               #CEJ ,,BC
          ,,PRIOR ,,ANALYTICS
               0,>I/OTLE
     TRANSLAT$ BY ;,A4 ,J4 ,J5K9SON

    ,TRANSLAT$ 6,GRADE ,,II ,BRL 0,MIKE
    ,KEI?LEY
                ,BOOK ,I
                   #A

  ,WE M/ F/ /ATE ! SUBJECT ( \R 9QUIRY &
! FACULTY 6: X 2L;GS3 XS SUBJECT IS
DEMON/R,N &! FACULTY T C>RIES X \
DEMON/RATIVE SCI;E4 ,WE M/ NEXT DEF9E A
PREMISS1 A T]M1 &A SYLLOGISM1 &! NATURE
(A P]FECT &( AN IMP]FECT SYLLOGISM2 & AF
T1 ! 9CLU.N OR NON9CLU.N ( "O T]M 9
ANO!R Z 9 A :OLE1 & :AT WE M1N 0PR$ICAT+
"O T]M ( ALL1 OR N"O1 ( ANO!R4
  ,A PREMISS !N IS A S5T;E A6IRM+ OR
D5Y+ "O ?+ ( ANO!R4 ,? IS EI UNIV]SAL OR
"PICUL> OR 9DEF9ITE4 ,0UNIV]SAL ,I M1N !
/ATE;T T "S?+ 2L;GS 6ALL OR N"O ( "S?+
ELSE2 0"PICUL> T X 2L;GS 6"S OR N 6"S OR
N 6ALL2 09DEF9ITE T X DOES OR DOES N
2L;G1 )\T ANY M>K 6%[ :E!R X IS UNIV]SAL
OR "PICUL>1 E4G4 ,83TR>IES >E SUBJECTS (
! SAME SCI;E0'1 OR ,8PL1SURE IS N GD0'4
,! DEMON/RATIVE PREMISS DI6]S F !
DIALECTICAL1 2C ! DEMON/RATIVE PREMISS
IS ! ASS];N ( "O ( TWO 3TRADICTORY
/ATE;TS 7! DEMON/RATOR DOES N ASK = 8
PREMISS1 B LAYS X D[N71 ":AS !
DIALECTICAL PREMISS DEP5DS ON !
ADV]S>Y'S *OICE 2T TWO 3TRADICTORIES4 ,B
? W MAKE NO DI6];E 6! PRODUC;N (A
SYLLOGISM 9 EI CASE2 = BO? ! DEMON/RATOR
&! DIALECTICIAN >GUE SYLLOGI/IC,Y AF
/AT+ T "S?+ DOES OR DOES N 2L;G 6"S?+
ELSE4 ,"!=E A SYLLOGI/IC PREMISS )\T
QUALIFIC,N W 2 AN A6IRM,N OR D5IAL (
"S?+ 3C]N+ "S?+ ELSE 9 ! WAY WE H
DESCRIB$2 X W 2 DEMON/RATIVE1 IF X IS
TRUE & OBTA9$ "? ! F/ PR9CIPLES ( XS
SCI;E2 :ILE A DIALECTICAL PREMISS IS !
GIV+ (A *OICE 2T TWO 3TRADICTORIES1 :5 A
MAN IS PROCE$+ 0"Q1 B :5 HE IS SYLLOGIZ+
X IS ! ASS];N ( T : IS APP>5T & G5],Y
ADMITT$1 Z HAS BE5 SD 9 ! ,TOPICS4 ,!
NATURE !N (A PREMISS &! DI6];E 2T
SYLLOGI/IC1 DEMON/RATIVE1 & DIALECTICAL
PREMISSES1 MAY 2 TAK5 Z SU6ICI5TLY DEF9$
0U 9 REL,N 6\R PRES5T NE$1 B W 2 /AT$
A3URATELY 9 ! SEQUEL4
  ,I CALL T A T]M 96: ! PREMISS IS
RESOLV$1 I4E4 BO? ! PR$ICATE & T ( : X
IS PR$ICAT$1 ,82+0' 2+ A4$ & ,8N 2+0'
REMOV$1 OR VICE V]SA4
  ,A SYLLOGISM IS 4C\RSE 9 :1 C]TA9 ?+S
2+ /AT$1 "S?+ O!R ?AN :AT IS /AT$ FOLL[S
( NECESS;Y F _! 2+ S4 ,I M1N 0! LA/
PHRASE T !Y PRODUCE ! 3SEQU;E1 & 0?1 T
NO FUR!R T]M IS REQUIR$ F )\T 9 ORD]
6MAKE ! 3SEQU;E NEC4
  ,I CALL T A P]FECT SYLLOGISM : NE$S
NO?+ O!R ?AN :AT HAS BE5 /AT$ 6MAKE PLA9
:AT NECESS>ILY FOLL[S2 A SYLLOGISM IS
IMP]FECT1 IF X NE$S EI "O OR M
PROPOSI;NS1 : >E 9DE$ ! NEC 3SEQU;ES (!
T]MS SET D[N1 B H N BE5 EXPRESSLY /AT$ Z
PREMISSES4
  ,T "O T]M %D 2 9CLUD$ 9 ANO!R Z 9 A
:OLE IS ! SAME Z =! O!R 6BE PR$ICAT$ (
ALL (! F/4 ,& WE SAY T "O T]M IS
PR$ICAT$ ( ALL ( ANO!R1 :5"E NO 9/.E (!
SUBJECT C 2 F.D ( : ! O!R T]M _C 2
ASS]T$3 ,86BE PR$ICAT$ ( N"O0' M/ 2
"U/OOD 9 ! SAME WAY4

                   #B

  ,E PREMISS /ATES T "S?+ EI IS OR M/ 2
OR MAY 2 ! ATTRIBUTE ( "S?+ ELSE2 (
PREMISSES ( ^! ?REE K9DS "S >E
A6IRMATIVE1 O!RS NEGATIVE1 9 RESPECT (
EA* (! ?REE MODES ( ATTRIBU;N2 AG "S
A6IRMATIVE & NEGATIVE PREMISSES >E
UNIV]SAL1 O!RS "PICUL>1 O!RS 9DEF9ITE4
,X IS NEC !N T 9 UNIV]SAL ATTRIBU;N !
T]MS (! NEGATIVE PREMISS %D 2 3V]TI#1
E4G4 IF NO PL1SURE IS GD1 !N NO GD W 2
PL1SURE2 ! T]MS (! A6IRMATIVE M/ 2
3V]TI#1 N H["E1 UNIV]S,Y1 B 9 "P1 E4G4
IF E PL1SURE1IS GD1 "S GD M/ 2 PL1SURE2
! "PICUL> A6IRMATIVE M/ 3V]T 9 "P 7= IF
"S PL1SURE IS GD1 !N "S GD W 2 PL1SURE72
B ! "PICUL> NEGATIVE NE$ N 3V]T1 = IF "S
ANIMAL IS N MAN1 X DOES N FOLL[ T "S MAN
IS N ANIMAL4
  ,F/ !N TAKE A UNIV]SAL NEGATIVE )!
T]MS ;,A & ,B4 ,IF NO ;,B IS ;,A1 NEI C
ANY ,A 2 ,B4 ,= IF "S ,A 7SAY ,C7 7 ;,B1
X WD N 2 TRUE T NO ;,B IS ,A2 = ;,C IS A
,B4 ,B IF E ;,B IS ,A !N "S ,A IS ,B4 ,=
IF NO ,A 7 ;,B1 !N NO ;,B CD 2 ,A4 ,B WE
ASSUM$ T E ;,B IS ,A4 ,SIMIL>LY TOO1 IF
! PREMISS IS "PICUL>4 ,= IF "S ;,B IS
;,A1 !N "S (! ,Z M/ 2 ,B4 ,= IF N"O W]E1
!N NO ;,B WD 2 ,A4 ,B IF "S ;,B IS N
;,A1 "! IS NO NECESS;Y T "S (! ,Z %D N 2
;,B2 E4G4 LET ;,B /& = ANIMAL & ;,A =
MAN4 ,N E ANIMAL IS A MAN2 B E MAN IS AN
ANIMAL4

                   #C

  ,! SAME MANN] ( 3V].N W HOLD GD AL 9
RESPECT ( NEC PREMISSES4 ,! UNIV]SAL
NEGATIVE 3V]TS UNIV]S,Y2 EA* (!
A6IRMATIVES 3V]TS 96A "PICUL>4 ,IF X IS
NEC T NO ;,B IS ;,A1 X IS NEC AL T NO ,A
IS ,B4 ,= IF X IS POSSI# T "S ,A IS ;,B1
X WD 2 POSSI# AL T "S ;,B IS ,A4 ,IF ALL
OR "S ;,B IS ;,A ( NECESS;Y1 X IS NEC AL
T "S ,A IS ;,B3 = IF "! 7 NO NECESS;Y1
NEI WD "S (! ,BS 2 ,A NECESS>ILY4 ,B !
"PICUL> NEGATIVE DOES N 3V]T1 =! SAME
R1SON : WE H ALR /AT$4
  ,9 RESPECT ( POSSI# PREMISSES1 S9CE
POSSIBIL;Y IS US$ 9 S"EAL S5SES 7= WE
SAY T :AT IS NEC & :AT IS N NEC & :AT IS
POT5TIAL IS POSSI#71 A6IRMATIVE /ATE;TS
W ALL 3V]T 9 A MANN] SIMIL> 6^?
DESCRIB$4 ,= IF X IS POSSI# T ALL OR "S
;,B IS ;,A1 X W 2 POSSI# T "S ,A IS ,B4
,= IF T 7 N POSSI#1 !N NO ;,B CD
POSSIBLY 2 ,A4 ,? HAS BE5 ALR PROV$4 ,B
9 NEGATIVE /ATE;TS ! CASE IS DI6]5T4
,:AT"E IS SD 6BE POSSI#1 EI 2C ;,B
NECESS>ILY IS ;,A1 OR 2C ;,B IS N
NECESS>ILY ;,A1 ADMITS ( 3V].N L O!R
NEGATIVE /ATE;TS1 E4G4 IF "O %D SAY1 X
IS POSSI# T MAN IS N HORSE1 OR T NO G>;T
IS :ITE4 ,= 9 ! =M] CASE ! "O T]M
NECESS>ILY DOES N 2L;G 6! O!R2 9 ! LATT]
"! IS NO NECESS;Y T X %D3 &! PREMISS
3V]TS L O!R NEGATIVE /ATE;TS4 ,= IF X IS
POSSI# = NO MAN 6BE A HORSE1 X IS AL
ADMISSI# = NO HORSE 6BE A MAN2 & IF X IS
ADMISSI# = NO G>;T 6BE :ITE1 X IS AL
ADMISSI# = NO?+ :ITE 6BE A G>;T4 ,= IF
ANY :ITE ?+ M/ 2 A G>;T1 !N "S G>;T W
NECESS>ILY 2 :ITE4 ,? HAS BE5 ALR PROV$4
,! "PICUL> NEGATIVE AL M/ 2 TR1T$ L ^?
D1LT ) ABV4 ,B IF ANY?+ IS SD 6BE POSSI#
2C X IS ! G5]AL RULE & NATURAL 7& X IS 9
? WAY WE DEF9E ! POSSI#71 ! NEGATIVE
PREMISSES C NO L;G] 2 3V]T$ L ! SIMPLE
NEGATIVES2 ! UNIV]SAL NEGATIVE PREMISS
DOES N 3V]T1 &! "PICUL> DOES4 ,? W 2
PLA9 :5 WE SP1K AB ! POSSI#4 ,AT PRES5T
WE MAY TAKE ? M* Z CLE> 9 A4I;N 6:AT HAS
BE5 SD3 ! /ATE;T T X IS POSSI# T NO ;,B
IS ,A OR "S ;,B IS N ,A IS A6IRMATIVE 9
=M3 =! EXPRES.N ,8IS POSSI#0' RANKS AL;G
) ,8IS0'1 & ,8IS0' MAKES AN A6IRM,N ALW
& 9 E CASE1 :AT"E ! T]MS 6: X IS A4$1 9
PR$IC,N1 E4G4 ,8X IS N-GD0' OR ,8X IS N-
:ITE0' OR 9 A ^W ,8X IS N-?0'4 ,B ? AL W
2 PROV$ 9 ! SEQUEL4 ,9 3V].N ^!
PREMISSES W 2HAVE L ! O!R A6IRMATIVE
PROPOSI;NS4

                   #D

  ,AF ^! 4T9C;NS WE N[ /ATE 0:AT M1NS1
:51 & H[ E SYLLOGISM IS PRODUC$2
SUBSEQU5TLY WE M/ SP1K ( DEMON/R,N4
,SYLLOGISM %D 2 4CUSS$ 2F DEMON/R,N 2C
SYLLOGISM IS ! G5]AL3 ! DEMON/R,N IS A
SORT ( SYLLOGISM1 B N E SYLLOGISM IS A
DEMON/R,N4
  ,:5"E ?REE T]MS >E S RELAT$ 6"O ANO!R
T ! LA/ IS 3TA9$ 9 ! MI4LE Z 9 A :OLE1 &
! MI4LE IS EI 3TA9$ IN1 OR EXCLUD$ F1 !
F/ Z 9 OR F A :OLE1 ! EXTREMES M/ 2
RELAT$ 0A P]FECT SYLLOGISM4 ,I CALL T
T]M MI4LE : IS XF 3TA9$ 9 ANO!R & 3TA9S
ANO!R 9 XF3 9 POSI;N AL ? -ES 9 ! MI4LE4
,0EXTREMES ,I M1N BO? T T]M : IS XF
3TA9$ 9 ANO!R & T 9 : ANO!R IS 3TA9$4
,IF ,A IS PR$ICAT$ ( ALL ;,B1 & ;,B (
ALL ;,C1 ,A M/ 2 PR$ICAT$ ( ALL ;,C3 WE
H ALR EXPLA9$ :AT WE M1N BY ,8PR$ICAT$ (
ALL0'4 ,SIMIL>LY AL1 IF ,A IS PR$ICAT$ (
NO ;,B1 & ;,B ( ALL ;,C1 X IS NEC T NO
;,C W 2 ,A4
  ,B IF ! F/ T]M 2L;GS 6ALL ! MI4LE1 B !
MI4LE 6N"O (! LA/ T]M1 "! W 2 NO
SYLLOGISM 9 RESPECT (! EXTREMES2 = NO?+
NEC FOLL[S F ! T]MS 2+ S RELAT$2 = X IS
POSSI# T ! F/ %D 2L;G EI 6ALL OR 6N"O (!
LA/1 S T NEI A "PICUL> NOR A UNIV]SAL
3CLU.N IS NEC4 ,B IF "! IS NO NEC
3SEQU;E1 "! _C 2 A SYLLOGISM 0M1NS ( ^!
PREMISSES4 ,Z AN EXAMPLE (A UNIV]SAL
A6IRMATIVE REL,N 2T ! EXTREMES WE MAY
TAKE ! T]MS ANIMAL1 MAN1 HORSE2 (A
UNIV]SAL NEGATIVE REL,N1 ! T]MS ANIMAL1
MAN1 /"O4 ,NOR AG C SYLLOGISM 2 =M$ :5
NEI ! F/ T]M 2L;GS 6ANY (! MI4LE1 NOR !
MI4LE 6ANY (! LA/4 ,Z AN EXAMPLE (A
POSITIVE REL,N 2T ! EXTREMES TAKE ! T]MS
SCI;E1 L9E1 M$IC9E3 (A NEGATIVE REL,N
SCI;E1 L9E1 UNIT4
  ,IF !N ! T]MS >E UNIV]S,Y RELAT$1 X IS
CLE> 9 ? FIGURE :5 A SYLLOGISM W 2
POSSI# & :5 N1 & T IF A SYLLOGISM IS
POSSI# ! T]MS M/ 2 RELAT$ Z DESCRIB$1 &
IF !Y >E S RELAT$ "! W 2 A SYLLOGISM4
  ,B IF "O T]M IS RELAT$ UNIV]S,Y1 ! O!R
9 "P ONLY1 6XS SUBJECT1 "! M/ 2 A P]FECT
SYLLOGISM :5"E UNIV]SAL;Y IS POSIT$ )
REF];E 6! MAJOR T]M EI A6IRMATIVELY OR
NEGATIVELY1 & "PICUL>;Y ) REF];E 6! M9OR
T]M A6IRMATIVELY3 B :5"E ! UNIV]SAL;Y IS
POSIT$ 9 REL,N 6! M9OR T]M1 OR ! T]MS >E
RELAT$ 9 ANY O!R WAY1 A SYLLOGISM IS
IMPOSSI#4 ,I CALL T T]M ! MAJOR 9 : !
MI4LE IS 3TA9$ & T T]M ! M9OR : -ES "U !
MI4LE4 ,LET ALL ;,B 2 ;,A & "S ;,C 2 ,B4
,!N IF ,8PR$ICAT$ ( ALL0' M1NS :AT 0 SD
ABV1 X IS NEC T "S ;,C IS ,A4 ,& IF NO
;,B IS ,A B "S ;,C IS ;,B1 X IS NEC T "S
;,C IS N ,A4 ,! M1N+ ( ,8PR$ICAT$ (
N"O0' HAS AL BE5 DEF9$4 ,S "! W 2 A
P]FECT SYLLOGISM4 ,? HOLDS GD AL IF !
PREMISS ,,BC %D 2 9DEF9ITE1 PROVID$ T X
IS A6IRMATIVE3 = WE % H ! SAME SYLLOGISM
:E!R ! PREMISS IS 9DEF9ITE OR "PICUL>4
  ,B IF ! UNIV]SAL;Y IS POSIT$ ) RESPECT
6! M9OR T]M EI A6IRMATIVELY OR
NEGATIVELY1 A SYLLOGISM W N 2 POSSI#1
:E!R ! MAJOR PREMISS IS POSITIVE OR
NEGATIVE1 9DEF9ITE OR "PICUL>3 E4G4 IF
"S ;,B IS OR IS N ;,A1 & ALL ;,C IS ,B4
,Z AN EXAMPLE (A POSITIVE REL,N 2T !
EXTREMES TAKE ! T]MS GD1 /ATE1 WISDOM3 (
A NEGATIVE REL,N1 GD1 /ATE1 IGNOR.E4 ,AG
IF NO ;,C IS ;,B1 B "S ;,B IS OR IS N ,A
OR N E ;,B IS ;,A1 "! _C 2 A SYLLOGISM4
,TAKE ! T]MS :ITE1 HORSE1 SWAN3 :ITE1
HORSE1 RAV54 ,! SAME T]MS MAY 2 TAK5 AL
IF ! PREMISS ,,BA IS 9DEF9ITE4
  ,NOR :5 ! MAJOR PREMISS IS UNIV]SAL1
:E!R A6IRMATIVE OR NEGATIVE1 &! M9OR
PREMISS IS NEGATIVE & "PICUL>1 C "! 2 A
SYLLOGISM1 :E!R ! M9OR PREMISS 2
9DEF9ITE OR "PICUL>3 E4G4 IF ALL ;,B IS
;,A & "S ;,C IS N ;,B1 OR IF N ALL ;,C
IS ,B4 ,=! MAJOR T]M MAY 2 PR$ICA# BO? (
ALL &( N"O (! M9OR1 6"S ( : ! MI4LE T]M
_C 2 ATTRIBUT$4 ,SUPPOSE ! T]MS >E
ANIMAL1 MAN1 :ITE3 NEXT TAKE "S (! :ITE
?+S ( : MAN IS N PR$ICAT$-SWAN & SN[3
ANIMAL IS PR$ICAT$ ( ALL (! "O1 B ( N"O
(! O!R4 ,3SEQU5TLY "! _C 2 A SYLLOGISM4
,AG LET NO ;,B 2 ;,A1 B LET "S ;,C N 2
,B4 ,TAKE ! T]MS 9ANIMATE1 MAN1 :ITE3 !N
TAKE "S :ITE ?+S ( : MAN IS N PR$ICAT$-
SWAN & SN[3 ! T]M 9ANIMATE IS PR$ICAT$ (
ALL (! "O1 ( N"O (! O!R4
  ,FUR!R S9CE X IS 9DEF9ITE 6SAY "S ;,C
IS N ;,B1 & X IS TRUE T "S ;,C IS N ;,B1
:E!R NO ;,C IS ;,B1 OR N ALL ;,C IS ;,B1
& S9CE IF T]MS >E ASSUM$ S* T NO ;,C IS
;,B1 NO SYLLOGISM FOLL[S 7? HAS ALR BE5
/AT$7 X IS CLE> T ? >RANGE;T ( T]MS W N
AF=D A SYLLOGISM3 O!RWISE "O WD H BE5
POSSI# )A UNIV]SAL NEGATIVE M9OR
PREMISS4 ,A SIMIL> PRO( MAY AL 2 GIV5 IF
! UNIV]SAL PREMISS IS NEGATIVE4
  ,NOR C "! 9 ANY WAY 2 A SYLLOGISM IF
BO? ! REL,NS ( SUBJECT & PR$ICATE >E
"PICUL>1 EI POSITIVELY OR NEGATIVELY1 OR
! "O NEGATIVE &! O!R A6IRMATIVE1 OR "O
9DEF9ITE &! O!R DEF9ITE1 OR BO?
9DEF9ITE4 ,T]MS -MON 6ALL ! ABV >E
ANIMAL1 :ITE1 HORSE3 ANIMAL1 :ITE1 /"O4
  ,X IS CLE> !N F :AT HAS BE5 SD T IF "!
IS A SYLLOGISM 9 ? FIGURE )A "PICUL>
3CLU.N1 ! T]MS M/ 2 RELAT$ Z WE H /AT$3
IF !Y >E RELAT$ O!RWISE1 NO SYLLOGISM IS
POSSI# ANYH[4 ,X IS EVID5T AL T ALL !
SYLLOGISMS 9 ? FIGURE >E P]FECT 7= !Y >E
ALL -PLET$ 0M1NS (! PREMISSES ORIG9,Y
TAK57 & T ALL 3CLU.NS >E PROV$ 0?
FIGURE1 VIZ4 UNIV]SAL & "PICUL>1
A6IRMATIVE & NEGATIVE4 ,S* A FIGURE ,I
CALL ! F/4

                   #E

  ,:5"E ! SAME ?+ 2L;GS 6ALL ( "O
SUBJECT1 & 6N"O ( ANO!R1 OR 6ALL ( EA*
SUBJECT OR 6N"O ( EI1 ,I CALL S* A
FIGURE ! SECOND2 0MI4LE T]M 9 X ,I M1N T
: IS PR$ICAT$ ( BO? SUBJECTS1 0EXTREMES
! T]MS ( : ? IS SD1 0MAJOR EXTREME T :
LIES NE> ! MI4LE1 0M9OR T : IS FUR!R
AWAY F ! MI4LE4 ,! MI4LE T]M /&S \TSIDE
! EXTREMES1 & IS F/ 9 POSI;N4 ,A
SYLLOGISM _C 2 P]FECT ANYH[ 9 ? FIGURE1
B X MAY 2 VALID :E!R ! T]MS >E RELAT$
UNIV]S,Y OR N4
  ,IF !N ! T]MS >E RELAT$ UNIV]S,Y A
SYLLOGISM W 2 POSSI#1 :5"E ! MI4LE 2L;GS
6ALL ( "O SUBJECT & 6N"O ( ANO!R 7X DOES
N MATT] : HAS ! NEGATIVE REL,N71 B 9 NO
O!R WAY4 ,LET ;,M 2 PR$ICAT$ ( NO ;,N1 B
( ALL ,O4 ,S9CE1 !N1 ! NEGATIVE REL,N IS
3V]TI#1 ;,N W 2L;G 6NO ;,M3 B ;,M 0
ASSUM$ 62L;G 6ALL ,O3 3SEQU5TLY ;,N W
2L;G 6NO ,O4 ,? HAS ALR BE5 PROV$4 ,AG
IF ;,M 2L;GS 6ALL ;,N1 B 6NO ,O1 !N ;,N
W 2L;G 6NO ,O4 ,= IF ;,M 2L;GS 6NO ,O1
,O 2L;GS 6NO ;,M3 B ;,M 7Z 0 SD7 2L;GS
6ALL ;,N3 ,O !N W 2L;G 6NO ;,N3 =! F/
FIGURE HAS AG BE5 =M$4 ,B S9CE !
NEGATIVE REL,N IS 3V]TI#1 ;,N W 2L;G 6NO
,O4 ,?US X W 2 ! SAME SYLLOGISM T PROVES
BO? 3CLU.NS4
  ,X IS POSSI# 6PROVE ^! RESULTS AL
0REDUCTIO AD IMPOSSIBILE4
  ,X IS CLE> !N T A SYLLOGISM IS =M$ :5
! T]MS >E S RELAT$1 B N A P]FECT
SYLLOGISM2 = NECESS;Y IS N P]FECTLY
E/ABLI%$ M]ELY F ! ORIG9AL PREMISSES2
O!RS AL >E NE$$4
  ,B IF ;,M IS PR$ICAT$ ( E ;,N & ,O1 "!
_C 2 A SYLLOGISM4 ,T]MS 6ILLU/RATE A
POSITIVE REL,N 2T ! EXTREMES >E SUB/.E1
ANIMAL1 MAN2 A NEGATIVE REL,N1 SUB/.E1
ANIMAL1 NUMB]-SUB/.E 2+ ! MI4LE T]M4
  ,NOR IS A SYLLOGISM POSSI# :5 ;,M IS
PR$ICAT$ NEI ( ANY ;,N NOR ( ANY ,O4
,T]MS 6ILLU/RATE A POSITIVE REL,N >E
L9E1 ANIMAL1 MAN3 A NEGATIVE REL,N1 L9E1
ANIMAL1 /"O4
  ,X IS CLE> !N T IF A SYLLOGISM IS =M$
:5 ! T]MS >E UNIV]S,Y RELAT$1 ! T]MS M/
2 RELAT$ Z WE /AT$ AT ! \TSET3 = IF !Y
>E O!RWISE RELAT$ NO NEC 3SEQU;E FOLL[S4
  ,IF ! MI4LE T]M IS RELAT$ UNIV]S,Y 6"O
(! EXTREMES1 A "PICUL> NEGATIVE
SYLLOGISM M/ RESULT :5"E ! MI4LE T]M IS
RELAT$ UNIV]S,Y 6! MAJOR :E!R POSITIVELY
OR NEGATIVELY1 & "PICUL>LY 6! M9OR & 9 A
MANN] OPPOSITE 6T (! UNIV]SAL /ATE;T3 BY
,8AN OPPOSITE MANN]0' ,I M1N1 IF !
UNIV]SAL /ATE;T IS NEGATIVE1 ! "PICUL>
IS A6IRMATIVE3 IF ! UNIV]SAL IS
A6IRMATIVE1 ! "PICUL> IS NEGATIVE4 ,= IF
;,M 2L;GS 6NO ;,N1 B 6"S ,O1 X IS NEC T
;,N DOES N 2L;G 6"S ,O4 ,= S9CE !
NEGATIVE /ATE;T IS 3V]TI#1 ;,N W 2L;G
6NO ;,M3 B ;,M 0 ADMITT$ 62L;G 6"S ,O3
"!=E ;,N W N 2L;G 6"S ,O3 =! RESULT IS
R1*$ 0M1NS (! F/ FIGURE4 ,AG IF ;,M
2L;GS 6ALL ;,N1 B N 6"S ,O1 X IS NEC T
;,N DOES N 2L;G 6"S ,O3 = IF ;,N 2L;GS
6ALL ,O1 & ;,M IS PR$ICAT$ AL ( ALL ;,N1
;,M M/ 2L;G 6ALL ,O3 B WE ASSUM$ T ;,M
DOES N 2L;G 6"S ,O4 ,& IF ;,M 2L;GS 6ALL
;,N B N 6ALL ,O1 WE % 3CLUDE T ;,N DOES
N 2L;G 6ALL ,O3 ! PRO( IS ! SAME Z !
ABV4 ,B IF ;,M IS PR$ICAT$ ( ALL ,O1 B N
( ALL ;,N1 "! W 2 NO SYLLOGISM4 ,TAKE !
T]MS ANIMAL1 SUB/.E1 RAV52 ANIMAL1 :ITE1
RAV54 ,NOR W "! 2 A 3CLU.N :5 ;,M IS
PR$ICAT$ ( NO ,O1 B ( "S ,N4 ,T]MS
6ILLU/RATE A POSITIVE REL,N 2T !
EXTREMES >E ANIMAL1 SUB/.E1 UNIT3 A
NEGATIVE REL,N1 ANIMAL1 SUB/.E1 SCI;E4
  ,IF !N ! UNIV]SAL /ATE;T IS OPPOS$ 6!
"PICUL>1 WE H /AT$ :5 A SYLLOGISM W 2
POSSI# & :5 N3 B IF ! PREMISSES >E
SIMIL> 9 =M1 ,I M1N BO? NEGATIVE OR BO?
A6IRMATIVE1 A SYLLOGISM W N 2 POSSI#
ANYH[4 ,F/ LET !M 2 NEGATIVE1 & LET !
MAJOR PREMISS 2 UNIV]SAL1 E4G4 LET ;,M
2L;G 6NO ;,N1 & N 6"S ,O4 ,X IS POSSI#
!N = ;,N 62L;G EI 6ALL ,O OR 6NO ,O4
,T]MS 6ILLU/RATE ! NEGATIVE REL,N >E
BLACK1 SN[1 ANIMAL4 ,B X IS N POSSI#
6F9D T]MS ( : ! EXTREMES >E RELAT$
POSITIVELY & UNIV]S,Y1 IF ;,M 2L;GS 6"S
,O1 & DOES N 2L;G 6"S ,O4 ,= IF ;,N
2L;G$ 6ALL ,O1 B ;,M 6NO ;,N1 !N ;,M WD
2L;G 6NO ,O3 B WE ASSUM$ T X 2L;GS 6"S
,O4 ,9 ? WAY !N X IS N ADMISSI# 6TAKE
T]MS3 \R PO9T M/ 2 PROV$ F ! 9DEF9ITE
NATURE (! "PICUL> /ATE;T4 ,= S9CE X IS
TRUE T ;,M DOES N 2L;G 6"S ,O1 EV5 IF X
2L;GS 6NO ,O1 & S9CE IF X 2L;GS 6NO ,O A
SYLLOGISM IS 7Z WE H SE57 N POSSI#1
CLE>LY X W N 2 POSSI# N[ EI4
  ,AG LET ! PREMISSES 2 A6IRMATIVE1 &
LET ! MAJOR PREMISS Z 2F 2 UNIV]SAL1
E4G4 LET ;,M 2L;G 6ALL ;,N & 6"S ,O4 ,X
IS POSSI# !N = ;,N 62L;G 6ALL ,O OR 6NO
,O4 ,T]MS 6ILLU/RATE ! NEGATIVE REL,N >E
:ITE1 SWAN1 /"O4 ,B X IS N POSSI# 6TAKE
T]MS 6ILLU/RATE ! UNIV]SAL A6IRMATIVE
REL,N1 =! R1SON ALR /AT$3 ! PO9T M/ 2
PROV$ F ! 9DEF9ITE NATURE (! "PICUL>
/ATE;T4 ,B IF ! M9OR PREMISS IS
UNIV]SAL1 & ;,M 2L;GS 6NO ,O1 & N 6"S
;,N1 X IS POSSI# = ;,N 62L;G EI 6ALL ,O
OR 6NO ,O4 ,T]MS =! POSITIVE REL,N >E
:ITE1 ANIMAL1 RAV53 =! NEGATIVE REL,N1
:ITE1 /"O1 RAV54 ,IF ! PREMISSES >E
A6IRMATIVE1 T]MS =! NEGATIVE REL,N >E
:ITE1 ANIMAL1 SN[2 =! POSITIVE REL,N1
:ITE1 ANIMAL1 SWAN4 ,EVID5TLY !N1 :5"E !
PREMISSES >E SIMIL> 9 =M1 & "O IS
UNIV]SAL1 ! O!R "PICUL>1 A SYLLOGISM C1
N 2 =M$ ANYH[4 ,NOR IS "O POSSI# IF !
MI4LE T]M 2L;GS 6"S ( EA* (! EXTREMES1
OR DOES N 2L;G 6"S ( EI1 OR 2L;GS 6"S (!
"O1 N 6"S (! O!R1 OR 2L;GS 6NEI
UNIV]S,Y1 OR IS RELAT$ 6!M 9DEF9ITELY4
,-MON T]MS = ALL ! ABV >E :ITE1 ANIMAL1
MAN3 :ITE1 ANIMAL1 9ANIMATE4
  ,X IS CLE> !N F :AT HAS BE5 SD T IF !
T]MS >E RELAT$ 6"O ANO!R 9 ! WAY /AT$1 A
SYLLOGISM RESULTS ( NECESS;Y2 & IF "! IS
A SYLLOGISM1 ! T]MS M/ 2 S RELAT$4 ,B X
IS EVID5T AL T ALL ! SYLLOGISMS 9 ?
FIGURE >E IMP]FECT3 = ALL >E MADE P]FECT
0C]TA9 SUPPLE;T>Y /ATE;TS1 : EI >E 3TA9$
9 ! T]MS ( NECESS;Y OR >E ASSUM$ Z
HYPO!SES1 I4E4 :5 WE PROVE P]
IMPOSSIBILE4 ,& X IS EVID5T T AN
A6IRMATIVE 3CLU.N IS N ATTA9$ 0M1NS ( ?
FIGURE1 B ALL >E NEGATIVE1 :E!R UNIV]SAL
OR "PICUL>4

                   #F

  ,B IF "O T]M 2L;GS 6ALL1 & ANO!R 6N"O1
(A ?IRD1 OR IF BO? 2L;G 6ALL1 OR 6N"O1 (
X1 ,I CALL S* A FIGURE ! ?IRD2 0MI4LE
T]M 9 X ,I M1N T ( : BO? ! PR$ICATES >E
PR$ICAT$1 0EXTREMES ,I M1N ! PR$ICATES1
0! MAJOR EXTREME T : IS FUR!R F ! MI4LE1
0! M9OR T : IS NE>] 6X4 ,! MI4LE T]M /&S
\TSIDE ! EXTREMES1 & IS LA/ 9 POSI;N4 ,A
SYLLOGISM _C 2 P]FECT 9 ? FIGURE EI1 B X
MAY 2 VALID :E!R ! T]MS >E RELAT$
UNIV]S,Y OR N 6! MI4LE T]M4
  ,IF !Y >E UNIV]SAL1 :5"E BO? ;,P & ;,R
2L;G TO ;,S1 X FOLL[S T ;,P W NECESS>ILY
2L;G 6"S ,R4 ,=1 S9CE ! A6IRMATIVE
/ATE;T IS 3V]TI#1 ;,S W 2L;G 6"S ;,R3
3SEQU5TLY S9CE ;,P 2L;GS 6ALL ;,S1 & ;,S
6"S ;,R1 ;,P M/ 2L;G 6"S ;,R3 =A
SYLLOGISM 9 ! F/ FIGURE IS PRODUC$4 ,X
IS POSSI# 6DEMON/RATE ? AL P]
IMPOSSIBILE & 0EXPOSI;N4 ,= IF BO? ;,P &
;,R 2L;G 6ALL ;,S1 %D "O (! ,SS1 E4G4
;,N1 2 TAK51 BO? ;,P & ;,R W 2L;G 6?1 &
?US ;,P W 2L;G 6"S ,R4
  ,IF ;,R 2L;GS 6ALL ;,S1 & ;,P 6NO ;,S1
"! W 2 A SYLLOGISM 6PROVE T ;,P W
NECESS>ILY N 2L;G 6"S ,R4 ,? MAY 2
DEMON/RAT$ 9 ! SAME WAY Z 2F 03V]T+ !
PREMISS ,,RS4 ,X MI<T 2 PROV$ AL P]
IMPOSSIBILE1 Z 9 ! =M] CASES4 ,B IF ;,R
2L;GS 6NO ;,S1 ;,P 6ALL ;,S1 "! W 2 NO
SYLLOGISM4 ,T]MS =! POSITIVE REL,N >E
ANIMAL1 HORSE1 MAN3 =! NEGATIVE REL,N
ANIMAL1 9ANIMATE1 MAN4
  ,NOR C "! 2 A SYLLOGISM :5 BO? T]MS >E
ASS]T$ ( NO ,S4 ,T]MS =! POSITIVE REL,N
>E ANIMAL1 HORSE1 9ANIMATE2 =! NEGATIVE
REL,N MAN1 HORSE1 9ANIMATE-9ANIMATE 2+ !
MI4LE T]M4
  ,X IS CLE> !N 9 ? FIGURE AL :5 A
SYLLOGISM W 2 POSSI# & :5 N1 IF ! T]MS
>E RELAT$ UNIV]S,Y4 ,= :5"E BO? ! T]MS
>E A6IRMATIVE1 "! W 2 A SYLLOGISM 6PROVE
T "O EXTREME 2L;GS 6"S (! O!R2 B :5 !Y
>E NEGATIVE1 NO SYLLOGISM W 2 POSSI#4 ,B
:5 "O IS NEGATIVE1 ! O!R A6IRMATIVE1 IF
! MAJOR IS NEGATIVE1 ! M9OR A6IRMATIVE1
"! W 2 A SYLLOGISM 6PROVE T ! "O EXTREME
DOES N 2L;G 6"S (! O!R3 B IF ! REL,N IS
REV]S$1 NO SYLLOGISM W 2 POSSI#4 ,IF "O
T]M IS RELAT$ UNIV]S,Y 6! MI4LE1 ! O!R 9
"P ONLY1 :5 BO? >E A6IRMATIVE "! M/ 2 A
SYLLOGISM1 NO MATT] : (! PREMISSES IS
UNIV]SAL4 ,= IF ;,R 2L;GS 6ALL ;,S1 ;,P
6"S ;,S1 ;,P M/ 2L;G 6"S ,R4 ,= S9CE !
A6IRMATIVE /ATE;T IS 3V]TI# ;,S W 2L;G
6"S ;,P3 3SEQU5TLY S9CE ;,R 2L;GS 6ALL
;,S1 & ;,S 6"S ;,P1 ;,R M/ AL 2L;G 6"S
;,P3 "!=E ;,P M/ 2L;G 6"S ,R4
  ,AG IF ;,R 2L;GS 6"S ;,S1 & ;,P 6ALL
;,S1 ;,P M/ 2L;G 6"S ,R4 ,? MAY 2
DEMON/RAT$ 9 ! SAME WAY Z ! PREC$+4 ,& X
IS POSSI# 6DEMON/RATE X AL P]
IMPOSSIBILE & 0EXPOSI;N1 Z 9 ! =M]
CASES4 ,B IF "O T]M IS A6IRMATIVE1 ! O!R
NEGATIVE1 & IF ! A6IRMATIVE IS UNIV]SAL1
A SYLLOGISM W 2 POSSI# :5"E ! M9OR T]M
IS A6IRMATIVE4 ,= IF ;,R 2L;GS 6ALL ;,S1
B ;,P DOES N 2L;G 6"S ;,S1 X IS NEC T
;,P DOES N 2L;G 6"S ,R4 ,= IF ;,P 2L;GS
6ALL ;,R1 & ;,R 2L;GS 6ALL ;,S1 !N ;,P W
2L;G 6ALL ;,S3 B WE ASSUM$ T X DID N4
,PRO( IS POSSI# AL )\T REDUC;N AD
IMPOSSIBILE1 IF "O (! ,SS 2 TAK5 6: ;,P
DOES N 2L;G4
  ,B :5"E ! MAJOR IS A6IRMATIVE1 NO
SYLLOGISM W 2 POSSI#1 E4G4 IF ;,P 2L;GS
6ALL ;,S & ;,R DOES N 2L;G 6"S ,S4 ,T]MS
=! UNIV]SAL A6IRMATIVE REL,N >E ANIMATE1
MAN1 ANIMAL4 ,=! UNIV]SAL NEGATIVE REL,N
X IS N POSSI# 6GET T]MS1 IF ;,R 2L;GS
6"S ;,S1 & DOES N 2L;G 6"S ,S4 ,= IF ;,P
2L;GS 6ALL ;,S1 & ;,R 6"S ;,S1 !N ;,P W
2L;G 6"S ;,R3 B WE ASSUM$ T X 2L;GS 6NO
,R4 ,WE M/ PUT ! MATT] Z 2F40' ,S9CE !
EXPRES.N ,8X DOES N 2L;G 6"S0' IS
9DEF9ITE1 X MAY 2 US$ TRULY ( T AL :
2L;GS 6N"O4 ,B IF ;,R 2L;GS 6NO ;,S1 NO
SYLLOGISM IS POSSI#1 Z HAS BE5 %[N4
,CLE>LY !N NO SYLLOGISM W 2 POSSI# "H4
  ,B IF ! NEGATIVE T]M IS UNIV]SAL1 :5"E
! MAJOR IS NEGATIVE &! M9OR A6IRMATIVE
"! W 2 A SYLLOGISM4 ,= IF ;,P 2L;GS 6NO
;,S1 & ;,R 2L;GS 6"S ;,S1 ;,P W N 2L;G
6"S ;,R3 = WE % H ! F/ FIGURE AG1 IF !
PREMISS ,,RS IS 3V]T$4
  ,B :5 ! M9OR IS NEGATIVE1 "! W 2 NO
SYLLOGISM4 ,T]MS =! POSITIVE REL,N >E
ANIMAL1 MAN1 WILD3 =! NEGATIVE REL,N1
ANIMAL1 SCI;E1 WILD-! MI4LE 9 BO? 2+ !
T]M WILD4
  ,NOR IS A SYLLOGISM POSSI# :5 BO? >E
/AT$ 9 ! NEGATIVE1 B "O IS UNIV]SAL1 !
O!R "PICUL>4 ,:5 ! M9OR IS RELAT$
UNIV]S,Y 6! MI4LE1 TAKE ! T]MS ANIMAL1
SCI;E1 WILD2 ANIMAL1 MAN1 WILD4 ,:5 !
MAJOR IS RELAT$ UNIV]S,Y 6! MI4LE1 TAKE
Z T]MS =A NEGATIVE REL,N RAV51 SN[1
:ITE4 ,=A POSITIVE REL,N T]MS _C 2 F.D1
IF ;,R 2L;GS 6"S ;,S1 & DOES N 2L;G 6"S
,S4 ,= IF ;,P 2L;GS 6ALL ;,R1 & ;,R 6"S
;,S1 !N ;,P 2L;GS 6"S ;,S3 B WE ASSUM$ T
X 2L;GS 6NO ,S4 ,\R PO9T1 !N1 M/ 2 PROV$
F ! 9DEF9ITE NATURE (! "PICUL> /ATE;T4
  ,NOR IS A SYLLOGISM POSSI# ANYH[1 IF
EA* (! EXTREMES 2L;GS 6"S (! MI4LE OR
DOES N 2L;G1 OR "O 2L;GS &! O!R DOES N
6"S (! MI4LE1 OR "O 2L;GS 6"S (! MI4LE1
! O!R N 6ALL1 OR IF ! PREMISSES >E
9DEF9ITE4 ,-MON T]MS = ALL >E ANIMAL1
MAN1 :ITE3 ANIMAL1 9ANIMATE1 :ITE4
  ,X IS CLE> !N 9 ? FIGURE AL :5 A
SYLLOGISM W 2 POSSI#1 & :5 N2 & T IF !
T]MS >E Z /AT$1 A SYLLOGISM RESULTS (
NECESS;Y1 & IF "! IS A SYLLOGISM1 ! T]MS
M/ 2 S RELAT$4 ,X IS CLE> AL T ALL !
SYLLOGISMS 9 ? FIGURE >E IMP]FECT 7= ALL
>E MADE P]FECT 0C]TA9 SUPPLE;T>Y
ASSUMP;NS71 & T X W N 2 POSSI# 6R1* A
UNIV]SAL 3CLU.N 0M1NS ( ? FIGURE1 :E!R
NEGATIVE OR A6IRMATIVE4

                   #G

  ,X IS EVID5T AL T 9 ALL ! FIGURES1
:5"E A PROP] SYLLOGISM DOES N RESULT1 IF
BO? ! T]MS >E A6IRMATIVE OR NEGATIVE
NO?+ NEC FOLL[S AT ALL1 B IF "O IS
A6IRMATIVE1 ! O!R NEGATIVE1 & IF !
NEGATIVE IS /AT$ UNIV]S,Y1 A SYLLOGISM
ALW RESULTS RELAT+ ! M9OR 6! MAJOR T]M1
E4G4 IF ,A 2L;GS 6ALL OR "S ;,B1 & ;,B
2L;GS 6NO ;,C3 = IF ! PREMISSES >E 3V]T$
X IS NEC T ;,C DOES N 2L;G 6"S ,A4
,SIMIL>LY AL 9 ! O!R FIGURES3 A
SYLLOGISM ALW RESULTS 0M1NS ( 3V].N4 ,X
IS EVID5T AL T ! SUB/ITU;N ( AN 9DEF9ITE
=A "PICUL> A6IRMATIVE W E6ECT ! SAME
SYLLOGISM 9 ALL ! FIGURES4
  ,X IS CLE> TOO T ALL ! IMP]FECT
SYLLOGISMS >E MADE P]FECT 0M1NS (! F/
FIGURE4 ,= ALL >E BR"\ 6A 3CLU.N EI
O/5SIVELY OR P] IMPOSSIBILE4 ,9 BO? WAYS
! F/ FIGURE IS =M$3 IF !Y >E MADE P]FECT
O/5SIVELY1 2C 7Z WE SAW7 ALL >E BR"\ 6A
3CLU.N 0M1NS ( 3V].N1 & 3V].N PRODUCES !
F/ FIGURE3 IF !Y >E PROV$ P]
IMPOSSIBILE1 2C ON ! ASSUMP;N (! FALSE
/ATE;T ! SYLLOGISM -ES AB 0M1NS (! F/
FIGURE1 E4G4 9 ! LA/ FIGURE1 IF ;,A &
;,B 2L;G 6ALL ;,C1 X FOLL[S T ,A 2L;GS
6"S ;,B3 = IF ,A 2L;G$ 6NO ;,B1 & ;,B
2L;GS 6ALL ;,C1 ,A WD 2L;G 6NO ;,C3 B 7Z
WE /AT$7 X 2L;GS 6ALL ,C4 ,SIMIL>LY AL )
! RE/4
  ,X IS POSSI# AL 6REDUCE ALL SYLLOGISMS
6! UNIV]SAL SYLLOGISMS 9 ! F/ FIGURE4
,^? 9 ! SECOND FIGURE >E CLE>LY MADE
P]FECT 0^!1 ?\< N ALL 9 ! SAME WAY2 !
UNIV]SAL SYLLOGISMS >E MADE P]FECT
03V]T+ ! NEGATIVE PREMISS1 EA* (!
"PICUL> SYLLOGISMS 0REDUCTIO AD
IMPOSSIBILE4 ,9 ! F/ FIGURE "PICUL>
SYLLOGISMS >E 9DE$ MADE P]FECT 0!MVS1 B
X IS POSSI# AL 6PROVE !M 0M1NS (! SECOND
FIGURE1 REDUC+ !M AD IMPOSSIBILE1 E4G4
IF ,A 2L;GS 6ALL ;,B1 & ;,B 6"S ;,C1 X
FOLL[S T ,A 2L;GS 6"S ,C4 ,= IF X 2L;G$
6NO ;,C1 & 2L;GS 6ALL ;,B1 !N ;,B W 2L;G
6NO ;,C3 ? WE "K 0M1NS (! SECOND FIGURE4
,SIMIL>LY AL DEMON/R,N W 2 POSSI# 9 !
CASE (! NEGATIVE4 ,= IF ,A 2L;GS 6NO
;,B1 & ;,B 2L;GS 6"S ;,C1 ,A W N 2L;G
6"S ;,C3 = IF X 2L;G$ 6ALL ;,C1 & 2L;GS
6NO ;,B1 !N ;,B W 2L;G 6NO ;,C3 & ? 7Z
WE SAW7 IS ! MI4LE FIGURE4 ,3SEQU5TLY1
S9CE ALL SYLLOGISMS 9 ! MI4LE FIGURE C 2
REDUC$ 6UNIV]SAL SYLLOGISMS 9 ! F/
FIGURE1 & S9CE "PICUL> SYLLOGISMS 9 ! F/
FIGURE C 2 REDUC$ 6SYLLOGISMS 9 ! MI4LE
FIGURE1 X IS CLE> T "PICUL> SYLLOGISMS C
2 REDUC$ 6UNIV]SAL SYLLOGISMS 9 ! F/
FIGURE4 ,SYLLOGISMS 9 ! ?IRD FIGURE1 IF
! T]MS >E UNIV]SAL1 >E DIRECTLY MADE
P]FECT 0M1NS ( ^? SYLLOGISMS2 B1 :5 "O (
! PREMISSES IS "PICUL>1 0M1NS (! "PICUL>
SYLLOGISMS 9 ! F/ FIGURE3 & ^! 7WE H
SE57 MAY 2 REDUC$ 6! UNIV]SAL SYLLOGISMS
9 ! F/ FIGURE3 3SEQU5TLY AL ! "PICUL>
SYLLOGISMS 9 ! ?IRD FIGURE MAY 2 S
REDUC$4 ,X IS CLE> !N T ALL SYLLOGISMS
MAY 2 REDUC$ 6! UNIV]SAL SYLLOGISMS 9 !
F/ FIGURE4
  ,WE H /AT$ !N H[ SYLLOGISMS : PROVE T
"S?+ 2L;GS OR DOES N 2L;G 6"S?+ ELSE >E
3/ITUT$1 BO? H[ SYLLOGISMS (! SAME
FIGURE >E 3/ITUT$ 9 !MVS1 & H[
SYLLOGISMS ( DI6]5T FIGURES >E RELAT$
6"O ANO!R4

                   #H

  ,S9CE "! IS A DI6];E AC Z "S?+ 2L;GS1
NECESS>ILY 2L;GS1 OR MAY 2L;G 6"S?+ ELSE
7= _M ?+S 2L;G 9DE$1 B N NECESS>ILY1
O!RS NEI NECESS>ILY NOR 9DE$ AT ALL1 B X
IS POSSI# = !M 62L;G71 X IS CLE> T "! W
2 DI6]5T SYLLOGISMS 6PROVE EA* ( ^!
REL,NS1 & SYLLOGISMS ) DI6]5TLY RELAT$
T]MS1 "O SYLLOGISM 3CLUD+ F :AT IS NEC1
ANO!R F :AT IS1 A ?IRD F :AT IS POSSI#4
  ,"! IS H>DLY ANY DI6];E 2T SYLLOGISMS
F NEC PREMISSES & SYLLOGISMS F PREMISSES
: M]ELY ASS]T4 ,:5 ! T]MS >E PUT 9 !
SAME WAY1 !N1 :E!R "S?+ 2L;GS OR
NECESS>ILY 2L;GS 7OR DOES N 2L;G7 6"S?+
ELSE1 A SYLLOGISM W OR W N RESULT ALIKE
9 BO? CASES1 ! ONLY DI6];E 2+ ! A4I;N (!
EXPRES.N ,8NECESS>ILY0' 6! T]MS4 ,=!
NEGATIVE /ATE;T IS 3V]TI# ALIKE 9 BO?
CASES1 & WE %D GIVE ! SAME A3.T (!
EXPRES.NS ,86BE 3TA9$ 9 "S?+ Z 9 A
:OLE0' & ,86BE PR$ICAT$ ( ALL ( "S?+0'4
,)! EXCEP;NS 6BE MADE 2L1 ! 3CLU.N W 2
PROV$ 6BE NEC 0M1NS ( 3V].N1 9 ! SAME
MANN] Z 9 ! CASE ( SIMPLE PR$IC,N4 ,B 9
! MI4LE FIGURE :5 ! UNIV]SAL /ATE;T IS
A6IRMATIVE1 &! "PICUL> NEGATIVE1 & AG 9
! ?IRD FIGURE :5 ! UNIV]SAL IS
A6IRMATIVE &! "PICUL> NEGATIVE1 !
DEMON/R,N W N TAKE ! SAME =M1 B X IS NEC
0! ,8EXPOSI;N0' (A "P (! SUBJECT (!
"PICUL> NEGATIVE PROPOSI;N1 6: !
PR$ICATE DOES N 2L;G1 6MAKE ! SYLLOGISM
9 REF];E 6?3 ) T]MS S *OS5 ! 3CLU.N W
NECESS>ILY FOLL[4 ,B IF ! REL,N IS NEC 9
RESPECT (! "P TAK51 X M/ HOLD ( "S ( T
T]M 9 : ? "P IS 9CLUD$3 =! "P TAK5 IS J
"S ( T4 ,& EA* (! RESULT+ SYLLOGISMS IS
9 ! APPROPRIATE FIGURE4

                   #I

  ,X HAPP5S "S"TS AL T :5 "O PREMISS IS
NEC ! 3CLU.N IS NEC1 N H["E :5 EI
PREMISS IS NEC1 B ONLY :5 ! MAJOR IS1
E4G4 IF ,A IS TAK5 Z NECESS>ILY 2L;G+ OR
N 2L;G+ TO ;,B1 B ;,B IS TAK5 Z SIMPLY
2L;G+ TO ;,C3 = IF ! PREMISSES >E TAK5 9
? WAY1 ,A W NECESS>ILY 2L;G OR N 2L;G TO
;,C4 ,= S9CE NECESS>ILY 2L;GS1 OR DOES N
2L;G1 6E ;,B1 & S9CE ;,C IS "O (! ,BS1 X
IS CLE> T = ;,C AL ! POSITIVE OR !
NEGATIVE REL,N TO ;,A W HOLD NECESS>ILY4
,B IF ! MAJOR PREMISS IS N NEC1 B ! M9OR
IS NEC1 ! 3CLU.N W N 2 NEC4 ,= IF X W]E1
X WD RESULT BO? "? ! F/ FIGURE & "? !
?IRD T ,A 2L;GS NECESS>ILY 6"S ,B4 ,B ?
IS FALSE2 = ;,B MAY 2 S* T X IS POSSI# T
,A %D 2L;G 6N"O ( X4 ,FUR!R1 AN EXAMPLE
AL MAKES X CLE> T ! 3CLU.N N 2 NEC1 E4G4
IF ,A 7 MOVE;T1 ;,B ANIMAL1 ;,C MAN3 MAN
IS AN ANIMAL NECESS>ILY1 B AN ANIMAL
DOES N MOVE NECESS>ILY1 NOR DOES MAN4
,SIMIL>LY AL IF ! MAJOR PREMISS IS
NEGATIVE2 =! PRO( IS ! SAME4
  ,9 "PICUL> SYLLOGISMS1 IF ! UNIV]SAL
PREMISS IS NEC1 !N ! 3CLU.N W 2 NEC2 B
IF ! "PICUL>1 ! 3CLU.N W N 2 NEC1 :E!R !
UNIV]SAL PREMISS IS NEGATIVE OR
A6IRMATIVE4 ,F/ LET ! UNIV]SAL 2 NEC1 &
LET ,A 2L;G 6ALL ;,B NECESS>ILY1 B LET
;,B SIMPLY 2L;G 6"S ;,C3 X IS NEC !N T
,A 2L;GS 6"S ;,C NECESS>ILY3 = ;,C FALLS
"U ;,B1 & ,A 0 ASSUM$ 62L;G NECESS>ILY
6ALL ,B4 ,SIMIL>LY AL IF ! SYLLOGISM %D
2 NEGATIVE3 =! PRO( W 2 ! SAME4 ,B IF !
"PICUL> PREMISS IS NEC1 ! 3CLU.N W N 2
NEC3 = F ! D5IAL ( S* A 3CLU.N NO?+
IMPOSSI# RESULTS1 J Z X DOES N 9 !
UNIV]SAL SYLLOGISMS4 ,! SAME IS TRUE (
NEGATIVE SYLLOGISMS4 ,TRY ! T]MS MOVE;T1
ANIMAL1 :ITE4

                  #AJ

  ,9 ! SECOND FIGURE1 IF ! NEGATIVE
PREMISS IS NEC1 !N ! 3CLU.N W 2 NEC1 B
IF ! A6IRMATIVE1 N NEC4 ,F/ LET !
NEGATIVE 2 NEC2 LET ,A 2 POSSI# ( NO
;,B1 & SIMPLY 2L;G TO ;,C4 ,S9CE !N !
NEGATIVE /ATE;T IS 3V]TI#1 ;,B IS POSSI#
( NO ,A4 ,B ,A 2L;GS 6ALL ;,C2 3SEQU5TLY
;,B IS POSSI# ( NO ,C4 ,= ;,C FALLS "U
,A4 ,! SAME RESULT WD 2 OBTA9$ IF ! M9OR
PREMISS 7 NEGATIVE3 = IF ,A IS POSSI# 2
( NO ;,C1 ;,C IS POSSI# ( NO ,A3 B ,A
2L;GS 6ALL ;,B1 3SEQU5TLY ;,C IS POSSI#
( N"O (! ,BS3 = AG WE H OBTA9$ ! F/
FIGURE4 ,NEI !N IS ;,B POSSI# ( ;,C3 =
3V].N IS POSSI# )\T MODIFY+ ! REL,N4
  ,B IF ! A6IRMATIVE PREMISS IS NEC1 !
3CLU.N W N 2 NEC4 ,LET ,A 2L;G 6ALL ;,B
NECESS>ILY1 B 6NO ;,C SIMPLY4 ,IF !N !
NEGATIVE PREMISS IS 3V]T$1 ! F/ FIGURE
RESULTS4 ,B X HAS BE5 PROV$ 9 ! CASE (!
F/ FIGURE T IF ! NEGATIVE MAJOR PREMISS
IS N NEC ! 3CLU.N W N 2 NEC EI4 ,"!=E !
SAME RESULT W OBTA9 "H4 ,FUR!R1 IF !
3CLU.N IS NEC1 X FOLL[S T ;,C NECESS>ILY
DOES N 2L;G 6"S ,A4 ,= IF ;,B NECESS>ILY
2L;GS 6NO ;,C1 ;,C W NECESS>ILY 2L;G 6NO
,B4 ,B ;,B AT ANY RATE M/ 2L;G 6"S ;,A1
IF X IS TRUE 7Z 0 ASSUM$7 T ,A
NECESS>ILY 2L;GS 6ALL ,B4 ,3SEQU5TLY X
IS NEC T ;,C DOES N 2L;G 6"S ,A4 ,B NO?+
PREV5TS S* AN ,A 2+ TAK5 T X IS POSSI# =
;,C 62L;G 6ALL ( X4 ,FUR!R "O MI<T %[
0AN EXPOSI;N ( T]MS T ! 3CLU.N IS N NEC
)\T QUALIFIC,N1 ?\< X IS A NEC 3CLU.N F
! PREMISSES4 ,= EXAMPLE LET ,A 2 ANIMAL1
;,B MAN1 ;,C :ITE1 & LET ! PREMISSES 2
ASSUM$ 6CORRESPOND 6:AT WE _H 2F3 X IS
POSSI# T ANIMAL %D 2L;G 6NO?+ :ITE4 ,MAN
!N W N 2L;G 6ANY?+ :ITE1 B N NECESS>ILY3
= X IS POSSI# = MAN 6BE BORN :ITE1 N
H["E S L;G Z ANIMAL 2L;GS 6NO?+ :ITE4
,3SEQU5TLY "U ^! 3DI;NS ! 3CLU.N W 2
NEC1 B X IS N NEC )\T QUALIFIC,N4
  ,SIMIL> RESULTS W OBTA9 AL 9 "PICUL>
SYLLOGISMS4 ,= :5"E ! NEGATIVE PREMISS
IS BO? UNIV]SAL & NEC1 !N ! 3CLU.N W 2
NEC3 B :5"E ! A6IRMATIVE PREMISS IS
UNIV]SAL1 ! NEGATIVE "PICUL>1 ! 3CLU.N W
N 2 NEC4 ,F/ !N LET ! NEGATIVE PREMISS 2
BO? UNIV]SAL & NEC3 LET X 2 POSSI# = NO
;,B T ,A %D 2L;G 6X1 & LET ,A SIMPLY
2L;G 6"S ,C4 ,S9CE ! NEGATIVE /ATE;T IS
3V]TI#1 X W 2 POSSI# = NO ,A T ;,B %D
2L;G 6X3 B ,A 2L;GS 6"S ;,C2 3SEQU5TLY
;,B NECESS>ILY DOES N 2L;G 6"S (! ,C'S4
,AG LET ! A6IRMATIVE PREMISS 2 BO?
UNIV]SAL & NEC1 & LET ! MAJOR PREMISS 2
A6IRMATIVE4 ,IF !N ,A NECESS>ILY 2L;GS
6ALL ;,B1 B DOES N 2L;G 6"S ;,C1 X IS
CLE> T ;,B W N 2L;G 6"S ;,C1 B N
NECESS>ILY4 ,=! SAME T]MS C 2 US$
6DEMON/RATE ! PO9T1 : 7 US$ 9 ! UNIV]SAL
SYLLOGISMS4 ,NOR AG1 IF ! NEGATIVE
/ATE;T IS NEC B "PICUL>1 W ! 3CLU.N 2
NEC4 ,! PO9T C 2 DEMON/RAT$ 0M1NS (!
SAME T]MS4

                  #AA

  ,9 ! LA/ FIGURE :5 ! T]MS >E RELAT$
UNIV]S,Y 6! MI4LE1 & BO? PREMISSES >E
A6IRMATIVE1 IF "O (! TWO IS NEC1 !N !
3CLU.N W 2 NEC4 ,B IF "O IS NEGATIVE1 !
O!R A6IRMATIVE1 :5"E ! NEGATIVE IS NEC !
3CLU.N AL W 2 NEC1 B :5"E ! A6IRMATIVE
IS NEC ! 3CLU.N W N 2 NEC4 ,F/ LET BO? !
PREMISSES 2 A6IRMATIVE1 & LET ;,A & ;,B
2L;G 6ALL ;,C1 & LET ;,,AC 2 NEC4 ,S9CE
!N ;,B 2L;GS 6ALL ;,C1 ;,C AL W 2L;G 6"S
;,B1 2C ! UNIV]SAL IS 3V]TI# 96!
"PICUL>3 3SEQU5TLY IF ,A 2L;GS
NECESS>ILY 6ALL ;,C1 & ;,C 2L;GS 6"S
;,B1 X IS NEC T ,A %D 2L;G 6"S ;,B AL4
,= ;,B IS "U ,C4 ,! F/ FIGURE !N IS =M$4
,A SIMIL> PRO( W 2 GIV5 AL IF ,,BC IS
NEC4 ,= ;,C IS 3V]TI# ) "S ,A3 3SEQU5TLY
IF ;,B 2L;GS NECESS>ILY 6ALL ;,C1 X W
2L;G NECESS>ILY AL 6"S ,A4
  ,AG LET ;,,AC 2 NEGATIVE1 ,,BC
A6IRMATIVE1 & LET ! NEGATIVE PREMISS 2
NEC4 ,S9CE !N ;,C IS 3V]TI# ) "S ;,B1 B
,A NECESS>ILY 2L;GS 6NO ;,C1 ,A W
NECESS>ILY N 2L;G 6"S ;,B EI3 = ;,B IS
"U ,C4 ,B IF ! A6IRMATIVE IS NEC1 !
3CLU.N W N 2 NEC4 ,= SUPPOSE ,,BC IS
A6IRMATIVE & NEC1 :ILE ;,,AC IS NEGATIVE
& N NEC4 ,S9CE !N ! A6IRMATIVE IS
3V]TI#1 ;,C AL W 2L;G 6"S ;,B
NECESS>ILY3 3SEQU5TLY IF ,A 2L;GS 6N"O (
! ,C'S1 :ILE ;,C 2L;GS 6"S (! ,BS1 ,A W
N 2L;G 6"S (! ,BS-B N ( NECESS;Y2 = X
HAS BE5 PROV$1 9 ! CASE (! F/ FIGURE1 T
IF ! NEGATIVE PREMISS IS N NEC1 NEI W !
3CLU.N 2 NEC4 ,FUR!R1 ! PO9T MAY 2 MADE
CLE> 03SID]+ ! T]MS4 ,LET ! T]M ,A 2
,8GD0'1 LET T : ;,B SIGNIFIES 2
,8ANIMAL0'1 LET ! T]M ;,C 2 ,8HORSE0'4
,X IS POSSI# !N T ! T]M GD %D 2L;G 6NO
HORSE1 & X IS NEC T ! T]M ANIMAL %D 2L;G
6E HORSE3 B X IS N NEC T "S ANIMAL %D N
2 GD1 S9CE X IS POSSI# = E ANIMAL 6BE
GD4 ,OR IF T IS N POSSI#1 TAKE Z ! T]M
,8AWAKE0' OR ,8ASLEEP0'3 = E ANIMAL C
A3EPT ^!4
  ,IF1 !N1 ! PREMISSES >E UNIV]SAL1 WE H
/AT$ :5 ! 3CLU.N W 2 NEC4 ,B IF "O
PREMISS IS UNIV]SAL1 ! O!R "PICUL>1 & IF
BO? >E A6IRMATIVE1 :5"E ! UNIV]SAL IS
NEC ! 3CLU.N AL M/ 2 NEC4 ,! DEMON/R,N
IS ! SAME Z 2F2 =! "PICUL> A6IRMATIVE AL
IS 3V]TI#4 ,IF !N X IS NEC T ;,B %D 2L;G
6ALL ;,C1 & ,A FALLS "U ;,C1 X IS NEC T
;,B %D 2L;G 6"S ,A4 ,B IF ;,B M/ 2L;G
6"S ;,A1 !N ,A M/ 2L;G 6"S ;,B3 = 3V].N
IS POSSI#4 ,SIMIL>LY AL IF ;,,AC %D 2
NEC & UNIV]SAL3 = ;,B FALLS "U ,C4 ,B IF
! "PICUL> PREMISS IS NEC1 ! 3CLU.N W N 2
NEC4 ,LET ! PREMISS ,,BC 2 BO? "PICUL> &
NEC1 & LET ,A 2L;G 6ALL ;,C1 N H["E
NECESS>ILY4 ,IF ! PROPOSI;N ,,BC IS
3V]T$ ! F/ FIGURE IS =M$1 &! UNIV]SAL
PREMISS IS N NEC1 B ! "PICUL> IS NEC4 ,B
:5 ! PREMISSES 7 ?US1 ! 3CLU.N 7Z WE
PROV$ 0 N NEC3 3SEQU5TLY X IS N "H EI4
,FUR!R1 ! PO9T IS CLE> IF WE LOOK AT !
T]MS4 ,LET ,A 2 WAK+1 ;,B BIP$1 & ;,C
ANIMAL4 ,X IS NEC T ;,B %D 2L;G 6"S ;,C1
B X IS POSSI# = ,A 62L;G TO ;,C1 & T ,A
%D 2L;G TO ;,B IS N NEC4 ,= "! IS NO
NECESS;Y T "S BIP$ %D 2 ASLEEP OR AWAKE4
,SIMIL>LY & 0M1NS (! SAME T]MS PRO( C 2
MADE1 %D ! PROPOSI;N ;,,AC 2 BO? "PICUL>
& NEC4
  ,B IF "O PREMISS IS A6IRMATIVE1 ! O!R
NEGATIVE1 :5"E ! UNIV]SAL IS BO?
NEGATIVE & NEC ! 3CLU.N AL W 2 NEC4 ,=
IF X IS N POSSI# T ,A %D 2L;G 6ANY ;,C1
B ;,B 2L;GS 6"S ;,C1 X IS NEC T ,A %D N
2L;G 6"S ,B4 ,B :5"E ! A6IRMATIVE
PROPOSI;N IS NEC1 :E!R UNIV]SAL OR
"PICUL>1 OR ! NEGATIVE IS "PICUL>1 !
3CLU.N W N 2 NEC4 ,! PRO( ( ? 0REDUC;N W
2 ! SAME Z 2F2 B IF T]MS >E WANT$1 :5 !
UNIV]SAL A6IRMATIVE IS NEC1 TAKE ! T]MS
,8WAK+0'-,8ANIMAL0'-,8MAN0'1 ,8MAN0' 2+
MI4LE1 & :5 ! A6IRMATIVE IS "PICUL> &
NEC1 TAKE ! T]MS ,8WAK+0'-,8ANIMAL0'-
,8:ITE0'3 = X IS NEC T ANIMAL %D 2L;G
6"S :ITE ?+1 B X IS POSSI# T WAK+ %D
2L;G 6N"O1 & X IS N NEC T WAK+ %D N 2L;G
6"S ANIMAL4 ,B :5 ! NEGATIVE PROPOSI;N
2+ "PICUL> IS NEC1 TAKE ! T]MS ,8BIP$0'1
,8MOV+0'1 ,8ANIMAL0'1 ,8ANIMAL0' 2+
MI4LE4

                  #AB

  ,X IS CLE> !N T A SIMPLE 3CLU.N IS N
R1*$ UN.S BO? PREMISSES >E SIMPLE
ASS];NS1 B A NEC 3CLU.N IS POSSI# AL? "O
ONLY (! PREMISSES IS NEC4 ,B 9 BO?
CASES1 :E!R ! SYLLOGISMS >E A6IRMATIVE
OR NEGATIVE1 X IS NEC T "O PREMISS %D 2
SIMIL> 6! 3CLU.N4 ,I M1N BY ,8SIMIL>0'1
IF ! 3CLU.N IS A SIMPLE ASS];N1 !
PREMISS M/ 2 SIMPLE2 IF ! 3CLU.N IS NEC1
! PREMISS M/ 2 NEC4 ,3SEQU5TLY ? AL IS
CLE>1 T ! 3CLU.N W 2 NEI NEC NOR SIMPLE
UN.S A NEC OR SIMPLE PREMISS IS ASSUM$4

                  #AC

  ,P]H 5 HAS BE5 SD AB ! PRO( (
NECESS;Y1 H[ X -ES AB & H[ X DI6]S F !
PRO( (A SIMPLE /ATE;T4 ,WE PROCE$ 64CUSS
T : IS POSSI#1 :5 & H[ & 0:AT M1NS X C 2
PROV$4 ,I USE ! T]MS ,86BE POSSI#0' &
,8! POSSI#0' ( T : IS N NEC B1 2+
ASSUM$1 RESULTS 9 NO?+ IMPOSSI#4 ,WE SAY
9DE$ AMBIGU\SLY (! NEC T X IS POSSI#4 ,B
T MY DEF9I;N (! POSSI# IS CORRECT IS
CLE> F ! PHRASES 0: WE D5Y OR ON ! 3TR>Y
A6IRM POSSIBIL;Y4 ,=! EXPRES.NS ,8X IS N
POSSI# 62L;G0'1 ,8X IS IMPOSSI# 62L;G0'1
& ,8X IS NEC N 62L;G0' >E EI ID5TICAL OR
FOLL[ F "O ANO!R2 3SEQU5TLY _! OPPOSITES
AL1 ,8X IS POSSI# 62L;G0'1 ,8X IS N
IMPOSSI# 62L;G0'1 & ,8X IS N NEC N
62L;G0'1 W EI 2 ID5TICAL OR FOLL[ F "O
ANO!R4 ,=( "EY?+ ! A6IRM,N OR ! D5IAL
HOLDS GD4 ,T : IS POSSI# !N W 2 N NEC &
T : IS N NEC W 2 POSSI#4 ,X RESULTS T
ALL PREMISSES 9 ! MODE ( POSSIBIL;Y >E
3V]TI# 96"O ANO!R4 ,I M1N N T !
A6IRMATIVE >E 3V]TI# 96! NEGATIVE1 B T
^? : >E A6IRMATIVE 9 =M ADMIT ( 3V].N
0OPPOSI;N1 E4G4 ,8X IS POSSI# 62L;G0'
MAY 2 3V]T$ 9TO ,8X IS POSSI# N 62L;G0'1
& ,8X IS POSSI# = ,A 62L;G 6ALL ,B0' 9TO
,8X IS POSSI# = ,A 62L;G 6NO ,B0' OR ,8N
6ALL ,B0'1 & ,8X IS POSSI# = ,A 62L;G
6"S ,B0' 9TO ,8X IS POSSI# = ,A N 62L;G
6"S ,B0'4 ,& SIMIL>LY ! O!R PROPOSI;NS 9
? MODE C 2 3V]T$4 ,= S9CE T : IS POSSI#
IS N NEC1 & T : IS N NEC MAY POSSIBLY N
2L;G1 X IS CLE> T IF X IS POSSI# T ,A %D
2L;G TO ;,B1 X IS POSSI# AL T X %D N
2L;G TO ;,B3 & IF X IS POSSI# T X %D
2L;G 6ALL1 X IS AL POSSI# T X %D N 2L;G
6ALL4 ,! SAME HOLDS GD 9 ! CASE (
"PICUL> A6IRM,NS3 =! PRO( IS ID5TICAL4
,& S* PREMISSES >E A6IRMATIVE & N
NEGATIVE2 = ,86BE POSSI#0' IS 9 ! SAME
RANK Z ,86BE0'1 Z 0 SD ABV4
  ,HAV+ MADE ^! 4T9C;NS WE NEXT PO9T \ T
! EXPRES.N ,86BE POSSI#0' IS US$ 9 TWO
WAYS4 ,9 "O X M1NS 6HAPP5 G5],Y & FALL
%ORT ( NECESS;Y1 E4G4 MAN'S TURN+ GREY
OR GR[+ OR DECAY+1 OR G5],Y :AT NATUR,Y
2L;GS 6A ?+ 7= ? HAS N XS NECESS;Y
UNBROK51 S9CE MAN'S EXI/;E IS N 3T9U\S =
"E1 AL? IF A MAN DOES EXI/1 X -ES AB EI
NECESS>ILY OR G5],Y74 ,9 ANO!R S5SE !
EXPRES.N M1NS ! 9DEF9ITE1 : C 2 BO? ?US
& N ?US1 E4G4 AN ANIMAL'S WALK+ OR AN
E>?QUAKE'S TAK+ PLACE :ILE X IS WALK+1
OR G5],Y :AT HAPP5S 0*.E3 = N"O ( ^!
9CL9ES 0NATURE 9 ! "O WAY M ?AN 9 !
OPPOSITE4
  ,T : IS POSSI# 9 EA* ( XS TWO S5SES IS
3V]TI# 96XS OPPOSITE1 N H["E 9 ! SAME
WAY3 B :AT IS NATURAL IS 3V]TI# 2C X
DOES N NECESS>ILY 2L;G 7= 9 ? S5SE X IS
POSSI# T A MAN %D N GR[ GREY7 & :AT IS
9DEF9ITE IS 3V]TI# 2C X 9CL9ES ? WAY NO
M ?AN T4 ,SCI;E & DEMON/RATIVE SYLLOGISM
>E N 3C]N$ ) ?+S : >E 9DEF9ITE1 2C !
MI4LE T]M IS UNC]TA92 B !Y >E 3C]N$ )
?+S T >E NATURAL1 & Z A RULE >GU;TS &
9QUIRIES >E MADE AB ?+S : >E POSSI# 9 ?
S5SE4 ,SYLLOGISMS 9DE$ C 2 MADE AB !
=M]1 B X IS UNUSUAL AT ANY RATE 69QUIRE
AB !M4
  ,^! MATT]S W 2 TR1T$ M DEF9ITELY 9 !
SEQUEL2 \R BUSI;S AT PRES5T IS 6/ATE !
MOODS & NATURE (! SYLLOGISM MADE F
POSSI# PREMISSES4 ,! EXPRES.N ,8X IS
POSSI# = ? 62L;G 6T0' MAY 2 "U/OOD 9 TWO
S5SES3 ,8T0' MAY M1N EI T 6: ,8T0' 2L;GS
OR T 6: X MAY 2L;G2 =! EXPRES.N ',A IS
POSSI# (! SUBJECT ( ,B0' M1NS T X IS
POSSI# EI ( T ( : ;,B IS /AT$ OR ( T ( :
;,B MAY POSSIBLY 2 /AT$4 ,X MAKES NO
DI6];E :E!R WE SAY1 ,A IS POSSI# (!
SUBJECT ( ;,B1 OR ALL ;,B ADMITS ( ,A4
,X IS CLE> !N T ! EXPRES.N ',A MAY
POSSIBLY 2L;G 6ALL ,B0' MI<T 2 US$ 9 TWO
S5SES4 ,F/ !N WE M/ /ATE ! NATURE &
"*I/ICS (! SYLLOGISM : >ISES IF ;,B IS
POSSI# (! SUBJECT ( ;,C1 & ,A IS POSSI#
(! SUBJECT ( ,B4 ,= ?US BO? PREMISSES >E
ASSUM$ 9 ! MODE ( POSSIBIL;Y2 B :5"E ,A
IS POSSI# ( T ( : ;,B IS TRUE1 "O
PREMISS IS A SIMPLE ASS];N1 ! O!R A
PRO#MATIC4 ,3SEQU5TLY WE M/ />T F
PREMISSES : >E SIMIL> 9 =M1 Z 9 ! O!R
CASES4

                  #AD

  ,:5"E ,A MAY POSSIBLY 2L;G 6ALL ;,B1 &
;,B 6ALL ;,C1 "! W 2 A P]FECT SYLLOGISM
6PROVE T ,A MAY POSSIBLY 2L;G 6ALL ,C4
,? IS CLE> F ! DEF9I;N3 = X 0 9 ? WAY T
WE EXPLA9$ ,86BE POSSI# = "O T]M 62L;G
6ALL ( ANO!R0'4 ,SIMIL>LY IF X IS POSSI#
= ,A 62L;G NO ;,B1 &= ;,B 62L;G 6ALL
;,C1 !N X IS POSSI# = ,A 62L;G 6NO ,C4
,=! /ATE;T T X IS POSSI# = ,A N 62L;G 6T
( : ;,B MAY 2 TRUE M1NS 7Z WE SAW7 T N"O
( ^? ?+S : C POSSIBLY FALL "U ! T]M ;,B
IS LEFT \ ( A3.T4 ,B :5"E ,A MAY 2L;G
6ALL ;,B1 & ;,B MAY 2L;G 6NO ;,C1 !N
9DE$ NO SYLLOGISM RESULTS F ! PREMISSES
ASSUM$1 B IF ! PREMISS ,,BC IS 3V]T$ AF
! MANN] ( PRO#MATIC PROPOSI;NS1 ! SAME
SYLLOGISM RESULTS Z 2F4 ,= S9CE X IS
POSSI# T ;,B %D 2L;G 6NO ;,C1 X IS
POSSI# AL T X %D 2L;G 6ALL ,C4 ,? HAS
BE5 /AT$ ABV4 ,3SEQU5TLY IF ;,B IS
POSSI# = ALL ;,C1 & ,A IS POSSI# = ALL
;,B1 ! SAME SYLLOGISM AG RESULTS4
,SIMIL>LY IF 9 BO? ! PREMISSES !
NEGATIVE IS JO9$ ) ,8X IS POSSI#0'3 E4G4
IF ,A MAY 2L;G 6N"O (! ,BS1 & ;,B 6N"O (
! ,C'S4 ,NO SYLLOGISM RESULTS F ! ASSUM$
PREMISSES1 B IF !Y >E 3V]T$ WE % H !
SAME SYLLOGISM Z 2F4 ,X IS CLE> !N T IF
! M9OR PREMISS IS NEGATIVE1 OR IF BO?
PREMISSES >E NEGATIVE1 EI NO SYLLOGISM
RESULTS1 OR IF "O X IS N P]FECT4 ,=!
NECESS;Y RESULTS F ! 3V].N4
  ,B IF "O (! PREMISSES IS UNIV]SAL1 !
O!R "PICUL>1 :5 ! MAJOR PREMISS IS
UNIV]SAL "! W 2 A P]FECT SYLLOGISM4 ,=
IF ,A IS POSSI# = ALL ;,B1 & ;,B = "S
;,C1 !N ,A IS POSSI# = "S ,C4 ,? IS CLE>
F ! DEF9I;N ( 2+ POSSI#4 ,AG IF ,A MAY
2L;G 6NO ;,B1 & ;,B MAY 2L;G 6"S (!
,C'S1 X IS NEC T ,A MAY POSSIBLY N 2L;G
6"S (! ,C'S4 ,! PRO( IS ! SAME Z ABV4 ,B
IF ! "PICUL> PREMISS IS NEGATIVE1 &!
UNIV]SAL IS A6IRMATIVE1 ! MAJOR / 2+
UNIV]SAL &! M9OR "PICUL>1 E4G4 ,A IS
POSSI# = ALL ;,B1 ;,B MAY POSSIBLY N
2L;G 6"S ;,C1 !N A CLE> SYLLOGISM DOES N
RESULT F ! ASSUM$ PREMISSES1 B IF !
"PICUL> PREMISS IS 3V]T$ & X IS LAID D[N
T ;,B POSSIBLY MAY 2L;G 6"S ;,C1 WE % H
! SAME 3CLU.N Z 2F1 Z 9 ! CASES GIV5 AT
! 2G9N+4
  ,B IF ! MAJOR PREMISS IS ! M9OR
UNIV]SAL1 :E!R BO? >E A6IRMATIVE1 OR
NEGATIVE1 OR DI6]5T 9 QUAL;Y1 OR IF BO?
>E 9DEF9ITE OR "PICUL>1 9 NO WAY W A
SYLLOGISM 2 POSSI#4 ,= NO?+ PREV5TS ;,B
F R1*+ 2Y ;,A1 S T Z PR$ICATES COV]
UNEQUAL >1S4 ,LET ;,C 2 T 0: ;,B EXT5DS
2Y ,A4 ,TO ;,C X IS N POSSI# T ,A %D
2L;G-EI 6ALL OR 6N"O OR 6"S OR N 6"S1
S9CE PREMISSES 9 ! MODE ( POSSIBIL;Y >E
3V]TI# & X IS POSSI# = ;,B 62L;G 6M ?+S
?AN ,A C4 ,FUR!R1 ? IS OBVI\S IF WE TAKE
T]MS2 = IF ! PREMISSES >E Z ASSUM$1 !
MAJOR T]M IS BO? POSSI# = N"O (! M9OR &
M/ 2L;G 6ALL ( X4 ,TAKE Z T]MS -MON 6ALL
! CASES "U 3SID],N ,8ANIMAL0'-,8:ITE0'-
,8MAN0'1 ": ! MAJOR 2L;GS NECESS>ILY 6!
M9OR2 ,8ANIMAL0'-,8:ITE0'-,8G>;T0'1 ": X
IS N POSSI# T ! MAJOR %D 2L;G 6! M9OR4
,X IS CLE> !N T IF ! T]MS >E RELAT$ 9 ?
MANN]1 NO SYLLOGISM RESULTS4 ,= E
SYLLOGISM PROVES T "S?+ 2L;GS EI SIMPLY
OR NECESS>ILY OR POSSIBLY4 ,X IS CLE> T
"! IS NO PRO( (! F/ OR (! SECOND4 ,=!
A6IRMATIVE IS DE/ROY$ 0! NEGATIVE1 &!
NEGATIVE 0! A6IRMATIVE4 ,"! REMA9S !
PRO( ( POSSIBIL;Y4 ,B ? IS IMPOSSI#4 ,=
X HAS BE5 PROV$ T IF ! T]MS >E RELAT$ 9
? MANN] X IS BO? NEC T ! MAJOR %D 2L;G
6ALL ! M9OR & N POSSI# T X %D 2L;G 6ANY4
,3SEQU5TLY "! _C 2 A SYLLOGISM 6PROVE !
POSSIBIL;Y2 =! NEC 7Z WE /AT$7 IS N
POSSI#4
  ,X IS CLE> T IF ! T]MS >E UNIV]SAL 9
POSSI# PREMISSES A SYLLOGISM ALW RESULTS
9 ! F/ FIGURE1 :E!R !Y >E A6IRMATIVE OR
NEGATIVE1 ONLY A P]FECT SYLLOGISM
RESULTS 9 ! F/ CASE1 AN IMP]FECT 9 !
SECOND4 ,B POSSIBIL;Y M/ 2 "U/OOD AC 6!
DEF9I;N LAID D[N1 N Z COV]+ NECESS;Y4 ,?
IS "S"TS =GOTT54

                  #AE

  ,IF "O PREMISS IS A SIMPLE PROPOSI;N1
! O!R A PRO#MATIC1 :5"E ! MAJOR PREMISS
9DICATES POSSIBIL;Y ALL ! SYLLOGISMS W 2
P]FECT & E/ABLI% POSSIBIL;Y 9 ! S5SE
DEF9$2 B :5"E ! M9OR PREMISS 9DICATES
POSSIBIL;Y ALL ! SYLLOGISMS W 2
IMP]FECT1 & ^? : >E NEGATIVE W E/ABLI% N
POSSIBIL;Y AC 6! DEF9I;N1 B T ! MAJOR
DOES N NECESS>ILY 2L;G 6ANY1 OR 6ALL1 (!
M9OR4 ,= IF ? IS S1 WE SAY X IS POSSI# T
X %D 2L;G 6N"O OR N 6ALL4 ,LET ,A 2
POSSI# = ALL ;,B1 & LET ;,B 2L;G 6ALL
,C4 ,S9CE ;,C FALLS "U ;,B1 & ,A IS
POSSI# = ALL ;,B1 CLE>LY X IS POSSI# =
ALL ;,C AL4 ,S A P]FECT SYLLOGISM
RESULTS4 ,LIKEWISE IF ! PREMISS ;,,AB IS
NEGATIVE1 &! PREMISS ,,BC IS A6IRMATIVE1
! =M] /AT+ POSSI#1 ! LATT] SIMPLE
ATTRIBU;N1 A P]FECT SYLLOGISM RESULTS
PROV+ T ,A POSSIBLY 2L;GS 6NO ,C4
  ,X IS CLE> T P]FECT SYLLOGISMS RESULT
IF ! M9OR PREMISS /ATES SIMPLE 2L;G+3 B
T SYLLOGISMS W RESULT IF ! MODAL;Y (!
PREMISSES IS REV]S$1 M/ 2 PROV$ P]
IMPOSSIBILE4 ,AT ! SAME "T X W 2 EVID5T
T !Y >E IMP]FECT3 =! PRO( PROCE$S N F !
PREMISSES ASSUM$4 ,F/ WE M/ /ATE T IF
;,B'S 2+ FOLL[S NECESS>ILY F ;,A'S 2+1
;,B'S POSSIBIL;Y W FOLL[ NECESS>ILY F
;,A'S POSSIBIL;Y4 ,SUPPOSE1 ! T]MS 2+ S
RELAT$1 T ,A IS POSSI#1 & ;,B IS
IMPOSSI#4 ,IF !N T : IS POSSI#1 :5 X IS
POSSI# = X 6BE1 MI<T HAPP51 & IF T : IS
IMPOSSI#1 :5 X IS IMPOSSI#1 CD N HAPP51
& IF AT ! SAME "T ,A IS POSSI# & ;,B
IMPOSSI#1 X WD 2 POSSI# = ,A 6HAPP5 )\T
;,B1 & IF 6HAPP51 !N 6BE4 ,= T : HAS
HAPP5$1 :5 X HAS HAPP5$1 IS4 ,B WE M/
TAKE ! IMPOSSI# &! POSSI# N ONLY 9 !
SPH]E ( 2COM+1 B AL 9 ! SPH]ES ( TRU? &
PR$ICABIL;Y1 &! V>I\S O!R SPH]ES 9 : WE
SP1K (! POSSI#3 = X W 2 ALIKE 9 ALL4
,FUR!R WE M/ "U/& ! /ATE;T T ;,B'S 2+
DEP5DS ON ;,A'S 2+1 N Z M1N+ T IF "S
S+LE ?+ ,A IS1 ;,B W BE3 = NO?+ FOLL[S (
NECESS;Y F ! 2+ ( "S "O ?+1 B F TWO AT
L1/1 I4E4 :5 ! PREMISSES >E RELAT$ 9 !
MANN] /AT$ 6BE T (! SYLLOGISM4 ,= IF ;,C
IS PR$ICAT$ ( ;,D1 & ;,D ( ;,F1 !N ;,C
IS NECESS>ILY PR$ICAT$ ( ,F4 ,& IF EA*
IS POSSI#1 ! 3CLU.N AL IS POSSI#4 ,IF
!N1 = EXAMPLE1 "O %D 9DICATE ! PREMISSES
BY ;,A1 &! 3CLU.N BY ;,B1 X WD N ONLY
RESULT T IF ,A IS NEC ;,B IS NEC1 B AL T
IF ,A IS POSSI#1 ;,B IS POSSI#4
  ,S9CE ? IS PROV$ X IS EVID5T T IF A
FALSE & N IMPOSSI# ASSUMP;N IS MADE1 !
3SEQU;E (! ASSUMP;N W AL 2 FALSE & N
IMPOSSI#3 E4G4 IF ,A IS FALSE1 B N
IMPOSSI#1 & IF ;,B IS ! 3SEQU;E ( ;,A1
;,B AL W 2 FALSE B N IMPOSSI#4 ,= S9CE X
HAS BE5 PROV$ T IF ;,B'S 2+ IS ! 3SEQU;E
( ;,A'S 2+1 !N ;,B'S POSSIBIL;Y W FOLL[
F ;,A'S POSSIBIL;Y 7& ,A IS ASSUM$ 6BE
POSSI#71 3SEQU5TLY ;,B W 2 POSSI#3 = IF
X 7 IMPOSSI#1 ! SAME ?+ WD AT ! SAME "T
2 POSSI# & IMPOSSI#4
  ,S9CE WE H DEF9$ ^! PO9TS1 LET ,A 2L;G
6ALL ;,B1 & ;,B 2 POSSI# = ALL ;,C3 X IS
NEC !N T %D 2 A POSSI# ATTRIBUTE = ALL
,C4 ,SUPPOSE T X IS N POSSI#1 B ASSUME T
;,B 2L;GS 6ALL ;,C3 ? IS FALSE B N
IMPOSSI#4 ,IF !N ,A IS N POSSI# = ;,C B
;,B 2L;GS 6ALL ;,C1 !N ,A IS N POSSI# =
ALL ;,B3 =A SYLLOGISM IS =M$ 9 ! ?IRD
DEGREE4 ,B X 0 ASSUM$ T ,A IS A POSSI#
ATTRIBUTE = ALL ,B4 ,X IS NEC !N T ,A IS
POSSI# = ALL ,C4 ,= ?\< ! ASSUMP;N WE
MADE IS FALSE & N IMPOSSI#1 ! 3CLU.N IS
IMPOSSI#4 ,X IS POSSI# AL 9 ! F/ FIGURE
6BR+ AB ! IMPOSSIBIL;Y1 0ASSUM+ T ;,B
2L;GS TO ;,C4 ,= IF ;,B 2L;GS 6ALL ;,C1
& ,A IS POSSI# = ALL ;,B1 !N ,A WD 2
POSSI# = ALL ,C4 ,B ! ASSUMP;N 0 MADE T
,A IS N POSSI# = ALL ,C4
  ,WE M/ "U/& ,8T : 2L;GS 6ALL0' ) NO
LIMIT,N 9 RESPECT ( "T1 E4G4 6! PRES5T
OR 6A "PICUL> P]IOD1 B SIMPLY )\T
QUALIFIC,N4 ,= X IS 0! HELP ( S*
PREMISSES T WE MAKE SYLLOGISMS1 S9CE IF
! PREMISS IS "U/OOD ) REF];E 6! PRES5T
MO;T1 "! _C 2 A SYLLOGISM4 ,= NO?+ P]H
PREV5TS ,8MAN0' 2L;G+ AT A "PICUL> "T
6"EY?+ T IS MOV+1 I4E4 IF NO?+ ELSE 7
MOV+3 B ,8MOV+0' IS POSSI# = E HORSE2
YET ,8MAN0' IS POSSI# = NO HORSE4 ,FUR!R
LET ! MAJOR T]M 2 ,8ANIMAL0'1 ! MI4LE
,8MOV+0'1 ! ! M9OR ,8MAN0'4 ,! PREMISSES
!N W 2 Z 2F1 B ! 3CLU.N NEC1 N POSSI#4
,= MAN IS NECESS>ILY ANIMAL4 ,X IS CLE>
!N T ! UNIV]SAL M/ 2 "U/OOD SIMPLY1 )\T
LIMIT,N 9 RESPECT ( "T4
  ,AG LET ! PREMISS ;,,AB 2 UNIV]SAL &
NEGATIVE1 & ASSUME T ,A 2L;GS 6NO ;,B1 B
;,B POSSIBLY 2L;GS 6ALL ,C4 ,^!
PROPOSI;NS 2+ LAID D[N1 X IS NEC T ,A
POSSIBLY 2L;GS 6NO ,C4 ,SUPPOSE T X _C
2L;G1 & T ;,B 2L;GS TO ;,C1 Z ABV4 ,X IS
NEC !N T ,A 2L;GS 6"S ;,B3 = WE H A
SYLLOGISM 9 ! ?IRD FIGURE3 B ? IS
IMPOSSI#4 ,?US X W 2 POSSI# = ,A 62L;G
6NO ;,C2 = IF AT IS SUPPOS$ FALSE1 !
3SEQU;E IS AN IMPOSSI# "O4 ,? SYLLOGISM
!N DOES N E/ABLI% T : IS POSSI# AC 6!
DEF9I;N1 B T : DOES N NECESS>ILY 2L;G
6ANY "P (! SUBJECT 7= ? IS ! 3TRADICTORY
(! ASSUMP;N : 0 MADE3 = X 0 SUPPOS$ T ,A
NECESS>ILY 2L;GS 6"S ;,C1 B ! SYLLOGISM
P] IMPOSSIBILE E/ABLI%ES ! 3TRADICTORY :
IS OPPOS$ 6?74 ,FUR!R1 X IS CLE> AL F AN
EXAMPLE T ! 3CLU.N W N E/ABLI%
POSSIBIL;Y4 ,LET ,A 2 ,8RAV50'1 ;,B
,89TELLIG5T0'1 & ;,C ,8MAN0'4 ,A !N
2L;GS 6NO ;,B3 = NO 9TELLIG5T ?+ IS A
RAV54 ,B ;,B IS POSSI# = ALL ;,C3 = E
MAN MAY POSSIBLY 2 9TELLIG5T4 ,B ,A
NECESS>ILY 2L;GS 6NO ;,C3 S ! 3CLU.N
DOES N E/ABLI% POSSIBIL;Y4 ,B NEI IS X
ALW NEC4 ,LET ,A 2 ,8MOV+0'1 ;,B
,8SCI;E0'1 ;,C ,8MAN0'4 ,A !N W 2L;G 6NO
;,B2 B ;,B IS POSSI# = ALL ,C4 ,&!
3CLU.N W N 2 NEC4 ,= X IS N NEC T NO MAN
%D MOVE2 R X IS N NEC T ANY MAN %D MOVE4
,CLE>LY !N ! 3CLU.N E/ABLI%ES T "O T]M
DOES N NECESS>ILY 2L;G 6ANY 9/.E ( ANO!R
T]M4 ,B WE M/ TAKE \R T]MS BETT]4
  ,IF ! M9OR PREMISS IS NEGATIVE &
9DICATES POSSIBIL;Y1 F ! ACTUAL
PREMISSES TAK5 "! C 2 NO SYLLOGISM1 B IF
! PRO#MATIC PREMISS IS 3V]T$1 A
SYLLOGISM W 2 POSSI#1 Z 2F4 ,LET ,A 2L;G
6ALL ;,B1 & LET ;,B POSSIBLY 2L;G 6NO
,C4 ,IF ! T]MS >E >RANG$ ?US1 NO?+
NECESS>ILY FOLL[S3 B IF ! PROPOSI;N ,,BC
IS 3V]T$ & X IS ASSUM$ T ;,B IS POSSI# =
ALL ;,C1 A SYLLOGISM RESULTS Z 2F3 =!
T]MS >E 9 ! SAME RELATIVE POSI;NS4
,LIKEWISE IF BO? ! REL,NS >E NEGATIVE1
IF ! MAJOR PREMISS /ATES T ,A DOES N
2L;G TO ;,B1 &! M9OR PREMISS 9DICATES T
;,B MAY POSSIBLY 2L;G 6NO ,C4 ,"? !
PREMISSES ACTU,Y TAK5 NO?+ NEC RESULTS 9
ANY WAY2 B IF ! PRO#MATIC PREMISS IS
3V]T$1 WE % H A SYLLOGISM4 ,SUPPOSE T ,A
2L;GS 6NO ;,B1 & ;,B MAY POSSIBLY 2L;G
6NO ,C4 ,"? ^! -ES NO?+ NEC4 ,B IF ;,B
IS ASSUM$ 6BE POSSI# = ALL ;,C 7& ? IS
TRUE7 & IF ! PREMISS ;,,AB REMA9S Z 2F1
WE % AG H ! SAME SYLLOGISM4 ,B IF X 2
ASSUM$ T ;,B DOES N 2L;G 6ANY ;,C1 9/1D
( POSSIBLY N 2L;G+1 "! _C 2 A SYLLOGISM
ANYH[1 :E!R ! PREMISS ;,,AB IS NEGATIVE
OR A6IRMATIVE4 ,Z -MON 9/.ES (A NEC &
POSITIVE REL,N WE MAY TAKE ! T]MS :ITE-
ANIMAL-SN[3 (A NEC & NEGATIVE REL,N1
:ITE-ANIMAL-PIT*4 ,CLE>LY !N IF ! T]MS
>E UNIV]SAL1 & "O (! PREMISSES IS
ASS]TORIC1 ! O!R PRO#MATIC1 :5"E ! M9OR
PREMISS IS PRO#MATIC A SYLLOGISM ALW
RESULTS1 ONLY "S"TS X RESULTS F !
PREMISSES T >E TAK51 "S"TS X REQUIRES !
3V].N ( "O PREMISS4 ,WE H /AT$ :5 EA* (
^! HAPP5S &! R1SON :Y4 ,B IF "O (!
REL,NS IS UNIV]SAL1 ! O!R "PICUL>1 !N
:5"E ! MAJOR PREMISS IS UNIV]SAL &
PRO#MATIC1 :E!R A6IRMATIVE OR NEGATIVE1
&! "PICUL> IS A6IRMATIVE & ASS]TORIC1 "!
W 2 A P]FECT SYLLOGISM1 J Z :5 ! T]MS >E
UNIV]SAL4 ,! DEMON/R,N IS ! SAME Z 2F4
,B :5"E ! MAJOR PREMISS IS UNIV]SAL1 B
ASS]TORIC1 N PRO#MATIC1 &! M9OR IS
"PICUL> & PRO#MATIC1 :E!R BO? PREMISSES
>E NEGATIVE OR A6IRMATIVE1 OR "O IS
NEGATIVE1 ! O!R A6IRMATIVE1 9 ALL CASES
"! W 2 AN IMP]FECT SYLLOGISM4 ,ONLY "S (
!M W 2 PROV$ P] IMPOSSIBILE1 O!RS 0!
3V].N (! PRO#MATIC PREMISS1 Z HAS BE5
%[N ABV4 ,&A SYLLOGISM W 2 POSSI# 0M1NS
( 3V].N :5 ! MAJOR PREMISS IS UNIV]SAL &
ASS]TORIC1 :E!R POSITIVE OR NEGATIVE1 &!
M9OR "PICUL>1 NEGATIVE1 & PRO#MATIC1
E4G4 IF ,A 2L;GS 6ALL ;,B OR 6NO ;,B1 &
;,B MAY POSSIBLY N 2L;G 6"S ,C4 ,= IF !
PREMISS ,,BC IS 3V]T$ 9 RESPECT (
POSSIBIL;Y1 A SYLLOGISM RESULTS4 ,B :5"E
! "PICUL> PREMISS IS ASS]TORIC &
NEGATIVE1 "! _C 2 A SYLLOGISM4 ,Z 9/.ES
(! POSITIVE REL,N WE MAY TAKE ! T]MS
:ITE-ANIMAL-SN[2 (! NEGATIVE1 :ITE-
ANIMAL-PIT*4 ,=! DEMON/R,N M/ 2 MADE "?
! 9DEF9ITE NATURE (! "PICUL> PREMISS4 ,B
IF ! M9OR PREMISS IS UNIV]SAL1 &! MAJOR
"PICUL>1 :E!R EI PREMISS IS NEGATIVE OR
A6IRMATIVE1 PRO#MATIC OR ASS]TORIC1 NOH[
IS A SYLLOGISM POSSI#4 ,NOR IS A
SYLLOGISM POSSI# :5 ! PREMISSES >E
"PICUL> OR 9DEF9ITE1 :E!R PRO#MATIC OR
ASS]TORIC1 OR ! "O PRO#MATIC1 ! O!R
ASS]TORIC4 ,! DEMON/R,N IS ! SAME Z ABV4
,Z 9/.ES (! NEC & POSITIVE REL,N WE MAY
TAKE ! T]MS ANIMAL-:ITE-MAN2 (! NEC &
NEGATIVE REL,N1 ANIMAL-:ITE-G>;T4 ,X IS
EVID5T !N T IF ! MAJOR PREMISS IS
UNIV]SAL1 A SYLLOGISM ALW RESULTS1 B IF
! M9OR IS UNIV]SAL NO?+ AT ALL C "E 2
PROV$4

                  #AF

  ,:5"E "O PREMISS IS NEC1 ! O!R
PRO#MATIC1 "! W 2 A SYLLOGISM :5 ! T]MS
>E RELAT$ Z 2F2 &A P]FECT SYLLOGISM :5 !
M9OR PREMISS IS NEC4 ,IF ! PREMISSES >E
A6IRMATIVE ! 3CLU.N W 2 PRO#MATIC1 N
ASS]TORIC1 :E!R ! PREMISSES >E UNIV]SAL
OR N3 B IF "O IS A6IRMATIVE1 ! O!R
NEGATIVE1 :5 ! A6IRMATIVE IS NEC !
3CLU.N W 2 PRO#MATIC1 N NEGATIVE
ASS]TORIC2 B :5 ! NEGATIVE IS NEC !
3CLU.N W 2 PRO#MATIC NEGATIVE1 &
ASS]TORIC NEGATIVE1 :E!R ! PREMISSES >E
UNIV]SAL OR N4 ,POSSIBIL;Y 9 ! 3CLU.N M/
2 "U/OOD 9 ! SAME MANN] Z 2F4 ,"! _C 2
AN 9F];E 6! NEC NEGATIVE PROPOSI;N3 =
,8N NECESS>ILY 62L;G0' IS DI6]5T F
,8NECESS>ILY N 62L;G0'4
  ,IF ! PREMISSES >E A6IRMATIVE1 CLE>LY
! 3CLU.N : FOLL[S IS N NEC4 ,SUPPOSE ,A
NECESS>ILY 2L;GS 6ALL ;,B1 & LET ;,B 2
POSSI# = ALL ,C4 ,WE % H AN IMP]FECT
SYLLOGISM 6PROVE T ,A MAY 2L;G 6ALL ,C4
,T X IS IMP]FECT IS CLE> F ! PRO(3 = X W
2 PROV$ 9 ! SAME MANN] Z ABV4 ,AG1 LET
,A 2 POSSI# = ALL ;,B1 & LET ;,B
NECESS>ILY 2L;G 6ALL ,C4 ,WE % !N H A
SYLLOGISM 6PROVE T ,A MAY 2L;G 6ALL ;,C1
N T ,A DOES 2L;G 6ALL ;,C3 & X IS
P]FECT1 N IMP]FECT3 = X IS -PLET$
DIRECTLY "? ! ORIG9AL PREMISSES4
  ,B IF ! PREMISSES >E N SIMIL> 9
QUAL;Y1 SUPPOSE F/ T ! NEGATIVE PREMISS
IS NEC1 & LET NECESS>ILY ,A N 2 POSSI# =
ANY ;,B1 B LET ;,B 2 POSSI# = ALL ,C4 ,X
IS NEC !N T ,A 2L;GS 6NO ,C4 ,= SUPPOSE
,A 62L;G 6ALL ;,C OR 6"S ,C4 ,N[ WE
ASSUM$ T ,A IS N POSSI# = ANY ,B4 ,S9CE
!N ! NEGATIVE PROPOSI;N IS 3V]TI#1 ;,B
IS N POSSI# = ANY ,A4 ,B ,A IS SUPPOS$
62L;G 6ALL ;,C OR 6"S ,C4 ,3SEQU5TLY ;,B
W N 2 POSSI# = ANY ;,C OR = ALL ,C4 ,B X
0 ORIG9,Y LAID D[N T ;,B IS POSSI# = ALL
,C4 ,& X IS CLE> T ! POSSIBIL;Y ( 2L;G+
C 2 9F]R$1 S9CE ! FACT ( N 2L;G+ IS
9F]R$4 ,AG1 LET ! A6IRMATIVE PREMISS 2
NEC1 & LET ,A POSSIBLY N 2L;G 6ANY ;,B1
& LET ;,B NECESS>ILY 2L;G 6ALL ,C4 ,!
SYLLOGISM W 2 P]FECT1 B X W E/ABLI% A
PRO#MATIC NEGATIVE1 N AN ASS]TORIC
NEGATIVE4 ,=! MAJOR PREMISS 0 PRO#MATIC1
& FUR!R X IS N POSSI# 6PROVE ! ASS]TORIC
3CLU.N P] IMPOSSIBILE4 ,= IF X 7 SUPPOS$
T ,A 2L;GS 6"S ;,C1 & X IS LAID D[N T ,A
POSSIBLY DOES N 2L;G 6ANY ;,B1 NO
IMPOSSI# REL,N 2T ;,B & ;,C FOLL[S F ^!
PREMISSES4 ,B IF ! M9OR PREMISS IS
NEGATIVE1 :5 X IS PRO#MATIC A SYLLOGISM
IS POSSI# 03V].N1 Z ABV2 B :5 X IS NEC
NO SYLLOGISM C 2 =M$4 ,NOR AG :5 BO?
PREMISSES >E NEGATIVE1 &! M9OR IS NEC4
,! SAME T]MS Z 2F S]VE BO? =! POSITIVE
REL,N-:ITE-ANIMAL-SN[1 &=! NEGATIVE
REL,N-:ITE-ANIMAL-PIT*4
  ,! SAME REL,N W OBTA9 9 "PICUL>
SYLLOGISMS4 ,:5"E ! NEGATIVE PROPOSI;N
IS NEC1 ! 3CLU.N W 2 NEGATIVE ASS]TORIC3
E4G4 IF X IS N POSSI# T ,A %D 2L;G 6ANY
;,B1 B ;,B MAY 2L;G 6"S (! ,C'S1 X IS
NEC T ,A %D N 2L;G 6"S (! ,C'S4 ,= IF ,A
2L;GS 6ALL ;,C1 B _C 2L;G 6ANY ;,B1 NEI
C ;,B 2L;G 6ANY ,A4 ,S IF ,A 2L;GS 6ALL
;,C1 6N"O (! ,C'S C ;,B 2L;G4 ,B X 0
LAID D[N T ;,B MAY 2L;G 6"S ,C4 ,B :5 !
"PICUL> A6IRMATIVE 9 ! NEGATIVE
SYLLOGISM1 E4G4 ,,BC ! M9OR PREMISS1 OR
! UNIV]SAL PROPOSI;N 9 ! A6IRMATIVE
SYLLOGISM1 E4G4 ;,,AB ! MAJOR PREMISS1
IS NEC1 "! W N 2 AN ASS]TORIC 3CLU.N4 ,!
DEMON/R,N IS ! SAME Z 2F4 ,B IF ! M9OR
PREMISS IS UNIV]SAL1 & PRO#MATIC1 :E!R
A6IRMATIVE OR NEGATIVE1 &! MAJOR PREMISS
IS "PICUL> & NEC1 "! _C 2 A SYLLOGISM4
,PREMISSES ( ? K9D >E POSSI# BO? ": !
REL,N IS POSITIVE & NEC1 E4G4 ANIMAL-
:ITE-MAN1 & ": X IS NEC & NEGATIVE1 E4G4
ANIMAL-:ITE-G>;T4 ,B :5 ! UNIV]SAL IS
NEC1 ! "PICUL> PRO#MATIC1 IF ! UNIV]SAL
IS NEGATIVE WE MAY TAKE ! T]MS ANIMAL-
:ITE-RAV5 6ILLU/RATE ! POSITIVE REL,N1
OR ANIMAL-:ITE-PIT* 6ILLU/RATE !
NEGATIVE2 & IF ! UNIV]SAL IS A6IRMATIVE
WE MAY TAKE ! T]MS ANIMAL-:ITE-SWAN
6ILLU/RATE ! POSITIVE REL,N1 & ANIMAL-
:ITE-SN[ 6ILLU/RATE ! NEGATIVE & NEC
REL,N4 ,NOR AG IS A SYLLOGISM POSSI# :5
! PREMISSES >E 9DEF9ITE1 OR BO? "PICUL>4
,T]MS APPLICA# 9 EI CASE 6ILLU/RATE !
POSITIVE REL,N >E ANIMAL-:ITE-MAN3
6ILLU/RATE ! NEGATIVE1 ANIMAL-:ITE-
9ANIMATE4 ,=! REL,N ( ANIMAL 6"S :ITE1 &
( :ITE 6"S 9ANIMATE1 IS BO? NEC &
POSITIVE & NEC & NEGATIVE4 ,SIMIL>LY IF
! REL,N IS PRO#MATIC3 S ! T]MS MAY 2 US$
= ALL CASES4
  ,CLE>LY !N F :AT HAS BE5 SD A
SYLLOGISM RESULTS OR N F SIMIL> REL,NS (
! T]MS :E!R WE >E D1L+ ) SIMPLE EXI/;E
OR NECESS;Y1 ) ? EXCEP;N1 T IF !
NEGATIVE PREMISS IS ASS]TORIC ! 3CLU.N
IS PRO#MATIC1 B IF ! NEGATIVE PREMISS IS
NEC ! 3CLU.N IS BO? PRO#MATIC & NEGATIVE
ASS]TORIC4 ,7,X IS CLE> AL T ALL !
SYLLOGISMS >E IMP]FECT & >E P]FECT$
0M1NS (! FIGURES ABV M5;N$47'

                  #AG

  ,9 ! SECOND FIGURE :5"E BO? PREMISSES
>E PRO#MATIC1 NO SYLLOGISM IS POSSI#1
:E!R ! PREMISSES >E A6IRMATIVE OR
NEGATIVE1 UNIV]SAL OR "PICUL>4 ,B :5 "O
PREMISS IS ASS]TORIC1 ! O!R PRO#MATIC1
IF ! A6IRMATIVE IS ASS]TORIC NO
SYLLOGISM IS POSSI#1 B IF ! UNIV]SAL
NEGATIVE IS ASS]TORIC A 3CLU.N C ALW 2
DRAWN4 ,SIMIL>LY :5 "O PREMISS IS NEC1 !
O!R PRO#MATIC4 ,"H AL WE M/ "U/& ! T]M
,8POSSI#0' 9 ! 3CLU.N1 9 ! SAME S5SE Z
2F4
  ,F/ WE M/ PO9T \ T ! NEGATIVE
PRO#MATIC PROPOSI;N IS N 3V]TI#1 E4G4 IF
,A MAY 2L;G 6NO ;,B1 X DOES N FOLL[ T
;,B MAY 2L;G 6NO ,A4 ,= SUPPOSE X 6FOLL[
& ASSUME T ;,B MAY 2L;G 6NO ,A4 ,S9CE !N
PRO#MATIC A6IRM,NS >E 3V]TI# ) NEG,NS1
:E!R !Y >E 3TR>IES OR 3TRADICTORIES1 &
S9CE ;,B MAY 2L;G 6NO ;,A1 X IS CLE> T
;,B MAY 2L;G 6ALL ,A4 ,B ? IS FALSE3 =
IF ALL ? C 2 T1 X DOES N FOLL[ T ALL T C
2 ?3 3SEQU5TLY ! NEGATIVE PROPOSI;N IS N
3V]TI#4 ,FUR!R1 ^! PROPOSI;NS >E N
9COMPATI#1 ',A MAY 2L;G 6NO ,B0'1 ',B
NECESS>ILY DOES N 2L;G 6"S (! ,Z0'2 E4G4
X IS POSSI# T NO MAN %D 2 :ITE 7= X IS
AL POSSI# T E MAN %D 2 :ITE71 B X IS N
TRUE 6SAY T X IS POSSI# T NO :ITE ?+ %D
2 A MAN3 = _M :ITE ?+S >E NECESS>ILY N
M51 &! NEC 7Z WE SAW7 O!R ?AN ! POSSI#4
  ,MOREOV] X IS N POSSI# 6PROVE !
3V]TIBIL;Y ( ^! PROPOSI;NS 0A REDUCTIO
AD ABSURDUM1 I4E4 0CLAIM+ ASS5T 6!
FOLL[+ >GU;T3 ,8S9CE X IS FALSE T ;,B
MAY 2L;G 6NO ;,A1 X IS TRUE T X _C 2L;G
6NO ;,A1 =! "O /ATE;T IS ! 3TRADICTORY (
! O!R4 ,B IF ? IS S1 X IS TRUE T ;,B
NECESS>ILY 2L;GS 6"S (! ,Z3 3SEQU5TLY ,A
NECESS>ILY 2L;GS 6"S (! ,BS4 ,B ? IS
IMPOSSI#40' ,! >GU;T _C 2 ADMITT$1 = X
DOES N FOLL[ T "S ,A IS NECESS>ILY ;,B1
IF X IS N POSSI# T NO ,A %D 2 ,B4 ,=!
LATT] EXPRES.N IS US$ 9 TWO S5SES1 "O IF
,A "S IS NECESS>ILY ;,B1 ANO!R IF "S ,A
IS NECESS>ILY N ,B4 ,= X IS N TRUE 6SAY
T T : NECESS>ILY DOES N 2L;G 6"S (! ,Z
MAY POSSIBLY N 2L;G 6ANY ;,A1 J Z X IS N
TRUE 6SAY T :AT NECESS>ILY 2L;GS 6"S ,A
MAY POSSIBLY 2L;G 6ALL ,A4 ,IF ANY "O !N
%D CLAIM T 2C X IS N POSSI# = ;,C 62L;G
6ALL ;,D1 X NECESS>ILY DOES N 2L;G 6"S
;,D1 HE WD MAKE A FALSE ASSUMP;N3 = X
DOES 2L;G 6ALL ;,D1 B 2C 9 "S CASES X
2L;GS NECESS>ILY1 "!=E WE SAY T X IS N
POSSI# = X 62L;G 6ALL4 ,H;E BO? !
PROPOSI;NS ',A NECESS>ILY 2L;GS 6"S ,B0'
& ',A NECESS>ILY DOES N 2L;G 6"S ,B0' >E
OPPOS$ 6! PROPOSI;N ',A 2L;GS 6ALL ,B0'4
,SIMIL>LY AL !Y >E OPPOS$ 6! PROPOSI;N
',A MAY 2L;G 6NO ,B0'4 ,X IS CLE> !N T 9
REL,N 6:AT IS POSSI# & N POSSI#1 9 !
S5SE ORIG9,Y DEF9$1 WE M/ ASSUME1 N T ,A
NECESS>ILY 2L;GS 6"S ;,B1 B T ,A
NECESS>ILY DOES N 2L;G 6"S ,B4 ,B IF ?
IS ASSUM$1 NO ABSURD;Y RESULTS3
3SEQU5TLY NO SYLLOGISM4 ,X IS CLE> F :AT
HAS BE5 SD T ! NEGATIVE PROPOSI;N IS N
3V]TI#4
  ,? 2+ PROV$1 SUPPOSE X POSSI# T ,A MAY
2L;G 6NO ;,B & 6ALL ,C4 ,0M1NS ( 3V].N
NO SYLLOGISM W RESULT3 =! MAJOR PREMISS1
Z HAS BE5 SD1 IS N 3V]TI#4 ,NOR C A PRO(
2 OBTA9$ 0A REDUCTIO AD ABSURDUM3 = IF X
IS ASSUM$ T ;,B C 2L;G 6ALL ;,C1 NO
FALSE 3SEQU;E RESULTS3 = ,A MAY 2L;G BO?
6ALL ;,C & 6NO ,C4 ,9 G5]AL1 IF "! IS A
SYLLOGISM1 X IS CLE> T XS 3CLU.N W 2
PRO#MATIC 2C NEI (! PREMISSES IS
ASS]TORIC2 & ? M/ 2 EI A6IRMATIVE OR
NEGATIVE4 ,B NEI IS POSSI#4 ,SUPPOSE !
3CLU.N IS A6IRMATIVE3 X W 2 PROV$ 0AN
EXAMPLE T ! PR$ICATE _C 2L;G 6! SUBJECT4
,SUPPOSE ! 3CLU.N IS NEGATIVE3 X W 2
PROV$ T X IS N PRO#MATIC B NEC4 ,LET ,A
2 :ITE1 ;,B MAN1 ;,C HORSE4 ,X IS POSSI#
!N = ,A 62L;G 6ALL (! "O & 6N"O (! O!R4
,B X IS N POSSI# = ;,B 62L;G NOR N 62L;G
TO ;,C4 ,T X IS N POSSI# = X 62L;G1 IS
CLE>4 ,= NO HORSE IS A MAN4 ,NEI IS X
POSSI# = X N 62L;G4 ,= X IS NEC T NO
HORSE %D 2 A MAN1 B ! NEC WE F.D 6BE
DI6]5T F ! POSSI#4 ,NO SYLLOGISM !N
RESULTS4 ,A SIMIL> PRO( C 2 GIV5 IF !
MAJOR PREMISS IS NEGATIVE1 ! M9OR
A6IRMATIVE1 OR IF BO? >E A6IRMATIVE OR
NEGATIVE4 ,! DEMON/R,N C 2 MADE 0M1NS (!
SAME T]MS4 ,& :5"E "O PREMISS IS
UNIV]SAL1 ! O!R "PICUL>1 OR BO? >E
"PICUL> OR 9DEF9ITE1 OR 9 :AT"E O!R WAY
! PREMISSES C 2 ALT]$1 ! PRO( W ALW
PROCE$ "? ! SAME T]MS4 ,CLE>LY !N1 IF
BO? ! PREMISSES >E PRO#MATIC1 NO
SYLLOGISM RESULTS4

                  #AH

  ,B IF "O PREMISS IS ASS]TORIC1 ! O!R
PRO#MATIC1 IF ! A6IRMATIVE IS ASS]TORIC
&! NEGATIVE PRO#MATIC NO SYLLOGISM W 2
POSSI#1 :E!R ! PREMISSES >E UNIV]SAL OR
"PICUL>4 ,! PRO( IS ! SAME Z ABV1 &
0M1NS (! SAME T]MS4 ,B :5 ! A6IRMATIVE
PREMISS IS PRO#MATIC1 &! NEGATIVE
ASS]TORIC1 WE % H A SYLLOGISM4 ,SUPPOSE
,A 2L;GS 6NO ;,B1 B C 2L;G 6ALL ,C4 ,IF
! NEGATIVE PROPOSI;N IS 3V]T$1 ;,B W
2L;G 6NO ,A4 ,B EX HYPO!SI C 2L;G 6ALL
;,C3 S A SYLLOGISM IS MADE1 PROV+ 0M1NS
(! F/ FIGURE T ;,B MAY 2L;G 6NO ,C4
,SIMIL>LY AL IF ! M9OR PREMISS IS
NEGATIVE4 ,B IF BO? PREMISSES >E
NEGATIVE1 "O 2+ ASS]TORIC1 ! O!R
PRO#MATIC1 NO?+ FOLL[S NECESS>ILY F ^!
PREMISSES Z !Y /&1 B IF ! PRO#MATIC
PREMISS IS 3V]T$ 96XS -PLE;T>Y
A6IRMATIVE A SYLLOGISM IS =M$ 6PROVE T
;,B MAY 2L;G 6NO ;,C1 Z 2F3 = WE % AG H
! F/ FIGURE4 ,B IF BO? PREMISSES >E
A6IRMATIVE1 NO SYLLOGISM W 2 POSSI#4 ,?
>RANGE;T ( T]MS IS POSSI# BO? :5 ! REL,N
IS POSITIVE1 E4G4 H1L?1 ANIMAL1 MAN1 &
:5 X IS NEGATIVE1 E4G4 H1L?1 HORSE1 MAN4
  ,! SAME W HOLD GD IF ! SYLLOGISMS >E
"PICUL>4 ,:5"E ! A6IRMATIVE PROPOSI;N IS
ASS]TORIC1 :E!R UNIV]SAL OR "PICUL>1 NO
SYLLOGISM IS POSSI# 7? IS PROV$ SIMIL>LY
& 0! SAME EXAMPLES Z ABV71 B :5 !
NEGATIVE PROPOSI;N IS ASS]TORIC1 A
3CLU.N C 2 DRAWN 0M1NS ( 3V].N1 Z 2F4
,AG IF BO? ! REL,NS >E NEGATIVE1 &!
ASS]TORIC PROPOSI;N IS UNIV]SAL1 AL? NO
3CLU.N FOLL[S F ! ACTUAL PREMISSES1 A
SYLLOGISM C 2 OBTA9$ 03V]T+ ! PRO#MATIC
PREMISS 96XS -PLE;T>Y A6IRMATIVE Z 2F4
,B IF ! NEGATIVE PROPOSI;N IS ASS]TORIC1
B "PICUL>1 NO SYLLOGISM IS POSSI#1 :E!R
! O!R PREMISS IS A6IRMATIVE OR NEGATIVE4
,NOR C A 3CLU.N 2 DRAWN :5 BO? PREMISSES
>E 9DEF9ITE1 :E!R A6IRMATIVE OR
NEGATIVE1 OR "PICUL>4 ,! PRO( IS ! SAME
& 0! SAME T]MS4

                  #AI

  ,IF "O (! PREMISSES IS NEC1 ! O!R
PRO#MATIC1 !N IF ! NEGATIVE IS NEC A
SYLLOGI/IC 3CLU.N C 2 DRAWN1 N M]ELY A
NEGATIVE PRO#MATIC B AL A NEGATIVE
ASS]TORIC 3CLU.N2 B IF ! A6IRMATIVE
PREMISS IS NEC1 NO 3CLU.N IS POSSI#4
,SUPPOSE T ,A NECESS>ILY 2L;GS 6NO ;,B1
B MAY 2L;G 6ALL ,C4 ,IF ! NEGATIVE
PREMISS IS 3V]T$ ;,B W 2L;G 6NO ,A3 B ,A
EX HYPO!SI IS CAPA# ( 2L;G+ 6ALL ;,C3 S
ONCE M A 3CLU.N IS DRAWN 0! F/ FIGURE T
;,B MAY 2L;G 6NO ,C4 ,B AT ! SAME "T X
IS CLE> T ;,B W N 2L;G 6ANY ,C4 ,=
ASSUME T X DOES3 !N IF ,A _C 2L;G 6ANY
;,B1 & ;,B 2L;GS 6"S (! ,C'S1 ,A _C 2L;G
6"S (! ,C'S3 B EX HYPO!SI X MAY 2L;G
6ALL4 ,A SIMIL> PRO( C 2 GIV5 IF ! M9OR
PREMISS IS NEGATIVE4 ,AG LET !
A6IRMATIVE PROPOSI;N 2 NEC1 &! O!R
PRO#MATIC2 I4E4 SUPPOSE T ,A MAY 2L;G
6NO ;,B1 B NECESS>ILY 2L;GS 6ALL ,C4 ,:5
! T]MS >E >RANG$ 9 ? WAY1 NO SYLLOGISM
IS POSSI#4 ,=

7#A7 X "S"TS TURNS \ T ;,B NECESS>ILY
  DOES N 2L;G TO ;,C4 ,LET ,A 2 :ITE1
  ;,B MAN1 ;,C SWAN4 ,:ITE !N NECESS>ILY
  2L;GS 6SWAN1 B MAY 2L;G 6NO MAN2 & MAN
  NECESS>ILY 2L;GS 6NO SWAN2 ,CLE>LY !N
  WE _C DRAW A PRO#MATIC 3CLU.N2 = T :
  IS NEC IS ADMITT$LY 4T9CT F T : IS
  POSSI#4
7#B7 ,NOR AG C WE DRAW A NEC 3CLU.N3 = T
  PRESUPPOSES T BO? PREMISSES >E NEC1 OR
  AT ANY RATE ! NEGATIVE PREMISS4
7#C7 ,FUR!R X IS POSSI# AL1 :5 ! T]MS >E
  S >RANG$1 T ;,B %D 2L;G TO ;,C3 = NO?+
  PREV5TS ;,C FALL+ "U ;,B1 ,A 2+ POSSI#
  = ALL ;,B1 & NECESS>ILY 2L;G+ TO ;,C2
  E4G4 IF ;,C /&S = ,8AWAKE0'1 ;,B =
  ,8ANIMAL0'1 ;,A = ,8MO;N0'4 ,= MO;N
  NECESS>ILY 2L;GS 6:AT IS AWAKE1 & IS
  POSSI# = E ANIMAL3 & "EY?+ T IS AWAKE
  IS ANIMAL4 ,CLE>LY !N ! 3CLU.N _C 2 !
  NEGATIVE ASS];N1 IF ! REL,N M/ 2
  POSITIVE :5 ! T]MS >E RELAT$ Z ABV4
  ,NOR C ! OPPOSITE A6IRM,NS 2 E/ABLI%$3
  3SEQU5TLY NO SYLLOGISM IS POSSI#4 ,A
  SIMIL> PRO( IS POSSI# IF ! MAJOR
  PREMISS IS A6IRMATIVE4

  ,B IF ! PREMISSES >E SIMIL> 9 QUAL;Y1
:5 !Y >E NEGATIVE A SYLLOGISM C ALW 2
=M$ 03V]T+ ! PRO#MATIC PREMISS 96XS
-PLE;T>Y A6IRMATIVE Z 2F4 ,SUPPOSE ,A
NECESS>ILY DOES N 2L;G TO ;,B1 &
POSSIBLY MAY N 2L;G TO ;,C3 IF !
PREMISSES >E 3V]T$ ;,B 2L;GS 6NO ;,A1 &
,A MAY POSSIBLY 2L;G 6ALL ;,C3 ?US WE H
! F/ FIGURE4 ,SIMIL>LY IF ! M9OR PREMISS
IS NEGATIVE4 ,B IF ! PREMISSES >E
A6IRMATIVE "! _C 2 A SYLLOGISM4 ,CLE>LY
! 3CLU.N _C 2 A NEGATIVE ASS]TORIC OR A
NEGATIVE NEC PROPOSI;N 2C NO NEGATIVE
PREMISS HAS BE5 LAID D[N EI 9 !
ASS]TORIC OR 9 ! NEC MODE4 ,NOR C !
3CLU.N 2 A PRO#MATIC NEGATIVE PROPOSI;N4
,= IF ! T]MS >E S RELAT$1 "! >E CASES 9
: ;,B NECESS>ILY W N 2L;G TO ;,C2 E4G4
SUPPOSE T ,A IS :ITE1 ;,B SWAN1 ;,C MAN4
,NOR C ! OPPOSITE A6IRM,NS 2 E/ABLI%$1
S9CE WE H %[N A CASE 9 : ;,B NECESS>ILY
DOES N 2L;G TO ;,C4 ,A SYLLOGISM !N IS N
POSSI# AT ALL4
  ,SIMIL> REL,NS W OBTA9 9 "PICUL>
SYLLOGISMS4 ,= :5"E ! NEGATIVE PROPOSI;N
IS UNIV]SAL & NEC1 A SYLLOGISM W ALW 2
POSSI# 6PROVE BO? A PRO#MATIC &A
NEGATIVE ASS]TORIC PROPOSI;N 7! PRO(
PROCE$S 03V].N72 B :5 ! A6IRMATIVE
PROPOSI;N IS UNIV]SAL & NEC1 NO
SYLLOGI/IC 3CLU.N C 2 DRAWN4 ,? C 2
PROV$ 9 ! SAME WAY Z = UNIV]SAL
PROPOSI;NS1 & 0! SAME T]MS4 ,NOR IS A
SYLLOGI/IC 3CLU.N POSSI# :5 BO?
PREMISSES >E A6IRMATIVE3 ? AL MAY 2
PROV$ Z ABV4 ,B :5 BO? PREMISSES >E
NEGATIVE1 &! PREMISS T DEF9ITELY
4CONNECTS TWO T]MS IS UNIV]SAL & NEC1
?\< NO?+ FOLL[S NECESS>ILY F ! PREMISSES
Z !Y >E /AT$1 A 3CLU.N C 2 DRAWN Z ABV
IF ! PRO#MATIC PREMISS IS 3V]T$ 96XS
-PLE;T>Y A6IRMATIVE4 ,B IF BO? >E
9DEF9ITE OR "PICUL>1 NO SYLLOGISM C 2
=M$4 ,! SAME PRO( W S]VE1 &! SAME T]MS4
  ,X IS CLE> !N F :AT HAS BE5 SD T IF !
UNIV]SAL & NEGATIVE PREMISS IS NEC1 A
SYLLOGISM IS ALW POSSI#1 PROV+ N M]ELY A
NEGATIVE PRO#MATIC1 B AL A NEGATIVE
ASS]TORIC PROPOSI;N2 B IF ! A6IRMATIVE
PREMISS IS NEC NO 3CLU.N C 2 DRAWN4 ,X
IS CLE> TOO T A SYLLOGISM IS POSSI# OR N
"U ! SAME 3DI;NS :E!R ! MODE (!
PREMISSES IS ASS]TORIC OR NEC4 ,& X IS
CLE> T ALL ! SYLLOGISMS >E IMP]FECT1 &
>E -PLET$ 0M1NS (! FIGURES M5;N$4

                  #BJ

,9 ! LA/ FIGURE A SYLLOGISM IS POSSI#
  :E!R BO? OR ONLY "O (! PREMISSES IS
  PRO#MATIC4 ,:5 ! PREMISSES >E
  PRO#MATIC ! 3CLU.N W 2 PRO#MATIC2 & AL
  :5 "O PREMISS IS PRO#MATIC1 ! O!R
  ASS]TORIC4 ,B :5 ! O!R PREMISS IS NEC1
  IF X IS A6IRMATIVE ! 3CLU.N W 2 NEI
  NEC OR ASS]TORIC2 B IF X IS NEGATIVE !
  SYLLOGISM W RESULT 9 A NEGATIVE
  ASS]TORIC PROPOSI;N1 Z ABV4 ,9 ^! AL
  WE M/ "U/& ! EXPRES.N ,8POSSI#0' 9 !
  3CLU.N 9 ! SAME WAY Z 2F4
,F/ LET ! PREMISSES 2 PRO#MATIC &
  SUPPOSE T BO? ;,A & ;,B MAY POSSIBLY
  2L;G 6E ,C4 ,S9CE !N ! A6IRMATIVE
  PROPOSI;N IS 3V]TI# 96A "PICUL>1 & ;,B
  MAY POSSIBLY 2L;G 6E ;,C1 X FOLL[S T
  ;,C MAY POSSIBLY 2L;G 6"S ,B4 ,S1 IF
  ,A IS POSSI# = E ;,C1 & ;,C IS POSSI#
  = "S (! ,BS1 !N ,A IS POSSI# = "S (!
  ,BS4 ,= WE H GOT ! F/ FIGURE4 ,& ,A IF
  MAY POSSIBLY 2L;G 6NO ;,C1 B ;,B MAY
  POSSIBLY 2L;G 6ALL ;,C1 X FOLL[S T ,A
  MAY POSSIBLY N 2L;G 6"S ;,B3 = WE % H
  ! F/ FIGURE AG 03V].N4 ,B IF BO?
  PREMISSES %D 2 NEGATIVE NO NEC 3SEQU;E
  W FOLL[ F !M Z !Y >E /AT$1 B IF !
  PREMISSES >E 3V]T$ 96_! CORRESPOND+
  A6IRMATIVES "! W 2 A SYLLOGISM Z 2F4
  ,= IF ;,A & ;,B MAY POSSIBLY N 2L;G TO
  ;,C1 IF ,8MAY POSSIBLY 2L;G0' IS
  SUB/ITUT$ WE % AG H ! F/ FIGURE 0M1NS
  ( 3V].N4 ,B IF "O (! PREMISSES IS
  UNIV]SAL1 ! O!R "PICUL>1 A SYLLOGISM W
  2 POSSI#1 OR N1 "U ! >RANGE;T (! T]MS
  Z 9 ! CASE ( ASS]TORIC PROPOSI;NS4
  ,SUPPOSE T ,A MAY POSSIBLY 2L;G 6ALL
  ;,C1 & ;,B 6"S ,C4 ,WE % H ! F/ FIGURE
  AG IF ! "PICUL> PREMISS IS 3V]T$4 ,=
  IF ,A IS POSSI# = ALL ;,C1 & ;,C = "S
  (! ,BS1 !N ,A IS POSSI# = "S (! ,BS4
  ,SIMIL>LY IF ! PROPOSI;N ,,BC IS
  UNIV]SAL4 ,LIKEWISE AL IF ! PROPOSI;N
  ;,,AC IS NEGATIVE1 &! PROPOSI;N ,,BC
  A6IRMATIVE3 = WE % AG H ! F/ FIGURE
  03V].N4 ,B IF BO? PREMISSES %D 2
  NEGATIVE-! "O UNIV]SAL &! O!R "PICUL>-
  AL? NO SYLLOGI/IC 3CLU.N W FOLL[ F !
  PREMISSES Z !Y >E PUT1 X W FOLL[ IF !Y
  >E 3V]T$1 Z ABV4 ,B :5 BO? PREMISSES
  >E 9DEF9ITE OR "PICUL>1 NO SYLLOGISM C
  2 =M$3 = ,A M/ 2L;G "S"TS 6ALL ;,B &
  "S"TS 6NO ,B4 ,6ILLU/RATE ! A6IRMATIVE
  REL,N TAKE ! T]MS ANIMAL-MAN-:ITE2
  6ILLU/RATE ! NEGATIVE1 TAKE ! T]MS
  HORSE-MAN-:ITE--:ITE 2+ ! MI4LE T]M4

                  #BA

  ,IF "O PREMISS IS PURE1 ! O!R
PRO#MATIC1 ! 3CLU.N W 2 PRO#MATIC1 N
PURE2 &A SYLLOGISM W 2 POSSI# "U ! SAME
>RANGE;T (! T]MS Z 2F4 ,F/ LET !
PREMISSES 2 A6IRMATIVE3 SUPPOSE T ,A
2L;GS 6ALL ;,C1 & ;,B MAY POSSIBLY 2L;G
6ALL ,C4 ,IF ! PROPOSI;N ,,BC IS 3V]T$1
WE % H ! F/ FIGURE1 &! 3CLU.N T ,A MAY
POSSIBLY 2L;G 6"S (! ,BS4 ,= :5 "O (!
PREMISSES 9 ! F/ FIGURE IS PRO#MATIC1 !
3CLU.N AL 7Z WE SAW7 IS PRO#MATIC4
,SIMIL>LY IF ! PROPOSI;N ,,BC IS PURE1
;,,AC PRO#MATIC2 OR IF ;,,AC IS
NEGATIVE1 ,,BC A6IRMATIVE1 NO MATT] : (!
TWO IS PURE2 9 BO? CASES ! 3CLU.N W 2
PRO#MATIC3 =! F/ FIGURE IS OBTA9$ ONCE
M1 & X HAS BE5 PROV$ T IF "O PREMISS IS
PRO#MATIC 9 T FIGURE ! 3CLU.N AL W 2
PRO#MATIC4 ,B IF ! M9OR PREMISS ,,BC IS
NEGATIVE1 OR IF BO? PREMISSES >E
NEGATIVE1 NO SYLLOGI/IC 3CLU.N C 2 DRAWN
F ! PREMISSES Z !Y /&1 B IF !Y >E 3V]T$
A SYLLOGISM IS OBTA9$ Z 2F4
  ,IF "O (! PREMISSES IS UNIV]SAL1 ! O!R
"PICUL>1 !N :5 BO? >E A6IRMATIVE1 OR :5
! UNIV]SAL IS NEGATIVE1 ! "PICUL>
A6IRMATIVE1 WE % H ! SAME SORT (
SYLLOGISMS3 = ALL >E -PLET$ 0M1NS (! F/
FIGURE4 ,S X IS CLE> T WE % H N A PURE B
A PRO#MATIC SYLLOGI/IC 3CLU.N4 ,B IF !
A6IRMATIVE PREMISS IS UNIV]SAL1 !
NEGATIVE "PICUL>1 ! PRO( W PROCE$ 0A
REDUCTIO AD IMPOSSIBILE4 ,SUPPOSE T ;,B
2L;GS 6ALL ;,C1 & ,A MAY POSSIBLY N 2L;G
6"S ;,C3 X FOLL[S T MAY POSSIBLY N 2L;G
6"S ,B4 ,= IF ,A NECESS>ILY 2L;GS 6ALL
;,B1 & ;,B 7Z HAS BE5 ASSUM$7 2L;GS 6ALL
;,C1 ,A W NECESS>ILY 2L;G 6ALL ;,C3 = ?
HAS BE5 PROV$ 2F4 ,B X 0 ASSUM$ AT !
\TSET T ,A MAY POSSIBLY N 2L;G 6"S ,C4
  ,:5"E BO? PREMISSES >E 9DEF9ITE OR
"PICUL>1 NO SYLLOGISM W 2 POSSI#4 ,!
DEMON/R,N IS ! SAME Z 0 GIV5 9 ! CASE (
UNIV]SAL PREMISSES1 & PROCE$S 0M1NS (!
SAME T]MS4

                  #BB

  ,IF "O (! PREMISSES IS NEC1 ! O!R
PRO#MATIC1 :5 ! PREMISSES >E A6IRMATIVE
A PRO#MATIC A6IRMATIVE 3CLU.N C ALW 2
DRAWN2 :5 "O PROPOSI;N IS A6IRMATIVE1 !
O!R NEGATIVE1 IF ! A6IRMATIVE IS NEC A
PRO#MATIC NEGATIVE C 2 9F]R$2 B IF !
NEGATIVE PROPOSI;N IS NEC BO? A
PRO#MATIC &A PURE NEGATIVE 3CLU.N >E
POSSI#4 ,B A NEC NEGATIVE 3CLU.N W N 2
POSSI#1 ANY M ?AN 9 ! O!R FIGURES4
,SUPPOSE F/ T ! PREMISSES >E A6IRMATIVE1
I4E4 T ,A NECESS>ILY 2L;GS 6ALL ;,C1 &
;,B MAY POSSIBLY 2L;G 6ALL ,C4 ,S9CE !N
,A M/ 2L;G 6ALL ;,C1 & ;,C MAY 2L;G 6"S
;,B1 X FOLL[S T ,A MAY 7N DOES7 2L;G 6"S
;,B3 = S X RESULT$ 9 ! F/ FIGURE4 ,A
SIMIL> PRO( MAY 2 GIV5 IF ! PROPOSI;N
,,BC IS NEC1 & ;,,AC IS PRO#MATIC4 ,AG
SUPPOSE "O PROPOSI;N IS A6IRMATIVE1 !
O!R NEGATIVE1 ! A6IRMATIVE 2+ NEC3 I4E4
SUPPOSE ,A MAY POSSIBLY 2L;G 6NO ;,C1 B
;,B NECESS>ILY 2L;GS 6ALL ,C4 ,WE % H !
F/ FIGURE ONCE M3 &-S9CE ! NEGATIVE
PREMISS IS PRO#MATIC-X IS CLE> T !
3CLU.N W 2 PRO#MATIC3 = :5 ! PREMISSES
/& ?US 9 ! F/ FIGURE1 ! 3CLU.N 7Z WE
F.D7 IS PRO#MATIC4 ,B IF ! NEGATIVE
PREMISS IS NEC1 ! 3CLU.N W 2 N ONLY T ,A
MAY POSSIBLY N 2L;G 6"S ;,B B AL T X
DOES N 2L;G 6"S ,B4 ,= SUPPOSE T ,A
NECESS>ILY DOES N 2L;G TO ;,C1 B ;,B MAY
2L;G 6ALL ,C4 ,IF ! A6IRMATIVE PROPOSI;N
,,BC IS 3V]T$1 WE % H ! F/ FIGURE1 &!
NEGATIVE PREMISS IS NEC4 ,B :5 !
PREMISSES /OOD ?US1 X RESULT$ T ,A MI<T
POSSIBLY N 2L;G 6"S ;,C1 & T X DID N
2L;G 6"S ;,C2 3SEQU5TLY "H X FOLL[S T ,A
DOES N 2L;G 6"S ,B4 ,B :5 ! M9OR PREMISS
IS NEGATIVE1 IF X IS PRO#MATIC WE % H A
SYLLOGISM 0ALT]+ ! PREMISS 96XS -PLE;T>Y
A6IRMATIVE1 Z 2F2 B IF X IS NEC NO
SYLLOGISM C 2 =M$4 ,= ,A "S"TS
NECESS>ILY 2L;GS 6ALL ;,B1 & "S"TS _C
POSSIBLY 2L;G 6ANY ,B4 ,6ILLU/RATE ! =M]
TAKE ! T]MS SLEEP-SLEEP+ HORSE-MAN2
6ILLU/RATE ! LATT] TAKE ! T]MS SLEEP-
WAK+ HORSE-MAN4
  ,SIMIL> RESULTS W OBTA9 IF "O (! T]MS
IS RELAT$ UNIV]S,Y 6! MI4LE1 ! O!R 9 "P4
,IF BO? PREMISSES >E A6IRMATIVE1 !
3CLU.N W 2 PRO#MATIC1 N PURE2 & AL :5 "O
PREMISS IS NEGATIVE1 ! O!R A6IRMATIVE1 !
LATT] 2+ NEC4 ,B :5 ! NEGATIVE PREMISS
IS NEC1 ! 3CLU.N AL W 2 A PURE NEGATIVE
PROPOSI;N2 =! SAME K9D ( PRO( C 2 GIV5
:E!R ! T]MS >E UNIV]SAL OR N4 ,=!
SYLLOGISMS M/ 2 MADE P]FECT 0M1NS (! F/
FIGURE1 S T A RESULT : FOLL[S 9 ! F/
FIGURE FOLL[S AL 9 ! ?IRD4 ,B :5 ! M9OR
PREMISS IS NEGATIVE & UNIV]SAL1 IF X IS
PRO#MATIC A SYLLOGISM C 2 =M$ 0M1NS (
3V].N2 B IF X IS NEC A SYLLOGISM IS N
POSSI#4 ,! PRO( W FOLL[ ! SAME C\RSE Z
": ! PREMISSES >E UNIV]SAL2 &! SAME T]MS
MAY 2 US$4
  ,X IS CLE> !N 9 ? FIGURE AL :5 & H[ A
SYLLOGISM C 2 =M$1 & :5 ! 3CLU.N IS
PRO#MATIC1 & :5 X IS PURE4 ,X IS EVID5T
AL T ALL SYLLOGISMS 9 ? FIGURE >E
IMP]FECT1 & T !Y >E MADE P]FECT 0M1NS (!
F/ FIGURE4
                  #BC

  ,X IS CLE> F :AT HAS BE5 SD T !
SYLLOGISMS 9 ^! FIGURES >E MADE P]FECT
0M1NS ( UNIV]SAL SYLLOGISMS 9 ! F/
FIGURE & >E REDUC$ 6!M4 ,T E SYLLOGISM
)\T QUALIFIC,N C 2 S TR1T$1 W 2 CLE>
PRES5TLY1 :5 X HAS BE5 PROV$ T E
SYLLOGISM IS =M$ "? "O OR O!R ( ^!
FIGURES4
  ,X IS NEC T E DEMON/R,N & E SYLLOGISM
%D PROVE EI T "S?+ 2L;GS OR T X DOES N1
& ? EI UNIV]S,Y OR 9 "P1 & FUR!R EI
O/5SIVELY OR HYPO!TIC,Y4 ,"O SORT (
HYPO!TICAL PRO( IS ! REDUCTIO AD
IMPOSSIBILE4 ,LET U SP1K F/ ( O/5SIVE
SYLLOGISMS3 = AF ^! H BE5 PO9T$ \ ! TRU?
( \R 3T5;N W 2 CLE> ) REG>D 6^? : >E
PROV$ P] IMPOSSIBILE1 & 9 G5]AL
HYPO!TIC,Y4
  ,IF !N "O WANTS 6PROVE SYLLOGI/IC,Y
;,A ( ;,B1 EI Z AN ATTRIBUTE ( X OR Z N
AN ATTRIBUTE ( X1 "O M/ ASS]T "S?+ (
"S?+ ELSE4 ,IF N[ ,A %D 2 ASS]T$ ( ;,B1
! PROPOSI;N ORIG9,Y 9 "Q W H BE5 ASSUM$4
,B IF ,A %D 2 ASS]T$ ( ;,C1 B ;,C %D N 2
ASS]T$ ( ANY?+1 NOR ANY?+ ( X1 NOR ANY?+
ELSE ( ;,A1 NO SYLLOGISM W 2 POSSI#4 ,=
NO?+ NECESS>ILY FOLL[S F ! ASS];N ( "S
"O ?+ 3C]N+ "S O!R S+LE ?+4 ,?US WE M/
TAKE ANO!R PREMISS Z WELL4 ,IF !N ,A 2
ASS]T$ ( "S?+ ELSE1 OR "S?+ ELSE ( ;,A1
OR "S?+ DI6]5T ( ;,C1 NO?+ PREV5TS A
SYLLOGISM 2+ =M$1 B X W N 2 9 REL,N TO
;,B "? ! PREMISSES TAK54 ,NOR :5 ;,C
2L;GS 6"S?+ ELSE1 & T 6"S?+ ELSE & S ON1
NO 3NEXION H["E 2+ MADE ) ;,B1 W A
SYLLOGISM 2 POSSI# 3C]N+ ,A 9 XS REL,N
TO ;,B4 ,= 9 G5]AL WE /AT$ T NO
SYLLOGISM C E/ABLI% ! ATTRIBU;N ( "O ?+
6ANO!R1 UN.S "S MI4LE T]M IS TAK51 : IS
"SH[ RELAT$ 6EA* 0WAY ( PR$IC,N4 ,=!
SYLLOGISM 9 G5]AL IS MADE \ ( PREMISSES1
&A SYLLOGISM REF]R+ 6? \ ( PREMISSES )!
SAME REF];E1 &A SYLLOGISM RELAT+ ? 6T
PROCE$S "? PREMISSES : RELATE ? 6T4 ,B X
IS IMPOSSI# 6TAKE A PREMISS 9 REF];E TO
;,B1 IF WE NEI A6IRM NOR D5Y ANY?+ ( X2
OR AG 6TAKE A PREMISS RELAT+ ,A TO ;,B1
IF WE TAKE NO?+ -MON1 B A6IRM OR D5Y
PECULI> ATTRIBUTES ( EA*4 ,S WE M/ TAKE
"S?+ MIDWAY 2T ! TWO1 : W 3NECT !
PR$IC,NS1 IF WE >E 6H A SYLLOGISM RELAT+
? 6T4 ,IF !N WE M/ TAKE "S?+ -MON 9
REL,N 6BO?1 & ? IS POSSI# 9 ?REE WAYS
7EI 0PR$ICAT+ ;,A ( ;,C1 & ;,C ( ;,B1 OR
;,C ( BO?1 OR BO? ( ,C71 & ^! >E !
FIGURES ( : WE H SPOK51 X IS CLE> T E
SYLLOGISM M/ 2 MADE 9 "O OR O!R ( ^!
FIGURES4 ,! >GU;T IS ! SAME IF S"EAL
MI4LE T]MS %D 2 NEC 6E/ABLI% ! REL,N TO
;,B2 =! FIGURE W 2 ! SAME :E!R "! IS "O
MI4LE T]M OR _M4
  ,X IS CLE> !N T ! O/5SIVE SYLLOGISMS
>E E6ECT$ 0M1NS (! A=ESD FIGURES2 ^!
3SID],NS W %[ T REDUC;NES AD AL >E
E6ECT$ 9 ! SAME WAY4 ,= ALL :O E6ECT AN
>GU;T P] IMPOSSIBILE 9F] SYLLOGI/IC,Y
:AT IS FALSE1 & PROVE ! ORIG9AL 3CLU.N
HYPO!TIC,Y :5 "S?+ IMPOSSI# RESULTS F !
ASSUMP;N ( XS 3TRADICTORY2 E4G4 T !
DIAGONAL (! SQU>E IS 9COMM5SURATE )!
SIDE1 2C ODD NUMB]S >E EQUAL 6EV5S IF X
IS SUPPOS$ 6BE -M5SURATE4 ,"O 9F]S
SYLLOGI/IC,Y T ODD NUMB]S -E \ EQUAL
6EV5S1 & "O PROVES HYPO!TIC,Y !
9COMM5SURABIL;Y (! DIAGONAL1 S9CE A
FALSEHOOD RESULTS "? 3TRADICT+ ?4 ,= ?
WE F.D 6BE R1SON+ P] IMPOSSIBILE1 VIZ4
PROV+ "S?+ IMPOSSI# 0M1NS ( AN HYPO!SIS
3C$$ AT ! 2G9N+4 ,3SEQU5TLY1 S9CE !
FALSEHOOD IS E/ABLI%$ 9 REDUC;NS AD
IMPOSSIBILE 0AN O/5SIVE SYLLOGISM1 &!
ORIG9AL 3CLU.N IS PROV$ HYPO!TIC,Y1 & WE
H ALR /AT$ T O/5SIVE SYLLOGISMS >E
E6ECT$ 0M1NS ( ^! FIGURES1 X IS EVID5T T
SYLLOGISMS P] IMPOSSIBILE AL W 2 MADE "?
^! FIGURES4 ,LIKEWISE ALL ! O!R
HYPO!TICAL SYLLOGISMS3 = 9 E CASE !
SYLLOGISM L1DS UP 6! PROPOSI;N T IS
SUB/ITUT$ =! ORIG9AL !SIS2 B ! ORIG9AL
!SIS IS R1*$ 0M1NS (A 3CES.N OR "S O!R
HYPO!SIS4 ,B IF ? IS TRUE1 E DEMON/R,N &
E SYLLOGISM M/ 2 =M$ 0M1NS (! ?REE
FIGURES M5;N$ ABV4 ,B :5 ? HAS BE5 %[N X
IS CLE> T E SYLLOGISM IS P]FECT$ 0M1NS (
! F/ FIGURE & IS REDUCI# 6! UNIV]SAL
SYLLOGISMS 9 ? FIGURE4


                  #BD

  ,FUR!R 9 E SYLLOGISM "O (! PREMISSES
M/ 2 A6IRMATIVE1 & UNIV]SAL;Y M/ 2
PRES5T3 UN.S "O (! PREMISSES IS UNIV]SAL
EI A SYLLOGISM W N 2 POSSI#1 OR X W N
REF] 6! SUBJECT PROPOS$1 OR ! ORIG9AL
POSI;N W 2 BE7$4 ,SUPPOSE WE H 6PROVE T
PL1SURE 9 MUSIC IS GD4 ,IF "O %D CLAIM Z
A PREMISS T PL1SURE IS GD )\T A4+
,8ALL0'1 NO SYLLOGISM W 2 POSSI#2 IF "O
%D CLAIM T "S PL1SURE IS GD1 !N IF X IS
DI6]5T F PL1SURE 9 MUSIC1 X IS N
RELEVANT 6! SUBJECT PROPOS$2 IF X IS ? V
PL1SURE1 "O IS ASSUM+ T : 0 PROPOS$ AT !
\TSET 6BE PROV$4 ,? IS M OBVI\S 9
GEOMETRICAL PRO(S1 E4G4 T ! ANGLES AT !
BASE ( AN ISOSCELES TRIANGLE >E EQUAL4
,SUPPOSE ! L9ES ;,A & ;,B H BE5 DRAWN 6!
C5TRE4 ,IF !N "O %D ASSUME T ! ANGLE
;,,AC IS EQUAL 6! ANGLE ,,BD1 )\T CLAIM+
G5],Y T ANGLES ( SEMICIRCLES >E EQUAL2 &
AG IF "O %D ASSUME T ! ANGLE ;,C IS
EQUAL 6! ANGLE ;,D1 )\T ! A4I;NAL
ASSUMP;N T E ANGLE (A SEG;T IS EQUAL 6E
O!R ANGLE (! SAME SEG;T2 & FUR!R IF "O
%D ASSUME T :5 EQUAL ANGLES >E TAK5 F !
:OLE ANGLES1 : >E !MVS EQUAL1 ! REMA9D]S
;,E & ;,F >E EQUAL1 HE W BEG ! ?+ 6BE
PROV$1 UN.S HE AL /ATES T :5 EQUALS >E
TAK5 F EQUALS ! REMA9D]S >E EQUAL4
  ,X IS CLE> !N T 9 E SYLLOGISM "! M/ 2
A UNIV]SAL PREMISS1 & T A UNIV]SAL
/ATE;T IS PROV$ ONLY :5 ALL ! PREMISSES
>E UNIV]SAL1 :ILE A "PICUL> /ATE;T IS
PROV$ BO? F TWO UNIV]SAL PREMISSES & F
"O ONLY3 3SEQU5TLY IF ! 3CLU.N IS
UNIV]SAL1 ! PREMISSES AL M/ 2 UNIV]SAL1
B IF ! PREMISSES >E UNIV]SAL X IS POSSI#
T ! 3CLU.N MAY N 2 UNIV]SAL4 ,& X IS
CLE> AL T 9 E SYLLOGISM EI BO? OR "O (!
PREMISSES M/ 2 L ! 3CLU.N4 ,I M1N N ONLY
9 2+ A6IRMATIVE OR NEGATIVE1 B AL 9 2+
NEC1 PURE1 PRO#MATIC4 ,WE M/ 3SID] AL !
O!R =MS ( PR$IC,N4
  ,X IS CLE> AL :5 A SYLLOGISM 9 G5]AL C
2 MADE & :5 X _C2 & :5 A VALID1 :5 A
P]FECT SYLLOGISM C 2 =M$2 & T IF A
SYLLOGISM IS =M$ ! T]MS M/ 2 >RANG$ 9 "O
(! WAYS T H BE5 M5;N$4
                  #BE

  ,X IS CLE> TOO T E DEMON/R,N W PROCE$
"? ?REE T]MS & NO M1 UN.S ! SAME 3CLU.N
IS E/ABLI%$ 0DI6]5T PAIRS ( PROPOSI;NS2
E4G4 ! 3CLU.N ;,E MAY 2 E/ABLI%$ "? !
PROPOSI;NS ;,A & ;,B1 & "? ! PROPOSI;NS
;,C & ;,D1 OR "? ! PROPOSI;NS ;,A & ;,B1
OR ;,A & ;,C1 OR ;,B & ,C4 ,= NO?+
PREV5TS "! 2+ S"EAL MI4LES =! SAME T]MS4
,B 9 T CASE "! IS N "O B S"EAL
SYLLOGISMS4 ,OR AG :5 EA* (! PROPOSI;NS
;,A & ;,B IS OBTA9$ 0SYLLOGI/IC 9F];E1
E4G4 0M1NS ( ;,D & ;,E1 & AG ;,B 0M1NS (
;,F & ,G4 ,OR "O MAY 2 OBTA9$
0SYLLOGI/IC1 ! O!R 09DUCTIVE 9F];E4 ,B
?US AL ! SYLLOGISMS >E _M2 =! 3CLU.NS >E
_M1 E4G4 ;,A & ;,B & ,C4 ,B IF ? C 2
CALL$ "O SYLLOGISM1 N _M1 ! SAME 3CLU.N
MAY 2 R1*$ 0M ?AN ?REE T]MS 9 ? WAY1 B X
_C 2 R1*$ Z ;,C IS E/ABLI%$ 0M1NS ( ;,A
& ,B4 ,SUPPOSE T ! PROPOSI;N ;,E IS
9F]R$ F ! PREMISSES ;,A1 ;,B1 ;,C1 & ,D4
,X IS NEC !N T ( ^! "O %D 2 RELAT$
6ANO!R Z :OLE 6"P3 = X HAS ALR BE5 PROV$
T IF A SYLLOGISM IS =M$ "S ( XS T]MS M/
2 RELAT$ 9 ? WAY4 ,SUPPOSE !N T ,A /&S 9
? REL,N TO ;,B4 ,"S 3CLU.N !N FOLL[S F
!M4 ,X M/ EI 2 ;,E OR "O OR O!R ( ;,C &
;,D1 OR "S?+ O!R ?AN ^!4

7#A7 ,IF X IS ;,E ! SYLLOGISM W H ;,A &
  ;,B = XS SOLE PREMISSES4 ,B IF ;,C &
  ;,D >E S RELAT$ T "O IS :OLE1 ! O!R
  "P1 "S 3CLU.N W FOLL[ F !M AL2 & X M/
  2 EI ;,E1 OR "O OR O!R (! PROPOSI;NS
  ;,A & ;,B1 OR "S?+ O!R ?AN ^!4 ,& IF X
  IS 7I7 ;,E1 OR 7;II7 ,A OR ;,B1 EI 7I7
  ! SYLLOGISMS W 2 M ?AN "O1 OR 7;II7 !
  SAME ?+ HAPP5S 6BE 9F]R$ 0M1NS ( S"EAL
  T]MS ONLY 9 ! S5SE : WE SAW 6BE
  POSSI#4 ,B IF 7;III7 ! 3CLU.N IS O!R
  ?AN ;,E OR ,A OR ;,B1 ! SYLLOGISMS W 2
  _M1 & UNCONNECT$ ) "O ANO!R4 ,B IF ;,C
  IS N S RELAT$ TO ;,D Z 6MAKE A
  SYLLOGISM1 ! PROPOSI;NS W H BE5 ASSUM$
  6NO PURPOSE1 UN.S =! SAKE ( 9DUC;N OR
  ( OBSCUR+ ! >GU;T OR "S?+ (! SORT4
7#B7 ,B IF F ! PROPOSI;NS ;,A & ;,B "!
  FOLL[S N ;,E B "S O!R 3CLU.N1 & IF F
  ;,C & ;,D EI ,A OR ;,B FOLL[S OR "S?+
  ELSE1 !N "! >E S"EAL SYLLOGISMS1 & !Y
  D N E/ABLI% ! 3CLU.N PROPOS$3 = WE
  ASSUM$ T ! SYLLOGISM PROV$ ,E4 ,& IF
  NO 3CLU.N FOLL[S F ;,C & ;,D1 X TURNS
  \ T ^! PROPOSI;NS H BE5 ASSUM$ 6NO
  PURPOSE1 &! SYLLOGISM DOES N PROVE !
  ORIG9AL PROPOSI;N4

  ,S X IS CLE> T E DEMON/R,N & E
SYLLOGISM W PROCE$ "? ?REE T]MS ONLY4
  ,? 2+ EVID5T1 X IS CLE> T A SYLLOGI/IC
3CLU.N FOLL[S F TWO PREMISSES & N F M
?AN TWO4 ,=! ?REE T]MS MAKE TWO
PREMISSES1 UN.S A NEW PREMISS IS ASSUM$1
Z 0 SD AT ! 2G9N+1 6P]FECT ! SYLLOGISMS4
,X IS CLE> "!=E T 9 :AT"E SYLLOGI/IC
>GU;T ! PREMISSES "? : ! MA9 3CLU.N
FOLL[S 7= "S (! PREC$+ 3CLU.NS M/ 2
PREMISSES7 >E N EV5 9 NUMB]1 ? >GU;T EI
HAS N BE5 DRAWN SYLLOGI/IC,Y OR X HAS
ASSUM$ M ?AN 0 NEC 6E/ABLI% XS !SIS4
  ,IF !N SYLLOGISMS >E TAK5 ) RESPECT
6_! MA9 PREMISSES1 E SYLLOGISM W 3SI/ (
AN EV5 NUMB] ( PREMISSES & AN ODD NUMB]
( T]MS 7=! T]MS EXCE$ ! PREMISSES 0"O71
&! 3CLU.NS W 2 HALF ! NUMB] (!
PREMISSES4 ,B :5"E A 3CLU.N IS R1*$
0M1NS ( PROSYLLOGISMS OR 0M1NS ( S"EAL
3T9U\S MI4LE T]MS1 E4G4 ! PROPOSI;N
;,,AB 0M1NS (! MI4LE T]MS ;,C & ;,D1 !
NUMB] (! T]MS W SIMIL>LY EXCE$ T (!
PREMISSES 0"O 7=! EXTRA T]M M/ EI 2 A4$
\TSIDE OR 9S]T$3 B 9 EI CASE X FOLL[S T
! REL,NS ( PR$IC,N >E "O FEW] ?AN ! T]MS
RELAT$71 &! PREMISSES W 2 EQUAL 9 NUMB]
6! REL,NS ( PR$IC,N4 ,! PREMISSES H["E W
N ALW 2 EV51 ! T]MS ODD2 B !Y W
ALT]NATE-:5 ! PREMISSES >E EV51 ! T]MS
M/ 2 ODD2 :5 ! T]MS >E EV51 ! PREMISSES
M/ 2 ODD3 = AL;G ) "O T]M "O PREMISS IS
A4$1 IF A T]M IS A4$ F ANY QU>T]4
,3SEQU5TLY S9CE ! PREMISSES 7 7Z WE SAW7
EV51 &! T]MS ODD1 WE M/ MAKE !M
ALT]NATELY EV5 & ODD AT EA* A4I;N4 ,B !
3CLU.NS W N FOLL[ ! SAME >RANGE;T EI 9
RESPECT 6! T]MS OR 6! PREMISSES4 ,= IF
"O T]M IS A4$1 3CLU.NS W 2 A4$ LESS 0"O
?AN ! PRE-EXI/+ T]MS3 =! 3CLU.N IS DRAWN
N 9 REL,N 6! S+LE T]M LA/ A4$1 B 9 REL,N
6ALL ! RE/1 E4G4 IF 6,,ABC ! T]M ;,D IS
A4$1 TWO 3CLU.NS >E "!BY A4$1 "O 9 REL,N
TO ;,A1 ! O!R 9 REL,N TO ;,B4 ,SIMIL>LY
) ANY FUR!R A4I;NS4 ,& SIMIL>LY TOO IF !
T]M IS 9S]T$ 9 ! MI4LE3 = 9 REL,N 6"O
T]M ONLY1 A SYLLOGISM W N 2 3/RUCT$4
,3SEQU5TLY ! 3CLU.NS W 2 M* M NUM]\S ?AN
! T]MS OR ! PREMISSES4

                  #BF

  ,S9CE WE "U/& ! SUBJECTS ) :
SYLLOGISMS >E 3C]N$1 :AT SORT ( 3CLU.N
IS E/ABLI%$ 9 EA* FIGURE1 & 9 H[ _M
MOODS ? IS D"O1 X IS EVID5T 6U BO? :AT
SORT ( PRO#M IS DI6ICULT & :AT SORT IS
EASY 6PROVE4 ,= T : IS 3CLUD$ 9 _M
FIGURES & "? _M MOODS IS EASI]2 T : IS
3CLUD$ 9 FEW FIGURES & "? FEW MOODS IS M
DI6ICULT 6ATTEMPT4 ,! UNIV]SAL
A6IRMATIVE IS PROV$ 0M1NS (! F/ FIGURE
ONLY & 0? 9 ONLY "O MOOD2 ! UNIV]SAL
NEGATIVE IS PROV$ BO? "? ! F/ FIGURE &
"? ! SECOND1 "? ! F/ 9 "O MOOD1 "? !
SECOND 9 TWO4 ,! "PICUL> A6IRMATIVE IS
PROV$ "? ! F/ & "? ! LA/ FIGURE1 9 "O
MOOD "? ! F/1 9 ?REE MOODS "? ! LA/4 ,!
"PICUL> NEGATIVE IS PROV$ 9 ALL !
FIGURES1 B ONCE 9 ! F/1 9 TWO MOODS 9 !
SECOND1 9 ?REE MOODS 9 ! ?IRD4 ,X IS
CLE> !N T ! UNIV]SAL A6IRMATIVE IS MO/
DI6ICULT 6E/ABLI%1 MO/ EASY 6OV]?R[4 ,9
G5]AL1 UNIV]SALS >E EASI] GAME =!
DE/ROY] ?AN "PICUL>S3 = :E!R ! PR$ICATE
2L;GS 6N"O OR N 6"S1 !Y >E DE/ROY$3 &!
"PICUL> NEGATIVE IS PROV$ 9 ALL !
FIGURES1 ! UNIV]SAL NEGATIVE 9 TWO4
,SIMIL>LY ) UNIV]SAL NEGATIVES3 !
ORIG9AL /ATE;T IS DE/ROY$1 :E!R !
PR$ICATE 2L;GS 6ALL OR 6"S3 & ? WE F.D
POSSI# 9 TWO FIGURES4 ,B "PICUL> /ATE;TS
C 2 REFUT$ 9 "O WAY ONLY-BY PROV+ T !
PR$ICATE 2L;GS EI 6ALL OR 6N"O4 ,B
"PICUL> /ATE;TS >E EASI] 6E/ABLI%3 =
PRO( IS POSSI# 9 M FIGURES & "? M MOODS4
,& 9 G5]AL WE M/ N =GET T X IS POSSI#
6REFUTE /ATE;TS 0M1NS ( "O ANO!R1 ,I
M1N1 UNIV]SAL /ATE;TS 0M1NS ( "PICUL>1 &
"PICUL> /ATE;TS 0M1NS ( UNIV]SAL3 B X IS
N POSSI# 6E/ABLI% UNIV]SAL /ATE;TS 0M1NS
( "PICUL>1 ?\< X IS POSSI# 6E/ABLI%
"PICUL> /ATE;TS 0M1NS ( UNIV]SAL4 ,AT !
SAME "T X IS EVID5T T X IS EASI] 6REFUTE
?AN 6E/ABLI%4
  ,! MANN] 9 : E SYLLOGISM IS PRODUC$1 !
NUMB] (! T]MS & PREMISSES "? : X
PROCE$S1 ! REL,N (! PREMISSES 6"O ANO!R1
! "* (! PRO#M PROV$ 9 EA* FIGURE1 &!
NUMB] (! FIGURES APPROPRIATE 6EA* PRO#M1
ALL ^! MATT]S >E CLE> F :AT HAS BE5 SD4

                  #BG

  ,WE M/ N[ /ATE H[ WE MAY \RVS ALW H A
SUPPLY ( SYLLOGISMS 9 REF];E 6! PRO#M
PROPOS$ & 0:AT ROAD WE MAY R1* !
PR9CIPLES RELATIVE 6! PRO#M3 = P]H WE "\
N ONLY 69VE/IGATE ! 3/RUC;N (
SYLLOGISMS1 B AL 6H ! P[] ( MAK+ !M4
  ,( ALL ! ?+S : EXI/ "S >E S* T !Y _C 2
PR$ICAT$ ( ANY?+ ELSE TRULY & UNIV]S,Y1
E4G4 ,CLEON & ,CALLIAS1 I4E4 ! 9DIVIDUAL
& S5SI#1 B O!R ?+S MAY 2 PR$ICAT$ ( !M
7= EA* ( ^! IS BO? MAN & ANIMAL72 & "S
?+S >E !MVS PR$ICAT$ ( O!RS1 B NO?+
PRIOR IS PR$ICAT$ ( !M2 & "S >E PR$ICAT$
( O!RS1 & YET O!RS ( !M1 E4G4 MAN (
,CALLIAS & ANIMAL ( MAN4 ,X IS CLE> !N T
"S ?+S >E NATUR,Y N /AT$ ( ANY?+3 = Z A
RULE EA* S5SI# ?+ IS S* T X _C 2
PR$ICAT$ ( ANY?+1 SAVE 9CID5T,Y3 = WE
"S"TS SAY T T :ITE OBJECT IS ,SOCRATES1
OR T T : APPROA*ES IS ,CALLIAS4 ,WE %
EXPLA9 9 ANO!R PLACE T "! IS AN UPW>D
LIMIT AL 6! PROCESS ( PR$ICAT+3 =!
PRES5T WE M/ ASSUME ?4 ,( ^! ULTIMATE
PR$ICATES X IS N POSSI# 6DEMON/RATE
ANO!R PR$ICATE1 SAVE Z A MATT] ( OP9ION1
B ^! MAY 2 PR$ICAT$ ( O!R ?+S4 ,NEI C
9DIVIDUALS 2 PR$ICAT$ ( O!R ?+S1 ?\< O!R
?+S C 2 PR$ICAT$ ( !M4 ,:AT"E LIES 2T ^!
LIMITS C 2 SPOK5 ( 9 BO? WAYS3 !Y MAY 2
/AT$ ( O!RS1 & O!RS /AT$ ( !M4 ,& Z A
RULE >GU;TS & 9QUIRIES >E 3C]N$ ) ^!
?+S4 ,WE M/ SELECT ! PREMISSES SUITA#
6EA* PRO#M 9 ? MANN]3 F/ WE M/ LAY D[N !
SUBJECT &! DEF9I;NS &! PROP]TIES (! ?+2
NEXT WE M/ LAY D[N ^? ATTRIBUTES : FOLL[
! ?+1 & AG ^? : ! ?+ FOLL[S1 & ^? : _C
2L;G 6X4 ,B ^? 6: X _C 2L;G NE$ N 2
SELECT$1 2C ! NEGATIVE /ATE;T IMPLI$ ABV
IS 3V]TI#4 ,(! ATTRIBUTES : FOLL[ WE M/
4T+UI% ^? : FALL )9 ! DEF9I;N1 ^? : >E
PR$ICAT$ Z PROP]TIES1 & ^? : >E PR$ICAT$
Z A3ID5TS1 &(! LATT] ^? : APP>5TLY & ^?
: RE,Y 2L;G4 ,! L>G] ! SUPPLY A MAN HAS
( ^!1 ! M QKLY W HE R1* A 3CLU.N2 & 9
PROPOR;N Z HE APPREH5DS ^? : >E TRU]1 !
M COG5TLY W HE DEMON/RATE4 ,B HE M/
SELECT N ^? : FOLL[ "S "PICUL> B ^? :
FOLL[ ! ?+ Z A :OLE1 E4G4 N :AT FOLL[S A
"PICUL> MAN B :AT FOLL[S E MAN3 =!
SYLLOGISM PROCE$S "? UNIV]SAL PREMISSES4
,IF ! /ATE;T IS 9DEF9ITE1 X IS UNC]TA9
:E!R ! PREMISS IS UNIV]SAL1 B IF !
/ATE;T IS DEF9ITE1 ! MATT] IS CLE>4
,SIMIL>LY "O M/ SELECT ^? ATTRIBUTES : !
SUBJECT FOLL[S Z :OLES1 =! R1SON GIV54
,B T : FOLL[S "O M/ N SUPPOSE 6FOLL[ Z A
:OLE1 E4G4 T E ANIMAL FOLL[S MAN OR E
SCI;E MUSIC1 B ONLY T X FOLL[S1 )\T
QUALIFIC,N1 & 9DE$ WE /ATE X 9 A
PROPOSI;N3 =! O!R /ATE;T IS USE.S &
IMPOSSI#1 E4G4 T E MAN IS E ANIMAL OR
JU/ICE IS ALL GD4 ,B T : "S?+ FOLL[S
RCVS ! M>K ,8E0'4 ,:5"E ! SUBJECT1 = :
WE M/ OBTA9 ! ATTRIBUTES T FOLL[1 IS
3TA9$ 0"S?+ ELSE1 :AT FOLL[S OR DOES N
FOLL[ ! HI<E/ T]M UNIV]S,Y M/ N 2
SELECT$ 9 D1L+ )! SUBORD9ATE T]M 7= ^!
ATTRIBUTES H BE5 TAK5 9 D1L+ )! SUP]IOR
T]M2 = :AT FOLL[S ANIMAL AL FOLL[S MAN1
& :AT DOES N 2L;G 6ANIMAL DOES N 2L;G
6MAN72 B WE M/ *OOSE ^? ATTRIBUTES : >E
PECULI> 6EA* SUBJECT4 ,= "S ?+S >E
PECULI> 6! SPECIES Z 4T9CT F ! G5US2 =
SPECIES 2+ 4T9CT "! M/ 2 ATTRIBUTES
PECULI> 6EA*4 ,NOR M/ WE TAKE Z ?+S : !
SUP]IOR T]M FOLL[S1 ^? ?+S : ! 9F]IOR
T]M FOLL[S1 E4G4 TAKE Z SUBJECTS (!
PR$ICATE ,8ANIMAL0' :AT >E RE,Y SUBJECTS
(! PR$ICATE ,8MAN0'4 ,X IS NEC 9DE$1 IF
ANIMAL FOLL[S MAN1 T X %D FOLL[ ALL ^!
AL4 ,B ^! 2L;G M PROP]LY 6! *OICE ( :AT
3C]NS MAN4 ,"O M/ APPREH5D AL NORMAL
3SEQU5TS & NORMAL ANTEC$5TS-1 =
PROPOSI;NS : OBTA9 NORM,Y >E E/ABLI%$
SYLLOGI/IC,Y F PREMISSES : OBTA9 NORM,Y1
"S IF N ALL ( !M HAV+ ? "* ( NORMAL;Y4
,=! 3CLU.N ( EA* SYLLOGISM RESEM#S XS
PR9CIPLES4 ,WE M/ N H["E *OOSE
ATTRIBUTES : >E 3SEQU5T ^U ALL ! T]MS3 =
NO SYLLOGISM C 2 MADE \ ( S* PREMISSES4
,! R1SON :Y ? IS S W 2 CLE> 9 ! SEQUEL4

                  #BH

  ,IF M5 WI% 6E/ABLI% "S?+ AB "S :OLE1
!Y M/ LOOK 6! SUBJECTS ( T : IS 2+
E/ABLI%$ 7! SUBJECTS ( : X HAPP5S 6BE
ASS]T$71 &! ATTRIBUTES : FOLL[ T ( : X
IS 6BE PR$ICAT$4 ,= IF ANY ( ^! SUBJECTS
IS ! SAME Z ANY ( ^! ATTRIBUTES1 !
ATTRIBUTE ORIG9,Y 9 "Q M/ 2L;G 6!
SUBJECT ORIG9,Y 9 "Q4 ,B IF ! PURPOSE IS
6E/ABLI% N A UNIV]SAL B A "PICUL>
PROPOSI;N1 !Y M/ LOOK =! T]MS ( : ! T]MS
9 "Q >E PR$ICA#3 = IF ANY ( ^! >E
ID5TICAL1 ! ATTRIBUTE 9 "Q M/ 2L;G 6"S (
! SUBJECT 9 "Q4 ,:5"E ! "O T]M HAS 62L;G
6N"O (! O!R1 "O M/ LOOK 6! 3SEQU5TS (!
SUBJECT1 & 6^? ATTRIBUTES : _C POSSIBLY
2 PRES5T 9 ! PR$ICATE 9 "Q3 OR 3V]SELY
6! ATTRIBUTES : _C POSSIBLY 2 PRES5T 9 !
SUBJECT1 & 6! 3SEQU5TS (! PR$ICATE4 ,IF
ANY MEMB]S ( ^! GR\PS >E ID5TICAL1 "O (!
T]MS 9 "Q _C POSSIBLY 2L;G 6ANY (! O!R4
,= "S"TS A SYLLOGISM 9 ! F/ FIGURE
RESULTS1 "S"TS A SYLLOGISM 9 ! SECOND4
,B IF ! OBJECT IS 6E/ABLI% A "PICUL>
NEGATIVE PROPOSI;N1 WE M/ F9D ANTEC$5TS
(! SUBJECT 9 "Q & ATTRIBUTES : _C
POSSIBLY 2L;G 6! PR$ICATE 9 "Q4 ,IF ANY
MEMB]S ( ^! TWO GR\PS >E ID5TICAL1 X
FOLL[S T "O (! T]MS 9 "Q DOES N 2L;G 6"S
(! O!R4 ,P]H EA* ( ^! /ATE;TS W 2COME
CLE>] 9 ! FOLL[+ WAY4 ,SUPPOSE !
3SEQU5TS ( ,A >E DESIGNAT$ BY ;,B1 !
ANTEC$5TS ( ,A BY ;,C1 ATTRIBUTES : _C
POSSIBLY 2L;G TO ;,A BY ;,D4 ,SUPPOSE AG
T ! ATTRIBUTES ( ;,E >E DESIGNAT$ BY
;,F1 ! ANTEC$5TS ( ;,E BY ;,G1 &
ATTRIBUTES : _C 2L;G TO ;,E BY ;,H4 ,IF
!N "O (! ,C'S %D 2 ID5TICAL ) "O (! ,FS1
,A M/ 2L;G 6ALL ;,E3 = ;,F 2L;GS 6ALL
;,E1 & ,A 6ALL ;,C1 3SEQU5TLY ,A 2L;GS
6ALL ,E4 ,IF ;,C & ;,G >E ID5TICAL1 ,A
M/ 2L;G 6"S (! ,ES3 = ,A FOLL[S ;,C1 &
;,E FOLL[S ALL ,G4 ,IF ;,F & ;,D >E
ID5TICAL1 ,A W 2L;G 6N"O (! ,ES 0A
PROSYLLOGISM3 = S9CE ! NEGATIVE
PROPOSI;N IS 3V]TI#1 & ;,F IS ID5TICAL )
;,D1 ,A W 2L;G 6N"O (! ,FS1 B ;,F 2L;GS
6ALL ,E4 ,AG1 IF ;,B & ;,H >E ID5TICAL1
,A W 2L;G 6N"O (! ,ES3 = ;,B W 2L;G 6ALL
;,A1 B 6NO ;,E3 = X 0 ASSUM$ 6BE
ID5TICAL ) ;,H1 & ;,H 2L;G$ 6N"O (! ,ES4
,IF ;,D & ;,G >E ID5TICAL1 ,A W N 2L;G
6"S (! ,ES3 = X W N 2L;G TO ;,G1 2C X
DOES N 2L;G TO ;,D3 B ;,G FALLS "U ;,E3
3SEQU5TLY ,A W N 2L;G 6"S (! ,ES4 ,IF
;,B IS ID5TICAL ) ;,G1 "! W 2 A 3V]T$
SYLLOGISM3 = ;,E W 2L;G 6ALL ,A S9CE ;,B
2L;GS TO ;,A & ;,E TO ;,B 7= ;,B 0 F.D
6BE ID5TICAL ) ,G73 B T ,A %D 2L;G 6ALL
;,E IS N NEC1 B X M/ 2L;G 6"S ;,E 2C X
IS POSSI# 63V]T ! UNIV]SAL /ATE;T 96A
"PICUL>4
  ,X IS CLE> !N T 9 E PROPOSI;N :
REQUIRES PRO( WE M/ LOOK 6! A=ESD REL,NS
(! SUBJECT & PR$ICATE 9 "Q3 = ALL
SYLLOGISMS PROCE$ "? ^!4 ,B IF WE >E
SEEK+ 3SEQU5TS & ANTEC$5TS WE M/ LOOK =
^? : >E PRIM>Y & MO/ UNIV]SAL1 E4G4 9
REF];E TO ;,E WE M/ LOOK 6,,KF R ?AN TO
;,F AL"O1 & 9 REF];E TO ;,A WE M/ LOOK
6,,KC R ?AN TO ;,C AL"O4 ,= IF ,A 2L;GS
6,,KF1 X 2L;GS BO? TO ;,F & TO ;,E3 B IF
X DOES N FOLL[ ,,KF1 X MAY YET FOLL[ ,F4
,SIMIL>LY WE M/ 3SID] ! ANTEC$5TS ( ,A
XF3 = IF A T]M FOLL[S ! PRIM>Y
ANTEC$5TS1 X W FOLL[ ^? AL : >E
SUBORD9ATE1 B IF X DOES N FOLL[ ! =M]1 X
MAY YET FOLL[ ! LATT]4
  ,X IS CLE> TOO T ! 9QUIRY PROCE$S "? !
?REE T]MS &! TWO PREMISSES1 & T ALL !
SYLLOGISMS PROCE$ "? ! A=ESD FIGURES4 ,=
X IS PROV$ T ,A 2L;GS 6ALL ;,E1 :5"E AN
ID5TICAL T]M IS F.D AM;G ! ,CS & ,FS4 ,?
W 2 ! MI4LE T]M2 ;,A & ;,E W 2 !
EXTREMES4 ,S ! F/ FIGURE IS =M$4 ,& ,A W
2L;G 6"S ;,E1 :5"E ;,C & ;,G >E
APPREH5D$ 6BE ! SAME4 ,? IS ! LA/
FIGURE3 = ;,G 2COMES ! MI4LE T]M4 ,& ,A
W 2L;G 6NO ;,E1 :5 ;,D & ;,F >E
ID5TICAL4 ,?US WE H BO? ! F/ FIGURE &!
MI4LE FIGURE2 ! F/1 2C ,A 2L;GS 6NO ;,F1
S9CE ! NEGATIVE /ATE;T IS 3V]TI#1 & ;,F
2L;GS 6ALL ;,E3 ! MI4LE FIGURE 2C ;,D
2L;GS 6NO ;,A1 & 6ALL ,E4 ,& ,A W N 2L;G
6"S ;,E1 :5"E ;,D & ;,G >E ID5TICAL4 ,?
IS ! LA/ FIGURE3 = ,A W 2L;G 6NO ;,G1 &
;,E W 2L;G 6ALL ,G4 ,CLE>LY !N ALL
SYLLOGISMS PROCE$ "? ! A=ESD FIGURES1 &
WE M/ N SELECT 3SEQU5TS ( ALL ! T]MS1 2C
NO SYLLOGISM IS PRODUC$ F !M4 ,= 7Z WE
SAW7 X IS N POSSI# AT ALL 6E/ABLI% A
PROPOSI;N F 3SEQU5TS1 & X IS N POSSI#
6REFUTE 0M1NS (A 3SEQU5T ( BO? ! T]MS 9
"Q3 =! MI4LE T]M M/ 2L;G 6! "O1 & N 2L;G
6! O!R4
  ,X IS CLE> TOO T O!R ME?ODS ( 9QUIRY
0SELEC;N ( MI4LE T]MS >E USE.S 6PRODUCE
A SYLLOGISM1 E4G4 IF ! 3SEQU5TS (! T]MS
9 "Q >E ID5TICAL1 OR IF ! ANTEC$5TS ( ,A
>E ID5TICAL ) ^? ATTRIBUTES : _C
POSSIBLY 2L;G TO ;,E1 OR IF ^?
ATTRIBUTES >E ID5TICAL : _C 2L;G 6EI
T]M3 = NO SYLLOGISM IS PRODUC$ 0M1NS (
^!4 ,= IF ! 3SEQU5TS >E ID5TICAL1 E4G4
;,B & ;,F1 WE H ! MI4LE FIGURE ) BO?
PREMISSES A6IRMATIVE3 IF ! ANTEC$5TS (
,A >E ID5TICAL ) ATTRIBUTES : _C 2L;G TO
;,E1 E4G4 ;,C ) ;,H1 WE H ! F/ FIGURE )
XS M9OR PREMISS NEGATIVE4 ,IF ATTRIBUTES
: _C 2L;G 6EI T]M >E ID5TICAL1 E4G4 ;,C
& ;,H1 BO? PREMISSES >E NEGATIVE1 EI 9 !
F/ OR 9 ! MI4LE FIGURE4 ,B NO SYLLOGISM
IS POSSI# 9 ? WAY4
  ,X IS EVID5T TOO T WE M/ F9D \ : T]MS
9 ? 9QUIRY >E ID5TICAL1 N : >E DI6]5T OR
3TR>Y1 F/ 2C ! OBJECT ( \R 9VE/IG,N IS !
MI4LE T]M1 &! MI4LE T]M M/ 2 N DIV]SE B
ID5TICAL4 ,SECONDLY1 :]"E X HAPP5S T A
SYLLOGISM RESULTS F TAK+ 3TR>IES OR T]MS
: _C 2L;G 6! SAME ?+1 ALL >GU;TS C 2
REDUC$ 6! A=ESD MOODS1 E4G4 IF ;,B & ;,F
>E 3TR>IES OR _C 2L;G 6! SAME ?+4 ,= IF
^! >E TAK51 A SYLLOGISM W 2 =M$ 6PROVE T
,A 2L;GS 6N"O (! ,ES1 N H["E F !
PREMISSES TAK5 B 9 ! A=ESD MOOD4 ,= ;,B
W 2L;G 6ALL ;,A & 6NO ,E4 ,3SEQU5TLY ;,B
M/ 2 ID5TICAL ) "O (! ,HS4 ,AG1 IF ;,B &
;,G _C 2L;G 6! SAME ?+1 X FOLL[S T ,A W
N 2L;G 6"S (! ,ES3 = !N TOO WE % H !
MI4LE FIGURE3 = ;,B W 2L;G 6ALL ;,A &
6NO ,G4 ,3SEQU5TLY ;,B M/ 2 ID5TICAL )
"S (! ,HS4 ,=! FACT T ;,B & ;,G _C 2L;G
6! SAME ?+ DI6]S 9 NO WAY F ! FACT T ;,B
IS ID5TICAL ) "S (! ,HS3 = T 9CLUDES
"EY?+ : _C 2L;G TO ;,E4
  ,X IS CLE> !N T F ! 9QUIRIES TAK5
0!MVS NO SYLLOGISM RESULTS2 B IF ;,B &
;,F >E 3TR>IES ;,B M/ 2 ID5TICAL ) "O (!
,HS1 &! SYLLOGISM RESULTS "? ^! T]MS4 ,X
TURNS \ !N T ^? :O 9QUIRE 9 ? MANN] >E
LOOK+ GRATUIT\SLY = "S O!R WAY ?AN ! NEC
WAY 2C !Y H FAIL$ 6OBS]VE ! ID5T;Y (!
,BS )! ,HS4

                  #BI

  ,SYLLOGISMS : L1D 6IMPOSSI# 3CLU.NS >E
SIMIL> 6O/5SIVE SYLLOGISMS2 !Y AL >E =M$
0M1NS (! 3SEQU5TS & ANTEC$5TS (! T]MS 9
"Q4 ,9 BO? CASES ! SAME 9QUIRY IS
9VOLV$4 ,= :AT IS PROV$ O/5SIVELY MAY AL
2 3CLUD$ SYLLOGI/IC,Y P] IMPOSSIBILE
0M1NS (! SAME T]MS2 & :AT IS PROV$ P]
IMPOSSIBILE MAY AL 2 PROV$ O/5SIVELY1
E4G4 T ,A 2L;GS 6N"O (! ,ES4 ,= SUPPOSE
,A 62L;G 6"S ;,E3 !N S9CE ;,B 2L;GS 6ALL
;,A & ,A 6"S (! ,ES1 ;,B W 2L;G 6"S (!
,ES3 B X 0 ASSUM$ T X 2L;GS 6N"O4 ,AG WE
MAY PROVE T ,A 2L;GS 6"S ;,E3 = IF ,A
2L;G$ 6N"O (! ,ES1 & ;,E 2L;GS 6ALL ;,G1
,A W 2L;G 6N"O (! ,GS3 B X 0 ASSUM$
62L;G 6ALL4 ,SIMIL>LY )! O!R PROPOSI;NS
REQUIR+ PRO(4 ,! PRO( P] IMPOSSIBILE W
ALW & 9 ALL CASES 2 F ! 3SEQU5TS &
ANTEC$5TS (! T]MS 9 "Q4 ,:AT"E ! PRO#M !
SAME 9QUIRY IS NEC :E!R "O WI%ES 6USE AN
O/5SIVE SYLLOGISM OR A REDUC;N
6IMPOSSIBIL;Y4 ,= BO? ! DEMON/R,NS />T F
! SAME T]MS1 E4G4 SUPPOSE X HAS BE5
PROV$ T ,A 2L;GS 6NO ;,E1 2C X TURNS \ T
O!RWISE ;,B 2L;GS 6"S (! ,ES & ? IS
IMPOSSI#-IF N[ X IS ASSUM$ T ;,B 2L;GS
6NO ;,E & 6ALL ;,A1 X IS CLE> T ,A W
2L;G 6NO ,E4 ,AG IF X HAS BE5 PROV$ 0AN
O/5SIVE SYLLOGISM T ,A 2L;GS 6NO ;,E1
ASSUME T ,A 2L;GS 6"S ;,E & X W 2 PROV$
P] IMPOSSIBILE 62L;G 6NO ,E4 ,SIMIL>LY )
! RE/4 ,9 ALL CASES X IS NEC 6F9D "S
-MON T]M O!R ?AN ! SUBJECTS ( 9QUIRY1 6:
! SYLLOGISM E/ABLI%+ ! FALSE 3CLU.N MAY
RELATE1 S T IF ? PREMISS IS 3V]T$1 &!
O!R REMA9S Z X IS1 ! SYLLOGISM W 2
O/5SIVE 0M1NS (! SAME T]MS4 ,=! O/5SIVE
SYLLOGISM DI6]S F ! REDUCTIO AD
IMPOSSIBILE 9 ?3 9 ! O/5SIVE SYLLOGISM
BO? REMISSES >E LAID D[N 9 A3ORD.E )!
TRU?1 9 ! REDUCTIO AD IMPOSSIBILE "O (!
PREMISSES IS ASSUM$ FALSELY4
  ,^! PO9TS W 2 MADE CLE>] 0! SEQUEL1 :5
WE 4CUSS ! REDUC;N 6IMPOSSIBIL;Y3 AT
PRES5T ? M* M/ 2 CLE>1 T WE M/ LOOK
6T]MS (! K9DS M5;N$ :E!R WE WI% 6USE AN
O/5SIVE SYLLOGISM OR A REDUC;N
6IMPOSSIBIL;Y4 ,9 ! O!R HYPO!TICAL
SYLLOGISMS1 ,I M1N ^? : PROCE$
0SUB/ITU;N1 OR 0POSIT+ A C]TA9 QUAL;Y1 !
9QUIRY W 2 DIRECT$ 6! T]MS (! PRO#M 6BE
PROV$-N ! T]MS (! ORIG9AL PRO#M1 B ! NEW
T]MS 9TRODUC$2 &! ME?OD (! 9QUIRY W 2 !
SAME Z 2F4 ,B WE M/ 3SID] & DET]M9E 9 H[
_M WAYS HYPO!TICAL SYLLOGISMS >E POSSI#4
  ,EA* (! PRO#MS !N C 2 PROV$ 9 ! MANN]
DESCRIB$2 B X IS POSSI# 6E/ABLI% "S ( !M
SYLLOGI/IC,Y 9 ANO!R WAY1 E4G4 UNIV]SAL
PRO#MS 0! 9QUIRY : L1DS UP 6A "PICUL>
3CLU.N1 )! A4I;N ( AN HYPO!SIS4 ,= IF !
,CS &! ,GS %D 2 ID5TICAL1 B ;,E %D 2
ASSUM$ 62L;G 6! ,GS ONLY1 !N ,A WD 2L;G
6E ;,E3 & AG IF ! ,DS &! ,GS %D 2
ID5TICAL1 B ;,E %D 2 PR$ICAT$ (! ,GS
ONLY1 X FOLL[S T ,A W 2L;G 6N"O (! ,ES4
,CLE>LY !N WE M/ 3SID] ! MATT] 9 ? WAY
AL4 ,! ME?OD IS ! SAME :E!R ! REL,N IS
NEC OR POSSI#4 ,=! 9QUIRY W 2 ! SAME1 &!
SYLLOGISM W PROCE$ "? T]MS >RANG$ 9 !
SAME ORD] :E!R A POSSI# OR A PURE
PROPOSI;N IS PROV$4 ,WE M/ F9D 9 ! CASE
( POSSI# REL,NS1 Z WELL Z T]MS T 2L;G1
T]MS : C 2L;G ?\< !Y ACTU,Y D N3 = WE H
PROV$ T ! SYLLOGISM : E/ABLI%ES A POSSI#
REL,N PROCE$S "? ^! T]MS Z WELL4
,SIMIL>LY AL )! O!R MODES ( PR$IC,N4
  ,X IS CLE> !N F :AT HAS BE5 SD N ONLY
T ALL SYLLOGISMS C 2 =M$ 9 ? WAY1 B AL T
!Y _C 2 =M$ 9 ANY O!R4 ,= E SYLLOGISM
HAS BE5 PROV$ 6BE =M$ "? "O (! A=EM5;N$
FIGURES1 & ^! _C 2 -POS$ "? O!R T]MS ?AN
! 3SEQU5TS & ANTEC$5TS (! T]MS 9 "Q3 = F
^! WE OBTA9 ! PREMISSES & F9D ! MI4LE
T]M4 ,3SEQU5TLY A SYLLOGISM _C 2 =M$
0M1NS ( O!R T]MS4

                  #CJ

  ,! ME?OD IS ! SAME 9 ALL CASES1 9
PHILOSOPHY1 9 ANY >T OR /UDY4 ,WE M/
LOOK =! ATTRIBUTES &! SUBJECTS ( BO? \R
T]MS1 & WE M/ SUPPLY \RVS ) Z _M ( ^! Z
POSSI#1 & 3SID] !M 0M1NS (! ?REE T]MS1
REFUT+ /ATE;TS 9 "O WAY1 3FIRM+ !M 9
ANO!R1 9 ! PURSUIT ( TRU? />T+ F
PREMISSES 9 : ! >RANGE;T (! T]MS IS 9
A3ORD.E ) TRU?1 :ILE IF WE LOOK =
DIALECTICAL SYLLOGISMS WE M/ />T F
PROBA# PREMISSES4 ,! PR9CIPLES (
SYLLOGISMS H BE5 /AT$ 9 G5]AL T]MS1 BO?
H[ !Y >E "*IZ$ & H[ WE M/ HUNT = !M1 S Z
N 6LOOK 6"EY?+ T IS SD AB ! T]MS (!
PRO#M OR 6! SAME PO9TS :E!R WE >E 3FIRM+
OR REFUT+1 OR AG :E!R WE >E 3FIRM+ ( ALL
OR ( "S1 & :E!R WE >E REFUT+ ( ALL OR
"S4 WE M/ LOOK 6FEW] PO9TS & !Y M/ 2
DEF9ITE4 ,WE H AL /AT$ H[ WE M/ SELECT )
REF];E 6"EY?+ T IS1 E4G4 AB GD OR K4 ,B
9 EA* SCI;E ! PR9CIPLES : >E PECULI> >E
! MO/ NUM]\S4 ,3SEQU5TLY X IS ! BUSI;S (
EXP]I;E 6GIVE ! PR9CIPLES : 2L;G 6EA*
SUBJECT4 ,I M1N = EXAMPLE T A/RONOMICAL
EXP]I;E SUPPLIES ! PR9CIPLES (
A/RONOMICAL SCI;E3 = ONCE ! PH5OM5A 7
ADEQUATELY APPREH5D$1 ! DEMON/R,NS (
A/RONOMY 7 4COV]$4 ,SIMIL>LY ) ANY O!R
>T OR SCI;E4 ,3SEQU5TLY1 IF ! ATTRIBUTES
(! ?+ >E APPREH5D$1 \R BUSI;S W !N 2
6EXHIBIT R1DILY ! DEMON/R,NS4 ,= IF N"O
(! TRUE ATTRIBUTES ( ?+S _H BE5 OMITT$ 9
! HI/ORICAL SURVEY1 WE %D 2 A# 64COV] !
PRO( & DEMON/RATE "EY?+ : ADMITT$ (
PRO(1 & 6MAKE T CLE>1 ^: NATURE DOES N
ADMIT ( PRO(4
  ,9 G5]AL !N WE H EXPLA9$ FAIRLY WELL
H[ WE M/ SELECT PREMISSES3 WE H 4CUSS$ !
MATT] A3URATELY 9 ! TR1TISE 3C]N+
DIALECTIC4

                  #CA

  ,X IS EASY 6SEE T DIVI.N 96CLASSES IS
A SMALL "P (! ME?OD WE H DESCRIB$3 =
DIVI.N IS1 S 6SP1K1 A W1K SYLLOGISM2 =
:AT X "\ 6PROVE1 X BEGS1 & X ALW
E/ABLI%ES "S?+ M G5]AL ?AN ! ATTRIBUTE 9
"Q4 ,F/1 ? V PO9T _H ESCAP$ ALL ^? :O
US$ ! ME?OD ( DIVI.N2 & !Y ATTEMPT$
6P]SUADE M5 T X 0 POSSI# 6MAKE A
DEMON/R,N ( SUB/.E & ESS;E4 ,3SEQU5TLY
!Y DID N "U/& :AT X IS POSSI# 6PROVE
SYLLOGI/IC,Y 0DIVI.N1 NOR DID !Y "U/& T
X 0 POSSI# 6PROVE SYLLOGI/IC,Y 9 ! MANN]
WE H DESCRIB$4 ,9 DEMON/R,NS1 :5 "! IS A
NE$ 6PROVE A POSITIVE /ATE;T1 ! MI4LE
T]M "? : ! SYLLOGISM IS =M$ M/ ALW 2
9F]IOR 6& N -PREH5D ! F/ (! EXTREMES4 ,B
DIVI.N HAS A 3TR>Y 9T5;N3 = X TAKES !
UNIV]SAL Z MI4LE4 ,LET ANIMAL 2 ! T]M
SIGNIFI$ BY ;,A1 MORTAL BY ;,B1 &
IMMORTAL BY ;,C1 & LET MAN1 ^: DEF9I;N
IS 6BE GOT1 2 SIGNIFI$ BY ;,D4 ,! MAN :O
DIVIDES ASSUMES T E ANIMAL IS EI MORTAL
OR IMMORTAL3 I4E4 :AT"E IS ,A IS ALL EI
;,B OR ,C4 ,AG1 ALW DIVID+1 HE LAYS X
D[N T MAN IS AN ANIMAL1 S HE ASSUMES ;,A
( ;,D Z 2L;G+ 6X4 ,N[ ! TRUE 3CLU.N IS T
E ;,D IS EI ;,B OR ;,C1 3SEQU5TLY MAN M/
2 EI MORTAL OR IMMORTAL1 B X IS N NEC T
MAN %D 2 A MORTAL ANIMAL-? IS BE7$3 & ?
IS :AT "\ 6H BE5 PROV$ SYLLOGI/IC,Y4 ,&
AG1 TAK+ ,A Z MORTAL ANIMAL1 ;,B Z
FOOT$1 ;,C Z FOOT.S1 & ;,D Z MAN1 HE
ASSUMES 9 ! SAME WAY T ,A 9"HS EI 9 ;,B
OR 9 ;,C 7= E MORTAL ANIMAL IS EI FOOT$
OR FOOT.S71 & HE ASSUMES ;,A ( ;,D 7= HE
ASSUM$ MAN1 Z WE SAW1 6BE A MORTAL
ANIMAL72 3SEQU5TLY X IS NEC T MAN %D 2
EI A FOOT$ OR A FOOT.S ANIMAL2 B X IS N
NEC T MAN %D 2 FOOT$3 ? HE ASSUMES3 & X
IS J ? AG : HE "\ 6H DEMON/RAT$4 ,ALW
DIVID+ !N 9 ? WAY X TURNS \ T ^!
LOGICIANS ASSUME Z MI4LE ! UNIV]SAL T]M1
& Z EXTREMES T : "\ 6H BE5 ! SUBJECT (
DEMON/R,N &! DI6]5TIAE4 ,9 3CLU.N1 !Y D
N MAKE X CLE>1 & %[ X 6BE NEC1 T ? IS
MAN OR :AT"E ! SUBJECT ( 9QUIRY MAY BE3
= !Y PURSUE ! O!R ME?OD ALT1 N"E EV5
SUSPECT+ ! PRES;E (! RI* SUPPLY ( EVID;E
: MI<T 2 US$4 ,X IS CLE> T X IS NEI
POSSI# 6REFUTE A /ATE;T 0? ME?OD (
DIVI.N1 NOR 6DRAW A 3CLU.N AB AN A3ID5T
OR PROP]TY (A ?+1 NOR AB XS G5US1 NOR 9
CASES 9 : X IS UN"KN :E!R X IS ?US OR
?US1 E4G4 :E!R ! DIAGONAL IS
9COMM5SURATE4 ,= IF HE ASSUMES T E L5G?
IS EI -M5SURATE OR 9COMM5SURATE1 &!
DIAGONAL IS A L5G?1 HE HAS PROV$ T !
DIAGONAL IS EI 9COMM5SURATE OR
-M5SURATE4 ,B IF HE %D ASSUME T X IS
9COMM5SURATE1 HE W H ASSUM$ :AT HE "\ 6H
PROV$4 ,HE _C !N PROVE X3 = ? IS 8
ME?OD1 B PRO( IS N POSSI# 0? ME?OD4 ,LET
,A /& = ,89COMM5SURATE OR -M5SURATE0'1
;,B = ,8L5G?0'1 ;,C = ,8DIAGONAL0'4 ,X
IS CLE> !N T ? ME?OD ( 9VE/IG,N IS N
SUITA# = E 9QUIRY1 NOR IS X USE;L 9 ^?
CASES 9 : X IS ?"\ 6BE MO/ SUITA#4
  ,F :AT HAS BE5 SD X IS CLE> F :AT
ELE;TS DEMON/R,NS >E =M$ & 9 :AT MANN]1
& 6:AT PO9TS WE M/ LOOK 9 EA* PRO#M4

                  #CB

  ,\R NEXT BUSI;S IS 6/ATE H[ WE C
REDUCE SYLLOGISMS 6! A=EM5;N$ FIGURES3 =
? "P (! 9QUIRY / REMA9S4 ,IF WE %D
9VE/IGATE ! PRODUC;N (! SYLLOGISMS & _H
! P[] ( 4COV]+ !M1 & FUR!R IF WE CD
RESOLVE ! SYLLOGISMS PRODUC$ 96!
A=EM5;N$ FIGURES1 \R ORIG9AL PRO#M WD 2
BR"\ 6A 3CLU.N4 ,X W HAPP5 AT ! SAME "T
T :AT HAS BE5 ALR SD W 2 3FIRM$ & XS
TRU? MADE CLE>] 0:AT WE >E AB 6SAY4 ,=
"EY?+ T IS TRUE M/ 9 E RESPECT AGREE )
XF ,F/ !N WE M/ ATTEMPT 6SELECT ! TWO
PREMISSES (! SYLLOGISM 7= X IS EASI]
6DIVIDE 96L>GE "PS ?AN 96SMALL1 &!
-POSITE "PS >E L>G] ?AN ! ELE;TS \ ( :
!Y >E MADE72 NEXT WE M/ 9QUIRE : >E
UNIV]SAL & : "PICUL>1 & IF BO? PREMISSES
H N BE5 /AT$1 WE M/ \RVS ASSUME ! "O :
IS MISS+4 ,= "S"TS M5 PUT =W>D !
UNIV]SAL PREMISS1 B D N POSIT ! PREMISS
: IS 3TA9$ 9 X1 EI 9 WRIT+ OR 9 4CUS.N3
OR M5 PUT =W>D ! PREMISSES (! PR9CIPAL
SYLLOGISM1 B OMIT ^? "? : !Y >E 9F]R$1 &
9VITE ! 3CES.N ( O!RS 6NO PURPOSE4 ,WE
M/ 9QUIRE !N :E!R ANY?+ UNNEC HAS BE5
ASSUM$1 OR ANY?+ NEC HAS BE5 OMITT$1 &
WE M/ POSIT ! "O & TAKE AWAY ! O!R1
UNTIL WE H R1*$ ! TWO PREMISSES3 = UN.S
WE H ^!1 WE _C REDUCE >GU;TS PUT =W>D 9
! WAY DESCRIB$4 ,9 "S >GU;TS X IS EASY
6SEE :AT IS WANT+1 B "S ESCAPE U1 &
APPE> 6BE SYLLOGISMS1 2C "S?+ NEC
RESULTS F :AT HAS BE5 LAID D[N1 E4G4 IF
! ASSUMP;NS 7 MADE T SUB/.E IS N
ANNIHILAT$ 0! ANNIHIL,N ( :AT IS N
SUB/.E1 & T IF ! ELE;TS \ ( : A ?+ IS
MADE >E ANNIHILAT$1 !N T : IS MADE \ (
!M IS DE/ROY$3 ^! PROPOSI;NS 2+ LAID
D[N1 X IS NEC T ANY "P ( SUB/.E IS
SUB/.E2 ? HAS N H["E BE5 DRAWN
0SYLLOGISM F ! PROPOSI;NS ASSUM$1 B
PREMISSES >E WANT+4 ,AG IF X IS NEC T
ANIMAL %D EXI/1 IF MAN DOES1 & T SUB/.E
%D EXI/1 IF ANIMAL DOES1 X IS NEC T
SUB/.E %D EXI/ IF MAN DOES3 B Z YET !
3CLU.N HAS N BE5 DRAWN SYLLOGI/IC,Y3 =!
PREMISSES >E N 9 ! %APE WE REQUIR$4 ,WE
>E DCVD 9 S* CASES 2C "S?+ NEC RESULTS F
:AT IS ASSUM$1 S9CE ! SYLLOGISM AL IS
NEC4 ,B T : IS NEC IS WID] ?AN !
SYLLOGISM3 = E SYLLOGISM IS NEC1 B N
"EY?+ : IS NEC IS A SYLLOGISM4
,3SEQU5TLY1 ?\< "S?+ RESULTS :5 C]TA9
PROPOSI;NS >E ASSUM$1 WE M/ N TRY
6REDUCE X DIRECTLY1 B M/ F/ /ATE ! TWO
PREMISSES1 !N DIVIDE !M 96_! T]MS4 ,WE
M/ TAKE T T]M Z MI4LE : IS /AT$ 9 BO? !
REMISSES3 = X IS NEC T ! MI4LE %D 2 F.D
9 BO? PREMISSES 9 ALL ! FIGURES4
  ,IF !N ! MI4LE T]M IS A PR$ICATE &A
SUBJECT ( PR$IC,N1 OR IF X IS A
PR$ICATE1 & "S?+ ELSE IS D5I$ ( X1 WE %
H ! F/ FIGURE3 IF X BO? IS A PR$ICATE &
IS D5I$ ( "S?+1 ! MI4LE FIGURE3 IF O!R
?+S >E PR$ICAT$ ( X1 OR "O IS D5I$1 !
O!R PR$ICAT$1 ! LA/ FIGURE4 ,= X 0 ?US T
WE F.D ! MI4LE T]M PLAC$ 9 EA* FIGURE4
,X IS PLAC$ SIMIL>LY TOO IF ! PREMISSES
>E N UNIV]SAL3 =! MI4LE T]M IS DET]M9$ 9
! SAME WAY4 ,CLE>LY !N1 IF ! SAME T]M IS
N /AT$ M ?AN ONCE 9 ! C\RSE ( AN >GU;T1
A SYLLOGISM _C 2 MADE3 =A MI4LE T]M HAS
N BE5 TAK54 ,S9CE WE "K :AT SORT ( !SIS
IS E/ABLI%$ 9 EA* FIGURE1 & 9 : !
UNIV]SAL1 9 :AT SORT ! "PICUL> IS
DESCRIB$1 CLE>LY WE M/ N LOOK = ALL !
FIGURES1 B = T : IS APPROPRIATE 6! !SIS
9 H&4 ,IF ! !SIS IS E/ABLI%$ 9 M FIGURES
?AN "O1 WE % RECOGNIZE ! FIGURE 0!
POSI;N (! MI4LE T]M4


                  #CC

  ,M5 >E FREQU5TLY DCVD AB SYLLOGISMS 2C
! 9F];E IS NEC1 Z HAS BE5 SD ABV2 "S"TS
!Y >E DCVD 0! SIMIL>;Y 9 ! POSIT+ (!
T]MS2 & ? "\ N 6ESCAPE \R NOTICE4 ,E4G4
IF ,A IS /AT$ ( ;,B1 & ;,B ( ;,C3 X WD
SEEM T A SYLLOGISM IS POSSI# S9CE ! T]MS
/& ?US3 B NO?+ NEC RESULTS1 NOR DOES A
SYLLOGISM4 ,LET ,A REPRES5T ! T]M ,82+
ET]NAL0'1 ;,B ,8,>I/OM5ES Z AN OBJECT (
?"\0'1 ;,C ,8,>I/OM5ES0'4 ,X IS TRUE !N
T ,A 2L;GS TO ;,B4 ,= ,>I/OM5ES Z AN
OBJECT ( ?"\ IS ET]NAL4 ,B ;,B AL 2L;GS
TO ;,C3 = ,>I/OM5ES IS ,>I/OM5ES Z AN
OBJECT ( ?"\4 ,B ,A DOES N 2L;G TO ;,C3
= ,>I/OM5ES IS P]I%A#4 ,= NO SYLLOGISM 0
MADE AL? ! T]MS /OOD ?US3 T REQUIR$ T !
PREMISS ;,,AB %D 2 /AT$ UNIV]S,Y4 ,B ?
IS FALSE1 T E ,>I/OM5ES :O IS AN OBJECT
( ?"\ IS ET]NAL1 S9CE ,>I/OM5ES IS
P]I%A#4 ,AG LET ;,C /& = ,8,MI3ALUS0'1
;,B = ,8MUSICAL ,MI3ALUS0'1 ;,A =
,8P]I%+ TO-MORR[0'4 ,X IS TRUE 6PR$ICATE
;,B ( ;,C3 = ,MI3ALUS IS MUSICAL
,MI3ALUS4 ,AL ,A C 2 PR$ICAT$ ( ;,B3 =
MUSICAL ,MI3ALUS MI<T P]I% TO-MORR[4 ,B
6/ATE ;,A ( ;,C IS FALSE AT ANY RATE4 ,?
>GU;T !N IS ID5TICAL )! =M]2 = X IS N
TRUE UNIV]S,Y T MUSICAL ,MI3ALUS P]I%ES
TO-MORR[3 B UN.S ? IS ASSUM$1 NO
SYLLOGISM 7Z WE H %[N7 IS POSSI#4
  ,? DECEP;N !N >ISES "? IGNOR+ A SMALL
4T9C;N4 ,= IF WE A3EPT ! 3CLU.N Z ?\< X
MADE NO DI6];E :E!R WE SD ,8,? 2L;G 6T0'
OR ,8,? 2L;GS 6ALL ( T0'4

                  #CD

  ,M5 W FREQU5TLY FALL 96FALLACIES "? N
SETT+ \ ! T]MS (! PREMISS WELL1 E4G4
SUPPOSE ,A 6BE H1L?1 ;,B 41SE1 ;,C MAN4
,X IS TRUE 6SAY T ,A _C 2L;G 6ANY ;,B 7=
H1L? 2L;GS 6NO 41SE7 & AG T ;,B 2L;GS 6E
;,C 7= E MAN IS CAPA# ( 41SE74 ,X WD
SEEM 6FOLL[ T H1L? _C 2L;G 6ANY MAN4 ,!
R1SON = ? IS T ! T]MS >E N SET \ WELL 9
! /ATE;T1 S9CE IF ! ?+S : >E 9 ! 3DI;NS
>E SUB/ITUT$1 NO SYLLOGISM C 2 MADE1
E4G4 IF ,8H1L?Y0' IS SUB/ITUT$ =
,8H1L?0' & ,841S$0' = ,841SE0'4 ,= X IS
N TRUE 6SAY T 2+ H1L?Y _C 2L;G 6"O :O IS
41S$4 ,B UN.S ? IS ASSUM$ NO 3CLU.N
RESULTS1 SAVE 9 RESPECT ( POSSIBIL;Y3 B
S* A 3CLU.N IS N IMPOSSI#3 = X IS POSSI#
T H1L? %D 2L;G 6NO MAN4 ,AG ! FALLACY
MAY O3UR 9 A SIMIL> WAY 9 ! MI4LE
FIGURE3 ,8X IS N POSSI# T H1L? %D 2L;G
6ANY 41SE1 B X IS POSSI# T H1L? %D 2L;G
6E MAN1 3SEQU5TLY X IS N POSSI# T 41SE
%D 2L;G 6ANY MAN0'4 ,9 ! ?IRD FIGURE !
FALLACY RESULTS 9 REF];E 6POSSIBIL;Y4 ,=
H1L? & 41E & K & IGNOR.E1 & 9 G5]AL
3TR>IES1 MAY POSSIBLY 2L;G 6! SAME ?+1 B
_C 2L;G 6"O ANO!R4 ,? IS N 9 AGREE;T )
:AT 0 SD 2F3 = WE /AT$ T :5 S"EAL ?+S CD
2L;G 6! SAME ?+1 !Y CD 2L;G 6"O ANO!R4
  ,X IS EVID5T !N T 9 ALL ^! CASES !
FALLACY >ISES F ! SETT+ \ (! T]MS3 = IF
! ?+S T >E 9 ! 3DI;NS >E SUB/ITUT$1 NO
FALLACY >ISES4 ,X IS CLE> !N T 9 S*
PREMISSES :AT POSSESSES ! 3DI;N "\ ALW
6BE SUB/ITUT$ =! 3DI;N & TAK5 Z ! T]M4


                  #CE

  ,WE M/ N ALW SEEK 6SET \ ! T]MS A S+LE
^W3 = WE % (T5 H -PLEXES ( ^WS 6: A S+LE
"N IS N GIV54 ,H;E X IS DI6ICULT 6REDUCE
SYLLOGISMS ) S* T]MS4 ,"S"TS TOO
FALLACIES W RESULT F S* A SE>*1 E4G4 !
2LIEF T SYLLOGISM C E/ABLI% T : HAS NO
M1N4 ,LET ,A /& = TWO "R ANGLES1 ;,B =
TRIANGLE1 ;,C = ISOSCELES TRIANGLE4 ,A
!N 2L;GS TO ;,C 2C ( ;,B3 B ,A 2L;GS TO
;,B )\T ! M$I,N ( ANO!R T]M3 =! TRIANGLE
9 VIRTUE ( XS [N NATURE 3TA9S TWO "R
ANGLES1 3SEQU5TLY "! W 2 NO MI4LE T]M =!
PROPOSI;N ;,,AB1 AL? X IS DEMON/RA#4 ,=
X IS CLE> T ! MI4LE M/ N ALW 2 ASSUM$
6BE AN 9DIVIDUAL ?+1 B "S"TS A -PLEX (
^WS1 Z HAPP5S 9 ! CASE M5;N$4

                  #CF

  ,T ! F/ T]M 2L;GS 6! MI4LE1 &! MI4LE
6! EXTREME1 M/ N 2 "U/OOD 9 ! S5SE T !Y
C ALW 2 PR$ICAT$ ( "O ANO!R OR T ! F/
T]M W 2 PR$ICAT$ (! MI4LE 9 ! SAME WAY Z
! MI4LE IS PR$ICAT$ (! LA/ T]M4 ,! SAME
HOLDS IF ! PREMISSES >E NEGATIVE4 ,B WE
M/ SUPPOSE ! V]B ,862L;G0' 6H Z _M M1N+S
Z ! S5SES 9 : ! V]B ,86BE0' IS US$1 & 9
: ! ASS];N T A ?+ ,8IS0' MAY 2 SD 6BE
TRUE4 ,TAKE = EXAMPLE ! /ATE;T T "! IS A
S+LE SCI;E ( 3TR>IES4 ,LET ,A /& = ,8"!
2+ A S+LE SCI;E0'1 & ;,B = ?+S : >E
3TR>Y 6"O ANO!R4 ,!N ,A 2L;GS TO ;,B1 N
9 ! S5SE T 3TR>IES >E ! FACT ( "! 2+ A
S+LE SCI;E ( !M1 B 9 ! S5SE T X IS TRUE
6SAY (! 3TR>IES T "! IS A S+LE SCI;E (
!M4
  ,X HAPP5S "S"TS T ! F/ T]M IS /AT$ (!
MI4LE1 B ! MI4LE IS N /AT$ (! ?IRD T]M1
E4G4 IF WISDOM IS K1 & WISDOM IS (! GD1
! 3CLU.N IS T "! IS K (! GD4 ,! GD !N IS
N K1 ?\< WISDOM IS K4 ,"S"TS ! MI4LE T]M
IS /AT$ (! ?IRD1 B ! F/ IS N /AT$ (!
MI4LE1 E4G4 IF "! IS A SCI;E ( "EY?+ T
HAS A QUAL;Y1 OR IS A 3TR>Y1 &! GD BO?
IS A 3TR>Y & HAS A QUAL;Y1 ! 3CLU.N IS T
"! IS A SCI;E (! GD1 B ! GD IS N SCI;E1
NOR IS T : HAS A QUAL;Y OR IS A 3TR>Y1
?\< ! GD IS BO? ( ^!4 ,"S"TS NEI ! F/
T]M IS /AT$ (! MI4LE1 NOR ! MI4LE (!
?IRD1 :ILE ! F/ IS "S"TS /AT$ (! ?IRD1 &
"S"TS N3 E4G4 IF "! IS A G5US ( T ( : "!
IS A SCI;E1 & IF "! IS A SCI;E (! GD1 WE
3CLUDE T "! IS A G5US (! GD4 ,B NO?+ IS
PR$ICAT$ ( ANY?+4 ,& IF T ( : "! IS A
SCI;E IS A G5US1 & IF "! IS A SCI;E (!
GD1 WE 3CLUDE T ! GD IS A G5US4 ,! F/
T]M !N IS PR$ICAT$ (! EXTREME1 B 9 !
PREMISSES "O ?+ IS N /AT$ ( ANO!R4
  ,! SAME HOLDS GD ": ! REL,N IS
NEGATIVE4 ,= ,8T DOES N 2L;G 6?0' DOES N
ALW M1N T ,8? IS N T0'1 B "S"TS T ,8? IS
N ( T0' OR ,8= T0'1 E4G4 ,8"! IS N A
MO;N (A MO;N OR A 2COM+ (A 2COM+1 B "!
IS A 2COM+ ( PL1SURE3 S PL1SURE IS N A
2COM+40' ,OR AG X MAY 2 SD T "! IS A
SIGN ( LAU<T]1 B "! IS N A SIGN (A SIGN1
3SEQU5TLY LAU<T] IS N A SIGN4 ,? HOLDS 9
! O!R CASES TOO1 9 : ! !SIS IS REFUT$ 2C
! G5US IS ASS]T$ 9 A "PICUL> WAY1 9
REL,N 6! T]MS (! !SIS4 ,AG TAKE ! 9F];E
,8OPPORTUN;Y IS N ! "R "T3 = OPPORTUN;Y
2L;GS 6,GOD1 B ! "R "T DOES N1 S9CE NO?+
IS USE;L 6,GOD0'4 ,WE M/ TAKE Z T]MS
OPPORTUN;Y-"R "T-,GOD3 B ! PREMISS M/ 2
"U/OOD AC 6! CASE (! N\N4 ,= WE /ATE ?
UNIV]S,Y )\T QUALIFIC,N1 T ! T]MS "\ ALW
6BE /AT$ 9 ! NOM9ATIVE1 E4G4 MAN1 GD1
3TR>IES1 N 9 OBLIQUE CASES1 E4G4 ( MAN1
(A GD1 ( 3TR>IES1 B ! PREMISSES "\ 6BE
"U/OOD ) REF];E 6! CASES ( EA* T]M-EI !
DATIVE1 E4G4 ,8EQUAL 6?0'1 OR ! G5ITIVE1
E4G4 ,8D\# ( ?0'1 OR ! A3USATIVE1 E4G4
,8T : /RIKES OR SEES ?0'1 OR !
NOM9ATIVE1 E4G4 ,8MAN IS AN ANIMAL0'1 OR
9 :AT"E O!R WAY ! ^W FALLS 9 ! PREMISS4

                  #CG

  ,! EXPRES.NS ,8? 2L;GS 6T0' & ,8?
HOLDS TRUE ( T0' M/ 2 "U/OOD 9 Z _M WAYS
Z "! >E DI6]5T CATEGORIES1 & ^!
CATEGORIES M/ 2 TAK5 EI ) OR )\T
QUALIFIC,N1 & FUR!R Z SIMPLE OR -P.D3 !
SAME HOLDS GD (! CORRESPOND+ NEGATIVE
EXPRES.NS4 ,WE M/ 3SID] ^! PO9TS & DEF9E
!M BETT]4


                  #CH

  ,A T]M : IS REP1T$ 9 ! PREMISSES "\
6BE JO9$ 6! F/ EXTREME1 N 6! MI4LE4 ,I
M1N = EXAMPLE T IF A SYLLOGISM %D 2 MADE
PROV+ T "! IS K ( JU/ICE1 T X IS GD1 !
EXPRES.N ,8T X IS GD0' 7OR ,8QUA GD0'7
%D 2 JO9$ 6! F/ T]M4 ,LET ,A /& = ,8K T
X IS GD0'1 ;,B = GD1 ;,C = JU/ICE4 ,X IS
TRUE 6PR$ICATE ;,A ( ,B4 ,=(! GD "! IS K
T X IS GD4 ,AL X IS TRUE 6PR$ICATE ;,B (
,C4 ,= JU/ICE IS ID5TICAL )A GD4 ,9 ?
WAY AN ANALYSIS (! >GU;T C 2 MADE4 ,B IF
! EXPRES.N ,8T X IS GD0' 7 A4$ TO ;,B1 !
3CLU.N W N FOLL[3 = ,A W 2 TRUE ( ;,B1 B
;,B W N 2 TRUE ( ,C4 ,= 6PR$ICATE (
JU/ICE ! T]M ,8GD T X IS GD0' IS FALSE &
N 9TELLIGI#4 ,SIMIL>LY IF X %D 2 PROV$ T
! H1L?Y IS AN OBJECT ( K QUA GD1 ( GOAT-
/AG AN OBJECT ( K QUA N EXI/+1 OR MAN
P]I%A# QUA AN OBJECT ( S5SE3 9 E CASE 9
: AN A4I;N IS MADE 6! PR$ICATE1 ! A4I;N
M/ 2 JO9$ 6! EXTREME4
  ,! POSI;N (! T]MS IS N ! SAME :5 "S?+
IS E/ABLI%$ )\T QUALIFIC,N & :5 X IS
QUALIFI$ 0"S ATTRIBUTE OR 3DI;N1 E4G4 :5
! GD IS PROV$ 6BE AN OBJECT ( K & :5 X
IS PROV$ 6BE AN OBJECT ( K T X IS GD4
,IF X HAS BE5 PROV$ 6BE AN OBJECT ( K
)\T QUALIFIC,N1 WE M/ PUT Z MI4LE T]M
,8T : IS0'1 B IF WE ADD ! QUALIFIC,N ,8T
X IS GD0'1 ! MI4LE T]M M/ 2 ,8T : IS
"S?+0'4 ,LET ,A /& = ,8K T X IS "S?+0'1
;,B /& = ,8"S?+0'1 & ;,C /& = ,8GD0'4 ,X
IS TRUE 6PR$ICATE ;,A ( ;,B3 = EX
HYPO!SI "! IS A SCI;E ( T : IS "S?+1 T X
IS "S?+4 ;,B TOO IS TRUE ( ;,C3 = T :
;,C REPRES5TS IS "S?+4 ,3SEQU5TLY ,A IS
TRUE ( ;,C3 "! W !N 2 K (! GD1 T X IS
GD3 = EX HYPO!SI ! T]M ,8"S?+0' 9DICATES
! ?+'S SPECIAL NATURE4 ,B IF ,82+0' 7
TAK5 Z MI4LE & ,82+0' SIMPLY 7 JO9$ 6!
EXTREME1 N ,82+ "S?+0'1 WE %D N H _H A
SYLLOGISM PROV+ T "! IS K (! GD1 T X IS
GD1 B T X IS2 E4G4 LET ,A /& = K T X IS1
;,B = 2+1 ;,C = GD4 ,CLE>LY !N 9
SYLLOGISMS : >E ?US LIMIT$ WE M/ TAKE !
T]MS 9 ! WAY /AT$4


                  #CI

  ,WE "\ AL 6EX*ANGE T]MS : H ! SAME
VALUE1 ^W = ^W1 & PHRASE = PHRASE1 & ^W
& PHRASE1 & ALW TAKE A ^W 9 PREF];E 6A
PHRASE3 = ?US ! SETT+ \ (! T]MS W 2
EASI]4 ,= EXAMPLE IF X MAKES NO DI6];E
:E!R WE SAY T ! SUPPOSA# IS N ! G5US (!
OP9A# OR T ! OP9A# IS N ID5TICAL )A
"PICUL> K9D ( SUPPOSA# 7= :AT IS M1NT IS
! SAME 9 BO? /ATE;TS71 X IS BETT] 6TAKE
Z ! T]MS ! SUPPOSA# &! OP9A# 9 PREF];E
6! PHRASE SU7E/$4

                  #DJ

  ,S9CE ! EXPRES.NS ,8PL1SURE IS GD0' &
,8PL1SURE IS ! GD0' >E N ID5TICAL1 WE M/
N SET \ ! T]MS 9 ! SAME WAY2 B IF !
SYLLOGISM IS 6PROVE T PL1SURE IS ! GD1 !
T]M M/ 2 ,8! GD0'1 B IF ! OBJECT IS
6PROVE T PL1SURE IS GD1 ! T]M W 2
,8GD0'4 ,SIMIL>LY 9 ALL O!R CASES4


                  #DA

  ,X IS N ! SAME1 EI 9 FACT OR 9 SPEE*1
T ,A 2L;GS 6ALL ( T 6: ;,B 2L;GS1 & T ,A
2L;GS 6ALL ( T 6ALL ( : ;,B 2L;GS3 =
NO?+ PREV5TS ;,B F 2L;G+ TO ;,C1 ?\< N
6ALL ;,C3 E4G4 LET ;,B /& = B1UTI;L1 &
;,C = :ITE4 ,IF B1UTY 2L;GS 6"S?+ :ITE1
X IS TRUE 6SAY T B1UTY 2L;GS 6T : IS
:ITE2 B N P]H 6"EY?+ T IS :ITE4 ,IF !N
,A 2L;GS TO ;,B1 B N 6"EY?+ ( : ;,B IS
PR$ICAT$1 !N :E!R ;,B 2L;GS 6ALL ;,C OR
M]ELY 2L;GS TO ;,C1 X IS N NEC T ,A %D
2L;G1 ,I D N SAY 6ALL ;,C1 B EV5 TO ;,C
AT ALL4 ,B IF ,A 2L;GS 6"EY?+ ( : ;,B IS
TRULY /AT$1 X W FOLL[ T ,A C 2 SD ( ALL
( T ( ALL ( : ;,B IS SD4 ,IF H["E ,A IS
SD ( T ( ALL ( : ;,B MAY 2 SD1 NO?+
PREV5TS ;,B 2L;G+ TO ;,C1 & YET ,A N
2L;G+ 6ALL ;,C OR 6ANY ;,C AT ALL4 ,IF
!N WE TAKE ?REE T]MS X IS CLE> T !
EXPRES.N ',A IS SD ( ALL ( : ;,B IS SD0'
M1NS ?1 ',A IS SD ( ALL ! ?+S ( : ;,B IS
SD0'4 ,& IF ;,B IS SD ( ALL (A ?IRD T]M1
S AL IS ,A3 B IF ;,B IS N SD ( ALL (!
?IRD T]M1 "! IS NO NECESS;Y T ,A %D 2 SD
( ALL ( X4
  ,WE M/ N SUPPOSE T "S?+ ABSURD RESULTS
"? SETT+ \ ! T]MS3 = WE D N USE ! EXI/;E
( ? "PICUL> ?+1 B IMITATE ! GEOMETRICIAN
:O SAYS T ,8? L9E A FOOT L;G0' OR ,8?
/RAI<T L9E0' OR ,8? L9E )\T BR1D?0'
EXI/S AL? X DOES N1 B DOES N USE !
DIAGRAMS 9 ! S5SE T HE R1SONS F !M4 ,= 9
G5]AL1 IF TWO ?+S >E N RELAT$ Z :OLE 6"P
& "P 6:OLE1 ! PROV] DOES N PROVE F !M1 &
S NO SYLLOGISM A IS =M$4 ,WE 7,I M1N !
LE>N]7 USE ! PROCESS ( SETT+ \ T]MS L
P]CEP;N 0S5SE1 N Z ?\< X 7 IMPOSSI#
6DEMON/RATE )\T ^! ILLU/RATIVE T]MS1 Z X
IS 6DEMON/RATE )\T ! PREMISSES (!
SYLLOGISM4

                  #DB

  ,WE %D N =GET T 9 ! SAME SYLLOGISM N
ALL 3CLU.NS >E R1*$ "? "O FIGURE1 B "O
"? "O FIGURE1 ANO!R "? ANO!R4 ,CLE>LY !N
WE M/ ANALYSE >GU;TS 9 A3ORD.E ) ?4
,S9CE N E PRO#M IS PROV$ 9 E FIGURE1 B
C]TA9 PRO#MS 9 EA* FIGURE1 X IS CLE> F !
3CLU.N 9 :AT FIGURE ! PREMISSES %D 2
S"\4

                  #DC

  ,9 REF];E 6^? >GU;TS AIM+ AT A DEF9I;N
: H BE5 DIRECT$ 6PROVE "S "P (! DEF9I;N1
WE M/ TAKE Z A T]M ! PO9T 6: ! >GU;T HAS
BE5 DIRECT$1 N ! :OLE DEF9I;N3 = S WE %
2 LESS LIKELY 6BE 4TURB$ 0! L5G? (! T]M3
E4G4 IF A MAN PROVES T WAT] IS A DR9KA#
LIQUID1 WE M/ TAKE Z T]MS DR9KA# & WAT]4

                  #DD

  ,FUR!R WE M/ N TRY 6REDUCE HYPO!TICAL
SYLLOGISMS2 =)! GIV5 PREMISSES X IS N
POSSI# 6REDUCE !M4 ,= !Y H N BE5 PROV$
0SYLLOGISM1 B ASS5T$ 60AGREE;T4 ,= 9/.E
IF A MAN %D SUPPOSE T UN.S "! IS "O
FACULTY ( 3TR>IES1 "! _C 2 "O SCI;E1 &
%D !N >GUE T N E FACULTY IS ( 3TR>IES1
E4G4 ( :AT IS H1L?Y & :AT IS SICKLY3 =!
SAME ?+ W !N 2 AT ! SAME "T H1L?Y &
SICKLY4 ,HE HAS %[N T "! IS N "O FACULTY
( ALL 3TR>IES1 B HE HAS N PROV$ T "! IS
N A SCI;E4 ,& YET "O M/ AGREE4 ,B !
AGREE;T DOES N -E F A SYLLOGISM1 B F AN
HYPO!SIS4 ,? >GU;T _C 2 REDUC$3 B ! PRO(
T "! IS N A S+LE FACULTY C4 ,! LATT]
>GU;T P]H 0 A SYLLOGISM3 B ! =M] 0 AN
HYPO!SIS4
  ,! SAME HOLDS GD ( >GU;TS : >E BR"\ 6A
3CLU.N P] IMPOSSIBILE4 ,^! _C 2 ANALYS$
EI2 B ! REDUC;N 6:AT IS IMPOSSI# C 2
ANALYS$ S9CE X IS PROV$ 0SYLLOGISM1 ?\<
! RE/ (! >GU;T _C1 2C ! 3CLU.N IS R1*$ F
AN HYPO!SIS4 ,B ^! DI6] F ! PREVI\S
>GU;TS3 = 9 ! =M] A PRELIM9>Y AGREE;T M/
2 R1*$ IF "O IS 6A3EPT ! 3CLU.N2 E4G4 AN
AGREE;T T IF "! IS PROV$ 6BE "O FACULTY
( 3TR>IES1 !N 3TR>IES FALL "U ! SAME
SCI;E2 ":AS 9 ! LATT]1 EV5 IF NO
PRELIM9>Y AGREE;T HAS BE5 MADE1 M5 /
A3EPT ! R1SON+1 2C ! FALS;Y IS PAT5T1
E4G4 ! FALS;Y ( :AT FOLL[S F ! ASSUMP;N
T ! DIAGONAL IS -M5SURATE1 VIZ4 T !N ODD
NUMB]S >E EQUAL 6EV5S4
  ,_M O!R >GU;TS >E BR"\ 6A 3CLU.N 0!
HELP ( AN HYPO!SIS2 ^! WE "\ 63SID] &
M>K \ CLE>LY4 ,WE % DESCRIBE 9 ! SEQUEL
_! DI6];ES1 &! V>I\S WAYS 9 : HYPO!TICAL
>GU;TS >E =M$3 B AT PRES5T ? M* M/ 2
CLE>1 T X IS N POSSI# 6RESOLVE S* >GU;TS
96! FIGURES4 ,& WE H EXPLA9$ ! R1SON4

                  #DE

  ,:AT"E PRO#MS >E PROV$ 9 M ?AN "O
FIGURE1 IF !Y H BE5 E/ABLI%$ 9 "O FIGURE
0SYLLOGISM1 C 2 REDUC$ 6ANO!R FIGURE1
E4G4 A NEGATIVE SYLLOGISM 9 ! F/ FIGURE
C 2 REDUC$ 6! SECOND1 &A SYLLOGISM 9 !
MI4LE FIGURE 6! F/1 N ALL H["E B "S
ONLY4 ,! PO9T W 2 CLE> 9 ! SEQUEL4 ,IF
,A 2L;GS 6NO ;,B1 & ;,B 6ALL ;,C1 !N ,A
2L;GS 6NO ,C4 ,?US ! F/ FIGURE2 B IF !
NEGATIVE /ATE;T IS 3V]T$1 WE % H ! MI4LE
FIGURE4 ,= ;,B 2L;GS 6NO ;,A1 & 6ALL ,C4
,SIMIL>LY IF ! SYLLOGISM IS N UNIV]SAL B
"PICUL>1 E4G4 IF ,A 2L;GS 6NO ;,B1 & ;,B
6"S ,C4 ,3V]T ! NEGATIVE /ATE;T & Y W H
! MI4LE FIGURE4
  ,! UNIV]SAL SYLLOGISMS 9 ! SECOND
FIGURE C 2 REDUC$ 6! F/1 B ONLY "O (!
TWO "PICUL> SYLLOGISMS4 ,LET ,A 2L;G 6NO
;,B & 6ALL ,C4 ,3V]T ! NEGATIVE /ATE;T1
& Y W H ! F/ FIGURE4 ,= ;,B W 2L;G 6NO
;,A & ,A 6ALL ,C4 ,B IF ! A6IRMATIVE
/ATE;T 3C]NS ;,B1 &! NEGATIVE ;,C1 ;,C
M/ 2 MADE F/ T]M4 ,= ;,C 2L;GS 6NO ;,A1
& ,A 6ALL ;,B3 "!=E ;,C 2L;GS 6NO ,B4
;,B !N 2L;GS 6NO ;,C3 =! NEGATIVE /ATE;T
IS 3V]TI#4
  ,B IF ! SYLLOGISM IS "PICUL>1 :5"E !
NEGATIVE /ATE;T 3C]NS ! MAJOR EXTREME1
REDUC;N 6! F/ FIGURE W 2 POSSI#1 E4G4 IF
,A 2L;GS 6NO ;,B & 6"S ;,C3 3V]T !
NEGATIVE /ATE;T & Y W H ! F/ FIGURE4 ,=
;,B W 2L;G 6NO ;,A & ,A 6"S ,C4 ,B :5 !
A6IRMATIVE /ATE;T 3C]NS ! MAJOR EXTREME1
NO RESOLU;N W 2 POSSI#1 E4G4 IF ,A 2L;GS
6ALL ;,B1 B N 6ALL ;,C3 =! /ATE;T ;,,AB
DOES N ADMIT ( 3V].N1 NOR WD "! 2 A
SYLLOGISM IF X DID4
  ,AG SYLLOGISMS 9 ! ?IRD FIGURE _C ALL
2 RESOLV$ 96! F/1 ?\< ALL SYLLOGISMS 9 !
F/ FIGURE C 2 RESOLV$ 96! ?IRD4 ,LET ,A
2L;G 6ALL ;,B & ;,B 6"S ,C4 ,S9CE !
"PICUL> A6IRMATIVE IS 3V]TI#1 ;,C W 2L;G
6"S ;,B3 B ,A 2L;G$ 6ALL ;,B3 S T ! ?IRD
FIGURE IS =M$4 ,SIMIL>LY IF ! SYLLOGISM
IS NEGATIVE3 =! "PICUL> A6IRMATIVE IS
3V]TI#3 "!=E ,A W 2L;G 6NO ;,B1 & 6"S
,C4
  ,(! SYLLOGISMS 9 ! LA/ FIGURE "O ONLY
_C 2 RESOLV$ 96! F/1 VIZ4 :5 ! NEGATIVE
/ATE;T IS N UNIV]SAL3 ALL ! RE/ C 2
RESOLV$4 ,LET ;,A & ;,B 2 A6IRM$ ( ALL
;,C3 !N ;,C C 2 3V]T$ "PI,Y ) EI ,A OR
;,B3 ;,C !N 2L;GS 6"S ,B4 ,3SEQU5TLY WE
% GET ! F/ FIGURE1 IF ,A 2L;GS 6ALL ;,C1
& ;,C 6"S (! ,BS4 ,IF ,A 2L;GS 6ALL ;,C
& ;,B 6"S ;,C1 ! >GU;T IS ! SAME3 = ;,B
IS 3V]TI# 9 REF];E TO ;,C4 ,B IF ;,B
2L;GS 6ALL ;,C & ,A 6"S ;,C1 ! F/ T]M M/
2 ;,B3 = ;,B 2L;GS 6ALL ;,C1 & ;,C 6"S
;,A1 "!=E ;,B 2L;GS 6"S ,A4 ,B S9CE !
"PICUL> /ATE;T IS 3V]TI#1 ,A W 2L;G 6"S
,B4 ,IF ! SYLLOGISM IS NEGATIVE1 :5 !
T]MS >E UNIV]SAL WE M/ TAKE !M 9 A
SIMIL> WAY4 ,LET ;,B 2L;G 6ALL ;,C1 & ,A
6NO ;,C3 !N ;,C W 2L;G 6"S ;,B1 & ,A 6NO
;,C2 & S ;,C W 2 MI4LE T]M4 ,SIMIL>LY IF
! NEGATIVE /ATE;T IS UNIV]SAL1 !
A6IRMATIVE "PICUL>3 = ,A W 2L;G 6NO ;,C1
& ;,C 6"S (! ,BS4 ,B IF ! NEGATIVE
/ATE;T IS "PICUL>1 NO RESOLU;N W 2
POSSI#1 E4G4 IF ;,B 2L;GS 6ALL ;,C1 & ,A
N 2L;G 6"S ;,C3 3V]T ! /ATE;T ,,BC & BO?
PREMISSES W 2 "PICUL>4
  ,X IS CLE> T 9 ORD] 6RESOLVE ! FIGURES
96"O ANO!R ! PREMISS : 3C]NS ! M9OR
EXTREME M/ 2 3V]T$ 9 BO? ! FIGURES3 = :5
? PREMISS IS ALT]$1 ! TRANSI;N 6! O!R
FIGURE IS MADE4
  ,"O (! SYLLOGISMS 9 ! MI4LE FIGURE C1
! O!R _C1 2 RESOLV$ 96! ?IRD FIGURE4
,:5"E ! UNIV]SAL /ATE;T IS NEGATIVE1
RESOLU;N IS POSSI#4 ,= IF ,A 2L;GS 6NO
;,B & 6"S ;,C1 BO? ;,B & ;,C ALIKE >E
3V]TI# 9 REL,N TO ;,A1 S T ;,B 2L;GS 6NO
;,A & ;,C 6"S ,A4 ,A "!=E IS MI4LE T]M4
,B :5 ,A 2L;GS 6ALL ;,B1 & N 6"S ;,C1
RESOLU;N W N 2 POSSI#3 = NEI (!
PREMISSES IS UNIV]SAL AF 3V].N4
  ,SYLLOGISMS 9 ! ?IRD FIGURE C 2
RESOLV$ 96! MI4LE FIGURE1 :5"E !
NEGATIVE /ATE;T IS UNIV]SAL1 E4G4 IF ,A
2L;GS 6NO ;,C1 & ;,B 6"S OR ALL ,C4 ,=
;,C !N W 2L;G 6NO ;,A & 6"S ,B4 ,B IF !
NEGATIVE /ATE;T IS "PICUL>1 NO RESOLU;N
W 2 POSSI#3 =! "PICUL> NEGATIVE DOES N
ADMIT ( 3V].N4
  ,X IS CLE> !N T ! SAME SYLLOGISMS _C 2
RESOLV$ 9 ^! FIGURES : CD N 2 RESOLV$
96! F/ FIGURE1 & T :5 SYLLOGISMS >E
REDUC$ 6! F/ FIGURE ^! AL"O >E 3FIRM$
0REDUC;N 6:AT IS IMPOSSI#4
  ,X IS CLE> F :AT WE H SD H[ WE "\
6REDUCE SYLLOGISMS1 & T ! FIGURES MAY 2
RESOLV$ 96"O ANO!R4

                  #DF

  ,9 E/ABLI%+ OR REFUT+1 X MAKES "S
DI6];E :E!R WE SUPPOSE ! EXPRES.NS ,8N
6BE ?0' & ,86BE N-?0' >E ID5TICAL OR
DI6]5T 9 M1N+1 E4G4 ,8N 6BE :ITE0' &
,86BE N-:ITE0'4 ,= !Y D N M1N ! SAME ?+1
NOR IS ,86BE N-:ITE0' ! NEG,N ( ,86BE
:ITE0'1 B ,8N 6BE :ITE0'4 ,! R1SON = ?
IS Z FOLL[S4 ,! REL,N ( ,8HE C WALK0' TO
,8HE C N-WALK0' IS SIMIL> 6! REL,N ( ,8X
IS :ITE0' TO ,8X IS N-:ITE0'2 S IS T (
,8HE "KS :AT IS GD0' TO ,8HE "KS :AT IS
N-GD0'4 ,= "! IS NO DI6];E 2T !
EXPRES.NS ,8HE "KS :AT IS GD0' & ,8HE IS
"K+ :AT IS GD0'1 OR ,8HE C WALK0' & ,8HE
IS A# 6WALK0'3 "!=E "! IS NO DI6];E 2T
_! 3TR>IES ,8HE _C WALK0'-,8HE IS N A#
6WALK0'4 ,IF !N ,8HE IS N A# 6WALK0'
M1NS ! SAME Z ,8HE IS A# N 6WALK0'1
CAPAC;Y 6WALK & 9CAPAC;Y 6WALK W 2L;G AT
! SAME "T 6! SAME P]SON 7=! SAME MAN C
BO? WALK & N-WALK1 & IS POSSESS$ ( K (
:AT IS GD &( :AT IS N-GD71 B AN A6IRM,N
&A D5IAL : >E OPPOS$ 6"O ANO!R D N 2L;G
AT ! SAME "T 6! SAME ?+4 ,Z !N ,8N 6"K
:AT IS GD0' IS N ! SAME Z ,86"K :AT IS N
GD0'1 S ,86BE N-GD0' IS N ! SAME Z ,8N
6BE GD0'4 ,= :5 TWO PAIRS CORRESPOND1 IF
! "O PAIR >E DI6]5T F "O ANO!R1 ! O!R
PAIR AL M/ 2 DI6]5T4 ,NOR IS ,86BE N-
EQUAL0' ! SAME Z ,8N 6BE EQUAL0'3 = "!
IS "S?+ "ULY+ ! "O1 VIZ4 T : IS N-EQUAL1
& ? IS ! UNEQUAL1 B "! IS NO?+ "ULY+ !
O!R4 ,":=E N "EY?+ IS EI EQUAL OR
UNEQUAL1 B "EY?+ IS EQUAL OR IS N EQUAL4
,FUR!R ! EXPRES.NS ,8X IS A N-:ITE LOG0'
& ,8X IS N A :ITE LOG0' D N IMPLY "O
ANO!R'S TRU?4 ,= IF ,8X IS A N-:ITE
LOG0'1 X M/ 2 A LOG3 B T : IS N A :ITE
LOG NE$ N 2 A LOG AT ALL4 ,"!=E X IS
CLE> T ,8X IS N-GD0' IS N ! D5IAL ( ,8X
IS GD0'4 ,IF !N E S+LE /ATE;T MAY TRULY
2 SD 6BE EI AN A6IRM,N OR A NEG,N1 IF X
IS N A NEG,N CLE>LY X M/ 9 A S5SE 2 AN
A6IRM,N4 ,B E A6IRM,N HAS A CORRESPOND+
NEG,N4 ,! NEG,N !N ( ,8X IS N-GD0' IS
,8X IS N N-GD0'4 ,! REL,N ( ^! /ATE;TS
6"O ANO!R IS Z FOLL[S4 ,LET ,A /& =
,86BE GD0'1 ;,B = ,8N 6BE GD0'1 LET ;,C
/& = ,86BE N-GD0' & 2 PLAC$ "U ;,B1 &
LET ;,D /& = N 6BE N-GD0' & 2 PLAC$ "U
,A4 ,!N EI ,A OR ;,B W 2L;G 6"EY?+1 B !Y
W N"E 2L;G 6! SAME ?+2 & EI ;,C OR ;,D W
2L;G 6"EY?+1 B !Y W N"E 2L;G 6! SAME ?+4
,& ;,B M/ 2L;G 6"EY?+ 6: ;,C 2L;GS4 ,=
IF X IS TRUE 6SAY ,8X IS A N-:ITE0'1 X
IS TRUE AL 6SAY ,8X IS N :ITE0'3 = X IS
IMPOSSI# T A ?+ %D SIMULTANE\SLY 2 :ITE
& 2 N-:ITE1 OR 2 A N-:ITE LOG & 2 A :ITE
LOG2 3SEQU5TLY IF ! A6IRM,N DOES N 2L;G1
! D5IAL M/ 2L;G4 ,B ;,C DOES N ALW 2L;G
TO ;,B3 = :AT IS N A LOG AT ALL1 _C 2 A
N-:ITE LOG EI4 ,ON ! O!R H& ;,D 2L;GS
6"EY?+ 6: ,A 2L;GS4 ,= EI ;,C OR ;,D
2L;GS 6"EY?+ 6: ,A 2L;GS4 ,B S9CE A ?+
_C 2 SIMULTANE\SLY N-:ITE & :ITE1 ;,D M/
2L;G 6"EY?+ 6: ,A 2L;GS4 ,=( T : IS :ITE
X IS TRUE 6SAY T X IS N N-:ITE4 ,B ,A IS
N TRUE ( ALL ,D4 ,=( T : IS N A LOG AT
ALL X IS N TRUE 6SAY ;,A1 VIZ4 T X IS A
:ITE LOG4 ,3SEQU5TLY ;,D IS TRUE1 B ,A
IS N TRUE1 I4E4 T X IS A :ITE LOG4 ,X IS
CLE> AL T ;,A & ;,C _C TGR 2L;G 6! SAME
?+1 & T ;,B & ;,D MAY POSSIBLY 2L;G 6!
SAME ?+4
  ,PRIVATIVE T]MS >E SIMIL>LY RELAT$
POSITIVE T] T]MS RESPECT ( ? >RANGE;T4
,LET ,A /& = ,8EQUAL0'1 ;,B = ,8N
EQUAL0'1 ;,C = ,8UNEQUAL0'1 ;,D = ,8N
UNEQUAL0'4
  ,9 _M ?+S AL1 6"S ( : "S?+ 2L;GS :
DOES N 2L;G 6O!RS1 ! NEG,N MAY 2 TRUE 9
A SIMIL> WAY1 VIZ4 T ALL >E N :ITE OR T
EA* IS N :ITE1 :ILE T EA* IS N-:ITE OR
ALL >E N-:ITE IS FALSE4 ,SIMIL>LY AL ,8E
ANIMAL IS N-:ITE0' IS N ! NEG,N ( ,8E
ANIMAL IS :ITE0' 7= BO? >E FALSE73 !
PROP] NEG,N IS ,8E ANIMAL IS N :ITE0'4
,S9CE X IS CLE> T ,8X IS N-:ITE0' & ,8X
IS N :ITE0' M1N DI6]5T ?+S1 & "O IS AN
A6IRM,N1 ! O!R A D5IAL1 X IS EVID5T T !
ME?OD ( PROV+ EA* _C 2 ! SAME1 E4G4 T
:AT"E IS AN ANIMAL IS N :ITE OR MAY N 2
:ITE1 & T X IS TRUE 6CALL X N-:ITE2 = ?
M1NS T X IS N-:ITE4 ,B WE MAY PROVE T X
IS TRUE 6CALL X :ITE OR N-:ITE 9 ! SAME
WAY = BO? >E PROV$ 3/RUCTIVELY 0M1NS (!
F/ FIGURE4 ,=! EXPRES.N ,8X IS TRUE0'
/&S ON A SIMIL> FOOT+ TO ,8X IS0'4 ,=!
NEG,N ( ,8X IS TRUE 6CALL X :ITE0' IS N
,8X IS TRUE 6CALL X N-:ITE0' B ,8X IS N
TRUE 6CALL X :ITE0'4 ,IF !N X IS 6BE
TRUE 6SAY T :AT"E IS A MAN IS MUSICAL OR
IS N-MUSICAL1 WE M/ ASSUME T :AT"E IS AN
ANIMAL EI IS MUSICAL OR IS N-MUSICAL2 &!
PRO( HAS BE5 MADE4 ,T :AT"E IS A MAN IS
N MUSICAL IS PROV$ DE/RUCTIVELY 9 ! ?REE
WAYS M5;N$4
  ,9 G5]AL :5"E ;,A & ;,B >E S* T !Y _C
2L;G AT ! SAME "T 6! SAME ?+1 & "O (!
TWO NECESS>ILY 2L;GS 6"EY?+1 & AG ;,C &
;,D >E RELAT$ 9 ! SAME WAY1 & ,A FOLL[S
;,C B ! REL,N _C 2 REV]S$1 !N ;,D M/
FOLL[ ;,B &! REL,N _C 2 REV]S$4 ,& ;,A &
;,D MAY 2L;G 6! SAME ?+1 B ;,B & ;,C _C4
,F/ X IS CLE> F ! FOLL[+ 3SID],N T ;,D
FOLL[S ,B4 ,= S9CE EI ;,C OR ;,D
NECESS>ILY 2L;GS 6"EY?+2 & S9CE ;,C _C
2L;G 6T 6: ;,B 2L;GS1 2C X C>RIES ,A
AL;G ) X & ;,A & ;,B _C 2L;G 6! SAME ?+2
X IS CLE> T ;,D M/ FOLL[ ,B4 ,AG S9CE
;,C DOES N RECIPROCATE ) B ;,A1 B ;,C OR
;,D 2L;GS 6"EY?+1 X IS POSSI# T ;,A &
;,D %D 2L;G 6! SAME ?+4 ,B ;,B & ;,C _C
2L;G 6! SAME ?+1 2C ,A FOLL[S ;,C2 & S
"S?+ IMPOSSI# RESULTS4 ,X IS CLE> !N T
;,B DOES N RECIPROCATE ) ;,D EI1 S9CE X
IS POSSI# T ;,D & ,A %D 2L;G AT ! SAME
"T 6! SAME ?+4
  ,X RESULTS "S"TS EV5 9 S* AN >RANGE;T
( T]MS T "O IS DCVD "? N APPREH5D+ !
OPPOSITES "RLY1 "O ( : M/ 2L;G 6"EY?+1
E4G4 WE MAY R1SON T ,8IF ;,A & ;,B _C
2L;G AT ! SAME "T 6! SAME ?+1 B X IS NEC
T "O ( !M %D 2L;G 6:AT"E ! O!R DOES N
2L;G TO3 & AG ;,C & ;,D >E RELAT$ 9 !
SAME WAY1 & FOLL[S "EY?+ : ;,C FOLL[S3 X
W RESULT T ;,B 2L;GS NECESS>ILY 6"EY?+
6: ;,D 2L;GS0'3 B ? IS FALSE4 ,8,ASSUME
T ;,F /&S =! NEG,N ( ;,A & ;,B1 & AG T
;,H /&S =! NEG,N ( ;,C & ,D4 ,X IS NEC
!N T EI ,A OR ;,F %D 2L;G 6"EY?+3 = EI !
A6IRM,N OR ! D5IAL M/ 2L;G4 ,& AG EI ;,C
OR ;,H M/ 2L;G 6"EY?+3 = !Y >E RELAT$ Z
A6IRM,N & D5IAL4 ,& EX HYPO!SI ,A 2L;GS
6"EY?+ "E ?+ 6: ;,C 2L;GS4 ,"!=E ;,H
2L;GS 6"EY?+ 6: ;,F 2L;GS4 ,AG S9CE EI
;,F OR ;,B 2L;GS 6"EY?+1 & SIMIL>LY EI
;,H OR ;,D1 & S9CE ;,H FOLL[S ;,F1 ;,B
M/ FOLL[ ;,D3 = WE "K ?4 ,IF !N ,A
FOLL[S ;,C1 ;,B M/ FOLL[ ,D0'4 ,B ? IS
FALSE3 = Z WE PROV$ ! SEQU;E IS REV]S$ 9
T]MS S 3/ITUT$4 ,! FALLACY >ISES 2C P]H
X IS N NEC T ,A OR ;,F %D 2L;G 6"EY?+1
OR T ;,F OR ;,B %D 2L;G 6"EY?+3 = ;,F IS
N ! D5IAL ( ,A4 ,= N GD IS ! NEG,N ( GD3
& N-GD IS N ID5TICAL ) ,8NEI GD NOR N-
GD0'4 ,SIMIL>LY AL ) ;,C & ,D4 ,= TWO
NEG,NS H BE5 ASSUM$ 9 RESPECT 6"O T]M4


