of　proving　the　contradictory　universally　and　in　the　same　respect　and
  relation　and　manner；　the　fallacy　may　be　dependent　on　some　limit　of
  extent　or　on　one　or　other　of　these　qualifications：　moreover；　there
  is　the　assumption　of　the　original　point　to　be　proved；　in　violation
  of　the　clause　'without　reckoning　in　the　original　point'。　Thus　we
  should　have　the　number　of　considerations　on　which　the　fallacious
  proofs　depend：　for　they　could　not　depend　on　more；　but　all　will
  depend　on　the　points　aforesaid。
  A　sophistical　refutation　is　a　refutation　not　absolutely　but
  relatively　to　some　one：　and　so　is　a　proof；　in　the　same　way。　For　unless
  that　which　depends　upon　ambiguity　assumes　that　the　ambiguous　term
  has　a　single　meaning；　and　that　which　depends　on　like　verbal　forms
  assumes　that　substance　is　the　only　category；　and　the　rest　in　the
  same　way；　there　will　be　neither　refutations　nor　proofs；　either
  absolutely　or　relatively　to　the　answerer：　whereas　if　they　do　assume
  these　things；　they　will　stand；　relatively　to　the　answerer；　but
  absolutely　they　will　not　stand：　for　they　have　not　secured　a
  statement　that　does　have　a　single　meaning；　but　only　one　that　appears
  to　have；　and　that　only　from　this　particular　man。
  9
  The　number　of　considerations　on　which　depend　the　refutations　of
  those　who　are　refuted；　we　ought　not　to　try　to　grasp　without　a
  knowledge　of　everything　that　is。　This；　however；　is　not　the　province　of
  any　special　study：　for　possibly　the　sciences　are　infinite　in　number；
  so　that　obviously　demonstrations　may　be　infinite　too。　Now
  refutations　may　be　true　as　well　as　false：　for　whenever　it　is
  possible　to　demonstrate　something；　it　is　also　possible　to　refute　the
  man　who　maintains　the　contradictory　of　the　truth；　e。g。　if　a　man　has
  stated　that　the　diagonal　is　commensurate　with　the　side　of　the
  square；　one　might　refute　him　by　demonstrating　that　it　is
  incommensurate。　Accordingly；　to　exhaust　all　possible　refutations　we
  shall　have　to　have　scientific　knowledge　of　everything：　for　some
  refutations　depend　upon　the　principles　that　rule　in　geometry　and　the
  conclusions　that　follow　from　these；　others　upon　those　that　rule　in
  medicine；　and　others　upon　those　of　the　other　sciences。　For　the
  matter　of　that；　the　false　refutations　likewise　belong　to　the　number　of
  the　infinite：　for　according　to　every　art　there　is　false　proof；　e。g。
  according　to　geometry　there　is　false　geometrical　proof；　and
  according　to　medicine　there　is　false　medical　proof。　By　'according　to
  the　art'；　I　mean　'according　to　the　principles　of　it'。　Clearly；　then；
  it　is　not　of　all　refutations；　but　only　of　those　that　depend　upon
  dialectic　that　we　need　to　grasp　the　common…place　rules：　for　these
  stand　in　a　common　relation　to　every　art　and　faculty。　And　as　regards
  the　refutation　that　is　according　to　one　or　other　of　the　particular
  sciences　it　is　the　task　of　that　particular　scientist　to　examine
  whether　it　is　merely　apparent　without　being　real；　and；　if　it　be
  real；　what　is　the　reason　for　it：　whereas　it　is　the　business　of
  dialecticians　so　to　examine　the　refutation　that　proceeds　from　the
  common　first　principles　that　fall　under　no　particular　special　study。
  For　if　we　grasp　the　startingpoints　of　the　accepted　proofs　on　any
  subject　whatever　we　grasp　those　of　the　refutations　current　on　that
  subject。　For　a　refutation　is　the　proof　of　the　contradictory　of　a　given
  thesis；　so　that　either　one　or　two　proofs　of　the　contradictory
  constitute　a　refutation。　We　grasp；　then；　the　number　of
  considerations　on　which　all　such　depend：　if；　however；　we　grasp　this；
  we　also　grasp　their　solutions　as　well；　for　the　objections　to　these　are
  the　solutions　of　them。　We　also　grasp　the　number　of　considerations　on
  which　those　refutations　depend；　that　are　merely　apparent…apparent；　I
  mean；　not　to　everybody；　but　to　people　of　a　certain　stamp；　for　it　is　an
  indefinite　task　if　one　is　to　inquire　how　many　are　the　considerations
  that　make　them　apparent　to　the　man　in　the　street。　Accordingly　it　is
  clear　that　the　dialectician's　business　is　to　be　able　to　grasp　on　how
  many　considerations　depends　the　formation；　through　the　common　first
  principles；　of　a　refutation　that　is　either　real　or　apparent；　i。e。
  either　dialectical　or　apparently　dialectical；　or　suitable　for　an
  examination。
  10
  It　is　no　true　distinction　between　arguments　which　some　people　draw
  when　they　say　that　some　arguments　are　directed　against　the　expression；
  and　others　against　the　thought　expressed：　for　it　is　absurd　to
  suppose　that　some　arguments　are　directed　against　the　expression　and
  others　against　the　thought；　and　that　they　are　not　the　same。　For　what
  is　failure　to　direct　an　argument　against　the　thought　except　what
  occurs　whenever　a　man　does　not　in　using　the　expression　think　it　to
  be　used　in　his　question　in　the　same　sense　in　which　the　person
  questioned　granted　it？　And　this　is　the　same　thing　as　to　direct　the
  argument　against　the　expression。　On　the　other　hand；　it　is　directed
  against　the　thought　whenever　a　man　uses　the　expression　in　the　same
  sense　which　the　answerer　had　in　mind　when　he　granted　it。　If　now　any
  （i。e。　both　the　questioner　and　the　person　questioned）；　in　dealing
  with　an　expression　with　more　than　one　meaning；　were　to　suppose　it　to
  have　one　meaning…as　e。g。　it　may　be　that　'Being'　and　'One'　have　many
  meanings；　and　yet　both　the　answerer　answers　and　the　questioner　puts
  his　question　supposing　it　to　be　one；　and　the　argument　is　to　the　effect
  that　'All　things　are　one'…will　this　discussion　be　directed　any　more
  against　the　expression　than　against　the　thought　of　the　person
  questioned？　If；　on　the　other　hand；　one　of　them　supposes　the　expression
  to　have　many　meanings；　it　is　clear　that　such　a　discussion　will　not
  be　directed　against　the　thought。　Such　being　the　meanings　of　the
  phrases　in　question；　they　clearly　cannot　describe　two　separate　classes
  of　argument。　For；　in　the　first　place；　it　is　possible　for　any　such
  argument　as　bears　more　than　one　meaning　to　be　directed　against　the
  expression　and　against　the　thought；　and　next　it　is　possible　for　any
  argument　whatsoever；　for　the　fact　of　being　directed　against　the
  thought　consists　not　in　the　nature　of　the　argument；　but　in　the　special
  attitude　of　the　answerer　towards　the　points　he　concedes。　Next；　all
  of　them　may　be　directed　to　the　expression。　For　'to　be　directed　against
  the　expression'　means　in　this　doctrine　'not　to　be　directed　against　the
  thought'。　For　if　not　all　are　directed　against　either　expression　or
  thought；　there　will　be　certain　other　arguments　directed　neither
  against　the　expression　nor　against　the　thought；　whereas　they　say
  that　all　must　be　one　or　the　other；　and　divide　them　all　as　directed
  either　against　the　expression　or　against　the　thought；　while　others
  （they　say）　there　are　none。　But　in　point　of　fact　those　that　depend　on
  mere　expression　are　only　a　branch　of　those　syllogisms　that　depend　on　a
  multiplicity　of　meanings。　For　the　absurd　statement　has　actually　been
  made　that　the　description　'dependent　on　mere　expression'　describes　all
  the　arguments　that　depend　on　language：　whereas　some　of　these　are
  fallacies　not　because　the　answerer　adopts　a　particular　attitude
  towards　them；　but　because　the　argument　itself　involves　the　asking　of　a
  question　such　as　bears　more　than　one　meaning。
  It　is；　too；　altogether　absurd　to　discuss　Refutation　without　first
  discussing　Proof：　for　a　refutation　is　a　proof；　so　that　one　ought　to
  discuss　proof　as　well　before　describing　false　refutation：　for　a
  refutation　of　that　kind　is　a　merely　apparent　proof　of　the
  contradictory　of　a　thesis。　Accordingly；　the　reason　of　the　falsity　will
  be　either　in　the　proof　or　in　the　contradiction　（for　mention　of　the
  'contradiction'　must　be　added）；　while　sometimes　it　is　in　both；　if
  the　refutation　be　merely　apparent。　In　the　argument　that　speaking　of
  the　silent　is　possible　it　lies　in　the　contradiction；　not　in　the　proof；
  in　the　argument　that　one　can　give　what　one　does　not　possess；　it　lies
  in　both；　in　the　proof　that　Homer's　poem　is　a　figure　through　its
  being　a　cycle　it　lies　in　the　proof。　An　argument　that　does　not　fail
  in　either　respect　is　a　true　proof。
  But；　to　return　to　the　point　whence　our　argument　digressed；　are
  mathematical　reasonings　directed　against　the　thought；　or　not？　And　if
  any　one　thinks　'triangle'　to　be　a　word　with　many　meanings；　and　granted
  it　in　some　different　sense　from　the　figure　which　was　proved　to　contain
  two　right　angles；　has　the　questioner　here　directed　his　argument
  against　the　thought　of　the　former　or　not？
  Moreover；　if　the　expression　bears　many　senses；　while　the　answerer
  does　not　understand　or　suppose　it　to　have　them；　surely　the
  questioner　here　has　directed　his　argument　against　his　thought！　Or
  how　else