science of logic-第15章

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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　are　followed；　after　the　insertion　of
relation；　by　modality；　which　may　therefore　be　mentioned　here。　This　category　has　there　the
meaning　of　being　the　relation　of　the　object　to　thought。　According　to　that　idealism　thought　generally
is　essentially　external　to　the　thing…in…itself。　In　so　far　as　the　other　categories　have　only　the
transcendental　character　of　belonging　to　consciousness；　but　to　the　objective　element　of　it；　so
modality　as　the　category　of　relation　to　the　subject；　to　this　extent　contains　relatively　the
determination　of　reflection…into…self；　i。e。　the　objectivity　which　belongs　to　the　other　categories　is
lacking　in　the　categories　of　modality；　these；　according　to　Kant；　do　not　in　the　least　add　to　the
concept　as　a　determination　of　the　object　but　only　express　the　relation　to　the　faculty　of　cognition。
The　categories　which　Kant　groups　under　modality　…　namely；　possibility；　actuality　and　necessity　will
occur　later　in　their　proper　place；　Kant　did　not　apply　the　infinitely　important　form　of　triplicity　…　with
him　it　manifested　itself　at　first　only　as　a　formal　spark　of　light　…　to　the　genera　of　his　categories
（quantity；　quality；　etc。）；　but　only　to　their　species　which；　too；　alone　he　called　categories。
Consequently　he　was　unable　to　hit　on　the　third　to　quality　and　quantity。

With　Spinoza；　the　mode　is　likewise　the　third　after　substance　and　attribute；　he　explains　it　to　be　the
affections　of　substance；　or　that　element　which　is　in　an　other　through　which　it　is　comprehended。
According　to　this　concept；　this　third　is　only　externality　as　such；　as　has　already　been　mentioned；
with。　Spinoza　generally；　the　rigid　nature　of　substance　lacks　the　return　into　itself。

The　observation　here　made　extends　generally　to　those　systems　of　pantheism　which　have　been
partially　developed　by　thought。　The　first　is　being；　the　one；　substance；　the　infinite；　essence；　in
contrast　to　this　abstraction　the　second；　namely；　all　determinateness　in　general；　what　is　only　finite；
accidental；　perishable；　non…essential；　etc。　can　equally　abstractly　be　grouped　together；　and　this　is
what　usually　happens　as　the　next　step　in　quite　formal　thinking。　But　the　connection　of　this　second
with　the　first　is　so　evident　that　one　cannot　avoid　grasping　it　as　also　in　a　unity　with　the　latter；　thus
with　Spinoza；　the　attribute　is　the　whole　substance；　but　is　apprehended　by　the　intellect　which　is　itself
a　limitation　or　mode；　but　in　this　way　the　mode；　the　non…substantial　generally；　which　can　only　be
grasped　through　an　other；　constitutes　the　other　extreme　to　substance；　the　third　generally。　Indian
pantheism；　too；　in　its　monstrous　fantasies　has　in　an　abstract　way　received　this　development　which
runs　like　a　moderating　thread　through　its　extravagances；　a　point　of　some　interest　in　the
development　is　that　Brahma；　the　one　of　abstract　thought；　progresses　through　the　shape　of　Vishnu；
particularly　in　the　form　of　Krishna；　to　a　third　form；　that　of　Siva。　The　determination　of　this　third　is
the　mode；　alteration；　coming…to…be　and　ceasing…to…be…the　field　of　externality　in　general。　This
Indian　trinity　has　misled　to　a　comparison　with　the　Christian　and　it　is　true　that　in　them　a　common
element　of　the　nature　of　the　Notion　can　be　recognised；　but　it　is　essential　to　gain　a　more　precise
consciousness　of　the　difference　between　them；　for　not　only　is　this　difference　infinite；　but　it　is　the
true；　the　genuine　infinite　which　constitutes　it。　This　third　principle　is；　according　to　its　determination；
the　dispersal　of　the　unity　of　substance　into　its　opposite；　not　the　return　of　the　unity　to　itself　…　not
spirit　but　rather　the　non…spiritual。　In　the　true　trinity　there　is　not　only　unity　but　union；　the　conclusion
of　the　syllogism　is　a　unity　possessing　content　and　actuality；　a　unity　which　in　its　wholly　concrete
determination　is　spirit。　This　principle　of　the　mode　and　of　alteration　does　not；　it　is　true；　altogether
exclude　the　unity；　in　Spinozism；　for　example；　it　is　precisely　the　mode　as　such　which　is　untrue；
substance　alone　is　true　and　to　it　everything　must　be　brought　back。　But　this　is　only　to　submerge　all
content　in　the　void；　in　a　merely　formal　unity　lacking　all　content。　Thus　Siva；　too；　is　again　the　great
whole；　not　distinct　from　Brahma；　but　Brahma　himself。　In　other　words；　the　difference　and　the
determinateness　only　vanish　again　but　are　not　preserved；　are　not　sublated；　and　the　unity　does　not
become　a　concrete　unity；　neither　is　the　disunity　reconciled。　The　supreme　goal　for　man　placed　in　the
sphere　of　coming…to…be　and　ceasing…to…be；　of　modality　generally；　is　submergence　in
unconsciousness；　unity　with　Brahma；　annihilation；　the　Buddhist　Nirvana；　Nibbana　etc。；　is　the　same。

Now　although　the　mode　as　such　is　abstract　externality；　indifference　to　qualitative　and　quantitative
determinations；　and　in　essence　the　external　and　unessential　elements　are　not　supposed　to　count；　it
is　still；　on　the　other　hand；　admitted　in　many　cases　that　everything　depends　on　the　kind　and　manner
of　the　mode；　such　an　admission　means　that　the　mode　itself　is　declared　to　belong　essentially　to　the
substantial　nature　of　a　thing；　a　very　indefinite　conne