o f  c o r p o r e a l m a t t e r , e v e n t h o u g h 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, t w o s u c h b o d i e s w o u l d h a v e d i f f e r e n t m a s s e s , e v e n if  they occupied  ferent conceptions  t h e same amount o f s p a c e :  that the d i f -  o f mass i n t h e C a r t e s i a n a n d t h e New-  t o n i a n scheme make a j u d g m e n t o f t h e C a r t e s i a n in and  Newtonian terms a l i t t l e  d o e s n o t n e e d t o be s p e l l e d o u t .  overlooked the  misleading  system  i sfairly  obvious,  A second p o i n t  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  which  seven r u l e s deal 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 t h e u n i v e r s e i s a plenum, t h e r e i s never any  actually  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 l a w s do n o t a p p l y  d i r e c t l y t o the world o f experience. P r o p o s i t i o n 31 S p i n o z a  I n t h e Scholium t o  states:  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 a r e m u t u a l l y i m p e l l e d we h a v e s o f a r c o n s i d e r e d two b o d i e s a s t h o u g h s e p a r a t e d f r o m a l l o t h e r s , no account b e i n g taken o f other impinging b o d i e s . T h a t i s , t h e s e v e n l a w s a r e w h a t we m i g h t c a l l  primary  l a w s , a n d 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 n e e d a s e t o f secondary  laws, d e r i v e d from the primary  a p p l y t o t h e o b s e r v a b l e phenomena.  l a w s , w h i c h do  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 secondary  laws, but the task i s not pursued  these  t o any great  extent. The  second notable aspect  o f t h e seven laws  i s t h a t a s h a r p d i s t i n c t i o n i s made b e t w e e n b o d i e s a t r e s t , and b o d i e s  i n motion,  no m a t t e r how s l o w l y .  g i v e n a n e x a m p l e , l e t u s l o o k a t R u l e s #4 a n d #7. a s m a l l body, s a y a b u l l e t , a cannonball, at rest.  Consider  striking a larger object,  R u l e #4 s t a t e s t h a t t h e b u l l e t  bounce b a c k w h i l e t h e c a n n o n b a l l r e m a i n s a t r e s t . imagine  To  will  Now  the. c a n n o n b a l l t o move i n t h e same d i r e c t i o n a s  the 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  that t h e q u a n t i t y o f motion ( s i z e times v e l o c i t y ) o f the b u l l e t i s l a r g e r than t h a t o f t h e cannonball.  This  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 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 the arid t h e b u l l e t w i l l different in  s m a l l change, cannonball, in  cannonball  move o n t o g e t h e r , w h i c h i s r a d i c a l l y  from the case of the cannonball  the Newtonian  first  at rest.  Ttfhat  s y s t e m w o u l d c o u n t as an e x t r e m e l y  namely a . s l i g h t  change o f v e l o c i t y i n t h e  which correspondingly  produces a small  the e f f e c t produced, i n the C a r t e s i a n system  a drastically different  situation.  change  produces  Several such cases  o f a r a d i c a l d i f f e r e n c e p r o d u c e d 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 , c a n be d i s c o v e r e d  these seven r u l e s .  The e x a m p l e I h a v e c o n s i d e r e d  particular significance the  important  Cartesian  l e t us i m a g i n e o u r s e l v e s  a r a i l r o a d c a r and o b s e r v i n g  c a s e i t w o u l d be i m p o s s i b l e  c a r were m o v i n g o r n o t .  the  To  sitting  the c o l l i s i o n s of  the observed c o l l i s i o n s of b o d i e s whether  special  and  t o moving frames o f r e f e r e n c e .  g i v e a homely example,  its  that  status i n the  d i f f e r e n c e between the Newtonian  I n the Newtonian  i s of  A l s o what i t b r i n g s o u t c l e a r l y i s a n  schemes w i t h r e s p e c t  in  i n t h a t i t makes c l e a r  state:-of r e s t does have a s p e c i a l  C a r t e s i a n scheme.  by e x a m i n i n g  bodies.  to t e l l  from  railroad  I n t h e C a r t e s i a n scheme, w i t h  l a w s f o r b o d i e s a t r e s t , we w o u l d be  able  t o determine whether  t h e r a i l r o a d c a r was m o v i n g o r n o t .  This  bearing  i s an i m p o r t a n t  on t h e q u e s t i o n  of the  " r e l a t i v i t y " of the C a r t e s i a n  space, a t o p i c I  will  return to shortly. The  reasoning  by which these r u l e s of  motion  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 . p r o p o s i t i o n i s argued s e p a r a t e l y , but  Each  the whole set  of  rules involves b a s i c a l l y four p r i n c i p l e s : (a) (as I c a l l  The  p r i n c i p l e of conservation  i t ) i s the b a s i c  are  fall  However,  rules violates this principle,  When t h e y a r e e x a m i n e d , t h e i n t o two  R u l e s #1, the  2,  classes. 3,  4 and  I n the part  (b)  f i n a l v e l o c i t i e s are  the other the  bodies.  not  one  r u l e s can  r e s u l t a n t v e l o c i t i e s are the  o f #7,  and  also  In  of the  of motion i n  i s s i g n i f i c a n t because the i s an  7(a),  incomplete i n that  guarantee the c o n s e r v a t i o n  of the u n i v e r s e  Proposition  the  f i n a l v e l o c i t i e s , while  l a t t e r r u l e s , t h e r e f o r e , are  This  includes  initial velocities, i t  The  universe.  seen t o  l e f t undetermined.  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  not  viola-  6 and  the  and  a l l rules  d e f i n i t e l y s p e c i f i e d , while  s i z e s and  i s p o s s i b l e t o c a l c u l a t e the  be  c l a s s , which  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,  former case, given  do  while  s p e c i f i c enough t o e x c l u d e the p o s s i b i l i t y o f  tion.  .26,  motion  rule that applies to a l l  c a s e s o f c o l l i s i o n b e t w e e n two none o f t h e  of  in rules. they  the  constancy  important issue i n both Descartes's  Spinoza's philosophies,  and  i t indicates that  the  physics  of the P r i n c i p l e s should  n o t b e 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 b l u e p r i n t f o r a f u l l y developed  or  physics.  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. are  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 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  t w o b o d i e s w i t h d i f f e r e n t s i z e a n d v e l o c i t y meet e a c h o t h e r head on. for  What i s m i s s i n g  bodies moving i n opposite  may be s i g n i f i c a n t i n v a r i o u s  i s a r u l e l i k e #7, b u t  directions.  n e c e s s a r i l y be  highly  s i n c e i t d o e s n o t 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 of t h i s p o i n t .  forego the d i s c u s s i o n  F o r my p u r p o s e 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 of motion are not developed t o the extent  omission  ways, b u t f o r l a c k o f c l u e s  the e x p l o r a t i o n o f i t s meaning w i l l speculative;  This  full  which 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 states  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 the  suffer  l e a s t p o s s i b l e change, and t h e weaker body undergoes  as much a s i s r e q u i r e d ;  relative strength  i s determined  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 a r e i n m o t i o n , and t h o s e c a s e s where one b o d y i s a t r e s t . the stronger  b o d y i s t h e one w i t h  I n the former case  the l a r g e r q u a n t i t y o f  motion, w h i l e i n the l a t t e r case s i z e alone superiority. principle  The c r u c i a l a x i o m i n c o n n e c t i o n w i t h t h i s  i s A x i o m 20:  "Variation  from a s t r o n g e r f o r c e . " . why  i n t h e way I h a v e  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  in  i n any o b j e c t p r o c e e d s  I t i s n o t e x p l a i n e d anywhere  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  described.  determines  that s t r e n g t h i s determined  the case o f r e s t  and i n the case of motion  differently i s rather  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 of  rest,  and I w i l l (c)  return to i t shortly.  The p r i n c i p l e o f s y m m e t r y ( a s I c a l l i t )  a p p l i e s t o R u l e s #1 a n d #6 a n d t o P r o p o s i t i o n 26.  It  s a y s t h a t when two b o d i e s a r e e q u a l i n s t r e n g t h , t h e result  of a c o l l i s i o n w i l l  to those bodies.  be s y m m e t r i c a l w i t h r e s p e c t  What i s i n t e r e s t i n g a b o u t t h i s  principle  i s that i t bears a k i n s h i p t o L e i b n i z ' s law of s u f f i c i e n t reason.  I n the case o f t h e f i r s t r u l e , there 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 w h a t h a p p e n s t o one b o d y s h o u l d be a n y d i f f e r e n t the r e s u l t s  from what happens t o t h e o t h e r ;  must be t h e same f o r t h o s e b o d i e s .  ergo, The  p r i n c i p l e does n o t a p p l y s o c l e a r l y t o P r o p o s i t i o n  26,  w h e r e t h e two b o d i e s a r e n o t c o m p l e t e l y s y m m e t r i c a l a n d o n l y e q u a l i n one r e s p e c t , n a m e l y 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 t h e s i x t h r u l e , where t h e b o d i e s a r e equal i n s i z e , but d i f f e r i n v e l o c i t y .  F o r a more  30 detailed  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 t h e s i x t h l a w , s e e "Appendix C. (d)  The p r i n c i p l e  o f economy ( a s I c a l l i t )  s t a t e s t h a t t h e c h a n g e s 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 .  This p r i n c i p l e i s i n t e r e s t i n g  i n that  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 . application and  i n the p r o o f s i s obscure and because of t h i s ,  a l s o b e c a u s e i t h a s no r e l e v a n c e  writings,  Its  I w i l l not delve i n t o  i t .  t o Spinoza's  later  The o n l y d i r e c t l y  relevant aspect  o f t h i s p r i n c i p l e i s i n t h e way  is  f o r t h e p u r p o s e o f d e c i d i n g how much  calculated;  change  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 m o t i o n 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 e x a m p l e , i n t h e c a s e o f R u l e #1, e a c h b o d y u n d e r g o e s no c h a n g e 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 r e t o w e i g h 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 important p o i n t i s t h a t motion i n the C a r t e s i a n p h y s i c s i s n o t a v e c t o r q u a n t i t y as a r e v e l o c i t y and momentum i n t h e N e w t o n i a n p h y s i c s . u s c o n s i d e r a b o d y whose v e l o c i t y  F o r example, l e t  i s 10 u n i t s a n d l e t us  say i t suddenly r e v e r s e s i t s d i r e c t i o n of motion completely. I n t h e N e w t o n i a n s y s t e m t h e 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 s y s t e m t h e r e h a s b e e n 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  to emphasize the r a t h e r d i f f e r e n t  serve  character of motion  31 i n t h e C a r t e s i a n s y s t e m and t h e d i f f i c u l t y o f m a k i n g judgments  of t h a t system i n Newtonian  terms.  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 t h e arguments f o r t h e r u l e s o f m o t i o n , and do n o t t h i n k t h i s i s n e c e s s a r y .  On t h e w h o l e t h e  I  system  i s c a r e f u l l y w o r k e d o u t a n d 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  rest.  A s I h a v e t r i e d t o show, t h e o b v i o u s i m p l a u s i b i l i t y  of  t h e l a w s o f m o t i o n i s n o t s o o b v i o u s when t h e i r and a p p l i c a t i o n i s e x a m i n e d more c l o s e l y . obscurities, will  a n y o n e who  derivation  Despite the  reads the P r i n c i p l e s  attentively  s e e 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  a t t e m p t 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 one  can sense a g r o p i n g towards  a fully  mathematical s c i e n c e of mechanics,  concepts;  developed  an e f f o r t t o  formalize  t h e 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 ,  force,  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 at r e s t , which i s connected w i t h the n o t i o n of of rest.  quantity  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  first  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 t h e d e f i n i t i o n motion i n the C a r t e s i a n system. 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 r t h a t we follows:  will  of  turn  32 Local motion i s the transference o f a p a r t i c l e of matter 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 stated of r e s t , t o the v i c i n i t y of others. Together w i t h  t h i s d e f i n i t i o n there  consisting of five points; abbreviated 1.  i s a long  discussion  I have p a r a p h r a s e d and  these: 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 ,  although  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 n o t t o be c o n f u s e d  force or a c t i o n which t r a n s f e r s . as and  i s generally believed,  This  with  force or action,  i s required only f o r motion,  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 requires  j u s t a s much f o r c e t o p u t a b o d y i n t o m o t i o n a s i t d o e s 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 proved by experience;  a ship requires  a b o u t t h e same  f o r c e t o b e p u t i n m o t i o n a s 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 w o u l d b e e x a c t l y t h e same i f we i g n o r e d t h e  weight and v i s c o s i t y o f t h e water. 3.  T r a n s f e r e n c e i s n o t made f r o m 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 o m t h e c o n t i g u i t y o f one b o d y to the c o n t i g u i t y o f another.  Place  i s not something  that  b e l o n g s t o a n o b j e c t , b u t 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 ,  t h a t t h e m o t i o n o f one w i t h r e s p e c t  i t i s apparent  t o the other i s  reciprocal.  When we  p u s h a b o a t o u t o f t h e s a n d we  the boat and the sand w i t h e q u a l f o r c e . the r e a c t i o n are e q u a l .  The  push  action  and  So t h e b o a t moves w i t h r e s p e c t  t o t h e s a n d a s much as t h e s a n d moves w i t h r e s p e c t t o the boat.  B u t t h e 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 speaking, which i s to  attribute  only t o the boat a motion. 5.  E v e r y b o d y h a s i t s own  one p r o p e r m o t i o n ,  b e c a u s e 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 rest. As r e g a r d s t h e 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 b e t w e e n p o i n t s 4 and 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  5.  motion  i s a r e l a t i o n b e t w e e n two o b j e c t s , w h e r e a s p o i n t 5  states  b l u n t l y t h a t e a c h b o d y h a s i t s one p r o p e r m o t i o n .  From  t h e s h a r p d i s t i n c t i o n t h a t i s made b y t h e l a w s 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 w h a t i t s a y s .  Both 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 of a b s o l u t e motion would read:  "motion i s  t r a n s f e r e n c e from bodies a t r e s t " w h i l e the d e f i n i t i o n of r e l a t i v e motion would read:  "motion i s t r a n s f e r e n c e  from  bodies considered at 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  d e f i n i t i o n of motion i n terms o f r e s t :  how  the  i s rest defined?  If run  r e s t were d e f i n e d i n t e r m s o f m o t i o n we w o u l d u n a v o i d a b l y into a circularity.  As a m a t t e r o f f a c t r e s t i s n o t  defined at a l l , except i n d i r e c t l y . to  T h i s b r i n g s us back  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 ( s e e page 2 9 ) .  This  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 ; of the  t h e f a s t e r a b o d y moves t h e more i t p a r t a k e s  motion and the g r e a t e r i t s q u a n t i t y o f motion i s ; s l o w e r a b o d y moves,  t h e more i t p a r t a k e s o f r e s t ,  and t h e 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 . which states that i f , i n a c o l l i s i o n ,  P r o p o s i t i o n 18,  one b o d y  acquires  no m o t i o n f r o m t h e c o l l i s i o n t h e n t h e 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 , h a s 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 y o u d e n y i t , l e t i t be s u p p o s e d t h a t A h a s l o s t some o f i t s m o t i o n b u t h a s n o t t r a n s f e r r e d i t t o a n o t h e r b o d y , a s , f o r e x a m p l e 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 N a t u r e t h a n b e f o r e w h i c h i s a b s u r d , ( s e e P r o p . 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 t h e same s t a t e o f r e s t a n d A w i l l r e t a i n t h e 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 " t h e d e m o n s t r a t i o n i n r e s p e c t to  t h e r e s t i n B i s t h e same";  h e r e i s one e x a m p l e o f  an a t t e m p t 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  follows that motion i s not the opposite of motion" I n d i r e c t l y t h i s implies that rest i s the opposite of motion, the general idea b e i n g t h a t a l o s s of motion 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 the demonstration t o Proposition  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 m o v i n g more s w i f t l y h a v e more motion (per Def. 8 ) . I n bodies 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 bodies having a g r e a t e r v e l o c i t y meeting those w h i c h h a v e l e s s f o r c e , r e s i s t more a n d a r e 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  important sentence here  i s " t h e 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 " . is,  The q u e s t i o n  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 , a n d 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 m i g h t  first  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 n e e d e d ,  what d o e s i t e x p l a i n ?  The a n s w e r t o t h e l a t t e r q u e s t i o n  c a n 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. there i s :  The k e y s e n t e n c e  "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  i s r e q u i r e d only f o r motion, p l a i n l y wrong.".  believed,  and n o t f o r r e s t , w h i c h i s  The r e a s o n i n g i n v o l v e d i s s o m e t h i n g  l i k e the following:  s i n c e j u s t a s much f o r c e i s r e q u i r e d  t o s p e e d t h i n g s up a s i s r e q u i r e d t o s l o w t h e m down, and r e s t , s p e e d  and slowness,  motion  are symmetrical opposites.  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, t h e more t h e y p a r t a k e of motion,  the g r e a t e r t h e i r q u a n t i t y of motion;  con-  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 rest, the greater t h e i r quantity of rest.  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  s o t h e f o r c e o f r e s i s t a n c e o f r e s t d e p e n d s on t h e of  quantity  rest. What i s i n v o l v e d h e r e i s t h e c o n c e p t o f  for  bodies at rest.  I n the Newtonian  system there  two s e p a r a t e l a w s i n t h e p r i n c i p l e o f i n e r t i a : bodies i n motion stay i n motion, at r e s t .  the C a r t e s i a n system there the  (b)  As I h a v e a l r e a d y m e n t i o n e d  are  (a)  bodies at rest stay (see page 21), i n  i s a c l e a r statement of  second p a r t of t h i s p r i n c i p l e .  there  inertia  The  question  of  only why  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 c o n n e c t e d w i t h  t h i s n o t i o n of r e s t not as a s t a t e of zero motion, but as s o m e t h i n g opposed  to motion.  I t i s not only  difficult  to state a p r i n c i p l e of i n e r t i a f o r r e s t , defined i n t h i s manner, i t i s a l s o d i f f i c u l t mulation  t o give a mathematical  of the notion of q u a n t i t y of r e s t :  the  for-  quantity  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 a n d 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  consider  how  the p r i n c i p l e of 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  l a w s o f m o t i o n , t h e n we w i l l s e e t h a t t h e  effective,  or 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 used i s the following:  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 the s i z e o f the body - the q u a n t i t y o f rest f o r bodies i n motion i s zero.  I n e f f e c t then, the  n o t i o n o f r e s t as s l o w n e s s , a s r e l a t i v e a b s e n c e apparently  of motion,  i s not even a p p l i e d i n the r u l e s o f motion.  If  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 s e e  On  t h i s point there  the physics  i s somewhat o f an i n c o n s i s t e n c y i n  of the P r i n c i p l e s .  o f r e s t , and  This n o t i o n of  r e s t as t h e o p p o s i t e  hard to grasp,  and  how.  quantity  of motion, i s rather  the 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 character.  What d o e s s t a n d  the P r i n c i p l e s there the  out c l e a r l y i s that  i s an e f f o r t  c o n c e p t o f i n e r t i a l mass, and  t o come t o g r i p s w i t h that this effort  t o a c o n c e p t o f r e s t as s o m e t h i n g o p p o s e d t o , b u t m e t r i c a l with motion.  This point  in  leads sym-  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 the E t h i c s about m o t i o n . Besides  the d i f f i c u l t i e s  associated  with  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 p r o b l e m s a r i s e f r o m 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 of p a r t i c u l a r concern t o the p h y s i c s t h e E t h i c s , and understanding  a r e , i n my  opinion, c r u c i a l to  of  the  o f what S p i n o z a says about p h y s i c a l substance  i n his other 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 the  same t h i n g , i n t h e p h y s i c s  us e x p l o r e  a r e one  of the P r i n c i p l e s ;  and let  the consequences of t h i s fundamental axiom,  assumption, p o s t u l a t e or hypothesis, to c a l l i t .  The  Extension  w h a t e v e r one  d e f i n i t i o n of extension  wishes  i s D e f i n i t i o n 1:  i s t h a t which c o n s i s t s of three  dimensions.  38 We do n o t u n d e r s t a n d b y t h e t e r m t h e a c t o f extending o r anything e l s e d i s t i n c t from q u a n t i t y . Extension  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 o m any  other;  any p a r t o f i t c a n a l w a y s be smaller parts. also infinite anything  i t is infinitely  divisible:  s e e n as c o n s i s t i n g o f  yet  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 i n extent;  i t makes no s e n s e t o t h i n k o f  "outside" of extension  (see Axiom 1 0 ) , nor  that matter  s o m e t h i n g " i n s i d e " e x t e n s i o n and y e t  p a r t of i t ,  s u c h a s t h e vacuum ( s e e P r o p o s i t i o n 3 ) .  E x t e n s i o n by  itself  i s not  e x p l a i n the v a r i e t y o f observed f o r that motion-and-rest " b r e a k s up"  but  sufficient  for  not  to  o b j e c t s a n d phenomena;  i s needed.  extension i n t o a myriad  Motion-and-rest fragments which  t o g e t h e r c o n s t i t u t e the w o r l d of v a r i e t y and I t i s t h i s p i c t u r e of the u n i v e r s e t o w h i c h  change. Descartes"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 g e o m e t r y i s applicable.  Descartes  said:  "Qu'on me  donne  e t l e mouvement, e t j e v a i s r e f a i r e l e monde",  l'etendue and,  " L ' u n i v e r s e e n t i e r e s t un m a c h i n e ou t o u t se f a i t  par  f i g u r e e t mouvement.". One  conceptual  p i c t u r e concerns the I f we  d i f f i c u l t y inherent i n this  separate existence of  particles.  i m a g i n e a c o m p o s i t e b o d y 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 at r e s t w i t h r e s p e c t t o each o t h e r , the  question  that immediately  a r i s e s i s , i n what s e n s e i s s u c h a b o d y  composite at a l l ?  And  i f i t i s composite,  why  consist of a p a r t i c u l a r set of p a r t i c l e s , a l s o be  conceived  of p a r t i c l e s .  There i s a profound  divided, at l e a s t ,  compatible  difficulty  be  I t i s d i f f i c u l t to  the e x i s t e n c e of separate  particles i s  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  space.  does n o t , a t f i r s t  sight,  A x i o m 16 s a y s :  moved i n d i f f e r e n t ways h a s  "Matter which i s  a t l e a s t a s many d i v i d e d  p a r t s as t h e r e were d e g r e e s o f s w i f t n e s s o b s e r v e d given time.".  t h e n we  I f the  But  i n contact  i t i s c l e a r t h a t any  relative  b e t w e e n a d j a c e n t p a r t i c l e s m u s t a l w a y s be  we  i f we  deleted  definition  t h e same d i f f i c u l t y c r o p s up  Since a l l p a r t i c l e s are at a l l times t h e i r neighbours,  at  "at l e a s t " i s i g n o r e d or  seem t o h a v e a n a c c e p t a b l e p r a g m a t i c  of a p a r t i c l e .  Now,  occur  connection w i t h p a r t i c l e s which are i n motion w i t h  respect to each other.  any  set  i n the  " A l l e x t e n s i o n can  i n thought.".  This d i f f i c u l t y in  s i n c e i t can  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  p h r a s e o c c u r r i n g i n A x i o m 9:  c o n c e i v e how  must i t  again. with motion  sliding  i m a g i n e two p a r t i c l e s s l i d i n g p a s t e a c h  c a n a s k t h e same q u e s t i o n a s a b o v e , n a m e l y , a t  motion. other, the  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 boundaries  b e t w e e n t h e two p a r t i c l e s ;  and  the  i f there i s  n o t h i n g , t h e n t h e two p a r t i c l e s a r e i n e f f e c t one  larger  one w h i c h i s c h a n g i n g i t s s h a p e , a n d i t f o l l o w s t h e r e f o r e all  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  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 motion t o  fused  "crack"  extension. This k i n d of conceptual an i n t u i t i v e understanding  i s admittedly  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 many o f S p i n o z a ' s u t t e r a n c e s , s o I w i l l t r y  to e x p l a i n i t a l i t t l e postulate  difficulty  further.  The  space = body  ( a s I c a l l i t ) o f f e r s no c o n c e p t u a l  difficulties  as l o n g as one h a s i n m i n d t h e f o l l o w i n g p i c t u r e : u n i v e r s e i s s p a c e f i l l e d w i t h some s o r t o f  the  transparent  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 extended.  Motion i s brought i n t o t h i s g l a s s y m a t e r i a l ,  a n d b r e a k s i t up i n t o f r a g m e n t s w h i c h f r o m t h e n on cease moving about.  This picture i s e a s i l y  never  understood  a n d i t i s t o t h i s p i c t u r e t h a t t h e w o r d "plenum", a 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 .  space  However, t h e  C a r t e s i a n u n i v e r s e does not 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, but t h a t s p a c e a n d b o d y a r e one  a n d t h e same.  rather  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 r o m w h a t t h e s a y s a b o u t t h e vacuum.  Principles  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 , w h e r e a s i n t h e p l e n u m u n i v e r s e t h e e x i s t e n c e o f t h e vacuum i s a  contingent  matter: not  i t i s q u i t e p o s s i b l e to t h i n k of a b i t of  c o n t a i n i n g any  corporeal  space  matter.  There are s e v e r a l d i f f i c u l t i e s  inherent  in  the C a r t e s i a n i d e n t i f i c a t i o n of c o r p o r e a l matter w i t h extension.  First,  i t l e a d s one  to speaking,  in effect,  o f a r e g i o n o f s p a c e m o v i n g i n t h e p l a c e o f some r e g i o n o f s p a c e , w h i c h i s q u i t e odd. it  Another i s that  g i v e s the e i g h t laws of motion 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 , isolation,  i s to begin  impossible premiss: contradiction.  t h a t two  bodies  anything  at a l l f o l l o w s from a  d e v o t e any  but  extremely  t h i s i s the d i f f i c u l t y of r e c o n c i l i n g  e x i s t e n c e of p a r t i c l e s w i t h the  character of  extension. s e r i o u s l y the  geometrical  since  a t t e n t i o n t o them,  the separate  How  thesis,  important,  i s a t h i r d k i n d of d i f f i c u l t y which i s  s i g n i f i c a n t , and  in  logically  From the p o i n t o f v i e w of t h i s  nowhere d o e s S p i n o z a there  collide  an a r g u m e n t w i t h t h e  the above m e n t i o n e d p r o b l e m s are not  and  other  continuous  i d e n t i f i c a t i o n of matter  space i s taken  c a n be  seen from Axiom  9:  A l l e x t e n s i o n c a n be d i v i d e d , a t l e a s t , i n t h o u g h t . C o n c e r n i n g t h e t r u t h o f t h i s a x i o m no one c a n d o u b t who h a s l e a r n e d e v e n t h e l e m e n t s o f m a t h e m a t i c s . 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 c a n a l w a y s be d i v i d e d by an i n f i n i t e number o f greater 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  Principles  r e c o g n i z e s two (a)  types of d i v i s i o n i n extension: d i v i s i o n i n thought;  extension  i s p e r f e c t l y continuous:  we  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 b y  plane,  a plane  figure being  d i v i d e d by a p o i n t ; c o n t i n u u m we p a p e r we  always t h i n k of  s p l i t up b y a l i n e ,  anywhere i n t h e t h r e e  can represent  surfaces or l i n e s .  actual division;  through  line  on  This i s the  the d a i l y p h y s i c a l events  the agency of  a c t u a l l y come t o  d i v i d e d i n p a r t s , whose m o t i o n s and  i n the w o r l d o f  experience.  the C a r t e s i a n p h y s i c s i s caught between  contradictory desiderata.  On  be  c o n f i g u r a t i o n s account  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 s e e how  a  thought".  the g e o m e t r i c a l continuum has  for  a  t h i s shape by p e n c i l l i n e s w h i c h  f o r c e of the phrase " i n (b)  a  dimensional  c a n m e n t a l l y c o n s t r u c t a s h a p e , and  represent geometrical  God  can  geometrical  t h e one  can two  hand i t wants  to  r e t a i n the p u r i t y of g e o m e t r i c a l e x t e n s i o n which i s continuous without time  and  c a n 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  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  i t wants t o import  i n t o t h i s realm the  a t the  same  actuality 8  of 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  stressed, at t h i s point, that I  do n o t presume t o h a v e g i v e n t h e d i f f i c u l t to  issue of  how  r e c o n c i l e the i n d i v i s i b i l i t y of the 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 my  e f f o r t has  been d i r e c t e d toward  treatment;  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  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 problem, and i n the  t h a t i s why  for this  Spinoza type  of  I have i n t r o d u c e d t h i s  topic  Principles. Looking  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 failure.  There are profound  premisses,  and  although these thought.  there are f l a w s i n the r u l e s of f l a w s are not as obvious  B u t , i n a way,  t h e r e i s an a t t e m p t , for a l l ,  c o n t r a d i c t i o n s i n the b a s i c  a s some h a v e  i t i s a magnificent  i n one  motion,  failure:  s h o r t work, t o l a y , once  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 .  and 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 f r o m w h a t w e r e t h o u g h t concepts,  t o be e m i n e n t l y  e x t e n s i o n a n d m o t i o n as t h e s o l e  q u a l i t i e s of matter,  c e r t a i n t y a b o u t them.  primary  and p r o c e e d i n g by a c a r e f u l  method, the t r u t h s a r r i v e d a t w o u l d have a  clear  deductive  mathematical  B e s i d e s , i t h e l d out the  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 o u t h a v i n g t o r e s o r t t o s u c h 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, s o m e t h i n g t h a t i s and y e t i s n o t h i n g , a t o m s , w h i c h a r e e x t e n d e d a n d  are  44 a t the  same t i m e i n d i v i s i b l e .  P r i n c i p l e s an science,  and  A l l t h i s makes  the  i n t e r e s t i n g document i n t h e h i s t o r y o f a worthwhile subject  f o r study i n i t s  own  right.  See,  for instance,  the  T r e a t i s e on t h e  Rainbow.  2  On w h a t p h i l o s o p h i c a l g r o u n d s t h e 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 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 w h a t 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 t h e s y s t e m 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 , b e c a u s e , f o r one t h i n g , i t w o u l d i n v o l v e us too f a r i n Descartes's metaphysical t h e o r i e s . 3  T h r o u g h o u t t h i s t h e s i s I use t h e t e r m " N e w t o n i a n " t o d e n o t e w h a t i s now l a b e l e d " c l a s s i c a l m e c h a n i c s " , w i t h o u t m a k i n g any i m p l i c a t i o n s a b o u t I s a a c Newton's t h o u g h t processes. 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 P l e n i s t h y p o t h e s i s , see C o n a n t , p a g e s 34-38. 4  the  5 T h r o u g h o u t t h e P r i n c i p l e s , " m o t i o n " and "quantity o f m o t i o n " a r e synonymous t e r m s , s o t h a t t h e w o r d " q u a n t i t y " i s generally superfluous. ^ S c o t t , page  163.  7 B r o a d , page  165.  8 I t m i g h t 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 the 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 g e o m e t r y , so t h a t t h e t r u t h s a b o u t t h e p h y s i c a l w o r l d do n o t 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 , b u t I would 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 Spinoza's  E t h i c s i s found i n the Scholium P a r t Two.  physics i n the  a f t e r P r o p o s i t i o n 13 o f  This p r o p o s i t i o n reads  as f o l l o w s :  "The  o b j e c t o f t h e i d e a c o n s t i t u t i n g t h e human m i n d i s a b o d y , 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 a n d nothing else.".  I t i s i n t e r e s t i n g t o n o t e how t h e  p h y s i c a l theory i s hidden,  we m i g h t a l m o s t  say, i n a scholium  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 t h e c o n n e c t i o n o f b o d y and mind.  T h i s i s i n d i c a t i v e o f how m i n o r a r o l e  as such p l a y s i n S p i n o z a ' s  grand  scheme;  physics  he m e n t i o n s t h e  subject only i n order t o reinforce c e r t a i n points o f metaphysical Spinoza  doctrine.  Because t h e purposes f o r w h i c h  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 a r e a good d e a l  c l e a r e r than the theory i t s e l f , o u t l i n i n g these  we m i g h t w e l l b e g i n b y  purposes.  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 b e t w e e n b o d y a n d m i n d , t o make s e n s e o f t h e n o t i o n t h a t t h e mind i s t h e i d e a o f t h e body.  The  Scholium  s t a r t s out as f o l l o w s : Hence we s e e n o t o n l y t h a t t h e human m i n d i s u n i t e d t o t h e b o d y , b u t a l s o w h a t i s t o be u n d e r s t o o d b y the u n i o n o f mind and body. B u t no one c a n u n d e r stand i t adequately o r d i s t i n c t l y without knowing adequately beforehand t h e nature o f o u r body; f o r  t h o s e t h i n g s w h i c h we h a v e p r o v e d h i t h e r t o a r e a l t o g e t h e r g e n e r a l , n o r do t h e y r e f e r more t o man than t o other i n d i v i d u a l s , a l l o f which are animate, although i n d i f f e r e n t degrees. 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 m i n d i n t e r m s o f t h e o r g a n i z e d c o m p l e x i t y o f t h e human b o d y ; although a l l bodies animation,  are animated, there are degrees o f  corresponding t o degrees o f organized  complexity.  S t i c k s and s t o n e s , w h i c h a r e a t t h e bottom o f t h e s c a l e , have a v e r y l o w 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 t h e t o p o f t h e 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 t h e "minds" o f s t i c k s a n d 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 to  c a n be s a i d  be a n i m a t e d t o a h i g h e r degree t h a n o t h e r s ,  Spinoza'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 p u r p o s e , n a m e l y how we have knowledge o f t h e o u t s i d e w o r l d .  From t h e f a c t  that  a m i n d i s t h e i d e a o f a b o d y , i t w o u l d seem t o f o l l o w t h a t m i n d s c a n o n l y know t h e b o d i e s w i t h w h i c h t h e y a r e associated. bodies  Spinoza's  solution to this  i s t o show t h a t  a r e a f f e c t e d b y b o d i e s e x t e r n a l t o them.  How  this  i s w o r k e d o u t we c a n s e e f r o m P o s t u l a t e 5: When a f l u i d p a r t o f t h e human b o d y i s d e t e 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 another 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 t h e s o f t p a r t , and l e a v e s upon i t , a s i t w e r e some t r a c e s o f t h e i m p e l l i n g e x t e r n a l b o d y . 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 the e x t e r n a l w o r l d because i t a f f e c t s  bodies.  our  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  apparent purpose f o r the i n t r o d u c t i o n of the of hardness,  s o f t n e s s and  fluidity,  and  i s the  definition  i t e x p l a i n s the  presence of t h i s b i t of p h y s i c a l t h e o r y i n the  Ethics.  A t h i r d purpose o f the E t h i c s i s to provide a way  o f e x p l a i n i n g how  t h e u n i v e r s e as a w h o l e i s  c h a n g e l e s s , even though a l l s o r t s of changes take within i t . little we  To  see how  t h i s i s d o n e , we  c l o s e r at Spinoza's  place  need t o l o o k a  theory of i n d i v i d u a l s .  do t h i s , h o w e v e r , i t m i g h t be b e t t e r , f i r s t ,  Before  to discuss  some o f t h e more g e n e r a l f e a t u r e s o f t h e p h y s i c s o f  the  Ethics. One  m a j o r , and  d e p l o r a b l e , f e a t u r e of  p h y s i c s of the E t h i c s i s i t s b r e v i t y .  At f i r s 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 of m a t e r i a l s t u c k away i n a c o r n e r ; a x i o m ( s e e page 49) Spinoza  look a l i t t l e  hangs t o g e t h e r , and  The  theory presented the t i t l e  c l o s e r , we w i l l  furthermore,  foundations of p h y s i c a l s c i e n c e are  seems  "physics".  find that i t  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  I will  incidental  f o r example the f o u r t h  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  all  sight  d o e s n o t seem t o f i t i n w i t h w h a t  says before o r a f t e r .  Y e t when we  the  t o l a y down t h e  there.  take advantage of the 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 t h e axioms, and in  definitions,  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 1 3 , P a r t Two, the order i n which they occur.  This by i t s e l f  will  g i v e a good i d e a o f t h e f o r m and s t y l e o f t h e p h y s i c s of  the Ethics.  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 almost  a l l o f these sooner to  or later,  s t a t e them h e r e a n d now.  postulates which  so t h a t i t i s convenient I have o m i t t e d t h e s i x  come a s a b o d y a t t h e e n d .  These  p o s t u l a t e s a r e 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 they c a n s a f e l y be p a r a p h r a s e d . bodies a r e composite  What t h e y s t a t e i s t h a t human  t o a h i g h degree,  that parts of the  human b o d y a r e 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 b y and c a n a f f e c t t h e e x t e r n a l w o r l d i n many w a y s , t h a t t h e y r e g e n e r a t e t h e m s e l v e s 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 bodies a t times l e a v e l a s t i n g e f f e c t s o n t h e human b o d y .  motion  A x i o m 1; or rest.  A x i o m 2: sometimes q u i c k l y .  A l l bodies are e i t h e r  i na state of  E v e r y b o d y moves, s o m e t i m e s s l o w 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 f r o m o n e another i n r e s p e c t o f motion and r e s t , q u i c k n e s s and slowness, and not i n respect o f substance. 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 b o d y i n m o t i o n o r a t r e s t must b e d e t e r m i n e d t o m o t i o n o r r e s t b y a n o t h e r b o d y , w h i c h was a l s o determined t o motion and r e s t b y another, and t h a t i n i t s t u r n b y another, and so on a d 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 b o d y i n m o t 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 d e t e r m i n e d t o a s t a t e o f r e s t b y 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 to a s t a t e o f motion by a n o t h e r body. A x i o m 3:^ A l l t h e modes b y w h i c h one b o d y i s a f f e c t e d by a n o t h e r f o l l o w from t h e nature o f t h e body a f f e c t e d , a n d a t t h e same t i m e f r o m t h e n a t u r e o f t h e a f f e c t i n g b o d y , s o t h a t o n e a n d t h e same b o d y 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 t h e 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 t h e 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 w a y s b y o n e a n d t h e same b o d y . A x i o m 4: "When a b o d y 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 , a n d t h e a n g l e of the l i n e o f r e f l e c t e d motion w i t h the plane o f the b o d y 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 a n g l e w h i c h t h e 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 t h e same p l a n e . Definition: 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 m a g n i t u d e a r e p r e s s e d t o g e t h e r b y o t h e r s , s o t h a t t h e y l i e one u p o n t h e o t h e r , o r i f t h e y a r e 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 d e g r e e s o f s p e e d , s o t h a t t h e y c o m m u n i c a t e t h e i r m o t i o n t o one a n o 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 , these bodies are s a i d t o be m u t u a l l y u n i t e d , a n d 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 b o d y 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 b y t h i s union o f b o d i e s . A x i o m 5: W h e t h e r 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 c o m p o s i n g a n 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 consequently whether i t i seasy 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 s h a p e , d e p e n d s u p o n w h e t h e r t h e p a r t s o f t h e 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 u p o n e a c h o t h e r with greater surfaces I w i l l c a l l hard; t h o s e s o f t , whose p a r t s l i e o n 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 ; a n d t h o s e f l u i d , whose p a r t s move a m o n g s t e a c h 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 f r o m t h e b o d y o r i n d i v i d u a l w h i c h i s composed o f a number o f b o d i e s , a n d i f t h e i r p l a c e b e s u p p l i e d b y t h e 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 the nature which i t had before  50 w i t h o u t a n y change o f f o r m . Lemma 5; I f t h e p a r t s c o m p o s i n g a n 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 , s o 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 a n d 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 t h e n a t u r e w h i c h i t h a d b e f o r e w i t h o u t a n y change o f f o r m . Lemma 6; I f a n y number o f b o d i e s c o m p o s i n g 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 the motion t h e y p r e v i o u s l y had i n another, b u t a r e 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 a n d r e c i p r o c a l l y comm u n i c a t e t h e i r m o t i o n s i n t h e same manner a s 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 a n y change of form. Lemma 7: The i n d i v i d u a l t h u s composed w i l l , m o r e o e v e r , r e t a i n i t s n a t u r e w h e t h e r i t move a s a w h o l e o r b e a t r e s t , o r w h e t h e r 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 of t h e Ethics  outstanding difference  between t h e p h y s i c s  and t h a t o f t h e P r i n c i p l e s  i sthat the  f o r m e r 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 powerful  t h e o r y o f composite body, namely t h e 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 Spinoza; it  a t l e a s t t h e r e i s no h i n t o f  i n the P r i n c i p l e s , so that t h i s part of the physical  t h e o r y c a n 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 " .  Although the theory of individuals r e a c h i n g a n d complex r a m i f i c a t i o n s , in outline:  i t i s rather  simple  the universe i sa hierarchy of d i f f e r e n t  kinds of individuals; the  has f a r  individuals  a t the bottom o f the scale  of the simplest kind,  there are  whose component  parts are the simplest bodies, the corpora  simplicissima;  these  l o w e s t l e v e l s combine t o f o r m i n d i v i d u a l s  of  s e c o n d 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 t h i r d o r d e r , and o n l y one  so on.  picture  of  the  At the h i g h e s t l e v e l t h e r e i s  i n d i v i d u a l , the u n i v e r s e The  the  itself.  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  c o m p o s i t e 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  the  p a r t i c l e s at the bottom, i s not hard to understand  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 . difficult to  to understand  form a l a r g e r  g e t h e r and  i s how  What i s more  a number o f e l e m e n t s c o m b i n e  u n i t , i . e . what b i n d s the elements t o -  i n w h a t way  c a n a number o f s i m p l e r u n i t s  p a r t o f a more c o m p l e x u n i t , w h a t d o e s t h e i n t e g r i t y of a p a r t i c u l a r  structural  individual consist  t o these 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 the c o n c i s e n e s s and  almost  physics of'the Ethics.  fairly clear  of.  Answers  because  enigmatic character of  T h a t somehow t h e c o n c e p t  organized complexity i n v o l v e s the motions of is  be  of  the of  particles  from the D e f i n i t i o n , b u t what the  prop-  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 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 determine  as t h e n a t u r e  individuals, related.  I n the next  q u e s t i o n s more  to  of organized complexity of  and o b v i o u s l y t h e s e q u e s t i o n s a r e two  the  inter-  c h a p t e r s I w i l l examine  these  closely.  A t t h i s p o i n t i t m i g h t be  useful  what  t o compare  the p h y s i c s  of the E t h i c s w i t h t h a t of the  Principles,  f o r t h e p u r p o s e o f c o n s i d e r i n g some o f t h e d i f f e r e n c e s and theory  similarities.  of i n d i v i d u a l s , there  physics  Outside of, perhaps, seems t o be  i n s t a n c e , the  of the  the  but  corresponding  t h i s has  in  the  something Principles.  latter.  regarded  I t i s true that  axioms f o r the  a ready e x p l a n a t i o n  the  of the P r i n c i p l e s  f o r m e r m i g h t w e l l a t f i r s t s i g h t be  a r e f o r m u l a t i o n of the a r e no  the  f o u r t h axiom i s q u i t e s i m i l a r t o  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) and  little  o f t h e E t h i c s t h a t w o u l d mark i t a s  r a d i c a l l y d i f f e r e n t from the physics For  obvious  other  there  r u l e s of  motion,  i n that, after a l l ,  E t h i c s i s n o t p r i m a r i l y a w o r k on p h y s i c a l s c i e n c e , that other purpose. may  be  laws of motion would not Why  physical theory  s i m i l a r i n other respects  and  not  others  o f t h e s e two w o r k s i s  as w e l l .  For instance,  b o t h cases the fundamental elements of s c i e n t i f i c 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  single reference  2  i s made i n t h e p h y s i c s  l i k e experimental  same.  of the  evidence or  T h e r e i s no m e n t i o n o f a c t i o n a t a  the f o u r t h axiom, the  in ex-  b a s i c method  procedure i s , s u p e r f i c i a l l y a t l e a s t , the  data .  so  insignificant.  The  to anything  the  be p e r t i n e n t t o i t s  S p i n o z a i n c l u d e s t h i s law  quite  as  Not  or a  Ethics  observational distance;  only item that deals with  the  i n t e r a c t i o n of bodies, suggests  that bodies  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 .  can i n t e r a c t On t h e  q u e s t i o n o f t h e vacuum t h e r e seems t o b e a g r e e m e n t a s wall;  i n the Scholium  the E t h i c s , S p i n o z a  t o P r o p o s i t i o n 1 5 , P a r t One o f  states:  E v e r y o n e 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 o u g h t t o a d m i t t h i s , a n d e s p e c i a l l y t h o s e who d e n y t h a t t h e vacuum c a n e x i s t . All  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  the t e n t a t i v e assumption t h a t Spinoza's  i d e a s about t h e  structure of the p h y s i c a l universe are w e l l b y P a r t Two o f t h e P r i n c i p l e s .  represented  What m i g h t a r g u e a g a i n s t  t h i s assumption 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 Spinoza's to  that of Descartes;  later.  position i s antithetical  some o f t h e s e w i l l be d i s c u s s e d  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  "principles of natural  t h i n g s " i n no u n c e r t a i n t e r m s ( l e t t e r t o T s c h i r n h a u s , May 1 6 7 6 ) ;  I will  return to this point i n a later  chapter.  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 a x i o m s a s A x i o m 1, 2 a n d 3 r e s p e c t i v e l y , b u t f o r c o n v e n i e n c e s a k e I w i l l c a l l t h e s e A x i o m 3, 4 a n d 5 respectively. 2 In the P r i n c i p l e s there i s a reference 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 r e m a i n l y u s e d as e x a m p l e s t o s t r e n g t h e n t h e a r g u m e n t .  CHAPTER V THE THEORY OF INDIVIDUALS  The  theory o f i n d i v i d u a l s has obviously a very  important r o l e t o p l a y i n Spinoza's i s not merely  grand  scheme; i t  a t h e o r y o f c o m p o s i t e b o d y b u t a l s o , a way  o f e x p l a i n i n g t h e 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 view 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 theory 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 will  be  l i m i t e d t o c o n s i d e r i n g t h e 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 individuals,  t h i s much i s c e r t a i n :  about the theory o f Spinoza 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 and t h e i n d i v i d u a l s .  The f i r s t  bodies  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 simplicissima it  (Iwill  as c o r p . s i m p . ) .  immediately  take the l i b e r t y o f a b b r e v i a t i n g This i s evident from the  f o l l o w i n g A x i o m 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 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 and to  rest,  speed and slowness  composite bodies.".  statement  alone;  by motion  l e t u s now a d v a n c e  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  first  q u e s t i o n we m i g h t a s k 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  together, Looking two  i n w h a t way t h e y c o m b i n e t o f o r m a l a r g e r  a t t h e d e f i n i t i o n , we s e e t h a t t h e r e  ways i n w h i c h t h i s i s done:  (a)  are b a s i c a l l y  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) of bodies  exhibit  certain  axle,  C a s e ( a ) c a n be u n d e r s t o o d  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  perhaps represented  by a wheel r o t a t i n g  o r a w a t c h , whose p a r t s e x h i b i t  relations  of motion.  case o f ( b ) :  (b) i s  about a f i x e d  certain  definite  I f we c o n s i d e r r e l a t i v e r e s t  special kind of regularity, special  a number  r e g u l a r i t i e s i n t h e i r motions  with respect to each other. by t h i n k i n g  unit.  t h e n (a) i s a c t u a l l y  we c a n s a y t h e n t h a t t h e  i n t e g r i t y o f an i n d i v i d u a l  as a  only a "structural  l i e s simply i n the r e g u l a r i t y  of the motions of the p a r t s of the i n d i v i d u a l . One h a s t o be somewhat c a r e f u l these examples.  Spinoza  g i v e s no s i m p l e  i n the use o f examples;  the  o n l y e x a m p l e he d o e s g i v e i s t h e human b o d y , w h i c h , a s we c a n s e e f r o m P o s t u l a t e 1, i s h i g h l y t h e 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 composite t o a h i g h degree.  complex i n t h a t are themselves  H e n c e we a r e somewhat a t a  l o s s when we t r y t o i m a g i n e how a l l t h e d e t a i l s a r e s u p p o s e d t o be w o r k e d o u t , n o r i s t h e r e a n y e v i d e n c e Spinoza  had worked these  details out.  So t h e t a l k  about  w a t c h e s , w h e e l s o r h o u s e s i s somewhat s p e c u l a t i v e i n nature.  that  What i s f a i r l y c l e a r , h o w e v e r , i s t h e c o n c e p t o f a n i n d i v i d u a l a s s o m e t h i n g more t h a n t h e sum o f i t s parts.  J u s t a s i n t h e c a s e w i t h t h e modern n o t i o n o f  t h e a t o m , 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 , neutrons  a n d e l e c t r o n s , t h e 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 organization of parts. as a w h o l e a s a s u p e r and  Spinoza conceives o f the universe individual  (see Scholium  t o Lemma 7)  t h i s i n d i c a t e s a c o s m o l o g y somewhat d i f f e r e n t  that of the Cartesian physics.  from  The p i c t u r e o f t h e  Cartesian universe i s that of a giant conglomeration o f all  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  unifying factor . 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 h a s s t r u c t u r e o n l y i n s o f a r a s t h e p a r t s o f t h e b o d y h a p p e n 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 of time, w h i l e i n t h e E t h i c s a composite body has d e f i nite organized complexity. and  On t h e o t h e r h a n d , t h e E t h i c s  t h e P r i n c i p l e s h a v e i n common t h a t i n n e i t h e r a r e  there 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 that binds p a r t i c l e s together. the p h r a s e  I n the d e f i n i t i o n  "pressed t o g e t h e r " o c c u r s , and t h i s  phrase t h a t suggests  f o r c e i n a n y f o r m o r way.  i s the only This  phrase i s w e l l i n accord w i t h the p i c t u r e o f the universe 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 , namely as a plenum, a  s p a c e 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 , a n d where t h e m o t i o n  57  o f a n y p a r t i c l e must i n v o l v e t h e m o t i o n s o f one o r more of i t s neighbours. This notion of organized complexity, that the c o m p o s i t e b o d y i s more t h a n t h e sum o f i t s p a r t s , ; i s , very important  t o Spinoza's  metaphysical  scheme;  the  u n i v e r s e i s t h e b o d y o f God, a n d h e n c e i n some way i t must be a u n i t ,  an o r g a n i z e d w h o l e a n d 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  individual,  i s a unit,  i s n o t so p r o b l e m a t i c , b u t i n  w h a t way t h e u n i v e r s e i s c h a n g e l e s s to understand.  difficult  T h i s i s b u t p a r t o f a more g e n e r a l p r o b l e m ,  n a m e l y i n w h a t way a r e i n d i v i d u a l s be u n d e r g o i n g  i s more  i n general said to  c h a n g e , w h a t c o n s t i t u t e s a c h a n g e i n an  individual. Lemmas 4, 5, 6, a n d 7 t e l l c o n s t i t u t e change i n an i n d i v i d u a l :  us w h a t d o e s n o t (1)  i f certain  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 t h e 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 ) 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 parts,  (4)  i f some  their relation with  other  i f t h e i n d i v i d u a l a s a w h o l e 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 c h a n g e i n t h e i n d i v i d u a l a s a whole.  What S p i n o z a h a s i n m i n d w i t h t h e s e  lemmas c a n  be s e e n more c l e a r l y b y c o n s i d e r i n g t h e 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 t h e same e v e n t h o u g h 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  retain  much t h e same shape a n d c o n s t i t u t i o n e v e n t h o u g h t h e y increase several f o l d i n s i z e over the p e r i o d of a time;  (3)  life-  human b o d i e s h a v e a c o n s i d e r a b l e amount o f  f r e e d o m o f movement i n t h e 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 a n 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  w h e t h e r t h e y move a r o u n d o r a r e a t r e s t . The t w o i m p o r t a n t d i f f e r e n c e s b e t w e e n 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 a n i n d i v i d u a l , i s t h a t human b o d i e s h a v e n e i g h b o u r s ,  s o 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 c h a n g e , w h i l e the u n i v e r s e , b y d e f i n i t i o n ,  i s alone and i s changeless.  I n t h e S c h o l i u m t o Lemma 7, S p i n o z a  states:  T h u s , i f we a d v a n c e a d 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 w h o l e o f n a t u r e t o b e 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 s a y , 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 a n y change i n t h e w h o l e individual. Although i t i s not s p e c i f i c a l l y stated, the proof o f the changelessness  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 :  a n y change i n a n 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 ; spontaneous change.  t h e r e i s no  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 determinate.  h a v e t h e c a u s e 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 finite  and  determinate  entities  ( s e e P r o p o s i t i o n 25,  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 a l w a y s 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  bodies.  Now,  f o r s i m p l e s t b o d i e s , how  t h e i r motion.  other  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 of the E t h i c s . b o d i e s h a v e o n l y one  Part  Simplest  p r o p e r t y t h a t can change, namely  A change f r o m 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 , s o t h a t i n o r d e r t o e x p l a i n why p a r t i c u l a r s i m p l e body has r e s t , we  a  a c e r t a i n s t a t e of motion  have t o r e f e r t o a h i s t o r y of c o l l i s i o n s .  the 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 , besides  the motion they possess  another  property that i n d i v i d u a l s possess,  internal constitution.  t o use  namely  I t i s the r e g u l a r i t y of  Spinoza's  terminology.  The  nature This sort  constitution  changes, w h i l e t h e c o r p . simp, change o n l y w i t h  The  their  individual i s said  t o c h a n g e o n l y i n s o f a r as i t s i n t e r n a l  t o m o t i o n and  because  the  i m p l i e s t h a t the 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 o f e n t i t y from the c o r p . simp.  But  as a w h o l e , t h e r e i s  motions of the p a r t s t h a t c o n s t i t u t e s the form or o f an i n d i v i d u a l ,  or  respect  rest. point i n a l l this  n o t show i n any way  why  i s that Spinoza  does  i n d i v i d u a l s do n o t c h a n g e  unless  they i n t e r a c t w i t h other w h a t he  individuals.  says about the c o r p .  ceivable that individuals  On  the b a s i s  simp., i t i s q u i t e  are u n d e r g o i n g  interaction  amongst i n d i v i d u a l s .  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  t h i s i n mind.  O l d e n b u r g , November 1665, on  He  did  I n the l e t t e r t o  Spinoza  discusses at  the r e l a t i o n o f the p a r t s of nature  nature.  as  individual  There i s evidence t h a t Spinoza  have something l i k e  de-  individual.  l o n g as the t o t a l motion of the p a r t s of the remains constant.  parts,  But t h i s  p e n d s on w h a t i s t o c o u n t a s change i n an One  con-  continuous  i n t e r n a l change o w i n g t o t h e c o l l i s i o n s o f t h e without  of  length  t o the whole  of  says:  Now, a l l t h e b o d i e s o f n a t u r e c a n and s h o u l d be c o n c e i v e d i n t h e same way as we h a v e h e r e c o n c e i v e d the blood: 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 the whole u n i v e r s e , the same p r o p o r t i o n o f m o t i o n and r e s t . This q u o t a t i o n would i n d i c a t e the  changelessness of the u n i v e r s e  that for  consists solely i n  the f a c t t h a t the t o t a l q u a n t i t y of motion i n the i s constant,  and by  implication,  changed o n l y i n s o f a r p a r t s i s changed.  a s t h e sum  Spinoza  universe  that each i n d i v i d u a l t o t a l of the motions  This i n t e r p r e t a t i o n  has  a d v a n t a g e t h a t i t makes f o r c o n s i s t e n c y : c a n show t h a t m o t i o n i s p r e s e r v e d  the  is of  definite  as l o n g a s  we  i n individual collisions,  t h e n i t 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 m o t i o n o f an individual w i l l  remain constant  as l o n g a s t h e 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 course, i t  a l s o f o l l o w s that the t o t a l quantity of motion i n the universe  i s constant. On t h e o t h e r h a n d , 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 a r e t h e same, j u s t i n c a s e t h e t o t a l q u a n t i t y o f m o t i o n i n e a c h i s t h e same, a n d t h i s to strange  consequences.  leads  A t r e e w o u l d 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 long as the t o t a l  quantity  o f m o t i o n o f a t r e e a n d a n e l e p h a n t a r e t h e same. A l l w a t c h e s 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 the be  that  sum o f t h e m o t i o n s o f t h e p a r t s o f e a c h w a t c h w o u l d t h e same. I t i s evident  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 t h e f o r m a n d 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 t h e m o t i o n s o f t h e p a r t s ; i t h a s 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 m o t i o n s of the 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 . 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  What  i s more t h a n  t h e mere f a c t t h a t o v e r a g i v e n p e r i o d o f t i m e t h e t o t a l sum o f t h e i r m o t i o n s i s r e l a t i v e l y c o n s t a n t . way t h e r e universe  i s organized  complexity,  I n some  a n d i n some way t h 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  following question is crucial:  does t h e t h e o r y  p h y s i c a l theory the p h y s i c s not.  The  about Spinoza's t h e o r y  of i n d i v i d u a l s  of i n d i v i d u a l s i n d i c a t e a  that i s s i g n i f i c a n t l y d i f f e r e n t from  of the P r i n c i p l e s ?  theory  My  c l a i m i s t h a t i t does  i s e s s e n t i a l l y an e x t e n s i o n  Cartesian physics,  and  of  the  s t e m s f r o m an e f f o r t o n  Spinoza'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 . d e f e c t of the C a r t e s i a n p h y s i c s universe a mad  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  conglomeration,  no o b s t a c l e , b u t  For Descartes's  metaphysics  f o r S p i n o z a ' s scheme t h e  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 (a) see  Cartesian  m i l l i n g a b o u t o f a l a r g e number o f p a r t i c l e s ;  short, i t i s chaotic. was  i s t h a t the  The  the u n i v e r s e  t h e b o d y o f God  this  Cartesian  ways:  i s t h e b o d y o f God  as a l o o s e  in  and  conglomeration of  to  particle  i s absurd, or at l e a s t repugnant. (b) body, and  t h e human m i n d i s t h e  i d e a o f t h e human  s u p e r i o r minds must " b e l o n g "  to superior  h e n c e t h e r e must be v a r y i n g d e g r e e s o f a n i m a t i o n corresponding  v a r y i n g degrees of organized  with  complexity.  What i s s e r i o u s l y l a c k i n g i n t h e  Cartesian  physics, from Spinoza's p o i n t of view, i s a theory composite body.  I n the C a r t e s i a n p h y s i c s  bodies  a  of  composite  b o d y 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  with  respect  the  t o . e a c h o t h e r and  "pressed  together"  in  phraseology of 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  b o d y a n d a s t o n e a r e n o t v e r y much d i f f e r e n t . h a l f o f the d e f i n i t i o n adequate.  The  first  ( s e e c a s e (a) o n p a g e 55) i s n o t  There o b v i o u s l y are composite b o d i e s , such  as a w a t c h , o r a human b o d y , 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 e a c h o t h e r , and y e t h a v e a d e f i n i t e w h i c h remains r e l a t i v e l y time.  structure  stable over a given p e r i o d of  Hence S p i n o z a ' s d e f i n i t i o n c a n be t a k e n as a n  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 t h e C a r t e s i a n t h e o r y o f composite  body. All  for  t h i s l e a v e s a number o f q u e s t i o n s u n a n s w e r e d ;  i n s t a n c e , p r e c i s e l y what a r e 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 , a n d w h a t i s t o c o u n t as change i n a n 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  individual; ready  a n s w e r s a r e t o be f o u n d t o t h e s e q u e s t i o n s , a n d i t i s d o u b t f u l t h a t Spinoza had worked out the f u l l of  h i s theory.  implications  I n h i s own w o r d s , a t t h e e n d o f t h e  S c h o l i u m t o Lemma 7: I f i t h a d b e e n 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 the q u e s t i o n o f a body, I s h o u l d have h a d t o e x p l a i n a n d d e m o n s t r a t e 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 , a n d I h a v e n o t i c e d them o n l y b e c a u s e I c a n e a s i l y d e d u c e f r o m 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 d e m o n s t r a t e . On t h e w h o l e ,  i t c a n 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 the t h e o r y of 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  there  a r e a c e r t a i n number o f i t e m s o n 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 h a d .  The m a j o r p o i n t i s t h a t t h e  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 s y s t e m r a d i c a l l y d i f f e r e n t from that 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 c a n be s e e n a s an e x t e n s i o n  C a r t e s i a n p h y s i c s , an added e l e m e n t t o f i l l  of the a certain  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  with  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 w o r d " C a r t e s i a n " i n t h e way I h a v e d e f i n e d i t i n C h a p t e r I I I .  65 CHAPTER V I MOTION I N SPINOZA'S PHYSICS  Although both the P r i n c i p l e s and the E t h i c s are 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 more e a s i l y u n d e r s t o o d  than the l a t t e r .  i s much  I t seems  almost  as i f t h e 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 Principles, conciseness.  and t h e 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 I n t h e E t h i c s S p i n o z a does n o t 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.  Furthermore,  on t h e s u b j e c t o f m o t i o n ,  and t h i s i s e s p e c i a l l y t r u e h i s terminology i s unfamiliar  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 m a i n t a s k ,  t h e r e f o r e , i s t o t r y t o make some s e n s e o u t 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  b e t w e e n them a n d c o r r e s p o n d i n g p a r t s o f t h e 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 t h e laws o r p r i n c i p l e s o f motion  fall  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 bodies c o n s i d e r e d i n i s o l a t i o n , and,  (b)  those governing t h e i n t e r a c t i o n o f bodies.  Category  (a) i s f i l l e d b y t h e C o r o l l a r y t o Lemma 3 ( s e e p a g e 49) w h i l e t h e f o u r t h a x i o m ( s e e p a g e 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 Spinoza's p r i n c i p l e of i n e r t i a : t o remain  bodies i nmotion  tend  i n motion, w h i l e bodies a t r e s t tend t o remain  i n that state. postulate  This 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  about nature,  b u t r a t h e r i t i s dependent on  statements e s t a b l i s h e d before.  The p r e c e e d i n g lemma  s t a t e s t h a t a change f r o m m o t i o n t o r e s t o r v i c e can  come o n l y f r o m i n t e r a c t i o n w i t h o t h e r  versa  bodies;  this  lemma i n t u r n d e p e n d s on P r o p o s i t i o n 28 o f P a r t One, which 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 existence  t h i n g must be s o u g h t i n t h e  and a c t i v i t y o f o t h e r  finite  things.  The  d e r i v a t i o n i s f u r t h e r augmented b y t h e d i s c u s s i o n  that  follows the Corollary: 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 b o d y A, f o r e x a m p l e , i s a t r e s t , i f I p a y 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 c a n 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 at r e s t . I f i t should afterwards happen t h a t t h e b o d y A s h o u l d move, i t s m o t i o n c o u l d n o t c e r t a i n l y be a r e s u l t o f i t s f o r m e r 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 than 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 the proof i s the exact  c o n v e r s e o f t h e above.  What i s c l e a r f r o m t h i s  proof  i s Spinoza's conception  o f m o t i o n as a q u a l i t y o f a body:  a body i s n o t u n d e r g o i n g any change as l o n g as i t c o n tinues  i n i t s m o t i o n , and t h e r e  required  f o r t h i s continuation of motion.  contrasted i n order and  i s no c a u s a l  explanation  This  c a n be  w i t h t h e 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  t o keep an o b j e c t  i n m o t i o n , a mover i s needed,  a b o d y 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. is  I n a sense t h e body i s undergoing  c h a n g e when i t  moving. In  t h i s respect, Spinoza's p r i n c i p l e  i s no d i f f e r e n t  from the e q u i v a l e n t statements  P r i n c i p l e s , where m o t i o n quality  of inertia  i s spoken o f as an  ( s e e P r o p o s i t i o n 14, P a r t Two).  i nthe  unchanging  But there 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 t h e t w o - s i d e d character of the p r i n c i p l e it  of i n e r t i a :  i n the Principles  i s s t a t e d c l e a r l y only i n respect t o motion,  for rest .  This difference  1  be e x p l a i n e d a l i t t l e  and n o t  i s s i g n i f i c a n t and s h o u l d  further.  I f we r e t u r n f o r a moment t o S p i n o z a ' s of  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 a b o v e , we  proof will  notice a c e r t a i n p e c u l i a r i t y i n that the proof  depends  on a d i c h o t o m o u s t r e a t m e n t o f m o t i o n  bodies  are e i t h e r account or  i n motion  or at rest.  or rest:  What i s n o t t a k e n  into  i s t h e p o s s i b i l i t y t h a t b o d i e s m i g h t s p e e d up  s l o w down, a n d w h a t i s m a n i f e s t l y l a c k i n g  i n Spinoza's  principle  o f i n e r t i a i s t h e phase  velocity"  or i t s equivalent.  principle  and t h e method o f p r o o f i n v o l v e a " t w o - s t a t e "  conception o f motion.  Both the statement  of the  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 d e g r e e s hard t o take t h i s s e r i o u s l y f a c t remains  "with undiminished  of velocity,  as p h y s i c a l  and i t i s  theory.  t h a t S p i n o z a does employ t h i s  But the  terminology  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 n o t apply only to the p r i n c i p l e of i n e r t i a ; closer look at the f i r s t t h e r e as w e l l . i n motion move.  t w o a x i o m s , we s e e i t i n e f f e c t  Axiom 1 s t a t e s t h a t a l l bodies are e i t h e r  or at rest.  I f we  i f we t a k e a  Axiom 2 s t a t e s t h a t a l l bodies  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 motion, then i tfollows  from the c o n j u n c t i o n o f t h e  two a x i o m s t h a t no b o d i e s a r e a t r e s t , a n d t h i s 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 : motion, remain  then i t i s t r i v i a l l y  i f a l lbodies are i n  true that bodies i n motion  i n motion and a l l b o d i e s a t r e s t remain a t r e s t .  Consequently is  makes  t h e e q u a t i o n o f "moves" w i t h " i n m o t i o n "  not correct. The r e l a t i o n b e t w e e n m o t i o n a n d r e s t i n S p i n o z a ' s  physics i s not at a l l a straightforward matter. t h i n g s a r e commonly s a i d o f t h i s (a)  rest i s infinitely  Two  relation: slow motion;  i . e . the  state o f r e s t i s the l i m i t of a s e r i e s of states of motion, 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 state o f r e s t but never a c t u a l l y reach i t . (b) is  r e s t i s a s p e c i a l case o f motion,  i.e. rest  zero v e l o c i t y . Neither of these i n t e r p r e t a t i o n s i s quite  69  adequate. d i c t e d by To  Interpretation A x i o m 1, w h i l e  e x p l a i n what I t h i n k  third  (a) (b)  seems t o be  flatly  runs contrary  S p i n o z a has  to Axiom  but  which, I f e e l ,  following  faster  a  without  nonetheless  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 Consider the  2.  i n mind, I o f f e r  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  p r o b l e m s o f i t s own,  contra-  other  two.  picture:  rest  faster  -> slower  slower  negative motion  (2)  ^  positive  rest  motion  slower  (2)  can  r e p r e s e n t s what I t h i n k  I t s h o u l d be as  (1)  N e w t o n i a n i d e a o f v e l o c i t y as  while  noted that  (2)  be  taken to  a vector  i n quite  represent  quantity,  S p i n o z a had  r e p r e s e n t s the  i n f i n i t e l y slow motion but  f r o m (a)  i n mind.  idea  rest  above.  c o n n e c t i o n b e t w e e n m o t i o n and  r e s t i n Spinoza's  I first  fact that  draw a t t e n t i o n  t o the  c o n s i s t e n t l y p a i r s up  "rest" with way  of  a d i f f e r e n t sense  I n defense of t h i s i n t e r p r e t a t i o n of  he  >  faster  In this picture, the  motion  "motion" w i t h  " s l o w n e s s " , and  of looking  i n the  the thought, Ethics  "quickness",  and  i t i s r e a l l y t h e most p l a u s i b l e  a t A x i o m s 1 and  2.  Axiom 1 s t a t e s  that  any  p a r t i c u l a r ' b o d y i s i n e i t h e r one  o f two  w h i l e Axiom 2 a s s e r t s t h a t a l l bodies are one  i n f i n i t e mode u n d e r t h e  possible  states  subject to  a t t r i b u t e Extension,  the  motion-  and-rest. I f we and  a s k why  Spinoza a r r i v e d at such a  unmanageable c o n c e p t i o n ,  answer i n the a connection 31 t o 3 7 ) . i n the  P r i n c i p l e s , and  t h e n I t h i n k we  can  i n p a r t i c u l a r we  strange find  can  trace  t o the n o t i o n of q u a n t i t y of r e s t (see As  I have a l r e a d y d i s c u s s e d  P r i n c i p l e s there  i s an  n o t i o n of q u a n t i t y of r e s t .  pages  i n Chapter I I I ,  attempt to formulate T h e r e was  the  somewhat o f  a  c o n t r a d i c t i o n b e t w e e n 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 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 s l o w e r b o d i e s move t h e and  by  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 ,  the e f f e c t i v e d e f i n i t i o n of q u a n t i t y of r e s t as  i n the  r u l e s of motion:  t o the  s i z e o f b o d i e s a t r e s t , and  m o t i o n , no m a t t e r how have n o t e d the  By  slowly  absence i n the  t a k i n g r e s t as t h e  zero f o r bodies i n  (see page 3 7 ) .  A l s o he  P r i n c i p l e s of the  opposite  t h a n a s p e c i a l c a s e o f m o t i o n , he was a c o m p l e t e p r i n c i p l e o f i n e r t i a and g i v e an e l e g a n t ideas  on  the  used  q u a n t i t y of r e s t i s p r o p o r t i o n a l  one  of the p r i n c i p l e of i n e r t i a t h a t deals w i t h bodies rest.  the  proof of i t ,  one  of motion, able  a t the  to  may half  at  rather  formulate  same t i m e  that f i t t e d i n with  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 .  his  71 T h i s i s i n c i d e n t a l t o my somewhat s p e c u l a t i v e , development of t o Newton. of  the  the  I think  p r i n c i p l e of  I n the  Principles  p r i n c i p l e of  in a straight  but  m a i n theme, we  can  see  an  interesting  i n e r t i a from Descartes  there i s a c l e a r  i n e r t i a as p e r t a i n i n g  l i n e , but  and  i t i s w i t h the  to uniform motion  other half  p r i n c i p l e that profound d i f f i c u l t i e s arose. f i c u l t i e s have t h e i r source i n the  statement  These  d e f i n i t i o n of  able to formulate a complete p r i n c i p l e  i n e r t i a by  taking  into a directed by  introducing  from body. were the  it  n o t i o n of  i n the  same, so  c o n c e i v e d as  of  c o r p o r e a l s u b s t a n c e and  o f m o t i o n and and  rest  as  t o the  a body, or a s t a t e  e x t e n s i o n , as  its  i n which  in  as  correlative  the  conception  concepts, of T h a t he  f o r m u l a t i o n i s not  motion  was  inertia  unable  surprising,  remembered t h a t Newton's p r i n c i p l e of  be  I s h a l l argue  rest  symmetrical opposites.  to  body  of  i s therefore l e d to a  be  only  identity  he  problem of  p u z z l e s of  had  and  i t should also  so  something separate  committed t o the  to achieve a s a t i s f a c t o r y but  of  making motion  c o u l d do  that motion n e c e s s a r i l y  S p i n o z a was  Chapter Eight,  space as  by  dif-  C a r t e s i a n u n i v e r s e s p a c e and  a quality  i s found.  z e r o m o t i o n and  q u a n t i t y , h o w e v e r , he the  But  as  the  rest.  Newton was  rest  of  solution  created  own.  Thus f a r I h a v e b e e n d e a l i n g w i t h t h e  first  category  o f laws o f m o t i o n , namely those  in isolation. there  i s i n t h e E t h i c s o n l y one  nothing  bodies  sample, the f o u r t h axiom.  f o u r t h a x i o m seems t o p l a y no  r o l e i n the p h y s i c s of the E t h i c s : and  f o l l o w s from i t .  nothing  The  particular  l e a d s up  to  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 a x i o m i s t o c o n s i d e r i t a s t h i n g necessary To  i s only necessary p a r t i c l e s and  a c t i o n of bodies  i s essential.  But  then,  the  as a p e r f e c t l y g e n e r a l  inter-  1  was  law c o v e r i n g a l l k i n d s  o r w h e t h e r i t was  intended  w i t h a c e r t a i n type o f c o l l i s i o n ,  similar  of  question  t h a t comes t o m i n d i s w h e t h e r t h e f o u r t h a x i o m  should  i t  t o give a h i s t o r y of the motions  f o r t h i s a law t h a t , d e a l s w i t h the  of c o l l i s i o n s ,  some-  t o make t h e p h y s i c s o f t h e E t h i c s c o m p l e t e .  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 ,  intended  bodie  Of l a w s 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  At f i r s t s i g h t the  it  dealing with  only to  i n which case  consider i t i s a prototype,  o r sample o f  deal  we other,  laws. To  t r y t o a n s w e r t h i s q u e s t i o n , we  look at i t a l i t t l e i s that i s being  more c l o s e l y , t o see  a s s e r t e d by t h e  axiom.  t r o v e r s i a l word i n the axiom i s the word  should  j u s t what i t The  most c o n -  "immovable".  I t m i g h t mean " p r a c t i c a l l y i m m o v a b l e " s u c h as i n t h e case of a very l a r g e s t a t i o n a r y o b j e c t being much s m a l l e r one,  s t r u c k by  a  w h i c h w o u l d mean t h a t t h e a x i o m a p p l i e s  only t o s p e c i a l cases. the o b j e c t b e i n g  "Immovable" m i g h t a l s o mean t h a t  struck i s n o t going  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 motion i n the P r i n c i p l e s ; i s not a general  i n t h i s case,  law of c o l l i s i o n .  t h e a x i o m m i g h t be c o n s i d e r e d i s t o read  "immovable"  a g a i n , t h e axiom  The o n l y way i n w h i c h  as a p e r f e c t l y g e n e r a l l a w ,  as "considered  immovable".  i t m i g h t 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 the  r e l a t i v e m o t i o n o f t h e two b o d i e s  What only  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 , take  temporarily e i t h e r of the bodies  we  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 m o v i n g 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 a p p r o a c h  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 i s nothing  t o support  there  the contention that Spinoza  was  t h i n k i n g i n t e r m s o f f r a m e s o f r e f e r e n c e , i t seems  very  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 t h e o n e h a n d , t h e  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 presented,  m i g h t 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, there  seems t o b e  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 s e n s e o f t h e axiom: as a g e n e r a l  law. Since there  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 t h e f o u r t h a x i o m i s b u t one member o f a g r o u p o r  system of laws of motion.  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 law as r e p r e s e n t a t i v e two  are  clues: (a)  The  developed of the that Spinoza, by  there  s c i e n c e o f o p t i c s was  s c i e n c e s o f t h a t day.  a s w e l l a s o t h e r s , was  the  saw  i n the  s c i e n c e , and  i n o p t i c s a model f o r a l l of s c i e n c e .  m e t r i c a l o p t i c s has and  I t i s certain  g r e a t l y impressed  t h e p o w e r and p r e c i s i o n o f o p t i c a l  l i k e l y saw  the most h i g h l y  two  b a s i c laws,  law of r e f r a c t i o n . law  My  the  law o f  conjecture  Geo-  reflection  i s that  of r e f l e c t i o n , w i t h i t s obvious  quite  Spinoza  connection  w i t h the behaviour of small bodies rebounding o f f l a r g e r o n e s , as one for  t h a t reason i n c l u d e d i t i n the (b)  the  o f t h e most f u n d a m e n t a l laws o f n a t u r e ,  I n the  about c o l l i s i o n s  considerable  s p a c e and  on s o u n d f o o t i n g . he  felt  Ethics.  P r i n c i p l e s S p i n o z a i s s e e n t o amend  fourth r u l e of motion.  nothing  and'  The  Descartes's  a t an a n g l e ,  e f f o r t t o put  version and  Spinoza  devotes  his modified  version  s u p p o s i t i o n , here, then,  q u i t e confident about the  says  i s that  soundness o f t h i s  o f m o t i o n , c o n f i d e n t e n o u g h t , a t any  rule  rate, to include i t  i n h i s magnum o p u s . Another i n t e r e s t i n g f e a t u r e of the i s i t s v a g u e n e s s on t h e motion.  The  s u b j e c t of the  f o u r t h axiom  conservation  p h r a s e " i n o r d e r t h a t i t may  continue  of its  m o t i o n " i s n o t s p e c i f i c e n o u g h t o make t h e a x i o m  into  a p r i n c i p l e o f conservation o f motion i n c o l l i s i o n s , of t o guarantee t h a t motion i s conserved 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  s u p p o s e d t o be d e a l i n g w i t h .  i s somewhat p u z z l i n g ;  if  o n t h e one h a n d , S p i n o z a  This  intended  the 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 d o e s h e n o t make i t more s p e c i f i c ?  I f , on the  o t h e r h a n d , he d o e s n o t i n t e n d t h e a x i o m t o s a y a n y t h i n g a b o u t 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 failure  t o deal w i t h t h i s  subject?  One m i g h t a r g u e t h a t s i n c e t h e E t h i c s i s n o t 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 , Spinoza not I  was  g r e a t l y concerned about c o n s e r v a t i o n o f motion, b u t  f i n d i t hard  hazard  t o b e l i e v e that Spinoza  i n t h i s matter.  w o u l d be s o h a p -  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 t h e t o p i c i m p o r t a n t .  In  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 chapter  ( s e e p a g e 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 which  " t h e same p r o p o r t i o n o f m o t i o n a n d r e s t "  i s conserved.  I f conservation of motion i s not guaranteed  in  individual  collisions,  the whole u n i v e r s e w i l l in  then there  n o t r u n down, s o t o s p e a k .  Spinoza's thought, the universe  maintains  i t s e l f without  i s no g u a r a n t e e  that Since,  i s a system t h a 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 the phrase  remains then the t a s k of e x p l a i n i n g  " i n o r d e r t h a t i t may  how  continue i t s motion"  c a n b e 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 principle  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 of the  o f i n e r t i a and n o t e t h a t w h a t i s m i s s i n g i n  both the 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  "with undiminished v e l o c i t y " , instances  phrase  and I t h i n k i n b o t h  t h i s o m i s s i o n f i n d s i t s cause  i n the  fact  t h a t S p i n o z a would have c o n s i d e r e d t h i s p h r a s e T h a t means, t h e n , t h a t t h e p h r a s e  "may  redundant.  continue 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  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 motion  of c e r t a i n t y  t o say  that  i s conserved. My m a j o r  concern i n t h i s c h a p t e r has been t o  d i s c u s s w h e t h e r S p i n o z a ' s t h e o r y o f m o t i o n marks t h e physics  o f t h e E t h i c s as something  f e r e n t from the C a r t e s i a n p h y s i c s , c l u s i o n i s t h a t i t does n o t .  fundamentally a n d my m a j o r  On t h e c o n t r a r y ,  i s g o o d e v i d e n c e t h a t i n t h e E t h i c s he essentially Principles.  t h e same k i n d o f p r o b l e m s  difcon-  there  i s dealing  with  a s c r o p up i n t h e  F o r i n s t a n c e , h i s amendment o f t h e  principle  of 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 bodies a t rest,  c a n b e t a k e n as an e f f o r t t o i m p r o v e  on  the  77 Cartesian physics. symmetrical  H i s c o n c e p t i o n o f m o t i o n and r e s t as  o p p o s i t e s c a n 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  to 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  quantity of rest i n the P r i n c i p l e s . bears he,  t o formulate  The f o u r t h a x i o m  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 of motion,  which  i n the P r i n c i p l e s , i s already subjecting t o consider-  able a l t e r a t i o n .  While  i t i s t r u e t h a t he does n o t t a k e  over from t h e P r i n c i p l e s t h e whole s e t o f laws o f motion, t h e m a i n r e a s o n may h a v e s i m p l y b e e n h i s d e s i r e t o k e e p t h e amount o f p h y s i c a l t h e o r y t o a b a r e minimum, a n d e v e n i f h e d i d h a v e q u a l m s c o n c e r n i n g t h e v a l i d i t y o f some of the r u l e s of motion,  there i s not a shred of evidence  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 l a w t o be  invalid. On t h e w h o l e , t h e p h y s i c s o f t h e E t h i c s s h o u l d  be  l o o k e d on a s a c o n t i n u a t i o n o f t h a t o f t h e P r i n c i p l e s ;  the former  i s b a s i c a l l y a condensation  of the l a t t e r ,  w i t h some amendments, some d e l e t i o n s , a n d some e x t e n s i o n s . Spinoza's  w r i t i n g of the P r i n c i p l e s i s often dismissed  as a mere c o m m e n t a r y o n D e s c a r t e s , p e r f o r m e d m a i n l y a s 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 consider t h i s a serious mistake, extent the ideas presented s e n t a t i v e o f Spinoza's  since t o a great  i n the P r i n c i p l e s are repre-  thought.  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 the P r i n c i p l e s the p r i n c i p l e of 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 straight line; 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 S I M P L I C I S S I M A  The c e n t r a l  idea i n the theory of  individuals  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 w h o l e i m p l i e s o r p r e s u p p o s e s t h e e x i s t e n c e of simplest elements,  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 . defines the simplest bodies  i n a n o f f - h a n d manner  a f t e r A x i o m 4, b u t a f t e r t h a t s a y s v e r y l i t t l e them s p e c i f i c a l l y .  Spinoza just  more a b o u t  He s a y s n o t h i n g , d i r e c t l y , a b o u t  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  w o r s e , he f a i l s t o make c l e a r w h e t h e r t h e r e e v e n a r e s u c h 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 w o r d s we a r e  not even sure whether t h e r e a c t u a l l y e x i s t particles,  simplest  o r w h e t h e r e a c h b o d y s h o u l d a l w a y s be  of as a n a l y z a b l e i n t o s i m p l e r  thought  elements.  The g e n e r a l l i t e r a t u r e o n t h e 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 n o t a g r e a t d e a l o f a t t e n t i o n seems t o h a v e b e e n d i r e c t e d t o w a r d  discovering exactly  what S p i n o z a h a d i n m i n d when he t a l k s a b o u t s i m p l e s t bodies.  As an e x a m p l e , t h e r e i s S t u a r t H a m p s h i r e ' s  commentary o n t h i s  topic : 1  I t was n o t u n t i l t h e e n d 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 a s 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 t h e e x t e n d e d w o r l d , a n d , (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 e n e r g y , . a n d , ( c ) o f c o n f i g u r a t i o n s of these 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 concepts. More s p e c i f i c a l l y a b o u t t h e p a r t i c l e s ,  Hampshire  says: 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 k n o w l e d g e , are represented i n t h e l i g h t o f systematic knowledge s o l e l y as measurable changes i n t h e 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 undifferentiated particles. Hampshire's book h a s been v e r y h e l p f u l on t h e subject  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 , a n d y e t w h a t he  says leaves  a great  d e a l t o be a s k e d .  For instance,  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 t h e u l t i m a t e p a r t i c l e s a r e o f t h e same s i z e o r t h e 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  ultimate p a r t i c l e s ultimate? "indivisible"?  Does " u l t i m a t e " mean  Or e v e n , i n what sense a r e t h e c o r p .  simp, p a r t i c l e s a t a l l ? as a b s t r a c t e n t i t i e s l i k e  P e r h a p s we s h o u l d  l o o k u p o n them  t h e 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 a c c o u n t f o r t h e phenomena o f t h e m a t e r i a l w o r l d .  A l l these  questions  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 says i n t h e 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 t h e n a t u r e o f t h e  c o r p . s i m p . , we  should d i r e c t our a t t e n t i o n to the  i n g q u e s t i o n : ' are the c o r p . simp, extended, C a r t e s i a n p a r t i c l e s , or are they not? n e g a t i v e and evidence;  like  For both  the  the  t h e a f f i r m a t i v e a n s w e r s t h e r e i s good  t h i s evidence 1.  i s as  follows:  Pro extended p a r t i c l e s :  (a)  A x i o m 4,  the o n l y law of c o l l i s i o n i n  the 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 another body. one  follow-  This c l e a r l y i n d i c a t e s that at  of  least  of the p a r t i e s to the 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 o r w i t h complex ones. correct,one  That the f i r s t  i s shown b y t h e s e n t e n c e  the statement  of the  alternative directly  bodies i s the  following  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 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 b y 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 ,  f o l l o w s the sentence phrase:  just referred to, contains  "When a number o f b o d i e s  a p p l i c a b l e t o any  a l s o apply t o the lowest l e v e l  For  individual,  dif-  this i t must  i n d i v i d u a l s , namely  whose c o n s t i t u e n t s a r e c o r p . s i m p . . c o r p . simp, have magnitude;  the  o f t h e same o r  f e r e n t magnitudes are p r e s s e d t o g e t h e r " . d e f i n i t i o n t o be  which  those  I t f o l l o w s t h a t the  t h i s , together with  the  82 phrase  "pressed together", (c)  particles.  A x i o m 5, a d e f i n i t i o n o f h a r d n e s s ,  ness and f l u i d i t y , d e f i n e s of contact  suggests extended  these i n terms o f t h e s u r f a c e s  between the c o n s t i t u e n t s o f a body.  absence o f evidence t o t h e c o n t r a r y , supposition that the lowest l e v e l  I n the  i ti sa legitimate  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 . as e x t e n d e d  soft-  simp, o u t  particles.  (d)  Lemma 5 s t a t e s t h a t i f " t h e 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  other  conditions  vidual w i l l  r e m a i n i n g t h e same, t h e n t h e i n d i -  " r e t a i n the nature i t had before".  same p o i n t a s made i n ( b ) a n d ( c ) above a p p l i e s 2. (a) the  corp.  Contra extended  The here.  particles:  The s t a t e m e n t f o l l o w i n g A x i o m 2  simp, as those b o d i e s  describes  "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 b y m o t i o n a n d r e s t , s p e e d a n d s l o w n e s s alone".  This  appears t o exclude u n e q u i v o c a l l y t h e  p o s s i b i l i t y that the corp.  simp, vary  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 -  tinguished not i n substance, but " i n respect and  rest".  says:  t o motion  A l s o , i n t h e S c h o l i u m a f t e r Lemma 7, S p i n o z a  83 Up t o t h i s p o i n t we h a v e 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 f r o m one a n o t h e r s o l e l y b y m o t i o n and r e s t , s p e e d a n d s l o w n e s s , t h a t i s t o s a y , t o be composed o f t h e most s i m p l e b o d i e s . Both these quotations serve t o r e i n f o r c e  the  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 Spinoza  say  t h a t the 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 s p e a k o f s h a p e ,  m a g n i t u d e a s p e r t a i n i n g t o them?  On  surface,  and  the b a s i s of the  e v i d e n c e o u t l i n e d a b o v e , 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 t h e p a r t i c l e s a r e e x t e n d e d , b u t a r e a l l o f t h e same and s h a p e .  size  B u t t h i s makes S p i n o z a i n t o a n a t o m i s t , a n d  I h a v e n o t f o u n d one this contention:  i o t a of evidence t h a t might  support  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  deal of evidence against i t , dispute w i t h Robert Boyle.  e s p e c i a l l y i n the Furthermore,  the  nitre  atomist  hypothesis i s almost 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 the d e n i a l o f t h e e x i s t e n c e o f a vacuum. f u r t h e r i n t o t h i s q u e s t i o n , we  Rather than  delving  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 p h r a s e  "distinguished i n respect to  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  explan-  a t i o n t h a t comes most r e a d i l y t o m i n d i s t h a t t h 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 , i s a n o t h e r way  of looking a t i t .  I f we  phrase  but there  t h i n k back t o  t h e 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 t h e 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 created the p a r t i c l e s ,  which  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 d e p e n d 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 .  It 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 ,  that  then,  t h e y a r e 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 . f o l l o w s from t h i s t h a t t o say t h a t the corp.  It  simp, a r e  d i s t i n g u i s h e d s o l e l y by m o t i o n and r e s t i s n o t 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 , a s l o n g a s we t h i n k o f t h e m i n t e r m s o f t h e Cartesian  physics. To s u p p o r t t h e c o n t e n t i o n  are v e r y following  that the corp.  s i m i l a r t o the Cartesian p a r t i c l e s ,  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  s t r o n g l y t h a t t h e lemma d o e s n o t a p p l y  that a l l bodies d i f f e r i n respect not w i t h respect  that a l l bodies,  t o substance.  The lemmas a s s e r t s  t o m o t i o n and r e s t , Now i t i s o b v i o u s  s u c h as p e o p l e , a p p l e s ,  or stones, can  s a i d t o d i f f e r i n a g r e a t many w a y s , w h i c h  s i z e and shape.  very  o n l y t o the corp.  simp., b u t t o the i n d i v i d u a l s as w e l l .  be  are the  considerations: (a)  and  there  simp,  includes  The r e a s o n why S p i n o z a d o e s n o t m e n t i o n  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 n o t d i f f e r w i t h r e s p e c t e l s e t h e y may d i f f e r i n .  t o substance, whatever  Hence t h e f a c t t h a t i n t h e  d e f i n i t i o n o f a s i m p l e s t b o d y he d o e s n o t m e n t i o n  size  o r s h a p e , i s n o t a s i m p o r t a n t a s i t seems a t f i r s t  sight.  A l s o , b y c o m p a r i n g Lemma 1 and t h e d e f i n i t i o n o f a  corp.  s i m p , we mind.  b e g i n t o see more c l e a r l y w h a t S p i n o z a h a s  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 t h e i r c o n s t i t u t i o n , and t h e they are not  composite,  corp. simp., which,  c a n n o t be  in  of  since  said to differ  i n their  constitution. (b)  A p o s s i b l e o b j e c t i o n t o comparing  the  corp. 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 account  i s given of the  origination  of the p a r t i c l e s , while i n the E t h i c s there i s nothing to  suggest  t h a t the  as r e l a t i v e l y  c o r p . s i m p , a r e t o be  stable particles.  The  thought  of  answer i s t h a t i n  the p h y s i c s of the 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 be  thought  has  time  o f as a c o n t i n u o u s p r o c e s s , s o m e t h i n g t h a t  a l w a y s gone o n ,  a l s o be  and w i l l  a l w a y s go o n .  I t should  noted t h a t the c r e a t i o n of p a r t i c l e s a t a  i s i n the P r i n c i p l e s presented  definite  as a h y p o t h e s i s ,  s o m e t h i n g t h a t m i g h t be r e a s o n a b l y s u p p o s e d t o h a v e p l a c e , and t h u s i s n o t o f P a r t Two  should  taken  a p a r t of the l o g i c a l s t r u c t u r e  of the P r i n c i p l e s :  e x p l a i n i n g how  as  some o t h e r way  of  t h e p r e s e n t s t a t e o f a f f a i r s came t o  m i g h t be e q u a l l y a c c e p t a b l e .  I n any  case, t o  be  Spinoza  the c r e a t i o n of a l l the p a r t i c l e s at a d e f i n i t e  point  i n t i m e i s q u i t e u n a c c e p t a b l e , s o t h a t i n h i s scheme i t i s n o t 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 enduring e n t i t i e s ;  b u t a t t h e same t i m e t h i s d o e s n o t  n e c e s s a r i l y imply a r a d i c a l s h i f t from the physics.  relatively  Cartesian  I n both cases the d e t a i l e d e x p l a n a t i o n of  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 t h e of p a r t i c l e s of v a r i o u s s i z e s and (c)  motions  shapes.  I n the d i s p u t e w i t h Robert Boyle over the  r e d i n t e g r a t i o n of n i t r e ,  S p i n o z a ' s arguments are  v i n c i n g p r o o f o f h i s acceptance of the p r a c t i c a l of the Cartesian physics.  i n character.  f o r proving that nitre i s H i s own  e x p l a n a t i o n s are  completely i n a c c o r d w i t h the p h y s i c s of the He  aspects  Spinoza considers Boyle's  experiments f a r from adequate heterogeneous  con-  Principles.  suggests t h a t the main d i f f e r e n c e between s p i r i t  of  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 t h e l a t t e r i n a s t a t e o f r e s t , w h i l e those of the former e a c h o t h e r w i t h no l i t t l e  vehemence".  The  are  agitate  s a l t of  nitre,  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 w h i c h t h e p a r t i c l e s o f n i t r e lodged.  The  taste of n i t r e  are  he a t t r i b u t e s t o t h e f a c t  the sharp p o i n t s o f the n i t r e p a r t i c l e s t o u c h the  that  tongue.  These a r e 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  spirited  87 defense of the  Cartesian  Points supporting corp.  physics.  ( a ) , (b)  and  (c) d i s c u s s e d above  e v i d e n c e f o r the main c o n c l u s i o n :  simp, of the E t h i c s are v e r y  of the C a r t e s i a n p h y s i c s . i s a great  To  sum  As  that  s i m i l a r to the up my  the particles  argument,  deal of m a t e r i a l t h a t p o i n t s t o the  ness of t h i s c o n c l u s i o n , w h i l e there one  are  there  correct-  i s i n e f f e c t only  s t a t e m e n t i n t h e E t h i c s t h a t c a s t s d o u b t on i t . I h a v e shown, t h e r e  is a plausible interpretation  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 The  difficulty.  most i m m e d i a t e i m p l i c a t i o n o f t h i s  c l u s i o n i s t h a t i f we  wish to study  o f t h e p h y s i c a l u n i v e r s e , we  are  m a t e r i a l o f t h e E t h i c s , b u t we t o c l a r i f y some o f t h e  Spinoza's  not  can  theories  limited to  use  con-  the  the P r i n c i p l e s  o b s c u r i t i e s of the E t h i c s .  are  i n the  had  s e r i o u s qualms a b o u t .  There  P r i n c i p l e s u n d o u b t e d l y many i t e m s t h a t One  c o n c e r n s the  creation of p a r t i c l e s ,  and  s i x t h r u l e of motion;  these are  direct textual confirmation o t h e r hand, there  i s no  there  original  i s a l s o the the  case o f  o n l y two  is available.  But  on  corp.  the  s o l i d e v i d e n c e t h a t he h a d  any physics,  i t s method.  A more f a r r e a c h i n g l a r i t y of the  the  f o r which  o b j e c t i o n s t o the b a s i c f e a t u r e s of the C a r t e s i a n i t s b a s i c p r e m i s s e s and  Spinoza  i m p l i c a t i o n of the  simp, t o the C a r t e s i a n  simi-  particles  88 i s t h a t i t c a s t s a new l i g h t o n t h e more f u n d a m e n t a l aspects  o f Spinoza's cosmology.  I t leads  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 of h i s doctrine of Substance, A t t r i b u t e a n d Mode, t o t h e one t h a t i s g e n e r a l l y I will  deal w i t h t h i s f u r t h e r i n the next  accepted.  chapter.  I t may seem t h a t S p i n o z a ' s a g r e e m e n t w i t h t h e basic features of the Cartesian physics i m p o r t a n c e a s an o r i g i n a l of the ideas of Descartes,  makes h i m o f l e s s e r  t h i n k e r a n d more o f a n e x p o s i t o r at l e a s t i n the realm of  physical science, but I f e e l t h i s impression Instead of merely expounding Descartes's  i s false.  v i e w s , he i s  e n g a g e d i n t h e t a s k o f s o r t i n g o u t t h e more f u n d a m e n t a l aspects  of the Cartesian physics  i n order  t o p u t i t on  a s o u n d e r f o o t i n g , a n d he i s g r a p p l i n g w i t h t h e p r o f o u n d contradictions inherent  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 of the modernity of Spinoza's ideas.  the topic  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 structure of the p h y s i c a l universe of science  a n d modern p h i l o s o p h i e s  are at t h e best very tenuous.  Besides,  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 n e e d 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  light.  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 impression b i t naive;  that the physical theory  i t presents  i s a  a closer examination reveals that 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 of motion,  o f i m p l a u s i b l e laws  t h a t i t deals w i t h the e x t r e m e l y  abstruse  i s s u e of the m e t a p h y s i c a l foundations of s c i e n c e .  See  Hampshire, page  79.  90 CHAPTER V I I I MOTION AND  i  PARTICLES  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  of the s t r u c t u r e of the p h y s i c a l universe the  same a s t h e C a r t e s i a n o n e ;  i s a plenum,  conception i s basically  t h a t i s , the  universe  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  s o 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 a c t i o n , by c o n t a c t a l o n e ,  of the b a s i c p a r t i c l e s .  evidence f o r t h i s contention f a l l s categories which I w i l l 1.  The  i n t o c e r t a i n major  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 .  I n the physics of the E t h i c s there i s  r e a l l y o n l y one  s t a t e m e n t t h a t does n o t f i t i n w i t h t h e  i n t e r p r e t a t i o n of the corp.  s i m p , 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 s h a p e s , namely t h a t the 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 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 chapter,  inter-  i n the  simplest alone.  previous  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 a r e  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, a s I have  there i s a p l a u s i b l e explanation f o r t h i s i n t h a t i n t h e C a r t e s i a n scheme, i t was  mentioned,  discrepancy*  the a d d i t i o n  of motion t o e x t e n s i o n which c r e a t e d the p a r t i c l e s t h a t t h e shapes and s i z e s o f t h e p a r t i c l e s depend  so directly  91 on o n l y one  v a r i a b l e , namely the  in extension. of the  Therefore,  d i s t r i b u t i o n of motion  i n a strong sense, i t i s t r u 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 they are  e n t i a t e d by m o t i o n and 2.  rest  differ-  alone.  T h r o u g h o u t 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 the p r o b l e m s o f the  continuum;  his  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 p r o b l e m s i s most readily explained  i f h i s concept of the  the p h y s i c a l universe  i s b a s e d on t h e  s t r u c t u r e of  same b a s i c p r e m i s s e s  as t h o s e o f t h e C a r t e s i a n p h y s i c s , t h e m a i n p r e m i s s that corporeal  s u b s t a n c e and e x t e n s i o n  a r e one  and  being the  same. Already  i n the  P r i n c i p l e s we  w i t h the problems of the continuum. t o P r o p o s i t i o n 6,  P a r t Two,  there  some o f t h e p a r a d o x e s o f Z e n o ; c r i b e d as a r i s i n g f r o m the  find a  In the  I n the  the paradoxes are  he  i n terms of the  1663,  to t h i s topic,  t o p i c s of time,  continuum.  the  motion i n t o  l e t t e r t o Mayer, A p r i l  Spinoza deals e x t e n s i v e l y w i t h the extension  des-  i l l e g i t i m a t e d i v i s i o n of  which i s greatly s i g n i f i c a n t with respect  and  Scholium  i s a discussion of  c o n t i n u u m i n t o p a r t s , t i m e i n t o moments and units of v e l o c i t y .  concern  For  duration  example,  a s s e r t s t h a t i f i t i s a s s u m e d t h a t t i m e i s composed  o f moments, i t w o u l d n o t be p o s s i b l e t o u n d e r s t a n d an h o u r c o u l d  pass:  how  92 F o r i n o r d e r t h a t t h e h o u r may p a s s i t w i l l be necessary 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 r e m a i n s o f t h e r e m a i n d e r ; and i f y o u t h u s go o n 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 , y o u w i l l n e v e r be a b l e t o r e a c h t h e e n d o f t h e h o u r . T h e r e f o r e , many who h a v e n o t g o t u s e d t o d i s t i n g u i s h i n g t h e t h i n g s of 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 c o m p o s e d o f moments. It  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  p a r a d o x e s b y means o f h i s t h e o r y o f k n o w l e d g e .  he c o n t r a s t s  "things of reason" with  "real things", while  i n o t h e r i n s t a n c e s he e m p h a s i z e s t h e d i s t i n c t i o n the  i n t e l l e c t and the i m a g i n a t i o n .  t i n c t i o n between  Here  between  Whether t h e d i s -  "things o f r e a s o n " and " r e a l t h i n g s " i s  the  same a s t h e d i s t i n c t i o n b e t w e e n  the  i m a g i n a t i o n i s one p r o b l e m ;  t h e i n t e l l e c t and  more g e n e r a l l y ,  how  Spinoza attempts t o r e s o l v e the paradoxes o f the continuum involves a thorough examination of h i s theory of knowledge, thesis.  w h i c h i s d e f i n i t e l y beyond  t h e scope o f t h i s  The m a i n p o i n t i s t h a t he d e v o t e s 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 p a r a d o x e s o f t h e c o n t i n u u m and t h a t t h e s e a r e 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 t h e p a r a d o x e s of  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 t h e p r o b l e m s  of  t h e c o n t i n u u m i s a b u n d a n t l y c l e a r , b u t s o f a r we  h a v e s e e n no c l e a r c o n n e c t i o n b e t w e e n  the paradoxes o f  Zeno a n d t h e p r o b l e m s o f t h e c o n t i n u u m g e n e r a t e d b y t h e  93 i d e n t i f i c a t i o n of p h y s i c a l substance with space i n the indeed  Cartesian physics.  c o n n e c t e d , we  P r o p o s i t i o n 15,  can  P a r t One  see  T h a t t h e s e two  from the  and  i . e . not by  a t the  c a n n o t be  the  c a n be  same t i m e be b o t h i n f i n i t e  a r g u m e n t s o f t h o s e who  who  to  Scholium  a  corporeal  and  simple,  He  does  so  believe that  God  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  is necessarily finite t o God  In that  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 .  a t t a c k i n g the  are  long Scholium  of the E t h i c s .  S p i n o z a d e f e n d s t h e p o s i t i o n t h a t God being  geometrical  and  hence cannot p r o p e r l y  i s a perfect being.  He  represents  pertain  some o f  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 s a y , 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 ; each 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 o f i n f i n i t e . I f e a c h p a r t be f i n i t e , t h e n t h e 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 . If e a c h 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 be m e a s u r e d b y e q u a l p a r t s o f a f o o t e a c h , i t must c o n t a i n an i n f i n i t e number o f s u c h p a r t s , and s i m i l a r l y i f i t be m e a s u r e d b y e q u a l p a r t s o f an i n c h e a c h ; 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. 1  2  Spinoza s t a t e s t h a t the argument l i e s  in their  f a l l a c y of h i s opponents'  "...suppostion  that b o d i l y substance  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 be  absurd.  He  considers  says:  And i n d e e d i t i s n o t l e s s a b s u r d t o s u p p o s e 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 s u p p o s e t h a t a b o d y i s composed o f  to  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 o u g h t t o a d m i t t h i s , a n d e s p e c i a l l y t h o s e who d e n y t h a t a vacuum c a n 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 ; like  t o know how h§_ r e s o l v e s  we w o u l d n a t u r a l l y  the problems t h a t a r i s e  from the s u p p o s i t i o n t h a t corporeal substance i s i n f i n i t e . H i s s o l u t i o n i s best expressed 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 , a n y one s h o u l d a s k why t h e r e i s a n a t u r a l tendency t o consider q u a n t i t y as capable of d i v i s i o n , I r e p l y that quantity 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 or s u p e r f i c i a l l y ; t h a t i s t o s a y , as we i m a g i n e i t , o r e l s e a s s u b s t a n c e , i n w h i c h way i t i s conceived by the i n t e l l e c t alone. I f , therefore, we r e g a r d q u a n t i t y ( a s we do o f t e n a n d 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 , a n d c o m p o s e d o f p a r t s ; b u t i f we r e g a r d i t a s i t e x i s t s i n t h e i n t e l l e c t , and c o n c e i v e i t i n s o f a r a s 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 a n d 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 o u t 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 of reason and r e a l t h i n g s ;  h e r e he g i v e s h i s s o l u t i o n  to the problem of d i v i s i b i l i t y the  intellect  evident  o f substance i n terms o f  and t h e i m a g i n a t i o n .  i n C h a p t e r Two o f t h e S h o r t  discusses  things  T h i s same theme i s T r e a t i s e , w h e r e he  t h e same t o p i c , t h e 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 a n d t h e s i m p l i c i t y o f God.  T h e r e he s a y s  and w h o l e a r e n o t t r u e o r r e a l e n t i t i e s ,  but only  "Part things  95 of  reason". In  involvement obvious for  a l l these v a r i o u s i n s t a n c e s o f  Spinoza's  w i t h the problem of t h e i n f i n i t e ,  i t is  that there  i s something very important  h i s s y s t e m , and what I t h i n k i s a t s t a k e  at stake  i s the  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  C h a p t e r T h r e e I h a v e m e n t i o n e d some o f t h e c o n c e p t u a l puzzles that a r i s e n a t u r a l l y out of the i d e n t i f i c a t i o n of c o r p o r e a l substance  with extension.  The f a c t i s t h a t  there i s a basic c o n t r a d i c t i o n i n p i c t u r e of the universe 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 m o t i o n t o c r e a t e t h e w o r l d o f v a r i e t y and change.  A s l o n g a s we t h i n k o f  e x t e n s i o n a s some s o r t o f g l a s s y s u b s t a n c e 3 , homogeneous a n d e x t e n d i n g t h e n we  perfectly  indefinitely i n a l l directions,  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 f r a g m e n t s a n d 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 i s not substance  substance  o r m a t e r i a l of any k i n d , i t i s pure  e x t e n s i o n , geometrical 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 substance  as being  p e r f e c t l y homogeneous, a c o n t i n u u m , a n d y e t a t t h e same time  t h i n k i n g o f i t a s 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 Spinoza's  view, leads t o the  p a r a d o x e s o f Zeno. 3.  Spinoza's  v i e w s o n t h e vacuum r e i n f o r c e  the p o i n t s  discussed  above.  Both i n the Scholium t o  P r o p o s i t i o n 1 5 , P a r t Two o f t h e E t h i c s a n d i n C h a p t e r  Two  of the Short T r e a t i s e Spinoza's d i s c u s s i o n o f the u n i t y of p h y s i c a l substance i s coupled w i t h a d e n i a l of the existence the  o f t h e vacuum.  S p i n o z a ' s argument i s e x a c t l y  same a s t h a t o f t h e P r i n c i p l e s .  l o g i c a l absurdity,  The vacuum i s a  " s o m e t h i n g p o s i t i v e a n d y e t no b o d y " ,  as he p u t s i t i n t h e S h o r t T r e a t i s e .  I n the Scholium  j u s t m e n t i o n e d , S p i n o z a makes a c l o s e c o n n e c t i o n the  between  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  of 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 s o 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 b e a n n i h i l a t e d , t h e r e s t r e m a i n i n g , a s 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 s o f i t t e d t o g e t h e r t h a t t h e r e c a n be no vacuum. Spinoza considers  t h a t a gap i n t h e c o n t i n u u m  i s contradictory t o the very  n o t i o n of a continuum.  above p a s s a g e 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  The  Spinoza  t h o u g h t 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 n o t on some abstract metaphysical plane,  but i n rather  concrete,  down-to-earth terms, unless,  o f c o u r s e , he was n o t  s p e a k i n g a b o u t t h e same k i n d o f vacuum w h i c h was investigated experimentally  being  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  physics.  97 4.  S p i n o z a ' s i d e a s on t h e n a t u r e o f  scientific  method are 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 t h e s t y l e o f h i s a r g u m e n t s a n d of  the c h a r a c t e r  h i s w r i t i n g there i s a great d e a l of s i m i l a r i t y  the b a s i c method of the P r i n c i p l e s . as o p e n i n g s t a t e m e n t  the  The  to  Principles  has  following:  I t i s o n l y a s k e d h e r e t h a t e a c h one a t t e n d a s 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 f r o m t h e obscure. This statement  a p p l i e s t o the method o f  and e s p e c i a l l y t o geometry.  mathematics  That S p i n o z a had g r e a t  i n t h e method o f geometry w h i c h proceeds t r u t h s t o l e s s obvious but l o g i c a l l y  from  faith  self-evident  indisputable  truths  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 t h e g e o m e t r i c a l s t y l e 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 t h e E t h i c s . letter  t o Oldenburg  of A p r i l  Boyle's attempt t o prove by  1662,  Spinoza  I n the  criticizes  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  experiments: One w i l l n e v e r 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 b y 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 ; . . . In  inertia  t h e 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  of  not as a p r o p e r t y of m a t t e r o r as a h y p o t h e s i s  a b o u t n a t u r e , b u t as s o m e t h i n g w h i c h evident".  Hardness,  of  " i s indeed  s o f t n e s s and f l u i d i t y a r e  selfnot  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 try on  t o account f o r , but  r a t h e r a r e d e f i n e d as  c e r t a i n p r o p e r t i e s of p a r t i c l e s .  exhibits considerable  confidence  A l l i n a l l he  i n the p o s s i b i l i t y  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 of arguing  from the  nature  o f the  the  similar,  and  Spinoza are considered  d i a m e t r i c a l l y o p p o s e d v i e w s , and t h o u g h t t o be  process  motion.  T h e r e a r e a g r e a t many m e t a p h y s i c a l  on w h i c h D e s c a r t e s and  of  concepts themselves,  c o n c e p t s s u c h as s u b s t a n c e , b o d y , e x t e n s i o n , 5.  depending  i t may  issues  to  hold  therefore  be  s u r p r i s i n g that t h e i r cosmologies are  as I h a v e s u g g e s t e d .  feasible to discuss  Of  course,  i t is  not  a l l t h e s e i s s u e s t o show t h a t  different philosophies  are not  c o s m o l o g i e s , but  i s one  there  so  the  reflected in their i t e m t h a t s h o u l d be  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  examined with  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 t h e  whole  Cartesian physics.  to  Tschirnhaus,  Spinoza  I n t h e l e t t e r o f May  1676,  says:  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 , a s a q u i e s c e n t m a s s , i t i s n o t o n l y , as y o u say, d i f f i c u l t t o prove the e x i s t e n c e of 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 . For matter at r e s t w i l l c o n t i n u e a t r e s t a s much a s 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 b y some s t r o n g e r e x t e r n a l cause. For t h i s reason 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 are u s e l e s s , not to say absurd. About t h i s passage Wolf^ says the f o l l o w i n g :  99 The u s e o f t h e same t e r m E x t e n s i o n b y S p i n o z a a n d D e s c a r t e s has u n f o r t u n a t e l y obscured f o r most p e o p l e t h e enormous d i f f e r e n c e b e t w e e n t h e 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 of matter. For Spinoza, Extension or Matter i s e s s e n t i a l l y p h y s i c a l energy. I t expresses i t s e l f i n t h e i n f i n i t e mode o f m o t i o n - a n d r e s t , w h i c h c o n s e q u e n t l y n e e d n o t 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 o m t h e o u t s i d e , a s was t h e c a s e i n D e s c a r t e s ' s , scheme o f t h i n g s . That there i s a g r e a t d i f f e r e n c e between 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^, b u t w h a t 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 ? at  What i s  stake i s whether motion i s something separate  p h y s i c a l substance stance.  Spinoza's  from  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 s u b -  I n the P r i n c i p l e s the c r e a t i o n of p a r t i c l e s by  m o t i o n was d e s c r i b e d a s h a v i n g t a k e n p l a c e i n t h e b e g i n n i n g , when God c r e a t e d t h e v i s i b l e w o r l d ; o r i g i n a l p a r t i c l e s w e r e p r o d u c e d i n one f e l l Spinoza's  philosophy this  p a r t i c l e s i s absurd; i n Spinoza's  swoop.  In  "one-shot" c r e a t i o n o f t h e  consequently  this creation of p a r t i c l e s  p h y s i c s i s more o f a c o n t i n u o u s  s o m e t h i n g t h a t h a s a l w a y s gone o n a n d w i l l Superficially,  a l l the  process,  go on f o r e v e r .  i t d o e s 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 m o t i o n came i n t o t h e w o r l d , as l o n g a s t h e present description of the universe i s unaffected.  How-  ever, there i s a s u b t l e but 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 t h e C a r t e s i a n p h y s i c s t h e e m p h a s i s 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 a s e n d u r i n g  entities,  100 on t h e w h o l e , 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 zistic  i s l a r g e l y a mystery).  I n the Spino-  p i c t u r e the i d e a t h a t motion i s the cause o f the  c h a r a c t e r a n d t h e e x i s t e n c e o f 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 a n d 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 extent r e a l or concrete e x i s t e n t s . little  differently,  To p u t i t a  i n the C a r t e s i a n p h y s i c s  scientific  explanations deal 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 Spinoza's p h y s i c s scientific  account b a s i c a l l y concerns i t s e l f  d i s t r i b u t i o n of motion-and-rest i n the The  with  the  the  universe.  g e n e r a l p i c t u r e o f t h e cosmos as one i n  which 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 m o t i o n and r e s t i s d i f f i c u l t harder to describe.  t o v i s u a l i z e and  of  even  The p h y s i c a l u n i v e r s e i s s p a c e ,  emptiness, which i s "shot through", so t o speak,  or  with  m o t i o n 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 -  zistic  schemes a r e t h e same:  scientific  both deal i n  terms of p a r t i c l e s i n m o t i o n , but the emphasis different.  i s quite  I n the C a r t e s i a n s y s t e m a composite body i s  a c o n g l o m e r a t i o n of p a r t i c l e s , w h i l e i n Spinoza's system it  i s a p p r o p r i a t e t o say t h a t  " t h e human b o d y , t h e r e f o r e ,  i s nothing e l s e than a c e r t a i n p r o p o r t i o n of motion rest"  ( A p p e n d i x Two, The  and  Short Treatise).  a r g u m e n t s I h a v e p r e s e n t e d i n t h e above  101 f i v e p o i n t s demonstrate c l e a r l y , I submit, t h a t  Spinoza  was s a t i s f i e d i n t h e m a i n , w i t h t h e k i n d o f p h y s i c a l theory  presented  i n the Principles,  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 s o much a t t h e C a r t e s i a n physics,  as a t t h e m e t a p h y s i c a l  system o f p h y s i c s . so l i t t l e  foundations  of that  I t e x p l a i n s why S p i n o z a  p h y s i c a l theory  character of the physics  presented  o f h i s own, a n d why t h e g e n e r a l of the Ethics i s quite  with that o f the Principles.  compatible  A t t h e same t i m e we  should  n o t e , h o w e v e r , 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 , b y fitting  i t i n t o h i s own m e t a p h y s i c a l  different  f l a v o u r , so t o speak.  scheme, a  distinctly  Or, p u t t i n g i t a  little  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 u p o n h i s m e t a p h y s i c s as a d e v e l o p m e n t o f t h e C a r t e s i a n p h y s i c s , the e f f o r t s t o deal w i t h t h e p u z z l e s C a r t e s i a n scheme. and  a result of  created  H i s doctrine o f substance,  by t h e attribute,  mode, c a n be s e e n a s a r i s i n g f r o m t h e 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 motion.  between e x t e n s i o n and  H i s d i s t i n c t i o n between i n f i n i t e ,  modes a n d f i n i t e motion breaking particulars.  o r mediate  modes c a n be i n t e r p r e t e d i n t e r m s o f up c o n t i n u o u s s p a c e i n t o t h e w o r l d o f  The t h e o r y  of individuals  as an e f f o r t t o f o u n d a t h e o r y  c o u l d be  of organized  considered  complexity  i n o r d e r 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 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 n o t needed s i n c e mind  and b o d y a r e s e p a r a t e  substances.  Spinoza's  three  kinds  o f k n o w l e d g e c a n be s e e n as d i r e c t l y r e l a t e d t o t h e d i f f e r e n t ways of l o o k i n g a t t h e u n i v e r s e : we  with  three  Imaginatio  see t h e w o r l d o f s i g h t s , s o u n d s , s m e l l s , e t c . ;  R a t i o we  see  with  t h e w o r l d a s made up o f p a r t i c l e s i 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 as e x t e n s i o n , c o n t i n u o u s between R a t i o and  see  corporeal  and i n d i v i s i b l e .  e f f o r t t o s o l v e the paradoxes of the  substance  His  S c i e n t i a I n t u i t i v a c a n be  motion,  distinction  seen as  an  i n f i n i t e , while his  p r o o f s of the u n i t y of p h y s i c a l substance  apply  directly  to the C a r t e s i a n cosmology. All  this  i s somewhat s p e c u l a t i v e and  beyond the scope of t h i s t h e s i s , but  i t serves t o emphasize  the n e c e s s i t y of paying c l o s e a t t e n t i o n t o physics. missed  goes w e l l  Spinoza's  H i s w r i t i n g of the P r i n c i p l e s i s u s u a l l y d i s -  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  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 the E t h i c s has b e n e f i t of a d e t a i l e d a n a l y s i s . a r e i g n o r e d b y and  not had  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 .  q u i t e u n c o n n e c t e d , do h a n g t o g e t h e r , and  are not  significant  My e f f o r t h a s  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  structure of matter  the  not been c o n s i d e r e d v e r y  they i n d i c a t e t h a t Spinoza's  the  H i s v i e w s on t h e vacuum  l a r g e , and h i s c o n c e r n w i t h  p a r a d o x e s o f Zeno has  the  sight  been are  that together  i d e a s on t h e n a t u r e radically different  and from.  103 or 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 ;  that i n s p i t e o f metaphysical disagreements, and D e s c a r t e s ' s s c i e n t i f i c  theories are quite  The c e n t r a l i s s u e t o w h i c h I h a v e d e v o t e d my  Spinoza's similar. attention  i s the nature of the corpora s i m p l i c i s s i m a i n Spinoza'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 t h e 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 motion. 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 a r e 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 of the C a r t e s i a n p h y s i c s , h a s n o t 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  scientific  t h e o r i e s , but has important 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 whole.  •^What i s a t s t a k e h e r e i s t h e f a c t t h a t a n i n f i n i t e s e t c a n be p u t i n t o a o n e - t o - o n e c o r r e s p o n d e n c e w i t h a proper subset of 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 substance 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 Principles; see, f o r i n s t a n c e , the d e f i n i t i o n of e x t e n s i o n ( D e f i n i t i o n 1, P a r t T w o ) . ^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 a s 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 a n d P a r m e n i d e s ' s i d e a o f t h e u n i v e r s e a s a homogeneous s p h e r e . W i t h b o t h P a r m e n i d e s a n d 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 , changel e s s whole, w i t h t h e p e r c e i v e d world, which i s f u l l of v a r i e t y and change. S e e , f o r example, t h e l e t t e r t o Oldenburg, J u l y , 1663. 4  5  S e e Wolf, page 62.  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Leipzig  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 Seventeenth 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 - 1 8 0 0 , Longmans, G r e e n a n d Co., 1954.  London,  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 American, Volume 217, Number 2 ( A u g u s t 1 9 6 7 ) . Hampshire, S t u a r t , S p i n o z a , P e n g u i n Books I n c . ,  1962.  J o a c h i m , H a r o l d H., A S t u d y o f t h e E t h i c s o f S p i n o z a , R u s s e l l a n d R u s s e l l I n c . , New Y o r k , 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, M o n a d o l o g y and O t h e r 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 Y o r k , B o b b s - M e r r i l Co. L t d . , 1965. 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F., The S c i e n t i f i c Work o f Rene D e s c a r t e s 1650, L o n d o n , T a y l o r a n d F r a n c i s , 1952.  1596  -  Spinoza, Baruch, 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 T h o u g h t s on M e t a p h y s i c s , t r a n s l a t e d b y F r a n k A. H a y e s w i t h a n i n t r o d u c t i o n b y 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 of C a r t e s i a n Philosophy, from L a t i n by. H a r r y E. Wedeck. P r e f a c e b y D a g o b e r t 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 , 1 9 6 1 .  106 S p i n o z a , B a r u c h , 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 , 1 9 6 1 . (Note: A l l q u o t a t i o n s a r e 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 Y o r k , 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.  W o l f , A r n o l d , The C o r r e s p o n d e n c e o f S p i n o z a , L o n d o n , F r a n k C a s s a n d Co., L t d . , 1 9 6 6 . . W o l f s o n , H a r r y A u s t r y n , " S p i n o z a 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 Q u a r t u s C h r o n i c o n S p i n o z a n u m , p a g e s 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 Spinoza's the l i s t  i n t e r e s t i n s c i e n c e , and a l s o because  i s hard 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 taken from Die Lebensgeschichte It  the l i s t  Spinozas which  i n Freudenthal s 1  c o n t a i n s 161 i t e m s .  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. ical,  Most o f t h e books r e l a t e t o S p i n o z a ' s t h e o l o g i c a l and p o l i t i c a l  philosoph-  s t u d i e s , but the s e l e c t i o n  I h a v e made d e a l s m o s t l y w i t h a s t r o n o m y , m e d i c i n e , and m a t h e m a t i c s .  Freudenthal's l i s t  physics  i s b e l i e v e d t o be  i n c o m p l e t e , t h e more v a l u a b l e b o o k s h a v i n g b e e n r e m o v e d b e f o r e t h e 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  titles.  I have t r a n s l a t e d t h e Dutch t i t l e s a f t e r the o r i g i n a l  i n brackets  title.  - L o n g o m o n t a n i A s t r o n o m i a d a n i c a cum a p p e n d i c e de s t e l l i s N o v i s e t C o m e t i s . 1640. A m s t e l . - Diophanti A l e x a n d r i n i Arithmeticorum 6 Paris. 1621. G r . L a t . - V i e t a e opera Mathematica.  Lugd.  - Hugenii Z u l i c h e m i i Horologium P a r i s . 1673.  Libri  1646.  Oscillatorium.  108 V e s l i n g i i Syntagma A n a t o m i c u m .  Patavii.  1647.  R i o l a n i Anatomica.  Paris.  1626.  Descartes Brieven.  (Letters of Descartes)  K e r c k r i n g i i S p e c i l e g i u m (!) Descartes Proeven.  anatomicum.  1670.  (Descartes'sproofs)  R e n a t u s D e s c a r t e s de p r i m a  Philosophia.  R e n a t u s D e s c a r t e s de G e o m e t r i a . R e n a t u s 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 . Descartes opera P h i l o s o p h i c a .  1650.  D e s c a r t e s de h o m i n e . a Schooten E x e r c i t a t i o n e s  Mathematicae.  Een R a b b i n s c h M a t h e m a t i s c h boeck. r a b b i n i c a l m a t h e m a t i c a l book)  (a  S n e l l i i Tiphys Batavus. 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  Univers.  L a n s b e r g i i Comm. i n Motum T e r r a e . 1630. Lansbergii Cyclometria  1651.  Middelb.  nova.  Algebra door Kinckhuysen.  (Algebra by  Kinckhuysen)  Gront der Meetkunst door Kinckhuysen. ( F o u n d a t i o n s o f geometry) De M e e t k u n s t d o o r K i n c k h u y s e n . Kinckhuysen) L a n s b e r g i i Progymnasmata a s t r o n . 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.  (Geometry  by  Restituta.  109 Metii Alcmariani Instit.  astron.  T u l p i i O b s e r v a t i o n e s Med.  Libri  3.  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 . Lond.  1663.  Kekkermanni L o g i c a . Metii Astrolabium. de G r a e f s d r i e h o e k s m e t i n g .  (trigonometry)  Klauberghs u y t b r e i d i n g van Descartes. ( K l a u b e r g h ' s commentary o n D e s c a r t e s ) Hobbes E l e m e n t a  Philosophica.  Boyle Paradoxa H y d r o s t a t i c a . Euclides. S t e n o n i s Observ.  anat.  Pharmacopaea A m s t e l r e d . Elementa P h y s i c a .  110 APPENDIX B THE  The  HYDROSTATIC EXPERIMENT  d e s c r i p t i o n of t h i s experiment of Spinoza's  i s found i n h i s l e t t e r t o J a r i g The e x p e r i m e n t a l simple is  Jelles  apparatus employed  o f September,  by S p i n o z a i s  1669.  fairly  and h i s d r a w i n g , w h i c h I have r e p r o d u c e d b e l o w ,  almost  self-explanatory. F D  c  The 1 and 2/3 are  t u b e , M,  inches.  drawn r o u g h l y  We  i s 10 f e e t l o n g a n d h a s a b o r e o f may  assume t h a t t h e o t h e r  to scale.  The  a k i n d of gate o r v a l v e , w h i l e  letter  "A"  tubes  designates  Spinoza a l s o had a  way  o f b l o c k i n g o f f t u b e B, n o t shown i n h i s d i a g r a m .  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 n e e d n o t d e t a i n us f o r l o n g ; i t s purpose rise  i s t o d e t e r m i n e t o what h e i g h t  i n s m a l l tube C w i t h  this with A open.  the h e i g h t  the water  g a t e A c l o s e d o f f and t o compare  t h e w a t e r r e a c h e s i n C and D  Spinoza's conclusion  with  i s that the f a c t that E i s  f a r t h e r r e m o v e d f r o m G t h a n B h a s no e f f e c t on t h e to which water r i s e s  will  i n C and D,  a n d more g e n e r a l l y  level that  Ill the  l e n g t h of tube M i s not The  a relevant  factor.  s e c o n d p a r t o f t h e e x p e r i m e n t i s more a  h y d r o d y n a m i c 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 t h e r a t e s o f w a t e r f l o w t u b e s B and  E  ( t h e s m a l l b o r e t u b e s C and D a r e  for t h i s experiment).  In order  the t i m e t a k e n t o f i l l  a v e s s e l o f one  by w a t e r f l o w i n g o u t  t o do  o f tubes B and  t h a t he  through  removed  measures  cubic foot  capacity  E respectively.  Rel-  a t i v e t i m e s a r e m e a s u r e d b y w e i g h i n g t h e amount o f w a t e r s i p h o n e d f r o m one  v e s s e l to another at a lower  through a narrow g l a s s tube i n the  shape o f the  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 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 clock available; accurate  i n any  B and  E i s at the beginning,  wise,  he  described  does n o t h a v e a p e n d u l u m probably  concludes,  o n l y time t h a t rates of flow  when E i s s l o w e r .  t h a t the  through Other-  t h a t i s , he  con-  t e r m i n a l r a t e of flow i s independent  l e n g t h o f t u b e M,  water i n the  there  i t w o u l d make no d i f f e r e n c e w h e t h e r  M i s 10 f e e t l o n g o r 40,000 f e e t l o n g ;  provided  J.  enough f o r h i s p u r p o s e s .  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  the  letter  case the w a t e r c l o c k i s  Spinoza observes t h a t the  cludes  level  but  d e p e n d s o n l y on  c o n t a i n e r F.  level  of  This conclusion i s correct  t h a t f r i c t i o n and In his efforts  the  of  v i s c o s i t y e f f e c t s are  t o e x p l a i n why  the water  ignored. flow  112 is  smaller i n E a t the beginning Spinoza gives a formula  t h a t i s supposed t o govern the rate of a c c e l e r a t i o n occurring i n the water: For 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 t h e tube G i m p a r t s t o t h e w a t e r i n t h e t u b e M one d e g r e e o f s p e e d i n t h e f i r s t moment, t h e n i n t h e s e c o n d 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 , a s i t i s supposed t o , i t w i l l communicate f o u r degrees o f speed t o t h e w a t e r , and s o f o r t h . U n t i l the water i n t h e l o n g t u b e M h a s r e c e i v e d j u s t a s 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 give the h i g h e r w a t e r , c o n t a i n e d i n t h e t u b e G. The m y s t e r y a b o u t t h i s s t a t e m e n t i s where S p i n o z a g o t if  from.  I t c e r t a i n l y does n o t f o l l o w from any e x p e r i -  m e n t a l o b s e r v a t i o n s n o r d o e s he s a y t h a t i t i s s u p p o s e d to.  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 of t h e e l a p s e d time: About t h i s .  V=at . 2  W o l f , says t h e f o l l o w i n g : 1  S p i n o z a must b e 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 . This i s p r o p o r t i o n a l t o t h e square o f the time. The a c t u a l v e l o c i t y d e v e l o p e d b y a b o d y u n d e r t h e action of a constant force i s simply proportional to the time. 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 constant force;  t h i s i s j u s t t h e r e l a t i o n v=at.  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 a n d t i m e was a l r e a d y  discovered  b y G a l i l e o i n 1609 f r o m h i s o b s e r v a t i o n s o f b a l l s down i n c l i n e s .  rolling  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 w r o n g , b e c a u s e constant;  This  the a c c e l e r a t i o n i snot  i t i s g r e a t e s t when t h e w a t e r s t a r t s  and d e c r e a s e s l i n e a r l y u n t i l  flowing  i t r e a c h e s z e r o when t h e  113 w a t e r r e a c h e s t e r m i n a l v e l o c i t y , so t h a t t h e b e t w e e n time, and aside  v e l o c i t y i s much more c o m p l i c a t e d .  f r o m w h e t h e r S p i n o z a was  t h i s statement, there he  is still  makes t h i s s t a t e m e n t .  only occasion  relation  The  Quite  r i g h t o r wrong i n making the  question  on what  l e t t e r to J e l l e s i s  basis  the  on w h i c h S p i n o z a e v e n m e n t i o n s 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 c o m p a r i s o n s .  s u p p o s e t h a t S p i n o z a was  acquainted  with  We  might  the work  of  G a l i l e o , e v e n t h o u g h no w o r k s o f G a l i l e o w e r e f o u n d i n his  l i b r a r y , and  Wolf suggests. The  t h a t he But  made a l i t t l e  s l i p here,  as  a l l this is highly conjectural.  c h i e f p o i n t of i n t e r e s t i n the  hydrostatic  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 s o i n c l i n e d , was elaborate  quite  experiments.  capable of conducting I t may  be  e x p e r i m e n t , and extensive  and  Robert Boyle,  indeed, i t pales  fairly  s a i d t h a t the  s t a t i c experiment i s a f a i r l y simple  and  i n comparison w i t h w o r k o f a man  b u t we  i t as  l o o k on  what S p i n o z a m i g h t have done, had  experiment, even though i t i s v e r y s a i d t h a t he  experimental  He  n e c e s s i t y of c o n t r o l l i n g the  of  he b e e n more i n t e r e s t e d .  concise,  of  the  i t can  shows a t l e a s t some c o m p e t e n c e a s  scientist.  the like  a sample  A l s o , from the d e s c r i p t i o n t h a t Spinoza gives  be  hydro-  straightforward  thorough experimental should  was  seems t o be  aware of  safely an  the  relevant variables i n  the  experiment, t a k e s note  a n d h i s o b s e r v a t i o n s a r e made c a r e f u l l y .  He  o f t h e 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 a r e s o u n d l y b a s e d on t h e 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 , p a g e  435.  115 APPENDIX C THE  It  S I X T H RULE OF MOTION  i s o f some i n t e r e s t t o e x p l o r e w h a t  S p i n o z a m i g h t have had r u l e of motion. i n paragraph r e a d s as  f o r changing Descartes's  Descartes's v e r s i o n , which  51 o f P a r t Two  reasons sixth  i s found  of h i s P r i n c i p l e s  of Philosophy  follows:  I f C, a t r e s t , i s e q u a l t o B w h i c h a p p r o a c h e s i t , t h e l a t t e r must t r a n s f e r some o f i t s m o t i o n t o t h e f o r m e r , and r e b o u n d w i t h t h e r e s t ; f o r example, i f B approach C w i t h f o u r degrees of speed, i t w i l l t r a n s f e r one a n d w i t h t h e 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. Descartes's three cases:  (a)  u n i t s of v e l o c i t y , two  reasoning involves considering  B and C move a l o n g t o g e t h e r w i t h  two  so t h a t B l o s e s two u n i t s and C  units of v e l o c i t y ,  (b)  gains  B i s reflected with four  degrees of v e l o c i t y w h i l e C remains a t r e s t ,  (c)  B is  r e f l e c t e d w i t h l e s s than 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 gains whatever B loses. noted,  q u a n t i t y of motion  In a l l three cases, i t w i l l i s conserved.  r e j e c t e d because i t i n v o l v e s changing w h i l e B i s not r e f l e c t e d ; p e r f e c t l y equal  C a s e (a) i s  C from r e s t t o  somehow t h i s i s n o t  "treatment".  motion,  considered  B and C a r e e q u a l i n s i z e  and h e n c e a r e e q u a l l y " s t r o n g " , s o t h a t t h e s h o u l d be e q u a l f o r t h e m .  be  results  C a s e (b) i s r e j e c t e d b e c a u s e  116  it  " 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 .  In  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 .  In  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 .  Since  n e i t h e r B n o r 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 half-way will  between case  (a) and case  ( b ) , w h i c h means B  l o s e one u n i t o f v e l o c i t y a n d C g a i n s one u n i t o f  velocity.  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  peculiar.  and  F o r i n s t a n c e , i t i s n o t a t a l l c l e a r why  other p o s s i b i l i t i e s are excluded;  certain  consider the following:  B s t o p s d e a d a n d 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 , or the 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 .  Both  these  p o s s i b i l i t i e s obey t h e 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 a n d C.  Spinoza's that of Descartes's. and  a r g u m e n t h a s t h e same c h a r a c t e r a s He a l s o p o s e s t h r e e  r e j e c t s two o f 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 a r e e q u a l . is  possibilities  that Spinoza  The m a j o r d i f f e r e n c e  does n o t c a r r y t h e argument from symmetry  as f a r a s 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  specifying the r e s u l t a n t v e l o c i t i e s . so i s d i f f i c u l t  t o d i s c o v e r , however.  something repugnant about  E x a c t l y why he d o e s He may h a v e  found  " s p l i t t i n g the difference"  b e t w e e n two  cases both of which  hypothesis.  He may  are c o n t r a r y t o the  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 w i t h a change f r o m r e s t t o one he may  velocity  unit of v e l o c i t y .  Or  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  felt  i t was  safer to restrict himself  to  a more l i m i t e d c o n c l u s i o n .  to  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  a r g u m e n t , we i t was  For lack of evidence  c a n 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  fallacious  i n one way  or another.  This  thought indicates  t h a t Spinoza's arguments i n the P r i n c i p l e s are not faithful  own  terms.  t h r o u g h c a r e f u l l y and  stated.in  T h i s means, t h e n , t h a t i f we  to  d e c i d e how  we  must l o o k f o r c l u e s i n t h e b a s i c p r e m i s s e s  system,  merely  copies of Descartes's reasonings, but t h a t the  arguments a r e thought his  as  Spinoza f e l t  are  trying  about the C a r t e s i a n . p h y s i c s ,  and n o t s o much i n i t s d e t a i l s .  of t h a t  

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