the　fact　of　a　connexion。　Now　definition　reveals　essential　nature；
  demonstration　reveals　that　a　given　attribute　attaches　or　does　not
  attach　to　a　given　subject；　but　different　things　require　different
  demonstrations…unless　the　one　demonstration　is　related　to　the　other　as
  part　to　whole。　I　add　this　because　if　all　triangles　have　been　proved　to
  possess　angles　equal　to　two　right　angles；　then　this　attribute　has　been
  proved　to　attach　to　isosceles；　for　isosceles　is　a　part　of　which　all
  triangles　constitute　the　whole。　But　in　the　case　before　us　the　fact　and
  the　essential　nature　are　not　so　related　to　one　another；　since　the
  one　is　not　a　part　of　the　other。
  So　it　emerges　that　not　all　the　definable　is　demonstrable　nor　all　the
  demonstrable　definable；　and　we　may　draw　the　general　conclusion　that
  there　is　no　identical　object　of　which　it　is　possible　to　possess　both　a
  definition　and　a　demonstration。　It　follows　obviously　that　definition
  and　demonstration　are　neither　identical　nor　contained　either　within
  the　other：　if　they　were；　their　objects　would　be　related　either　as
  identical　or　as　whole　and　part。
  4
  So　much；　then；　for　the　first　stage　of　our　problem。　The　next　step
  is　to　raise　the　question　whether　syllogism…i。e。　demonstration…of　the
  definable　nature　is　possible　or；　as　our　recent　argument　assumed；
  impossible。
  We　might　argue　it　impossible　on　the　following　grounds：…（a）　syllogism
  proves　an　attribute　of　a　subject　through　the　middle　term；　on　the　other
  hand　（b）　its　definable　nature　is　both　'peculiar'　to　a　subject　and
  predicated　of　it　as　belonging　to　its　essence。　But　in　that　case　（1）　the
  subject；　its　definition；　and　the　middle　term　connecting　them　must　be
  reciprocally　predicable　of　one　another；　for　if　A　is　to　C；　obviously
  A　is　'peculiar'　to　B　and　B　to　C…in　fact　all　three　terms　are　'peculiar'
  to　one　another：　and　further　（2）　if　A　inheres　in　the　essence　of　all　B
  and　B　is　predicated　universally　of　all　C　as　belonging　to　C's
  essence；　A　also　must　be　predicated　of　C　as　belonging　to　its　essence。
  If　one　does　not　take　this　relation　as　thus　duplicated…if；　that　is；　A
  is　predicated　as　being　of　the　essence　of　B；　but　B　is　not　of　the
  essence　of　the　subjects　of　which　it　is　predicated…A　will　not
  necessarily　be　predicated　of　C　as　belonging　to　its　essence。　So　both
  premisses　will　predicate　essence；　and　consequently　B　also　will　be
  predicated　of　C　as　its　essence。　Since；　therefore；　both　premisses　do
  predicate　essence…i。e。　definable　form…C's　definable　form　will　appear
  in　the　middle　term　before　the　conclusion　is　drawn。
  We　may　generalize　by　supposing　that　it　is　possible　to　prove　the
  essential　nature　of　man。　Let　C　be　man；　A　man's　essential
  naturetwo…footed　animal；　or　aught　else　it　may　be。　Then；　if　we　are　to
  syllogize；　A　must　be　predicated　of　all　B。　But　this　premiss　will　be
  mediated　by　a　fresh　definition；　which　consequently　will　also　be　the
  essential　nature　of　man。　Therefore　the　argument　assumes　what　it　has　to
  prove；　since　B　too　is　the　essential　nature　of　man。　It　is；　however；　the
  case　in　which　there　are　only　the　two　premisses…i。e。　in　which　the
  premisses　are　primary　and　immediate…which　we　ought　to　investigate；
  because　it　best　illustrates　the　point　under　discussion。
  Thus　they　who　prove　the　essential　nature　of　soul　or　man　or
  anything　else　through　reciprocating　terms　beg　the　question。　It　would
  be　begging　the　question；　for　example；　to　contend　that　the　soul　is　that
  which　causes　its　own　life；　and　that　what　causes　its　own　life　is　a
  self…moving　number；　for　one　would　have　to　postulate　that　the　soul　is　a
  self…moving　number　in　the　sense　of　being　identical　with　it。　For　if　A
  is　predicable　as　a　mere　consequent　of　B　and　B　of　C；　A　will　not　on　that
  account　be　the　definable　form　of　C：　A　will　merely　be　what　it　was
  true　to　say　of　C。　Even　if　A　is　predicated　of　all　B　inasmuch　as　B　is
  identical　with　a　species　of　A；　still　it　will　not　follow：　being　an
  animal　is　predicated　of　being　a　man…since　it　is　true　that　in　all
  instances　to　be　human　is　to　be　animal；　just　as　it　is　also　true　that
  every　man　is　an　animal…but　not　as　identical　with　being　man。
  We　conclude；　then；　that　unless　one　takes　both　the　premisses　as
  predicating　essence；　one　cannot　infer　that　A　is　the　definable　form　and
  essence　of　C：　but　if　one　does　so　take　them；　in　assuming　B　one　will
  have　assumed；　before　drawing　the　conclusion；　what　the　definable　form
  of　C　is；　so　that　there　has　been　no　inference；　for　one　has　begged　the
  question。
  5
  Nor；　as　was　said　in　my　formal　logic；　is　the　method　of　division　a
  process　of　inference　at　all；　since　at　no　point　does　the
  characterization　of　the　subject　follow　necessarily　from　the
  premising　of　certain　other　facts：　division　demonstrates　as　little　as
  does　induction。　For　in　a　genuine　demonstration　the　conclusion　must　not
  be　put　as　a　question　nor　depend　on　a　concession；　but　must　follow
  necessarily　from　its　premisses；　even　if　the　respondent　deny　it。　The
  definer　asks　'Is　man　animal　or　inanimate？'　and　then　assumes…he　has　not
  inferred…that　man　is　animal。　Next；　when　presented　with　an　exhaustive
  division　of　animal　into　terrestrial　and　aquatic；　he　assumes　that　man
  is　terrestrial。　Moreover；　that　man　is　the　complete　formula；
  terrestrial…animal；　does　not　follow　necessarily　from　the　premisses：
  this　too　is　an　assumption；　and　equally　an　assumption　whether　the
  division　comprises　many　differentiae　or　few。　（Indeed　as　this　method　of
  division　is　used　by　those　who　proceed　by　it；　even　truths　that　can　be
  inferred　actually　fail　to　appear　as　such。）　For　why　should　not　the
  whole　of　this　formula　be　true　of　man；　and　yet　not　exhibit　his
  essential　nature　or　definable　form？　Again；　what　guarantee　is　there
  against　an　unessential　addition；　or　against　the　omission　of　the
  final　or　of　an　intermediate　determinant　of　the　substantial　being？
  The　champion　of　division　might　here　urge　that　though　these　lapses　do
  occur；　yet　we　can　solve　that　difficulty　if　all　the　attributes　we
  assume　are　constituents　of　the　definable　form；　and　if；　postulating　the
  genus；　we　produce　by　division　the　requisite　uninterrupted　sequence
  of　terms；　and　omit　nothing；　and　that　indeed　we　cannot　fail　to　fulfil
  these　conditions　if　what　is　to　be　divided　falls　whole　into　the
  division　at　each　stage；　and　none　of　it　is　omitted；　and　that　this…the
  dividendum…must　without　further　question　be　（ultimately）　incapable
  of　fresh　specific　division。　Nevertheless；　we　reply；　division　does
  not　involve　inference；　if　it　gives　knowledge；　it　gives　it　in　another
  way。　Nor　is　there　any　absurdity　in　this：　induction；　perhaps；　is　not
  demonstration　any　more　than　is　division；　et　it　does　make　evident
  some　truth。　Yet　to　state　a　definition　reached　by　division　is　not　to
  state　a　conclusion：　as；　when　conclusions　are　drawn　without　their
  appropriate　middles；　the　alleged　necessity　by　which　the　inference
  follows　from　the　premisses　is　open　to　a　question　as　to　the　reason
  for　it；　so　definitions　reached　by　division　invite　the　same　question。
  Thus　to　the　question　'What　is　the　essential　nature　of　man？'　the
  divider　replies　'Animal；　mortal；　footed；　biped；　wingless'；　and　when　at
  each　step　he　is　asked　'Why？'；　he　will　say；　and；　as　he　thinks；　proves
  by　division；　that　all　animal　is　mortal　or　immortal：　but　such　a　formula
  taken　in　its　entirety　is　not　definition；　so　that　even　if　division　does
  demonstrate　its　formula；　definition　at　any　rate　does　not　turn　out　to
  be　a　conclusion　of　inference。
  6
  Can　we　nevertheless　actually　demonstrate　what　a　thing　essentially
  and　substantially　is；　but　hypothetically；　i。e。　by　premising　（1）　that
  its　definable　form　is　constituted　by　the　'peculiar'　attributes　of
  its　essential　nature；　（2）　that　such　and　such　are　the　only　attributes
  of　its　essential　nature；　and　that　the　complete　synthesis　of　them　is
  peculiar　to　the　thing；　and　thus…since　in　this　synthesis　consists　the
  being　of　the　thing…obtaining　our　conclusion？　Or　is　the　truth　that；
  since　proof　must　be　through　the　middle　term；　the　definable　form　is
  once　more　assumed　in　this　minor　premiss　too？
  Further；　just　as　in　syllogizing　we　do　not　premise　what　syllogistic
  inference　is　（since　the　premisses　from　which　we　conclude　must　be
  related　as　whole　and　part）；　so　the　definable　form　must　not　fall　within
  the　syllogism　but　remain　outside　the　premisses　posited。　It　is　only
  against　a　doubt　as　to　its　having　been　a　syllogistic　inference　at　all
  that　we　have　to　defend