science of logic-第20节

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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　when　the　empirical　quanta　are　made　to
disappear　and　they　are　raised　into　a　universal　form　of　determinations　of　quantity　so　that　they
become　moments　of　a　law　or　of　measure　…　immortal　services　which　Galileo　for　the　descent　of
falling　bodies　and　Kepler　for　the　motion　of　the　celestial　bodies；　have　achieved。　The　laws　they
discovered　they　have　proved　in　this　sense；　that　they　have　shown　the　whole　compass　of　the
particulars　of　observation　to　correspond　to　them。　But　yet　a　still　higher　proof　is　required　for　these
laws；　nothing　else；　that　is；　than　that　their　quantitative　relations　be　known　from　the　qualities　or
specific　Notions　of　time　and　space　that　are　correlated。

Of　this　kind　of　proof　there　is　still　no　trace　in　the　said　mathematical　principles　of　natural　philosophy；
neither　is　there　in　the　subsequent　works　of　this　kind。　It　has　already　been　remarked　in　connection
with　the　show　of　mathematical　proofs　of　certain　relationships　in　nature；　a　show　based　on　the
misuse　of　the　infinitely　small；　that　it　is　absurd　to　try　todemonstrate　such　proofs　on　a　strictly
mathematical　basis；　i。e。　neither　empirically　nor　from　the　standpoint　of　the　Notion。　These　proofs
presuppose　thir　theorems；　those　very　laws；　from　experience；　what　they　succeed　in　doing　is　to
reduce　them　to　abstract　expressions　and　convenient　formulae。

Undoubtedly　the　time　will　come　when；　with　a　clearer　understanding　of　what　mathematics　can
accomplish　and　has　accomplished；　the　entire；　real　merit　of　Newton　as　against　Kepler　—　the　sham
scaffolding　of　proofs　being　discarded　—　will　clearly　be　seen　to　be　restricted　to　the　said
transformation　of　Kepler's　formula　and　to　the　elementary　analytical　treatment　accorded　to　it。

Undoubtedly　the　time　will　come　when；　with　a　clearer　understanding　of　what　mathematics　can
accomplish　and　has　accomplished；　he　restricted　to　the　said　transformation　of　Kepler's　formula　and
to　the　lem　en；　ta　analytical　treatment　accorded　to　it。

C　Being…for…self　in　Measure

Chapter　2　Real　Measure

A　The　Relation　of　Self…Subsistent　Measures

　　　　　（a）　Combination　of　Two　Measures

　　　　　（b）　Measure　of　a　Series　of　Measure　Relations

　　　　　（c）　Elective　Affinity

Remark：　Berthollet　on　Chemical　Affinity　and　Berzelius's　Theory　of　it

B　Nodal　Line　of　Measure　Relations

Remark：　Examples　of　Such　Nodal　Lines；　the　Maxim；　‘Nature　Does　Not
Make　Leaps’

The　system　of　natural　numbers　already　shows　a　nodal　line　of　qualitative　moments　which　emerge　in
a　merely　external　succession。　It　is　on　the　one　hand　a　merely　quantitative　progress　and　regress；　a
perpetual　adding　or　subtracting；　so　that　each　number　has　the　same　arithmetical　relation　to　the　one
before　it　and　after　it；　as　these　have　to　their　predecessors　and　successors；　and　so　on。　But　the
numbers　so　formed　also　have　a　specific　relation　to　other　numbers　preceding　and　following　them；
being　either　an　integral　multiple　of　one　of　them　or　else　a　power　or　a　root。　In　the　musical　scale
which　is　built　up　on　quantitative　differences；　a　quantum　gives　rise　to　an　harmonious　relation　without
its　own　relation　to　those　on　either　side　of　it　in　the　scale　differing　from　the　relation　between　these
again　and　their　predecessors　and　successors。　While　successive　notes　seem　to　be　at　an
ever…increasing　distance　from　the　keynote；　or　numbers　in　succeeding　each　other　arithmetically
seem　only　to　become　other　numbers；　the　fact　is　that　there　suddenly　emerges　a　return；　a　surprising
accord；　of　which　no　hint　was　given　by　the　quality　of　what　immediately　preceded　it；　but　which
appears　as　an　actio　in　distans；　as　a　connection　with　something　far　removed。　There　is　a　sudden
interruption　of　the　succession　of　merely　indifferent　relations　which　do　not　alter　the　preceding
specific　reality　or　do　not　even　form　any　such；　and　although　the　succession　is　continued
quantitatively　in　the　same　manner；　a　specific　relation　breaks　in　per　saltum。

Such　qualitative　nodes　and　leaps　occur　in　chemical　combinations　when　the　mixture　proportions　are
progressively　altered；　at　certain　points　in　the　scale　of　mixtures；　two　substances　form　products
exhibiting　p