philosophy of nature-第4章

按键盘上方向键 ← 或 → 可快速上下翻页，按键盘上的 Enter 键可回到本书目录页，按键盘上方向键 ↑ 可回到本页顶部！
————未阅读完？加入书签已便下次继续阅读！


dissolution　into　the　differences　of　being　as　the　transition　into　nothingness；　and　of　Nothingness　as
the　transition　into　being。　The　immediate　disappearance　of　these　differences　into　individuality　is　the
present　as　now；　which　is　itself　only　this　disappearance　of　being　into　nothingness；　and　of
nothingness　into　being。　

（1）　The　finite　present　is　differentiated　from　the　infinite　in　that　the　finite　is　the　moment　now　and
hence　as　its　abstract　moments；　as　past　and　future；　which　is　different　from　the　infinite　as　from　the
concrete　unity。　Eternity　as　concept；　h　r；　contains　these　moments　in　itself　and　its　concrete　unity　is
therefore　not　the　moment　now；　because　it　is　motionless　identity；　concrete　being　as　universal；　and
not　that　which　is　disappearing　into　nothingness；　as　becoming。…Furthermore　in　nature；　where　time　is
now；　there　does　not　occur　the　subsisting　difference　of　these　dimensions；　they　are　necessarily　only
in　subjective　representation；　in　memory；　fear；　or　hope。　The　abstract　past；　however；　and　future　of
time　is　space；　as　the　suspended　space　is　at　first　the　point　and　time。　

（2）　There　is　no　science　of　time　in　opposition　to　the　finite　science　of　space；　geometry；　because　the
differences　of　time　do　not　have　the　indifference　of　being　outside　of　itself　which　constitutes　the
immediate　determinacy　of　space；　and　therefore　they　can　not　be　expressed　as　spatial
configurations。　The　principle　of　time　only　reaches　this　ability　when　the　understanding　has　paralysed
it　and　reduced　its　negativity　to　the　unit。　This　motionless　unit；　as　the　sheer　carnality　of　thought；　can
be　used　to　form　external　combinations；　and　these；　the　numbers　of　arithmetic；　can　themselves　be
brought　under　the　categories　of　the　truth　as　intuition　or　as　understanding　merely　for　itself　because
the　latter　is　only　abstract；　whereas　the　former　is　concrete。　This　dead　unit；　now　the　highest
externality　of　thought；　can　be　used　to　form　external　combinations；　and　these　combinations；　the
figures　of　arithmetic；　can　in　turn　be　organised　by　the　determination　of　the　understanding　in　terms　of
equality　and　inequality；　identity　and　difference。　The　science　which　has　unity　as　its　principle　is
therefore　constituted　in　opposition　to　geometry。　

（3）　The　name　of　mathematics　has　moreover　been　used　for　the　philosophical　observation　of　space
and　time；　because　it　lies　close　to　this　observation；　despite　the　fact　that　mathematics；　as　noted；
considers　strictly　the　determinations　of　magnitude　of　its　objects　and　not　time　itself　but　only　the　unit
in　its　configurations　and　connections。　To　be　sure；　time　becomes　in　the　theory　of　movement　an
object　of　science；　but　applied　mathematics　is　generally　not　an　immanent　science；　precisely　because
it　involves　the　application　of　pure　mathematics　to　a　given　material　and　its　determinations　as　derived
from　experience。　

（4）　One　could　still；　however；　conceive　the　thought　of　a　philosophical　mathematics；　namely；　as　a
science　which　would　recognise　those　concepts　which　constitute　what　the　conventional
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
det