shorter logic-第34章

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regarded　as　consisting　solely　in　their　unity。　

German　physicists　for　some　time　accepted　this　pure　dynamic。　But　in　spite　of　this；　the　majority　of
these　physicists　in　modern　times　have　found　it　more　convenient　to　return　to　the　Atomic　point　of
view；　and　in　spite　of　the　warnings　of　K？stner；　one　of　their　number；　have　begun　to　regard　Matter
as　consisting　of　infinitesimally　small　particles；　termed　'atoms　which　atoms　have　then　to　be　brought
into　relation　with　one　another　by　the　play　of　forces　attaching　to　them…attractive；　repulsive；　or
whatever　they　may　be。　This　too　is　metaphysics；　and　metaphysics　which；　for　its　utter　unintelligence；
there　would　be　sufficient　reason　to　guard　against。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　Quantity　and　Quality
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§98n2

The　transition　from　Quality　to　Quantity；　indicated　in　the　paragraph　before　us；　is　not　found　in　our
ordinary　way　of　thinking；　which　deems　each　of　these　categories　to　exist　independently　beside　the
other。　We　are　in　the　habit　of　saying　that　things　are　not　merely　qualitatively；　but　also　quantitatively
defined；　but　whence　these　categories　originate；　and　how　they　are　related　to　each　other；　are
questions　not　further　examined。　The　fact　is；　quantity　just　means　quality　superseded　and　absorbed：
and　it　is　by　the　dialectic　of　quality　here　examined　that　this　supersession　is　effected。　
？

First　of　all；　we　had　Being：　as　the　truth　of　Being；　came　Becoming：　which　formed　the　passage　into
Being　Determinate：　and　the　truth　of　that　we　found　to　be　Alteration。　And　in　its　result　Alteration
showed　itself　to　be　Being…for…self；　finally；　in　the　two　sides　of　the　process；　Repulsion　and
Attraction；　was　clearly　seen　to　annul　itself；　and　thereby　to　annul　quality　in　the　totality　of　its　stages。　

Still　this　superseded　and　absorbed　quality　is　neither　an　abstract　nothing；　nor　an　equally　abstract
and　featureless　being：　it　is　only　being　as　indifferent　to　determinateness　or　character。　This　aspect　of
being　is　also　what　appears　as　quantity　in　our　ordinary　conceptions。　We　observe　things；　first　of　all；
with　an　eye　to　their　quality　…　which　we　take　to　be　the　character　identical　with　the　being　of　the　thing。
If　we　proceed　to　consider　their　quantity；　we　get　the　conception　of　an　indifferent　and　external
character　or　mode；　of　such　a　kind　that　a　thing　remains　what　it　is；　though　its　quantity　is　altered；　and
the　thing　becomes　greater　or　less。　



　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　B。　QUANTITY



　　　　　　　　　　　　　　　　　　　　　　　　　　　C。　MEASURE

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§107

Measure　is　the　qualitative　quantum；　in　the　first　place　as　immediate　…　a　quantum；
to　which　a　determinate　being　or　a　quality　is　attached。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§107n

Measure；　where　quality　and　quantity　are　in　one；　is　thus　the　completion　of　Being。　Being；　as　we　first
apprehend　it；　is　something　utterly　abstract　and　characterless；　but　it　is　the　very　essence　of　Being　to
characterise　itself；　and　its　complete　characterisation　is　reached　in　Measure。　Measure；　like　the　other
stages　of　Being；　may　serve　as　a　definition　of　the　Absolute；　God；　it　has　been　said；　is　the　Measure　of
all　things。　It　is　this　idea　which　forms　the　ground…note　of　many　of　the　ancient　Hebrew　hymns；　in
which　the　glorification　of　God　tends　in　the　main　to　show　that　he　has　appointed　to　everything　its
bound：　to　the　sea　and　the　solid　land；　to　the　rivers　and　mountains；　and　also　to　the　various　kinds　of
plants　and　animals。　To　the　religious　sense　of　the　Greeks　the　divinity　of　measure；　especially　in
respect　of　social　ethics；　was　represented　by　Nemesis。　That　conception　implies　a　general　theory
that　all　human　beings；　riches；　honour；　and　power；　as　well　as　joy　and　pain；　have　their　definite
measure；　the　transgression　of　which　brings　ruin　and　destruction。　In　the　world　of　objects　too；　we
have　measure。　We　see；　in　the　first　place；　existences　in　Nature；　of　which　measure　forms　the
essential　structure。　This　is　the　case；　for　example；　with　the　solar　system；　which　may　be　described　as
the　realm　of　free　measures。　As　we　next　proceed　to　the　study　of　inorganic　nature；　measure　retires；
as　it　were；　into　the　background；　at　least　we　often　find　the　quantitative　and　qualitative
characteristics　showing　indifference　to　each　other。　Thus　the　quality　of　a　rock　or　a　river　is　not　tied
to　a　definite　magnitude。　

But　even　these　objects　when　closely　inspected　are　found　to　be　not　quite　measureless：　the　water　of
a　river；　and　the　single　constituents　of　a　rock；　when　chemically　analysed；　are　seen　to　be　qualities
conditioned　by　the　quantitative　ratios　between　the　matters　they　contain。　In　organic　nature；
however；　measure　again　rises　into　immediate　perception。　The　various　kinds　of　plants　and　animals；
in　the　whole　as　well　as　in　their　parts；　have　a　certain　measure：　though　it　is　worth　noticing　that　the
more　imperfect　forms；　those　which　are　least　removed　from　inorganic　nature；　are　partly
distinguished　from　the　higher　forms　by　the　greater　indefiniteness　of　their　measure。　Thus　among
fossils　we　find　some　ammonites　discernible　only　by　the　microscope　and　others　as　large　as　a
cart…wheel。　The　same　vagueness　of　measure　appears　in　several　plants；　which　stand　on　a　low　level
of　organic　development　…　for　instance　ferns。　



　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§108

In　so　far　as　in　Measure　quality　and　quantity　are　only　in　immediate　unity；　to　that
extent　their　difference　presents　itself　in　a　manner　equally　immediate。　Two　cases
are　then　possible。　Either　the　specific　quantum　or　measure　is　a　bare　quantum；　and
the　definite　being　（there…and…then）　is　capable　of　an　increase　or　a　diminution；
without　Measure　（which　to　that　extent　is　a　Rule）　being　thereby　set　completely
aside。　Or　the　alteration　of　the　quantum　is　also　an　alteration　of　the　quality。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§　108n
The　identity　between　quantity　and　quality；　which　is　found　in　Measure；　is　at　first　only　implicit；　and
not　yet　explicitly　realised。　In　other　words；　these　two　categories；　which　unite　in　Measure；　each
claim　an　independent　authority。　On　the　one　hand；　the　quantitative　features　of　existence　may　be
altered；　without　affecting　its　quality。　On　the　other　hand；　this　increase　and　diminution；　immaterial
though　it　be；　has　its　limit；　by　exceeding　which　the　quality　suffers　change。　Thus　the　temperature　of
water　is；　in　the　first　place；　a　point　of　no　consequence　in　respect　of　its　liquidity：　still　with　the　increase
of　diminution　of　the　temperature　of　the　liquid　water；　there　comes　a　point　where　this　state　of
cohesion　suffers　a　qualitative　change；　and　the　water　is　converted　into　steam　or　ice。　A　quantitative
change　takes　place；　apparently　without　any　further　significance：　but　there　is　something　lurking
behind；　and　a　seemingly　innocent　change　of　quantity　acts　as　a　kind　of　snare；　to　catch　hold　of　the
quality。　The　antinomy　of　Measure　which　this　implies　was　exemplified　under　more　than　one　garb
among　the　Greeks。　It　was　asked；　for　example；　whether　a　single　grain　makes　a　heap　of　wheat；　or
whether　it　makes　a　bald…tail　to　tear　out　a　single　hair　from　the　horse's　tail。　At　first；　no　doubt；　looking
at　the　nature　of　quantity　as　an　indifferent　and　external　character　of　being；　we　are　disposed　to
answer　these　questions　in　the　negative。　And　yet；　as　we　must　admit；　this　indifferent　increase　and
diminution　has　its　limit：　a　point　is　finally　reached；　where　a　single　additional　grain　makes　a　heap　of
wheat；　and　the　bald…tail　is　produced；　if　we　continue　plucking　out　single　hairs。　These　examples　find
a　parallel　in　the　story　of　the　peasant　who；　as　his　ass　trudged　cheerfully　along；　went　on　adding
ounce　after　ounce　to　its　load；　till　at　length　it　sunk　under　the　unendurable　burden。　It　would　be　a
mistake　to　treat　these　examples　as　pedantic　futility；　they　really　turn　on　thoughts；　an　acquaintance
with　which　is　of　great　importance　in　practical　life；　especially　in　ethics。　Thus　in　the　matter　of
expenditure；　there　is　a　certain　latitude　within　which　a　more　or　less　does　not　matter；　but　when　the
Measure；　imposed　by　the　individual　circumstances　of　the　special　case；　is　exceeded　on　the　one　side
or　the　other；　the　qualitative　nature　of　Measure　（as　in　the　above　examples　of　the　different
temperature　of　water）　makes　itself　felt；　and　a　course；　which　a　moment　before　was　held　good
economy；　turns　into　avarice　or　prodigality。　The　same　principles　may　be　applied　in　politics；　when
the　constitution　of　a　state　has　to　be　looked　at　as　independent　of；　no　less　than　as　dependent　on；　the
extent　of　its　territory；　the　number　of　its　inhabitants；　and　other　quantitative　points　of　the　same　kind。
If　we　look；　e。g。　at　a　state　with　a　territory　of　ten　thousand　square　miles　and　a　population　of　four
millions　we　should；　without　hesitation；　admit　that　a　few　square　miles　of　land　or　a　few　thousand
inhabitants　more　or　less　could　exercise　no　essential　influence　on　the　character　of　its　constitution。
But　on　the　other　hand；　we　must　not　forget　that　by　the　continual　increase　or　diminishing　of　a　state；
we　finally　get　to　a　point　where；　apart　from　all　other　circumstances；　this　quantitative　alteration　alone
necessarily　draws　with　it　an　alteration　in　the　quality　of　the　constitution。　The　constitution　of　a　little
Swiss　canton　does　not　suit　a　great　kingdom；　and；　similarly；　the　constitution　of　the　Roman　republic
was　unsuitable　when　transferred　to　the　small　imperial　towns　of　Germany。　
？



　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§109

In　this　case；　when　a　measure　through　its　quantitative　nature　has　gone　in　excess　of
its　qualitative　character；　we　meet　what　is　at　first　an　absence　of　measure；　the
Measureless。　But　seeing　that　the　second　quantitative　ratio；　which　in　comparison
with　the　first　is　measureless；　is　none　the　less　qualitative；　the　measureless　is　also　a
measure。　These　two　transitions；　from　quality　to　quantum；　and　from　the　latter
back　again　to　quality；　may　be　represented　under　the　image　of　an　infinite
progression…as　the　self…abrogation　and　restoration　of　measure　in　the　measureless。　

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§109n

Quantity；　as　we　have　seen；　is　not　only　capable　of　alteration；　i。e。　of　increase　or　diminution：　it　is
naturally　and　necessarily　a　tendency　to　exceed　itself。　This　tendency　is　maintained　even　in　measure。
But　if　the　quantity　present　in　measure　exceeds　a　certain　limit；　the　quality　corresponding　to　it　is　also
put　in　abeyance。　This　however　is　not　a　negation　of　quality　altogether；　but　only　of　this　definite
quality；　the　place　of　which　is　at　once　occupied　by　another。　This　process　of　measure；　which
appears　alternately　as　a　mere　change　in　quantity；　and　then　as　a　sudden　revulsion　of　quantity　into
quality；　may　be　envisaged　under　the　figure　of　a　nodal　（knotted）　line。　Such　lines　we　find　in　Nature
under　a　variety　of　forms。　We　have　already　referred　to　the　qualitatively　different　states　of
aggregation　water　exhibits　under　increase　or　diminution　of　temperature。　The　same　phenomenon　is
presented　by　the　different　degrees　in　the　oxidation　of　metals。　Even　the　difference　of　musical　notes
may　be　regarded　as　an　example　of　what　takes　place　in　the　process　of　measure　the　revulsion　from
what　is　at　first　merely　quantitative　into　qualitative　alteration。　



　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　§110

What　really　takes　place　here　is　that　the　immediacy；　which　still　attaches　to　measure