science of logic-第23章

按键盘上方向键 ← 或 → 可快速上下翻页，按键盘上的 Enter 键可回到本书目录页，按键盘上方向键 ↑ 可回到本页顶部！
————未阅读完？加入书签已便下次继续阅读！


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　particular　qualities。　These　products　are　distinguished　from　one　another　not　merely　by　a
more　or　less；　and　they　are　not　already　present；　or　only　perhaps　in　a　weaker　degree；　in　the
proportions　close　to　the　nodal　proportions；　but　are　bound　up　with　these　nodes　themselves。　For
example；　different　oxides　of　nitrogen　and　nitric　acids　having　essentially　different　qualities　are
formed　only　when　oxygen　and　nitrogen　are　combined　in　certain　specific　proportions；　and　no　such
specific　compounds　are　formed　by　the　intermediate　proportions。　Metal　oxides；　e。g。　the　lead
oxides；　are　formed　at　certain　quantitative　points　of　oxidation　and　are　distinguished　by　colours　and
other　qualities。　They　do　not　pass　gradually　into　one　another；　the　proportions　lying　in　between　these
nodes　do　not　produce　a　neutral　or　a　specific　substance。　Without　having　passed　through　the
intervening　stages；　a　specific　compound　appears　which　is　based　on　a　measure　relation　and
possesses　characteristic　qualities。　Again；　water　when　its　temperature　is　altered　does　not　merely　get
more　or　less　hot　but　passes　through　from　the　liquid　into　either　the　solid　or　gaseous　states；　these
states　do　not　appear　gradually；　on　the　contrary；　each　new　state　appears　as　a　leap；　suddenly
interrupting　and　checking　the　gradual　succession　of　temperature　changes　at　these　points。　Every
birth　and　death；　far　from　being　a　progressive　gradualness；　is　an　interruption　of　it　and　is　the　leap
from　a　quantitative　into　a　qualitative　alteration。

It　is　said；　natura　non　facit　saltum　＇there　are　no　leaps　in　nature＇；　and　ordinary　thinking　when　it　has
to　grasp　a　coming…to…be　or　a　ceasing…to…be；　fancies　it　has　done　so　by　representing　it　as　a　gradual
emergence　or　disappearance。　But　we　have　seen　that　the　alterations　of　being　in　general　are　not　only
the　transition　of　one　magnitude　into　another；　but　a　transition　from　quality　into　quantity　and　vice
versa；　a　becoming…other　which　is　an　interruption　of　gradualness　and　the　production　of　something
qualitatively　different　from　the　reality　which　preceded　it。　Water；　in　cooling；　does　not　gradually
harden　as　if　it　thickened　like　porridge；　gradually　solidifying　until　it　reached　the　consistency　of　ice；　it
suddenly　solidifies；　all　at　once。　It　can　remain　quite　fluid　even　at　freezing　point　if　it　is　standing
undisturbed；　and　then　a　slight　shock　will　bring　it　into　the　solid　state。

In　thinking　about　the　gradualness　of　the　coming…to…be　of　something；　it　is　ordinarily　assumed　that
what　comes　to　be　is　already　sensibly　or　actually　in　existence；　it　is　not　yet　perceptible　only
because　of　its　smallness。　Similarly　with　the　gradual　disappearance　of　something；　the　non…being　or
other　which　takes　its　place　is　likewise　assumed　to　be　really　there；　only　not　observable；　and　there；
too；　not　in　the　sense　of　being　implicitly　or　ideally　contained　in　the　first　something；　but　really　there；
only　not　observable。　In　this　way；　the　form　of　the　in…itself；　the　inner　being　of　something　before　it
actually　exists；　is　transformed　into　a　smallness　of　an　outer　existence；　and　the　essential　difference；
that　of　the　Notion；　is　converted　into　an　external　difference　of　mere　magnitude。　The　attempt　to
explain　coming…to…be　or　ceasing…to…be　on　the　basis　of　gradualness　of　the　alteration　is　tedious　like
any　tautology；　what　comes　to　be　or　ceases　to　be　is　assumed　as　already　complete　and　in　existence
beforehand　and　the　alteration　is　turned　into　a　mere　change　of　an　external　difference；　with　the　result
that　the　explanation　is　in　fact　a　mere　tautology。　The　intellectual　difficulty　attendant　on　such　an
attempted　explanation　comes　from　the　qualitative　transition　from　something　into　its　other　in　general；
and　then　into　its　opposite；　but　the　identity　and　the　alteration　are　misrepresented　as　the　indifferent；
external　determinations　of　the　quantitative　sphere。

In　the　moral　sphere；　in　so　far　as　it　is　considered　under　the　categories　of　being；　there　occurs　the
same　transition　from　quantity　into　quality　and　different　qualities　appear　to　be　based　in　a　difference
of　magnitude。

It　is　through　a　more　or　less　that　the　measure　of　frivolity　or　thought