science of logic-第13章

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into　each　other；　as　we　saw　above　when　they　were　considered　in　their　truth。　I　go　on　to　consider
these　other　distinctions　as　they　are　stated　by　Kant。

He　defines　the　force　of　attraction　as　a　penetrative　force　by　which　one　bit　of　matter　can　act　directly
on　the　parts　of　another　even　beyond　the　area　of　contact；　the　force　of　repulsion；　on　the　other　hand；
he　defines　as　a　surface　force　through　which　bits　of　matter　can　act　on　each　other　only　in　the
common　area　of　contact。　The　reason　adduced　that　the　latter　can　be　only　a　surface　force　is　as
follows：　'The　parts　in　contact　each　limit　the　sphere　of　action　of　the　other；　and　the　force　of
repulsion　cannot　move　any　more　distant　part　except　through　the　agency　of　the　intervening　parts；　an
immediate　action　of　one　part　of　matter　on　another　passing　right　across　these　intervening　parts　by
forces　of　expansion　（which　means　here；　forces　of　repulsion）　is　impossible。'

But　here　we　must　remember　that　in　assuming　'nearer'　or　'more　distant'　parts　of　matter；　the　same
distinction　would　likewise　arise　with　respect　to　attraction；　namely；　that　though　one　atom　acted　on
another；　yet　a　third；　more　distant　atom　（between　which　and　the　first　atom；　the　second　atom　would
be）；　would　first　enter　into　the　sphere　of　attraction　of　the　intervening　atom　nearer　to　it；　therefore　the
first　atom　would　not　have　an　immediate；　simple　action　on　the　third；　from　which　it　would　follow
that　the　action　of　the　force　of　attraction；　like　that　of　repulsion；　is　equally　mediated。　Further；　the
genuine　penetration　of　the　force　of　attraction　could　of　necessity　consist　only　in　this；　that　every
part　of　matter　was　in　and　for　itself　attractive；　not　that　a　certain　number　of　atoms　behaved　passively
and　only　one　atom　actively。　But　we　must　at　once　remark　with　respect　to　the　force　of　repulsion
itself　that　in　the　passage　quoted；　'parts　in　contact'　are　mentioned　which　implies　solidity　and
continuity　of　a　matter　already　finished　and　complete　which　would　not　permit　the　passage
through　it　of　a　repelling　force。　But　this　solidity　of　matter　in　which　parts　are　in　contact　and　are　no
longer　separated　by　the　void　already　presupposes　that　the　force　of　repulsion　is　sublated；　according
to　the　sensuous　conception　of　repulsion　which　prevails　here；　parts　in　contact　are　to　be　taken　as
those　which　do　not　repel　each　other。　It　therefore　follows；　quite　tautologically；　that　where　repulsion
is　assumed　to　be　not；　there　no　repulsion　can　take　place。　But　from　this　nothing　else　follows　which
could　serve　to　determine　the　force　of　repulsion。　However；　reflection　on　the　statement　that　parts　in
contact　are　in　contact　only　in　so　far　as　they　hold　themselves　apart；　leads　directly　to　the　conclusion
that　the　force　of　repulsion　is　not　merely　on　the　surface　of　matter　but　within　the　sphere　which　was
supposed　to　be　only　a　sphere　of　attraction。

Kant　assumes　further　that　'through　the　force　of　attraction；　matter　only　occupies　space　but　does　not
fill　it'；　and　'because　matter　through　the　force　of　attraction　does　not　fill　space；　this　force　can　act
across　empty　space　since　there　is　no　intervening　matter　to　limit　it'。　This　distinction　is　much　the　same
as　the　one　mentioned　above　where　a　determination　was　supposed　to　belong　to　the　concept　of　a
thing　but　not　to　be　contained　in　it；　here；　then；　matter　is　supposed　only　to　occupy　a　space　but　not　to
fill　it。　There　it　is　repulsion；　if　we　stop　at　the　first　determination　of　matter；　through　which　the　ones
repel　one　another　and　so　are　only　negatively　related　to　one　another；　here　that　means；　by　empty
space。　Here；　however；　it　is　the　force　of　attraction　which　keeps　space　empty；　it　does　not　fill　space
by　its　connection　of　the　atoms；　in　other　words；　it　keeps　the　atoms　in　a　negative　relation　to　one
another。　We　see　that　Kant　here　unconsciously　realises　what　is　implicit　in　the　nature　of　the　subject
matter；　when　he　attributes　to　the　force　of　attraction　precisely　what；　in　accordance　with　the　first
determination；　he　attributed　to　the　opposite　force。　While　he　was　busy　with　establishing　the
difference　between　the　two　forces；　it　happened　that　one　had　passed　over　into　the　other。　Thus
through　repulsion；　on　the　other　hand；　matter　is　supposed　to　fill　a　space；　and　consequently　through
repulsion　the　empty　space　left　by　the　force　of　attraction　vanishes。　In　point　of　fact　repulsion；　in
doing　away　with　empty　space；　also　destroys　the　negative　relation　of　the　atoms　or　ones；　that　is；
their　repulsion　of　one　another；　in　…other　words；　repulsion　is　determined　as　the　opposite　of　itself。

To　this　effacing　of　the　differences　there　is　added　the　confusion　arising　from　the　fact　that；　as　we
observed　at　the　beginning；　Kant's　exposition　of　the　opposed　forces　is　analytic；　and　whereas　matter
is　supposed　to　be　derived　from　its　elements；　it　is　presented　throughout　the　entire　discourse　as
already　formed　and　constituted。　In　the　definition　of　surface　and　penetrative　force　both　are　assumed
as　motive　forces　by　means　of　which　matter　is　supposed　to　be　able　to　act　in　one　or　other　of　these
ways。　Here；　therefore；　they　are　represented　as　forces；　not　through　which　matter　first　comes　into
being　but　through　which　matter；　as　an　already　finished　product；　is　only　set　in　motion。　But　in　so　far
as　we　are　speaking　of　the　forces　through　which　different　bodies　act　on　one　another　and　are　set　in
motion；　this　is　something　quite　different　from　the　determination　and　relation　which　these　forces
were　supposed　to　have　as　＇constitutive＇　moments　of　matter。

The　same　opposition　of　attractive　and　repulsive　forces　is　made　by　their　more　developed　form　of
centripetal　and　centrifugal　forces。　These　appear　to　offer　an　essential　distinction；　since　in　their
sphere　there　is　a　fixed　single　one；　a　centre；　in　relation　to　which　the　other　ones　behave　as　not　for
themselves；　so　that　the　difference　between　the　forces　can　be　linked　to　this　presupposed　difference
between　a　single　central　one　and　the　others　which　are　not　independent　relatively　to　it。　But　if　they
are　to　be　used　for　explanation…for　which　purpose　they　are　assumed　to　be　（like　the　forces　of
repulsion　and　attraction）　in　an　inverse　quantitative　ratio　so　that　the　one　increases　as　the　other
decreases…then　the　phenomenon　of　the　motion　and　its　inequality　ought　to　be　the　result　of　these
forces　which　were　assumed　for　the　purpose　of　explanation。　However；　one　need　only　examine　the
accounts　（any　of　them　will　do）　of　a　phenomenon　like　the　unequal　velocity　of　a　planet　in　its　orbit
round　the　sun；　based　on　the　opposition　of　these　forces；　to　become　aware　of　the　confusion　which
prevails　in　such　explanations；　and　the　impossibility　of　disentangling　the　magnitudes　of　the　forces；　so
that　the　one　which　in　the　explanation　is　assumed　to　be　decreasing　can　just　as　well　be　assumed　to
be　increasing；　and　vice　versa。　To　make　this　evident　would　require　a　lengthier　exposition　than
could　be　given　here；　but　what　is　necessary　for　this　purpose　is　adduced　later　on　in　connection　with
the　inverted　relation。

　　　　　　　Section　Two：　Magnitude　（Quantity）

The　difference　between　quantity　and　quality　has　been　stated。　Quality　is　the　first；　immediate
determinateness；　quantity　is　the　determinateness　which　has　become　indifferent　to　being；　a　limit
which　is　just　as　much　no　limit；　being…for…self　which　is　absolutely　identical　with　being…for…other…a
repulsion　of　the　many　ones　which　is　directly　the　non…repulsion；　the　continuity　of　them。

Because　that　which　is　for　itself　is　now　posited　as　not　excluding　its　other；　but　rather　as　affirmatively
continuing　itself　into　it；　it　is　otherness　in　so　far　as　determinate　being　again　appears　in　this
continuity　and　its　determinateness　is　at　the　same　time　no　longer　in　a　simple　self…relation；　no　longer
an　immediate　determinateness　of　the　determinately　existent　something；　but　is　posited　as
self…repelling；　as　in　fact　having　the　relation…to…self　as　a　determinateness　in　another　something
（which　is　for　itself；　and　since　they　are　at　the　same　time　indifferent；　relationless　limits　reflected　into
themselves；　the　determinateness　in　general　is　outside　itself；　an　absolutely　self…external
determinateness　and　an　equally　external　something；　such　a　limit；　the　indifference　of　the　limit　within
itself　and　of　the　something　to　the　limit；　constitutes　the　quantitative　determinateness　of　the
something。

In　the　first　place；　pure　quantity　is　to　be　distinguished　from　itself　as　a　determinate　quantity；　from
quantum。　As　the　former；　it　is　in　the　first　place　real　being…for…self　which　has　returned　into　itself　and
which　as　yet　contains　no　determinateness：　a　compact；　infinite　unity　which　continues　itself　into　itself。

Secondly；　this　develops　a　determinateness　which　is　posited　in　it　as　one　which　is　at　the　same　time
no　determinateness；　as　only　an　external　one。　It　becomes　quantum。　Quantum　is　indifferent
determinateness；　that　is；　a　self…transcending；　self…negating　determinateness；　as　this　otherness　of
otherness　it　relapses　into　the　infinite　progress。　But　the　infinite　quantum　is　the　indifferent
determinateness　sublated；　it　is　the　restoration　of　quality。

Thirdly；　quantum　in　a　qualitative　form　is　quantitative　ratio。　Quantum　transcends　itself　only　generally：
in　ratio；　however；　its　transition　into　its　otherness　is　such　that　this　otherness　in　which　it　has　its
determination　is　at　the　same　time　posited；　is　another　quantum。　Thus　quantum　has　returned　into
itself　and　in　its　otherness　is　related　to　itself。

At　the　base　of　this　ratio　there　is　still　the　externality　of　quantum；　the　quanta　which　are　related　to
each　other　are　indifferent；　that　is；　they　have　their　self…relation　in　such　self…externality。　The　ratio　is
thus　only　a　formal　unity　of　quality　and　quantity。　Its　dialectic　is　its　transition　into　their　absolute　unity；
into　Measure。

Remark：　Something's　Limit　as　Quality

Chapter　1　Quantity

Quantity　is　sublated　being…for…self；　the　repelling　one　which　related　itself　only　negatively　to　the
excluded　one；　having　passed　over　into　relation　to　it；　treats　the　other　as　identical　with　itself；　and　in
doing　so　has　lost　its　determination：　being…for…self　has　passed　over　into　attraction。　The　absolute
brittleness　of　the　repelling　one　has　melted　away　into　this　unity　which；　however；　as　containing　this
one；　is　at　the　same　time　determined　by　the　immanent　repulsion；　and　as　unity　of　the　self…externality
is　unity　with　itself。　Attraction　is　in　this　way　the　moment　of　continuity　in　quantity。

Continuity　is；　therefore；　simple；　self…same　self…relation；　which　is　not　interrupted　by　any　limit　or
exclusion；　it　is　not；　however；　an　immediate　unity；　but　a　unity　of　ones　which　possess　being…for…self。
The　asunderness　of　the　plurality　is　still　contained　in　this　unity；　but　at　the　same　time　as　not
differentiating　or　interrupting　it。　In　continuity；　the　plurality　is　posited　as　it　is　in　itself；　the　many　are
all　alike；　each　is　the　same　as　the　other　and　the　plurality　is；　consequently；　a　simple；　undifferentiated
sameness。　Continuity　is　this　moment　of　self…sameness　of　the　asunderness；　the　self…continuation　of
the　different　ones　into　those　from　which　they　are　distinguished。

In　continuity；　therefore；　magnitude　immediately　possesses　the　moment　of　discreteness…repulsion；
as　now　a　moment　in　quantity。　Continuity　is　self…sameness；　but　of　the　Many　which；　however；　do　not
become　exclusive；　it　is　repulsion　which　expands　th