qualified　sense；　but　universally。　Finally；　the　first　figure　has　no
  need　of　the　others；　while　it　is　by　means　of　the　first　that　the　other
  two　figures　are　developed；　and　have　their　intervals　closepacked
  until　immediate　premisses　are　reached。
  Clearly；　therefore；　the　first　figure　is　the　primary　condition　of
  knowledge。
  15
  Just　as　an　attribute　A　may　（as　we　saw）　be　atomically　connected
  with　a　subject　B；　so　its　disconnexion　may　be　atomic。　I　call　'atomic'
  connexions　or　disconnexions　which　involve　no　intermediate　term；
  since　in　that　case　the　connexion　or　disconnexion　will　not　be
  mediated　by　something　other　than　the　terms　themselves。　It　follows　that
  if　either　A　or　B；　or　both　A　and　B；　have　a　genus；　their　disconnexion
  cannot　be　primary。　Thus：　let　C　be　the　genus　of　A。　Then；　if　C　is　not
  the　genus　of　B…for　A　may　well　have　a　genus　which　is　not　the　genus　of
  B…there　will　be　a　syllogism　proving　A's　disconnexion　from　B　thus：
  all　A　is　C；
  no　B　is　C；
  therefore　no　B　is　A。
  Or　if　it　is　B　which　has　a　genus　D；　we　have
  all　B　is　D；
  no　D　is　A；
  therefore　no　B　is　A；　by　syllogism；
  and　the　proof　will　be　similar　if　both　A　and　B　have　a　genus。　That　the
  genus　of　A　need　not　be　the　genus　of　B　and　vice　versa；　is　shown　by
  the　existence　of　mutually　exclusive　coordinate　series　of
  predication。　If　no　term　in　the　series　ACD。。。is　predicable　of　any
  term　in　the　series　BEF。。。；and　if　G…a　term　in　the　former　series…is
  the　genus　of　A；　clearly　G　will　not　be　the　genus　of　B；　since；　if　it
  were；　the　series　would　not　be　mutually　exclusive。　So　also　if　B　has　a
  genus；　it　will　not　be　the　genus　of　A。　If；　on　the　other　hand；　neither　A
  nor　B　has　a　genus　and　A　does　not　inhere　in　B；　this　disconnexion　must
  be　atomic。　If　there　be　a　middle　term；　one　or　other　of　them　is　bound　to
  have　a　genus；　for　the　syllogism　will　be　either　in　the　first　or　the
  second　figure。　If　it　is　in　the　first；　B　will　have　a　genus…for　the
  premiss　containing　it　must　be　affirmative：　if　in　the　second；　either
  A　or　B　indifferently；　since　syllogism　is　possible　if　either　is
  contained　in　a　negative　premiss；　but　not　if　both　premisses　are
  negative。
  Hence　it　is　clear　that　one　thing　may　be　atomically　disconnected　from
  another；　and　we　have　stated　when　and　how　this　is　possible。
  16
  Ignorance…defined　not　as　the　negation　of　knowledge　but　as　a　positive
  state　of　mind…is　error　produced　by　inference。
  （1）　Let　us　first　consider　propositions　asserting　a　predicate's
  immediate　connexion　with　or　disconnexion　from　a　subject。　Here；　it　is
  true；　positive　error　may　befall　one　in　alternative　ways；　for　it　may
  arise　where　one　directly　believes　a　connexion　or　disconnexion　as
  well　as　where　one's　belief　is　acquired　by　inference。　The　error；
  however；　that　consists　in　a　direct　belief　is　without　complication；　but
  the　error　resulting　from　inference…which　here　concerns　us…takes　many
  forms。　Thus；　let　A　be　atomically　disconnected　from　all　B：　then　the
  conclusion　inferred　through　a　middle　term　C；　that　all　B　is　A；　will
  be　a　case　of　error　produced　by　syllogism。　Now；　two　cases　are　possible。
  Either　（a）　both　premisses；　or　（b）　one　premiss　only；　may　be　false。
  （a）　If　neither　A　is　an　attribute　of　any　C　nor　C　of　any　B；　whereas
  the　contrary　was　posited　in　both　cases；　both　premisses　will　be
  false。　（C　may　quite　well　be　so　related　to　A　and　B　that　C　is　neither
  subordinate　to　A　nor　a　universal　attribute　of　B：　for　B；　since　A　was
  said　to　be　primarily　disconnected　from　B；　cannot　have　a　genus；　and　A
  need　not　necessarily　be　a　universal　attribute　of　all　things。
  Consequently　both　premisses　may　be　false。）　On　the　other　hand；　（b）
  one　of　the　premisses　may　be　true；　though　not　either　indifferently
  but　only　the　major　A…C　since；　B　having　no　genus；　the　premiss　C…B
  will　always　be　false；　while　A…C　may　be　true。　This　is　the　case　if；
  for　example；　A　is　related　atomically　to　both　C　and　B；　because　when　the
  same　term　is　related　atomically　to　more　terms　than　one；　neither　of
  those　terms　will　belong　to　the　other。　It　is；　of　course；　equally　the
  case　if　A…C　is　not　atomic。
  Error　of　attribution；　then；　occurs　through　these　causes　and　in
  this　form　only…for　we　found　that　no　syllogism　of　universal　attribution
  was　possible　in　any　figure　but　the　first。　On　the　other　hand；　an
  error　of　non…attribution　may　occur　either　in　the　first　or　in　the
  second　figure。　Let　us　therefore　first　explain　the　various　forms　it
  takes　in　the　first　figure　and　the　character　of　the　premisses　in　each
  case。
  （c）　It　may　occur　when　both　premisses　are　false；　e。g。　supposing　A
  atomically　connected　with　both　C　and　B；　if　it　be　then　assumed　that
  no　C　is　and　all　B　is　C；　both　premisses　are　false。
  （d）　It　is　also　possible　when　one　is　false。　This　may　be　either
  premiss　indifferently。　A…C　may　be　true；　C…B　false…A…C　true　because　A
  is　not　an　attribute　of　all　things；　C…B　false　because　C；　which　never
  has　the　attribute　A；　cannot　be　an　attribute　of　B；　for　if　C…B　were
  true；　the　premiss　A…C　would　no　longer　be　true；　and　besides　if　both
  premisses　were　true；　the　conclusion　would　be　true。　Or　again；　C…B　may
  be　true　and　A…C　false；　e。g。　if　both　C　and　A　contain　B　as　genera；　one
  of　them　must　be　subordinate　to　the　other；　so　that　if　the　premiss　takes
  the　form　No　C　is　A；　it　will　be　false。　This　makes　it　clear　that　whether
  either　or　both　premisses　are　false；　the　conclusion　will　equally　be
  false。
  In　the　second　figure　the　premisses　cannot　both　be　wholly　false；
  for　if　all　B　is　A；　no　middle　term　can　be　with　truth　universally
  affirmed　of　one　extreme　and　universally　denied　of　the　other：　but
  premisses　in　which　the　middle　is　affirmed　of　one　extreme　and　denied　of
  the　other　are　the　necessary　condition　if　one　is　to　get　a　valid
  inference　at　all。　Therefore　if；　taken　in　this　way；　they　are　wholly
  false；　their　contraries　conversely　should　be　wholly　true。　But　this
  is　impossible。　On　the　other　hand；　there　is　nothing　to　prevent　both
  premisses　being　partially　false；　e。g。　if　actually　some　A　is　C　and　some
  B　is　C；　then　if　it　is　premised　that　all　A　is　C　and　no　B　is　C；　both
  premisses　are　false；　yet　partially；　not　wholly；　false。　The　same　is
  true　if　the　major　is　made　negative　instead　of　the　minor。　Or　one
  premiss　may　be　wholly　false；　and　it　may　be　either　of　them。　Thus；
  supposing　that　actually　an　attribute　of　all　A　must　also　be　an
  attribute　of　all　B；　then　if　C　is　yet　taken　to　be　a　universal　attribute
  of　all　but　universally　non…attributable　to　B；　C…A　will　be　true　but　C…B
  false。　Again；　actually　that　which　is　an　attribute　of　no　B　will　not
  be　an　attribute　of　all　A　either；　for　if　it　be　an　attribute　of　all　A；
  it　will　also　be　an　attribute　of　all　B；　which　is　contrary　to
  supposition；　but　if　C　be　nevertheless　assumed　to　be　a　universal
  attribute　of　A；　but　an　attribute　of　no　B；　then　the　premiss　C…B　is　true
  but　the　major　is　false。　The　case　is　similar　if　the　major　is　made　the
  negative　premiss。　For　in　fact　what　is　an　attribute　of　no　A　will　not　be
  an　attribute　of　any　B　either；　and　if　it　be　yet　assumed　that　C　is
  universally　non…attributable　to　A；　but　a　universal　attribute　of　B；　the
  premiss　C…A　is　true　but　the　minor　wholly　false。　Again；　in　fact　it　is
  false　to　assume　that　that　which　is　an　attribute　of　all　B　is　an
  attribute　of　no　A；　for　if　it　be　an　attribute　of　all　B；　it　must　be　an
  attribute　of　some　A。　If　then　C　is　nevertheless　assumed　to　be　an
  attribute　of　all　B　but　of　no　A；　C…B　will　be　true　but　C…A　false。
  It　is　thus　clear　that　in　the　case　of　atomic　propositions　erroneous
  inference　will　be　possible　not　only　when　both　premisses　are　false
  but　also　when　only　one　is　false。
  17
  In　the　case　of　attributes　not　atomically　connected　with　or
  disconnected　from　their　subjects；　（a）　（i）　as　long　as　the　false
  conclusion　is　inferred　through　the　'appropriate'　middle；　only　the
  major　and　not　both　premisses　can　be　false。　By　'appropriate　middle'　I
  mean　the　middle　term　through　which　the　contradictory…i。e。　the
  true…conclusion　is　inferrible。　Thus；　let　A　be　attributable　to　B
  through　a　middle　term　C：　then；　since　to　produce　a　conclusion　the
  premiss　C…B　must　be　taken　affirmatively；　it　is　clear　that　this　premiss
  must　always　be　true；　for　its　quality　is　not　changed。　But　the　major　A…C
  is　false；　for　it　is　by　a　change　in　the　quality　of　A…C　that　the
  conclusion　becomes　its　contradictory…i。e。　true。　Similarly　（ii）　if
  th