science of logic-第16部分

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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　sense　this　is　correct；　but　on　the　other　hand　none　of　the　hundred　ones　has
precedence　over　any　other　for　they　are　only　equal　—　each　is　equally　the　hundredth；　thus　they　all
belong　to　the　limit　which　makes　the　number　a　hundred　and　the　number　cannot　dispense　with　any　of
them　for　its　determinateness。　Hence；　relatively　to　the　hundredth　one；　the　others　do　not　constitute　a
determinate　being　that　is　in　any　way　different　from　the　limit；　whether　they　are　outside　or　inside　it。
Consequently；　the　number　is　not　a　plurality　over　against　the　enclosing；　limiting　one；　but　itself
constitutes　this　limitation　which　is　a　specific　quantum；　the　many　constitute　a　number；　a　two；　a　ten；　a
hundred；　and　so　on。

Now　the　limiting　one　is　the　number　as　determined　relatively　to　other　numbers；　as　distinguished
from　them。　But　this　distinguishing　does　not　become　a　qualitative　determinateness　but　remains
quantitative；　falling　only　within　the　comparing　external　reflection；　the　number；　as　a　one；　remains
returned　into　itself　and　indifferent　to　others。　This　indifference　of　a　number　to　others　is　an　essential
determination　of　it　and　constitutes　the　implicit　determinedness　of　the　number；　but　also　the　number's
own　externality。　Number　is　thus　a　numerical　one　as　the　absolutely　determinate　one；　which　at　the
same　time　has　the　form　of　simple　immediacy　and　for　which；　therefore；　the　relation　to　other　is
completely　external。　Further；　one　as　a　number　possesses　determinateness　（in　so　far　as　this　is　a
relation　to　other）　as　the　moments　of　itself　contained　within　it；　in　its　difference　of　unit　and　amount；
and　amount　is　itself　a　plurality　of　ones；　that　is；　this　absolute　externality　is　in　the　one　itself。　This
contradiction　of　number　or　of　quantum　as　such　within　itself　is　the　quality　of　quantum；　in　the　further
determinations　of　which　this　contradiction　is　developed。

Remark　1：　The　Species　of　Calculation　in　Arithmetic；　Kant's　Synthetic　Propositions　a　priori

Remark　2：　The　Employment　of　Numerical　Distinctions　for　Expressing　Philosophical
Notions

B　Extensive　and　Intensive　Quantum

　　　　　（a）　Their　Difference

　　　　　（b）　Identity　of　Extensive　and　Intensive　Magnitude

Remark　1：　Examples　of　This　Identity

Remark　2：　The　determination　of　degree　as　applied　by　Kant　to　the　soul

　　　　　（c）　Alteration　of　Quantum

C　Quantitative　Infinity

　　　　　（a）　Its　Notion

　　　　　（b）　The　Quantitative　Infinite　Progress

Remark　1：　The　High　Repute　of　the　Progress　to　Infinity

Remark　2：　The　Kantian　Antinomy　of　the　Limitation　and　Nonlimitation　of　the　World

　　　　　（c）　The　Infinity　of　Quantum

Remark　1：　The　Specific　Nature　of　the　Notion　of　the　Mathematical　Infinite

Remark　2：　The　Purpose　of　the　Differential　Calculus　Deduced　from　its　Application

Remark　3：　Further　Forms　Connected　With　the　Qualitative　Determinateness　of　Magnitude

Chapter　3　The　Quantitative　Relation　or　Quantitative　Ratio

A　The　Direct　Ratio

B　Inverse　Ratio

C　The　Ratio　of　Powers

Remark

In　the　Remarks　above　on　the　quantitative　infinite；　it　was　shown　that　this　infinite　and　also　the
difficulties　associated　with　it　have　their　origin　in　the　qualitative　moment　which　makes　its
appearance　in　the　sphere　of　quantity；　and　also　how　the　qualitative　moment　of　the　ratio　of　powers
in　particular　is　the　source　of　various　developments　and　complexities。　It　was　shown　that　the　chief
obstacle　to　a　grasp　of　the　Notion　of　this　infinite　is　the　stopping　short　at　its　merely　negative
determination　as　the　negation　of　quantum；　instead　of　advancing　to　the　simple　affirmative
determination　which　is　the　qualitative　moment。　The　only　further　remark　to　be　made　here　concerns
the　intrusion　of　quantitative　forms　into　the　pure　qualitative　forms　of　powers　in　of　thought　in
philosophy。　It　is　the　relationship　particular　which　has　been　applied　recently　to　the　determinations　of
the　Notion。　The　Notion　in　its　immediacy　was　called　the　first　power　or　potence；　in　its　otherness
or　difference；　in　the　determinate　being　of　its　moments；　the　second　power；　and　in　its　return　into
itself　or　as　a　totality；　the　third　power。　It　is　at　once　evident　that　power　as　used　thus　is　a　category
which　essentially　belongs　to　quantum　…　these　powers　do　not　bear　the　meaning　of　the　potentia；　the
dynamis　of　Aristotle。　Thus；　the　relationship　of　powers　expresses　determinateness　in　the　form　or
difference　which　has　reached　its　truth；　but　difference　as　it　is　in　the　particular　Notion　of　quantum；
not　as　it　is　in　the　Notion　as　such。　In　quantum；　the　negativity　which　belongs　to　the　nature　of　the
Notion　is　still　far　from　being　posited　in　the　determination　proper　to　the　Notion；　differences　which
are　proper　to　quantum　are　superficial　determinations　for　the　Notion　itself　and　are　still　far　from
being　determined　as　they　are　in　the　Notion。　It　was　in　the　infancy　of　philosophic　thinking　that
numbers　were　used；　as　by　Pythagoras；　to　designate　universal；　essential　distinctions…and　first　and
second　power；　and　so　on　are　in　this　respect　not　a　whit　better　than　numbers。　This　was　a　preliminary
stage　to　comprehension　in　the　element　of　pure　thought；　it　was　not　until　after　Pythagoras　that
thought　determinations　themselves　were　discovered；　i。e。；　became　on　their　own　account　objects
for　consciousness。　But　to　retrogress　from　such　determinations　to　those　of　number　is　the　action　of　a
thinking　which　feels　its　own　incapacity；　a　thinking　which；　in　Opposition　to　current　philosophical
culture　which　is　accustomed　to　thought　determinations；　now　also　makes　itself　ridiculous　by
pretending　that　this　impotence　is　something　new；　superior；　and　an　advance。

There　is　as　little　to　be　said　against　the　expression　power　when　it　is　used　only　as　a　symbol；　as　there
is　against　the　use　of　numbers　or　any　other　kind　of　symbols　for　Notions…but　also　there　is　just　as
much　to　be　said　against　them　as　against　all　symbolism　whatever　in　which　pure　determinations　of
the　Notion　or　of　philosophy　are　supposed　to　be　represented。

Philosophy　needs　no　such　help　either　from　the　world　of　sense　or　from　the　products　of　the
imagination；　or　from　subordinate　spheres　in　its　own　peculiar　province；　for　the　determinations　of
such　spheres　are　unfitted　for　higher　spheres　and　for　the　whole。　This　unfitness　is　manifest　whenever
categories　of　the　finite　are　applied　to　the　infinite；　the　current　determinations　of　force；　or
substantiality；　cause　and　effect；　and　so　on；　are　likewise　only　symbols　for　expressing；　for　example；
vital　or　spiritual　relationships；　i。e。　they　are　untrue　determinations　for　such　relationships；　and　still
more　so　are　the　powers　of　quantum　and　degrees　of　powers；　both　for　such　and　for　speculative
relationships　generally。

If　numbers；　powers；　the　mathematical　infinite；　and　suchlike　are　to　be　used　not　as　symbols　but　as
forms　for　philosophical　determinations　and　hence　themselves　as　philosophical　forms；　then　it　would
be　necessary　first　of　all　to　demonstrate　their　philosophical　meaning；　i。e。　the　specific　nature　of　their
Notion。　If　this　is　done；　then　they　themselves　are　superfluous　designations；　the　determinateness　of
the　Notion　specifies　its　own　self　and　its　specification　alone　is　the　correct　and　fitting　designation。
The　use　of　those　forms　is；　therefore；　nothing　more　than　a　convenient　means　of　evading　the　task　of
grasping　the　determinations　of　the　Notion；　of　specifying　and　of　justifying　them。



　　　　　　　　　　　　　　　　Section　Three：　Measure

Abstractly　expressed；　in　measure　quality　and　quantity　are　united。　Being　as　such　is　an　immediate
identity　of　the　determinateness　with　itself。　This　immediacy　of　the　determinateness　has　sublated
itself。　Quantity　is　being　which　has　returned　into　itself　in　such　a　manner　that　it　is　a　simple
self…identity　as　indifference　to　the　determinateness。

But　this　indifference　is　only　the　externality　of　having　the　determinateness　not　in　its　own　self　but　in　an
other。　Thirdly；　we　now　have　self…related　externality；　as　self…related　it　is　also　a　sublated　externality
and　has　within　itself　the　difference　from　itself…the　difference　which；　as　an　externality　is　the
quantitative；　and　as　taken　back　into　itself　is　the　qualitative；　moment。

In　transcendental　idealism　the　categories　of　quantity　and　quality