philosophy of nature-第4部分

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mathematical　science　of　the　understanding　derives　from　its　presupposed　determinations；　and
according　to　the　method　of　the　understanding；　without　concepts。　However；　since　mathematics　is
the　science　of　the　finite　determinations　of　magnitude；　which　remain　fixed　in　their　finitude　and　valid；
and　should　not　change　in　transit；　thus　it　is　essentially　a　science　of　the　understanding。　And　since　it
has　the　ability　to　express　spatial　figures　and　numbers；　which　gives　it　an　advantage　over　other
sciences　of　this　kind；　it　ought　to　retain　this　ability　for　itself　and　to　avoid　contamination　by　either
concepts；　like　time；　which　are　heterogeneous　to　it；　or　empirical　purposes。　It　therefore　remains
open　for　the　concept　to　establish　a　more　fundamental　consciousness　than　has　hitherto　been　shown；
both　in　terms　of　the　leading　principles　of　the　understanding　and　in　terms　of　order　and　its　necessity
in　arithmetical　operations；　as　well　as　in　the　theses　of　geometry。…If　one　wanted　to　treat　the　forms　of
space　and　the　unit　philosophically；　they　would　lose　on　these　grounds　their　particular　significance；　a
philosophy　of　them　would　become　a　matter　of　logic；　or　would　even　assume　the　character　of
another　concrete　philosophical　science；　according　to　the　ways　one　imparted　a　more　concrete
significance　to　the　concepts。…　

It　would；　however；　be　a　superfluous　and　thankless　task　to　try　to　use　such　an　unmanageable　and
inadequate　medium　as　spatial　figures　and　numbers　for　the　expression　of　thoughts；　and　to　treat　them
violently　for　this　purpose。　For　the　specific　concept　would　always　be　related　only　externally　to
them。　The　simple　elementary　figures　and　numbers　can　in　any　case　be　used　as　symbols；　which；
however；　are　a　subordinate　and　poor　expression　for　thoughts。　The　first　attempts　of　pure　thought
took　recourse　to　such　aids：　the　Pythagorean　system　of　numbers　is　the　famous　example　of　this。　But
with　richer　concepts　these　means　became　completely　unsatisfactory；　since　their　external
juxtaposition　and　contingent　combination　are　not　at　all　appropriate　to　the　nature　of　the　concept；
and　make　it　altogether　ambiguous　which　of　the　many　possible　relationships　in　complex　numbers
and　figures　should　be　adhered　to。　Besides；　the　fluid　character　of　the　concept　is　dissipated　in　such
an　external　medium；　in　which　each　determination　falls　into　the　indifferent　being　outside　the　others。
This　ambiguity　could　only　be　removed　by　an　explanation。　The　essential　expression　of　the　thought　is
in　that　case　this　explanation；　and　this　symbolising　is　an　empty　superfluity。　

Other　mathematical　determinations；　such　as　infinity　and　its　relationships；　the　infinitesimal；　factors；
powers；　and　so　'　on；　have　their　true　concepts　in　philosophy　itself。　It　is　awkward　to　want　to　take
and　derive　these　from　mathematics；　where　they　are　employed　in　a　nonconceptual；　often
meaningless　way；　rather；　they　must　await　their　justification　and　significance　from　philosophy。　The
truly　philosophical　science　of　mathematics　as　theory　of　magnitude　would　be　the　science　of
measures；　but　this　already　presupposes　the　real　particularity　of　things；　which　is　only　at　hand　in
concrete　nature。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　203。

（5）　Space　and　time　constitute　the　idea　in　and　for　itself；　with　space　the　real　or　immediately
objective　side　and　time　the　purely　subjective　side。　Space　is　in　itself　the　contradiction　of　indifferent
being　outside　of　others　and　undifferentiated　continuity；　and　thereby　the　pure　negativity　of　itself　and
the　transition　into　time。　Space　converts　into　the　individuality　of　the　place。　Time　is；　equally；　since　its
moments　held　together　in　unity　suspend　themselves　immediately；　the　immediate　convergence　into
indifference；　into　undifferentiated　being　apart　from　one　another；　or　into　space；　so　that　its　place　is
precisely　in　that　way　immediate　as　sheer　indifferent　spatiality。　This　disappearance　and　regeneration
of　space　in　time　and　of　time　in　space　is　motion；…a　becoming；　which；　however；　is　itself　just　as　much
immediately　the　identically　existing　unity　of　both；　or　matter。　

The　transition　from　ideality　to　reality；　from　abstraction　to　concrete　existence；　in　this　case　from
space　and　time　to　reality；　which　appears　as　matter；　is　incomprehensible　to　the　understanding；　and
always　converts　therefore　externally　for　the　understanding；　and　as　a　given　entity。　The　usual
conception　is　to　take　space　and　time　as　empty　and　to　be　filled　with　matter　from　the　outside。　In　this
way　material　things　are；　on　the　one　hand；　to　be　taken　as　indifferent　to　space　and　time；　and　on　the
other　hand　to　be　taken　at　the　same　time　as　essentially　spatial　and　temporal。　

What　is　usually　said　of　matter　is：　（a）　that　it　is　composite；　this　refers　to　its　identity　with　space。
Insofar　as　abstractions　are　made　from　time　and　from　all　form　generally；　it　is　asserted　that　matter　is
eternal　and　immutable。　In　fact；　this　follows　immediately；　but　such　a　matter　is　also　only　an　untrue
abstraction。　（b）　It　is　said　that　matter　is　impenetrable　and　offers　resistance；　is　tangible；　visible；　and
so　on。　These　predicates　mean　nothing　else　than　that　matter　exists；　partly　for　specific　forms　of
perception；　in　general　for　an　other；　but　partly　just　as　much　for　itself　Both　of　these　are
determinations　which　belong　to　matter　precisely　because　it　is　the　identity　of　space　and　time；　of
immediate　being　apart　from　itself　or　of　becoming。　

The　transition　of　ideality　into　reality　is　demonstrated　therefore　in　the　familiar　mechanical
phenomena；　namely；　that　ideality　can　take　the　place　of　reality　and　vice　versa；　and　only　the　usual
thoughtlessness　of　the　representation　and　of　the　understanding　are　to　blame　that；　for　them；　their
identity　does　not　derive　from　the　interchangeability　of　both。　In　connection　with　the　lever；　for
example；　distance　can　be　posited　in　the　place　of　mass　and　vice　versa；　and　a　quantum　of　the　ideal
moment　produces　the　same　effect　as　the　corresponding　real　moment。　

Similarly；　velocity；　in　the　magnitude　of　motion；　the　quantitative　relationship　of　space　and　time；
represents　mass；　and　conversely；　the　same　real　effect　emerges　if　the　mass　is　increased　and　the
velocity　proportionately　decreased。　By　itself　a　brick　does　not　kill　a　person；　but　produces　this
effect　only　though　the　velocity　it　achieves；　in　other　words；　the　person　is　killed　through　space　and
time。　

It　is　force；　a　category　of　reflection　fixed　by　the　understanding；　which　presents　itself　here　as　the
ultimate；　and　therefore　prevents　understanding　and　lets　it　seem　superfluous　to　inquire　further　after
the　concept。　But　this　at　least　appears　without　thought；　namely；　that　the　effect　of　force　is　something
real　and　appealing　to　the　senses；　and　in　force　there　is　realised　that　which　is　in　its　expression；
indeed；　it　appears　that　force　achieves　precisely　this　force　of　its　expression　through　the　relationship
of　its　ideal　moments；　of　space　and　time。　

Further；　it　is　also　in　keeping　with　this　nonconceptual　reflection　that　〃forces'　are　seen　as　implanted　in
matter；　and　as　originally　external　to　it；　so　that　this　very　identity　of　time…and　space；　which　vaguely
appears　in　the　reflective　category　of　force；　and　which　in　truth　constitutes　the　essence　of　matter；　is
posited　as　something　alien　to　it　and　contingent；　something　introduced　into　it　from　outside。　




II
　　　　　　　　　　　　　　　　Inorganic　Physics

　　　　　　　A。　Mechanics　…　B。　Elementary　Physics　…　C。　The　Physics　of　Individuality

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　204。

Matter　in　itself　holds　itself　apart　from　itself　through　the　moment　of　its　negativity；　diversity；　or
abstract　separation　into　parts；　it　has　repulsion。　Its　being　apart　from　itself　is　just　as　essential；
however；　because　these　differences　are　one　and　the　same：　the　negative　unity　of　this　existence　apart
from　itself　as　being　for　itself；　and　thus　continuous。　Matter　therefore　has　attraction。　The　unity　of
these　moments　is　gravity。　

Kant　has；　among　other　things；　through　the　attempt　at　a　“construction”　of　matter　in　his
metaphysical　elements　of　the　natural　sciences；　the　merit　of　having　started　towards　a　concept　of
matter；　after　it　had　been　attributed　merely　to　the　deadness　of　the　understanding　and　its
determinations　had　been　conceived　as　the　relations　of　attributes。　With　this　attempt　Kant　revived
the　concept　of　the　philosophy　of　nature；　which　is　nothing　other　than　the　comprehension　of　nature
or；　what　is　the　same；　the　knowledge　of　the　concept　in　nature。　But　in　so　doing　he　assumed　that　the
reflective　categories　of　attraction　and　repulsion　were　readymade；　and　further；　he　presupposed　that
the　category　of　the　reflection　itself　out　of　which　matter　should　emerge；　is　readymade。　This
confusion　is　a　necessary　consequence　of　Kant's　procedure；　because　the　former　abstract　moments
can　not　be　conceptualised　without　their　identity；　moreover；　because　the　observation　of　these
opposing　determinations　suspends　itself　immediately　in　their　identity；　there　is　the　danger　that　they
will　appear；　like　attraction；　as　a　mere　continuity。　I　have　demonstrated　in　detail　the　confusion　which
dominates　Kant's　exposition　in　my　system　of　Logic；　vol。　1；　part　1；　pp。　119ff。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　205。

Matter；　as　having　gravity；　is　only：　（1）　matter　existing　in　itself　or　general。　But　this　conce