attempts　have　been　made　to　introduce　the　synthetic　method　into　philosophy。　Thus　Spinoza；　in
  particular；　begins　with　definitions。　He　says；　for　instance；　that　substance　is　the　causa　sui。　His
  definitions　are　unquestionably　a　storehouse　of　the　most　speculative　truth；　but　it　takes　the　shape　of
  dogmatic　assertions。　The　same　thing　is　also　true　of　Schelling。
  §　230
  （b）　The　statement　of　the　second　element　of　the　notion；　i。e。　of　the　specific
  character　of　the　universal　as　particularising；　is　given　by　Division　in　accordance
  with　some　external　consideration。
  §　230n
  Division　we　are　told　ought　to　be　complete。　That　requires　a　principle　or　ground　of　division　so
  constituted　that　the　division　based　upon　it　embraces　the　whole　extent　of　the　region　designated　by
  the　definition　in　general。　But；　in　division；　there　is　the　further　requirement　that　the　principle　of　it　must
  be　borrowed　from　the　nature　of　the　object　in　question。　If　this　condition　be　satisfied；　the　division　is
  natural　and　not　merely　artificial；　that　is　to　say；　arbitrary。　Thus；　in　zoology；　the　ground　of　division
  adopted　in　the　classification　of　the　mammalia　is　mainly　afforded　by　their　teeth　and　claws。　That　is　so
  far　sensible；　as　the　mammals　themselves　distinguish　themselves　from　one　another　by　these　parts　of
  their　bodies　back　to　which　therefore　the　general　type　of　their　various　classes　is　to　be　traced。　In
  every　case　the　genuine　division　must　be　controlled　by　the　notion。　To　that　extent　a　division；　in　the
  first　instance；　has　three　members：　but　as　particularity　exhibits　itself　as　double；　the　division　may　go
  to　the　extent　even　of　four　members。　In　the　sphere　of　mind　trichotomy　is　predominant；　a
  circumstance　which　Kant　has　the　credit　for　bringing　into　notice
  Theorem
  §　231
  ＇c＇　In　the　concrete　individuality；　where　the　mere　unanalysed　quality　of　the
  definition　is　regarded　as　a　correlation　of　elements；　the　object　is　a　synthetic　nexus
  of　distinct　characteristics。　It　is　a　Theorem。　Being　different；　these　characteristics
  possess　but　a　mediated　identity。　To　supply　the　materials；　which　form　the　middle
  terms；　is　the　office　of　Construction：　and　the　process　of　mediation　itself；　from
  which　cognition　derives　the　necessity　of　that　nexus；　is　the　Demonstration。
  As　the　difference　between　the　analytical　and　synthetic　methods　is　commonly
  stated；　it　seems　entirely　optional　which　of　the　two　we　employ。　If　we　assume；　to
  start　with；　the　concrete　thing　which　the　synthetic　method　presents　as　a　result；　we
  can　analyse　from　it　as　consequences　the　abstract　propositions　which　formed　the
  pre…suppositions　and　the　material　for　the　proof。　Thus；　algebraical　definitions　of
  curved　lines　are　theorems　in　the　method　of　geometry。　Similarly　even　the
  Pythagorean　theorem；　if　made　the　definition　of　a　right…angled　triangle；　might　yield
  to　analysis　those　propositions　which　geometry　had　already　demonstrated　on　is
  behoof。　The　optionalness　of　either　method　is　due　to　both　alike　starting　from　an
  external　presupposition。　So　far　as　the　nature　of　the　notion　is　concerned；　analysis　is
  prior；　since　it　has　to　raise　the　given　material　with　its　empirical　concreteness　into
  the　form　of　general　abstractions；　which　may　then　be　set　in　the　front　of　the
  synthetic　method　as　definitions。
  That　these　methods；　however　indispensable　and　brilliantly　successful　in　their　own
  province；　are　unserviceable　for　philosophical　cognition；　is　self…evident。　They　have
  presuppositions；　and　their　style　of　cognition　is　that　of　understanding；　proceeding
  under　the　canon　of　formal　identity。　In　Spinoza；　who　was　especially　addicted　to
  the　use　of　the　geometrical　method；　we　are　at　once　struck　by　its　characteristic
  formalism。　Yet　his　ideas　were　speculative　in　spirit；　whereas　the　system　of　Wolf；
  who　carried　the　method　out　to　the　height　of　pedantry；　was　even　in　subject…matter
  a　metaphysic　of　the　understanding。
  The　abuses　which　these　methods　with　their　formalism　once　led　to　in　philosophy
  and　science　have　in　modern　times　been　followed　by　the　abuses　of　what　is　called
  'Construction'。　Kant　brought　into　vogue　the　phrase　that　mathematics　'construes'
  its　notions。　All　that　was　meant　by　the　phrase　was　that　mathematics　has　not　to　do
  with　notions；　but　with　abstract　qualities　of　sense…perceptions。　The　name
  'Construction　（construing）　of　notions'　has　since　been　given　to　a　sketch　or
  statement　of　sensible　attributes　which　were　picked　up　from　perception；　quite
  guiltless　of　any　influence　of　the　notion；　and　to　the　additional　formalism　of
  classifying　scientific　and　philosophical　objects　in　a　tabular　form　on　some
  presupposed　rubric；　but　in　other　respects　at　the　fancy　and　discretion　of　the
  observer。　In　the　background　of　all　this；　certainly；　there　is　a　dim　consciousness　of
  the　Idea；　of　the　unity　of　the　notion　and　objectivity　…　a　consciousness　too　that　the
  idea　is　concrete。　But　that　play　of　what　is　styled　'construing'　is　far　from　presenting
  this　unity　adequately；　a　unity　which　is　none　other　than　the　notion　properly　so
  called：　a　perception　is　as　little　the　concreteness　of　reason　and　the　idea。
  Another　point　calls　for　notice。　Geometry　works　with　the　sensuous　but　abstract
  perception　of　space；　and　in　space　it　experiences　no　difficulty　in　isolating　and
  defining　certain　simple　analytical　modes。
  To　geometry　alone　therefore　belongs　in　its　perfection　the　synthetic　method　of
  finite　cognition。　In　its　course；　however　（and　this　is　the　remarkable　point）；　it　finally
  stumbles　upon　what　are　termed　irrational　and　incommensurable　quantities；　and　in
  their　case　any　attempt　at　further　specification　drives　it　beyond　the　principle　of　the
  understanding。　This　is　only　one　of　many　instances　in　terminology；　where　the　title
  'rational'　is　perversely　applied　to　the　province　of　understanding；　while　we
  stigmatise　as　irrational　that　which　shows　a　beginning　and　a　trace　of　rationality。
  Other　sciences；　removed　as　they　are　from　the　simplicity　of　space　or　number；
  often　and　necessarily　reach　a　point　where　understanding　permits　no　further
  advance：　but　they　get　over　the　difficulty　without　trouble。　They　make　a　break　in
  the　strict　sequence　of　their　procedure；　and　assume　whatever　they　require；　though
  it　be　the　reverse　of　what　preceded；　from　some　external　quarter　…　opinion；
  perception；　conception；　or　any　other　source。　Its　inobservancy　as　to　the　nature　of
  its　methods　and　their　relativity　to　the　subject…matter　prevents　this　finite　cognition
  from　seeing　that；　when　it　proceeds　by　definitions　and　divisions；　etc。；　it　is　really　led
  on　by　the　necessity　of　the　laws　of　the　notion。　For　the　same　reason　it　cannot　see
  when　it　has　reached　its　limit；　nor；　if　it　have　transgressed　that　limit；　does　it　perceive
  that　it　is　in　a　sphere　where　the　categories　of　understanding；　which　it　still　continues
  rudely　to　apply；　have　lost　all　authority。
  §232
  The　necessity　which　finite　cognition　produces　in　the　Demonstration　is；　in　the　first
  place；　an　external　necessity；　intended　for　the　subjective　intelligence　alone。　But　in
  necessity　as　such；　cognition　itself　has　left　behind　its　presupposition　and
  starting…point；　which　consisted　in　accepting　its　content　as　given　or　found。
  Necessity　qua　necessity　is　implicitly　the　self…relating　notion。　The　subjective　idea
  has　thus　implicitly　reached　an　original　and　objective　determinateness　…　a
  something　not…given；　and　for　that　reason　immanent　in　the　subject。　It　has　passed
  over　into　the　idea　of　Will。
  §　232n
  The　necessity　which　cognition　reaches　by　means　of　the　demonstration　is　the　reverse　of　what
  formed　its　starting…point。　In　its　starting…point　cognition　had　a　given　and　a　contingent　content；　but
  now；　at　the　close　of　its　movement；　it　knows　its　content　to　be　necessary。　This　necessity　is　reached
  by　means　of　subjective　agency。　Similarly；　subjectivity　at　starting　was　quite　abstract；　a　bare　tabula
  rasa。　It　now　shows　itself　as　a　modifying　and　determining　principle。　In　this　way　we　pass　from　the
  idea　of　cognition　to　that　of　will。　The　passage；　as　will　be　apparent　on　a　closer　examination；　means
  that　the　universal；　to　be　truly　apprehended；　must　be　apprehended　as　subjectivity；　as　a　notion
  self…moving；　active；　and　form…imposing。
  ＇b＇　Volition
  §233
  The　subjective　idea　as　original　and　objective　determinateness；　and　as　a　simple
  uniform　content；　is　the　Good。　Its　impulse　towards　self…realisation　is　in　its
  behaviour　the　reverse　of　the　idea　of　truth；　and　rather　directed　towards　moulding
  the　world　it　finds　before　it　into　a　shape　conformable　to　its　purposed　End。　This
  Volition　has；　on　the　one　hand；　the　certitude　of　the　nothingness　of　the
  presupposed　object；　but；　on　the　other；　as　finite；　it　at　the　same　time　presupposes
  the　purposed　End　of　the　Good　to　be　a　mere　subjective　idea；　and　the　object　to　be
  independent。
  §　234
  This　action　of　the　Will　is　finite：　and　its　finitude　lies　in　the　contradiction　that　in　the
  inconsistent　terms　applied　to　the　objective　world　the　End　of　the　Good　is　just　as
  much　not　executed　as　executed；　the　en