much　better　than　a　manipulation　of　rods　of　unequal　length　in　order　to　sort　and　group　them
  according　to　size　—　than　a　childish　game　of　fitting　together　the　pieces　of　a　coloured　picture　puzzle。
  Consequently；　this　thinking　has　been　equated；　not　incorrectly；　with　reckoning；　and　reckoning　again
  with　this　thinking。　In　arithmetic；　numbers　are　regarded　as　devoid　of　any　concrete　conceptual
  content；　so　apart　from　their　wholly　external　relationship　they　have　no　meaning；　and　neither　in
  themselves　nor　in　their　interrelationships　are　thoughts。　When　it　is　calculated　in　mechanical　fashion
  that　three…fourths　multiplied　by　two…thirds　makes　one…half；　this　operation　contains　about　as　much
  and　as　little　thought　as　calculating　whether　in　a　logical　figure　this　or　that　kind　of　syllogism　is　valid。
  Before　these　dead　bones　of　logic　can　be　quickened　by　spirit；　and　so　become　possessed　of　a
  substantial；　significant　content；　its　method　must　be　that　which　alone　can　enable　it　to　be　pure
  science。　In　the　present　state　of　logic　one　can　scarcely　recognise　even　a　trace　of　scientific　method。
  It　has　roughly　the　form　of　an　empirical　science。　The　empirical　sciences　have　found　for　their　own
  appropriate　purposes　their　own　peculiar　method；　such　as　it　is；　of　defining　and　classifying　their
  material。　Pure　mathematics；　too；　has　its　method　which　is　appropriate　for　its　abstract　objects　and
  for　the　quantitative　form　in　which　alone　it　considers　them。　I　have　said　what　is　essential　in　the
  preface　to　the　Phenomenology　of　Spirit　about　this　method　and；　in　general；　the　subordinate　form
  of　scientific　method　which　can　be　employed　in　mathematics；　but　it　will　also　be　considered　in　more
  detail　in　the　logic　itself。　Spinoza；　Wolff　and　others　have　let　themselves　be　misled　in　applying　it　also
  to　philosophy　and　in　making　the　external　course　followed　by　Notion…less　quantity；　the　course　of
  the　Notion；　a　procedure　which　is　absolutely　contradictory。
  Hitherto　philosophy　had　not　found　its　method；　it　regarded　with　envy　the　systematic　structure　of
  mathematics；　and；　as　we　have　said；　borrowed　it　or　had　recourse　to　the　method　of　sciences　which
  are　only　amalgams　of　given　material；　empirical　propositions　and　thoughts　—　or　even　resorted　to
  crude　rejection　of　all　method。
  However；　the　exposition　of　what　alone　can　be　the　true　method　of　philosophical　science　falls　within
  the　treatment　of　logic　itself；　for　the　method　is　the　consciousness　of　the　form　of　the　inner
  self…movement　of　the　content　of　logic。
  In　the　Phenomenology　of　Mind　I　have　expounded　an　example　of　this　method　in　application　to　a
  more　concrete　object；　namely　to　consciousness。　Here　we　are　dealing　with　forms　of　consciousness
  each　of　which　in　realising　itself　at　the　same　time　resolves　itself；　has　for　its　result　its　own　negation　—
  and　so　passes　into　a　higher　form　。　All　that　is　necessary　to　achieve　scientific　progress　—　and　it　is
  essential　to　strive　to　gain　this　quite　simple　insight　—　is　the　recognition　of　the　logical　principle　that
  the　negative　is　just　as　much　positive；　or　that　what　is　self…contradictory　does　not　resolve　itself　into　a
  nullity；　into　abstract　nothingness；　but　essentially　only　into　the　negation　of　its　particular　content；　in
  other　words；　that　such　a　negation　is　not　all　and　every　negation　but　the　negation　of　a　specific
  subject　matter　which　resolves　itself；　and　consequently　is　a　specific　negation；　and　therefore　the
  result　essentially　contains　that　from　which　it　results；　which　strictly　speaking　is　a　tautology；　for
  otherwise　it　would　be　an　immediacy；　not　a　result。　Because　the　result；　the　negation；　is　a　specific
  negation；　it　has　content。　It　is　a　fresh　Notion　but　higher　and　richer　than　its　predecessor；　for　it　is
  richer　by　the　negation　or　opposite　of　the　latter；　therefore　contains　it；　but　also　something　more；　and
  is　the　unity　of　itself　and　its　opposite。　It　is　in　this　way　that　the　system　of　Notions　as　such　has　to　be
  formed　—　and　has　to　complete　itself　in　a　purely　continuous　course　in　which　nothing　extraneous　is
  introduced。
  I　could　not　pretend　that　the　method　which　I　follow　in　this　system　of　logic　—　or　rather　which　this
  system　in　its　own　self　follows　—　is　not　capable　of　greater　completeness；　of　much　elaboration　in
  detail；　but　at　the　same　time　I　know　that　it　is　the　only　true　method。　This　is　self…evident　simply　from
  the　fact　that　it　is　not　something　distinct　from　its　object　and　content；　for　it　is　the　inwardness　of　the
  content；　the　dialectic　which　it　possesses　within　itself；　which　is　the　mainspring　of　its　advance。　It　is
  clear　that　no　expositions　can　be　accepted　as　scientifically　valid　which　do　not　pursue　the　course　of
  this　method　and　do　not　conform　to　its　simple　rhythm；　for　this　is　the　course　of　the　subject　matter
  itself。
  In　conformity　with　this　method；　I　would　point　out　that　the　divisions　and　headings　of　the　books；
  sections　and　chapters　given　in　this　work　as　well　as　the　explanations　associated　with　them；　are
  made　to　facilitate　a　preliminary　survey　and　strictly　are　only　of　historical　value。　They　do　not　belong
  to　the　content　and　body　of　the　science　but　are　compilations　of　an　external　reflection　which　has
  already　run　through　the　whole　of　the　exposition　and　consequently　knows　and　indicates　in　advance
  the　sequence　of　its　moments　before　these　are　brought　forward　by　the　subject　matter　itself。
  Similarly　in　the　other　sciences；　such　preliminary　definitions　and　divisions　are　in　themselves　nothing
  else　but　such　external　indications；　but　even　within　the　particular　science　they　are　not　raised　above
  this　status。　Even　in　logic；　for　example；　we　may　be　told　perhaps　that　'logic　has　two　main　parts；　the
  theory　of　elements　and　methodology'；　then　under　the　former　there　straightway　follows　perhaps　the
  superscription；　Laws　of　Thought；　and　then；　Chapter　I：　Concepts。　First　Section：　Of　the
  Clearness　of　Concepts；　and　so　on。　These　definitions　and　divisions；　made　without　any　deduction
  or　justification；　constitute　the　systematic　framework　and　the　entire　connectedness　of　such　sciences。
  Such　a　logic　regards　it　as　its　vocation　to　talk　about　the　necessity　of　deducing　concepts　and　truths
  from　principles；　but　as　regards　what　it　calls　method；　the　thought　of　a　deduction　of　it　simply　does
  not　occur　to　it。　The　procedure　consists；　perhaps；　in　grouping　together　what　is　similar　and　making
  what　is　simple　precede　what　is　complex；　and　other　external　considerations。
  But　as　regards　any　inner；　necessary　connectedness；　there　is　nothing　more　than　the　list　of　headings
  of　the　various　parts　and　the　transition　is　effected　simply　by　saying　Chapter　II；　or　We　come　now　to
  the　judgements；　and　the　like。
  The　superscriptions　and　divisions；　too；　which　appear　in　this　system　are　not　themselves　intended　to
  have　any　other　significance　than　that　of　a　list　of　contents。　Besides；　the　immanent　coming…to…be　of
  the　distinctions　and　the　necessity　of　their　connection　with　each　other　must　present　themselves　in
  the　exposition　of　the　subject　matter　itself　for　it　falls　within　the　spontaneous　progressive
  determination　of　the　Notion。？
  That　which　enables　the　Notion　to　advance　itself　is　the　already　mentioned　negative　which　it
  possesses　within　itself；　it　is　this　which　constitutes　the　genuine　dialectical　moment。　Dialectic　in　this
  way　acquires　an　entirely　different　significance　from　what　it　had　when　it　was　considered　as　a
  separate　part　of　Logic　and　when　its　aim　and　standpoint　were；　one　may　say；　completely
  misunderstood。　Even　the　Platonic　dialectic；　in　the　Parmenides　itself　and　elsewhere　even　more
  directly；　on　the　one　hand；　aims　only　at　abolishing　and　refuting　assertions　through　themselves　and　on
  the　other　hand；　has　for　its　result　simply　nothingness。
  Dialectic　is　commonly　regarded　as　an　external；　negative　activity　which　does　not　pertain　to　the
  subject　matter　itself；　having　its　ground　in　mere　conceit　as　a　subjective　itch　for　unsettling　and
  destroying　what　is　fixed　and　substantial；　or　at　least　having　for　its　result　nothing　but　the
  worthlessness　of　the　object　dialectically　considered。
  Kant　rated　dialectic　higher　—　and　this　is　among　his　greatest　merits　—　for　he　freed　it　from　the
  seeming　arbitrariness　which　it　possesses　from　the　standpoint　of　ordinary　thought　and　exhibited　it　as
  a　necessary　function　of　reason。　Because　dialectic　was　held　to　be　merely　the　art　of　practising
  deceptions　and　producing　illusions；　the　assumption　was　made　forthwith　that　it　is　only　a　spurious
  game；　the　whole　of　its　power　resting　solely　on　concealment　of　the　deceit　and　that　its　results　are
  obtained　only　surreptitiously　and　are　a　subjective　illusion。　True；　Kant's　expositions　in　the
  antinomies　of　pure　reason；　when　closely　examined　as　they　will　be　at　length　in　the　course　of　this
  work；　do　not　indeed　deserve　any　great　praise；　but　the　general　idea　on　which　he　based　his
  expositions　and　which　he　vindicated；　is　the　objectivity　of　the　illusion　and　the　necessity　of　the
  contradiction　which　belongs　to　the　nature　of　thought　determinations：　primarily；　it　is　true；　with　the
  significance　that　these　determinations　are　applied　by　reason　to　things　in　themselves；　but　their
  nature　is　precisely　what　they　are　in　reason　and　with　reference　to　what　is　intrinsic　or　in　itself。
  This　result；　grasped　in　its　positive　aspect；　is　nothing　else　but　the　inner　negativity　of　the
  determinations　a