science of logic-第22章

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reflected。　Measure；　'　having　thus　realised　its　own　Notion；　has　passed　into　essence。

At　first；　measure　is　only　an　immediate　unity　of　quality　and　quantity；　so　that：　（1）；　we　have　a
quantum　with　a　qualitative　significance；　a　measure。　The　progressive　determining　of　this　consists　in
explicating　what　is　only　implicit　in　it；　namely；　the　difference　of　its　moments；　of　its　qualitatively　and
quantitatively　determined　being。　These　moments　further　develop　themselves　into　wholes　of
measure　which　as　such　are　self…subsistent。　These　are　essentially　in　relationship　with　each　other；
and　so　measure　becomes　（2）；　a　ratio　of　specific　quanta　having　the　form　of　self…subsistent
measures。　But　their　self…subsistence　also　rests　essentially　on　quantitative　relation　and　quantitative
difference；　and　so　their　self…subsistence　becomes　a　transition　of　each　into　the　other；　with　the　result
that　measure　perishes　in　the　measureless。　But　this　beyond　of　measure　is　the　negativity　of　measure
only　in　principle；　this　results　（3）；　in　the　positing　of　the　indifference　of　the　determinations　of
measure；　and　the　positing　of　real　measure　…　real　through　the　negativity　contained　in　the　indifference
…　as　an　inverse　ratio　of　measures　which；　as　self…subsistent　qualities；　are　essentially　based　only　on
their　quantity　and　on　their　negative　relation　to　one　another；　thereby　demonstrating　themselves　to　be
only　moments　of　their　truly　self…subsistent　unity　which　is　their　reflection…into…self　and　the　positing
thereof；　essence。

The　development　of　measure　which　has　been　attempted　in　the　following　chapters　is　extremely
difficult。　Starting　from　immediate；　external　measure　it　should；　on　the　one　hand；　go　on　to　develop
the　abstract　determination　of　the　quantitative　aspects　of　natural　objects　（a　mathematics　of
nature）；　and　on　the　other　hand；　to　indicate　the　connection　between　this　determination　of　measure
and　the　qualities　of　natural　objects；　at　least　in　general；　for　the　specific　proof；　derived　from　the
Notion　of　the　concrete　object；　of　the　connection　between　its　qualitative　and　quantitative　aspects；
belongs　to　the　special　science　of　the　concrete。　Examples　of　this　kind　concerning　the　law　of　falling
bodies　and　free；　celestial　motion　will　be　found　in　the　Encyclopedia。　of　the　Phil。　Sciences；　3rd
ed。；　Sections　267　and　270；　Remark。　In　this　connection　the　general　observation　may　be　made　that
the　different　forms　in　which　measure　is　realised　belong　also　to　different　spheres　of　natural　reality。
The　complete；　abstract　indifference　of　developed　measure；　i。e。　the　laws　of　measure；　can　only　be
manifested　in　the　sphere　of　mechanics　in　which　the　concrete　bodily　factor　is　itself　only　abstract
matter；　the　qualitative　differences　of　such　matter　are　essentially　quantitatively　determined；　space
and　time　are　the　purest　forms　of　externality；　and　the　multitude　of　matters；　masses；　intensity　of
weight；　are　similarly　external　determinations　which　have　their　characteristic　determinateness　in　the
quantitative　element。　On　the　other　hand；　such　quantitative　determinateness　of　abstract　matter　is
deranged　simply　by　the　plurality　of　conflicting　qualities　in　the　inorganic　sphere　a　rid　still　more　even
in　the　organic　world。　But　here　there　is　involved　not　merely　a　conflict　of　qualities；　for　measure　here
is　subordinated　to　higher　relationships　and　the　immanent　development　of　measure　tends　to　be
reduced　to　the　simple　form　of　immediate　measure。　The　limbs　of　the　animal　organism　have　a
measure　which；　as　a　simple　quantum；　stands　in　a　ratio　to　the　other　quanta　of　the　other　limbs；　the
proportions　of　the　human　body　are　the　fixed　ratio　of　such　quanta。　Natural　science　is　stil1　far　from
possessing　an　insight　into　the　connection　between　such　quantities　and　the　organic　functions　on
which　they　wholly　depend。　But　the　readiest　example　of　the　reduction　of　an　immanent　measure　to　a
merely　externally　determined　magnitude　is　motion。　In　the　celestial　bodies　it　is　free　motion；　a
motion　which　is　determined　solely　by　the　Notion　and　whose　quantitative　elements　therefore　equally
depend　solely　on　the　Notion　（see　above）；　but　such　free　motion　is　reduced　by　the　living　creature　to
arbitrary　or　mechanically　regular；　i。e。　a　wholly　abstract；　formal　motion。

And　in　the　realm　of　spirit　there　is　still　less　to　be　found　a　characteristic；　free　development　of
measure。　It　is　quite　evident；　for　example；　that　a　republican　constitution　like　that　of　Athens；　or　an
aristocratic　constitution　tempered　by　democracy；　is　suitable　only　for　States　of　a　certain　size；　and
that　in　a　developed　civil　society　the　numbers　of　individuals　belonging　to　different　occupations　stand
in　a　certain　relations　to　one　another；　but　all　this　yields　neither　laws　of　measure　nor　characteristic
forms　of　it。　In　the　spiritual　sphere　as　such　there　occur　differences　of　intensity　of　character；
strength　of　imagination；　sensations；　general　ideas；　and　so　on；　but　the　determination　does　not　go
beyond　the　indefiniteness　of　strength　or　weakness。　How　insipid　and　completely　empty　the
so…called　laws　turn　out　to　be　which　have　been　laid　down　about　the　relation　of　strength　and
weakness　of　sensations；　general　ideas；　and　so　on；　comes　home　to　one　on　reading　the　psychologies
which　occupy　themselves　with　such　laws。

Chapter　1：　Specific　Quantity

A　The　Specific　Quantum

B　Specifying　Measure

　　　　　（a）　The　Rule

　　　　　（b）　Specifying　Measure

　　　　　（c）　Relation　of　the　Two　Sides　as　Qualities

Remark

The　exposition　here　of　the　connection　between　the　qualitative　nature　of　something　and　its
quantitative　determination　has　its　application　in　the　already　indicated　example　of　motion。　First　of
all；　in　velocity　as　the　direct　ratio　of　space　traversed　and　time　elapsed；　the　magnitude　of　time　is
taken　as　denominator　while　that　of　space　is　taken　as　numerator。　If　velocity　as　such　is　only　a　ratio
of　the　space　and　time　in　a　motion；　it　is　immaterial　which　of　the　two　moments　is　to　be　considered　as
amount　or　as　unit。　Space；　however；　like　weight　in　specific　gravity；　is　an　external；　real　whole　as
such　…　hence　amount　…　whereas　time；　like　volume；　is　the　ideal；　negative　factor；　the　side　of　unity。
But　here　there　essentially　belongs　the　more　important　ratio；　that　which　holds　between　the
magnitudes　of　space　and　time　in　free　motion；　at　first；　in　the　still　conditioned　motion　of　a　falling
body　where　the　time　factor　is　determined　as　a　root　and　the　space　factor　as　a　square；　or　in　the
absolutely　free　motion　of　the　celestial　bodies　where　the　period　of　revolution　is　lower　by　one　power
than　the　distance　from　the　sun；　the　former　being　a　square　and　the　latter　a　cube。　Fundamental
relationships　of　this　kind　rest　on　the　nature　of　the　interrelated　qualities　of　space　and　time　and　on　the
kind　of　relation　in　which　they　stand；　either　as　a　mechanical　motion；　i。e。　as　an　unfree　motion　which
is　not　determined　by　the　Notion　of　the　moments　of　space　and　time；　or　as　the　descent　of　a　falling
body；　i。e。　as　a　conditionally　free　motion；　or　as　the　absolutely　free　celestial　motion。　These　kinds　of
motion；　no　less　than　their　laws；　rest　on　the　development　of　the　Notion　of　their　moments；　of　space
and　time；　since　these　qualities　as　such　（space　and　time）　prove　to　be　in　themselves；　i。e。　in　their
Notion；　inseparable　and　their　quantitative　relationship　is　the　being…for…self　of　measure；　is　only　one
measure…determination。

In　regard　to　the　absolute　relations　of　measure；　it　is　well　to　bear　in　mind　that　the　mathematics　of
nature；　if　it　is　to　be　worthy　of　the　name　of　science；　must　be　essentially　the　science　of　measures　…　a
science　for　which　it　is　true　much　has　been　done　empirically；　but　little　as　yet　from　a　strictly　scientific；
that　is；　philosophical　point　of　view。　Mathematical　principles　of　natural　philosophy…as　Newton
called　his　work…if　they　are　to　fulfil　this　description　in　a　profounder　sense　than　that　accorded　to
them　by　Newton　and　by　the　entire　Baconian　species　of　philosophy　and　science；　must　contain
things　of　quite　a　different　character　in　order　to　bring　light　into　these　still　obscure　regions　which　are；
however；　worthy　in　the　highest　degree　of　consideration。　

It　is　a　great　service　to　ascertain　the　empirical　numbers　of　nature；　e。g。；　the　distances　of　the　planets
from　one　another；　but　it　is　an　infinitely　greater　service