#CEJ ,,BC ,,PO/]IOR ,,ANALYTICS 0,>I/OTLE TRANSLAT$ BY ;,G4 ,R4 ,G4 ,MURE ,TRANSLAT$ 0,MIKE ,KEI?LEY ,BOOK,I #A ,,ALL 9/RUC;N GIV5 OR RCVD 0WAY ( >GU;T PROCE$S F PRE-EXI/5T K4 ,? 2COMES EVID5T ^U A SURVEY ( ALL ! SPECIES ( S* 9/RUC;N4 ,! MA!MATICAL SCI;ES & ALL O!R SPECULATIVE 4CIPL9ES >E ACQUIR$ 9 ? WAY1 & S >E ! TWO =MS ( DIALECTICAL R1SON+1 SYLLOGI/IC & 9DUCTIVE2 = EA* ( ^! LATT] MAKE USE ( OLD K 6IM"P NEW1 ! SYLLOGISM ASSUM+ AN AUDI;E T A3EPTS XS PREMISSES1 9DUC;N EXHIBIT+ ! UNIV]SAL Z IMPLICIT 9 ! CLE>LY "KN "PICUL>4 ,AG1 ! P]SUA.N EX]T$ 0RHETORICAL >GU;TS IS 9 PR9CIPLE ! SAME1 S9CE !Y USE EI EXAMPLE1 A K9D ( 9DUC;N1 OR 5?YMEME1 A =M ( SYLLOGISM4 ,! PRE-EXI/5T K REQUIR$ IS ( TWO K9DS4 ,9 "S CASES ADMIS.N (! FACT M/ 2 ASSUM$1 9 O!RS -PREH5.N (! M1N+ (! T]M US$1 & "S"TS BO? ASSUMP;NS >E ESS5TIAL4 ,?US1 WE ASSUME T E PR$ICATE C 2 EI TRULY A6IRM$ OR TRULY D5I$ ( ANY SUBJECT1 & T ,8TRIANGLE0' M1NS S & S2 Z REG>DS ,8UNIT0' WE H 6MAKE ! D\# ASSUMP;N (! M1N+ (! ^W &! EXI/;E (! ?+4 ,! R1SON IS T ^! S"EAL OBJECTS >E N EQU,Y OBVI\S 6U4 ,RECOGNI;N (A TRU? MAY 9 "S CASES 3TA9 Z FACTORS BO? PREVI\S K & AL K ACQUIR$ SIMULTANE\SLY ) T RECOGNI;N-K1 ? LATT]1 (! "PICUL>S ACTU,Y FALL+ "U ! UNIV]SAL & "!9 ALR VIRTU,Y "KN4 ,= EXAMPLE1 ! /UD5T KNEW 2FH& T ! ANGLES ( E TRIANGLE >E EQUAL 6TWO "R ANGLES2 B X 0 ONLY AT ! ACTUAL MO;T AT : HE 0 2+ L$ ON 6RECOGNIZE ? Z TRUE 9 ! 9/.E 2F HM T HE CAME 6"K ,8? FIGURE 9SCRIB$ 9 ! SEMICIRCLE0' 6BE A TRIANGLE4 ,= "S ?+S 7VIZ4 ! S+UL>S F9,Y R1*$ : >E N PR$ICA# ( ANY?+ ELSE Z SUBJECT7 >E ONLY LE>NT 9 ? WAY1 I4E4 "! IS "H NO RECOGNI;N "? A MI4LE (A M9OR T]M Z SUBJECT 6A MAJOR4 ,2F HE 0 L$ ON 6RECOGNI;N OR 2F HE ACTU,Y DREW A 3CLU.N1 WE %D P]H SAY T 9 A MANN] HE KNEW1 9 A MANN] N4 ,IF HE DID N 9 AN UNQUALIFI$ S5SE (! T]M "K ! EXI/;E ( ? TRIANGLE1 H[ CD HE "K )\T QUALIFIC,N T XS ANGLES 7 EQUAL 6TWO "R ANGLES8 ,NO3 CLE>LY HE "KS N )\T QUALIFIC,N B ONLY 9 ! S5SE T HE "KS UNIV]S,Y4 ,IF ? 4T9C;N IS N DRAWN1 WE >E FAC$ )! DILEMMA 9 ! ,M5O3 EI A MAN W LE>N NO?+ OR :AT HE ALR "KS2 = WE _C A3EPT ! SOLU;N : "S P (F]4 ,A MAN IS ASK$1 ,8,D Y1 OR D Y N1 "K T E PAIR IS EV580' ,HE SAYS HE DOES "K X4 ,! "Q] !N PRODUCES A "PICUL> PAIR1 (! EXI/;E1 & S A =TIORI (! EV5;S1 ( : HE 0 UNAW>E4 ,! SOLU;N : "S P (F] IS 6ASS]T T !Y D N "K T E PAIR IS EV51 B ONLY T "EY?+ : !Y "K 6BE A PAIR IS EV53 YET :AT !Y "K 6BE EV5 IS T ( : !Y H DEMON/RAT$ EV5;S1 I4E4 :AT !Y MADE ! SUBJECT ( _! PREMISS1 VIZ4 N M]ELY E TRIANGLE OR NUMB] : !Y "K 6BE S*1 B ANY & E NUMB] OR TRIANGLE )\T RES]V,N4 ,= NO PREMISS IS "E C\*$ 9 ! =M ,8E NUMB] : Y "K 6BE S*0'1 OR ,8E RECTIL9E> FIGURE : Y "K 6BE S*0'3 ! PR$ICATE IS ALW 3/RU$ Z APPLICA# 6ANY & E 9/.E (! ?+4 ,ON ! O!R H&1 ,I IMAG9E "! IS NO?+ 6PREV5T A MAN 9 "O S5SE "K+ :AT HE IS LE>N+1 9 ANO!R N "K+ X4 ,! /RANGE ?+ WD BE1 N IF 9 "S S5SE HE KNEW :AT HE 0 LE>N+1 B IF HE 7 6"K X 9 T PRECISE S5SE & MANN] 9 : HE 0 LE>N+ X4 #B ,WE SUPPOSE \RVS 6POSSESS UNQUALIFI$ SCI5TIFIC K (A ?+1 Z OPPOS$ 6"K+ X 9 ! A3ID5TAL WAY 9 : ! SOPHI/ "KS1 :5 WE ?9K T WE "K ! CAUSE ON : ! FACT DEP5DS1 Z ! CAUSE ( T FACT &( NO O!R1 &1 FUR!R1 T ! FACT CD N 2 O!R ?AN X IS4 ,N[ T SCI5TIFIC "K+ IS "S?+ ( ? SORT IS EVID5T-WIT;S BO? ^? :O FALSELY CLAIM X & ^? :O ACTU,Y POSSESS X1 S9CE ! =M] M]ELY IMAG9E !MVS 6BE1 :ILE ! LATT] >E AL ACTU,Y1 9 ! 3DI;N DESCRIB$4 ,3SEQU5TLY ! PROP] OBJECT ( UNQUALIFI$ SCI5TIFIC K IS "S?+ : _C 2 O!R ?AN X IS4 ,"! MAY 2 ANO!R MANN] ( "K+ Z WELL-T W 2 4CUSS$ LAT]4 ,:AT ,I N[ ASS]T IS T AT ALL EV5TS WE D "K 0DEMON/R,N4 ,0DEMON/R,N ,I M1N A SYLLOGISM PRODUCTIVE ( SCI5TIFIC K1 A SYLLOGISM1 T IS1 ! GRASP ( : IS EO IPSO S* K4 ,ASSUM+ !N T MY !SIS Z 6! NATURE ( SCI5TIFIC "K+ IS CORRECT1 ! PREMISSES ( DEMON/RAT$ K M/ 2 TRUE1 PRIM>Y1 IMM1 BETT] "KN ?AN & PRIOR 6! 3CLU.N1 : IS FUR!R RELAT$ 6!M Z E6ECT 6CAUSE4 ,UN.S ^! 3DI;NS >E SATISFI$1 ! BASIC TRU?S W N 2 ,8APPROPRIATE0' 6! 3CLU.N4 ,SYLLOGISM "! MAY 9DE$ 2 )\T ^! 3DI;NS1 B S* SYLLOGISM1 N 2+ PRODUCTIVE ( SCI5TIFIC K1 W N 2 DEMON/R,N4 ,! PREMISSES M/ 2 TRUE3 = T : IS NON-EXI/5T _C 2 "KN-WE _C "K1 E4G4 T ! DIAGONAL (A SQU>E IS -M5SURATE ) XS SIDE4 ,! PREMISSES M/ 2 PRIM>Y & 9DEMON/RA#2 O!RWISE !Y W REQUIRE DEMON/R,N 9 ORD] 6BE "KN1 S9CE 6H K1 IF X 2 N A3ID5TAL K1 ( ?+S : >E DEMON/RA#1 M1NS PRECISELY 6H A DEMON/R,N ( !M4 ,! PREMISSES M/ 2 ! CAUSES (! 3CLU.N1 BETT] "KN ?AN X1 & PRIOR 6X2 XS CAUSES1 S9CE WE POSSESS SCI5TIFIC K (A ?+ ONLY :5 WE "K XS CAUSE2 PRIOR1 9 ORD] 6BE CAUSES2 ANTEC$5TLY "KN1 ? ANTEC$5T K 2+ N \R M]E "U/&+ (! M1N+1 B K (! FACT Z WELL4 ,N[ ,8PRIOR0' & ,8BETT] "KN0' >E AMBIGU\S T]MS1 = "! IS A DI6];E 2T :AT IS PRIOR & BETT] "KN 9 ! ORD] ( 2+ & :AT IS PRIOR & BETT] "KN 6MAN4 ,I M1N T OBJECTS NE>] 6S5SE >E PRIOR & BETT] "KN 6MAN2 OBJECTS )\T QUALIFIC,N PRIOR & BETT] "KN >E ^? FUR!R F S5SE4 ,N[ ! MO/ UNIV]SAL CAUSES >E FUR!/ F S5SE & "PICUL> CAUSES >E NE>E/ 6S5SE1 & !Y >E ?US EXACTLY OPPOS$ 6"O ANO!R4 ,9 SAY+ T ! PREMISSES ( DEMON/RAT$ K M/ 2 PRIM>Y1 ,I M1N T !Y M/ 2 ! ,8APPROPRIATE0' BASIC TRU?S1 = ,I ID5TIFY PRIM>Y PREMISS & BASIC TRU?4 ,A ,8BASIC TRU?0' 9 A DEMON/R,N IS AN IMM PROPOSI;N4 ,AN IMM PROPOSI;N IS "O : HAS NO O!R PROPOSI;N PRIOR 6X4 ,A PROPOSI;N IS EI "P ( AN ENUNCI,N1 I4E4 X PR$ICATES A S+LE ATTRIBUTE (A S+LE SUBJECT4 ,IF A PROPOSI;N IS DIALECTICAL1 X ASSUMES EI "P 9DI6]5TLY2 IF X IS DEMON/RATIVE1 X LAYS D[N "O "P 6! DEF9ITE EXCLU.N (! O!R 2C T "P IS TRUE4 ,! T]M ,8ENUNCI,N0' DENOTES EI "P (A 3TRADIC;N 9DI6]5TLY4 ,A 3TRADIC;N IS AN OPPOSI;N : ( XS [N NATURE EXCLUDES A MI4LE4 ,! "P (A 3TRADIC;N : 3JO9S A PR$ICATE )A SUBJECT IS AN A6IRM,N2 ! "P 4JO9+ !M IS A NEG,N4 ,I CALL AN IMM BASIC TRU? ( SYLLOGISM A ,8!SIS0' :51 ?\< X IS N SUSCEPTI# ( PRO( 0! T1*]1 YET IGNOR.E ( X DOES N 3/ITUTE A TOTAL B> 6PROGRESS ON ! "P (! PUPIL3 "O : ! PUPIL M/ "K IF HE IS 6LE>N ANY?+ :AT"E IS AN AXIOM4 ,I CALL X AN AXIOM 2C "! >E S* TRU?S & WE GIVE !M ! "N ( AXIOMS P> EXCELL;E4 ,IF A !SIS ASSUMES "O "P OR ! O!R ( AN ENUNCI,N1 I4E4 ASS]TS EI ! EXI/;E OR ! NON-EXI/;E (A SUBJECT1 X IS A HYPO!SIS2 IF X DOES N S ASS]T1 X IS A DEF9I;N4 ,DEF9I;N IS A ,8!SIS0' OR A ,8LAY+ "S?+ D[N0'1 S9CE ! >I?METICIAN LAYS X D[N T 6BE A UNIT IS 6BE QUANTITATIVELY 9DIVISI#2 B X IS N A HYPO!SIS1 = 6DEF9E :AT A UNIT IS IS N ! SAME Z 6A6IRM XS EXI/;E4 ,N[ S9CE ! REQUIR$ GR.D ( \R K-I4E4 ( \R 3VIC;N-(A FACT IS ! POSSES.N ( S* A SYLLOGISM Z WE CALL DEMON/R,N1 &! GR.D ( ! SYLLOGISM IS ! FACTS 3/ITUT+ XS PREMISSES1 WE M/ N ONLY "K ! PRIM>Y PREMISSES-"S IF N ALL ( !M-2FH&1 B "K !M BETT] ?AN ! 3CLU.N3 =! CAUSE ( AN ATTRIBUTE'S 9H];E 9 A SUBJECT ALW XF 9"HS 9 ! SUBJECT M FIRMLY ?AN T ATTRIBUTE2 E4G4 ! CAUSE ( \R LOV+ ANY?+ IS DE>] 6U ?AN ! OBJECT ( \R LOVE4 ,S S9CE ! PRIM>Y PREMISSES >E ! CAUSE ( \R K-I4E4 ( \R 3VIC;N-X FOLL[S T WE "K !M BETT]-T IS1 >E M 3V9C$ ( !M-?AN _! 3SEQU;ES1 PRECISELY 2C ( \R K (! LATT] IS ! E6ECT ( \R K (! PREMISSES4 ,N[ A MAN _C 2LIEVE 9 ANY?+ M ?AN 9 ! ?+S HE "KS1 UN.S HE HAS EI ACTUAL K ( X OR "S?+ BETT] ?AN ACTUAL K4 ,B WE >E FAC$ ) ? P>ADOX IF A /UD5T ^: 2LIEF RE/S ON DEMON/R,N HAS N PRIOR K2 A MAN M/ 2LIEVE 9 "S1 IF N 9 ALL1 (! BASIC TRU?S M ?AN 9 ! 3CLU.N4 ,MOREOV]1 IF A MAN SETS \ 6ACQUIRE ! SCI5TIFIC K T -ES "? DEMON/R,N1 HE M/ N ONLY H A BETT] K (! BASIC TRU?S &A FIRM] 3VIC;N ( !M ?AN (! 3NEXION : IS 2+ DEMON/RAT$3 M ?AN ?1 NO?+ M/ 2 M C]TA9 OR BETT] "KN 6HM ?AN ^! BASIC TRU?S 9 _! "* Z 3TRADICT+ ! FUNDA;TAL PREMISSES : L1D 6! OPPOS$ & ]RONE\S 3CLU.N4 ,= 9DE$ ! 3VIC;N ( PURE SCI;E M/ 2 UN%AKA#4 #C ,"S HOLD T1 [+ 6! NECESS;Y ( "K+ ! PRIM>Y PREMISSES1 "! IS NO SCI5TIFIC K4 ,O!RS ?9K "! IS1 B T ALL TRU?S >E DEMON/RA#4 ,NEI DOCTR9E IS EI TRUE OR A NEC DEDUC;N F ! PREMISSES4 ,! F/ S*OOL1 ASSUM+ T "! IS NO WAY ( "K+ O!R ?AN 0DEMON/R,N1 MA9TA9 T AN 9F9ITE REGRESS IS 9VOLV$1 ON ! GR.D T IF 2H ! PRIOR /&S NO PRIM>Y1 WE CD N "K ! PO/]IOR "? ! PRIOR 7":9 !Y >E "R1 = "O _C TRAV]SE AN 9F9ITE S]IES73 IF ON ! O!R H&-!Y SAY-! S]IES T]M9ATES & "! >E PRIM>Y PREMISSES1 YET ^! >E UN"KA# 2C 9CAPA# ( DEMON/R,N1 : AC 6!M IS ! ONLY =M ( K4 ,& S9CE ?US "O _C "K ! PRIM>Y PREMISSES1 K (! 3CLU.NS : FOLL[ F !M IS N PURE SCI5TIFIC K NOR PROP]LY "K+ AT ALL1 B RE/S ON ! M]E SUPPOSI;N T ! PREMISSES >E TRUE4 ,! O!R "PY AGREE ) !M Z REG>DS "K+1 HOLD+ T X IS ONLY POSSI# 0DEMON/R,N1 B !Y SEE NO DI6ICULTY 9 HOLD+ T ALL TRU?S >E DEMON/RAT$1 ON ! GR.D T DEMON/R,N MAY 2 CIRCUL> & RECIPROCAL4 ,\R [N DOCTR9E IS T N ALL K IS DEMON/RATIVE3 ON ! 3TR>Y1 K (! IMM PREMISSES IS 9DEP5D5T ( DEMON/R,N4 7,! NECESS;Y ( ? IS OBVI\S2 = S9CE WE M/ "K ! PRIOR PREMISSES F : ! DEMON/R,N IS DRAWN1 & S9CE ! REGRESS M/ 5D 9 IMM TRU?S1 ^? TRU?S M/ 2 9DEMON/RA#47 ,S*1 !N1 IS \R DOCTR9E1 & 9 A4I;N WE MA9TA9 T 2SS SCI5TIFIC K "! IS XS ORIG9ATIVE S\RCE : 5A#S U 6RECOGNIZE ! DEF9I;NS4 ,N[ DEMON/R,N M/ 2 BAS$ ON PREMISSES PRIOR 6& BETT] "KN ?AN ! 3CLU.N2 &! SAME ?+S _C SIMULTANE\SLY 2 BO? PRIOR & PO/]IOR 6"O ANO!R3 S CIRCUL> DEMON/R,N IS CLE>LY N POSSI# 9 ! UNQUALIFI$ S5SE ( ,8DEMON/R,N0'1 B ONLY POSSI# IF ,8DEMON/R,N0' 2 EXT5D$ 69CLUDE T O!R ME?OD ( >GU;T : RE/S ON A 4T9C;N 2T TRU?S PRIOR 6U & TRU?S )\T QUALIFIC,N PRIOR1 I4E4 ! ME?OD 0: 9DUC;N PRODUCES K4 ,B IF WE A3EPT ? EXT5.N ( XS M1N+1 \R DEF9I;N ( UNQUALIFI$ K W PROVE FAULTY2 = "! SEEM 6BE TWO K9DS ( X4 ,P]H1 H["E1 ! SECOND =M ( DEMON/R,N1 T : PROCE$S F TRU?S BETT] "KN 6U1 IS N DEMON/R,N 9 ! UNQUALIFI$ S5SE (! T]M4 ,! ADVOCATES ( CIRCUL> DEMON/R,N >E N ONLY FAC$ )! DI6ICULTY WE H J /AT$3 9 A4I;N _! !ORY REDUCES 6! M]E /ATE;T T IF A ?+ EXI/S1 !N X DOES EXI/-AN EASY WAY ( PROV+ ANY?+4 ,T ? IS S C 2 CLE>LY %[N 0TAK+ ?REE T]MS1 = 63/ITUTE ! CIRCLE X MAKES NO DI6];E :E!R _M T]MS OR FEW OR EV5 ONLY TWO >E TAK54 ,?US 0DIRECT PRO(1 IF ,A IS1 ;,B M/ BE2 IF ;,B IS1 ;,C M/ BE2 "!=E IF ,A IS1 ;,C M/ BE4 ,S9CE !N- BY ! CIRCUL> PRO(-IF ,A IS1 ;,B M/ BE1 & IF ;,B IS1 ,A M/ BE1 ,A MAY 2 SUB/ITUT$ = ;,C ABV4 ,!N ,8IF ;,B IS1 ,A M/ BE0' .K ,8IF ;,B IS1 ;,C M/ BE0'1 : ABV GAVE ! 3CLU.N ,8IF ,A IS1 ;,C M/ BE0'3 B ;,C & ,A H BE5 ID5TIFI$4 ,3SEQU5TLY ! UPHOLD]S ( CIRCUL> DEMON/R,N >E 9 ! POSI;N ( SAY+ T IF ,A IS1 ,A M/ BE-A SIMPLE WAY ( PROV+ ANY?+4 ,MOREOV]1 EV5 S* CIRCUL> DEMON/R,N IS IMPOSSI# EXCEPT 9 ! CASE ( ATTRIBUTES T IMPLY "O ANO!R1 VIZ4 ,8PECULI>0' PROP]TIES4 ,N[1 X HAS BE5 %[N T ! POSIT+ ( "O ?+- BE X "O T]M OR "O PREMISS-N"E 9VOLVES A NEC 3SEQU5T3 TWO PREMISSES 3/ITUTE ! F/ & SMALLE/ F.D,N = DRAW+ A 3CLU.N AT ALL & "!=E A =TIORI =! DEMON/RATIVE SYLLOGISM ( SCI;E4 ,IF1 !N1 ,A IS IMPLI$ 9 ;,B & ;,C1 & ;,B & ;,C >E RECIPROC,Y IMPLI$ 9 "O ANO!R & 9 ;,A1 X IS POSSI#1 Z HAS BE5 %[N 9 MY WRIT+S ON ! SYLLOGISM1 6PROVE ALL ! ASSUMP;NS ON : ! ORIG9AL 3CLU.N RE/$1 0CIRCUL> DEMON/R,N 9 ! F/ FIGURE4 ,B X HAS AL BE5 %[N T 9 ! O!R FIGURES EI NO 3CLU.N IS POSSI#1 OR AT L1/ N"O : PROVES BO? ! ORIG9AL PREMISSES4 ,PROPOSI;NS ! T]MS ( : >E N 3V]TI# _C 2 CIRCUL>LY DEMON/RAT$ AT ALL1 & S9CE 3V]TI# T]MS O3UR R>ELY 9 ACTUAL DEMON/R,NS1 X IS CLE>LY FRIVOL\S & IMPOSSI# 6SAY T DEMON/R,N IS RECIPROCAL & T "!=E "EY?+ C 2 DEMON/RAT$4 #D ,S9CE ! OBJECT ( PURE SCI5TIFIC K _C 2 O!R ?AN X IS1 ! TRU? OBTA9$ 0DEMON/RATIVE K W 2 NEC4 ,& S9CE DEMON/RATIVE K IS ONLY PRES5T :5 WE H A DEMON/R,N1 X FOLL[S T DEMON/R,N IS AN 9F];E F NEC PREMISSES4 ,S WE M/ 3SID] :AT >E ! PREMISSES ( DEMON/R,N-I4E4 :AT IS _! "*3 & Z A PRELIM9>Y1 LET U DEF9E :AT WE M1N 0AN ATTRIBUTE ,8TRUE 9 E 9/.E ( XS SUBJECT0'1 AN ,8ESS5TIAL0' ATTRIBUTE1 &A ,8-M5SURATE & UNIV]SAL0' ATTRIBUTE4 ,I CALL ,8TRUE 9 E 9/.E0' :AT IS TRULY PR$ICA# ( ALL 9/.ES-N ( "O 6! EXCLU.N ( O!RS-& AT ALL "TS1 N AT ? OR T "T ONLY2 E4G4 IF ANIMAL IS TRULY PR$ICA# ( E 9/.E ( MAN1 !N IF X 2 TRUE 6SAY ,8? IS A MAN0'1 ,8? IS AN ANIMAL0' IS AL TRUE1 & IF ! "O 2 TRUE N[ ! O!R IS TRUE N[4 ,A CORRESPOND+ A3.T HOLDS IF PO9T IS 9 E 9/.E PR$ICA# Z 3TA9$ 9 L9E4 ,"! IS EVID;E = ? 9 ! FACT T ! OBJEC;N WE RAISE AG/ A PROPOSI;N PUT 6U Z TRUE 9 E 9/.E IS EI AN 9/.E 9 :1 OR AN O3A.N ON :1 X IS N TRUE4 ,ESS5TIAL ATTRIBUTES >E 7#A7 S* Z 2L;G 6_! SUBJECT Z ELE;TS 9 XS ESS5TIAL NATURE 7E4G4 L9E ?US 2L;GS 6TRIANGLE1 PO9T 6L9E2 =! V 2+ OR ,8SUB/.E0' ( TRIANGLE & L9E IS -POS$ ( ^! ELE;TS1 : >E 3TA9$ 9 ! =MULAE DEF9+ TRIANGLE & L9E73 7#B7 S* T1 :ILE !Y 2L;G 6C]TA9 SUBJECTS1 ! SUBJECTS 6: !Y 2L;G >E 3TA9$ 9 ! ATTRIBUTE'S [N DEF9+ =MULA4 ,?US /RAIE & OBL;G1 6NUMB]2 & AL ! =MULA DEF9+ ANY "O ( ^! ATTRIBUTES 3TA9S XS SUBJECT-E4G4 L9E OR NUMB] Z ! CASE MAY BE4 ,EXT5D+ ? CLASSIFIC,N 6ALL O!R ATTRIBUTES1 ,I 4T+UI% ^? T ANSW] ! ABV DESCRIP;N Z 2L;G+ ESS5TI,Y 6_! RESPECTIVE SUBJECTS2 ":AS ATTRIBUTES RELAT$ 9 NEI ( ^! TWO WAYS 6_! SUBJECTS ,I CALL A3ID5TS OR ,8CO9CID5TS0'2 E4G4 MUSICAL OR :ITE IS A ,8CO9CID5T0' ( ANIMAL4 ,FUR!R 7A7 T IS ESS5TIAL : IS N PR$ICAT$ (A SUBJECT O!R ?AN XF3 E4G4 ,8! WALK+ ,7?+7'0' WALKS & IS :ITE 9 VIRTUE ( 2+ "S?+ ELSE 2SS2 ":AS SUB/.E1 9 ! S5SE ( :AT"E SIGNIFIES A ,8? "S:AT0'1 IS N :AT X IS 9 VIRTUE ( 2+ "S?+ ELSE 2SS4 ,?+S1 !N1 N PR$ICAT$ (A SUBJECT ,I CALL ESS5TIAL2 ?+S PR$ICAT$ (A SUBJECT ,I CALL A3ID5TAL OR ,8CO9CID5TAL0'4 ,9 ANO!R S5SE AG 7B7 A ?+ 3SEQU5TI,Y 3NECT$ ) ANY?+ IS ESS5TIAL2 "O N S 3NECT$ IS ,8CO9CID5TAL0'4 ,AN EXAMPLE (! LATT] IS ,8,:ILE HE 0 WALK+ X LI !N Z 3C]NS ! SPH]E ( 3NEXIONS SCI5TIFIC,Y "KN 9 ! UNQUALIFI$ S5SE ( T T]M1 ALL ATTRIBUTES : 7)9 T SPH]E7 >E ESS5TIAL EI 9 ! S5SE T _! SUBJECTS >E 3TA9$ 9 !M1 OR 9 ! S5SE T !Y >E 3TA9$ 9 _! SUBJECTS1 >E NEC Z WELL Z 3SEQU5TI,Y 3NECT$ ) _! SUBJECTS4 ,= X IS IMPOSSI# = !M N 69"H 9 _! SUBJECTS EI SIMPLY OR 9 ! QUALIFI$ S5SE T "O OR O!R (A PAIR ( OPPOSITES M/ 9"H 9 ! SUBJECT2 E4G4 9 L9E M/ 2 EI /RAIY (A GIV5 ATTRIBUTE IS EI XS PRIVATIVE OR XS 3TRADICTORY2 E4G4 )9 NUMB] :AT IS N ODD IS EV51 9ASM* Z )9 ? SPH]E EV5 IS A NEC 3SEQU5T ( N-ODD4 ,S1 S9CE ANY GIV5 PR$ICATE M/ 2 EI A6IRM$ OR D5I$ ( ANY SUBJECT1 ESS5TIAL ATTRIBUTES M/ 9"H 9 _! SUBJECTS ( NECESS;Y4 ,?US1 !N1 WE H E/ABLI%$ ! 4T9C;N 2T ! ATTRIBUTE : IS ,8TRUE 9 E 9/.E0' &! ,8ESS5TIAL0' ATTRIBUTE4 ,I T]M ,8-M5SURATELY UNIV]SAL0' AN ATTRIBUTE : 2L;GS 6E 9/.E ( XS SUBJECT1 & 6E 9/.E ESS5TI,Y & Z S*2 F : X CLE>LY FOLL[S T ALL -M5SURATE UNIV]SALS 9"H NECESS>ILY 9 _! SUBJECTS4 ,! ESS5TIAL ATTRIBUTE1 &! ATTRIBUTE T 2L;GS 6XS SUBJECT Z S*1 >E ID5TICAL4 ,E4G4 PO9T & /RAID1 NOR 9 DEMON/RAT+ DOES "O TAKE A FIGURE AT R&OM-A SQU>E IS A FIGURE B XS ANGLES >E N EQUAL 6TWO "R ANGLES4 ,ON ! O!R H&1 ANY ISOSCELES TRIANGLE HAS XS ANGLES EQUAL 6TWO "R ANGLES1 YET ISOSCELES TRIANGLE IS N ! PRIM>Y SUBJECT ( ? ATTRIBUTE B TRIANGLE IS PRIOR4 ,S :AT"E C 2 %[N 6H XS ANGLES EQUAL 6TWO "R ANGLES1 OR 6POSSESS ANY O!R ATTRIBUTE1 9 ANY R&OM 9/.E ( XF & PRIM>ILY-T IS ! F/ SUBJECT 6: ! PR$ICATE 9 "Q 2L;GS -M5SURATELY & UNIV]S,Y1 &! DEMON/R,N1 9 ! ESS5TIAL S5SE1 ( ANY PR$ICATE IS ! PRO( ( X Z 2L;G+ 6? F/ SUBJECT -M5SURATELY & UNIV]S,Y3 :ILE ! PRO( ( X Z 2L;G+ 6! O!R SUBJECTS 6: X ATTA*ES IS DEMON/R,N ONLY 9 A SECOND>Y & UNESS5TIAL S5SE4 ,NOR AG 7#B7 IS EQUAL;Y 6TWO "R ANGLES A -M5SURATELY UNIV]SAL ATTRIBUTE ( ISOSCELES2 X IS ( WID] APPLIC,N4 #E ,WE M/ N FAIL 6OBS]VE T WE (T5 FALL 96]ROR 2C \R 3CLU.N IS N 9 FACT PRIM>Y & -M5SURATELY UNIV]SAL 9 ! S5SE 9 : WE ?9K WE PROVE X S4 ,WE MAKE ? MISTAKE 7#A7 :5 ! SUBJECT IS AN 9DIVIDUAL OR 9DIVIDUALS ABV : "! IS NO UNIV]SAL 6BE F.D3 7#B7 :5 ! SUBJECTS 2L;G 6DI6]5T SPECIES & "! IS A HI<] UNIV]SAL1 B X HAS NO "N3 7#C7 :5 ! SUBJECT : ! DEMON/RATOR TAKES Z A :OLE IS RE,Y ONLY A "P (A L>G] :OLE2 = !N ! DEMON/R,N W 2 TRUE (! 9DIVIDUAL 9/.ES )9 ! "P & W HOLD 9 E 9/.E ( X1 YET ! DEMON/R,N W N 2 TRUE ( ? SUBJECT PRIM>ILY & -M5SURATELY & UNIV]S,Y4 ,:5 A DEMON/R,N IS TRUE (A SUBJECT PRIM>ILY & -M5SURATELY & UNIV]S,Y1 T IS 6BE TAK5 6M1N T X IS TRUE (A GIV5 SUBJECT PRIM>ILY & Z S*4 ,CASE 7#C7 MAY 2 ?US EXEMPLIFI$4 ,IF A PRO( 7 GIV5 T P]P5DICUL>S 6! SAME L9E >E P>ALLEL1 X MI 7 ! PROP] SUBJECT (! DEMON/R,N 2C 2+ P>ALLEL IS TRUE ( E 9/.E ( !M4 ,B X IS N S1 =! P>ALLELISM DEP5DS N ON ^! ANGLES 2+ EQUAL 6"O ANO!R 2C EA* IS A "R ANGLE1 B SIMPLY ON _! 2+ EQUAL 6"O ANO!R4 ,AN EXAMPLE ( 7#A7 WD 2 Z FOLL[S3 IF ISOSCELES 7 ! ONLY TRIANGLE1 X WD 2 ?"\ 6H XS ANGLES EQUAL 6TWO "R ANGLES QUA ISOSCELES4 ,AN 9/.E ( 7#B7 WD 2 ! LAW T PROPOR;NALS ALT]NATE4 ,ALT]N,N US$ 6BE DEMON/RAT$ SEP>ATELY ( NUMB]S1 L9ES1 SOLIDS1 & DUR,NS1 ?\< X CD H BE5 PROV$ ( !M ALL 0A S+LE DEMON/R,N4 ,2C "! 0 NO S+LE "N 6DENOTE T 9 : NUMB]S1 L5G?S1 DUR,NS1 & SOLIDS >E ID5TICAL1 & 2C !Y DI6]$ SPECIFIC,Y F "O ANO!R1 ? PROP]TY 0 PROV$ ( EA* ( !M SEP>ATELY4 ,TO-"D1 H["E1 ! PRO( IS -M5SURATELY UNIV]SAL1 = !Y D N POSSESS ? ATTRIBUTE QUA L9ES OR QUA NUMB]S1 B QUA MANIFE/+ ? G5]IC "* : !Y >E PO/ULAT$ Z POSSESS+ UNIV]S,Y4 ,H;E1 EV5 IF "O PROVE ( EA* K9D ( TRIANGLE T XS ANGLES >E EQUAL 6TWO "R ANGLES1 :E!R 0M1NS (! SAME OR DI6]5T PRO(S2 /1 Z L;G Z "O TR1TS SEP>ATELY EQUILAT]AL1 SCAL5E1 & ISOSCELES1 "O DOES N YET "K1 EXCEPT SOPHI/IC,Y1 T TRIANGLE HAS XS ANGLES EQUAL 6TWO "R ANGLES1 NOR DOES "O YET "K T TRIANGLE HAS ? PROP]TY -M5SURATELY & UNIV]S,Y1 EV5 IF "! IS NO O!R SPECIES ( TRIANGLE B ^!4 ,= "O DOES N "K T TRIANGLE Z S* HAS ? PROP]TY1 NOR EV5 T ,8ALL0' TRIANGLES H X-UN.S ,8ALL0' M1NS ,8EA* TAK5 S+LY0'3 IF ,8ALL0' M1NS ,8Z A :OLE CLASS0'1 !N1 ?\< "! 2 N"O 9 : "O DOES N RECOGNIZE ? PROP]TY1 "O DOES N "K X ( ,8ALL TRIANGLES0'4 ,:51 !N1 DOES \R K FAIL ( -M5SURATE UNIV]SAL;Y1 & :5 X IS UNQUALIFI$ K8 ,IF TRIANGLE 2 ID5TICAL 9 ESS;E ) EQUILAT]AL1 I4E4 ) EA* OR ALL EQUILAT]ALS1 !N CLE>LY WE H UNQUALIFI$ K3 IF ON ! O!R H& X 2 N1 &! ATTRIBUTE 2L;GS 6EQUILAT]AL QUA TRIANGLE2 !N \R K FAILS ( -M5SURATE UNIV]SAL;Y4 ,8,B0'1 X W 2 ASK$1 ,8DOES ? ATTRIBUTE 2L;G 6! SUBJECT ( : X HAS BE5 DEMON/RAT$ QUA TRIANGLE OR QUA ISOSCELES8 ,:AT IS ! PO9T AT : ! SUBJECT4 6: X 2L;GS IS PRIM>Y8 7I4E4 6:AT SUBJECT C X 2 DEMON/RAT$ Z 2L;G+ -M5SURATELY & UNIV]S,Y870' ,CLE>LY ? PO9T IS ! F/ T]M 9 : X IS F.D 69"H Z ! ELIM9,N ( 9F]IOR DI6]5TIAE PROCE$S4 ,?US ! ANGLES (A BRAZ5 ISOSCELES TRIANGLE >E EQUAL 6TWO "R ANGLES3 B ELIM9ATE BRAZ5 & ISOSCELES &! ATTRIBUTE REMA9S4 ,8,B'-Y MAY SAY- ,8ELIM9ATE FIGURE OR LIMIT1 &! ATTRIBUTE VANI%ES40' ,TRUE1 B FIGURE & LIMIT >E N ! F/ DI6]5TIAE ^: ELIM9,N DE/ROYS ! ATTRIBUTE4 ,8,!N :AT IS ! F/80' ,IF X IS TRIANGLE1 X W 2 9 VIRTUE ( TRIANGLE T ! ATTRIBUTE 2L;GS 6ALL ! O!R SUBJECTS ( : X IS PR$ICA#1 & TRIANGLE IS ! SUBJECT 6: X C 2 DEMON/RAT$ Z 2L;G+ -M5SURATELY & UNIV]S,Y4 #F ,DEMON/RATIVE K M/ RE/ ON NEC BASIC TRU?S2 =! OBJECT ( SCI5TIFIC K _C 2 O!R ?AN X IS4 ,N[ ATTRIBUTES ATTA*+ ESS5TI,Y 6_! SUBJECTS ATTA* NECESS>ILY 6!M3 = ESS5TIAL ATTRIBUTES >E EI ELE;TS 9 ! ESS5TIAL NATURE ( _! SUBJECTS1 OR 3TA9 _! SUBJECTS Z ELE;TS 9 _! [N ESS5TIAL NATURE4 7,! PAIRS ( OPPOSITES : ! LATT] CLASS 9CLUDES >E NEC 2C "O MEMB] OR ! O!R NECESS>ILY 9"HS47 ,X FOLL[S F ? T PREMISSES (! DEMON/RATIVE SYLLOGISM M/ 2 3NEXIONS ESS5TIAL 9 ! S5SE EXPLA9$3 = ALL ATTRIBUTES M/ 9"H ESS5TI,Y OR ELSE 2 A3ID5TAL1 & A3ID5TAL ATTRIBUTES >E N NEC 6_! SUBJECTS4 ,WE M/ EI /ATE ! CASE ?US1 OR ELSE PREMISE T ! 3CLU.N ( DEMON/R,N IS NEC & T A DEMON/RAT$ 3CLU.N _C 2 O!R ?AN X IS1 & !N 9F] T ! 3CLU.N M/ 2 DEVELOP$ F NEC PREMISSES4 ,= ?\< Y MAY R1SON F TRUE PREMISSES )\T DEMON/RAT+1 YET IF YR PREMISSES >E NEC Y W ASSUR$LY DEMON/RATE-IN S* NECESS;Y Y H AT ONCE A 4T9CTIVE "* ( DEMON/R,N4 ,T DEMON/R,N PROCE$S F NEC PREMISSES IS AL 9DICAT$ 0! FACT T ! OBJEC;N WE RAISE AG/ A PROFESS$ DEMON/R,N IS T A PREMISS ( X IS N A NEC TRU?-:E!R WE ?9K X ALT DEVOID ( NECESS;Y1 OR AT ANY RATE S F> Z \R OPPON5T'S PREVI\S >GU;T GOES4 ,? %[S H[ NAIVE X IS 6SUPPOSE "O'S BASIC TRU?S "RLY *OS5 IF "O />TS )A PROPOSI;N : IS 7#A7 POPUL>LY A3EPT$ & 7#B7 TRUE1 S* Z ! SOPHI/S' ASSUMP;N T 6"K IS ! SAME Z 6POSSESS K4 ,= 7#A7 POPUL> A3EPT.E OR REJEC;N IS NO CRIT]ION (A BASIC TRU?1 : C ONLY 2 ! PRIM>Y LAW (! G5US 3/ITUT+ ! SUBJECT MATT] (! DEMON/R,N2 & 7#B7 N ALL TRU? IS ,8APPROPRIATE0'4 ,A FUR!R PRO( T ! 3CLU.N M/ 2 ! DEVELOP;T ( NEC PREMISSES IS Z FOLL[S4 ,": DEMON/R,N IS POSSI#1 "O :O C GIVE NO A3.T : 9CLUDES ! CAUSE HAS NO SCI5TIFIC K4 ,IF1 !N1 WE SUPPOSE A SYLLOGISM 9 :1 ?\< ,A NECESS>ILY 9"HS 9 ;,C1 YET ;,B1 ! MI4LE T]M (! DEMON/R,N1 IS N NECESS>ILY 3NECT$ ) ;,A & ;,C1 !N ! MAN :O >GUES ?US HAS NO R1SON$ K (! 3CLU.N1 S9CE ? 3CLU.N DOES N [E XS NECESS;Y 6! MI4LE T]M2 = ?\< ! 3CLU.N IS NEC1 ! M$IAT+ L9K IS A 3T+5T FACT4 ,OR AG1 IF A MAN IS )\T K N[1 ?\< HE / RETA9S ! /EPS (! >GU;T1 ?\< "! IS NO *ANGE 9 HMF OR 9 ! FACT & NO LAPSE ( MEMORY ON 8 "P2 !N NEI _H HE K PREVI\SLY4 ,B ! M$IAT+ L9K1 N 2+ NEC1 MAY H P]I%$ 9 ! 9T]VAL2 & IF S1 ?\< "! 2 NO *ANGE 9 HM NOR 9 ! FACT1 & ?\< HE W / RETA9 ! /EPS (! >GU;T1 YET HE HAS N K1 & "!=E _H N K 2F4 ,EV5 IF ! L9K HAS N ACTU,Y P]I%$ B IS LIA# 6P]I%1 ? SITU,N IS POSSI# & MIILY PR$ICAT$ ( ;,B & ;,B ( ;,C1 !N ,A IS NECESS>ILY PR$ICAT$ ( ,C4 ,B :5 ! 3CLU.N IS NONNEC ! MI4LE _C 2 NEC EI4 ,?US3 LET ,A 2 PR$ICAT$ NON-NECESS>ILY ( ;,C B NECESS>ILY ( ;,B1 & LET ;,B 2 A NEC PR$ICATE ( ;,C2 !N ,A TOO W 2 A NEC PR$ICATE ( ;,C1 : 0HYPO!SIS X IS N4 ,6SUM UP1 !N3 DEMON/RATIVE K M/ 2 K (A NEC NEXUS1 & "!=E M/ CLE>LY 2 OBTA9$ "? A NEC MI4LE T]M2 O!RWISE XS POSSESSOR W "K NEI ! CAUSE NOR ! FACT T 8 3CLU.N IS A NEC 3NEXION4 ,EI HE W MISTAKE ! NON- NEC =! NEC & 2LIEVE ! NECESS;Y (! 3CLU.N )\T "K+ X1 OR ELSE HE W N EV5 2LIEVE X- IN : CASE HE W 2 EQU,Y IGNORANT1 :E!R HE ACTU,Y 9F]S ! M]E FACT "? MI4LE T]MS OR ! R1SON$ FACT & F IMM PREMISSES4 ,( A3ID5TS T >E N ESS5TIAL AC 6\R DEF9I;N ( ESS5TIAL "! IS NO DEMON/RATIVE K2 = S9CE AN A3ID5T1 9 ! S5SE 9 : ,I "H SP1K ( X1 MAY AL N 9"H1 X IS IMPOSSI# 6PROVE XS 9H];E Z A NEC 3CLU.N4 ,A DI6ICULTY1 H["E1 MIE PROPOSI;NS : IF ! ANSW]] A6IRM1 HE M/ A6IRM ! 3CLU.N & A6IRM X ) TRU? IF !Y >E TRUE4 ,S9CE X IS J ^? ATTRIBUTES )9 E G5US : >E ESS5TIAL & POSSESS$ 0_! RESPECTIVE SUBJECTS Z S* T >E NEC X IS CLE> T BO? ! 3CLU.NS &! PREMISSES ( DEMON/R,NS : PRODUCE SCI5TIFIC K >E ESS5TIAL4 ,= A3ID5TS >E N NEC3 &1 FUR!R1 S9CE A3ID5TS >E N NEC "O DOES N NECESS>ILY H R1SON$ K (A 3CLU.N DRAWN F !M 7? IS S EV5 IF ! A3ID5TAL PREMISSES >E 9V>IA# B N ESS5TIAL1 Z 9 PRO(S "? SIGNS2 = ?\< ! 3CLU.N 2 ACTU,Y ESS5TIAL1 "O W N "K X Z ESS5TIAL NOR "K XS R1SON72 B 6H R1SON$ K (A 3CLU.N IS 6"K X "? XS CAUSE4 ,WE MAY 3CLUDE T ! MI4LE M/ 2 3SEQU5TI,Y 3NECT$ )! M9OR1 &! MAJOR )! MI4LE4 #G ,X FOLL[S T WE _C 9 DEMON/RAT+ PASS F "O G5US 6ANO!R4 ,WE _C1 = 9/.E1 PROVE GEOMETRICAL TRU?S 0>I?METIC4 ,= "! >E ?REE ELE;TS 9 DEMON/R,N3 7#A7 :AT IS PROV$1 ! 3CLU.N-AN ATTRIBUTE 9H]+ ESS5TI,Y 9 A G5US2 7#B7 ! AXIOMS1 I4E4 AXIOMS : >E PREMISSES ( DEMON/R,N2 7#C7 ! SUBJECT-G5US ^: ATTRIBUTES1 I4E4 ESS5TIAL PROP]TIES1 >E REV1L$ 0! DEMON/R,N4 ,! AXIOMS : >E PREMISSES ( DEMON/R,N MAY 2 ID5TICAL 9 TWO OR M SCI;ES3 B 9 ! CASE ( TWO DI6]5T G5]A S* Z >I?METIC & GEOMETRY Y _C APPLY >I?METICAL DEMON/R,N 6! PROP]TIES ( MAGNITUDES UN.S ! MAGNITUDES 9 "Q >E NUMB]S4 ,H[ 9 C]TA9 CASES TRANSF];E IS POSSI# ,I W EXPLA9 LAT]4 ,>I?METICAL DEMON/R,N &! O!R SCI;ES LIKEWISE POSSESS1 EA* ( !M1 _! [N G5]A2 S T IF ! DEMON/R,N IS 6PASS F "O SPH]E 6ANO!R1 ! G5US M/ 2 EI ABSOLUTELY OR 6"S EXT5T ! SAME4 ,IF ? IS N S1 TRANSF];E IS CLE>LY IMPOSSI#1 2C ! EXTREME &! MI4LE T]MS M/ 2 DRAWN F ! SAME G5US3 O!RWISE1 Z PR$ICAT$1 !Y W N 2 ESS5TIAL & W ?US 2 A3ID5TS4 ,T IS :Y X _C 2 PROV$ 0GEOMETRY T OPPOSITES FALL "U "O SCI;E1 NOR EV5 T ! PRODUCT ( TWO CUBES IS A CUBE4 ,NOR C ! !OREM ( ANY "O SCI;E 2 DEMON/RAT$ 0M1NS ( ANO!R SCI;E1 UN.S ^! !OREMS >E RELAT$ Z SUBORD9ATE 6SUP]IOR 7E4G4 Z OPTICAL !OREMS 6GEOMETRY OR H>MONIC !OREMS 6>I?METIC74 ,GEOMETRY AG _C PROVE ( L9ES ANY PROP]TY : !Y D N POSSESS QUA L9ES1 I4E4 9 VIRTUE (! FUNDA;TAL TRU?S ( _! PECULI> G5US3 X _C %[1 = EXAMPLE1 T ! /RAIY (! CIRCLE2 = ^! QUALITIES D N 2L;G 6L9ES 9 VIRTUE ( _! PECULI> G5US1 B "? "S PROP]TY : X %>ES ) O!R G5]A4 #H ,X IS AL CLE> T IF ! PREMISSES F : ! SYLLOGISM PROCE$S >E -M5SURATELY UNIV]SAL1 ! 3CLU.N ( S* I4E4 9 ! UNQUALIFI$ S5SE-M/ AL 2 ET]NAL4 ,"!=E NO ATTRIBUTE C 2 DEMON/RAT$ NOR "KN 0/RICTLY SCI5TIFIC K 69"H 9 P]I%A# ?+S4 ,! PRO( C ONLY 2 A3ID5TAL1 2C ! ATTRIBUTE'S 3NEXION ) XS P]I%A# SUBJECT IS N -M5SURATELY UNIV]SAL B TEMPOR>Y & SPECIAL4 ,IF S* A DEMON/R,N IS MADE1 "O PREMISS M/ 2 P]I%A# & N -M5SURATELY UNIV]SAL 7P]I%A# 2C ONLY IF X IS P]I%A# W ! 3CLU.N 2 P]I%A#2 N -M5SURATELY UNIV]SAL1 2C ! PR$ICATE W 2 PR$ICA# ( "S 9/.ES (! SUBJECT & N ( O!RS72 S T ! 3CLU.N C ONLY 2 T A FACT IS TRUE AT ! MO;T-N -M5SURATELY & UNIV]S,Y4 ,! SAME IS TRUE ( DEF9I;NS1 S9CE A DEF9I;N IS EI A PRIM>Y PREMISS OR A 3CLU.N (A DEMON/R,N1 OR ELSE ONLY DI6]S F A DEMON/R,N 9 ! ORD] ( XS T]MS4 ,DEMON/R,N & SCI;E ( M]ELY FREQU5T O3URR;ES-E4G4 ( ECLIPSE Z HAPP5+ 6! MOON->E1 Z S*1 CLE>LY ET]NAL3 ":AS S F> Z !Y >E N ET]NAL !Y >E N FULLY -M5SURATE4 ,O!R SUBJECTS TOO H PROP]TIES ATTA*+ 6!M 9 ! SAME WAY Z ECLIPSE ATTA*ES 6! MOON4 #I ,X IS CLE> T IF ! 3CLU.N IS 6%[ AN ATTRIBUTE 9H]+ Z S*1 NO?+ C 2 DEMON/RAT$ EXCEPT F XS ,8APPROPRIATE0' BASIC TRU?S4 ,3SEQU5TLY A PRO( EV5 F TRUE1 9DEMON/RA#1 & IMM PREMISSES DOES N 3/ITUTE K4 ,S* PRO(S >E L ,BRYSON'S ME?OD ( SQU>+ ! CIRCLE2 = !Y OP]ATE 0TAK+ Z _! MI4LE A -MON "*-A "*1 "!=E1 : ! SUBJECT MAY %>E ) ANO!R-& 3SEQU5TLY !Y APPLY EQU,Y 6SUBJECTS DI6]5T 9 K9D4 ,!Y "!=E AF=D K ( AN ATTRIBUTE ONLY Z 9H]+ A3ID5T,Y1 N Z 2L;G+ 6XS SUBJECT Z S*3 O!RWISE !Y WD N H BE5 APPLICA# 6ANO!R G5US4 ,\R K ( ANY ATTRIBUTE'S 3NEXION )A SUBJECT IS A3ID5TAL UN.S WE "K T 3NEXION "? ! MI4LE T]M 9 VIRTUE ( : X 9"HS1 & Z AN 9F];E F BASIC PREMISSES ESS5TIAL & ,8APPROPRIATE0' 6! SUBJECT-UN.S WE "K1 E4G4 ! PROP]TY ( POSSESS+ ANGLES EQUAL 6TWO "R ANGLES Z 2L;G+ 6T SUBJECT 9 : X 9"HS ESS5TI,Y1 & Z 9F]R$ F BASIC PREMISSES ESS5TIAL & ,8APPROPRIATE0' 6T SUBJECT3 S T IF T MI4LE T]M AL 2L;GS ESS5TI,Y 6! M9OR1 ! MI4LE M/ 2L;G 6! SAME K9D Z ! MAJOR & M9OR T]MS4 ,! ONLY EXCEP;NS 6? RULE >E S* CASES Z !OREMS 9 H>MONICS : >E DEMON/RA# 0>I?METIC4 ,S* !OREMS >E PROV$ 0! SAME MI4LE T]MS Z >I?METICAL PROP]TIES1 B )A QUALIFIC,N-! FACT FALLS "U A SEP>ATE SCI;E 7=! SUBJECT G5US IS SEP>ATE71 B ! R1SON$ FACT 3C]NS ! SUP]IOR SCI;E1 6: ! ATTRIBUTES ESS5TI,Y 2L;G4 ,?US1 EV5 ^! APP>5T EXCEP;NS %[ T NO ATTRIBUTE IS /RICTLY DEMON/RA# EXCEPT F XS ,8APPROPRIATE0' BASIC TRU?S1 :1 H["E1 9 ! CASE ( ^! SCI;ES H ! REQUISITE ID5T;Y ( "*4 ,X IS NO LESS EVID5T T ! PECULI> BASIC TRU?S ( EA* 9H]+ ATTRIBUTE >E 9DEMON/RA#2 = BASIC TRU?S F : !Y MIE1 DEMON/R,N IS N TRANSF]A# 6ANO!R G5US1 ) S* EXCEP;NS Z WE H M5;N$ (! APPLIC,N ( GEOMETRICAL DEMON/R,NS 6!OREMS 9 ME*ANICS OR OPTICS1 OR ( >I?METICAL DEMON/R,NS 6^? ( H>MONICS4 ,X IS H>D 6BE SURE :E!R "O "KS OR N2 = X IS H>D 6BE SURE :E!R "O'S K IS BAS$ ON ! BASIC TRU?S APPROPRIATE 6EA* ATTRIBUTE-! DI6]5TIA ( TRUE K4 ,WE ?9K WE H SCI5TIFIC K IF WE H R1SON$ F TRUE & PRIM>Y PREMISSES4 ,B T IS N S3 ! 3CLU.N M/ 2 HOMOG5E\S )! BASIC FACTS (! SCI;E4 #AJ ,I CALL ! BASIC TRU?S ( E G5US ^? CLE;TS 9 X ! EXI/;E ( : _C 2 PROV$4 ,Z REG>DS BO? ^! PRIM>Y TRU?S &! ATTRIBUTES DEP5D5T ON !M ! M1N+ (! "N IS ASSUM$4 ,! FACT ( _! EXI/;E Z REG>DS ! PRIM>Y TRU?S M/ 2 ASSUM$2 B X HAS 6BE PROV$ (! REMA9D]1 ! ATTRIBUTES4 ,?US WE ASSUME ! M1N+ ALIKE ( UN;Y1 /RAI2 B :ILE Z REG>DS UN;Y & MAGNITUDE WE ASSUME AL ! FACT ( _! EXI/;E1 9 ! CASE ( ! REMA9D] PRO( IS REQUIR$4 ,(! BASIC TRU?S US$ 9 ! DEMON/RATIVE SCI;ES "S >E PECULI> 6EA* SCI;E1 & "S >E -MON1 B -MON ONLY 9 ! S5SE ( ANALOG\S1 2+ ( USE ONLY 9 S F> Z !Y FALL )9 ! G5US 3/ITUT+ ! PROV9CE (! SCI;E 9 "Q4 ,PECULI> TRU?S >E1 E4G4 ! DEF9I;NS ( L9E & /RAIE S* Z ,8TAKE EQUALS F EQUALS & EQUALS REMA9'4 ,ONLY S M* ( ^! -MON TRU?S IS REQUIR$ Z FALLS )9 ! G5US 9 "Q3 =A TRU? ( ? K9D W H ! SAME =CE EV5 IF N US$ G5],Y B APPLI$ 0! GEOMET] ONLY 6MAGNITUDES1 OR 0! >I?METICIAN ONLY 6NUMB]S4 ,AL PECULI> 6A SCI;E >E ! SUBJECTS ! EXI/;E Z WELL Z ! M1N+ ( : X ASSUMES1 &! ESS5TIAL ATTRIBUTES ( : X 9VE/IGATES1 E4G4 9 >I?METIC UNITS1 9 GEOMETRY PO9TS & L9ES4 ,BO? ! EXI/;E &! M1N+ (! SUBJECTS >E ASSUM$ 0^! SCI;ES2 B ( _! ESS5TIAL ATTRIBUTES ONLY ! M1N+ IS ASSUM$4 ,= EXAMPLE >I?METIC ASSUMES ! M1N+ ( ODD & EV51 SQU>E & CUBE1 GEOMETRY T ( 9COMM5SURA#1 OR ( DEFLEC;N OR V]G+ ( L9ES1 ":AS ! EXI/;E ( ^! ATTRIBUTES IS DEMON/RAT$ 0M1NS (! AXIOMS & F PREVI\S 3CLU.NS Z PREMISSES4 ,A/RONOMY TOO PROCE$S 9 ! SAME WAY4 ,= 9DE$ E DEMON/RATIVE SCI;E HAS ?REE ELE;TS3 7#A7 T : X POSITS1 ! SUBJECT G5US ^: ESS5TIAL ATTRIBUTES X EXAM9ES2 7#B7 ! S-CALL$ AXIOMS1 : >E PRIM>Y PREMISSES ( XS DEMON/R,N2 7#C7 ! ATTRIBUTES1 ! M1N+ ( : X ASSUMES4 ,YET "S SCI;ES MAY V WELL PASS OV] "S ( ^! ELE;TS2 E4G4 WE MIE ?REE3 ! SUBJECT1 ! ATTRIBUTES1 &! BASIC PREMISSES4 ,T : EXPRESSES NEC SELF-GR.D$ FACT1 & : WE M/ NECESS>ILY 2LIEVE1 IS 4T9CT BO? F ! HYPO!SES (A SCI;E & F ILLEGITIMATE PO/ULATE-,I SAY ,8M/ 2LIEVE0'1 2C ALL SYLLOGISM1 & "!=E A =TIORI DEMON/R,N1 IS A4RESS$ N 6! SPOK5 ^W1 B 6! 4C\RSE )9 ! S\L1 & ?\< WE C ALW RAISE OBJEC;NS 6! SPOK5 ^W1 6! 9W>D 4C\RSE WE _C ALW OBJECT4 ,T : IS CAPA# ( PRO( B ASSUM$ 0! T1*] )\T PRO( IS1 IF ! PUPIL 2LIEVES & A3EPTS X1 HYPO!SIS1 ?\< ONLY 9 A LIMIT$ S5SE HYPO!SIS-T IS1 RELATIVELY 6! PUPIL2 IF ! PUPIL HAS NO OP9ION OR A 3TR>Y OP9ION ON ! MATT]1 ! SAME ASSUMP;N IS AN ILLEGITIMATE PO/ULATE4 ,"!9 LIES ! 4T9C;N 2T HYPO!SIS & ILLEGITIMATE PO/ULATE3 ! LATT] IS ! 3TR>Y (! PUPIL'S OP9ION1 DEMON/RA#1 B ASSUM$ & US$ )\T DEMON/R,N4 ,! DEF9I;N-VIZ4 ^? : >E N EXPRESS$ Z /ATE;TS T ANY?+ IS OR IS N->E N HYPO!SES3 B X IS 9 ! PREMISSES (A SCI;E T XS HYPO!SES >E 3TA9$4 ,DEF9I;NS REQUIRE ONLY 6BE "U/OOD1 & ? IS N HYPO!SIS-UN.S X 2 3T5D$ T ! PUPIL'S HE>+ IS AL AN HYPO!SIS REQUIR$ 0! T1*]4 ,HYPO!SES1 ON ! 3TR>Y1 PO/ULATE FACTS ON ! 2+ ( : DEP5DS ! 2+ (! FACT 9F]R$4 ,NOR >E ! GEOMET]'S HYPO!SES FALSE1 Z "S H HELD1 URG+ T "O M/ N EMPLOY FALSEHOOD & T ! GEOMET] IS UTT]+ FALSEHOOD 9 /AT+ T ! L9E : HE DRAWS IS A FOOT L;G OR /RAI L9E ( : HE SP1KS1 B F :AT 8 DIAGRAMS SYMBOLIZE4 ,A FUR!R 4T9C;N IS T ALL HYPO!SES & ILLEGITIMATE PO/ULATES >E EI UNIV]SAL OR "PICUL>1 ":AS A DEF9I;N IS NEI4 #AA ,S DEMON/R,N DOES N NECESS>ILY IMPLY ! 2+ ( ,=MS NOR A ,"O 2S A ,_M1 B X DOES NECESS>ILY IMPLY ! POSSIBIL;Y ( TRULY PR$ICAT+ "O ( _M2 S9CE )\T ? POSSIBIL;Y WE _C SAVE ! UNIV]SAL1 & IF ! UNIV]SAL GOES1 ! MI4LE T]M GOES WITB4 X1 & S DEMON/R,N 2COMES IMPOSSI#4 ,WE 3CLUDE1 !N1 T "! M/ 2 A S+LE ID5TICAL T]M UNEQUIVOC,Y PR$ICA# (A NUMB] ( 9DIVIDUALS4 ,! LAW T X IS IMPOSSI# 6A6IRM & D5Y SIMULTANE\SLY ! SAME PR$ICATE (! SAME SUBJECT IS N EXPRESSLY POSIT$ 0ANY DEMON/R,N EXCEPT :5 ! 3CLU.N AL HAS 6BE EXPRESS$ 9 T =M2 9 : CASE ! PRO( LAYS D[N Z XS MAJOR PREMISS T ! MAJOR IS TRULY A6IRM$ (! MI4LE B FALSELY D5I$4 ,X MAKES NO DI6];E1 H["E1 IF WE ADD 6! MI4LE1 OR AG 6! M9OR T]M1 ! CORRESPOND+ NEGATIVE4 ,= GRANT A M9OR T]M ( : X IS TRUE 6PR$ICATE MAN-EV5 IF X 2 AL TRUE 6PR$ICATE N-MAN ( X--/ GRANT SIMPLY T MAN IS ANIMAL & N N-ANIMAL1 &! 3CLU.N FOLL[S3 = X W / 2 TRUE 6SAY T ,CALLIAS-- EV5 IF X 2 AL TRUE 6SAY T N-,CALLIAS--IS ANIMAL & N N-ANIMAL4 ,! R1SON IS T ! MAJOR T]M IS PR$ICA# N ONLY (! MI4LE1 B ( "S?+ O!R ?AN ! MI4LE Z WELL1 2+ ( WID] APPLIC,N2 S T ! 3CLU.N IS N A6ECT$ EV5 IF ! MI4LE IS EXT5D$ 6COV] ! ORIG9AL MI4LE T]M & AL :AT IS N ! ORIG9AL MI4LE T]M4 ,! LAW T E PR$ICATE C 2 EI TRULY A6IRM$ OR TRULY D5I$ ( E SUBJECT IS POSIT$ 0S* DEMON/R,N Z USES REDUCTIO AD IMPOSSIBILE1 & !N N ALW UNIV]S,Y1 B S F> Z X IS REQUISITE2 )9 ! LIMITS1 T IS1 (! G5US-! G5US1 ,I M1N 7Z ,I H ALR EXPLA9$71 6: ! MAN ( SCI;E APPLIES 8 DEMON/R,NS4 ,9 VIRTUE (! -MON ELE;TS ( DEMON/R,N-,I M1N ! -MON AXIOMS : >E US$ Z PREMISSES ( DEMON/R,N1 N ! SUBJECTS NOR ! ATTRIBUTES DEMON/RAT$ Z 2L;G+ 6!M- ALL ! SCI;ES H -MUNION ) "O ANO!R1 & 9 -MUNION ) !M ALL IS DIALECTIC & ANY SCI;E : MIR$ 6! DEMON/RATOR1 :O _C USE ! OPPOSITE FACTS 6PROVE ! SAME NEXUS4 ,? 0 %[N 9 MY "W ON ! SYLLOGISM4 #AB ,IF A SYLLOGI/IC "Q IS EQUIVAL5T 6A PROPOSI;N EMBODY+ "O (! TWO SIDES (A 3TRADIC;N1 & IF EA* SCI;E HAS XS PECULI> PROPOSI;NS F : XS PECULI> 3CLU.N IS DEVELOP$1 !N "! IS S* A ?+ Z A 4T9CTIVELY SCI5TIFIC "Q1 & X IS ! 9T]ROGATIVE =M (! PREMISSES F : ! ,8APPROPRIATE0' 3CLU.N ( EA* SCI;E IS DEVELOP$4 ,H;E X IS CLE> T N E "Q W 2 RELEVANT 6GEOMETRY1 NOR 6M$IC9E1 NOR 6ANY O!R SCI;E3 ONLY ^? "QS W 2 GEOMETRICAL : =M PREMISSES =! PRO( (! !OREMS ( GEOMETRY OR ( ANY O!R SCI;E1 S* Z OPTICS1 : USES ! SAME BASIC TRU?S Z GEOMETRY4 ,(! O!R SCI;ES ! L IS TRUE4 ,( ^! "QS ! GEOMET] IS B.D 6GIVE 8 A3.T1 US+ ! BASIC TRU?S ( GEOMETRY 9 3JUNC;N ) 8 PREVI\S 3CLU.NS2 (! BASIC TRU?S ! GEOMET]1 Z S*1 IS N B.D 6GIVE ANY A3.T4 ,! L IS TRUE (! O!R SCI;ES4 ,"! IS A LIMIT1 !N1 6! "QS : WE MAY PUT 6EA* MAN ( SCI;E2 NOR IS EA* MAN ( SCI;E B.D 6ANSW] ALL 9QUIRIES ON EA* S"EAL SUBJECT1 B ONLY S* Z FALL )9 ! DEF9$ FIELD ( 8 [N SCI;E4 ,IF1 !N1 9 3TROV]SY )A GEOMET] QUA GEOMET] ! 4PUTANT 3F9ES HMF 6GEOMETRY & PROVES ANY?+ F GEOMETRICAL PREMISSES1 HE IS CLE>LY 6BE APPLAUD$2 IF HE GOES \TSIDE ^! HE W 2 AT FAULT1 & OBVI\SLY _C EV5 REFUTE ! GEOMET] EXCEPT A3ID5T,Y4 ,"O %D "!=E N 4CUSS GEOMETRY AM;G ^? :O >E N GEOMET]S1 = 9 S* A -PANY AN UNS.D >GU;T W PASS UNNOTIC$4 ,? IS CORRESPOND+LY TRUE 9 ! O!R SCI;ES4 ,S9CE "! >E ,8GEOMETRICAL0' "QS1 DOES X FOLL[ T "! >E AL 4T9CTIVELY ,8UNGEOMETRICAL0' "QS8 ,FUR!R1 9 EA* SPECIAL SCI;E-GEOMETRY = 9/.E-:AT K9D ( ]ROR IS X T MAY VITIATE "QS1 & YET N EXCLUDE !M F T SCI;E8 ,AG1 IS ! ]RONE\S 3CLU.N "O 3/RUCT$ F PREMISSES OPPOSITE 6! TRUE PREMISSES1 OR IS X =MAL FALLACY ?\< DRAWN F GEOMETRICAL PREMISSES8 ,OR1 P]H1 ! ]RONE\S 3CLU.N IS DUE 6! DRAW+ ( PREMISSES F ANO!R SCI;E2 E4G4 9 A GEOMETRICAL 3TROV]SY A MUSICAL "Q IS 4T9CTIVELY UNGEOMETRICAL1 ":AS ! NO;N T P>ALLELS MEET IS 9 "O S5SE GEOMETRICAL1 2+ UNGEOMETRICAL 9 A DI6]5T FA%ION3 ! R1SON 2+ T ,8UNGEOMETRICAL0'1 L ,8UNRHY?MICAL0'1 IS EQUIVOCAL1 M1N+ 9 ! "O CASE N GEOMETRY AT ALL1 9 ! O!R BAD GEOMETRY8 ,X IS ? ]ROR1 I4E4 ]ROR BAS$ ON PREMISSES ( ? K9D-,8(0' ! SCI;E B FALSE-T IS ! 3TR>Y ( SCI;E4 ,9 MA!MATICS ! =MAL FALLACY IS N S -MON1 2C X IS ! MI4LE T]M 9 : ! AMBIGU;Y LIES1 S9CE ! MAJOR IS PR$ICAT$ (! :OLE (! MI4LE &! MI4LE (! :OLE (! M9OR 7! PR$ICATE ( C\RSE N"E HAS ! PREFIX ,8ALL0'72 & 9 MA!MATICS "O C1 S 6SP1K1 SEE ^! MI4LE T]MS ) AN 9TELLECTUAL VI.N1 :ILE 9 DIALECTIC ! AMBIGU;Y MAY ESCAPE DETEC;N4 ,E4G4 ,8,IS E CIRCLE A FIGURE80' ,A DIAGRAM %[S T ? IS S1 B ! M9OR PREMISS ,8,>E EPICS CIRCLES80' IS %[N 0! DIAGRAM 6BE FALSE4 ,IF A PRO( HAS AN 9DUCTIVE M9OR PREMISS1 "O %D N BR+ AN ,8OBJEC;N0' AG/ X4 ,= S9CE E PREMISS M/ 2 APPLICA# 6A NUMB] ( CASES 7O!RWISE X W N 2 TRUE 9 E 9/.E1 :1 S9CE ! SYLLOGISM PROCE$S F UNIV]SALS1 X M/ BE71 !N ASSUR$LY ! SAME IS TRUE ( AN ,8OBJEC;N0'2 S9CE PREMISSES & ,8OBJEC;NS0' >E S F> ! SAME T ANY?+ : C 2 VALIDLY ADV.ED Z AN ,8OBJEC;N0' M/ 2 S* T X CD TAKE ! =M (A PREMISS1 EI DEMON/RATIVE OR DIALECTICAL4 ,ON ! O!R H&1 >GU;TS =M,Y ILLOGICAL D "S"TS O3UR "? TAK+ Z MI4LES M]E ATTRIBUTES (! MAJOR & M9OR T]MS4 ,AN 9/.E ( ? IS ,CAENEUS' PRO( T FIRE 9CR1SES 9 GEOMETRICAL PROPOR;N3 ,8,FIRE0'1 HE >GUES1 ,89CR1SES RAPIDLY1 & S DOES GEOMETRICAL PROPOR;N0'4 ,"! IS NO SYLLOGISM S1 B "! IS A SYLLOGISM IF ! MO/ RAPIDLY 9CR1S+ PROPOR;N IS GEOMETRICAL &! MO/ RAPIDLY 9CR1S+ PROPOR;N IS ATTRIBUTA# 6FIRE 9 XS MO;N4 ,"S"TS1 NO D\BT1 X IS IMPOSSI# 6R1SON F PREMISSES PR$ICAT+ M]E ATTRIBUTES3 B "S"TS X IS POSSI#1 ?\< ! POSSIBIL;Y IS OV]LOOK$4 ,IF FALSE PREMISSES CD N"E GIVE TRUE 3CLU.NS ,8RESOLU;N0' WD 2 EASY1 = PREMISSES & 3CLU.N WD 9 T CASE 9EVITABLY RECIPROCATE4 ,I MIGUE ?US3 LET ,A 2 AN EXI/+ FACT2 LET ! EXI/;E ( ,A IMPLY S* & S* FACTS ACTU,Y "KN 6ME 6EXI/1 : WE MAY CALL ,B4 ,I C N[1 S9CE !Y RECIPROCATE1 9F] ,A F ,B4 ,RECIPROCATION ( PREMISSES & 3CLU.N IS M FREQU5T 9 MA!MATICS1 2C MA!MATICS TAKES DEF9I;NS1 B N"E AN A3ID5T1 = XS PREMISSES-A SECOND "*I/IC 4T+UI%+ MA!MATICAL R1SON+ F DIALECTICAL 4PUT,NS4 ,A SCI;E EXP&S N 0! 9T]POSI;N ( FRE% MI4LE T]MS1 B 0! APPOSI;N ( FRE% EXTREME T]MS4 ,E4G4 ,A IS PR$ICAT$ ( ;,B1 ;,B ( ;,C1 ;,C ( ;,D1 & S 9DEF9ITELY4 ,OR ! EXPAN.N MAY 2 LAT]AL3 E4G4 "O MAJOR ;,A1 MAY 2 PROV$ ( TWO M9ORS1 ;,C & ,E4 ,?US LET ,A REPRES5T NUMB]-A NUMB] OR NUMB] TAK5 9DET]M9ATELY2 ;,B DET]M9ATE ODD NUMB]2 ;,C ANY "PICUL> ODD NUMB]4 ,WE C !N PR$ICATE ;,A ( ,C4 ,NEXT LET ;,D REPRES5T DET]M9ATE EV5 NUMB]1 & ;,E EV5 NUMB]4 ,!N ,A IS PR$ICA# ( ,E4 #AC ,K (! FACT DI6]S F K (! R1SON$ FACT4 ,62G9 )1 !Y DI6] )9 ! SAME SCI;E & 9 TWO WAYS3 7#A7 :5 ! PREMISSES (! SYLLOGISM >E N IMM 7= !N ! PROXIMATE CAUSE IS N 3TA9$ 9 !M-A NEC 3DI;N ( K (! R1SON$ FACT73 7#B7 :5 ! PREMISSES >E IMM1 B 9/1D (! CAUSE ! BETT] "KN (! TWO RECIPROCALS IS TAK5 Z ! MI4LE2 =( TWO RECIPROC,Y PR$ICA# T]MS ! "O : IS N ! CAUSE MAY Q EASILY 2 ! BETT] "KN & S 2COME ! MI4LE T]M (! DEMON/R,N4 ,?US 7#B7 7A7 Y MIE NE> 2C !Y D N TW9KLE3 LET ;,C 2 ! PLANETS1 ;,B N TW9KL+1 ,A PROXIM;Y4 ,!N ;,B IS PR$ICA# ( ;,C2 =! PLANETS D N TW9KLE4 ,B ,A IS AL PR$ICA# ( ;,B1 S9CE T : DOES N TW9KLE IS NE>--WE M/ TAKE ? TRU? Z HAV+ BE5 R1*$ 09DUC;N OR S5SE- P]CEP;N4 ,"!=E ,A IS A NEC PR$ICATE ( ;,C2 S T WE H DEMON/RAT$ T ! PLANETS >E NE>4 ,? SYLLOGISM1 !N1 PROVES N ! R1SON$ FACT B ONLY ! FACT2 S9CE !Y >E N NE> 2C !Y D N TW9KLE1 B1 2C !Y >E NE>1 D N TW9KLE4 ,! MAJOR & MI4LE (! PRO(1 H["E1 MAY 2 REV]S$1 & !N ! DEMON/R,N W 2 (! R1SON$ FACT4 ,?US3 LET ;,C 2 ! PLANETS1 ;,B PROXIM;Y1 ,A N TW9KL+4 ,!N ;,B IS AN ATTRIBUTE ( ;,C1 & ,A-N TW9KL+-( ,B4 ,3SEQU5TLY ,A IS PR$ICA# ( ;,C1 &! SYLLOGISM PROVES ! R1SON$ FACT1 S9CE XS MI4LE T]M IS ! PROXIMATE CAUSE4 ,ANO!R EXAMPLE IS ! 9F];E T ! MOON IS SPH]ICAL F XS MANN] ( WAX+4 ,?US3 S9CE T : S WAXES IS SPH]ICAL1 & S9CE ! MOON S WAXES1 CLE>LY ! MOON IS SPH]ICAL4 ,PUT 9 ? =M1 ! SYLLOGISM TURNS \ 6BE PRO( (! FACT1 B IF ! MI4LE & MAJOR 2 REV]S$ X IS PRO( (! R1SON$ FACT2 S9CE ! MOON IS N SPH]ICAL 2C X WAXES 9 A C]TA9 MANN]1 B WAXES 9 S* A MANN] 2C X IS SPH]ICAL4 7,LET ;,C 2 ! MOON1 ;,B SPH]ICAL1 & ,A WAX+47 ,AG 7B71 9 CASES ": ! CAUSE &! E6ECT >E N RECIPROCAL &! E6ECT IS ! BETT] "KN1 ! FACT IS DEMON/RAT$ B N ! R1SON$ FACT4 ,? AL O3URS 7#A7 :5 ! MI4LE FALLS \TSIDE ! MAJOR & M9OR1 = "H TOO ! /RICT CAUSE IS N GIV51 & S ! DEMON/R,N IS (! FACT1 N (! R1SON$ FACT4 ,= EXAMPLE1 ! "Q ,8,:Y DOES N A WALL BR1!80' MIE L F>-FET*$ EXPLAN,NS1 : PRECISELY 3SI/ 9 MAK+ ! CAUSE TOO REMOTE1 Z 9 ,ANA*>SIS0' A3.T ( :Y ! ,SCY?IANS H NO FLUTE-PLAY]S2 "NLY 2C !Y H NO V9ES4 ,?US1 !N1 D ! SYLLOGISM (! FACT &! SYLLOGISM (! R1SON$ FACT DI6] )9 "O SCI;E & AC 6! POSI;N (! MI4LE T]MS4 ,B "! IS ANO!R WAY TOO 9 : ! FACT &! R1SON$ FACT DI6]1 & T IS :5 !Y >E 9VE/IGAT$ RESPECTIVELY 0DI6]5T SCI;ES4 ,? O3URS 9 ! CASE ( PRO#MS RELAT$ 6"O ANO!R Z SUBORD9ATE & SUP]IOR1 Z :5 OPTICAL PRO#MS >E SUBORD9AT$ 6GEOMETRY1 ME*ANICAL PRO#MS 6/]EOMETRY1 H>MONIC PRO#MS 6>I?METIC1 ! DATA ( OBS]V,N 6A/RONOMY4 7,"S ( ^! SCI;ES BE> ALM ! SAME "N2 E4G4 MA!MATICAL & NAUTICAL A/RONOMY1 MA!MATICAL & AC\/ICAL H>MONICS47 ,"H X IS ! BUSI;S (! EMPIRICAL OBS]V]S 6"K ! FACT1 (! MA!MATICIANS 6"K ! R1SON$ FACT2 =! LATT] >E 9 POSSES.N (! DEMON/R,NS GIV+ ! CAUSES1 & >E (T5 IGNORANT (! FACT3 J Z WE H (T5 A CLE> 9SIE IGNORANT ( "S ( XS "PICUL> 9/.ES4 ,^! 3NEXIONS H A P]CEPTI# EXI/;E ?\< !Y >E MANIFE/,NS ( =MS4 ,=! MA!MATICAL SCI;ES 3C]N =MS3 !Y D N DEMON/RATE PROP]TIES (A SUB/RATUM1 S9CE1 EV5 ?\< ! GEOMETRICAL SUBJECTS >E PR$ICA# Z PROP]TIES (A P]CEPTI# SUB/RATUM1 X IS N Z ?US PR$ICA# T ! MA!MATICIAN DEMON/RATES PROP]TIES ( !M4 ,Z OPTICS IS RELAT$ 6GEOMETRY1 S ANO!R SCI;E IS RELAT$ 6OPTICS1 "NLY ! !ORY (! RA9B[4 ,"H K (! FACT IS )9 ! PROV9CE (! NATURAL PHILOSOPH]1 K (! R1SON$ FACT )9 T (! OPTICIAN1 EI QUA OPTICIAN OR QUA MA!MATICAL OPTICIAN4 ,_M SCI;ES N /&+ 9 ? MUTUAL REL,N 5T] 96X AT PO9TS2 E4G4 M$IC9E & GEOMETRY3 X IS ! PHYSICIAN'S BUSI;S 6"K T CIRCUL> W.DS H1L M SL[LY1 ! GEOMET]'S 6"K ! R1SON :Y4 #AD ,( ALL ! FIGURES ! MO/ SCI5TIFIC IS ! F/4 ,?US1 X IS ! VEHICLE (! DEMON/R,NS ( ALL ! MA!MATICAL SCI;ES1 S* Z >I?METIC1 GEOMETRY1 & OPTICS1 & PRACTIC,Y ALL ( ALL SCI;ES T 9VE/IGATE CAUSES3 =! SYLLOGISM (! R1SON$ FACT IS EI EXCLUSIVELY OR G5],Y SP1K+ & 9 MO/ CASES 9 ? FIGURE-A SECOND PRO( T ? FIGURE IS ! MO/ SCI5TIFIC2 = GRASP (A R1SON$ 3CLU.N IS ! PRIM>Y 3DI;N ( K4 ,?IRDLY1 ! F/ IS ! ONLY FIGURE : 5A#S U 6PURSUE K (! ESS;E (A ?+4 ,9 ! SECOND FIGURE NO A6IRMATIVE 3CLU.N IS POSSI#1 & K (A ?+'S ESS;E M/ 2 A6IRMATIVE2 :ILE 9 ! ?IRD FIGURE ! 3CLU.N C 2 A6IRMATIVE1 B _C 2 UNIV]SAL1 & ESS;E M/ H A UNIV]SAL "*3 E4G4 MAN IS N TWO-FOOT$ ANIMAL 9 ANY QUALIFI$ S5SE1 B UNIV]S,Y4 ,F9,Y1 ! F/ FIGURE HAS NO NE$ (! O!RS1 :ILE X IS 0M1NS (! F/ T ! O!R TWO FIGURES >E DEVELOP$1 & H _! 9T]VALS CLOSEPACK$ UNTIL IMM PREMISSES >E R1*$4 ,CLE>LY1 "!=E1 ! F/ FIGURE IS ! PRIM>Y 3DI;N ( K4 #AE ,J Z AN ATTRIBUTE ,A MAY 7Z WE SAW7 2 ATOMIC,Y 3NECT$ )A SUBJECT ;,B1 S XS 4CONNEXION MAY 2 ATOMIC4 ,I CALL ,8ATOMIC0' 3NEXIONS OR 4CONNEXIONS : 9VOLVE NO 9T]M$IATE T]M2 S9CE 9 T CASE ! 3NEXION OR 4CONNEXION W N 2 M$IAT$ 0"S?+ O!R ?AN ! T]MS !MVS4 ,X FOLL[S T IF EI ,A OR ;,B1 OR BO? ;,A & ;,B1 H A G5US1 _! 4CONNEXION _C 2 PRIM>Y4 ,?US3 LET ;,C 2 ! G5US ( ,A4 ,!N1 IF ;,C IS N ! G5US ( ;,B-= ,A MAY WELL H A G5US : IS N ! G5US ( ;,B-"! W 2 A SYLLOGISM PROV+ ;,A'S 4CONNEXION F ;,B ?US3 ALL ,A IS ;,C1 NO ;,B IS ;,C1 "!=E NO ;,B IS ,A4 ,OR IF X IS ;,B : HAS A G5US ;,D1 WE H ALL ;,B IS ;,D1 NO ;,D IS ;,A1 "!=E NO ;,B IS ;,A1 0SYLLOGISM2 &! PRO( W 2 SIMIL> IF BO? ;,A & ;,B H A G5US4 ,T ! G5US ( ,A NE$ N 2 ! G5US ( ;,B & VICE V]SA1 IS %[N 0! EXI/;E ( MUTU,Y EXCLUSIVE COORD9ATE S]IES ( PR$IC,N4 ,IF NO T]M 9 ! S]IES ,,ACD ''' IS PR$ICA# ( ANY T]M 9 ! S]IES ,,BEF '''1& IF ;,G-;A T]M 9 ! =M] S]IES-IS ! G5US ( ;,A1 CLE>LY ;,G W N 2 ! G5US ( ;,B2 S9CE1 IF X W]E1 ! S]IES WD N 2 MUTU,Y EXCLUSIVE4 ,S AL IF ;,B HAS A G5US1 X W N 2 ! G5US ( ,A4 ,IF1 ON ! O!R H&1 NEI ,A NOR ;,B HAS A G5US & ,A DOES N 9"H 9 ;,B1 ? 4CONNEXION M/ 2 ATOMIC4 ,IF "! 2 A MI4LE T]M1 "O OR O!R ( !M IS B.D 6H A G5US1 =! SYLLOGISM W 2 EI 9 ! F/ OR ! SECOND FIGURE4 ,IF X IS 9 ! F/1 ;,B W H A G5US-=! PREMISS 3TA9+ X M/ 2 A6IRMATIVE3 IF 9 ! SECOND1 EI ,A OR ;,B 9DI6]5TLY1 S9CE SYLLOGISM IS POSSI# IF EI IS 3TA9$ 9 A NEGATIVE PREMISS1 B N IF BO? PREMISSES >E NEGATIVE4 ,H;E X IS CLE> T "O ?+ MAY 2 ATOMIC,Y 4CONNECT$ F ANO!R1 & WE H /AT$ :5 & H[ ? IS POSSI#4 #AF ,IGNOR.E-DEF9$ N Z ! NEG,N ( K B Z A POSITIVE /ATE ( M9D-IS ]ROR PRODUC$ 09F];E4 7#A7 ,LET U F/ 3SID] PROPOSI;NS ASS]T+ A PR$ICATE'S IMM 3NEXION ) OR 4CONNEXION F A SUBJECT4 ,"H1 X IS TRUE1 POSITIVE ]ROR MAY 2FALL "O 9 ALT]NATIVE WAYS2 = X MAY >ISE ": "O DIRECTLY 2LIEVES A 3NEXION OR 4CONNEXION Z WELL Z ": "O'S 2LIEF IS ACQUIR$ 09F];E4 ,! ]ROR1 H["E1 T 3SI/S 9 A DIRECT 2LIEF IS )\T -PLIC,N2 B ! ]ROR RESULT+ F 9F];E-: "H 3C]NS U- TAKES _M =MS4 ,?US1 LET ,A 2 ATOMIC,Y 4CONNECT$ F ALL ;,B3 !N ! 3CLU.N 9F]R$ "? A MI4LE T]M ;,C1 T ALL ;,B IS ;,A1 W 2 A CASE ( ]ROR PRODUC$ 0SYLLOGISM4 ,N[1 TWO CASES >E POSSI#4 ,EI 7A7 BO? PREMISSES1 OR 7B7 "O PREMISS ONLY1 MAY 2 FALSE4 7A7 ,IF NEI ,A IS AN ATTRIBUTE ( ANY ;,C NOR ;,C ( ANY ;,B1 ":AS ! 3TR>Y 0 POSIT$ 9 BO? CASES1 BO? PREMISSES W 2 FALSE4 7;,C MAY Q WELL 2 S RELAT$ TO ;,A & ;,B T ;,C IS NEI SUBORD9ATE TO ;,A NOR A UNIV]SAL ATTRIBUTE ( ;,B3 = ;,B1 S9CE ,A 0 SD 6BE PRIM>ILY 4CONNECT$ F ;,B1 _C H A G5US1 & ,A NE$ N NECESS>ILY 2 A UNIV]SAL ATTRIBUTE ( ALL ?+S4 ,3SEQU5TLY BO? PREMISSES MAY 2 FALSE47 ,ON ! O!R H&1 7B7 "O (! PREMISSES MAY 2 TRUE1 ?\< N EI 9DI6]5TLY B ONLY ! MAJOR ;,A-;,C S9CE1 ;,B HAV+ NO G5US1 ! PREMISS ;,C- ;,B W ALW 2 FALSE1 :ILE ;,A-;,C MAY 2 TRUE4 ,? IS ! CASE IF1 = EXAMPLE1 ,A IS RELAT$ ATOMIC,Y 6BO? ;,C & ;,B2 2C :5 ! SAME T]M IS RELAT$ ATOMIC,Y 6M T]MS ?AN "O1 NEI ( ^? T]MS W 2L;G 6! O!R4 ,X IS1 ( C\RSE1 EQU,Y ! CASE IF ;,A-;,C IS N ATOMIC4 ,]ROR ( ATTRIBU;N1 !N1 O3URS "? ^! CAUSES & 9 ? =M ONLY-= WE F.D T NO SYLLOGISM ( UNIV]SAL ATTRIBU;N 0 POSSI# 9 ANY FIGURE B ! F/4 ,ON ! O!R H&1 AN ]ROR ( NON-ATTRIBU;N MAY O3UR EI 9 ! F/ OR 9 ! SECOND FIGURE4 ,LET U "!=E F/ EXPLA9 ! V>I\S =MS X TAKES 9 ! F/ FIGURE &! "* (! PREMISSES 9 EA* CASE4 7C7 ,X MAY O3UR :5 BO? PREMISSES >E FALSE2 E4G4 SUPPOS+ ,A ATOMIC,Y 3NECT$ ) BO? ;,C & ;,B1 IF X 2 !N ASSUM$ T NO ;,C IS & ALL ;,B IS ;,C1 BO? PREMISSES >E FALSE4 7D7 ,X IS AL POSSI# :5 "O IS FALSE4 ,? MAY 2 EI PREMISS 9DI6]5TLY4 ;,A-;,C MAY 2 TRUE1 ;,C-;,B FALSE-;,A-;,C TRUE 2C ,A IS N AN ATTRIBUTE ( ALL ?+S1 ;,C-;,B FALSE 2C ;,C1 : N"E HAS ! ATTRIBUTE ;,A1 _C 2 AN ATTRIBUTE ( ;,B2 = IF ;,C-;,B 7 TRUE1 ! PREMISS ;,A-;,C WD NO L;G] 2 TRUE1 & 2SS IF BO? PREMISSES 7 TRUE1 ! 3CLU.N WD 2 TRUE4 ,OR AG1 ;,C-;,B MAY 2 TRUE & ;,A-;,C FALSE2 E4G4 IF BO? ;,C & ,A 3TA9 ;,B Z G5]A1 "O ( !M M/ 2 SUBORD9ATE 6! O!R1 S T IF ! PREMISS TAKES ! =M ,NO ;,C IS ;,A1 X W 2 FALSE4 ,? MAKES X CLE> T :E!R EI OR BO? PREMISSES >E FALSE1 ! 3CLU.N W EQU,Y 2 FALSE4 ,9 ! SECOND FIGURE ! PREMISSES _C BO? 2 :OLLY FALSE2 = IF ALL ;,B IS ;,A1 NO MI4LE T]M C 2 ) TRU? UNIV]S,Y A6IRM$ ( "O EXTREME & UNIV]S,Y D5I$ (! O!R3 B PREMISSES 9 : ! MI4LE IS A6IRM$ ( "O EXTREME & D5I$ (! O!R >E ! NEC 3DI;N IF "O IS 6GET A VALID 9F];E AT ALL4 ,"!=E IF1 TAK5 9 ? WAY1 !Y >E :OLLY FALSE1 _! 3TR>IES 3V]SELY %D 2 :OLLY TRUE4 ,B ? IS IMPOSSI#4 ,ON ! O!R H&1 "! IS NO?+ 6PREV5T BO? PREMISSES 2+ "PI,Y FALSE2 E4G4 IF ACTU,Y "S ,A IS ;,C & "S ;,B IS ;,C1 !N IF X IS PREMIS$ T ALL ,A IS ;,C & NO ;,B IS ;,C1 BO? PREMISSES >E FALSE1 YET "PI,Y1 N :OLLY1 FALSE4 ,! SAME IS TRUE IF ! MAJOR IS MADE NEGATIVE 9/1D (! M9OR4 ,OR "O PREMISS MAY 2 :OLLY FALSE1 & X MAY 2 EI ( !M4 ,?US1 SUPPOS+ T ACTU,Y AN ATTRIBUTE ( ALL ,A M/ AL 2 AN ATTRIBUTE ( ALL ;,B1 !N IF ;,C IS YET TAK5 6BE A UNIV]SAL ATTRIBUTE ( ALL B UNIV]S,Y NON-ATTRIBUTA# TO ;,B1 ;,C-;,A W 2 TRUE B ;,C-;,B FALSE4 ,AG1 ACTU,Y T : IS AN ATTRIBUTE ( NO ;,B W N 2 AN ATTRIBUTE ( ALL ,A EI2 = IF X 2 AN ATTRIBUTE ( ALL ;,A1 X W AL 2 AN ATTRIBUTE ( ALL ;,B1 : IS 3TR>Y 6SUPPOSI;N2 B IF ;,C 2 N"E!.S ASSUM$ 6BE A UNIV]SAL ATTRIBUTE ( ;,A1 B AN ATTRIBUTE ( NO ;,B1 !N ! PREMISS ;,C-;,B IS TRUE B ! MAJOR IS FALSE4 ,! CASE IS SIMIL> IF ! MAJOR IS MADE ! NEGATIVE PREMISS4 ,= 9 FACT :AT IS AN ATTRIBUTE ( NO ,A W N 2 AN ATTRIBUTE ( ANY ;,B EI2 & IF X 2 YET ASSUM$ T ;,C IS UNIV]S,Y NON- ATTRIBUTA# TO ;,A1 B A UNIV]SAL ATTRIBUTE ( ;,B1 ! PREMISS ;,C-;,A IS TRUE B ! M9OR :OLLY FALSE4 ,AG1 9 FACT X IS FALSE 6ASSUME T T : IS AN ATTRIBUTE ( ALL ;,B IS AN ATTRIBUTE ( NO ;,A1 = IF X 2 AN ATTRIBUTE ( ALL ;,B1 X M/ 2 AN ATTRIBUTE ( "S ,A4 ,IF !N ;,C IS N"E!.S ASSUM$ 6BE AN ATTRIBUTE ( ALL ;,B B ( NO ;,A1 ;,C-;,B W 2 TRUE B ;,C-;,A FALSE4 ,X IS ?US CLE> T 9 ! CASE ( ATOMIC PROPOSI;NS ]RONE\S 9F];E W 2 POSSI# N ONLY :5 BO? PREMISSES >E FALSE B AL :5 ONLY "O IS FALSE4 #AG ,9 ! CASE ( ATTRIBUTES N ATOMIC,Y 3NECT$ ) OR 4CONNECT$ F _! SUBJECTS1 7A7 7I7 Z L;G Z ! FALSE 3CLU.N IS 9F]R$ "? ! ,8APPROPRIATE0' MI4LE1 ONLY ! MAJOR & N BO? PREMISSES C 2 FALSE4 ,BY ,8APPROPRIATE MI4LE0' ,I M1N ! MI4LE T]M "? : ! 3TRADICTORY-I4E4 ! TRUE-3CLU.N IS 9F]RI#4 ,?US1 LET ,A 2 ATTRIBUTA# TO ;,B "? A MI4LE T]M ;,C3 !N1 S9CE 6PRODUCE A 3CLU.N ! PREMISS ;,C-;,B M/ 2 TAK5 A6IRMATIVELY1 X IS CLE> T ? PREMISS M/ ALW 2 TRUE1 = XS QUAL;Y IS N *ANG$4 ,B ! MAJOR ;,A-;,C IS FALSE1 = X IS 0A *ANGE 9 ! QUAL;Y ( ;,A-;,C T ! 3CLU.N 2COMES XS 3TRADICTORY-I4E4 TRUE4 ,SIMIL>LY 7;II7 IF ! MI4LE IS TAK5 F ANO!R S]IES ( PR$IC,N2 E4G4 SUPPOSE ;,D 6BE N ONLY 3TA9$ )9 ,A Z A "P )9 XS :OLE B AL PR$ICA# ( ALL ,B4 ,!N ! PREMISS ;,D-;,B M/ REMA9 UN*ANG$1 B ! QUAL;Y ( ;,A-;,D M/ 2 *ANG$2 S T ;,D-;,B IS ALW TRUE1 ;,A-;,D ALW FALSE4 ,S* ]ROR IS PRACTIC,Y ID5TICAL ) T : IS 9F]R$ "? ! ,8APPROPRIATE0' MI4LE4 ,ON ! O!R H&1 7B7 IF ! 3CLU.N IS N 9F]R$ "? ! ,8APPROPRIATE0' MI4LE-7I7 :5 ! MI4LE IS SUBORD9ATE TO ;,A B IS PR$ICA# ( NO ;,B1 BO? PREMISSES M/ 2 FALSE1 2C IF "! IS 6BE A 3CLU.N BO? M/ 2 POSIT$ Z ASS]T+ ! 3TR>Y ( :AT IS ACTU,Y ! FACT1 & S POSIT$ BO? 2COME FALSE3 E4G4 SUPPOSE T ACTU,Y ALL ;,D IS ,A B NO ;,B IS ;,D2 !N IF ^! PREMISSES >E *ANG$ 9 QUAL;Y1 A 3CLU.N W FOLL[ & BO? (! NEW PREMISSES W 2 FALSE4 ,:51 H["E1 7;II7 ! MI4LE ;,D IS N SUBORD9ATE TO ;,A1 ;,A-;,D W 2 TRUE1 ;,D-;,B FALSE-;,A-;,D TRUE 2C ,A 0 N SUBORD9ATE TO ;,D1 ;,D-;,B FALSE 2C IF X _H BE5 TRUE1 ! 3CLU.N TOO WD H BE5 TRUE2 B X IS EX HYPO!SI FALSE4 ,:5 ! ]RONE\S 9F];E IS 9 ! SECOND FIGURE1 BO? PREMISSES _C 2 5TIRELY FALSE2 S9CE IF ;,B IS SUBORD9ATE TO ;,A1 "! C 2 NO MI4LE PR$ICA# ( ALL ( "O EXTREME &( N"O (! O!R1 Z 0 /AT$ 2F4 ,"O PREMISS1 H["E1 MAY 2 FALSE1 & X MAY 2 EI ( !M4 ,?US1 IF ;,C IS ACTU,Y AN ATTRIBUTE ( BO? ;,A & ;,B1 B IS ASSUM$ 6BE AN ATTRIBUTE ( ,A ONLY & N ( ;,B1 ;,C-;,A W 2 TRUE1 ;,C-;,B FALSE3 OR AG IF ;,C 2 ASSUM$ 6BE ATTRIBUTA# TO ;,B B 6NO ;,A1 ;,C-;,B W 2 TRUE1 ;,C-;,A FALSE4 ,WE H /AT$ :5 & "? :AT K9DS ( PREMISSES ]ROR W RESULT 9 CASES ": ! ]RONE\S 3CLU.N IS NEGATIVE4 ,IF ! 3CLU.N IS A6IRMATIVE1 7A7 7I7 X MAY 2 9F]R$ "? ! ,8APPROPRIATE0' MI4LE T]M4 ,9 ? CASE BO? PREMISSES _C 2 FALSE S9CE1 Z WE SD 2F1 ;,C-;,B M/ REMA9 UN*ANG$ IF "! IS 6BE A 3CLU.N1 & 3SEQU5TLY ;,A-;,C1 ! QUAL;Y ( : IS *ANG$1 W ALW 2 FALSE4 ,? IS EQU,Y TRUE IF 7;II7 ! MI4LE IS TAK5 F ANO!R S]IES ( PR$IC,N1 Z 0 /AT$ 6BE ! CASE AL ) REG>D 6NEGATIVE ]ROR2 = ;,D- ;,B M/ REMA9 UN*ANG$1 :ILE ! QUAL;Y ( ;,A-;,D M/ 2 3V]T$1 &! TYPE ( ]ROR IS ! SAME Z 2F4 7B7 ,! MI4LE MAY 2 9APPROPRIATE4 ,!N 7I7 IF ;,D IS SUBORD9ATE TO ;,A1 ;,A-;,D W 2 TRUE1 B ;,D-;,B FALSE2 S9CE ,A MAY Q WELL 2 PR$ICA# ( S"EAL T]MS NO "O ( : C 2 SUBORD9AT$ 6ANO!R4 ,IF1 H["E1 7;II7 ;,D IS N SUBORD9ATE TO ;,A1 OBVI\SLY ;,A-;,D1 S9CE X IS A6IRM$1 W ALW 2 FALSE1 :ILE ;,D-;,B MAY 2 EI TRUE OR FALSE2 = ,A MAY V WELL 2 AN ATTRIBUTE ( NO ;,D1 ":AS ALL ;,B IS ;,D1 E4G4 NO SCI;E IS ANIMAL1 ALL MUSIC IS SCI;E4 ,EQU,Y WELL ,A MAY 2 AN ATTRIBUTE ( NO ;,D1 & ;,D ( NO ,B4 ,X EM]GES1 !N1 T IF ! MI4LE T]M IS N SUBORD9ATE 6! MAJOR1 N ONLY BO? PREMISSES B EI S+LY MAY 2 FALSE4 ,?US WE H MADE X CLE> H[ _M V>IETIES ( ]RONE\S 9F];E >E LIA# 6HAPP5 & "? :AT K9DS ( PREMISSES !Y O3UR1 9 ! CASE BO? ( IMM &( DEMON/RA# TRU?S4 #AH ,X IS AL CLE> T ! LOSS ( ANY "O (! S5SES 5TAILS ! LOSS (A CORRESPOND+ POR;N ( K1 & T1 S9CE WE LE>N EI 09DUC;N OR 0DEMON/R,N1 ? K _C 2 ACQUIR$4 ,?US DEMON/R,N DEVELOPS F UNIV]SALS1 9DUC;N F "PICUL>S2 B S9CE X IS POSSI# 6FAMILI>IZE ! PUPIL ) EV5 ! S-CALL$ MA!MATICAL AB/RAC;NS ONLY "? 9DUC;N-I4E4 ONLY 2C EA* SUBJECT G5US POSSESSES1 9 VIRTUE (A DET]M9ATE MA!MATICAL "*1 C]TA9 PROP]TIES : C 2 TR1T$ Z SEP>ATE EV5 ?\< !Y D N EXI/ 9 ISOL,N-X IS 3SEQU5TLY IMPOSSI# 6-E 6GRASP UNIV]SALS EXCEPT "? 9DUC;N4 ,B 9DUC;N IS IMPOSSI# = ^? :O H N S5SE- P]CEP;N4 ,= X IS S5SE-P]CEP;N AL"O : IS ADEQUATE = GRASP+ ! "PICUL>S3 !Y _C 2 OBJECTS ( SCI5TIFIC K1 2C NEI C UNIV]SALS GIVE U K ( !M )\T 9DUC;N1 NOR C WE GET X "? 9DUC;N )\T S5SE-P]CEP;N4 #AI ,E SYLLOGISM IS E6ECT$ 0M1NS ( ?REE T]MS4 ,"O K9D ( SYLLOGISM S]VES 6PROVE T ,A 9"HS 9 ;,C 0%[+ T ,A 9"HS 9 ;,B & ;,B 9 ;,C2 ! O!R IS NEGATIVE & "O ( XS PREMISSES ASS]TS "O T]M ( ANO!R1 :ILE ! O!R D5IES "O T]M ( ANO!R4 ,X IS CLE>1 !N1 T ^! >E ! FUNDA;TALS & S-CALL$ HYPO!SES ( SYLLOGISM4 ,ASSUME !M Z !Y H BE5 /AT$1 & PRO( IS B.D 6FOLL[-PRO( T ,A 9"HS 9 ;,C "? ;,B1 & AG T ,A 9"HS 9 ;,B "? "S O!R MI4LE T]M1 & SIMIL>LY T ;,B 9"HS 9 ,C4 ,IF \R R1SON+ AIMS AT GA9+ CR$;E & S IS M]ELY DIALECTICAL1 X IS OBVI\S T WE H ONLY 6SEE T \R 9F];E IS BAS$ ON PREMISSES Z CR$I# Z POSSI#3 S T IF A MI4LE T]M 2T ;,A & ;,B IS CR$I# ?\< N R1L1 "O C R1SON "? X & -PLETE A DIALECTICAL SYLLOGISM4 ,IF1 H["E1 "O IS AIM+ AT TRU?1 "O M/ 2 GUID$ 0! R1L 3NEXIONS ( SUBJECTS & ATTRIBUTES4 ,?US3 S9CE "! >E ATTRIBUTES : >E PR$ICAT$ (A SUBJECT ESS5TI,Y OR NATUR,Y & N CO9CID5T,Y-N1 T IS1 9 ! S5SE 9 : WE SAY ,8,T :ITE 7?+7 IS A MAN0'1 : IS N ! SAME MODE ( PR$IC,N Z :5 WE SAY ,8,! MAN IS :ITE0'3 ! MAN IS :ITE N 2C HE IS "S?+ ELSE B 2C HE IS MAN1 B ! :ITE IS MAN 2C ,82+ :ITE0' CO9CIDES ) ,8HUMAN;Y0' )9 "O SUB/RATUM-"!=E "! >E T]MS S* Z >E NATUR,Y SUBJECTS ( PR$ICATES4 ,SUPPOSE1 !N1 ;,C S* A T]M N XF ATTRIBUTA# 6ANY?+ ELSE Z 6A SUBJECT1 B ! PROXIMATE SUBJECT (! ATTRIBUTE ;,B--I4E4 S T ;,B-;,C IS IMM2 SUPPOSE FUR!R ;,E RELAT$ IMMLY TO ;,F1 & ;,F TO ;,B4 ,! F/ "Q IS1 M/ ? S]IES T]M9ATE1 OR C X PROCE$ 69F9;Y8 ,! SECOND "Q IS Z FOLL[S3 ,SUPPOSE NO?+ IS ESS5TI,Y PR$ICAT$ ( ;,A1 B ,A IS PR$ICAT$ PRIM>ILY ( ;,H &( NO 9T]M$IATE PRIOR T]M1 & SUPPOSE ;,H SIMIL>LY RELAT$ TO ;,G & ;,G TO ;,B2 !N M/ ? S]IES AL T]M9ATE1 OR C X TOO PROCE$ 69F9;Y8 ,"! IS ? M* DI6];E 2T ! "QS3 ! F/ IS1 IS X POSSI# 6/>T F T : IS N XF ATTRIBUTA# 6ANY?+ ELSE B IS ! SUBJECT ( ATTRIBUTES1 & ASC5D 69F9;Y8 ,! SECOND IS ! PRO#M :E!R "O C />T F T : IS A PR$ICATE B N XF A SUBJECT ( PR$ICATES1 & DESC5D 69F9;Y8 ,A ?IRD "Q IS1 IF ! EXTREME T]MS >E FIX$1 C "! 2 AN 9F9;Y ( MI4LES8 ,I M1N ?3 SUPPOSE = EXAMPLE T ,A 9"HS 9 ;,C & ;,B IS 9T]M$IATE 2T !M1 B 2T ;,B & ,A "! >E O!R MI4LES1 & 2T ^! AG FRE% MI4LES2 C ^! PROCE$ 69F9;Y OR C !Y N8 ,? IS ! EQUIVAL5T ( 9QUIR+1 D DEMON/R,NS PROCE$ 69F9;Y1 I4E4 IS "EY?+ DEMON/RA#8 ,OR D ULTIMATE SUBJECT & PRIM>Y ATTRIBUTE LIMIT "O ANO!R8 ,I HOLD T ! SAME "QS >ISE ) REG>D 6NEGATIVE 3CLU.NS & PREMISSES3 VIZ4 IF ,A IS ATTRIBUTA# 6NO ;,B1 !N EI ? PR$IC,N W 2 PRIM>Y1 OR "! W 2 AN 9T]M$IATE T]M PRIOR TO ;,B 6: A IS N ATTRIBUTA#-;,G1 LET U SAY1 : IS ATTRIBUTA# 6ALL ;,B-& "! MAY / 2 ANO!R T]M ;,H PRIOR TO ;,G1 : IS ATTRIBUTA# 6ALL ,G4 ,! SAME "QS >ISE1 ,I SAY1 2C 9 ^! CASES TOO EI ! S]IES ( PRIOR T]MS 6: A IS N ATTRIBUTA# IS 9F9ITE OR X T]M9ATES4 ,"O _C ASK ! SAME "QS 9 ! CASE ( RECIPROCAT+ T]MS1 S9CE :5 SUBJECT & PR$ICATE >E 3V]TI# "! IS NEI PRIM>Y NOR ULTIMATE SUBJECT1 SEE+ T ALL ! RECIPROCALS QUA SUBJECTS /& 9 ! SAME REL,N 6"O ANO!R1 :E!R WE SAY T ! SUBJECT HAS AN 9F9;Y ( ATTRIBUTES OR T BO? SUBJECTS & ATTRIBUTES-& WE RAIS$ ! "Q 9 BO? CASES->E 9F9ITE 9 NUMB]4 ,^! "QS !N _C 2 ASK$-UN.S1 9DE$1 ! T]MS C RECIPROCATE 0TWO DI6]5T MODES1 0A3ID5TAL PR$IC,N 9 "O REL,N & NATURAL PR$IC,N 9 ! O!R4 #BJ ,N[1 X IS CLE> T IF ! PR$IC,NS T]M9ATE 9 BO? ! UPW>D &! D[NW>D DIREC;N 7BY ,8UPW>D0' ,I M1N ! ASC5T 6! M UNIV]SAL1 BY ,8D[NW>D0' ! DESC5T 6! M "PICUL>71 ! MI4LE T]MS _C 2 9F9ITE 9 NUMB]4 ,= SUPPOSE T ,A IS PR$ICAT$ ( ;,F1 & T ! 9T]M$IATES-CALL !M ,,BB'B0 '''->E 9F9ITE1 !N CLE>LY Y MIE 9F9ITE T]MS 2T Y & ,A4 ,X FOLL[S T IF ^! PROCESSES >E IMPOSSI# "! _C 2 AN 9F9;Y ( 9T]M$IATES 2T ;,A & ,F4 ,NOR IS X ( ANY E6ECT 6URGE T "S T]MS (! S]IES ;,,AB ''' ;,F >E 3TIGU\S S Z 6EXCLUDE 9T]M$IATES1 :ILE O!RS _C 2 TAK5 96! >GU;T AT ALL3 :I*"E T]MS (! S]IES ,B ''' ,I TAKE1 ! NUMB] ( 9T]M$IATES 9 ! DIREC;N EI ( ,A OR ( ;,F M/ 2 F9ITE OR 9F9ITE3 ": ! 9F9ITE S]IES />TS1 :E!R F ! F/ T]M OR F A LAT] "O1 IS ( NO MO;T1 =! SU3E$+ T]MS 9 ANY CASE >E 9F9ITE 9 NUMB]4 #BA ,FUR!R1 IF 9 A6IRMATIVE DEMON/R,N ! S]IES T]M9ATES 9 BO? DIREC;NS1 CLE>LY X W T]M9ATE TOO 9 NEGATIVE DEMON/R,N4 ,LET U ASSUME T WE _C PROCE$ 69F9;Y EI 0ASC5D+ F ! ULTIMATE T]M 7BY ,8ULTIMATE T]M0' ,I M1N A T]M S* Z WAS1 N XF ATTRIBUTA# 6A SUBJECT B XF ! SUBJECT ( ATTRIBUTES71 OR 0DESC5D+ T[>DS AN ULTIMATE F ! PRIM>Y T]M 7BY ,8PRIM>Y T]M0' ,I M1N A T]M PR$ICA# (A SUBJECT B N XF A SUBJECT74 ,IF ? ASSUMP;N IS JU/IFI$1 ! S]IES W AL T]M9ATE 9 ! CASE ( NEG,N4 ,=A NEGATIVE 3CLU.N C 2 PROV$ 9 ALL ?REE FIGURES4 ,9 ! F/ FIGURE X IS PROV$ ?US3 NO ;,B IS ;,A1 ALL ;,C IS ,B4 ,9 PACK+ ! 9T]VAL ;,B-;,C WE M/ R1* IMM PROPOSI;NS--Z IS ALW ! CASE )! M9OR PREMISS--S9CE ;,B-;,C IS A6IRMATIVE4 ,Z REG>DS ! O!R PREMISS X IS PLA9 T IF ! MAJOR T]M IS D5I$ (A T]M ;,D PRIOR TO ;,B1 ;,D W H 6BE PR$ICA# ( ALL ;,B1 & IF ! MAJOR IS D5I$ ( YET ANO!R T]M PRIOR TO ;,D1 ? T]M M/ 2 PR$ICA# ( ALL ,D4 ,3SEQU5TLY1 S9CE ! ASC5D+ S]IES IS F9ITE1 ! DESC5T W AL T]M9ATE & "! W 2 A SUBJECT ( : ,A IS PRIM>ILY NON-PR$ICA#4 ,9 ! SECOND FIGURE ! SYLLOGISM IS1 ALL ,A IS ;,B1 NO ;,C IS ;,B144NO ;,C IS ,A4 ,IF PRO( ( ? IS REQUIR$1 PLA9LY X MAY 2 %[N EI 9 ! F/ FIGURE Z ABV1 9 ! SECOND Z "H1 OR 9 ! ?IRD4 ,! F/ FIGURE HAS BE5 4CUSS$1 & WE W PROCE$ 64PLAY ! SECOND1 PRO( 0: W 2 Z FOLL[S3 ALL ;,B IS ;,D1 NO ;,C IS ,D '''1 S9CE X IS REQUIR$ T ;,B %D 2 A SUBJECT ( : A PR$ICATE IS A6IRM$4 ,NEXT1 S9CE ;,D IS 6BE PROV$ N 62L;G TO ;,C1 !N ;,D HAS A FUR!R PR$ICATE : IS D5I$ ( ,C4 ,"!=E1 S9CE ! SU3ES.N ( PR$ICATES A6IRM$ ( AN "E HI<] UNIV]SAL T]M9ATES1 ! SU3ES.N ( PR$ICATES D5I$ T]M9ATES TOO4 ,! ?IRD FIGURE %[S X Z FOLL[S3 ALL ;,B IS ;,A1 "S ;,B IS N ,C4 ,"!=E "S ,A IS N ,C4 ,? PREMISS1 I4E4 ;,C-;,B1 W 2 PROV$ EI 9 ! SAME FIGURE OR 9 "O (! TWO FIGURES 4CUSS$ ABV4 ,9 ! F/ & SECOND FIGURES ! S]IES T]M9ATES4 ,IF WE USE ! ?IRD FIGURE1 WE % TAKE Z PREMISSES1 ALL ;,E IS ;,B1 "S ;,E IS N ;,C1 & ? PREMISS AG W 2 PROV$ 0A SIMIL> PROSYLLOGISM4 ,B S9CE X IS ASSUM$ T ! S]IES ( DESC5D+ SUBJECTS AL T]M9ATES1 PLA9LY ! S]IES ( M UNIV]SAL NON-PR$ICA#S W T]M9ATE AL4 ,EV5 SUPPOS+ T ! PRO( IS N 3F9$ 6"O ME?OD1 B EMPLOYS !M ALL & IS N[ 9 ! F/ FIGURE1 N[ 9 ! SECOND OR ?IRD-EV5 S ! REGRESS W T]M9ATE1 =! ME?ODS >E F9ITE 9 NUMB]1 & IF F9ITE ?+S >E -B9$ 9 A F9ITE NUMB] ( WAYS1 ! RESULT M/ 2 F9ITE4 ,?US X IS PLA9 T ! REGRESS ( MI4LES T]M9ATES 9 ! CASE ( NEGATIVE DEMON/R,N1 IF X DOES S AL 9 ! CASE ( A6IRMATIVE DEMON/R,N4 ,T 9 FACT ! REGRESS T]M9ATES 9 BO? ^! CASES MAY 2 MADE CLE> 0! FOLL[+ DIALECTICAL 3SID],NS4 #BB ,9 ! CASE ( PR$ICATES 3/ITUT+ ! ESS5TIAL NATURE (A ?+1 X CLE>LY T]M9ATES1 SEE+ T IF DEF9I;N IS POSSI#1 OR 9 O!R ^WS1 IF ESS5TIAL =M IS "KA#1 & AN 9F9ITE S]IES _C 2 TRAV]S$1 PR$ICATES 3/ITUT+ A ?+'S ESS5TIAL NATURE M/ 2 F9ITE 9 NUMB]4 ,B Z REG>DS PR$ICATES G5],Y WE H ! FOLL[+ PREFATORY REM>KS 6MAKE4 7#A7 ,WE C A6IRM )\T FALSEHOOD ,8! :ITE 7?+7 IS WALK+0'1 & T BIG 7?+7 IS A LOG0'2 OR AG1 ,8! LOG IS BIG0'1 & ,8! MAN WALKS0'4 ,B ! A6IRM,N DI6]S 9 ! TWO CASES4 ,:5 ,I A6IRM ,8! :ITE IS A LOG0'1 ,I M1N T "S?+ : HAPP5S 6BE :ITE IS A LOG-N T :ITE IS ! SUB/RATUM 9 : LOG 9"HS1 = X 0 N QUA :ITE OR QUA A SPECIES ( :ITE T ! :ITE 7?+7 CAME 6BE A LOG1 &! :ITE 7?+7 IS 3SEQU5TLY N A LOG EXCEPT 9CID5T,Y4 ,ON ! O!R H&1 :5 ,I A6IRM ,8! LOG IS :ITE0'1 ,I D N M1N T "S?+ ELSE1 : HAPP5S AL 6BE A LOG1 IS :ITE 7Z ,I %D IF ,I SD ,8! MUSICIAN IS :ITE10' : WD M1N ,8! MAN :O HAPP5S AL 6BE A MUSICIAN IS :ITE0'72 ON ! 3TR>Y1 LOG IS "H ! SUB/RATUM-! SUB/RATUM : ACTU,Y CAME 6BE :ITE1 & DID S QUA WOOD OR QUA A SPECIES ( WOOD & QUA NO?+ ELSE4 ,IF WE M/ LAY D[N A RULE1 LET U 5TITLE ! LATT] K9D ( /ATE;T PR$IC,N1 &! =M] N PR$IC,N AT ALL1 OR N /RICT B A3ID5TAL PR$IC,N4 ,8,:ITE0' & ,8LOG0' W ?US S]VE Z TYPES RESPECTIVELY ( PR$ICATE & SUBJECT4 ,WE % ASSUME1 !N1 T ! PR$ICATE IS 9V>IABLY PR$ICAT$ /RICTLY & N A3ID5T,Y ( ! SUBJECT1 = ON S* PR$IC,N DEMON/R,NS DEP5D = _! =CE4 ,X FOLL[S F ? T :5 A S+LE ATTRIBUTE IS PR$ICAT$ (A S+LE SUBJECT1 ! PR$ICATE M/ A6IRM (! SUBJECT EI "S ELE;T 3/ITUT+ XS ESS5TIAL NATURE1 OR T X IS 9 "S WAY QUALIFI$1 QUANTIFI$1 ESS5TI,Y RELAT$1 ACTIVE1 PASSIVE1 PLAC$1 OR DAT$4 7#B7 ,PR$ICATES : SIGNIFY SUB/.E SIGNIFY T ! SUBJECT IS ID5TICAL )! PR$ICATE OR )A SPECIES (! PR$ICATE4 ,PR$ICATES N SIGNIFY+ SUB/.E : >E PR$ICAT$ (A SUBJECT N ID5TICAL ) !MVS OR )A SPECIES ( !MVS >E A3ID5TAL OR CO9CID5TAL2 E4G4 :ITE IS A CO9CID5T ( MAN1 SEE+ T MAN IS N ID5TICAL ) :ITE OR A SPECIES ( :ITE1 B R ) ANIMAL1 S9CE MAN IS ID5TICAL )A SPECIES ( ANIMAL4 ,^! PR$ICATES : D N SIGNIFY SUB/.E M/ 2 PR$ICATES ( "S O!R SUBJECT1 & NO?+ C 2 :ITE : IS N AL O!R ?AN :ITE4 ,! ,=MS WE C 4P5SE )1 = !Y >E M]E S.D )\T S5SE2 & EV5 IF "! >E S* ?+S1 !Y >E N RELEVANT 6\R 4CUS.N1 S9CE DEMON/R,NS >E 3C]N$ ) PR$ICATES S* Z WE H DEF9$4 7#C7 ,IF ,A IS A QUAL;Y ( ;,B1 ;,B _C 2 A QUAL;Y ( ;,A-;A QUAL;Y (A QUAL;Y4 ,"!=E ;,A & ;,B _C 2 PR$ICAT$ RECIPROC,Y ( "O ANO!R 9 /RICT PR$IC,N3 !Y C 2 A6IRM$ )\T FALSEHOOD ( "O ANO!R1 B N G5U9ELY PR$ICAT$ ( EA* O!R4 ,= "O ALT]NATIVE IS T !Y %D 2 SUB/ANTI,Y PR$ICAT$ ( "O ANO!R1 I4E4 ;,B WD 2COME ! G5US OR DI6]5TIA ( ,A-! PR$ICATE N[ 2COME SUBJECT4 ,B X HAS BE5 %[N T 9 ^! SUB/ANTIAL PR$IC,NS NEI ! ASC5D+ PR$ICATES NOR ! DESC5D+ SUBJECTS =M AN 9F9ITE S]IES2 E4G4 NEI ! S]IES1 MAN IS BIP$1 BIP$ IS ANIMAL1 &C41 NOR ! S]IES PR$ICAT+ ANIMAL ( MAN1 MAN ( ,CALLIAS1 ,CALLIAS (A FUR!R4 SUBJECT Z AN ELE;T ( XS ESS5TIAL NATURE1 IS 9F9ITE4 ,= ALL S* SUB/.E IS DEF9A#1 & AN 9F9ITE S]IES _C 2 TRAV]S$ 9 ?"\3 3SEQU5TLY NEI ! ASC5T NOR ! DESC5T IS 9F9ITE1 S9CE A SUB/.E ^: PR$ICATES 7 9F9ITE WD N 2 DEF9A#4 ,H;E !Y W N 2 PR$ICAT$ EA* Z ! G5US (! O!R2 = ? WD EQUATE A G5US ) "O ( XS [N SPECIES4 ,NOR 7! O!R ALT]NATIVE7 C A QUALE 2 RECIPROC,Y PR$ICAT$ (A QUALE1 NOR ANY T]M 2L;G+ 6AN ADJECTIVAL CATEGORY ( ANO!R S* T]M1 EXCEPT 0A3ID5TAL PR$IC,N2 = ALL S* PR$ICATES >E CO9CID5TS & >E PR$ICAT$ ( SUB/.ES4 ,ON ! O!R H&-IN PRO( (! IMPOSSIBIL;Y ( AN 9F9ITE ASC5D+ S]IES-E PR$IC,N 4PLAYS ! SUBJECT Z "SH[ QUALIFI$ OR QUANTIFI$ OR Z "*IZ$ "U "O ( ! O!R ADJECTIVAL CATEGORIES1 OR ELSE IS AN ELE;T 9 XS SUB/ANTIAL NATURE3 ^! LATT] >E LIMIT$ 9 NUMB]1 &! NUMB] (! WIDE/ K9DS "U : PR$IC,NS FALL IS AL LIMIT$1 = E PR$IC,N M/ EXHIBIT XS SUBJECT Z "SH[ QUALIFI$1 QUANTIFI$1 ESS5TI,Y RELAT$1 ACT+ OR SU6]+1 OR 9 "S PLACE OR AT "S "T4 ,I ASSUME F/ T PR$IC,N IMPLIES A S+LE SUBJECT &A S+LE ATTRIBUTE1 & SECONDLY T PR$ICATES : >E N SUB/ANTIAL >E N PR$ICAT$ ( "O ANO!R4 ,WE ASSUME ? 2C S* PR$ICATES >E ALL CO9CID5TS1 & ?\< "S >E ESS5TIAL CO9CID5TS1 O!RS (A DI6]5T TYPE1 YET WE MA9TA9 T ALL ( !M ALIKE >E PR$ICAT$ ( "S SUB/RATUM & T A CO9CID5T IS N"E A SUB/RATUM-S9CE WE D N CLASS Z A CO9CID5T ANY?+ : DOES N [E XS DESIGN,N 6XS 2+ "S?+ O!R ?AN XF1 B ALW HOLD T ANY CO9CID5T IS PR$ICAT$ ( "S SUB/RATUM O!R ?AN XF1 & T ANO!R GR\P ( CO9CID5TS MAY H A DI6]5T SUB/RATUM4 ,SUBJECT 6^! ASSUMP;NS !N1 NEI ! ASC5D+ NOR ! DESC5D+ S]IES ( PR$IC,N 9 : A S+LE ATTRIBUTE IS PR$ICAT$ (A S+LE SUBJECT IS 9F9ITE4 ,=! SUBJECTS ( : CO9CID5TS >E PR$ICAT$ >E Z _M Z ! 3/ITUTIVE ELE;TS ( EA* 9DIVIDUAL SUB/.E1 & ^! WE H SE5 >E N 9F9ITE 9 NUMB]1 :ILE 9 ! ASC5D+ S]IES >E 3TA9$ ^? 3/ITUTIVE ELE;TS ) _! CO9CID5TS-BO? ( : >E F9ITE4 ,WE 3CLUDE T "! IS A GIV5 SUBJECT 7,D7 ( : "S ATTRIBUTE 7,C7 IS PRIM>ILY PR$ICA#2 T "! M/ 2 AN ATTRIBUTE 7,B7 PRIM>ILY PR$ICA# (! F/ ATTRIBUTE1 & T ! S]IES M/ 5D )A T]M 7,A7 N PR$ICA# ( ANY T]M PRIOR 6! LA/ SUBJECT ( : X 0 PR$ICAT$ 7,B71 &( : NO T]M PRIOR 6X IS PR$ICA#4 ,! >GU;T WE H GIV5 IS "O (! S-CALL$ PRO(S2 AN ALT]NATIVE PRO( FOLL[S4 ,PR$ICATES S RELAT$ 6_! SUBJECTS T "! >E O!R PR$ICATES PRIOR 6!M PR$ICA# ( ^? SUBJECTS >E DEMON/RA#2 B ( DEMON/RA# PROPOSI;NS "O _C H "S?+ BETT] ?AN K1 NOR C "O "K !M )\T DEMON/R,N4 ,SECONDLY1 IF A 3SEQU5T IS ONLY "KN "? AN ANTEC$5T 7VIZ4 PREMISSES PRIOR 6X7 & WE NEI "K ? ANTEC$5T NOR H "S?+ BETT] ?AN K ( X1 !N WE % N H SCI5TIFIC K (! 3SEQU5T4 ,"!=E1 IF X IS POSSI# "? DEMON/R,N 6"K ANY?+ )\T QUALIFIC,N & N M]ELY Z DEP5D5T ON ! A3EPT.E ( C]TA9 PREMISSES-I4E4 HYPO!TIC,Y-! S]IES ( 9T]M$IATE PR$IC,NS M/ T]M9ATE4 ,IF X DOES N T]M9ATE1 & 2Y ANY PR$ICATE TAK5 Z HI<] ?AN ANO!R "! REMA9S ANO!R / HI<]1 !N E PR$ICATE IS DEMON/RA#4 ,3SEQU5TLY1 S9CE ^! DEMON/RA# PR$ICATES >E 9F9ITE 9 NUMB] & "!=E _C 2 TRAV]S$1 WE % N "K !M 0DEMON/R,N4 ,IF1 "!=E1 WE H N "S?+ BETT] ?AN K ( !M1 WE _C "? DEMON/R,N H UNQUALIFI$ B ONLY HYPO!TICAL SCI;E ( ANY?+4 ,Z DIALECTICAL PRO(S ( \R 3T5;N ^! MAY C>RY 3VIC;N1 B AN ANALYTIC PROCESS W %[ M BRIEFLY T NEI ! ASC5T NOR ! DESC5T ( PR$IC,N C 2 9F9ITE 9 ! DEMON/RATIVE SCI;ES : >E ! OBJECT ( \R 9VE/IG,N4 ,DEMON/R,N PROVES ! 9H];E ( ESS5TIAL ATTRIBUTES 9 ?+S4 ,N[ ATTRIBUTES MAY 2 ESS5TIAL = TWO R1SONS3 EI 2C !Y >E ELE;TS 9 ! ESS5TIAL NATURE ( _! SUBJECTS1 OR 2C _! SUBJECTS >E ELE;TS 9 _! ESS5TIAL NATURE4 ,AN EXAMPLE (! LATT] IS ODD Z AN ATTRIBUTE ( NUMB]-?\< X IS NUMB]'S ATTRIBUTE1 YET NUMB] XF IS AN ELE;T 9 ! DEF9I;N ( ODD2 (! =M]1 MULTIPLIC;Y OR ! 9DIVISI#1 : >E ELE;TS 9 ! DEF9I;N ( NUMB]4 ,9 NEI K9D ( ATTRIBU;N C ! T]MS 2 9F9ITE4 ,!Y >E N 9F9ITE ": EA* IS RELAT$ 6! T]M 2L X Z ODD IS 6NUMB]1 = ? WD M1N ! 9H];E 9 ODD ( ANO!R ATTRIBUTE ( ODD 9 ^: NATURE ODD 0 AN ESS5TIAL ELE;T3 B !N NUMB] W 2 AN ULTIMATE SUBJECT (! :OLE 9F9ITE *A9 ( ATTRIBUTES1 & 2 AN ELE;T 9 ! DEF9I;N ( EA* ( !M4 ,H;E1 S9CE AN 9F9;Y ( ATTRIBUTES S* Z 3TA9 _! SUBJECT 9 _! DEF9I;N _C 9"H 9 A S+LE ?+1 ! ASC5D+ S]IES IS EQU,Y F9ITE4 ,NOTE1 MOREOV]1 T ALL S* ATTRIBUTES M/ S 9"H 9 ! ULTIMATE SUBJECT-E4G4 XS ATTRIBUTES 9 NUMB] & NUMB] 9 !M-Z 6BE -M5SURATE )! SUBJECT & N ( WID] EXT5T4 ,ATTRIBUTES : >E ESS5TIAL ELE;TS 9 ! NATURE ( _! SUBJECTS >E EQU,Y F9ITE3 O!RWISE DEF9I;N WD 2 IMPOSSI#4 ,H;E1 IF ALL ! ATTRIBUTES PR$ICAT$ >E ESS5TIAL & ^! _C 2 9F9ITE1 ! ASC5D+ S]IES W T]M9ATE1 & 3SEQU5TLY ! DESC5D+ S]IES TOO4 ,IF ? IS S1 X FOLL[S T ! 9T]M$IATES 2T ANY TWO T]MS >E AL ALW LIMIT$ 9 NUMB]4 ,AN IMMLY OBVI\S 3SEQU;E ( ? IS T DEMON/R,NS NECESS>ILY 9VOLVE BASIC TRU?S1 & T ! 3T5;N ( "S-REF]R$ 6AT ! \TSET-T ALL TRU?S >E DEMON/RA# IS MISTAK54 ,= IF "! >E BASIC TRU?S1 7A7 N ALL TRU?S >E DEMON/RA#1 & 7B7 AN 9F9ITE REGRESS IS IMPOSSI#2 S9CE IF EI 7A7 OR 7B7 7 N A FACT1 X WD M1N T NO 9T]VAL 0 IMM & 9DIVISI#1 B T ALL 9T]VALS 7 DIVISI#4 ,? IS TRUE 2C A 3CLU.N IS DEMON/RAT$ 0! 9T]POSI;N1 N ! APPOSI;N1 ( A FRE% T]M4 ,IF S* 9T]POSI;N CD 3T9UE 69F9;Y "! MIY ( ^! 3CLU.NS T IF ! SAME ATTRIBUTE ,A 9"HS 9 TWO T]MS ;,C & ;,D PR$ICA# EI N AT ALL1 OR N ( ALL 9/.ES1 ( "O ANO!R1 X DOES N ALW 2L;G 6!M 9 VIRTUE (A -MON MI4LE T]M4 ,ISOSCELES & SCAL5E POSSESS ! ATTRIBUTE ( HAV+ _! ANGLES EQUAL 6TWO "R ANGLES 9 VIRTUE (A -MON MI4LE2 = !Y POSSESS X 9 S F> Z !Y >E BO? A C]TA9 K9D ( FIGURE1 & N 9 S F> Z !Y DI6] F "O ANO!R4 ,B ? IS N ALW ! CASE3 =1 7 X S1 IF WE TAKE ;,B Z ! -MON MI4LE 9 VIRTUE ( : ,A 9"HS 9 ;,C & ;,D1 CLE>LY ;,B WD 9"H 9 ;,C & ;,D "? A SECOND -MON MI4LE1 & ? 9 TURN WD 9"H 9 ;,C & ;,D "? A ?IRD1 S T 2T TWO T]MS AN 9F9;Y ( 9T]M$IATES WD FALL-AN IMPOSSIBIL;Y4 ,?US X NE$ N ALW 2 9 VIRTUE (A -MON MI4LE T]M T A S+LE ATTRIBUTE 9"HS 9 S"EAL SUBJECTS1 S9CE "! M/ 2 IMM 9T]VALS4 ,YET IF ! ATTRIBUTE 6BE PROV$ -MON 6TWO SUBJECTS IS 6BE "O ( _! ESS5TIAL ATTRIBUTES1 ! MI4LE T]MS 9VOLV$ M/ 2 )9 "O SUBJECT G5US & 2 DERIV$ F ! SAME GR\P ( IMM PREMISSES2 = WE H SE5 T PROCESSES ( PRO( _C PASS F "O G5US 6ANO!R4 ,X IS AL CLE> T :5 ,A 9"HS 9 ;,B1 ? C 2 DEMON/RAT$ IF "! IS A MI4LE T]M4 ,FUR!R1 ! ,8ELE;TS0' ( S* A 3CLU.N >E ! PREMISSES 3TA9+ ! MI4LE 9 "Q1 & !Y >E ID5TICAL 9 NUMB] )! MI4LE T]MS1 SEE+ T ! IMM PROPOSI;NS-OR AT L1/ S* IMM PROPOSI;NS Z >E UNIV]SAL->E ! ,8ELE;TS0'4 ,IF1 ON ! O!R H&1 "! IS NO MI4LE T]M1 DEMON/R,N C1SES 6BE POSSI#3 WE >E ON ! WAY 6! BASIC TRU?S4 ,SIMIL>LY IF ,A DOES N 9"H 9 ;,B1 ? C 2 DEMON/RAT$ IF "! IS A MI4LE T]M OR A T]M PRIOR TO ;,B 9 : ,A DOES N 9"H3 O!RWISE "! IS NO DEMON/R,N &A BASIC TRU? IS R1*$4 ,"! >E1 MOREOV]1 Z _M ,8ELE;TS0' (! DEMON/RAT$ 3CLU.N Z "! >E MI4LE T]MS1 S9CE X IS PROPOSI;NS 3TA9+ ^! MI4LE T]MS T >E ! BASIC PREMISSES ON : ! DEMON/R,N RE/S2 & Z "! >E "S 9DEMON/RA# BASIC TRU?S ASS]T+ T ,8? IS T0' OR T ,8? 9"HS 9 T0'1 S "! >E O!RS D5Y+ T ,8? IS T0' OR T ,8? 9"HS 9 T'-IN FACT "S BASIC TRU?S W A6IRM & "S W D5Y 2+4 ,:5 WE >E 6PROVE A 3CLU.N1 WE M/ TAKE A PRIM>Y ESS5TIAL PR$ICATE-SUPPOSE X ;,C-(! SUBJECT ;,B1 & !N SUPPOSE ,A SIMIL>LY PR$ICA# ( ,C4 ,IF WE PROCE$ 9 ? MANN]1 NO PROPOSI;N OR ATTRIBUTE : FALLS 2Y ,A IS ADMITT$ 9 ! PRO(3 ! 9T]VAL IS 3/ANTLY 3D5S$ UNTIL SUBJECT & PR$ICATE 2COME 9DIVISI#1 I4E4 "O4 ,WE H \R UNIT :5 ! PREMISS 2COMES IMM1 S9CE ! IMM PREMISS AL"O IS A S+LE PREMISS 9 ! UNQUALIFI$ S5SE ( ,8S+LE0'4 ,& Z 9 O!R SPH]ES ! BASIC ELE;T IS SIMPLE B N ID5TICAL 9 ALL-IN A SY/EM ( WEIT]-T"O1 & S ON--S 9 SYLLOGISM ! UNIT IS AN IMM PREMISS1 & 9 ! K T DEMON/R,N GIVES X IS AN 9TUI;N4 ,9 SYLLOGISMS1 !N1 : PROVE ! 9H];E ( AN ATTRIBUTE1 NO?+ FALLS \TSIDE ! MAJOR T]M4 ,9 ! CASE ( NEGATIVE SYLLOGISMS ON ! O!R H&1 7#A7 9 ! F/ FIGURE NO?+ FALLS \TSIDE ! MAJOR T]M ^: 9H];E IS 9 "Q2 E4G4 6PROVE "? A MI4LE ;,C T ,A DOES N 9"H 9 ;,B ! PREMISSES REQUIR$ >E1 ALL ;,B IS ;,C1 NO ;,C IS ,A4 ,!N IF X HAS 6BE PROV$ T NO ;,C IS ;,A1 A MI4LE M/ 2 F.D 2T & ;,C2 & ? PROC$URE W N"E V>Y4 7#B7 ,IF WE H 6%[ T ;,E IS N ;,D 0M1NS (! PREMISSES1 ALL ;,D IS ;,C2 NO ;,E1 OR N ALL ;,E1 IS ;,C2 !N ! MI4LE W N"E FALL 2Y ;,E1 & ;,E IS ! SUBJECT ( : ;,D IS 6BE D5I$ 9 ! 3CLU.N4 7#C7 ,9 ! ?IRD FIGURE ! MI4LE W N"E FALL 2Y ! LIMITS (! SUBJECT &! ATTRIBUTE D5I$ ( X4 #BD ,S9CE DEMON/R,NS MAY 2 EI -M5SURATELY UNIV]SAL OR "PICUL>1 & EI A6IRMATIVE OR NEGATIVE2 ! "Q >ISES1 : =M IS ! BETT]8 ,&! SAME "Q MAY 2 PUT 9 REG>D 6S-CALL$ ,8DIRECT0' DEMON/R,N & REDUCTIO AD IMPOSSIBILE4 ,LET U F/ EXAM9E ! -M5SURATELY UNIV]SAL &! "PICUL> =MS1 & :5 WE H CLE>$ UP ? PRO#M PROCE$ 64CUSS ,8DIRECT0' DEMON/R,N & REDUCTIO AD IMPOSSIBILE4 ,! FOLL[+ 3SID],NS MI DEMON/R,N4 7#A7 ,! SUP]IOR DEMON/R,N IS ! DEMON/R,N : GIVES U GRT] K 7= ? IS ! ID1L ( DEMON/R,N71 & WE H GRT] K (A "PICUL> 9DIVIDUAL :5 WE "K X 9 XF ?AN :5 WE "K X "? "S?+ ELSE2 E4G4 WE "K ,CORISCUS ! MUSICIAN BETT] :5 WE "K T ,CORISCUS IS MUSICAL ?AN :5 WE "K ONLY T MAN IS MUSICAL1 &A L >GU;T HOLDS 9 ALL O!R CASES4 ,B -M5SURATELY UNIV]SAL DEMON/R,N1 9/1D ( PROV+ T ! SUBJECT XF ACTU,Y IS ;X1 PROVES ONLY T "S?+ ELSE IS ;X- E4G4 9 ATTEMPT+ 6PROVE T ISOSCELES IS ;X1 X PROVES N T ISOSCELES B ONLY T TRIANGLE IS ;X- ":AS "PICUL> DEMON/R,N PROVES T ! SUBJECT XF IS X4 ,! DEMON/R,N1 !N1 T A SUBJECT1 Z S*1 POSSESSES AN ATTRIBUTE IS SUP]IOR4 ,IF ? IS S1 & IF ! "PICUL> R ?AN ! -M5SURATELY UNIV]SAL =MS DEMON/RATES1 "PICUL> DEMON/R,N IS SUP]IOR4 7#B7 ,! UNIV]SAL HAS N A SEP>ATE 2+ OV] AG/ GR\PS ( S+UL>S4 ,DEMON/R,N N"E!.S CR1TES ! OP9ION T XS FUNC;N IS 3DI;N$ 0"S?+ L ?-"S SEP>ATE 5T;Y 2L;G+ 6! R1L _W2 T1 = 9/.E1 ( TRIANGLE OR ( FIGURE OR NUMB]1 OV] AG/ "PICUL> TRIANGLES1 FIGURES1 & NUMB]S4 ,B DEMON/R,N : T\*ES ! R1L & W N MISL1D IS SUP]IOR 6T : MOVES AM;G UNR1LITIES & IS DELUSORY4 ,N[ -M5SURATELY UNIV]SAL DEMON/R,N IS (! LATT] K9D3 IF WE 5GAGE 9 X WE F9D \RVS R1SON+ AF A FA%ION WELL ILLU/RAT$ 0! >GU;T T ! PROPOR;NATE IS :AT ANSW]S 6! DEF9I;N ( "S 5T;Y : IS NEI L9E1 NUMB]1 SOLID1 NOR PLANE1 B A PROPOR;NATE A"P F ALL ^!4 ,S9CE1 !N1 S* A PRO( IS "*I/IC,Y -M5SURATE & UNIV]SAL1 & LESS T\*ES R1L;Y ?AN DOES "PICUL> DEMON/R,N1 & CR1TES A FALSE OP9ION1 X W FOLL[ T -M5SURATE & UNIV]SAL IS 9F]IOR 6"PICUL> DEMON/R,N4 ,WE MAY RETORT ?US4 7#A7 ,! F/ >GU;T APPLIES NO M 6-M5SURATE & UNIV]SAL ?AN 6"PICUL> DEMON/R,N4 ,IF EQUAL;Y 6TWO "R ANGLES IS ATTRIBUTA# 6XS SUBJECT N QUA ISOSCELES B QUA TRIANGLE1 HE :O "KS T ISOSCELES POSSESSES T ATTRIBUTE "KS ! SUBJECT Z QUA XF POSSESS+ ! ATTRIBUTE1 6A LESS DEGREE ?AN HE :O "KS T TRIANGLE HAS T ATTRIBUTE4 ,6SUM UP ! :OLE MATT]3 IF A SUBJECT IS PROV$ 6POSSESS QUA TRIANGLE AN ATTRIBUTE : X DOES N 9 FACT POSSESS QUA TRIANGLE1 T IS N DEMON/R,N3 B IF X DOES POSSESS X QUA TRIANGLE ! RULE APPLIES T ! GRT] K IS 8 :O "KS ! SUBJECT Z POSSESS+ XS ATTRIBUTE QUA T 9 VIRTUE ( : X ACTU,Y DOES POSSESS X4 ,S9CE1 !N1 TRIANGLE IS ! WID] T]M1 & "! IS "O ID5TICAL DEF9I;N ( TRIANGLE-I4E4 ! T]M IS N EQUIVOCAL-& S9CE EQUAL;Y 6TWO "R ANGLES 2L;GS 6ALL TRIANGLES1 X IS ISOSCELES QUA TRIANGLE & N TRIANGLE QUA ISOSCELES : HAS XS ANGLES S RELAT$4 ,X FOLL[S T HE :O "KS A 3NEXION UNIV]S,Y HAS GRT] K ( X Z X 9 FACT IS ?AN HE :O "KS ! "PICUL>2 &! 9F];E IS T -M5SURATE & UNIV]SAL IS SUP]IOR 6"PICUL> DEMON/R,N4 7#B7 ,IF "! IS A S+LE ID5TICAL DEF9I;N I4E4 IF ! -M5SURATE UNIV]SAL IS UNEQUIVOCAL-!N ! UNIV]SAL W POSSESS 2+ N LESS B M ?AN "S (! "PICUL>S1 9ASM* Z X IS UNIV]SALS : -PRISE ! IMP]I%A#1 "PICUL>S T T5D 6P]I%4 7#C7 ,2C ! UNIV]SAL HAS A S+LE M1N+1 WE >E N "!=E -PELL$ 6SUPPOSE T 9 ^! EXAMPLES X HAS 2+ Z A SUB/.E A"P F XS "PICUL>S-ANY M ?AN WE NE$ MAKE A SIMIL> SUPPOSI;N 9 ! O!R CASES ( UNEQUIVOCAL UNIV]SAL PR$IC,N1 VIZ4 ": ! PR$ICATE SIGNIFIES N SUB/.E B QUAL;Y1 ESS5TIAL RELAT$;S1 OR AC;N4 ,IF S* A SUPPOSI;N IS 5T]TA9$1 ! BLAME RE/S N )! DEMON/R,N B ) ! HE>]4 7#D7 ,DEMON/R,N IS SYLLOGISM T PROVES ! CAUSE1 I4E4 ! R1SON$ FACT1 & X IS R ! -M5SURATE UNIV]SAL ?AN ! "PICUL> : IS CAUSATIVE 7Z MAY 2 %[N ?US3 T : POSSESSES AN ATTRIBUTE "? XS [N ESS5TIAL NATURE IS XF ! CAUSE (! 9H];E1 &! -M5SURATE UNIV]SAL IS PRIM>Y2 H;E ! -M5SURATE UNIV]SAL IS ! CAUSE74 ,3SEQU5TLY -M5SURATELY UNIV]SAL DEMON/R,N IS SUP]IOR Z M ESPECI,Y PROV+ ! CAUSE1 T IS ! R1SON$ FACT4 7#E7 ,\R SE>* =! R1SON C1SES1 & WE ?9K T WE "K1 :5 ! -+ 6BE OR EXI/;E (! FACT 2F U IS N DUE 6! -+ 6BE OR EXI/;E ( "S O!R FACT1 =! LA/ /EP (A SE>* ?US 3DUCT$ IS EO IPSO ! 5D & LIMIT (! PRO#M4 ,?US3 ,8,:Y DID HE -E80' ,8,6GET ! M"OY-":) 6PAY A DEBT-T HE MID ! LA/ /EP ( X Z ! 5D (! -+-OR 2+ OR -+ 6BE-& WE REG>D \RVS Z !N ONLY HAV+ FULL K (! R1SON :Y HE CAME4 ,IF1 !N1 ALL CAUSES & R1SONS >E ALIKE 9 ? RESPECT1 & IF ? IS ! M1NS 6FULL K 9 ! CASE ( F9AL CAUSES S* Z WE H EXEMPLIFI$1 X FOLL[S T 9 ! CASE (! O!R CAUSES AL FULL K IS ATTA9$ :5 AN ATTRIBUTE NO L;G] 9"HS 2C ( "S?+ ELSE4 ,?US1 :5 WE LE>N T EXT]IOR ANGLES >E EQUAL 6F\R "R ANGLES 2C !Y >E ! EXT]IOR ANGLES ( AN ISOSCELES1 "! / REMA9S ! "Q ,8,:Y HAS ISOSCELES ? ATTRIBUTE80' & XS ANSW] ,8,2C X IS A TRIANGLE1 &A TRIANGLE HAS X 2C A TRIANGLE IS A RECTIL9E> FIGURE40' ,IF RECTIL9E> FIGURE POSSESSES ! PROP]TY = NO FUR!R R1SON1 AT ? PO9T WE H FULL K-B AT ? PO9T \R K HAS 2COME -M5SURATELY UNIV]SAL1 & S WE 3CLUDE T -M5SURATELY UNIV]SAL DEMON/R,N IS SUP]IOR4 7#F7 ,! M DEMON/R,N 2COMES "PICUL> ! M X S9KS 96AN 9DET]M9ATE MANIFOLD1 :ILE UNIV]SAL DEMON/R,N T5DS 6! SIMPLE & DET]M9ATE4 ,B OBJECTS S F> Z !Y >E AN 9DET]M9ATE MANIFOLD >E UN9TELLIGI#1 S F> Z !Y >E DET]M9ATE1 9TELLIGI#3 !Y >E "!=E 9TELLIGI# R 9 S F> Z !Y >E UNIV]SAL ?AN 9 S F> Z !Y >E "PICUL>4 ,F ? X FOLL[S T UNIV]SALS >E M DEMON/RA#3 B S9CE RELATIVE & CORRELATIVE 9CR1SE 3COMITANTLY1 (! M DEMON/RA# "! W 2 FULL] DEMON/R,N4 ,H;E ! -M5SURATE & UNIV]SAL =M1 2+ M TRULY DEMON/R,N1 IS ! SUP]IOR4 7#G7 ,DEMON/R,N : T1*ES TWO ?+S IS PREF]A# 6DEMON/R,N : T1*ES ONLY "O4 ,HE :O POSSESSES -M5SURATELY UNIV]SAL DEMON/R,N "KS ! "PICUL> Z WELL1 B HE :O POSSESSES "PICUL> DEMON/R,N DOES N "K ! UNIV]SAL4 ,S T ? IS AN A4I;NAL R1SON = PREF]R+ -M5SURATELY UNIV]SAL DEMON/R,N4 ,& "! IS YET ? FUR!R >GU;T3 7#H7 ,PRO( 2COMES M & M PRO( (! -M5SURATE UNIV]SAL Z XS MI4LE T]M APPROA*ES NE>] 6! BASIC TRU?1 & NO?+ IS S NE> Z ! IMM PREMISS : IS XF ! BASIC TRU?4 ,IF1 !N1 PRO( F ! BASIC TRU? IS M A3URATE ?AN PRO( N S DERIV$1 DEMON/R,N : DEP5DS M CLOSELY ON X IS M A3URATE ?AN DEMON/R,N : IS LESS CLOSELY DEP5D5T4 ,B -M5SURATELY UNIV]SAL DEMON/R,N IS "*IZ$ 0? CLOS] DEP5D;E1 & IS "!=E SUP]IOR4 ,?US1 IF ,A _H 6BE PROV$ 69"H 9 ;,D1 &! MI4LES 7 ;,B & ;,C1 ;,B 2+ ! HI<] T]M WD R5D] ! DEMON/R,N : X M$IAT$ ! M UNIV]SAL4 ,"S ( ^! >GU;TS1 H["E1 >E DIALECTICAL4 ,! CLE>E/ 9DIC,N (! PREC$;E ( -M5SURATELY UNIV]SAL DEMON/R,N IS Z FOLL[S3 IF ( TWO PROPOSI;NS1 A PRIOR &A PO/]IOR1 WE H A GRASP (! PRIOR1 WE H A K9D ( K-A POT5TIAL GRASP-(! PO/]IOR Z WELL4 ,= EXAMPLE1 IF "O "KS T ! ANGLES ( ALL TRIANGLES >E EQUAL 6TWO "R ANGLES1 "O "KS 9 A S5SE-POT5TI,Y-T ! ISOSCELES' ANGLES AL >E EQUAL 6TWO "R ANGLES1 EV5 IF "O DOES N "K T ! ISOSCELES IS A TRIANGLE2 B 6GRASP ? PO/]IOR PROPOSI;N IS 0NO M1NS 6"K ! -M5SURATE UNIV]SAL EI POT5TI,Y OR ACTU,Y4 ,MOREOV]1 -M5SURATELY UNIV]SAL DEMON/R,N IS "? & "? 9TELLIGI#2 "PICUL> DEMON/R,N ISSUES 9 S5SE-P]CEP;N4 #BE ,! PREC$+ >GU;TS 3/ITUTE \R DEF;E (! SUP]IOR;Y ( -M5SURATELY UNIV]SAL 6"PICUL> DEMON/R,N4 ,T A6IRMATIVE DEMON/R,N EXCELS NEGATIVE MAY 2 %[N Z FOLL[S4 7#A7 ,WE MAY ASSUME ! SUP]IOR;Y CET]IS P>IBUS (! DEMON/R,N : DERIVES F FEW] PO/ULATES OR HYPO!SES-IN %ORT F FEW] PREMISSES2 =1 GIV5 T ALL ^! >E EQU,Y WELL "KN1 ": !Y >E FEW] K W 2 M SPE$ILY ACQUIR$1 & T IS A DESID]ATUM4 ,! >GU;T IMPLI$ 9 \R 3T5;N T DEMON/R,N F FEW] ASSUMP;NS IS SUP]IOR MAY 2 SET \ 9 UNIV]SAL =M Z FOLL[S4 ,ASSUM+ T 9 BO? CASES ALIKE ! MI4LE T]MS >E "KN1 & T MI4LES : >E PRIOR >E BETT] "KN ?AN S* Z >E PO/]IOR1 WE MAY SUPPOSE TWO DEMON/R,NS (! 9H];E ( ,A 9 ;,E1 ! "O PROV+ X "? ! MI4LES ;,B1 ;,C & ;,D1 ! O!R "? ;,F & ,G4 ,!N ;,A-;,D IS "KN 6! SAME DEGREE Z ;,A-;,E 7IN ! SECOND PRO(71 B ;,A-;,D IS BETT] "KN ?AN & PRIOR TO ;,A-;,E 7IN ! F/ PRO(72 S9CE ;,A-;,E IS PROV$ "? ;,A-;,D1 &! GR.D IS M C]TA9 ?AN ! 3CLU.N4 ,H;E DEMON/R,N 0FEW] PREMISSES IS CET]IS P>IBUS SUP]IOR4 ,N[ BO? A6IRMATIVE & NEGATIVE DEMON/R,N OP]ATE "? ?REE T]MS & TWO PREMISSES1 B ":AS ! =M] ASSUMES ONLY T "S?+ IS1 ! LATT] ASSUMES BO? T "S?+ IS & T "S?+ ELSE IS N1 & ?US OP]AT+ "? M K9DS ( PREMISS IS 9F]IOR4 7#B7 ,X HAS BE5 PROV$ T NO 3CLU.N FOLL[S IF BO? PREMISSES >E NEGATIVE1 B T "O M/ 2 NEGATIVE1 ! O!R A6IRMATIVE4 ,S WE >E -PELL$ 6LAY D[N ! FOLL[+ A4I;NAL RULE3 Z ! DEMON/R,N EXP&S1 ! A6IRMATIVE PREMISSES M/ 9CR1SE 9 NUMB]1 B "! _C 2 M ?AN "O NEGATIVE PREMISS 9 EA* -PLETE PRO(4 ,?US1 SUPPOSE NO ;,B IS ;,A1 & ALL ;,C IS ,B4 ,!N IF BO? ! PREMISSES >E 6BE AG EXP&$1 A MI4LE M/ 2 9T]POS$4 ,LET U 9T]POSE ;,D 2T ;,A & ;,B1 & ;,E 2T ;,B & ,C4 ,!N CLE>LY ;,E IS A6IRMATIVELY RELAT$ TO ;,B & ;,C1 :ILE ;,D IS A6IRMATIVELY RELAT$ TO ;,B B NEGATIVELY TO ;,A2 = ALL ;,B IS ;,D1 B "! M/ 2 NO ;,D : IS ,A4 ,?US "! PROVES 6BE A S+LE NEGATIVE PREMISS1 ;,A-;,D4 ,9 ! FUR!R PROSYLLOGISMS TOO X IS ! SAME1 2C 9 ! T]MS ( AN A6IRMATIVE SYLLOGISM ! MI4LE IS ALW RELAT$ A6IRMATIVELY 6BO? EXTREMES2 9 A NEGATIVE SYLLOGISM X M/ 2 NEGATIVELY RELAT$ ONLY 6"O ( !M1 & S ? NEG,N -ES 6BE A S+LE NEGATIVE PREMISS1 ! O!R PREMISSES 2+ A6IRMATIVE4 ,IF1 !N1 T "? : A TRU? IS PROV$ IS A BETT] "KN & M C]TA9 TRU?1 & IF ! NEGATIVE PROPOSI;N IS PROV$ "? ! A6IRMATIVE & N VICE V]SA1 A6IRMATIVE DEMON/R,N1 2+ PRIOR & BETT] "KN & M C]TA91 W 2 SUP]IOR4 7#C7 ,! BASIC TRU? ( DEMON/RATIVE SYLLOGISM IS ! UNIV]SAL IMM PREMISS1 &! UNIV]SAL PREMISS ASS]TS 9 A6IRMATIVE DEMON/R,N & 9 NEGATIVE D5IES3 &! A6IRMATIVE PROPOSI;N IS PRIOR 6& BETT] "KN ?AN ! NEGATIVE 7S9CE A6IRM,N EXPLA9S D5IAL & IS PRIOR 6D5IAL1 J Z 2+ IS PRIOR 6N-2+74 ,X FOLL[S T ! BASIC PREMISS ( A6IRMATIVE DEMON/R,N IS SUP]IOR 6T ( NEGATIVE DEMON/R,N1 &! DEMON/R,N : USES SUP]IOR BASIC PREMISSES IS SUP]IOR4 7#D7 ,A6IRMATIVE DEMON/R,N IS M (! NATURE (A BASIC =M ( PRO(1 2C X IS A S9E QUA NON ( NEGATIVE DEMON/R,N4 #BF ,S9CE A6IRMATIVE DEMON/R,N IS SUP]IOR 6NEGATIVE1 X IS CLE>LY SUP]IOR AL 6REDUCTIO AD IMPOSSIBILE4 ,WE M/ F/ MAKE C]TA9 :AT IS ! DI6];E 2T NEGATIVE DEMON/R,N & REDUCTIO AD IMPOSSIBILE4 ,LET U SUPPOSE T NO ;,B IS ;,A1 & T ALL ;,C IS ;,B3 ! 3CLU.N NECESS>ILY FOLL[S T NO ;,C IS ,A4 ,IF ^! PREMISSES >E ASSUM$1 "!=E1 ! NEGATIVE DEMON/R,N T NO ;,C IS ,A IS DIRECT4 ,REDUCTIO AD IMPOSSIBILE1 ON ! O!R H&1 PROCE$S Z FOLL[S4 ,SUPPOS+ WE >E 6PROVE T DOES N 9"H 9 ;,B1 WE H 6ASSUME T X DOES 9"H1 & FUR!R T ;,B 9"HS 9 ;,C1 )! RESULT+ 9F];E T ,A 9"HS 9 ,C4 ,? WE H 6SUPPOSE A "KN & ADMITT$ IMPOSSIBIL;Y2 & WE !N 9F] T ,A _C 9"H 9 ,B4 ,?US IF ! 9H];E ( ;,B 9 ;,C IS N "Q$1 ;,A'S 9H];E 9 ;,B IS IMPOSSI#4 ,! ORD] (! T]MS IS ! SAME 9 BO? PRO(S3 !Y DI6] AC 6: (! NEGATIVE PROPOSI;NS IS ! BETT] "KN1 ! "O D5Y+ ;,A ( ;,B OR ! "O D5Y+ ;,A ( ,C4 ,:5 ! FALS;Y (! 3CLU.N IS ! BETT] "KN1 WE USE REDUCTIO AD IMPOSSI#2 :5 ! MAJOR PREMISS (! SYLLOGISM IS ! M OBVI\S1 WE USE DIRECT DEMON/R,N4 ,ALL ! SAME ! PROPOSI;N D5Y+ ;,A ( ;,B IS1 9 ! ORD] ( 2+1 PRIOR 6T D5Y+ ;,A ( ;,C2 = PREMISSES >E PRIOR 6! 3CLU.N : FOLL[S F !M1 & ,8NO ;,C IS ,A0' IS ! 3CLU.N1 ,8NO ;,B IS ,A0' "O ( XS PREMISSES4 ,=! DE/RUCTIVE RESULT ( REDUCTIO AD IMPOSSIBILE IS N A PROP] 3CLU.N1 NOR >E XS ANTEC$5TS PROP] PREMISSES4 ,ON ! 3TR>Y3 ! 3/ITU5TS ( SYLLOGISM >E PREMISSES RELAT$ 6"O ANO!R Z :OLE 6"P OR "P 6:OLE1 ":AS ! PREMISSES ;,A-;,C & ;,A-;,B >E N ?US RELAT$ 6"O ANO!R4 ,N[ ! SUP]IOR DEMON/R,N IS T : PROCE$S F BETT] "KN & PRIOR PREMISSES1 & :ILE BO? ^! =MS DEP5D = CR$;E ON ! N-2+ ( "S?+1 YET ! S\RCE (! "O IS PRIOR 6T (! O!R4 ,"!=E NEGATIVE DEMON/R,N W H AN UNQUALIFI$ SUP]IOR;Y 6REDUCTIO AD IMPOSSIBILE1 & A6IRMATIVE DEMON/R,N1 2+ SUP]IOR 6NEGATIVE1 W 3SEQU5TLY 2 SUP]IOR AL 6REDUCTIO AD IMPOSSIBILE4 #BG ,! SCI;E : IS K AT ONCE (! FACT &(! R1SON$ FACT1 N (! FACT 0XF )\T ! R1SON$ FACT1 IS ! M EXACT &! PRIOR SCI;E4 ,A SCI;E S* Z >I?METIC1 : IS N A SCI;E ( PROP]TIES QUA 9H]+ 9 A SUB/RATUM1 IS M EXACT ?AN & PRIOR 6A SCI;E L H>MONICS1 : IS A SCI;E ( PR1OP]TIES 9H]+ 9 A SUB/RATUM2 & SIMIL>LY A SCI;E L >I?METIC1 : IS 3/ITUT$ ( FEW] BASIC ELE;TS1 IS M EXACT ?AN & PRIOR 6GEOMETRY1 : REQUIRES A4I;NAL ELE;TS4 ,:AT ,I M1N BY ,8A4I;NAL ELE;TS0' IS ?3 A UNIT IS SUB/.E )\T POSI;N1 :ILE A PO9T IS SUB/.E ) POSI;N2 ! LATT] 3TA9S AN A4I;NAL ELE;T4 #BH ,A S+LE SCI;E IS "O ^: DOMA9 IS A S+LE G5US1 VIZ4 ALL ! SUBJECTS 3/ITUT$ \ (! PRIM>Y 5TITIES (! G5US-I4E4 ! "PS ( ? TOTAL SUBJECT-& _! ESS5TIAL PROP]TIES4 ,"O SCI;E DI6]S F ANO!R :5 _! BASIC TRU?S H NEI A -MON S\RCE NOR >E DERIV$ ^? (! "O SCI;E F ^? ! O!R4 ,? IS V]IFI$ :5 WE R1* ! 9DEMON/RA# PREMISSES (A SCI;E1 = !Y M/ 2 )9 "O G5US ) XS 3CLU.NS3 & ? AG IS V]IFI$ IF ! 3CLU.NS PROV$ 0M1NS ( !M FALL )9 "O G5US-I4E4 >E HOMOG5E\S4 #BI ,"O C H S"EAL DEMON/R,NS (! SAME 3NEXION N ONLY 0TAK+ F ! SAME S]IES ( PR$IC,N MI4LES : >E O!R ?AN ! IMMLY COH]+ T]M E4G4 0TAK+ ;,C1 ;,D1 & ;,F S"E,Y 6PROVE ;,A-;,B--B AL 0TAK+ A MI4LE F ANO!R S]IES4 ,?US LET ,A 2 *ANGE1 ;,D ALT],N (A PROP]TY1 ;,B FEEL+ PL1SURE1 & ;,G RELAX,N4 ,WE C !N )\T FALSEHOOD PR$ICATE ;,D ( ;,B & ;,A ( ;,D1 = HE :O IS PL1S$ SU6]S ALT],N (A PROP]TY1 & T : ALT]S A PROP]TY *ANGES4 ,AG1 WE C PR$ICATE ;,A ( ;,G )\T FALSEHOOD1 & ;,G ( ;,B2 = 6FEEL PL1SURE IS 6RELAX1 & 6RELAX IS 6*ANGE4 ,S ! 3CLU.N C 2 DRAWN "? MI4LES : >E DI6]5T1 I4E4 N 9 ! SAME S]IES-YET N S T NEI ( ^! MI4LES IS PR$ICA# (! O!R1 = !Y M/ BO? 2 ATTRIBUTA# 6"S "O SUBJECT4 ,A FUR!R PO9T WOR? 9VE/IGAT+ IS H[ _M WAYS ( PROV+ ! SAME 3CLU.N C 2 OBTA9$ 0V>Y+ ! FIGURE1 #CJ ,"! IS NO K 0DEMON/R,N ( *.E 3JUNC;NS2 = *.E 3JUNC;NS EXI/ NEI 0NECESS;Y NOR Z G5]AL 3NEXIONS B -PRISE :AT -ES 6BE Z "S?+ 4T9CT F ^!4 ,N[ DEMON/R,N IS 3C]N$ ONLY ) "O OR O!R ( ^! TWO2 = ALL R1SON+ PROCE$S F NEC OR G5]AL PREMISSES1 ! 3CLU.N 2+ NEC IF ! PREMISSES >E NEC & G5]AL IF ! PREMISSES >E G5]AL4 ,3SEQU5TLY1 IF *.E 3JUNC;NS >E NEI G5]AL NOR NEC1 !Y >E N DEMON/RA#4 #CA ,SCI5TIFIC K IS N POSSI# "? ! ACT ( P]CEP;N4 ,EV5 IF P]CEP;N Z A FACULTY IS ( ,8! S*0' & N M]ELY (A ,8? "S:AT0'1 YET "O M/ AT ANY RATE ACTU,Y P]CV A ,8? "S:AT0'1 & AT A DEF9ITE PRES5T PLACE & "T3 B T : IS -M5SURATELY UNIV]SAL & TRUE 9 ALL CASES "O _C P]CV1 S9CE X IS N ,8?0' & X IS N ,8N[0'2 IF X W]E1 X WD N 2 -M5SURATELY UNIV]SAL-! T]M WE APPLY 6:AT IS ALW & "EY":4 ,SEE+1 "!=E1 T DEMON/R,NS >E -M5SURATELY UNIV]SAL & UNIV]SALS IMP]CEPTI#1 WE CLE>LY _C OBTA9 SCI5TIFIC K 0! ACT ( P]CEP;N3 NAY1 X IS OBVI\S T EV5 IF X 7 POSSI# 6P]CV T A TRIANGLE HAS XS ANGLES EQUAL 6TWO "R ANGLES1 WE %D / 2 LOOK+ =A DEMON/R,N-WE %D N 7Z "S SAY7 POSSESS K ( X2 = P]CEP;N M/ 2 (A "PICUL>1 ":AS SCI5TIFIC K 9VOLVES ! RECOGNI;N (! -M5SURATE UNIV]SAL4 ,S IF WE 7 ON ! MOON1 & SAW ! E>? %UTT+ \ ! SUN'S LIS4 ,! -M5SURATE UNIV]SAL IS PRECI\S 2C X MAKES CLE> ! CAUSE2 S T 9 ! CASE ( FACTS L ^! : H A CAUSE O!R ?AN !MVS UNIV]SAL K IS M PRECI\S ?AN S5SE-P]CEP;NS & ?AN 9TUI;N4 7,Z REG>DS PRIM>Y TRU?S "! IS ( C\RSE A DI6]5T A3.T 6BE GIV547 ,H;E X IS CLE> T K ( ?+S DEMON/RA# _C 2 ACQUIR$ 0P]CEP;N1 UN.S ! T]M P]CEP;N IS APPLI$ 6! POSSES.N ( SCI5TIFIC K "? DEMON/R,N4 ,N"E!.S C]TA9 PO9TS D >ISE ) REG>D 63NEXIONS 6BE PROV$ : >E REF]R$ = _! EXPLAN,N 6A FAILURE 9 S5SE-P]CEP;N3 "! >E CASES :5 AN ACT ( VI.N WD T]M9ATE \R 9QUIRY1 N 2C 9 SEE+ WE %D 2 "K+1 B 2C WE %D H ELICIT$ ! UNIV]SAL F SEE+2 IF1 = EXAMPLE1 WE SAW ! PORES 9 ! GLASS &! LI 6U 2C WE %D AT ! SAME "T SEE X 9 EA* 9/.E & 9TUIT T X M/ 2 S 9 ALL 9/.ES4 #CB ,ALL SYLLOGISMS _C H ! SAME BASIC TRU?S4 ,? MAY 2 %[N F/ ( ALL 0! FOLL[+ DIALECTICAL 3SID],NS4 7#A7 ,"S SYLLOGISMS >E TRUE & "S FALSE3 = ?\< A TRUE 9F];E IS POSSI# F FALSE PREMISSES1 YET ? O3URS ONCE ONLY-,I M1N IF ;,A = 9/.E1 IS TRULY PR$ICA# ( ;,C1 B ;,B1 ! MI4LE1 IS FALSE1 BO? ;,A-;,B & ;,B-;,C 2+ FALSE2 N"E!.S1 IF MI4LES >E TAK5 6PROVE ^! PREMISSES1 !Y W 2 FALSE 2C E 3CLU.N : IS A FALSEHOOD HAS FALSE PREMISSES1 :ILE TRUE 3CLU.NS H TRUE PREMISSES1 & FALSE & TRUE DI6] 9 K9D4 ,!N AG1 7#B7 FALSEHOODS >E N ALL DERIV$ F A S+LE ID5TICAL SET ( PR9CIPLES3 "! >E FALSEHOODS : >E ! 3TR>IES ( "O ANO!R & _C COEXI/1 E4G4 ,8JU/ICE IS 9JU/ICE0'1 & ,8JU/ICE IS C[>DICE0'2 ,8MAN IS HORSE0'1 & ,8MAN IS OX0'2 ,8! EQUAL IS GRT]0'1 & ,8! EQUAL IS LESS40' ,F E/ABLI%$ PR9CIPLES WE MAY >GUE ! CASE Z FOLL[S1 3F9+-\RVS "!=E 6TRUE 3CLU.NS4 ,N EV5 ALL ^! >E 9F]R$ F ! SAME BASIC TRU?S2 _M ( !M 9 FACT H BASIC TRU?S : DI6] G5]IC,Y & >E N TRANSF]A#2 UNITS1 = 9/.E1 : >E )\T POSI;N1 _C TAKE ! PLACE ( PO9TS1 : H POSI;N4 ,! TRANSF]R$ T]MS CD ONLY FIT 9 Z MI4LE T]MS OR Z MAJOR OR M9OR T]MS1 OR ELSE H "S (! O!R T]MS 2T !M1 O!RS \TSIDE !M4 ,NOR C ANY (! -MON AXIOMS-S*1 ,I M1N1 Z ! LAW ( EXCLUD$ MI4LE-S]VE Z PREMISSES =! PRO( ( ALL 3CLU.NS4 ,=! K9DS ( 2+ >E DI6]5T1 & "S ATTRIBUTES ATTA* 6QUANTA & "S 6QUALIA ONLY2 & PRO( IS A*IEV$ 0M1NS (! -MON AXIOMS TAK5 9 3JUNC;N ) ^! S"EAL K9DS & _! ATTRIBUTES4 ,AG1 X IS N TRUE T ! BASIC TRU?S >E M* FEW] ?AN ! 3CLU.NS1 =! BASIC TRU?S >E ! PREMISSES1 &! PREMISSES >E =M$ 0! APPOSI;N (A FRE% EXTREME T]M OR ! 9T]POSI;N (A FRE% MI4LE4 ,MOREOV]1 ! NUMB] ( 3CLU.NS IS 9DEF9ITE1 ?\< ! NUMB] ( MI4LE T]MS IS F9ITE2 & LA/LY "S (! BASIC TRU?S >E NEC1 O!RS V>IA#4 ,LOOK+ AT X 9 ? WAY WE SEE T1 S9CE ! NUMB] ( 3CLU.NS IS 9DEF9ITE1 ! BASIC TRU?S _C 2 ID5TICAL OR LIMIT$ 9 NUMB]4 ,IF1 ON ! O!R H&1 ID5T;Y IS US$ 9 ANO!R S5SE1 & X IS SD1 E4G4 ,8^! & NO O!R >E ! FUNDA;TAL TRU?S ( GEOMETRY1 ^! ! FUNDA;TALS ( CALCUL,N1 ^! AG ( M$IC9E0'2 WD ! /ATE;T M1N ANY?+ EXCEPT T ! SCI;ES H BASIC TRU?S8 ,6CALL !M ID5TICAL 2C !Y >E SELF-ID5TICAL IS ABSURD1 S9CE "EY?+ C 2 ID5TIFI$ ) "EY?+ 9 T S5SE ( ID5T;Y4 ,NOR AG C ! 3T5;N T ALL 3CLU.NS H ! SAME BASIC TRU?S M1N T F ! MASS ( ALL POSSI# PREMISSES ANY 3CLU.N MAY 2 DRAWN4 ,T WD 2 EXCE$+LY NAIVE1 = X IS N ! CASE 9 ! CLE>LY EVID5T MA!MATICAL SCI;ES1 NOR IS X POSSI# 9 ANALYSIS1 S9CE X IS ! IMM PREMISSES : >E ! BASIC TRU?S1 &A FRE% 3CLU.N IS ONLY =M$ 0! A4I;N (A NEW IMM PREMISS3 B IF X 2 ADMITT$ T X IS ^! PRIM>Y IMM PREMISSES : >E BASIC TRU?S1 EA* SUBJECT-G5US W PROVIDE "O BASIC TRU?4 ,IF1 H["E1 X IS N >GU$ T F ! MASS ( ALL POSSI# PREMISSES ANY 3CLU.N MAY 2 PROV$1 NOR YET ADMITT$ T BASIC TRU?S DI6] S Z 6BE G5]IC,Y DI6]5T = EA* SCI;E1 X REMA9S 63SID] ! POSSIBIL;Y T1 :ILE ! BASIC TRU?S ( ALL K >E )9 "O G5US1 SPECIAL PREMISSES >E REQUIR$ 6PROVE SPECIAL 3CLU.NS4 ,B T ? _C 2 ! CASE HAS BE5 %[N 0\R PRO( T ! BASIC TRU?S ( ?+S G5]IC,Y DI6]5T !MVS DI6] G5]IC,Y4 ,= FUNDA;TAL TRU?S >E ( TWO K9DS1 ^? : >E PREMISSES ( DEMON/R,N &! SUBJECT-G5US2 & ?\< ! =M] >E -MON1 ! LATT]-NUMB]1 = 9/.E1 & MAGNITUDE->E PECULI>4 #CC ,SCI5TIFIC K & XS OBJECT DI6] F OP9ION &! OBJECT ( OP9ION 9 T SCI5TIFIC K IS -M5SURATELY UNIV]SAL & PROCE$S 0NEC 3NEXIONS1 & T : IS NEC _C 2 O!RWISE4 ,S ?\< "! >E ?+S : >E TRUE & R1L & YET C 2 O!RWISE1 SCI5TIFIC K CLE>LY DOES N 3C]N !M3 IF X DID1 ?+S : C 2 O!RWISE WD 2 9CAPA# ( 2+ O!RWISE4 ,NOR >E !Y ANY 3C]N ( R,NAL 9TUI;N-BY R,NAL 9TUI;N ,I M1N AN ORIG9ATIVE S\RCE ( SCI5TIFIC K-NOR ( 9DEMON/RA# K1 : IS ! GRASP+ (! IMM PREMISS4 ,S9CE !N R,NAL 9TUI;N1 SCI;E1 & OP9ION1 & :AT IS REV1L$ 0^! T]MS1 >E ! ONLY ?+S T C 2 ,8TRUE0'1 X FOLL[S T X IS OP9ION T IS 3C]N$ ) T : MAY 2 TRUE OR FALSE1 & C 2 O!RWISE3 OP9ION 9 FACT IS ! GRASP (A PREMISS : IS IMM B N NEC4 ,? VIEW AL FITS ! OBS]V$ FACTS1 = OP9ION IS UN/A#1 & S IS ! K9D ( 2+ WE H DESCRIB$ Z XS OBJECT4 ,2SS1 :5 A MAN ?9KS A TRU? 9CAPA# ( 2+ O!RWISE HE ALW ?9KS T HE "KS X1 N"E T HE OP9ES X4 ,HE ?9KS T HE OP9ES :5 HE ?9KS T A 3NEXION1 ?\< ACTU,Y S1 MAY Q EASILY 2 O!RWISE2 = HE 2LIEVES T S* IS ! PROP] OBJECT ( OP9ION1 :ILE ! NEC IS ! OBJECT ( K4 ,9 :AT S5SE1 !N1 C ! SAME ?+ 2 ! OBJECT ( BO? OP9ION & K8 ,& IF ANY "O *OOSES 6MA9TA9 T ALL T HE "KS HE C AL OP9E1 :Y %D N OP9ION 2 K8 ,= HE T "KS & HE T OP9ES W FOLL[ ! SAME TRA9 ( ?"\ "? ! SAME MI4LE T]MS UNTIL ! IMM PREMISSES >E R1*$2 2C X IS POSSI# 6OP9E N ONLY ! FACT B AL ! R1SON$ FACT1 &! R1SON IS ! MI4LE T]M2 S T1 S9CE ! =M] "KS1 HE T OP9ES AL HAS K4 ,! TRU? P]H IS T IF A MAN GRASP TRU?S T _C 2 O!R ?AN !Y >E1 9 ! WAY 9 : HE GRASPS ! DEF9I;NS "? : DEMON/R,NS TAKE PLACE1 HE W H N OP9ION B K3 IF ON ! O!R H& HE APPREH5DS ^! ATTRIBUTES Z 9H]+ 9 _! SUBJECTS1 B N 9 VIRTUE (! SUBJECTS' SUB/.E & ESS5TIAL NATURE POSSESSES OP9ION & N G5U9E K2 & 8 OP9ION1 IF OBTA9$ "? IMM PREMISSES1 W 2 BO? (! FACT &(! R1SON$ FACT2 IF N S OBTA9$1 (! FACT AL"O4 ,! OBJECT ( OP9ION & K IS N Q ID5TICAL2 X IS ONLY 9 A S5SE ID5TICAL1 J Z ! OBJECT ( TRUE & FALSE OP9ION IS 9 A S5SE ID5TICAL4 ,! S5SE 9 : "S MA9TA9 T TRUE & FALSE OP9ION C H ! SAME OBJECT L1DS !M 6EMBRACE _M /RANGE DOCTR9ES1 "PICUL>LY ! DOCTR9E T :AT A MAN OP9ES FALSELY HE DOES N OP9E AT ALL4 ,"! >E RE,Y _M S5SES ( ,8ID5TICAL0'1 & 9 "O S5SE ! OBJECT ( TRUE & FALSE OP9ION C 2 ! SAME1 9 ANO!R X _C4 ,?US1 6H A TRUE OP9ION T ! DIAGONAL IS -M5SURATE )! SIDE WD 2 ABSURD3 B 2C ! DIAGONAL ) : !Y >E BO? 3C]N$ IS ! SAME1 ! TWO OP9IONS H OBJECTS S F> ! SAME3 ON ! O!R H&1 Z REG>DS _! ESS5TIAL DEF9A# NATURE ^! OBJECTS DI6]4 ,! ID5T;Y (! OBJECTS ( K & OP9ION IS SIMIL>4 ,K IS ! APPREH5.N (1 E4G4 ! ATTRIBUTE ,8ANIMAL0' Z 9CAPA# ( 2+ O!RWISE1 OP9ION ! APPREH5.N ( ,8ANIMAL0' Z CAPA# ( 2+ O!RWISE-E4G4 ! APPREH5.N T ANIMAL IS AN ELE;T 9 ! ESS5TIAL NATURE ( MAN IS K2 ! APPREH5.N ( ANIMAL Z PR$ICA# ( MAN B N Z AN ELE;T 9 MAN'S ESS5TIAL NATURE IS OP9ION3 MAN IS ! SUBJECT 9 BO? JUDGE;TS1 B ! MODE ( 9H];E DI6]S4 ,? AL %[S T "O _C OP9E & "K ! SAME ?+ SIMULTANE\SLY2 = !N "O WD APPREH5D ! SAME ?+ Z BO? CAPA# & 9CAPA# ( 2+ O!RWISE-AN IMPOSSIBIL;Y4 ,K & OP9ION (! SAME ?+ C CO-EXI/ 9 TWO DI6]5T P 9 ! S5SE WE H EXPLA9$1 B N SIMULTANE\SLY 9 ! SAME P]SON4 ,T WD 9VOLVE A MAN'S SIMULTANE\SLY APPREH5D+1 E4G4 7#A7 T MAN IS ESS5TI,Y ANIMAL-I4E4 _C 2 O!R ?AN ANIMAL-& 7#B7 T MAN IS N ESS5TI,Y ANIMAL1 T IS1 WE MAY ASSUME1 MAY 2 O!R ?AN ANIMAL4 ,FUR!R 3SID],N ( MODES ( ?9K+ & _! 4TRIBU;N "U ! H1DS ( 4CURSIVE ?"\1 9TUI;N1 SCI;E1 >T1 PRACTICAL WISDOM1 & METAPHYSICAL ?9K+1 2L;GS R "PLY 6NATURAL SCI;E1 "PLY 6MORAL PHILOSOPHY4 #CD ,QK WIT IS A FACULTY ( HITT+ ^U ! MI4LE T]M 9/ANTANE\SLY4 ,X WD 2 EXEMPLIFI$ 0A MAN :O SAW T ! MOON HAS H] B"R SIDE ALW TURN$ T[>DS ! SUN1 & QKLY GRASP$ ! CAUSE ( ?1 "NLY T %E BORR[S H] LID0'1 ;,B ,8LIDS ! S\RCE ( H] LIE Z _M Z ! K9DS ( ?+S : WE "K4 ,!Y >E 9 FACT F\R3-7#A7 :E!R ! 3NEXION ( AN ATTRIBUTE )A ?+ IS A FACT1 7#B7 :AT IS ! R1SON (! 3NEXION1 7#C7 :E!R A ?+ EXI/S1 7#D7 ,:AT IS ! NATURE (! ?+4 ,?US1 :5 \R "Q 3C]NS A -PLEX ( ?+ & ATTRIBUTE & WE ASK :E!R ! ?+ IS ?US OR O!RWISE QUALIFI$-:E!R1 E4G4 ! SUN SU6]S ECLIPSE OR N-!N WE >E ASK+ Z 6! FACT (A 3NEXION4 ,T \R 9QUIRY C1SES ) ! 4COV]Y T ! SUN DOES SU6] ECLIPSE IS AN 9DIC,N ( ?2 & IF WE "K F ! />T T ! SUN SU6]S ECLIPSE1 WE D N 9QUIRE :E!R X DOES S OR N4 ,ON ! O!R H&1 :5 WE "K ! FACT WE ASK ! R1SON2 Z1 = EXAMPLE1 :5 WE "K T ! SUN IS 2+ ECLIPS$ & T AN E>?QUAKE IS 9 PROGRESS1 X IS ! R1SON ( ECLIPSE OR E>?QUAKE 96: WE 9QUIRE4 ,": A -PLEX IS 3C]N$1 !N1 ^? >E ! TWO "QS WE ASK2 B = "S OBJECTS ( 9QUIRY WE H A DI6]5T K9D ( "Q 6ASK1 S* Z :E!R "! IS OR IS N A C5TAUR OR A ,GOD4 7,BY ,8IS OR IS N0' ,I M1N ,8IS OR IS N1 )\T FUR!R QUALIFIC,N0'2 Z OPPOS$ TO ,8IS OR IS N ,7E4G47' :ITE0'47 ,ON ! O!R H&1 :5 WE H ASC]TA9$ ! ?+'S EXI/;E1 WE 9QUIRE Z 6XS NATURE1 ASK+1 = 9/.E1 ,8:AT1 !N1 IS ,GOD80' OR ,8:AT IS MAN80'4 #B ,^!1 !N1 >E ! F\R K9DS ( "Q WE ASK1 & X IS 9 ! ANSW]S 6^! "QS T \R K 3SI/S4 ,N[ :5 WE ASK :E!R A 3NEXION IS A FACT1 OR :E!R A ?+ )\T QUALIFIC,N IS1 WE >E RE,Y ASK+ :E!R ! 3NEXION OR ! ?+ HAS A ,8MI4LE0'2 & :5 WE H ASC]TA9$ EI T ! 3NEXION IS A FACT OR T ! ?+ IS-I4E4 ASC]TA9$ EI ! "PIAL OR ! UNQUALIFI$ 2+ ( ! ?+-& >E PROCE$+ 6ASK ! R1SON (! 3NEXION OR ! NATURE (! ?+1 !N WE >E ASK+ :AT ! ,8MI4LE0' IS4 7,04T+UI%+ ! FACT (! 3NEXION &! EXI/;E (! ?+ Z RESPECTIVELY ! "PIAL &! UNQUALIFI$ 2+ (! ?+1 ,I M1N T IF WE ASK ,8DOES ! MOON SU6] ECLIPSE80'1 OR ,8DOES ! MOON WAX80'1 ! "Q 3C]NS A "P (! ?+'S 2+2 = :AT WE >E ASK+ 9 S* "QS IS :E!R A ?+ IS ? OR T1 I4E4 HAS OR HAS N ? OR T ATTRIBUTE3 ":AS1 IF WE ASK :E!R ! MOON OR NIE ASK+ EI :E!R "! IS A ,8MI4LE0' OR :AT ! ,8MI4LE0' IS3 =! ,8MI4LE0' "H IS PRECISELY ! CAUSE1 & X IS ! CAUSE T WE SEEK 9 ALL \R 9QUIRIES4 ,?US1 ,8,DOES ! MOON SU6] ECLIPSE80' M1NS ,8,IS "! OR IS "! N A CAUSE PRODUC+ ECLIPSE (! MOON80'1 & :5 WE H LE>NT T "! IS1 \R NEXT "Q IS1 ,8,:AT1 !N1 IS ? CAUSE8 =! CAUSE "? : A ?+ IS-N IS ? OR T1 I4E4 HAS ? OR T ATTRIBUTE1 B )\T QUALIFIC,N IS-&! CAUSE "? : X IS-N IS )\T QUALIFIC,N1 B IS ? OR T Z HAV+ "S ESS5TIAL ATTRIBUTE OR "S A3ID5T->E BO? ALIKE ! MI4LE0'4 ,0T : IS )\T QUALIFIC,N ,I M1N ! SUBJECT1 E4G4 MOON OR E>? OR SUN OR TRIANGLE2 0T : A SUBJECT IS 7IN ! "PIAL S5SE7 ,I M1N A PROP]TY1 E4G4 ECLIPSE1 EQUAL;Y OR 9EQUAL;Y1 9T]POSI;N OR NON-9T]POSI;N4 ,= 9 ALL ^! EXAMPLES X IS CLE> T ! NATURE ( ! ?+ &! R1SON (! FACT >E ID5TICAL3 ! "Q ,8,:AT IS ECLIPSE80' & XS ANSW] ,8,! PRIV,N (! MOON'S LI?0' >E ID5TICAL )! "Q ,8,:AT IS ! R1SON ( ECLIPSE80' OR ,8,:Y DOES ! MOON SU6] ECLIPSE80' &! REPLY ,8,2C (! FAILURE ( LI?'S %UTT+ X \0'4 ,AG1 = ,8,:AT IS A 3CORD8 ,A -M5SURATE NUM]ICAL RATIO (A HI< &A L[ NOTE0'1 WE MAY SUB/ITUTE ,8,:AT RATIO MAKES A HI< & A L[ NOTE 3CORDANT8 ,_! REL,N AC 6A -M5SURATE NUM]ICAL RATIO40' ,8,>E ! HI< &! L[ NOTE 3CORDANT80' IS EQUIVAL5T TO ,8,IS _! RATIO -M5SURATE80'2 & :5 WE F9D T X IS -M5SURATE1 WE ASK ,8,:AT1 !N1 IS _! RATIO80'4 ,CASES 9 : ! ,8MI4LE0' IS S5SI# %[ T ! OBJECT ( \R 9QUIRY IS ALW ! ,8MI4LE0'3 WE 9QUIRE1 2C WE H N P]CVD X1 :E!R "! IS OR IS N A ,8MI4LE0' CAUS+1 E4G4 AN ECLIPSE4 ,ON ! O!R H&1 IF WE 7 ON ! MOON WE %D N 2 9QUIR+ EI Z 6! FACT OR ! R1SON1 B BO? FACT & R1SON WD 2 OBVI\S SIMULTANE\SLY4 ,=! ACT ( P]CEP;N WD H 5A#D U 6"K ! UNIV]SAL TOO2 S9CE1 ! PRES5T FACT ( AN ECLIPSE 2+ EVID5T1 P]CEP;N WD !N AT ! SAME "T GIVE U ! PRES5T FACT (! E>?'S SCRE5+ ! SUN'S LIISE ! UNIV]SAL4 ,?US1 Z WE MA9TA91 6"K A ?+'S NATURE IS 6"K ! R1SON :Y X IS2 & ? IS EQU,Y TRUE ( ?+S 9 S F> Z !Y >E SD )\T QUALIFIC,N 6HE Z OPPOS$ 62+ POSSESS$ ( "S ATTRIBUTE1 & 9 S F> Z !Y >E SD 6BE POSSESS$ ( "S ATTRIBUTE S* Z EQUAL 6"R ANGLES1 OR GRT] OR LESS4 #C ,X IS CLE>1 !N1 T ALL "QS >E A SE>* =A ,8MI4LE0'4 ,LET U N[ /ATE H[ ESS5TIAL NATURE IS REV1L$ & 9 :AT WAY X C 2 REDUC$ 6DEMON/R,N2 :AT DEF9I;N IS1 & :AT ?+S >E DEF9A#4 ,& LET U F/ 4CUSS C]TA9 DI6ICULTIES : ^! "QS RAISE1 2G9N+ :AT WE H 6SAY )A PO9T MO/ 9TIMATELY 3NECT$ ) \R IMMLY PREC$+ REM>KS1 "NLY ! D\BT T MIE NEGATIVE & "S >E N UNIV]SAL2 E4G4 ALL 9 ! SECOND FIGURE >E NEGATIVE1 N"O 9 ! ?IRD >E UNIV]SAL4 ,& AG1 N EV5 ALL A6IRMATIVE 3CLU.NS 9 ! F/ FIGURE >E DEF9A#1 E4G4 ,8E TRIANGLE HAS XS ANGLES EQUAL 6TWO "R ANGLES0'4 ,AN >GU;T PROV+ ? DI6];E 2T DEMON/R,N & DEF9I;N IS T 6H SCI5TIFIC K (! DEMON/RA# IS ID5TICAL ) POSSESS+ A DEMON/R,N ( X3 H;E IF DEMON/R,N ( S* 3CLU.NS Z ^! IS POSSI#1 "! CLE>LY _C AL 2 DEF9I;N ( !M4 ,IF "! CD1 "O MIE N SUB/.ES4 ,X IS EVID5T1 !N1 T N "EY?+ DEMON/RA# C 2 DEF9$4 ,:AT !N8 ,C "EY?+ DEF9A# 2 DEMON/RAT$1 OR N8 ,"! IS "O ( \R PREVI\S >GU;TS : COV]S ? TOO4 ,(A S+LE ?+ QUA S+LE "! IS A S+LE SCI5TIFIC K4 ,H;E1 S9CE 6"K ! DEMON/RA# SCI5TIFIC,Y IS 6POSSESS ! DEMON/R,N ( X1 AN IMPOSSI# 3SEQU;E W FOLL[3-POSSES.N ( XS DEF9I;N )\T XS DEMON/R,N W GIVE K (! DEMON/RA#4 ,MOREOV]1 ! BASIC PREMISSES ( DEMON/R,NS >E DEF9I;NS1 & X HAS ALR BE5 %[N T ^! W 2 F.D 9DEMON/RA#2 EI ! BASIC PREMISSES W 2 DEMON/RA# & W DEP5D ON PRIOR PREMISSES1 &! REGRESS W 2 5D.S2 OR ! PRIM>Y TRU?S W 2 9DEMON/RA# DEF9I;NS4 ,B IF ! DEF9A# &! DEMON/RA# >E N :OLLY ! SAME1 MAY !Y YET 2 "PI,Y ! SAME8 ,OR IS T IMPOSSI#1 2C "! C 2 NO DEMON/R,N (! DEF9A#8 ,"! C 2 N"O1 2C DEF9I;N IS (! ESS5TIAL NATURE OR 2+ ( "S?+1 & ALL DEMON/R,NS EVID5TLY POSIT & ASSUME ! ESS5TIAL NATURE-MA!MATICAL DEMON/R,NS1 = EXAMPLE1 ! NATURE ( UN;Y &! ODD1 & ALL ! O!R SCI;ES LIKEWISE4 ,MOREOV]1 E DEMON/R,N PROVES A PR$ICATE (A SUBJECT Z ATTA*+ OR Z N ATTA*+ 6X1 B 9 DEF9I;N "O ?+ IS N PR$ICAT$ ( ANO!R2 WE D N1 E4G4 PR$ICATE ANIMAL ( BIP$ NOR BIP$ ( ANIMAL1 NOR YET FIGURE ( PLANE-PLANE N 2+ FIGURE NOR FIGURE PLANE4 ,AG1 6PROVE ESS5TIAL NATURE IS N ! SAME Z 6PROVE ! FACT (A 3NEXION4 ,N[ DEF9I;N REV1LS ESS5TIAL NATURE1 DEMON/R,N REV1LS T A GIV5 ATTRIBUTE ATTA*ES OR DOES N ATTA* 6A GIV5 SUBJECT2 B DI6]5T ?+S REQUIRE DI6]5T DEMON/R,NS-UN.S ! "O DEMON/R,N IS RELAT$ 6! O!R Z "P 6:OLE4 ,I ADD ? 2C IF ALL TRIANGLES H BE5 PROV$ 6POSSESS ANGLES EQUAL 6TWO "R ANGLES1 !N ? ATTRIBUTE HAS BE5 PROV$ 6ATTA* 6ISOSCELES2 = ISOSCELES IS A "P ( : ALL TRIANGLES 3/ITUTE ! :OLE4 ,B 9 ! CASE 2F U ! FACT &! ESS5TIAL NATURE >E N S RELAT$ 6"O ANO!R1 S9CE ! "O IS N A "P (! O!R4 ,S X EM]GES T N ALL ! DEF9A# IS DEMON/RA# NOR ALL ! DEMON/RA# DEF9A#2 & WE MAY DRAW ! G5]AL 3CLU.N T "! IS NO ID5TICAL OBJECT ( : X IS POSSI# 6POSSESS BO? A DEF9I;N &A DEMON/R,N4 ,X FOLL[S OBVI\SLY T DEF9I;N & DEMON/R,N >E NEI ID5TICAL NOR 3TA9$ EI )9 ! O!R3 IF !Y W]E1 _! OBJECTS WD 2 RELAT$ EI Z ID5TICAL OR Z :OLE & "P4 #D ,S M*1 !N1 =! F/ /AGE ( \R PRO#M4 ,! NEXT /EP IS 6RAISE ! "Q :E!R SYLLOGISM- I4E4 DEMON/R,N-(! DEF9A# NATURE IS POSSI# OR1 Z \R REC5T >GU;T ASSUM$1 IMPOSSI#4 ,WE MIGUE X IMPOSSI# ON ! FOLL[+ GR.DS3-7A7 SYLLOGISM PROVES AN ATTRIBUTE (A SUBJECT "? ! MI4LE T]M2 ON ! O!R H& 7B7 XS DEF9A# NATURE IS BO? ,8PECULI>0' 6A SUBJECT & PR$ICAT$ ( X Z 2L;G+ 6XS ESS;E4 ,B 9 T CASE 7#A7 ! SUBJECT1 XS DEF9I;N1 &! MI4LE T]M 3NECT+ !M M/ 2 RECIPROC,Y PR$ICA# ( "O ANO!R2 = IF ,A IS TO ;,C1 OBVI\SLY ,A IS ,8PECULI>0' TO ;,B & ;,B TO ;,C-IN FACT ALL ?REE T]MS >E ,8PECULI>0' 6"O ANO!R3 & FUR!R 7#B7 IF ,A 9"HS 9 ! ESS;E ( ALL ;,B & ;,B IS PR$ICAT$ UNIV]S,Y ( ALL ;,C Z 2L;G+ TO ;,C'S ESS;E1 ,A AL M/ 2 PR$ICAT$ ( ;,C Z 2L;G+ 6XS ESS;E4 ,IF "O DOES N TAKE ? REL,N Z ?US DUPLICAT$-IF1 T IS1 ,A IS PR$ICAT$ Z 2+ (! ESS;E ( ;,B1 B ;,B IS N (! ESS;E (! SUBJECTS ( : X IS PR$ICAT$-,A W N NECESS>ILY 2 PR$ICAT$ ( ;,C Z 2L;G+ 6XS ESS;E4 ,S BO? PREMISSES W PR$ICATE ESS;E1 & 3SEQU5TLY ;,B AL W 2 PR$ICAT$ ( ;,C Z XS ESS;E4 ,S9CE1 "!=E1 BO? PREMISSES D PR$ICATE ESS;E-I4E4 DEF9A# =M-;,C'S DEF9A# =M W APPE> 9 ! MI4LE T]M 2F ! 3CLU.N IS DRAWN4 ,WE MAY G5]ALIZE 0SUPPOS+ T X IS POSSI# 6PROVE ! ESS5TIAL NATURE ( MAN4 ,LET ;,C 2 MAN1 ,A MAN'S ESS5TIAL NATURE --TWO-FOOT$ ANIMAL1 OR AUE 6SYLLOGIZE1 ,A M/ 2 PR$ICAT$ ( ALL ,B4 ,B ? PREMISS W 2 M$IAT$ 0A FRE% DEF9I;N1 : 3SEQU5TLY W AL 2 ! ESS5TIAL NATURE ( MAN4 ,"!=E ! >GU;T ASSUMES :AT X HAS 6PROVE1 S9CE ;,B TOO IS ! ESS5TIAL NATURE ( MAN4 ,X IS1 H["E1 ! CASE 9 : "! >E ONLY ! TWO PREMISSES- I4E4 9 : ! PREMISSES >E PRIM>Y & IMM-: WE "\ 69VE/IGATE1 2C X BE/ ILLU/RATES ! PO9T "U 4CUS.N4 ,?US !Y :O PROVE ! ESS5TIAL NATURE ( S\L OR MAN OR ANY?+ ELSE "? RECIPROCAT+ T]MS BEG ! "Q4 ,X WD 2 BE7+ ! "Q1 = EXAMPLE1 63T5D T ! S\L IS T : CAUSES XS [N LIFE1 & T :AT CAUSES XS [N LIFE IS A SELF-MOV+ NUMB]2 = "O WD H 6PO/ULATE T ! S\L IS A SELF-MOV+ NUMB] 9 ! S5SE ( 2+ ID5TICAL ) X4 ,= IF ,A IS PR$ICA# Z A M]E 3SEQU5T ( ;,B & ;,B ( ;,C1 ,A W N ON T A3.T 2 ! DEF9A# =M ( ;,C3 ,A W M]ELY 2 :AT X 0 TRUE 6SAY ( ,C4 ,EV5 IF ,A IS PR$ICAT$ ( ALL ;,B 9ASM* Z ;,B IS ID5TICAL )A SPECIES ( ;,A1 / X W N FOLL[3 2+ AN ANIMAL IS PR$ICAT$ ( 2+ A MAN-S9CE X IS TRUE T 9 ALL 9/.ES 6BE HUMAN IS 6BE ANIMAL1 J Z X IS AL TRUE T E MAN IS AN ANIMAL-B N Z ID5TICAL ) 2+ MAN4 ,WE 3CLUDE1 !N1 T UN.S "O TAKES BO? ! PREMISSES Z PR$ICAT+ ESS;E1 "O _C 9F] T ,A IS ! DEF9A# =M & ESS;E ( ;,C3 B IF "O DOES S TAKE !M1 9 ASSUM+ ;,B "O W H ASSUM$1 2F DRAW+ ! 3CLU.N1 :AT ! DEF9A# =M ( ;,C IS2 S T "! HAS BE5 NO 9F];E1 = "O HAS BE7$ ! "Q4 #E ,NOR1 Z 0 SD 9 MY =MAL LOGIC1 IS ! ME?OD ( DIVI.N A PROCESS ( 9F];E AT ALL1 S9CE AT NO PO9T DOES ! "*IZ,N (! SUBJECT FOLL[ NECESS>ILY F ! PREMIS+ ( C]TA9 O!R FACTS3 DIVI.N DEMON/RATES Z LL Z DOES 9DUC;N4 ,= 9 A G5U9E DEMON/R,N ! 3CLU.N M/ N 2 PUT Z A "Q NOR DEP5D ON A 3CES.N1 B M/ FOLL[ NECESS>ILY F XS PREMISSES1 EV5 IF ! RESPOND5T D5Y X4 ,! DEF9] ASKS ,8,IS MAN ANIMAL OR 9ANIMATE80' & !N ASSUMES-HE HAS N 9F]R$-T MAN IS ANIMAL4 ,NEXT1 :5 PRES5T$ ) AN EXHAU/IVE DIVI.N ( ANIMAL 96T]RE/RIAL & AQUATIC1 HE ASSUMES T MAN IS T]RE/RIAL4 ,MOREOV]1 T MAN IS ! -PLETE =MULA1 T]RE/RIAL-ANIMAL1 DOES N FOLL[ NECESS>ILY F ! PREMISSES3 ? TOO IS AN ASSUMP;N1 & EQU,Y AN ASSUMP;N :E!R ! DIVI.N -PRISES _M DI6]5TIAE OR FEW4 7,9DE$ Z ? ME?OD ( DIVI.N IS US$ 0^? :O PROCE$ 0X1 EV5 TRU?S T C 2 9F]R$ ACTU,Y FAIL 6APPE> Z S*47 ,= :Y %D N ! :OLE ( ? =MULA 2 TRUE ( MAN1 & YET N EXHIBIT 8 ESS5TIAL NATURE OR DEF9A# =M8 ,AG1 :AT GU>ANTEE IS "! AG/ AN UNESS5TIAL A4I;N1 OR AG/ ! OMIS.N (! F9AL OR ( AN 9T]M$IATE DET]M9ANT (! SUB/ANTIAL 2+8 ,! *AMPION ( DIVI.N MIE 3/ITU5TS (! DEF9A# =M1 & IF1 PO/ULAT+ ! G5US1 WE PRODUCE 0DIVI.N ! REQUISITE UN9T]RUPT$ SEQU;E ( T]MS1 & OMIT NO?+2 & T 9DE$ WE _C FAIL 6FULFIL ^! 3DI;NS IF :AT IS 6BE DIVID$ FALLS :OLE 96! DIVI.N AT EA* /AGE1 & N"O ( X IS OMITT$2 & T ?- ! DIVID5DUM-M/ )\T FUR!R "Q 2 7ULTIMATELY7 9CAPA# ( FRE% SPECIFIC DIVI.N4 ,N"E!.S1 WE REPLY1 DIVI.N DOES N 9VOLVE 9F];E2 IF X GIVES K1 X GIVES X 9 ANO!R WAY4 ,NOR IS "! ANY ABSURD;Y 9 ?3 9DUC;N1 P]H1 IS N DEMON/R,N ANY M ?AN IS DIVI.N1 ET X DOES MAKE EVID5T "S TRU?4 ,YET 6/ATE A DEF9I;N R1*$ 0DIVI.N IS N 6/ATE A 3CLU.N3 Z1 :5 3CLU.NS >E DRAWN )\T _! APPROPRIATE MI4LES1 ! ALLEG$ NECESS;Y 0: ! 9F];E FOLL[S F ! PREMISSES IS OP5 6A "Q Z 6! R1SON = X1 S DEF9I;NS R1*$ 0DIVI.N 9VITE ! SAME "Q4 ,?US 6! "Q ,8,:AT IS ! ESS5TIAL NATURE ( MAN80' ! DIVID] REPLIES ,8,ANIMAL1 MORTAL1 FOOT$1 BIP$1 W+.S0'2 & :5 AT EA* /EP HE IS ASK$ ,8,:Y80'1 HE W SAY1 &1 Z HE ?9KS1 PROVES 0DIVI.N1 T ALL ANIMAL IS MORTAL OR IMMORTAL3 B S* A =MULA TAK5 9 XS 5TIRETY IS N DEF9I;N2 S T EV5 IF DIVI.N DOES DEMON/RATE XS =MULA1 DEF9I;N AT ANY RATE DOES N TURN \ 6BE A 3CLU.N ( 9F];E4 #F ,C WE N"E!.S ACTU,Y DEMON/RATE :AT A ?+ ESS5TI,Y & SUB/ANTI,Y IS1 B HYPO!TIC,Y1 I4E4 0PREMIS+ 7#A7 T XS DEF9A# =M IS 3/ITUT$ 0! ,8PECULI>0' ATTRIBUTES ( XS ESS5TIAL NATURE2 7#B7 T S* & S* >E ! ONLY ATTRIBUTES ( XS ESS5TIAL NATURE1 & T ! -PLETE SYN!SIS ( !M IS PECULI> 6! ?+2 & ?US-S9CE 9 ? SYN!SIS 3SI/S ! 2+ (! ?+-OBTA9+ \R 3CLU.N8 ,OR IS ! TRU? T1 S9CE PRO( M/ 2 "? ! MI4LE T]M1 ! DEF9A# =M IS ONCE M ASSUM$ 9 ? M9OR PREMISS TOO8 ,FUR!R1 J Z 9 SYLLOGIZ+ WE D N PREMISE :AT SYLLOGI/IC 9F];E IS 7S9CE ! PREMISSES F : WE 3CLUDE M/ 2 RELAT$ Z :OLE & "P71 S ! DEF9A# =M M/ N FALL )9 ! SYLLOGISM B REMA9 \TSIDE ! PREMISSES POSIT$4 ,X IS ONLY AG/ A D\BT Z 6XS HAV+ BE5 A SYLLOGI/IC 9F];E AT ALL T WE H 6DEF5D \R >GU;T Z 3=M+ 6! DEF9I;N ( SYLLOGISM4 ,X IS ONLY :5 "S "O D\BTS :E!R ! 3CLU.N PROV$ IS ! DEF9A# =M T WE H 6DEF5D X Z 3=M+ 6! DEF9I;N ( DEF9A# =M : WE ASSUM$4 ,H;E SYLLOGI/IC 9F];E M/ 2 POSSI# EV5 )\T ! EXPRESS /ATE;T ( :AT SYLLOGISM IS OR :AT DEF9A# =M IS4 ,! FOLL[+ TYPE ( HYPO!TICAL PRO( AL BEGS ! "Q4 ,IF EVIL IS DEF9A# Z ! DIVISI#1 &! DEF9I;N (A ?+'S 3TR>Y-IF X HAS "O ! 3TR>Y (! ?+'S DEF9I;N2 !N1 IF GD IS ! 3TR>Y ( EVIL &! 9DIVISI# (! DIVISI#1 WE 3CLUDE T 6BE GD IS ESS5TI,Y 6BE 9DIVISI#4 ,! "Q IS BE7$ 2C DEF9A# =M IS ASSUM$ Z A PREMISS1 & Z A PREMISS : IS 6PROVE DEF9A# =M4 ,8,B N ! SAME DEF9A# =M0'1 Y MAY OBJECT4 ,T ,I ADMIT1 = 9 DEMON/R,NS AL WE PREMISE T ,8?0' IS PR$ICA# ( ,8T0'2 B 9 ? PREMISS ! T]M WE ASS]T (! M9OR IS NEI ! MAJOR XF NOR A T]M ID5TICAL 9 DEF9I;N1 OR 3V]TI#1 )! MAJOR4 ,AG1 BO? PRO( 0DIVI.N &! SYLLOGISM J DESCRIB$ >E OP5 6! "Q :Y MAN %D 2 ANIMAL-BIP$-T]RE/RIAL & N M]ELY ANIMAL & T]RE/RIAL1 S9CE :AT !Y PREMISE DOES N 5SURE T ! PR$ICATES % 3/ITUTE A G5U9E UN;Y & N M]ELY 2L;G 6A S+LE SUBJECT Z D MUSICAL & GRAMMATICAL :5 PR$ICAT$ (! SAME MAN4 #G ,H[ !N 0DEF9I;N % WE PROVE SUB/.E OR ESS5TIAL NATURE8 ,WE _C %[ X Z A FRE% FACT NECESS>ILY FOLL[+ F ! ASSUMP;N ( PREMISSES ADMITT$ 6BE FACTS-! ME?OD ( DEMON/R,N3 WE MAY N PROCE$ Z 09DUC;N 6E/ABLI% A UNIV]SAL ON ! EVID;E ( GR\PS ( "PICUL>S : (F] NO EXCEP;N1 2C 9DUC;N PROVES N :AT ! ESS5TIAL NATURE (A ?+ IS B T X HAS OR HAS N "S ATTRIBUTE4 ,"!=E1 S9CE PRESUMABLY "O _C PROVE ESS5TIAL NATURE 0AN APP1L 6S5SE P]CEP;N OR 0PO9T+ )! F+]1 :AT O!R ME?OD REMA9S8 ,6PUT X ANO!R WAY3 H[ % WE 0DEF9I;N PROVE ESS5TIAL NATURE8 ,HE :O "KS :AT HUMAN-OR ANY O!R-NATURE IS1 M/ "K AL T MAN EXI/S2 = NO "O "KS ! NATURE ( :AT DOES N EXI/-"O C "K ! M1N+ (! PHRASE OR "N ,8GOAT-/AG0' B N :AT ! ESS5TIAL NATURE (A GOAT-/AG IS4 ,B FUR!R1 IF DEF9I;N C PROVE :AT IS ! ESS5TIAL NATURE (A ?+1 C X AL PROVE T X EXI/S8 ,& H[ W X PROVE !M BO? 0! SAME PROCESS1 S9CE DEF9I;N EXHIBITS "O S+LE ?+ & DEMON/R,N ANO!R S+LE ?+1 & :AT HUMAN NATURE IS &! FACT T MAN EXI/S >E N ! SAME ?+8 ,!N TOO WE HOLD T X IS 0DEMON/R,N T ! 2+ ( "EY?+ M/ 2 PROV$-UN.S 9DE$ 6BE 7 XS ESS;E2 &1 S9CE 2+ IS N A G5US1 X IS N ! ESS;E ( ANY?+4 ,H;E ! 2+ ( ANY?+ Z FACT IS MATT] = DEMON/R,N2 & ? IS ! ACTUAL PROC$URE (! SCI;ES1 =! GEOMET] ASSUMES ! M1N+ (! ^W TRIANGLE1 B T X IS POSSESS$ ( "S ATTRIBUTE HE PROVES4 ,:AT IS X1 !N1 T WE % PROVE 9 DEF9+ ESS5TIAL NATURE8 ,TRIANGLE8 ,9 T CASE A MAN W "K 0DEF9I;N :AT A ?+'S NATURE IS )\T "K+ :E!R X EXI/S4 ,B T IS IMPOSSI#4 ,MOREOV] X IS CLE>1 IF WE 3SID] ! ME?ODS ( DEF9+ ACTU,Y 9 USE1 T DEF9I;N DOES N PROVE T ! ?+ DEF9$ EXI/S3 S9CE EV5 IF "! DOES ACTU,Y EXI/ "S?+ : IS EQUIDISTANT F A C5TRE1 YET :Y %D ! ?+ "ND 9 ! DEF9I;N EXI/8 ,:Y1 9 O!R ^WS1 %D ? 2 ! =MULA DEF9+ CIRCLE8 ,"O MIRY A FUR!R GU>ANTEE T ! ?+ DEF9$ C EXI/ OR T X IS :AT !Y CLAIM 6DEF9E3 "O C ALW ASK :Y4 ,S9CE1 "!=E1 6DEF9E IS 6PROVE EI A ?+'S ESS5TIAL NATURE OR ! M1N+ ( XS "N1 WE MAY 3CLUDE T DEF9I;N1 IF X 9 NO S5SE PROVES ESS5TIAL NATURE1 IS A SET ( ^WS SIGNIFY+ PRECISELY :AT A "N SIGNIFIES4 ,B T 7 A /RANGE 3SEQU;E2 = 7#A7 BO? :AT IS N SUB/.E & :AT DOES N EXI/ AT ALL WD 2 DEF9A#1 S9CE EV5 NON-EXI/5TS C 2 SIGNIFI$ 0A "N3 7#B7 ALL SETS ( ^WS OR S5T;ES WD 2 DEF9I;NS1 S9CE ANY K9D ( S5T;E CD 2 GIV5 A "N2 S T WE %D ALL 2 TALK+ 9 DEF9I;NS1 & EV5 ! ,ILIAD WD 2 A DEF9I;N3 7#C7 NO DEMON/R,N C PROVE T ANY "PICUL> "N M1NS ANY "PICUL> ?+3 NEI1 "!=E1 D DEF9I;NS1 9 A4I;N 6REV1L+ ! M1N+ (A "N1 AL REV1L T ! "N HAS ? M1N+4 ,X APPE>S !N F ^! 3SID],NS T NEI DEF9I;N & SYLLOGISM NOR _! OBJECTS >E ID5TICAL1 & FUR!R T DEF9I;N NEI DEMON/RATES NOR PROVES ANY?+1 & T K ( ESS5TIAL NATURE IS N 6BE OBTA9$ EI 0DEF9I;N OR 0DEMON/R,N4 #H ,WE M/ N[ />T AFRE% & 3SID] : ( ^! 3CLU.NS >E S.D & : >E N1 & :AT IS ! NATURE ( DEF9I;N1 & :E!R ESS5TIAL NATURE IS 9 ANY S5SE DEMON/RA# & DEF9A# OR 9 N"O4 ,N[ 6"K XS ESS5TIAL NATURE IS1 Z WE SD1 ! SAME Z 6"K ! CAUSE (A ?+'S EXI/;E1 &! PRO( ( ? DEP5DS ON ! FACT T A ?+ M/ H A CAUSE4 ,MOREOV]1 ? CAUSE IS EI ID5TICAL )! ESS5TIAL NATURE (! ?+ OR 4T9CT F X2 & IF XS CAUSE IS 4T9CT F X1 ! ESS5TIAL NATURE (! ?+ IS EI DEMON/RA# OR 9DEMON/RA#4 ,3SEQU5TLY1 IF ! CAUSE IS 4T9CT F ! ?+'S ESS5TIAL NATURE & DEMON/R,N IS POSSI#1 ! CAUSE M/ 2 ! MI4LE T]M1 &1 ! 3CLU.N PROV$ 2+ UNIV]SAL & A6IRMATIVE1 ! PRO( IS 9 ! F/ FIGURE4 ,S ! ME?OD J EXAM9$ ( PROV+ X "? ANO!R ESS5TIAL NATURE WD 2 "O WAY ( PROV+ ESS5TIAL NATURE1 2C A 3CLU.N 3TA9+ ESS5TIAL NATURE M/ 2 9F]R$ "? A MI4LE : IS AN ESS5TIAL NATURE J Z A ,8PECULI>0' PROP]TY M/ 2 9F]R$ "? A MI4LE : IS A ,8PECULI>0' PROP]TY2 S T (! TWO DEF9A# NATURES (A S+LE ?+ ? ME?OD W PROVE "O & N ! O!R4 ,N[ X 0 SD 2F T ? ME?OD CD N AM.T 6DEMON/R,N ( ESS5TIAL NATURE-X IS ACTU,Y A DIALECTICAL PRO( ( X-S LET U 2G9 AG & EXPLA9 0:AT ME?OD X C 2 DEMON/RAT$4 ,:5 WE >E AW>E (A FACT WE SEEK XS R1SON1 & ?\< "S"TS ! FACT &! R1SON DAWN ON U SIMULTANE\SLY1 YET WE _C APPREH5D ! R1SON A MO;T SOON] ?AN ! FACT2 & CLE>LY 9 J ! SAME WAY WE _C APPREH5D A ?+'S DEF9A# =M )\T APPREH5D+ T X EXI/S1 S9CE :ILE WE >E IGNORANT :E!R X EXI/S WE _C "K XS ESS5TIAL NATURE4 ,MOREOV] WE >E AW>E :E!R A ?+ EXI/S OR N "S"TS "? APPREH5D+ AN ELE;T 9 XS "*1 & "S"TS A3ID5T,Y1 Z1 = EXAMPLE1 :5 WE >E AW>E ( ?"U Z A NOISE 9 ! CL\DS1 ( ECLIPSE Z A PRIV,N ( LIDS AW>E;S ( XS ESS5TIAL NATURE2 = WE H N GOT G5U9E K EV5 ( XS EXI/;E1 & 6SE>* =A ?+'S ESS5TIAL NATURE :5 WE >E UNAW>E T X EXI/S IS 6SE>* = NO?+4 ,ON ! O!R H&1 :5"E WE APPREH5D AN ELE;T 9 ! ?+'S "* "! IS LESS DI6ICULTY4 ,?US X FOLL[S T ! DEGREE ( \R K (A ?+'S ESS5TIAL NATURE IS DET]M9$ 0! S5SE 9 : WE >E AW>E T X EXI/S4 ,LET U !N TAKE ! FOLL[+ Z \R F/ 9/.E ( 2+ AW>E ( AN ELE;T 9 ! ESS5TIAL NATURE4 ,LET ,A 2 ECLIPSE1 ;,C ! MOON1 ;,B ! E>?'S ACT+ Z A SCRE54 ,N[ 6ASK :E!R ! MOON IS ECLIPS$ OR N IS 6ASK :E!R OR N ;,B HAS O3URR$4 ,B T IS PRECISELY ! SAME Z ASK+ :E!R ,A HAS A DEF9+ 3DI;N2 & IF ? 3DI;N ACTU,Y EXI/S1 WE ASS]T T ,A AL ACTU,Y EXI/S4 ,OR AG WE MAY ASK : SIDE (A 3TRADIC;N ! DEF9+ 3DI;N NECESSITATES3 DOES X MAKE ! ANGLES (A TRIANGLE EQUAL OR N EQUAL 6TWO "R ANGLES8 ,:5 WE H F.D ! ANSW]1 IF ! PREMISSES >E IMM1 WE "K FACT & R1SON TGR2 IF !Y >E N IMM1 WE "K ! FACT )\T ! R1SON1 Z 9 ! FOLL[+ EXAMPLE3 LET ;,C 2 ! MOON1 ,A ECLIPSE1 ;,B ! FACT T ! MOON FAILS 6PRODUCE %AD[S ?\< %E IS FULL & ?\< NO VISI# BODY 9T]V5ES 2T U & H]4 ,!N IF ;,B1 FAILURE 6PRODUCE %AD[S 9 SPITE ( ! ABS;E ( AN 9T]V5+ BODY1 IS ATTRIBUTA# ,A TO ;,C1 & ECLIPSE1 IS ATTRIBUTA# TO ;,B1 X IS CLE> T ! MOON IS ECLIPS$1 B ! R1SON :Y IS N YET CLE>1 & WE "K T ECLIPSE EXI/S1 B WE D N "K :AT XS ESS5TIAL NATURE IS4 ,B :5 X IS CLE> T ,A IS ATTRIBUTA# TO ;,C & WE PROCE$ 6ASK ! R1SON ( ? FACT1 WE >E 9QUIR+ :AT IS ! NATURE ( ;,B3 IS X ! E>?'S ACT+ Z A SCRE51 OR ! MOON'S ROT,N OR H] EXT9C;N8 ,B ;,B IS ! DEF9I;N (! O!R T]M1 VIZ4 9 ^! EXAMPLES1 (! MAJOR T]M ,A2 = ECLIPSE IS 3/ITUT$ 0! E>? ACT+ Z A SCRE54 ,?US1 7#A7 ,8,:AT IS ?"U80' ,8,! QU5*+ ( FIRE 9 CL\D0'1 & 7#B7 ,8,:Y DOES X ?"U80' ,8,2C FIRE IS QU5*$ 9 ! CL\D0'1 >E EQUIVAL5T4 ,LET ;,C 2 CL\D1 ,A ?"U1 ;,B ! QU5*+ ( FIRE4 ,!N ;,B IS ATTRIBUTA# TO ;,C1 CL\D1 S9CE FIRE IS QU5*$ 9 X2 & ;,A1 NOISE1 IS ATTRIBUTA# TO ;,B2 & ;,B IS ASSUR$LY ! DEF9I;N (! MAJOR T]M ,A4 ,IF "! 2 A FUR!R M$IAT+ CAUSE ( ;,B1 X W 2 "O (! REMA9+ "PIAL DEF9I;NS ( ,A4 ,WE H /AT$ !N H[ ESS5TIAL NATURE IS 4COV]$ & 2COMES "KN1 & WE SEE T1 :ILE "! IS NO SYLLOGISM-I4E4 NO DEMON/RATIVE SYLLOGISM-( ESS5TIAL NATURE1 YET X IS "? SYLLOGISM1 VIZ4 DEMON/RATIVE SYLLOGISM1 T ESS5TIAL NATURE IS EXHIBIT$4 ,S WE 3CLUDE T NEI C ! ESS5TIAL NATURE ( ANY?+ : HAS A CAUSE 4T9CT F XF 2 "KN )\T DEMON/R,N1 NOR C X 2 DEMON/RAT$2 & ? IS :AT WE 3T5D$ 9 \R PRELIM9>Y 4CUS.NS4 #I ,N[ :ILE "S ?+S H A CAUSE 4T9CT F !MVS1 O!RS H N4 ,H;E X IS EVID5T T "! >E ESS5TIAL NATURES : >E IMM1 T IS >E BASIC PREMISSES2 &( ^! N ONLY T !Y >E B AL :AT !Y >E M/ 2 ASSUM$ OR REV1L$ 9 "S O!R WAY4 ,? TOO IS ! ACTUAL PROC$URE (! >I?METICIAN1 :O ASSUMES BO? ! NATURE &! EXI/;E ( UNIT4 ,ON ! O!R H&1 X IS POSSI# 7IN ! MANN] EXPLA9$7 6EXHIBIT "? DEMON/R,N ! ESS5TIAL NATURE ( ?+S : H A ,8MI4LE0'1 I4E4 A CAUSE ( _! SUB/ANTIAL 2+ O!R ?AN T 2+ XF2 B WE D N "!BY DEMON/RATE X4 #AJ ,S9CE DEF9I;N IS SD 6BE ! /ATE;T (A ?+'S NATURE1 OBVI\SLY "O K9D ( DEF9I;N W 2 A /ATE;T (! M1N+ (! "N1 OR ( AN EQUIVAL5T NOM9AL =MULA4 ,A DEF9I;N 9 ? S5SE TELLS Y1 E4G4 ! M1N+ (! PHRASE ,8TRIANGUL> "*0'4 ,:5 WE >E AW>E T TRIANGLE EXI/S1 WE 9QUIRE ! R1SON :Y X EXI/S4 ,B X IS DI6ICULT ?US 6LE>N ! DEF9I;N ( ?+S ! EXI/;E ( : WE D N G5U9ELY "K-! CAUSE ( ? DI6ICULTY 2+1 Z WE SD 2F1 T WE ONLY "K A3ID5T,Y :E!R OR N ! ?+ EXI/S4 ,MOREOV]1 A /ATE;T MAY 2 A UN;Y 9 EI ( TWO WAYS1 03JUNC;N1 L ! ,ILIAD1 OR 2C X EXHIBITS A S+LE PR$ICATE Z 9H]+ N A3ID5T,Y 9 A S+LE SUBJECT4 ,T !N IS "O WAY ( DEF9+ DEF9I;N4 ,ANO!R K9D ( DEF9I;N IS A =MULA EXHIBIT+ ! CAUSE (A ?+'S EXI/;E4 ,?US ! =M] SIGNIFIES )\T PROV+1 B ! LATT] W CLE>LY 2 A QUASI-DEMON/R,N ( ESS5TIAL NATURE1 DI6]+ F DEMON/R,N 9 ! >RANGE;T ( XS T]MS4 ,= "! IS A DI6];E 2T /AT+ :Y X ?"US1 & /AT+ :AT IS ! ESS5TIAL NATURE ( ?"U2 S9CE ! F/ /ATE;T W 2 ,8,2C FIRE IS QU5*$ 9 ! CL\DS0'1 :ILE ! /ATE;T ( :AT ! NATURE ( ?"U IS W 2 ,8,! NOISE ( FIRE 2+ QU5*$ 9 ! CL\DS0'4 ,?US ! SAME /ATE;T TAKES A DI6]5T =M3 9 "O =M X IS 3T9U\S DEMON/R,N1 9 ! O!R DEF9I;N4 ,AG1 ?"U C 2 DEF9$ Z NOISE 9 ! CL\DS1 : IS ! 3CLU.N ( ! DEMON/R,N EMBODY+ ESS5TIAL NATURE4 ,ON ! O!R H& ! DEF9I;N ( IMMS IS AN 9DEMON/RA# POSIT+ ( ESS5TIAL NATURE4 ,WE 3CLUDE !N T DEF9I;N IS 7A7 AN 9DEMON/RA# /ATE;T ( ESS5TIAL NATURE1 OR 7B7 A SYLLOGISM ( ESS5TIAL NATURE DI6]+ F DEMON/R,N 9 GRAMMATICAL =M1 OR 7C7 ! 3CLU.N (A DEMON/R,N GIV+ ESS5TIAL NATURE4 ,\R 4CUS.N HAS "!=E MADE PLA9 7#A7 9 :AT S5SE &( :AT ?+S ! ESS5TIAL NATURE IS DEMON/RA#1 & 9 :AT S5SE &( :AT ?+S X IS N2 7#B7 :AT >E ! V>I\S M1N+S (! T]M DEF9I;N1 & 9 :AT S5SE &( :AT ?+S X PROVES ! ESS5TIAL NATURE1 & 9 :AT S5SE & ( :AT ?+S X DOES N2 7#C7 :AT IS ! REL,N ( DEF9I;N 6DEMON/R,N1 & H[ F> ! SAME ?+ IS BO? DEF9A# & DEMON/RA# & H[ F> X IS N4 #AA ,WE ?9K WE H SCI5TIFIC K :5 WE "K ! CAUSE1 & "! >E F\R CAUSES3 7#A7 ! DEF9A# =M1 7#B7 AN ANTEC$5T : NECESSITATES A 3SEQU5T1 7#C7 ! E6ICI5T CAUSE1 7#D7 ! F9AL CAUSE4 ,H;E EA* ( ^! C 2 ! MI4LE T]M (A PRO(1 = 7A7 ?\< ! 9F];E F ANTEC$5T 6NEC 3SEQU5T DOES N HOLD IF ONLY "O PREMISS IS ASSUM$-TWO IS ! M9IMUM-/ :5 "! >E TWO X HOLDS ON 3DI;N T !Y H A S+LE -MON MI4LE T]M4 ,S X IS F ! ASSUMP;N ( ? S+LE MI4LE T]M T ! 3CLU.N FOLL[S NECESS>ILY4 ,! FOLL[+ EXAMPLE W AL %[ ?4 ,:Y IS ! ANGLE 9 A SEMICIRCLE A "R ANGLE8-OR F :AT ASSUMP;N DOES X FOLL[ T X IS A "R ANGLE8 ,?US1 LET ,A 2 "R ANGLE1 ;,B ! HALF ( TWO "R ANGLES1 ;,C ! ANGLE 9 A SEMICIRCLE4 ,!N ;,B IS ! CAUSE 9 VIRTUE ( : ;,A1 "R ANGLE1 IS ATTRIBUTA# TO ;,C1 ! ANGLE 9 A SEMICIRCLE1 S9CE ;,B .K ;,A &! O!R1 VIZ4 ;,C1 .K ;,B1 = ;,C IS HALF ( TWO "R ANGLES4 ,"!=E X IS ! ASSUMP;N ( ;,B1 ! HALF ( TWO "R ANGLES1 F : X FOLL[S T ,A IS ATTRIBUTA# TO ;,C1 I4E4 T ! ANGLE 9 A SEMICIRCLE IS A "R ANGLE4 ,MOREOV]1 ;,B IS ID5TICAL ) 7B7 ! DEF9+ =M ( ;,A1 S9CE X IS :AT ;,A'S DEF9I;N SIGNIFIES4 ,MOREOV]1 ! =MAL CAUSE HAS ALR BE5 %[N 6BE ! MI4LE4 7C7 ,8,:Y DID ! ,A!NIANS 2COME 9VOLV$ 9 ! ,P]SIAN W>80' M1NS ,8,:AT CAUSE ORIG9AT$ ! WAG+ ( W> AG/ ! ,A!NIANS80' &! ANSW] IS1 ,8,2C !Y RAID$ ,S>DIS )! ,]ETRIANS0'1 S9CE ? ORIG9AT$ ! W>4 ,LET ,A 2 W>1 ;,B UNPROVOK$ RAID+1 ;,C ! ,A!NIANS4 ,!N ;,B1 UNPROVOK$ RAID+1 IS TRUE ( ;,C1 ! ,A!NIANS1 & ,A IS TRUE ( ;,B1 S9CE M5 MAKE W> ON ! UNJU/ A7RESSOR4 ,S ;,A1 HAV+ W> WAG$ ^U !M1 IS TRUE ( ;,B1 ! 9ITIAL A7RESSORS1 & ;,B IS TRUE ( ;,C1 ! ,A!NIANS1 :O 7 ! A7RESSORS4 ,H;E "H TOO ! CAUSE-IN ? CASE ! E6ICI5T CAUSE-IS ! MI4LE T]M4 7D7 ,? IS NO LESS TRUE ": ! CAUSE IS ! F9AL CAUSE4 ,E4G4 :Y DOES "O TAKE A WALK AF SUPP]8 ,=! SAKE ( "O'S H1L?4 ,:Y DOES A H\SE EXI/8 ,=! PRES]V,N ( "O'S GDS4 ,! 5D 9 VIEW IS 9 ! "O CASE H1L?1 9 ! O!R PRES]V,N4 ,6ASK ! R1SON :Y "O M/ WALK AF SUPP] IS PRECISELY 6ASK 6:AT 5D "O M/ D X4 ,LET ;,C 2 WALK+ AF SUPP]1 ;,B ! NON- REGURGIT,N ( FOOD1 ,A H1L?4 ,!N LET WALK+ AF SUPP] POSSESS ! PROP]TY ( PREV5T+ FOOD F RIS+ 6! ORIFICE (! /OMA*1 & LET ? 3DI;N 2 H1L?Y2 S9CE X SEEMS T ;,B1 ! NON-REGURGIT,N ( FOOD1 IS ATTRIBUTA# TO ;,C1 TAK+ A WALK1 & T ;,A1 H1L?1 IS ATTRIBUTA# TO ;,B4 ,:AT1 !N1 IS ! CAUSE "? : ;,A1 ! F9AL CAUSE1 9"HS 9 ;,C8 ,X IS ;,B1 ! NON-REGURGIT,N ( FOOD2 B ;,B IS A K9D ( DEF9I;N ( ;,A1 = ,A W 2 EXPLA9$ 0X4 ,:Y IS ;,B ! CAUSE ( ;,A'S 2L;G+ TO ;,C8 ,2C 6BE 9 A 3DI;N S* Z ;,B IS 6BE 9 H1L?4 ,! DEF9I;NS M/ 2 TRANSPOS$1 & !N ! DETAIL W 2COME CLE>]4 ,9CID5T,Y1 "H ! ORD] ( -+ 6BE IS ! REV]SE ( :AT X IS 9 PRO( "? ! E6ICI5T CAUSE3 9 ! E6ICI5T ORD] ! MI4LE T]M M/ -E 6BE F/1 ":AS 9 ! TELEOLOGICAL ORD] ! M9OR1 ;,C1 M/ F/ TAKE PLACE1 &! 5D 9 VIEW -ES LA/ 9 "T4 ,! SAME ?+ MAY EXI/ = AN 5D & 2 NECESSITAT$ Z WELL4 ,= EXAMPLE1 LIILY PASSES "? PORES L>G] ?AN ^? "PICLES- ASSUM+ T LI NECESS>ILY PRODUC$ 0! QU5*+ ( FIRE1 & AL DESIGN$1 Z ! ,PY?AGOR1NS SAY1 =A ?R1T 6T]RIFY ^? T LIE 9 ,T>T>US8 ,9DE$1 "! >E V _M S* CASES1 MO/LY AM;G ! PROCESSES & PRODUCTS (! NATURAL _W2 = NATURE1 9 DI6]5T S5SES (! T]M ,8NATURE0'1 PRODUCES N[ = AN 5D1 N[ 0NECESS;Y4 ,NECESS;Y TOO IS ( TWO K9DS4 ,X MAY "W 9 A3ORD.E )A ?+'S NATURAL T5D5CY1 OR 03/RA9T & 9 OPPOSI;N 6X2 Z1 = 9/.E1 0NECESS;Y A /"O IS BORNE BO? UPW>DS & D[NW>DS1 B N 0! SAME NECESS;Y4 ,(! PRODUCTS ( MAN'S 9TELLIG;E "S >E N"E DUE 6*.E OR NECESS;Y B ALW 6AN 5D1 Z = EXAMPLE A H\SE OR A /ATUE2 O!RS1 S* Z H1L? OR SAFETY1 MAY RESULT F *.E Z WELL4 ,X IS MO/LY 9 CASES ": ! ISSUE IS 9DET]M9ATE 7?\< ONLY ": ! PRODUC;N DOES N ORIG9ATE 9 *.E1 &! 5D IS 3SEQU5TLY GD71 T A RESULT IS DUE 6AN 5D1 & ? IS TRUE ALIKE 9 NATURE OR 9 >T4 ,0*.E1 ON ! O!R H&1 NO?+ -ES 6BE = AN 5D4 #AB ,! E6ECT MAY 2 / -+ 6BE1 OR XS O3URR;E MAY 2 PA/ OR FUTURE1 YET ! CAUSE W 2 ! SAME Z :5 X IS ACTU,Y EXI/5T-= X IS ! MI4LE : IS ! CAUSE-EXCEPT T IF ! E6ECT ACTU,Y EXI/S ! CAUSE IS ACTU,Y EXI/5T1 IF X IS -+ 6BE S IS ! CAUSE1 IF XS O3URR;E IS PA/ ! CAUSE IS PA/1 IF FUTURE ! CAUSE IS FUTURE4 ,= EXAMPLE1 ! MOON 0 ECLIPS$ 2C ! E>? 9T]V5$1 IS 2COM+ ECLIPS$ 2C ! E>? IS 9 PROCESS ( 9T]V5+1 W 2 ECLIPS$ 2C ! E>? W 9T]V5E1 IS ECLIPS$ 2C ! E>? 9T]V5ES4 ,6TAKE A SECOND EXAMPLE3 ASSUM+ T ! DEF9I;N ( ICE IS SOLIDIFI$ WAT]1 LET ;,C 2 WAT]1 ,A SOLIDIFI$1 ;,B ! MI4LE1 : IS ! CAUSE1 "NLY TOTAL FAILURE ( H1T4 ,!N ;,B IS ATTRIBUT$ TO ;,C1 & ;,A1 SOLIDIFIC,N1 TO ;,B3 ICE :5 ;,B IS O3URR+1 HAS =M$ :5 ;,B HAS O3URR$1 & W =M :5 ;,B % O3UR4 ,? SORT ( CAUSE1 !N1 & XS E6ECT -E 6BE SIMULTANE\SLY :5 !Y >E 9 PROCESS ( 2COM+1 & EXI/ SIMULTANE\SLY :5 !Y ACTU,Y EXI/2 &! SAME HOLDS GD :5 !Y >E PA/ & :5 !Y >E FUTURE4 ,B :AT ( CASES ": !Y >E N SIMULTANE\S8 ,C CAUSES & E6ECTS DI6]5T F "O ANO!R =M1 Z !Y SEEM 6U 6=M1 A 3T9U\S SU3ES.N1 A PA/ E6ECT RESULT+ F A PA/ CAUSE DI6]5T F XF1 A FUTURE E6ECT F A FUTURE CAUSE DI6]5T F X1 & AN E6ECT : IS -+-TO-BE F A CAUSE DI6]5T F & PRIOR 6X8 ,N[ ON ? !ORY X IS F ! PO/]IOR EV5T T WE R1SON 7& ? ?\< ^! LAT] EV5TS ACTU,Y H _! S\RCE ( ORIG9 9 PREVI\S EV5TS--A FACT : %[S T AL :5 ! E6ECT IS -+-TO-BE WE / R1SON F ! PO/]IOR EV5T71 & F ! EV5T WE _C R1SON 7WE _C >GUE T 2C AN EV5T ,A HAS O3URR$1 "!=E AN EV5T ;,B HAS O3URR$ SUBSEQU5TLY TO ;,A B / 9 ! PA/-&! SAME HOLDS GD IF ! O3URR;E IS FUTURE7-_C R1SON 2C1 2 ! "T 9T]VAL DEF9ITE OR 9DEF9ITE1 X W N"E 2 POSSI# 69F] T 2C X IS TRUE 6SAY T ,A O3URR$1 "!=E X IS TRUE 6SAY T ;,B1 ! SUBSEQU5T EV5T1 O3URR$2 = 9 ! 9T]VAL 2T ! EV5TS1 ?\< ,A HAS ALR O3URR$1 ! LATT] /ATE;T W 2 FALSE4 ,&! SAME >GU;T APPLIES AL 6FUTURE EV5TS2 I4E4 "O _C 9F] F AN EV5T : O3URR$ 9 ! PA/ T A FUTURE EV5T W O3UR4 ,! R1SON ( ? IS T ! MI4LE M/ 2 HOMOG5E\S1 PA/ :5 ! EXTREMES >E PA/1 FUTURE :5 !Y >E FUTURE1 -+ 6BE :5 !Y >E -+-TO-BE1 ACTU,Y EXI/5T :5 !Y >E ACTU,Y EXI/5T2 & "! _C 2 A MI4LE T]M HOMOG5E\S ) EXTREMES RESPECTIVELY PA/ & FUTURE4 ,& X IS A FUR!R DI6ICULTY 9 ? !ORY T ! "T 9T]VAL C 2 NEI 9DEF9ITE NOR DEF9ITE1 S9CE DUR+ X ! 9F];E W 2 FALSE4 ,WE H AL 69QUIRE :AT X IS T HOLDS EV5TS TGR S T ! -+-TO-BE N[ O3URR+ 9 ACTUAL ?+S FOLL[S ^U A PA/ EV5T4 ,X IS EVID5T1 WE MAY SU7E/1 T A PA/ EV5T &A PRES5T PROCESS _C 2 ,83TIGU\S0'1 = N EV5 TWO PA/ EV5TS C 2 ,83TIGU\S0'4 ,= PA/ EV5TS >E LIMITS & ATOMIC2 S J Z PO9TS >E N ,83TIGU\S0' NEI >E PA/ EV5TS1 S9CE BO? >E 9DIVISI#4 ,=! SAME R1SON A PA/ EV5T &A PRES5T PROCESS _C 2 ,83TIGU\S0'1 =! PROCESS IS DIVISI#1 ! EV5T 9DIVISI#4 ,?US ! REL,N ( PRES5T PROCESS 6PA/ EV5T IS ANALOG\S 6T ( L9E 6PO9T1 S9CE A PROCESS 3TA9S AN 9F9;Y ( PA/ EV5TS4 ,^! "QS1 H["E1 M/ RCV A M EXPLICIT TR1T;T 9 \R G5]AL !ORY ( *ANGE4 ,! FOLL[+ M/ SU6ICE Z AN A3.T (! MANN] 9 : ! MI4LE WD 2 ID5TICAL )! CAUSE ON ! SUPPOSI;N T -+-TO-BE IS A S]IES ( 3SECUTIVE EV5TS3 = 9 ! T]MS ( S* A S]IES TOO ! MI4LE & MAJOR T]MS M/ =M AN IMM PREMISS2 E4G4 WE >GUE T1 S9CE ;,C HAS O3URR$1 "!=E ,A O3URR$3 & ;,C'S O3URR;E 0 PO/]IOR1 ;,A'S PRIOR2 B ;,C IS ! S\RCE (! 9F];E 2C X IS NE>] 6! PRES5T MO;T1 &! />T+-PO9T ( "T IS ! PRES5T4 ,WE NEXT >GUE T1 S9CE ;,D HAS O3URR$1 "!=E ;,C O3URR$4 ,!N WE 3CLUDE T1 S9CE ;,D HAS O3URR$1 "!=E ,A M/ H O3URR$2 &! CAUSE IS ;,C1 = S9CE ;,D HAS O3URR$ ;,C M/ H O3URR$1 & S9CE ;,C HAS O3URR$ ,A M/ PREVI\SLY H O3URR$4 ,IF WE GET \R MI4LE T]M 9 ? WAY1 W ! S]IES T]M9ATE 9 AN IMM PREMISS1 OR S9CE1 Z WE SD1 NO TWO EV5TS >E ,83TIGU\S0'1 W A FRE% MI4LE T]M ALW 9T]V5E 2C "! IS AN 9F9;Y ( MI4LES8 ,NO3 ?\< NO TWO EV5TS >E ,83TIGU\S0'1 YET WE M/ />T F A PREMISS 3SI/+ (A MI4LE &! PRES5T EV5T Z MAJOR4 ,! L IS TRUE ( FUTURE EV5TS TOO1 S9CE IF X IS TRUE 6SAY T ;,D W EXI/1 X M/ 2 A PRIOR TRU? 6SAY T ,A W EXI/1 &! CAUSE ( ? 3CLU.N IS ;,C2 = IF ;,D W EXI/1 ;,C W EXI/ PRIOR TO ;,D1 & IF ;,C W EXI/1 ,A W EXI/ PRIOR 6X4 ,& "H TOO ! SAME 9F9ITE DIVISIBIL;Y MIE N ,83TIGU\S0'4 ,B "H TOO AN IMM BASIC PREMISS M/ 2 ASSUM$4 ,& 9 ! _W ( FACT ? IS S3 IF A H\SE HAS BE5 BUILT1 !N BLOCKS M/ H BE5 QU>RI$ & %AP$4 ,! R1SON IS T A H\SE HAV+ BE5 BUILT NECESSITATES A F.D,N HAV+ BE5 LAID1 & IF A F.D,N HAS BE5 LAID BLOCKS M/ H BE5 %AP$ 2FH&4 ,AG1 IF A H\SE W 2 BUILT1 BLOCKS W SIMIL>LY 2 %AP$ 2FH&2 & PRO( IS "? ! MI4LE 9 ! SAME WAY1 =! F.D,N W EXI/ 2F ! H\SE4 ,N[ WE OBS]VE 9 ,NATURE A C]TA9 K9D ( CIRCUL> PROCESS ( -+-TO-BE2 & ? IS POSSI# ONLY IF ! MI4LE & EXTREME T]MS >E RECIPROCAL1 S9CE 3V].N IS 3DI;N$ 0RECIPROC;Y 9 ! T]MS (! PRO(4 ,?-! 3V]TIBIL;Y ( 3CLU.NS & PREMISSES-HAS BE5 PROV$ 9 \R E>LY *APT]S1 &! CIRCUL> PROCESS IS AN 9/.E ( ?4 ,9 ACTUAL FACT X IS EXEMPLIFI$ ?US3 :5 ! E>? _H BE5 MOI/5$ AN EXHAL,N 0 B.D 6RISE1 & :5 AN EXHAL,N _H RIS5 CL\D 0 B.D 6=M1 & F ! =M,N ( CL\D RA9 NECESS>ILY RESULT$ & 0! FALL ( RA9 ! E>? 0 NECESS>ILY MOI/5$3 B ? 0 ! />T+-PO9T1 S T A CIRCLE IS -PLET$2 = POSIT ANY "O (! T]MS & ANO!R FOLL[S F X1 & F T ANO!R1 & F T AG ! F/4 ,"S O3URR;ES >E UNIV]SAL 7= !Y >E1 OR -E-TO-BE :AT !Y >E1 ALW & 9 "E CASE72 O!RS AG >E N ALW :AT !Y >E B ONLY Z A G5]AL RULE3 = 9/.E1 N E MAN C GR[ A BE>D1 B X IS ! G5]AL RULE4 ,9 ! CASE ( S* 3NEXIONS ! MI4LE T]M TOO M/ 2 A G5]AL RULE4 ,= IF ,A IS PR$ICAT$ UNIV]S,Y ( ;,B & ;,B ( ;,C1 ,A TOO M/ 2 PR$ICAT$ ALW & 9 E 9/.E ( ;,C1 S9CE 6HOLD 9 E 9/.E & ALW IS (! NATURE (! UNIV]SAL4 ,B WE H ASSUM$ A 3NEXION : IS A G5]AL RULE2 3SEQU5TLY ! MI4LE T]M ;,B M/ AL 2 A G5]AL RULE4 ,S 3NEXIONS : EMBODY A G5]AL RULE-I4E4 : EXI/ OR -E 6BE Z A G5]AL RULE-W AL DERIVE F IMM BASIC PREMISSES4 #AC ,WE H ALR EXPLA9$ H[ ESS5TIAL NATURE IS SET \ 9 ! T]MS (A DEMON/R,N1 &! S5SE 9 : X IS OR IS N DEMON/RA# OR DEF9A#2 S LET U N[ 4CUSS ! ME?OD 6BE ADOPT$ 9 TRAC+ ! ELE;TS PR$ICAT$ Z 3/ITUT+ ! DEF9A# =M4 ,N[ (! ATTRIBUTES : 9"H ALW 9 EA* S"EAL ?+ "! >E "S : >E WID] 9 EXT5T ?AN X B N WID] ?AN XS G5US 70ATTRIBUTES ( WID] EXT5T M1N ALL S* Z >E UNIV]SAL ATTRIBUTES ( EA* S"EAL SUBJECT1 B 9 _! APPLIC,N >E N 3F9$ 6T SUBJECT74 :ILE AN ATTRIBUTE MAY 9"H 9 E TRIAD1 YET AL 9 A SUBJECT N A TRIAD-Z 2+ 9"HS 9 TRIAD B AL 9 SUBJECTS N NUMB]S AT ALL-ODD ON ! O!R H& IS AN ATTRIBUTE 9H]+ 9 E TRIAD &( WID] APPLIC,N 79H]+ Z X DOES AL 9 P5TAD71 B : DOES N EXT5D 2Y ! G5US ( TRIAD2 = P5TAD IS A NUMB]1 B NO?+ \TSIDE NUMB] IS ODD4 ,X IS S* ATTRIBUTES : WE H 6SELECT1 UP 6! EXACT PO9T AT : !Y >E S"E,Y ( WID] EXT5T ?AN ! SUBJECT B COLLECTIVELY COEXT5SIVE ) X2 = ? SYN!SIS M/ 2 ! SUB/.E (! ?+4 ,= EXAMPLE E TRIAD POSSESSES ! ATTRIBUTES NUMB]1 ODD1 & PRIME 9 BO? S5SES1 I4E4 N ONLY Z POSSESS+ NO DIVISORS1 B AL Z N 2+ A SUM ( NUMB]S4 ,?1 !N1 IS PRECISELY :AT TRIAD IS1 VIZ4 A NUMB]1 ODD1 & PRIME 9 ! =M] & AL ! LATT] S5SE (! T]M3 = ^! ATTRIBUTES TAK5 S"E,Y APPLY1 ! F/ TWO 6ALL ODD NUMB]S1 ! LA/ 6! DYAD AL Z WELL Z 6! TRIAD1 B1 TAK5 COLLECTIVELY1 6NO O!R SUBJECT4 ,N[ S9CE WE H %[N ABV0' T ATTRIBUTES PR$ICAT$ Z 2L;G+ 6! ESS5TIAL NATURE >E NEC & T UNIV]SALS >E NEC1 & S9CE ! ATTRIBUTES : WE SELECT Z 9H]+ 9 TRIAD1 OR 9 ANY O!R SUBJECT ^: ATTRIBUTES WE SELECT 9 ? WAY1 >E PR$ICAT$ Z 2L;G+ 6XS ESS5TIAL NATURE1 TRIAD W ?US POSSESS ^! ATTRIBUTES NECESS>ILY4 ,FUR!R1 T ! SYN!SIS ( !M 3/ITUTES ! SUB/.E ( TRIAD IS %[N 0! FOLL[+ >GU;T4 ,IF X IS N ID5TICAL )! 2+ ( TRIAD1 X M/ 2 RELAT$ 6TRIAD Z A G5US "ND OR "N.S4 ,X W !N 2 ( WID] EXT5T ?AN TRIAD-ASSUM+ T WID] POT5TIAL EXT5T IS ! "* (A G5US4 ,IF ON ! O!R H& ? SYN!SIS IS APPLICA# 6NO SUBJECT O!R ?AN ! 9DIVIDUAL TRIADS1 X W 2 ID5TICAL )! 2+ ( TRIAD1 2C WE MAKE ! FUR!R ASSUMP;N T ! SUB/.E ( EA* SUBJECT IS ! PR$IC,N ( ELE;TS 9 XS ESS5TIAL NATURE D[N 6! LA/ DI6]5TIA "*IZ+ ! 9DIVIDUALS4 ,X FOLL[S T ANY O!R SYN!SIS ?US EXHIBIT$ W LIKEWISE 2 ID5TICAL )! 2+ (! SUBJECT4 ,! AU?OR (A H&-BOOK ON A SUBJECT T IS A G5]IC :OLE %D DIVIDE ! G5US 96XS F/ 9FIMAE SPECIES-NUMB] E4G4 96TRIAD & DYAD-& !N 5D1V\R 6SEIZE _! DEF9I;NS 0! ME?OD WE H DESCRIB$-! DEF9I;N1 = EXAMPLE1 ( /RAI0' 6! SPECIES1 "W+ "? ! PROXIMATE -MON DI6]5TIAE4 ,HE %D PROCE$ ?US 2C ! ATTRIBUTES (! G5]A -P.D$ (! 9FIMAE SPECIES W 2 CLE>LY GIV5 0! DEF9I;NS (! SPECIES2 S9CE ! BASIC ELE;T ( !M ALL IS ! DEF9I;N1 I4E4 ! SIMPLE 9FIRMA SPECIES1 &! ATTRIBUTES 9"H ESS5TI,Y 9 ! SIMPLE 9FIMAE SPECIES1 9 ! G5]A ONLY 9 VIRTUE ( ^!4 ,DIVI.NS AC 6DI6]5TIAE >E A USE;L A3ESSORY 6? ME?OD4 ,:AT =CE !Y H Z PRO(S WE DID1 9DE$1 EXPLA9 ABV1 B T M]ELY T[>DS COLLECT+ ! ESS5TIAL NATURE !Y MAY 2 ( USE WE W PROCE$ 6%[4 ,!Y MIT & 6BE NO BETT] ?AN AN 9ITIAL ASSUMP;N MADE )\T DIVI.N4 ,B1 9 FACT1 ! ORD] 9 : ! ATTRIBUTES >E PR$ICAT$ DOES MAKE A DI6];E--X MATT]S :E!R WE SAY ANIMAL-TAME-BIP$1 OR BIP$- ANIMAL-TAME4 ,= IF E DEF9A# ?+ 3SI/S ( TWO ELE;TS & ,8ANIMAL-TAME0' =MS A UN;Y1 & AG \ ( ? &! FUR!R DI6]5TIA MAN 7OR :AT"E ELSE IS ! UN;Y "U 3/RUC;N7 IS 3/ITUT$1 !N ! ELE;TS WE ASSUME H NECESS>ILY BE5 R1*$ 0DIVI.N4 ,AG1 DIVI.N IS ! ONLY POSSI# ME?OD ( AVOID+ ! OMIS.N ( ANY ELE;T (! ESS5TIAL NATURE4 ,?US1 IF ! PRIM>Y G5US IS ASSUM$ & WE !N TAKE "O (! L[] DIVI.NS1 ! DIVID5DUM W N FALL :OLE 96? DIVI.N3 E4G4 X IS N ALL ANIMAL : IS EI :OLE-W+$ OR SPLIT-W+$ B ALL W+$ ANIMAL1 = X IS W+$ ANIMAL 6: ? DI6]5TI,N 2L;GS4 ,! PRIM>Y DI6]5TI,N ( ANIMAL IS T )9 : ALL ANIMAL FALLS4 ,! L IS TRUE ( E O!R G5US1 :E!R \TSIDE ANIMAL OR A SUBALT]N G5US ( ANIMAL2 E4G4 ! PRIM>Y DI6]5TI,N ( BIRD IS T )9 : FALLS E BIRD1 ( FI% T )9 : FALLS E FI%4 ,S1 IF WE PROCE$ 9 ? WAY1 WE C 2 SURE T NO?+ HAS BE5 OMITT$3 0ANY O!R ME?OD "O IS B.D 6OMIT "S?+ )\T "K+ X4 ,6DEF9E & DIVIDE "O NE$ N "K ! :OLE ( EXI/;E4 ,YET "S HOLD X IMPOSSI# 6"K ! DI6]5TIAE 4T+UI%+ EA* ?+ F E S+LE O!R ?+ )\T "K+ E S+LE O!R ?+2 & "O _C1 !Y SAY1 "K EA* ?+ )\T "K+ XS DI6]5TIAE1 S9CE "EY?+ IS ID5TICAL ) T F : X DOES N DI6]1 & O!R ?AN T F : X DI6]S4 ,N[ F/ ( ALL ? IS A FALLACY3 N E DI6]5TIA PRECLUDES ID5T;Y1 S9CE _M DI6]5TIAE 9"H 9 ?+S SPECIFIC,Y ID5TICAL1 ?\< N 9 ! SUB/.E ( ^! NOR ESS5TI,Y4 ,SECONDLY1 :5 "O HAS TAK5 "O'S DI6]+ PAIR ( OPPOSITES & ASSUM$ T ! TWO SIDES EXHAU/ ! G5US1 & T ! SUBJECT "O SEEKS 6DEF9E IS PRES5T 9 "O OR O!R ( !M1 & "O HAS FUR!R V]IFI$ XS PRES;E 9 "O ( !M2 !N X DOES N MATT] :E!R OR N "O "KS ALL ! O!R SUBJECTS ( : ! DI6]5TIAE >E AL PR$ICAT$4 ,= X IS OBVI\S T :5 0? PROCESS "O R1*ES SUBJECTS 9CAPA# ( FUR!R DI6]5TI,N "O W POSSESS ! =MULA DEF9+ ! SUB/.E4 ,MOREOV]1 6PO/ULATE T ! DIVI.N EXHAU/S ! G5US IS N ILLEGITIMATE IF ! OPPOSITES EXCLUDE A MI4LE2 S9CE IF X IS ! DI6]5TIA ( T G5US1 ANY?+ 3TA9$ 9 ! G5US M/ LIE ON "O (! TWO SIDES4 ,9 E/ABLI%+ A DEF9I;N 0DIVI.N "O %D KEEP ?REE OBJECTS 9 VIEW3 7#A7 ! ADMIS.N ONLY ( ELE;TS 9 ! DEF9A# =M1 7#B7 ! >RANGE;T ( ^! 9 ! "R ORD]1 7#C7 ! OMIS.N ( NO S* ELE;TS4 ,! F/ IS F1SI# 2C "O C E/ABLI% G5US & DI6]5TIA "? ! TOPIC (! G5US1 J Z "O C 3CLUDE ! 9H];E ( AN A3ID5T "? ! TOPIC (! A3ID5T4 ,! "R ORD] W 2 A*IEV$ IF ! "R T]M IS ASSUM$ Z PRIM>Y1 & ? W 2 5SUR$ IF ! T]M SELECT$ IS PR$ICA# ( ALL ! O!RS B N ALL !Y ( X2 S9CE "! M/ 2 "O S* T]M4 ,HAV+ ASSUM$ ? WE AT ONCE PROCE$ 9 ! SAME WAY )! L[] T]MS2 = \R SECOND T]M W 2 ! F/ (! REMA9D]1 \R ?IRD ! F/ ( ^? : FOLL[ ! SECOND 9 A ,83TIGU\S0' S]IES1 S9CE :5 ! HI<] T]M IS EXCLUD$1 T T]M (! REMA9D] : IS ,83TIGU\S0' 6X W 2 PRIM>Y1 & S ON4 ,\R PROC$URE MAKES X CLE> T NO ELE;TS 9 ! DEF9A# =M H BE5 OMITT$3 WE H TAK5 ! DI6]5TIA T -ES F/ 9 ! ORD] ( DIVI.N1 PO9T+ \ T ANIMAL1 E4G4 IS DIVISI# EXHAU/IVELY 9TO ;,A & ;,B1 & T ! SUBJECT A3EPTS "O (! TWO Z XS PR$ICATE4 ,NEXT WE H TAK5 ! DI6]5TIA (! :OLE ?US R1*$1 & %[N T ! :OLE WE F9,Y R1* IS N FUR!R DIVISI#-I4E4 T Z SOON Z WE H TAK5 ! LA/ DI6]5TIA 6=M ! 3CRETE TOTAL;Y1 ? TOTAL;Y ADMITS ( NO DIVI.N 96SPECIES4 ,= X IS CLE> T "! IS NO SUP]FLU\S A4I;N1 S9CE ALL ^! T]MS WE H SELECT$ >E ELE;TS 9 ! DEF9A# =M2 & NO?+ LACK+1 S9CE ANY OMIS.N WD H 6BE A G5US OR A DI6]5TIA4 ,N[ ! PRIM>Y T]M IS A G5US1 & ? T]M TAK5 9 3JUNC;N ) XS DI6]5TIAE IS A G5US3 MOREOV] ! DI6]5TIAE >E ALL 9CLUD$1 2C "! IS N[ NO FUR!R DI6]5TIA2 IF "! W]E1 ! F9AL 3CRETE WD ADMIT ( DIVI.N 96SPECIES1 :1 WE SD1 IS N ! CASE4 ,6RESUME \R A3.T (! "R ME?OD ( 9VE/IG,N3 ,WE M/ />T 0OBS]V+ A SET ( SIMIL>-I4E4 SPECIFIC,Y ID5TICAL- 9DIVIDUALS1 & 3SID] :AT ELE;T !Y H 9 -MON4 ,WE M/ !N APPLY ! SAME PROCESS 6ANO!R SET ( 9DIVIDUALS : 2L;G 6"O SPECIES & >E G5]IC,Y B N SPECIFIC,Y ID5TICAL )! =M] SET4 ,:5 WE H E/ABLI%$ :AT ! -MON ELE;T IS 9 ALL MEMB]S ( ? SECOND SPECIES1 & LIKEWISE 9 MEMB]S ( FUR!R SPECIES1 WE %D AG 3SID] :E!R ! RESULTS E/ABLI%$ POSSESS ANY ID5T;Y1 & P]SEV]E UNTIL WE R1* A S+LE =MULA1 S9CE ? W 2 ! DEF9I;N (! ?+4 ,B IF WE R1* N "O =MULA B TWO OR M1 EVID5TLY ! DEF9I5DUM _C 2 "O ?+ B M/ 2 M ?AN "O4 ,I MAY ILLU/RATE MY M1N+ Z FOLL[S4 ,IF WE 7 9QUIR+ :AT ! ESS5TIAL NATURE ( PRIDE IS1 WE %D EXAM9E 9/.ES ( PR\D M5 WE "K ( 6SEE :AT1 Z S*1 !Y H 9 -MON2 E4G4 IF ,ALCIBIADES 0 PR\D1 OR ,A*ILLES & ,AJAX 7 PR\D1 WE %D F9D ON 9QUIR+ :AT !Y ALL _H 9 -MON1 T X 0 9TOL].E ( 9SULT2 X 0 ? : DROVE ,ALCIBIADES 6W>1 ,A*ILLES WRA?1 & ,AJAX 6SUICIDE4 ,WE %D NEXT EXAM9E O!R CASES1 ,LYS&]1 = EXAMPLE1 OR ,SOCRATES1 & !N IF ^! H 9 -MON 9DI6];E ALIKE 6GD & ILL =TUNE1 ,I TAKE ^! TWO RESULTS & 9QUIRE :AT -MON ELE;T H EQUANIM;Y AMID ! VICISSITUDES ( LIFE & IMPATI;E ( 4HON\R4 ,IF !Y H N"O1 "! W 2 TWO G5]A ( PRIDE4 ,2SS1 E DEF9I;N IS ALW UNIV]SAL & -M5SURATE3 ! PHYSICIAN DOES N PRESCRIBE :AT IS H1L?Y =A S+LE EYE1 B = ALL EYES OR =A DET]M9ATE SPECIES ( EYE4 ,X IS AL EASI] 0? ME?OD 6DEF9E ! S+LE SPECIES ?AN ! UNIV]SAL1 & T IS :Y \R PROC$URE %D 2 F ! S"EAL SPECIES 6! UNIV]SAL G5]A-? =! FUR!R R1SON TOO T EQUIVOC,N IS LESS R1DILY DETECT$ 9 G5]A ?AN 9 9FIMAE SPECIES4 ,9DE$1 P]SPICU;Y IS ESS5TIAL 9 DEF9I;NS1 J Z 9F]5TIAL MOVE;T IS ! M9IMUM REQUIR$ 9 DEMON/R,NS2 & WE % ATTA9 P]SPICU;Y IF WE C COLLECT SEP>ATELY ! DEF9I;N ( EA* SPECIES "? ! GR\P ( S+UL>S : WE H E/ABLI%$ E4G4 ! DEF9I;N ( SIMIL>;Y N UNQUALIFI$ B RE/RICT$ 6COL\RS & 6FIGURES2 ! DEF9I;N ( ACUTE;S1 B ONLY ( S.D-& S PROCE$ 6! -MON UNIV]SAL )A C>E;L AVOID.E ( EQUIVOC,N4 ,WE MAY ADD T IF DIALECTICAL 4PUT,N M/ N EMPLOY METAPHORS1 CLE>LY METAPHORS & METAPHORICAL EXPRES.NS >E PRECLUD$ 9 DEF9I;N3 O!RWISE DIALECTIC WD 9VOLVE METAPHORS4 #AD ,9 ORD] 6=MULATE ! 3NEXIONS WE WI% 6PROVE WE H 6SELECT \R ANALYSES & DIVI.NS4 ,! ME?OD ( SELEC;N 3SI/S 9 LAY+ D[N ! -MON G5US ( ALL \R SUBJECTS ( 9VE/IG,N-IF E4G4 !Y >E ANIMALS1 WE LAY D[N :AT ! PROP]TIES >E : 9"H 9 E ANIMAL4 ,^! E/ABLI%$1 WE NEXT LAY D[N ! PROP]TIES ESS5TI,Y 3NECT$ )! F/ (! REMA9+ CLASSES-E4G4 IF ? F/ SUBG5US IS BIRD1 ! ESS5TIAL PROP]TIES ( E BIRD-& S ON1 ALW "*IZ+ ! PROXIMATE SUBG5US4 ,? W CLE>LY AT ONCE 5A# U 6SAY 9 VIRTUE ( :AT "* ! SUBG5]A-MAN1 E4G4 OR HORSE-POSSESS _! PROP]TIES4 ,LET ,A 2 ANIMAL1 ;,B ! PROP]TIES ( E ANIMAL1 ;,C ;,D ;,E V>I\S SPECIES ( ANIMAL4 ,!N X IS CLE> 9 VIRTUE ( :AT "* ;,B 9"HS 9 ;,D-"NLY ,A-& T X 9"HS 9 ;,C & ;,E =! SAME R1SON3 & "?\T ! REMA9+ SUBG5]A ALW ! SAME RULE APPLIES4 ,WE >E N[ TAK+ \R EXAMPLES F ! TRADI;NAL CLASS-"NS1 B WE M/ N 3F9E \RVS 63SID]+ ^!4 ,WE M/ COLLECT ANY O!R -MON "* : WE OBS]VE1 & !N 3SID] ) :AT SPECIES X IS 3NECT$ & :AT4PROP]TIES 2L;G 6X4 ,= EXAMPLE1 Z ! -MON PROP]TIES ( HORN$ ANIMALS WE COLLECT ! POSSES.N (A ?IRD /OMA* & ONLY "O R[ ( TEE?4 ,!N S9CE X IS CLE> 9 VIRTUE ( :AT "* !Y POSSESS ^! ATTRIBUTES-"NLY _! HORN$ "*-! NEXT "Q IS1 6:AT SPECIES DOES ! POSSES.N ( HORNS ATTA*8 ,YET A FUR!R ME?OD ( SELEC;N IS 0ANALOGY3 = WE _C F9D A S+LE ID5TICAL "N 6GIVE 6A SQUID'S P\NCE1 A FI%'S SP9E1 & AN ANIMAL'S B"O1 AL? ^! TOO POSSESS -MON PROP]TIES Z IF "! 7 A S+LE OSSE\S NATURE4 #AE ,"S 3NEXIONS T REQUIRE PRO( >E ID5TICAL 9 T !Y POSSESS AN ID5TICAL ,8MI4LE0' E4G4 A :OLE GR\P MIE ID5TICAL 9 G5US1 "NLY ALL ^? ^: DI6];E 3SI/S 9 _! 3C]N+ DI6]5T SUBJECTS OR 9 _! MODE ( MANIFE/,N4 ,? LATT] CLASS MAY 2 EXEMPLIFI$ 0! "QS Z 6! CAUSES RESPECTIVELY ( E*O1 ( REFLEC;N1 &(! RA9B[3 ! 3NEXIONS 6BE PROV$ : ^! "QS EMBODY >E ID5TICAL G5]IC,Y1 2C ALL ?REE >E =MS ( REP]CUS.N2 B SPECIFIC,Y !Y >E DI6]5T4 ,O!R 3NEXIONS T REQUIRE PRO( ONLY DI6] 9 T ! ,8MI4LE0' (! "O IS SUBORD9ATE 6! ,8MI4LE0' (! O!R4 ,= EXAMPLE3 ,:Y DOES ! ,NILE RISE T[>DS ! 5D (! MON?8 ,2C T[>DS XS CLOSE ! MON? IS M /ORMY4 ,:Y IS ! MON? M /ORMY T[>DS XS CLOSE8 ,2C ! MOON IS WAN+4 ,"H ! "O CAUSE IS SUBORD9ATE 6! O!R4 #AF ,! "Q MID 6CAUSE & E6ECT :E!R :5 ! E6ECT IS PRES5T ! CAUSE AL IS PRES5T2 :E!R1 = 9/.E1 IF A PLANT %$S XS L1VES OR ! MOON IS ECLIPS$1 "! IS PRES5T AL ! CAUSE (! ECLIPSE OR (! FALL (! L1VES-! POSSES.N ( BROAD L1VES1 LET U SAY1 9 ! LATT] CASE1 9 ! =M] ! E>?'S 9T]POSI;N4 ,=1 "O MIGUE1 IF ? CAUSE IS N PRES5T1 ^! PH5OM5A W H "S O!R CAUSE3 IF X IS PRES5T1 XS E6ECT W 2 AT ONCE IMPLI$ 0X-! ECLIPSE 0! E>?'S 9T]POSI;N1 ! FALL (! L1VES 0! POSSES.N ( BROAD L1VES2 B IF S1 !Y W 2 LOGIC,Y CO9CID5T & EA* CAPA# ( PRO( "? ! O!R4 ,LET ME ILLU/RATE3 ,LET ,A 2 DECIDU\S "*1 ;,B ! POSSES.N ( BROAD L1VES1 ;,C V9E4 ,N[ IF ,A 9"HS 9 ;,B 7= E BROAD- L1V$ PLANT IS DECIDU\S71 & ;,B 9 ;,C 7E V9E POSSESS+ BROAD L1VES72 !N ,A 9"HS 9 ;,C 7E V9E IS DECIDU\S71 &! MI4LE T]M ;,B IS ! CAUSE4 ,B WE C AL DEMON/RATE T ! V9E HAS BROAD L1VES 2C X IS DECIDU\S4 ,?US1 LET ;,D 2 BROAD-L1V$1 ;,E DECIDU\S1 ;,F V9E4 ,!N ;,E 9"HS 9 ;,F 7S9CE E V9E IS DECIDU\S71 & ;,D 9 ;,E 7= E DECIDU\S PLANT HAS BROAD L1VES73 "!=E E V9E HAS BROAD L1VES1 &! CAUSE IS XS DECIDU\S "*4 ,IF1 H["E1 !Y _C EA* 2 ! CAUSE (! O!R 7= CAUSE IS PRIOR 6E6ECT1 & ! E>?'S 9T]POSI;N IS ! CAUSE (! MOON'S ECLIPSE & N ! ECLIPSE (! 9T]POSI;N7-IF1 !N1 DEMON/R,N "? ! CAUSE IS (! R1SON$ FACT & DEMON/R,N N "? ! CAUSE IS (! B>E FACT1 "O :O "KS X "? ! ECLIPSE "KS ! FACT (! E>?'S 9T]POSI;N B N ! R1SON$ FACT4 ,MOREOV]1 T ! ECLIPSE IS N ! CAUSE (! 9T]POSI;N1 B ! 9T]POSI;N (! ECLIPSE1 IS OBVI\S 2C ! 9T]POSI;N IS AN ELE;T 9 ! DEF9I;N ( ECLIPSE1 : %[S T ! ECLIPSE IS "KN "? ! 9T]POSI;N & N VICE V]SA4 ,ON ! O!R H&1 C A S+LE E6ECT H M ?AN "O CAUSE8 ,"O MIGUE Z FOLL[S3 IF ! SAME ATTRIBUTE IS PR$ICA# ( M ?AN "O ?+ Z XS PRIM>Y SUBJECT1 LET ;,B 2 A PRIM>Y SUBJECT 9 : ,A 9"HS1 & ;,C ANO!R PRIM>Y SUBJECT ( ;,A1 & ;,D & ;,E PRIM>Y SUBJECTS ( ;,B & ;,C RESPECTIVELY4 ,A W !N 9"H 9 ;,D & ;,E1 & ;,B W 2 ! CAUSE ( ;,A'S 9H];E 9 ;,D1 ;,C ( ;,A'S 9H];E 9 ,E4 ,! PRES;E (! CAUSE ?US NECESSITATES T (! E6ECT1 B ! PRES;E (! E6ECT NECESSITATES ! PRES;E N ( ALL T MAY CAUSE X B ONLY (A CAUSE : YET NE$ N 2 ! :OLE CAUSE4 ,WE MAY1 H["E1 SU7E/ T IF ! 3NEXION 6BE PROV$ IS ALW UNIV]SAL & -M5SURATE1 N ONLY W ! CAUSE 2 A :OLE B AL ! E6ECT W 2 UNIV]SAL & -M5SURATE4 ,= 9/.E1 DECIDU\S "* W 2L;G EXCLUSIVELY 6A SUBJECT : IS A :OLE1 &1 IF ? :OLE HAS SPECIES1 UNIV]S,Y & -M5SURATELY 6^? SPECIES-I4E4 EI 6ALL SPECIES ( PLANT OR 6A S+LE SPECIES4 ,S 9 ^! UNIV]SAL & -M5SURATE 3NEXIONS ! ,8MI4LE0' & XS E6ECT M/ RECIPROCATE1 I4E4 2 3V]TI#4 ,SUPPOS+1 = EXAMPLE1 T ! R1SON :Y TREES >E DECIDU\S IS ! COAGUL,N ( SAP1 !N IF A TREE IS DECIDU\S1 COAGUL,N M/ 2 PRES5T1 & IF COAGUL,N IS PRES5T-N 9 ANY SUBJECT B 9 A TREE-!N T TREE M/ 2 DECIDU\S4 #AG ,C ! CAUSE ( AN ID5TICAL E6ECT 2 N ID5TICAL 9 E 9/.E (! E6ECT B DI6]5T8 ,OR IS T IMPOSSI#8 ,P]H X IS IMPOSSI# IF ! E6ECT IS DEMON/RAT$ Z ESS5TIAL & N Z 9H]+ 9 VIRTUE (A SYMPTOM OR AN A3ID5T-2C ! MI4LE IS !N ! DEF9I;N (! MAJOR T]M-?\< POSSI# IF ! DEMON/R,N IS N ESS5TIAL4 ,N[ X IS POSSI# 63SID] ! E6ECT & XS SUBJECT Z AN A3ID5TAL 3JUNC;N1 ?\< S* 3JUNC;NS WD N 2 REG>D$ Z 3NEXIONS DEM&+ SCI5TIFIC PRO(4 ,B IF !Y >E A3EPT$ Z S*1 ! MI4LE W CORRESPOND 6! EXTREMES1 & 2 EQUIVOCAL IF !Y >E EQUIVOCAL1 G5]IC,Y "O IF !Y >E G5]IC,Y "O4 ,TAKE ! "Q :Y PROPOR;NALS ALT]NATE4 ,! CAUSE :5 !Y >E L9ES1 & :5 !Y >E NUMB]S1 IS BO? DI6]5T & ID5TICAL2 DI6]5T 9 S F> Z L9ES >E L9ES & N NUMB]S1 ID5TICAL Z 9VOLV+ A GIV5 DET]M9ATE 9CRE;T4 ,9 ALL PROPOR;NALS ? IS S4 ,AG1 ! CAUSE ( LIKE;S 2T COL\R & COL\R IS O!R ?AN T 2T FIGURE & FIGURE2 = LIKE;S "H IS EQUIVOCAL1 M1N+ P]H 9 ! LATT] CASE EQUAL;Y (! RATIOS (! SIDES & EQUAL;Y (! ANGLES1 9 ! CASE ( COL\RS ID5T;Y (! ACT ( P]CVG !M1 OR "S?+ ELSE (! SORT4 ,AG1 3NEXIONS REQUIR+ PRO( : >E ID5TICAL 0ANALOGY MI4LES AL ANALOG\S4 ,! TRU? IS T CAUSE1 E6ECT1 & SUBJECT >E RECIPROC,Y PR$ICA# 9 ! FOLL[+ WAY4 ,IF ! SPECIES >E TAK5 S"E,Y1 ! E6ECT IS WID] ?AN ! SUBJECT 7E4G4 ! POSSES.N ( EXT]NAL ANGLES EQUAL 6F\R "R ANGLES IS AN ATTRIBUTE WID] ?AN TRIANGLE OR >E71 B X IS COEXT5SIVE )! SPECIES TAK5 COLLECTIVELY 7IN ? 9/.E ) ALL FIGURES ^: EXT]NAL ANGLES >E EQUAL 6F\R "R ANGLES74 ,&! MI4LE LIKEWISE RECIPROCATES1 =! MI4LE IS A DEF9I;N (! MAJOR2 : IS 9CID5T,Y ! R1SON :Y ALL ! SCI;ES >E BUILT UP "? DEF9I;N4 ,WE MAY ILLU/RATE Z FOLL[S4 ,DECIDU\S IS A UNIV]SAL ATTRIBUTE ( V9E1 & IS AT ! SAME "T ( WID] EXT5T ?AN V9E2 &( FIG1 & IS ( WID] EXT5T ?AN FIG3 B X IS N WID] ?AN B COEXT5SIVE )! TOTAL;Y (! SPECIES4 ,!N IF Y TAKE ! MI4LE : IS PROXIMATE1 X IS A DEF9I;N ( DECIDU\S4 ,I SAY T1 2C Y W F/ R1* A MI4LE NEXT ! SUBJECT1 &A PREMISS ASS]T+ X (! :OLE SUBJECT1 & AF T A MI4LE-! COAGUL,N ( SAP OR "S?+ (! SORT-PROV+ ! 3NEXION (! F/ MI4LE )! MAJOR3 B X IS ! COAGUL,N ( SAP AT ! JUNC;N ( L1F-/ALK & /EM : DEF9ES DECIDU\S4 ,IF AN EXPLAN,N 9 =MAL T]MS (! 9T]- REL,N ( CAUSE & E6ECT IS DEM&$1 WE % (F] ! FOLL[+4 ,LET ,A 2 AN ATTRIBUTE ( ALL ;,B1 & ;,B ( E SPECIES ( ;,D1 B S T BO? ;,A & ;,B >E WID] ?AN _! RESPECTIVE SUBJECTS4 ,!N ;,B W 2 A UNIV]SAL ATTRIBUTE ( EA* SPECIES ( ;,D 7S9CE ,I CALL S* AN ATTRIBUTE UNIV]SAL EV5 IF X IS N -M5SURATE1 & ,I CALL AN ATTRIBUTE PRIM>Y UNIV]SAL IF X IS -M5SURATE1 N ) EA* SPECIES S"E,Y B ) _! TOTAL;Y71 & X EXT5DS 2Y EA* ( !M TAK5 SEP>ATELY4 ,?US1 ;,B IS ! CAUSE ( ;,A'S 9H];E 9 ! SPECIES ( ;,D3 3SEQU5TLY ,A M/ 2 ( WID] EXT5T ?AN ;,B2 O!RWISE :Y %D ;,B 2 ! CAUSE ( ;,A'S 9H];E 9 ;,D ANY M ?AN ;,A ! CAUSE ( ;,B'S 9H];E 9 ;,D8 ,N[ IF ,A IS AN ATTRIBUTE ( ALL ! SPECIES ( ;,E1 ALL ! SPECIES ( ;,E W 2 UNIT$ 0POSSESS+ "S -MON CAUSE O!R ?AN ;,B3 O!RWISE H[ % WE 2 A# 6SAY T ,A IS PR$ICA# ( ALL ( : ;,E IS PR$ICA#1 :ILE ;,E IS N PR$ICA# ( ALL ( : ,A C 2 PR$ICAT$8 ,I M1N H[ C "! FAIL 6BE "S SPECIAL CAUSE ( ;,A'S 9H];E 9 ;,E1 Z "! 0 ( ;,A'S 9H];E 9 ALL ! SPECIES ( ;,D8 ,!N >E ! SPECIES ( ;,E1 TOO1 UNIT$ 0POSSESS+ "S -MON CAUSE8 ,? CAUSE WE M/ LOOK =4 ,LET U CALL X ,C4 ,WE 3CLUDE1 !N1 T ! SAME E6ECT MAY H M ?AN "O CAUSE1 B N 9 SUBJECTS SPECIFIC,Y ID5TICAL4 ,= 9/.E1 ! CAUSE ( L;GEV;Y 9 QUADRUP$S IS LACK ( BILE1 9 BIRDS A DRY 3/ITU;N-OR C]TA9LY "S?+ DI6]5T4 #AH ,IF IMM PREMISSES >E N R1*$ AT ONCE1 & "! IS N M]ELY "O MI4LE B S"EAL MI4LES1 I4E4 S"EAL CAUSES2 IS ! CAUSE (! PROP]TY'S 9H];E 9 ! S"EAL SPECIES ! MI4LE : IS PROXIMATE 6! PRIM>Y UNIV]SAL1 OR ! MI4LE : IS PROXIMATE 6! SPECIES8 ,CLE>LY ! CAUSE IS T NE>E/ 6EA* SPECIES S"E,Y 9 : X IS MANIFE/$1 = T IS ! CAUSE (! SUBJECT'S FALL+ "U ! UNIV]SAL4 ,6ILLU/RATE =M,Y3 ;,C IS ! CAUSE ( ;,B'S 9H];E 9 ;,D2 H;E ;,C IS ! CAUSE ( ;,A'S 9H];E 9 ;,D1 ;,B ( ;,A'S 9H];E 9 ;,C1 :ILE ! CAUSE ( ;,A'S 9H];E 9 ;,B IS ;,B XF4 #AI ,Z REG>DS SYLLOGISM & DEMON/R,N1 ! DEF9I;N (1 &! 3DI;NS REQUIR$ 6PRODUCE EA* ( !M1 >E N[ CLE>1 &) T AL ! DEF9I;N (1 &! 3DI;NS REQUIR$ 6PRODUCE1 DEMON/RATIVE K1 S9CE X IS ! SAME Z DEMON/R,N4 ,Z 6! BASIC PREMISSES1 H[ !Y 2COME "KN & :AT IS ! DEVELOP$ /ATE ( K ( !M IS MADE CLE> 0RAIS+ "S PRELIM9>Y PRO#MS4 ,WE H ALR SD T SCI5TIFIC K "? DEMON/R,N IS IMPOSSI# UN.S A MAN "KS ! PRIM>Y IMM PREMISSES4 ,B "! >E "QS : MIE N 9NATE B -E 6BE 9 U1 OR >E 9NATE B AT F/ UNNOTIC$4 ,N[ X IS /RANGE IF WE POSSESS !M F BIR?2 = X M1NS T WE POSSESS APPREH5.NS M A3URATE ?AN DEMON/R,N & FAIL 6NOTICE !M4 ,IF ON ! O!R H& WE ACQUIRE !M & D N PREVI\SLY POSSESS !M1 H[ CD WE APPREH5D & LE>N )\T A BASIS ( PRE-EXI/5T K8 ,= T IS IMPOSSI#1 Z WE US$ 6F9D 9 ! CASE ( DEMON/R,N4 ,S X EM]GES T NEI C WE POSSESS !M F BIR?1 NOR C !Y -E 6BE 9 U IF WE >E )\T K ( !M 6! EXT5T ( HAV+ NO S* DEVELOP$ /ATE AT ALL4 ,"!=E WE M/ POSSESS A CAPAC;Y ( "S SORT1 B N S* Z 6RANK HI<] 9 A3URACY ?AN ^! DEVELOP$ /ATES4 ,& ? AT L1/ IS AN OBVI\S "*I/IC ( ALL ANIMALS1 = !Y POSSESS A 3G5ITAL 4CRIM9ATIVE CAPAC;Y : IS CALL$ S5SE- P]CEP;N4 ,B ?\< S5SE-P]CEP;N IS 9NATE 9 ALL ANIMALS1 9 "S ! S5SE-IMPRES.N -ES 6P]SI/1 9 O!RS X DOES N4 ,S ANIMALS 9 : ? P]SI/;E DOES N -E 6BE H EI NO K AT ALL \TSIDE ! ACT ( P]CVG1 OR NO K ( OBJECTS ( : NO IMPRES.N P]SI/S2 ANIMALS 9 : X DOES -E 962+ H P]CEP;N & C 3T9UE 6RETA9 ! S5SE-IMPRES.N 9 ! S\L3 & :5 S* P]SI/;E IS FREQU5TLY REP1T$ A FUR!R 4T9C;N AT ONCE >ISES 2T ^? : \ (! P]SI/;E ( S* S5SE-IMPRES.NS DEVELOP A P[] ( SY/EMATIZ+ !M & ^? : D N4 ,S \ ( S5SE- P]CEP;N -ES 6BE :AT WE CALL MEMORY1 & \ ( FREQU5TLY REP1T$ MEMORIES (! SAME ?+ DEVELOPS EXP]I;E2 =A NUMB] ( MEMORIES 3/ITUTE A S+LE EXP]I;E4 ,F EXP]I;E AG- I4E4 F ! UNIV]SAL N[ /ABILIZ$ 9 XS 5TIRETY )9 ! S\L1 ! "O 2S ! _M : IS A S+LE ID5T;Y )9 !M ALL-ORIG9ATE ! SKILL ( ! CRAFTSMAN &! K (! MAN ( SCI;E1 SKILL 9 ! SPH]E ( -+ 6BE & SCI;E 9 ! SPH]E ( 2+4 ,WE 3CLUDE T ^! /ATES ( K >E NEI 9NATE 9 A DET]M9ATE =M1 NOR DEVELOP$ F O!R HI<] /ATES ( K1 B F S5SE-P]CEP;N4 ,X IS L A R\T 9 BATTLE /OPP$ 0F/ "O MAN MAK+ A /& & !N ANO!R1 UNTIL ! ORIG9AL =M,N HAS BE5 RE/OR$4 ,! S\L IS S 3/ITUT$ Z 6BE CAPA# ( ? PROCESS4 ,LET U N[ RE/ATE ! A3.T GIV5 ALR1 ?\< ) 9SU6ICI5T CLE>;S4 ,:5 "O (A NUMB] ( LOGIC,Y 9DISCRIM9A# "PICUL>S HAS MADE A /&1 ! E>LIE/ UNIV]SAL IS PRES5T 9 ! S\L3 = ?\< ! ACT ( S5SE-P]CEP;N IS (! "PICUL>1 XS 3T5T IS UNIV]SAL-IS MAN1 = EXAMPLE1 N ! MAN ,CALLIAS4 ,A FRE% /& IS MADE AM;G ^! RUDI;T>Y UNIV]SALS1 &! PROCESS DOES N C1SE UNTIL ! 9DIVISI# 3CEPTS1 ! TRUE UNIV]SALS1 >E E/ABLI%$3 E4G4 S* & S* A SPECIES ( ANIMAL IS A /EP T[>DS ! G5US ANIMAL1 : 0! SAME PROCESS IS A /EP T[>DS A FUR!R G5]ALIZ,N4 ,?US X IS CLE> T WE M/ GET 6"K ! PRIM>Y PREMISSES 09DUC;N2 =! ME?OD 0: EV5 S5SE-P]CEP;N IMPLANTS ! UNIV]SAL IS 9DUCTIVE4 ,N[ (! ?9K+ /ATES 0: WE GRASP TRU?1 "S >E UNFAIL+LY TRUE1 O!RS ADMIT ( ]ROR-OP9ION1 = 9/.E1 & CALCUL,N1 ":AS SCI5TIFIC "K+ & 9TUI;N >E ALW TRUE3 FUR!R1 NO O!R K9D ( ?"\ EXCEPT 9TUI;N IS M A3URATE ?AN SCI5TIFIC K1 ":AS PRIM>Y PREMISSES >E M "KA# ?AN DEMON/R,NS1 & ALL SCI5TIFIC K IS 4CURSIVE4 ,F ^! 3SID],NS X FOLL[S T "! W 2 NO SCI5TIFIC K (! PRIM>Y PREMISSES1 & S9CE EXCEPT 9TUI;N NO?+ C 2 TRU] ?AN SCI5TIFIC K1 X W 2 9TUI;N T APPREH5DS ! PRIM>Y PREMISSES-A RESULT : AL FOLL[S F ! FACT T DEMON/R,N _C 2 ! ORIG9ATIVE S\RCE ( DEMON/R,N1 NOR1 3SEQU5TLY1 SCI5TIFIC K ( SCI5TIFIC K4,IF1 "!=E1 X IS ! ONLY O!R K9D ( TRUE ?9K+ EXCEPT SCI5TIFIC "K+1 9TUI;N W 2 ! ORIG9ATIVE S\RCE ( SCI5TIFIC K4 ,&! ORIG9ATIVE S\RCE ( SCI;E GRASPS ! ORIG9AL BASIC PREMISS1 :ILE SCI;E Z A :OLE IS SIMIL>LY RELAT$ Z ORIG9ATIVE S\RCE 6! :OLE BODY ( FACT4