philosophy of nature-第3部分

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Nature　is；　in　itself　a　living　whole。　The　movement　of　its　idea　through　its　sequence　of　stages　is　more
precisely　this：　the　idea　posits　itself　as　that　which　it　is　in　itself；　or；　what　is　the　same　thing；　it　goes　into
itself　out　of　that　immediacy　and　externality　which　is　death　in　order　to　go　into　itself；　yet　further；　it
suspends　this　determinacy　of　the　idea；　in　which　it　is　only　life；　and　becomes　spirit；　which　is　its　truth。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　196。

The　idea　as　nature　is：　（1）　as　universal；　ideal　being　outside　of　itself　space　and　time；　（2）　as　real　and
mutual　being　apart　from　itself　particular　or　material　existence；　…　inorganic　nature；　（3）　as　living
actuality；　organic　nature。　The　three　sciences　can　thus　be　named　mathematics；　physics；　and
physiology。　


I
　　　　　　　　　　　　　　　　　　　　　　Mathematics

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　197。

（1）　The　first　or　immediate　determination　of　nature　is　the　abstract　generality　of　its
self…externality；…its　unmediated　indifference；　space。　It　is　the　wholly　ideal　juxtaposition；　because　it　is
being　outside　of　itself　and　absolutely　continuous；　because　this　being　apart　from　itself　is　still　entirely
abstract；　and　has　no　specific　difference　within　itself。　

Much　has　been　said；　from　different　theoretical　positions；　about　the　nature　of　space。　I　will　mention
only　the　Kantian　determination　that　space　is；　like　time；　a　form　of　sensory　intuition。　It　has　also
become　customary　to　establish　fundamentally　that　space　must　be　regarded　only　as　something
subjective　in　representation。　Disregarding　what；　in　the　Kantian　conception；　belongs　to　subjective
idealism　and　its　determinations　（cf　§　5）；　the　correct　determination　remains　that　space　is　a　mere
form；　i。e。；　an　abstraction；　that　of　immediate　externality。…To　speak　of　points　of　space；　as　if　they
constituted　the　positive　element　of　space；　is　inadmissible；　since　space；　on　account　of　its　lack　of
differentiation；　is　only　the　possibility　and　not　the　positing　of　that　which　is　negative　and　therefore
absolutely　continuous。　The　point　is　therefore　rather　the　negation　of　space。…This　also　settles　the
question　of　the　infinitude　of　space。　Space　is　in　general　pure　quantity　（§　53f）；　though　no　longer　as　a
logical　determination；　but　rather　as　existing　immediately　and　externally。　Nature；　consequently；　does
not　begin　with　quality　but　with　quantity；　because　its　determination　is　not；　like　logical　being；　the
absolute　first　and　immediate；　but　essentially　a　mediated　being；　a　being　external　to　and　other　than
itself　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　198。

Space　has；　as　the　concept　in　general　（and　more　determinate　than　an　indifferent　self…externality）　its
differences　within　it：　（a）　in　its　indifference　these　are　immediately　the　three　dimensions；　which　are
merely　diverse　and　quite　indeterminate。　

But　geometry　is　not　required　to　deduce　that　space　necessarily　has　precisely　three　dimensions；　for　it
is　not　a　philosophical　science；　and　may　therefore　presuppose　space　as　its　object。　Moreover；　even
apart　from　this；　no　thought　is　given　to　the　demonstration　of　such　a　necessity。　The　necessity　rests　on
the　nature　of　the　concept；　whose　determinations；　however；　because　they　depict　themselves　in
these　first　elements　of　being　apart　from　themselves；　in　abstract　quantity；　are　only　entirely　superficial
and　a　completely　empty　difference。　One　can　also；　therefore；　not　say　how　height；　length；　and　width
differ　from　each　other；　because　they　only　ought　to　be　different；　but　are　not　yet　differences。…Height
has　its　more　precise　determination　as　direction　according　to　the　center　of　the　earth；　but　this　does
not　at　all　concern　the　nature　of　space　for　itself　Following　from　this　point　it　is　equally　as　indifferent
whether　this　direction　is　called　height　or　depth；　or　length　or　breadth；　which　is　also　often　called
depth。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　199。

（b）　But　the　difference　of　space　is　essentially　a　determinate；　qualitative　difference。　As　such　it　is　（a）
first；　the　negation　of　space　itself　because　this　is　immediate　and　undifferentiated　self…externality；　the
point。　（b）　The　negation　as　negation；　however；　is　itself　spatial；　and　the　relation　of　the　point　to　space
is　the　line；　the　first　otherness　of　the　point。　（c）　The　truth　of　the　otherness　is；　however；　the　negation
of　the　negation。　The　line；　therefore；　passes　over　into　the　plane；　which　on　the　one　hand　is　a
determinacy　opposed　to　line　and　point；　and　thus　is　plane　in　general；　but　on　the　other　hand　is　the
suspended　negation　of　space；　and　thus　the　re…establishment　of　spatial　totality；　which；　however；
now　contains　the　negative　moment　within　itself　an　enclosing　surface；　which　splits　off　an　individual；
whole　space。　

That　the　line　does　not　consist　of　points；　nor　the　plane　of　lines；　follows　from　their　concepts；　for　the
line　is　the　point　existing　outside　of　itself　relating　itself　to　space；　and　suspending　itself　and　the　plane
is　just　as　much　the　suspended　line　existing　outside　of　itself。…Here　the　point　is　represented　as　the
first　and　positive　entity；　and　taken　as　the　starting　point。　The　converse；　though；　is　also　true：　in　as　far
as　space　is　positive；　the　plane　is　the　first　negation　and　the　line　is　the　second；　which；　however；　is　in
its　truth　the　negation　relating　self　to　self　the　point。　The　necessity　of　the　transition　is　the　same。…　

The　other　configurations　of　space　considered　by　geometry　are　further　qualitative　limitations　of　a
spatial　abstraction；　of　the　plane；　or　of　a　limited　spatial　whole。　Here　there　occur　a　few　necessary
moments；　for　example；　that　the　triangle　is　the　first　rectilinear　figure；　that　all　other　figures　must；　to　be
determined；　be　reduced　to　it　or　to　the　square；　and　so　on。…The　principle　of　these　figures　is　the
identity　of　the　understanding；　which　determines　the　figurations　as　regular；　and　in　this　way　grounds
the　relationships　and　sets　them　in　place；　which　it　now　becomes　the　purpose　of　science　to　know。　

It　may　be　noted　in　passing　that　it　was　an　extraordinary　notion　of　Kant's　to　claim　that　the　definition
of　the　straight　line　as　the　shortest　distance　between　two　points　is　a　synthetic　proposition；　for　my
concept　of　straightness　contains　nothing　of　size；　but　only　a　quality。　In　this　sense　every　definition　is　a
synthetic　proposition。　What　is　defined；　the　straight　line；　is　in　the　first　place　the　intuition　or
representation；　and　the　determination　that　it　is　the　shortest　distance　between　two　points　constitutes
in　the　first　place　the　concept　（namely；　as　it　appears　in　such　definitions；　cf。　§　110）。　That　the
concept　is　not　already　given　by　the　intuition　constitutes　precisely　the　difference　between　the　two；
and　is　what　calls　for　a　definition。　That　something　seems　to　the　representation　to　be　a　quality；
though　its　specificity　rests　on　a　quantitative　determination；　is　something　very　simple；　and　also　the
case　for　example　with　the　right　angle；　the　straight　line；　and　so　on。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　200。

（2）　Negativity；　which　as　point　relates　itself　to　space　and　in　space　develops　its　determinations　as
line　and　plane；　is；　however；　in　the　sphere　of　self…externality　equally　for　itself　and　appearing
indifferent　to　the　motionless　coexistence　of　space。　Negativity；　thus　posite