philosophy of nature-第3部分

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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　posited　for　itself　is　time。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　201。

Time；　as　the　negative　unity　of　being　outside　of　itself；　is　just　as　thoroughly　abstract；　ideal　being：
being　which；　since　it　is；　is　not；　and　since　it　is　not；　is。　

Tune；　like　space；　is　a　pure　form　of　sensuousness；　or　intuition；　but；　as　with　space；　the　difference
between　objectivity　and　a　contrastingly　subjective　consciousness　does　not　matter　to　time。　If　these
determinations　are　applied　to　space　and　time；　then　space　is　abstract　objectivity；　whereas　time　is
abstract　subjectivity。　Time　is　the　same　principle　as　the　I　=　I　of　pure　self…consciousness；　but　the
same　principle　or　the　simple　concept　still　in　its　entire　externality；　intuited　mere　becoming；　pure
being　in　itself　as　sheer　coming　out　of　itself。　Time　is　just　as　continuous　as　space；　for　it　is　abstract
negativity　relating　itself　to　itself　and　in　this　abstraction　there　is　as　yet　no　real　difference。　

In　time；　it　is　said；　everything　arises　and　passes　away；　or　rather；　there　appears　precisely　the
abstraction　of　arising　and　falling　away。　If　abstractions　are　made　from　everything；　namely；　from　the
fullness　of　time　just　as　much　as　from　the　fullness　of　space；　then　there　remains　both　empty　time　and
empty　space　left　over；　that　is；　there　are　then　posited　these　abstractions　of　exteriority。…But　time
itself　is　this　becoming；　this　existing　abstraction；　the　Chronos　who　gives　birth　to　everything　and
destroys　his　offspring。…That　which　is　real；　however；　is　just　as　identical　to　as　distinct　from　time。
Everything　is　transitory　that　is　temporal；　that　is；　exists　only　in　time　or；　like　the　concept；　is　not　in
itself　pure　negativity。　To　be　sure；　this　negativity　is　in　everything　as　its　immanent；　universal　essence；
but　the　temporal　is　not　adequate　to　this　essence；　and　therefore　relates　to　this　negativity　in　terms　of
its　power。　Time　itself　is　eternal；　for　it　is　neither　just　any　time；　nor　the　moment　now；　but　time　as　time
is　its　concept。　The　concept；　however；　in　its　identity　with　itself　I=　1；　is　in　and　for　itself　absolute
negativity　and　freedom。　Time；　is　not；　therefore；　the　power　of　the　concept；　nor　is　the　concept　in
time　and　temporal；　on　the　contrary；　the　concept　is　the　power　of　time；　which　is　only　this　negativity
as　externality。…The　natural　is　therefore　subordinate　to　time；　insofar　as　it　is　finite；　that　which　is　true；
by　contrast；　the　idea；　the　spirit；　is　eternal。　Thus　the　concept　of　eternity　must　not　be　grasped　as　if　it
were　suspended　time；　or　in　any　case　not　in　the　sense　that　eternity　would　come　after　time；　for　this
would　turn　eternity　into　the　future；　in　other　words　into　a　moment　of　time。　And　the　concept　of
eternity　must　also　not　be　understood　in　the　sense　of　a　negation　of　time；　so　that　it　would　be　merely
an　abstraction　of　time。　For　time　in　its　concept　is；　like　the　concept　itself　generally；　eternal；　and
therefore　also　absolute　presence。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　202。

The　dimensions　of　time；　the　present；　future；　and　past；　are　only　that　which　is　becoming　and　its
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　determ