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Additional resources for Science and Convention. Essays on Henri Poincaré's Philosophy of Science and the Conventionalist Tradition
Example text
T h e b a s i c p r i n c i p l e s of m a t h e m a t i c s a n d of s c i e n c e t u r n e d o u t n o t t o b e s y n t h e t i c a priori t r u t h s ; f a c t s t u r n e d o u t t o b e n o t as s i m p l e a n d o b j e c t i v e as t r a d i tional empiricists c l a i m e d t h e y w e r e . O n e h a d to a d m i t t h a t b o t h m a t h e m a t i c s a n d s c i e n c e w e r e m a n - m a d e in a g r e a t e r m e a s u r e t h a n h a d b e e n t r a d i t i o n a l l y t h o u g h t , t h a t in this c o n s t r u c t i v e activity m a n is n o t a p a s s i v e r e c o r d e r of h a p p e n i n g s in t h e w o r l d , t h a t in d o i n g science h e uses n o t only his b r a i n a n d his senses b u t also his i m a g i n a t i o n a n d d e c i s i o n s .
Scientific k n o w l e d g e c o n c e r n s t h e r e l a t i o n s b e t w e e n t h e p h e n o m e n a o r b e t w e e n t h e e l e m e n t s of t h e h i d d e n "profound r e a l i t y " ; it is i n d e p e n d e n t of t h e t r a n s i e n t i m a g e s o r m e t a p h o r s i n w h i c h o u r m i n d f i n d s it c o n v e n i e n t t o c l o t h e t h o s e r e l a t i o n s . Concluding remarks I t m u s t b e e m p h a s i s e d t h a t t h e a i m of t h i s a r t i c l e w a s not t o criticise P o i n c a r é ' s c o n v e n t i o n a l i s t p h i l o s o p h y b u t r a t h e r to c o n t r i b u t e t o its u n d e r s t a n d i n g .
F o r e v e r y d i f f e r e n t i a l e q u a t i o n t h e r e is a g r o u p of ( c o n t i n u o u s ) t r a n s f o r m a t i o n s w h i c h l e a v e t h e f o r m of t h e e q u a t i o n i n v a r i a n t ; h e h a s also s h o w n t h a t o n l y w h e n t h e g r o u p of t h e e q u a t i o n is f o u n d is it p o s s i b l e t o i n t e g r a t e t h e e q u a t i o n b y q u a d r a t u r e s : t h u s t h e p r o b l e m of f i n d i n g t h e g r o u p o r of i n t e g r a t i n g t h e e q u a t i o n s b y q u a d r a t u r e s is o n e a n d t h e s a m e .