philosophy of nature-第5部分

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particular　forces　corresponding　to　the　power　of　attraction　and　repulsion；　of　being　conceived　more
precisely　as　the　centripetal　and　the　centrifugal　forces；　which　are　supposed；　like　gravity；　to　act　on
bodies；　and　independently　of　each　other　and　contingently；　to　meet　together　in　a　third　entity；　the
body。　In　this　way　whatever　profundity　was　contained　in　the　thought　of　general　gravitation　is
destroyed　again；　and　the　concept　and　reason　will　be　unable　to　penetrate　into　the　theory　of
absolute　motion；　as　long　as　the　vaunted　discoveries　of　forces　prevail　there。　

if　one　closely　considers　the　quantitative　determinations　which　have　been　identified　in　the　laws　of
the　centripetal　and　the　centrifugal　forces；　one　very　quickly　discovers　the　confusion　which　emerges
from　their　separation。　This　confusion　becomes　even　greater　if　the　separation　is　mentioned　in
relation　to　gravitation；　gravitation；　also　called　attraction；　then　seems　to　be　the　same　as　centripetal
force；　the　law　of　this　individual　force　is　taken　as　the　law　of　the　whole　of　gravitation；　and　the
centrifugal　force；　which　at　another　time　is　valued　as　thoroughly　essential；　is　viewed　as　something
quite　superfluous。…In　the　above　proposition；　which　contains　the　immediate　idea　of　gravitation；
gravity　itself　namely；　as　the　concept；　which　shows　itself　in　the　particularity　of　the　body　through　the
external　reality　of　motion；　the　rational　identity　and　inseparability　of　these　two　moments　are
contained。…The　relativity　of　motion　also　shows　itself　in　this　proposition；　which　only　makes　sense　in
a　system　of　several　bodies　standing　in　relation　to　each　other　in　accordance　with　a　varied
determination；　so　that　a　different　determination　will　immediately　result。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　211。

The　particular　bodies　in　which　gravity　is　realised　have；　as　the　determinations　of　their　different
natures；　the　moments　of　their　concept。　One　body；　therefore；　is　the　general　centre　of　being　in　itself。
Opposing　this　extreme　stands　individuality；　existing　outside　of　itself　and　without　a　centre。　But　the
particular　bodies　are　others；　which　stand　in　the　determination　of　being　outside　of　themselves　and
are　at　the　same　time；　as　being　in　themselves；　also　centres　for　themselves；　and　are　related　to　the
first　body　as　to　their　essential　unity。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　212。

（1）　The　motion　of　bodies　of　relative　centrality；　in　relation　to　bodies　of　abstract；　general　centrality；
is　absolutely　free　motion；　and　the　conclusion　of　this　system　is　that　the　general　central　body　is
brought　together　through　relative　centrality　with　dependent　corporeality。　

As　is　well…known；　the　laws　of　absolutely　free　motion　were　discovered　by　Kepler；　a　discovery　of
immortal　fame。　Kepler　proved　them；　too；　in　the　sense　that　he　found　the　general　expression　for　the
empirical　data　（cf　§　145）。　Since　then　it　has　become　a　commonplace　that　Newton　first　found　the
proofs　of　these　laws。　Not　often　has　fame　been　more　unjustly　transferred　from　the　first　discoverer
to　another。　Here　I　only　want　to　point　out　what　has　basically　already　been　admitted　by
mathematicians；　namely：　（1）　that　the　Newtonian　formulas　can　be　derived　from　Keplerian　laws；　（2）
that　the　Newtonian　proof　of　the　proposition　that　a　body　governed　by　the　law　of　gravitation　moves
in　an　ellipse　around　the　central　body　proceeds　in　general　in　a　conic　section；　whereas　the　main　point
that　was　to　be　proven　consists　precisely　in　this；　that　the　course　of　such　a　body　is　neither　a　circle
nor　any　other　conic　section；　but　solely　the　ellipse。　The　conditions　which　make　the　course　of　the
body　into　a　specific　conic　section　are　referred　back　to　an　empirical　condition；　namely；　a　particular
situation　of　the　body　at　a　specific　point　in　time；　and　to　the　contingent　strength　of　an　impulse　which
it　is　supposed　to　have　received　at　the　beginning。　（3）　Newton's　'law〃　of　the　force　of　gravity　has
likewise　only　been　demonstrated　inductively　from　experience。　

On　closer　inspection　it　appears　that　what　Kepler；　in　a　simple　and　sublime　manner；　articulated　in
the　form　of　laws　of　celestial　motion；　Newton　converted　into　the　nonconceptual；　reflective　form　of
the　force　of　gravity。　The　whole　manner　of　this　〃proof〃　presents　in　general　a　confused　tissue　of　lines
of　merely　geometrical　construction　to　which　a　physical　meaning　of　independent　forces　is　given；　of
the　empty　concepts　of　the　understanding　of　a　force　of　acceleration；　of　particles　of　time；　at　whose
beginning　those　forces　always　play　a　renewed　role；　and　of　a　force　of　inertia；　which　presumably
continues　its　previous　effect；　and　so　on。　A　rational　proof　of　the　quantitative　determinations　of　free
motion　can　only　rest　on　the　determinations　of　the　concepts　of　space　and　time；　the　moments　whose
relation　is　motion。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　213。

（2）　The　absolute　relation　of　those　dependent　bodies；　which　are　merely　the　extreme　of　the　being
outside　of　itself　of　gravity　and　therefore　lack　their　own　centrality　to　their　relative　central　bodies；　is
the　residual　element　of　their　gravity　in　them；　which　because　of　physical　being　outside　of　themselves
is　mere　striving　and；　therefore；　a　pressure　directed　towards　the　centre　lying　outside　of　them。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　214。

The　separation　of　the　immediate　connection　in　which　such　a　body　rests　is　a　contingent　condition；
which　the　body；　if　confronted　with　an　external　impediment；　suspends　as　motion；　…　relatively　free
motion　in　which　the　distancing　from　the　body　is　not　attributed　as　dependent；　but　the　motion；　if　the
impediment　is　removed；　is　immanent　to　the　body　and　a　manifestation　of　its　own　gravity。　This
motion　transforms　itself　for　itself　into　rest。　

The　attractive　force　of　the　sun；　for　example　towards　the　planets；　or　of　the　earth　towards　those
independent　bodies　belonging　to　it；　seems　to　suggest　the　skewed　view　that　the　force　would　be　an
activity　inhabiting　the　central　body；　and　that　the　bodies　found　in　its　sphere　would　behave　only
passively　and　externally。　Thus　absolute　motion　is　also　viewed；　through　the　application　of　terms
from　common　mechanics；　as　the　dead　conflict　of　an　independent；　tangential　force　and　of　a　force
deriving　equally　independently　from　the　middle　point；　from　which　the　body　would　be　passively
drawn。　

The　Galilean　law　of　falling；　namely；　that　traversed　spaces　behave　as　the　squares　of　transpired
times；　shows；　in　contrast　to　the　abstract；　homogeneous　velocity　of　the　lifeless　mechanism；　where
spaces　are　proportional　to　times；　the　liberation　of　the　conceptual　determinations　of　time　and　space。
In　these　terms　the　former　has　the　determination　of　the　root　as　the　negative　moment　or　principle　of
one；　whereas　the　latter　has　the　determination　of　the　square　as　a　being　outside　of　itself　more
specifically；　without　another　determinacy　like　that　of　the　root；　a　coming　outside　of　itself。　In　this　law
both　moments　still　remain　in　the　relation；　because　the　freedom　of　motion　in　falling；　which　is　also
conditioned；　is　only　formal。　By　contrast；　in　absolute　motion　there　is　the　relation　in　its　totality；　since
this　is　the　realm　of　free　measures　in　which　each　determinacy　attains　its　totality。　Because　the　law　is
essentially　relational；　time　and　space　are　retained　in　their　original　difference。　Dimensionless　time
achieves　therefore　only　a　formal　identity　with　itself；　space；　on　the　other　hand；　as　positive　being
outside　of　itself　achieves　the　dimension　of　the　concept。　The　Keplerian　law　is　thus　the　relation　of　the
cubes　of　the　distances　to　the　squares　of　the　times；…a　law　which　is　so　great　because　it　simply　and
directly　depicts　the　reason　of　the　thing。　The　Newtonian　formula；　however；　which　transforms　it　into
a　law　for　the　force　of　gravity；　exhibits　only　the　perversion　and　inversion　of　reflection　which　has
stopped　halfway。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　215。

（3）　In　the　extremity　of　dependent　bodies；　general　gravitation；　which　bodies　have　as　matter　toward
each　other；　is　subordinated　to　the　gravitation　which　they　have　towards　their　shared　central　bodies。
Towards　each　other；　then；　their　motion　is　external　and　contingent；　the　cause　of　the　motion　is　thrust
and　pressure。　In　this　common　mechanical　motion　the　size　of　the　mass；　which　has　no　meaning　in　the
fall；　and　the　resistance；　which　the　size　achieves　through　its　particular　constitution；　are　moments　of
determination。　But　because　this　motion　contradicts　the　essential　relation　of　the　dependent　body；
namely；　that　relation　to　its　central　body；　it　suspends　itself　through　itself　in　rest。　This　necessity　of　the
concept　appears；　however；　in　the　sphere　of　externality；　as　an　external　impediment　or　friction。　

The　law　of　inertia　is　initially　taken　from　the　nature　of　the　motion　of　dependent　bodies；　for　which　the
motion；　because　it　involves　the　difference　from　themselves　for　themselves；　is　external。　But
precisely　for　this　reason　rest　is　immanent　to　the　bodies；　namely；　the　identity　with　the　centre　lying
outside　of　them。　Their　motion　converts　therefore　essentially　into　rest；　but　not　into　absolute　rest；
rather　into　the　pressure　of　striving　towards　their　centre。　This　centre；　if　it　is　to　be　seen　as　a　striving
moment；　is　at　the　least　the　transformation　of　that　external　movement　into　the　striving　which
constitutes　the　nature　of　the　body。　

The　individual　impediment；　or　the　general　one；　the　friction；　is　external；　to　be　sure；　but　also
necessary。　It　is　the　manifestation　of　that　transition　posited　by　the　concept　of　the　dependent　body。
And　precisely　this　can　also　be　found　in　consideration　of　the　pendulum；　the　motion　of　which；　it　is
said；　would　continue　without　stopping　if　friction　could　be　removed。　

For　itself　the　law　of　inertia　expresses　nothing　but　the　fixation　of　the　understanding　on　the
abstractions　of　rest　and　motion；　which　state　that　rest　is　only　rest　and　motion　is　only　motion。　The
transformation　of　these　abstractions　into　each　other；　which　is　the　concept；　is　for　the　understanding
something　external。　This　law　of　inertia；　together　with　thrust；　attraction；　and　other　determinations
have　been　inadmissibly　transposed　from　common　mechanics　into　absolute　mechanics；　where
motion　is　rather　to　be　found　in　its　free　concept。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　216。

The　difference　between　centra