"The s c ie n c e o f e v e ry s u b je c t," i f i t i s d e m o n s tra b le , c a n th e r e f o r e b e s a id t o b e a g e o m e try . B u t i n t h e ab o v e p a ssa g e H obbes a lso m akes i t p la in t h a t th i s h olds t r u e i n c iv il philosop hy a s w ell s in c e i t , t o o , c a n b e sa id t o b e m an-m ad e.
I f a l l kno w led ge i s "o rig in a l sen se," i t m u st b e a sk e d th e n from w here d o e s t h e k now ledge o f g e o m e try sp rin g ? H obbes d id n o t s h a r e in t h e C a rte s ia n in tu itio n is m t h a t h um an b ein g s 'ju s t know 1 t h a t t h e g e o m e tr ic a l s h a p e s an d p a tte r n s w ere t r u e o n es, o r i n K an t's b e lie f t h a t t h e p rin c ip le s o f m a th e m a tic s a r e know n t o u s a s s y n th e tic a p r io r i tr u t h s . H obbes d e a rL y s t a t e s t h a t g e o m e try i s m an -m ad e, a c c u r a te ly r e f le c tin g t h e w orld. G e o m e try c o m e s a f t e r m an, n o t b e f o r e , a n d n e ith e r is i t p a r t o f w h a t i t m eans t o b e hu m an , f o r H obbes, sin c e n o t a l l m en w an d er a ro u n d n a tu ra lly know ing g e o m e tr ic th e o re m s . A t t h e s a m e tim e t h e m eth o d s o f g e o m e try w ere f o r H obbes t h e t r u e fo u n d a tio n s o f kno w ledg e, w ith d i r e c t a p p lic a tio n t o t h e n a t u r a l a n d m o ra l s c ie n c e s . No lo n g e r d id o n e h a v e t o c o n te n d w ith t h e d e f e c ts o f n a t u r a l v isio n i n o r d e r t o a r r iv e a t a r a t h e r lim ite d kn ow led ge o f f a c t . The g e o m e tric m eth o d co u ld o f f e r t r u e k no w ledg e t o t h e p h ilo so p h e r a n d t h e s c ie n tis t. Y e t t h e v e ry b asis f o r con clu d in g t h a t g e o m e try r e v e a le d s c ie n tif ic k n o w led ge i s l e f t u n reso lv ed .
H obbes's c la im s f o r g e o m e try only lo o k e d c o r r e c t t o him b e c a u s e th e r e s e e m e d t o b e a d i r e c t co rre sp o n d e n c e b e tw e e n g e o m e tric p a t te r n s an d t h e pro blem o f c a u s a tio n i n s c ie n c e . On w h a t b asis, th e n , d id H obbes a lig h t u pon E u clid ea n g e o m e try a s a m o d el f o r a l l t h e sc ie n c e s ?
On th i s q u e stio n o ne c a n only s p e c u la te - b u t t h e s tro n g lik e lih o o d is t h a t g e o m e try c o n fo rm e d t o H obbes's th e o r y o f s c ie n tif ic k n ow led ge p re c is e ly b e c a u se i t w as a v is u a l medium w hen o th e r s y s te m s o f m a th e m a tic s a n d lo g ic w ere n o t. In e v e ry s e n s e o f t h e w ord, g e o m e try o f f e r e d H obbes a " p ic tu re " o f kn o w led g e. G e o m e try , in d e e d , w as " th e philo so ph y o f fig u re s." H obbes's th e o r y o f o p tic s l e f t him w ith t h e "know ledge o f f a c t" w hich w as, a t b e s t, in c o m p le te a s i t w as im p o ssib le t o d e m o n s tra te a p ro p o sitio n 's t r u t h t o a n o th e r p e rs o n by p o in tin g t o a n i n t e r n a l p ic tu r e o f a f a c t ' i n o n e 's m ind. One could, h o w ev er, d e m o n s tr a te a t r u t h w hich c o rre sp o n d e d t o a v is u a l g e o m e tric im a g e w hich w as t o b e s h a re d by a ll k n o w led g ea b le men.
H obbes th e o r y o f kn ow led ge i s a n a c t o f d o u b le v isio n . The e q u a tio n t h a t en d ed t h e p re v io u s s e c tio n s a id t h a t f o r H obbes " P e rc e p tio n + t h e S c ie n tific M ethod = K now ledge." Y et, a s w e h a v e s e e n , t h e c o n t e n t o f t h e s c ie n tif ic m eth o d - o r g e o m e tr ic re a s o n in g - w as i t s e l f p rim a rily v is u a l, th u s re n d e rin g H obbes's th e o r y o f k n o w led ge i n d is ti n c t v is u a l s e n s a tio n s. I n t h e p rim a ry s e n s e h is th e o r y o f o p tic s h a d le d him t o co n c lu d e t h a t n a t u r a l v isio n , o r t h e k n o w led g e o f f a c t , c a n n o t b e d ism issed fro m c la im s o f k no w led ge. To s e e so m e th in g i s a t l e a s t t o know t h a t o n e i s s e e in g so m e th in g , a s H obbes a n d h is fello w p o s t-s c e p tic s a v e rre d , a lth o u g h i t m ig h t on ly b e a p h a n ta sm . B u t i n t h e m o re e la b o r a te s e c o n d se n s e , i n t h e a b ility t o s e e c a u s a l c o n n e c tio n s b e tw e e n th in g s, t h e a c t o f v isio n b e c o m e s e q u a lly
fu n d a m e n ta l.
B ased upon t h e in s ig h ts t h a t t h e g e o m e tr ic m eth o d h a d o ffe re d , H obbes f e l t t h a t t h e c o m p o n e n ts o f o b je c ts i n m o tion c o u ld b e b ro k en dow n in to t h e i r c o n s titu e n t c a u s e s a n d th e n g e o m e tr ic a lly sy n th e s iz e d a g a in b a c k in t o a w hole. T his w as t h e p u rp o se o f sc ie n c e : t o show t h e c o n se q u e n c e o f one a f f ir m a tio n t o a n o th e r. B u t t h e m o d el u se d i n th is s e c o n d s e n s e o f k no w ledge w as a lso v is u a l. G e o m e try i s n o th in g m ore th a n re a s o n in g fro m v is ib le s h a p e s a n d fig u re s . I t i s s ig n ific a n t, in t h a t r e s p e c t, t h a t H obbes d id n o t claim t h a t m a th e m a tic s a lo n e w as t h e algorism o f a l l o u r s c ie n tif ic k n o w led g e. D uring h is d a y s i n O xford H obbes w ould h a v e b e e n in tro d u c e d t o e le m e n ta r y m ath s, b u t h e c le a r ly d id n o t 's e e ' t h e p o s sib ilitie s t h a t m a th e m a tic s co u ld h a v e u n til h e w as visib ly s tr u c k i n t h a t g e n tle m a n 's lib r a r y b y t h e fig u re s an d sh a p e s o f E u clid 's g e o m e try . F o r H obbes, g e o m e try r a t h e r th a n m a th e m a tic s , h eld t h e k e y t o kn ow led ge. G e o m e try c a n b e t i e d dow n t o p h y s ic a l sh a p e s an d fig u r e s w h ilst m a th e m a tic s m ig h t f ly o f f in to t h e s p h e re s o f ab su rd fa n c y lik e t h e lo g ic f o r w hich t h e r a tio n a lis ts and t h e s c h o la s tic s w e re ren o w n ed . B u t g e o m e try w as " th e philoso ph y o f fig u re s" a n d i t w as im p o ssib le t o c o n d u c t n a t u r a l philoso ph y w ith o u t i t . And c iv il philosophy, s in c e i t w as c r e a te d b y m an lik e t h e g e o m e tric ia n 's sh a p e s a n d fig u re s , a ls o f a ll s p r e y t o t h e g e o m e tric
m etho d.
M oreover, i t c a n f u r t h e r b e s a id t h a t H obbes u s e s t h e stu d y o f o p tic s a n d o f g e o m e try a s m e ta p h o rs f o r h u m a n kn o w led g e. I n th i s r e g a r d H obbes w as n o t v e ry d if f e r e n t fro m so m e o f h is s e v e n te e n th c e n tu r y b r e th r e n , m any o f whom a lso b e lie v e d t h a t d iv e rs e fie ld s o f s tu d y h ad a sin g le u n ify in g , g e o m e tr ic a l th e m e - a l b e i t a th e m e co m p o sed o f m e ta p h o ric n o te s an d p h ra se s. T his is n o t m e a n t t o b e a
claim t h a t H obbes b e lie v e d t h a t aH k n ow ledg e w as a t r o o t o n ly v isu al. H obbes e x p lic itly s t a t e d t h a t only o ne fo rm o f kn o w led g e w as visual: t h e k n ow ledge o f f a c t . B u t th i s sh o u ld n o t p r e v e n t u s fro m n o tic in g