science of logic-第19章

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repulsion　is；　therefore；　the　creative　flowing　away　of　itself。　On　account　of　the　self…sameness　of　what
is　repelled；　this　distinguishing　or　differentiation　is　an　uninterrupted　continuity；　and　because　of　the
coming…out…of…itself　this　continuity；　without　being　interrupted；　is　at　the　same　time　a　plurality；　which
no　less　immediately　remains　in　its　self…identicalness。

Remark　1：　The　Conception　of　Pure　Quantity

Remark　2：　The　Kantian　Antinomy　of　the　Indivisibility　and　the　Infinite　Divisibility

B　Continuous　and　Discrete　Magnitude

Remark：　The　Usual　Separation　of　These　Magnitudes

In　the　usual　ideas　of　continuous　and　discrete　magnitude；　it　is　overlooked　that　each　of　these
magnitudes　contains　both　moments；　continuity　and　discreteness；　and　that　the　distinction　between
them　consists　only　in　this；　that　in　one　of　the　moments　the　determinateness　is　posited　and　in　the
other　it　is　only　implicit。　Space；　time；　matter；　and　so　forth　are　continuous　magnitudes　in　that　they
are　repulsions　from　themselves；　a　streaming　forth　out　of　themselves　which　at　the　same　time　is　not
their　transition　or　relating　of　themselves　to　a　qualitative　other。　They　possess　the　absolute　possibility
that　the　one　may　be　posited　in　them　at　any　point…not　the　empty　possibility　of　a　mere　otherness　（as
when　it　is　said；　it　is　possible　that　a　tree　might　stand　in　the　place　of　this　stone）；　but　they　contain　the
principle　of　the　one　within　themselves；　it　is　one　of　the　determinations　which　constitute　them。

Conversely；　in　discrete　magnitude　continuity　is　not　to　be　overlooked；　this　moment　is；　as　has　been
shown；　the　one　as　unity。

Continuous　and　discrete　magnitude　can　be　regarded　as　species　of　quantity；　provided　that
magnitude　is　posited；　not　under　any　external　determinateness；　but　under　the　determinatenesses　of
its　own　moments；　the　ordinary　transition　from　genus　to　species　allows　external　characteristics　to
be　attributed　to　the　former　according　to　some　external　basis　of　classification。　And　besides；
continuous　and　discrete　magnitude　are　not　yet　quanta；　they　are　only　quantity　itself　in　each　of　its
two　forms。　They　are　perhaps；　called　magnitudes　in　so　far　as　they　have　in　common　with　quantum
simply　this…to　be　a　determinateness　in　quantity。

C。　LIMITATION　OF　QUANTITY

Discrete　magnitude　has　first　the　one　for　its　principle；　secondly；　it　is　a　plurality　of　ones；　and　thirdly；
it　is　essentially　continuous；　it　is　the　one　as　at　the　same　time　sublated；　as　unity；　the　continuation　of
itself　as　such　in　the　discreteness　of　the　ones。　Consequently；　it　is　posited　as　one　magnitude；　the
determinateness　of　which　is　the　one　which；　in　this　posited　and　determinate　being　is　the　excluding
one；　a　limit　in　the　unity。　Discrete　magnitude　as　such　is　immediately　not　limited；　but　as　distinguished
from　continuous　magnitude　it　is　a　determinate　being；　a　something；　with　the　one　as　its
determinateness　and　also　as　its　first　negation　and　limit。

This　limit；　which　is　related　to　the　unity　and　is　the　negation　in　it；　is　also；　as　the　one；　self…related；　it　is
thus　the　enclosing；　encompassing　limit。　Limit　here　is　not　at　first　distinguished　from　its　determinate
being　as　something；　but；　as　the　one；　is　immediately　this　negative　point　itself。　But　the　being　which
here　is　limited　is　essentially　a　continuity；　by　virtue　of　which　it　passes　beyond　the　limit；　beyond　this
one；　to　which　it　is　indifferent。　Real　discrete　quantity　is　thus　a　quantity；　or　quantum…quantity　as　a
determinate　being　and　a　something。

Since　the　one　which　is　a　limit　includes　within　itself　the　many　ones　of　discrete　quantity；　it　equally
posits　them　as　sublated　within　it；　and　because　it　is　a　limit　of　continuity　simply　as　such；　the
distinction　between　continuous　and　discrete　magnitude　is　here　of　no　significance；　or；　more
correctly；　it　is　a　limit　to　the　continuity　of　the　one　as　much　as　of　the　other；　both　undergo　transition
into　quanta。

Chapter　2　Quantum

Quantum；　which　to　begin　with　is　quantity　with　a　determinateness　or　limit　in　general　is；　in　its
complete　determinateness；　number。　Quantum　differentiates　itself　secondly；　into　（a）　extensive
quantum；　in　which　the　limit　is　a　limitation　of　the　determinately　existent　plurality；　and　（b）　intensive
quantum　or　degree；　the　determinate　being　having　made　the　transition　into　being…for…self。　Intensive
quantum　as　both　for　itself　and　at　the　same　time　immediately　outside　itself　—　since　it　is　an
indifferent　limit　—　has　its　determinateness　in　an　other。　As　this　manifest　contradiction　of　being
determined　simply　within　itself　yet　having　its　determinateness　outside　it；　pointing　outside　itself　for　it；
quantum　posited　as　being　in　its　own　self　external　to　itself；　passes　over　thirdly；　into　quantitative
infinity。

A。　NUMBER

Quantity　is　quantum；　or　has　a　limit；　both　as　continuous　and　as　discrete　magnitude。　The　difference
between　these　two　kinds　has　here；　in　the　first　instance；　no　immediate　significance。

The　very　nature　of　quantity　as　sublated　being…for…self　is　ipso　facto　to　be　indifferent　to　its　limit。　But
equally；　too；　quantity　is　not　unaffected　by　the　limit　or　by　being；　a　quantum；　for　it　contains　within
itself　as　its　own　moment　the　one；　which　is　absolutely　determined　and　which；　therefore；　as　posited
in　the　continuity　or　unity　of　quantity；　is　its　limit；　but　a　limit　which　remains　what　it　has　become；
simply　a　one。　

This　one　is　thus　the　principle　of　quantum；　but　as　the　one　of　quantity。　Hence；　first；　it　is　continuous；
it　is　a　unity；　secondly；　it　is　discrete；　a　plurality　of　ones；　which　is　implicit　in　continuous；　or　explicit　in
discrete　magnitude；　the　ones　having　equality　with　one　another；　possessing　the　said　continuity；　the
same　unity。　Thirdly；　this　one　is　also　a　negation　of　the　many　ones　as　a　simple　limit；　an　excluding　of
its　otherness　from　itself；　a　determination　of　itself　in　opposition　to　other　quanta。　Thus　the　one　is　＇a＇
self…relating；　＇b＇　enclosing　and　＇c＇　other…excluding　limit。

Quantum　completely　posited　in　these　determinations　is　number。　The　complete　positedness　lies　in
the　existence　of　the　limit　as　a　plurality　and　so　in　its　distinction　from　the　unity。　Consequently；
number　appears　as　a　discrete　magnitude；　but　in　the　unity　it　equally　possesses　continuity。　It　is；
therefore；　also　quantum　in　its　complete　determinateness；　for　its　principle　the　one；　the　absolutely
determinate。　Continuity；　in　which　the　one　is　present　only　in　principle；　as　a　sublated　moment　—
posited　as　a　unity　—　is　the　form　of　indeterminateness。

Quantum；　merely　as　such；　is　limited　generally；　its　limit　is　an　abstract　simple　determinateness　of　it。
But　in　quantum　as　number；　this　limit　is　posited　as　manifold　within　itself。　It　contains　the　many　ones
which　constitute　its　determinate　being；　but　does　not　contain　them　in　an　indeterminate　manner；　for
the　determinateness　of　the　limit　falls　in　them；　the　limit　excludes　other　determinate　being；　that　is；
other　pluralities　and　the　ones　it　encloses　are　a　specific　aggregate；　the　amount　—　which　is　the　form
taken　by　discreteness　in　number　—　the　other　to　which　is　the　unit；　the　continuity　of　the　amount。
Amount　and　unit　constitute　the　moments　of　number。

As　regards　amount；　we　must　see　more　closely　how　the　many　ones　of　which　it　consists　are　present
in　the　limit；　it　is　correct　to　say　of　amount　that　it　consists　of　the　many；　for　the　ones　are　in　it　not　as
sublated　but　as　affirmatively　present；　only　posited　with　the　excluding　limit　to　which　they　are
indifferent。　This；　however；　is　not　indifferent　to　them。　In　the　sphere　of　determinate　being；　the　relation
of　the　limit　to　it　was　primarily　such　that　the　determinate　being　persisted　as　the　affirmative　on　this
side　of　its　limit；　while　the　limit；　the　negation；　was　found　outside　on　the　border　of　the　determinate
being；　similarly；　the　breaking…off　＇in　the　counting＇　of　the　many　ones　and　the　exclusion　of　other　ones
appears　as　a　determination　falling　outside　the　enclosed　ones。　But　in　the　qualitative　sphere　it　was
found　that　the　limit　pervades　the　determinate　being；　is　coextensive　with　it；　and　consequently　that　it
lies　in　the　nature　of　something　to　be　limited；　that　is；　finite。　In　the　quantitative　sphere　a　number；　say　a
hundred；　is　conceived　in　such　a　manner　that　the　hundredth　one　alone　limits　the　many　to　make　them
a　hundred。　In　one