Galen and the Logic of Proposition

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JAMES W. STAKELUM, C. M.

GALEN AND

THE LOGIC OF PROPOSITION PARS DISSE RTATIO NIS AD LA UREAM IN FACULTATE PHILOSOPHIAE APUD INSTITUTUM « ANGELICUM

>>

K.OMAE 1940

DE URBE

PREFACE These JIUges , restrictedly entitled > originally formed part of an academic dissertation, Galen's Introduction to Dialectic. The thteefold purpose of the larger study was to present Galen's Dialectic in a clear light, to examine his doctrine and weigh its importance as to originality or historical precedent, and from these considerations to draw conclusions as to its influence on succeeding generations. The doctrine , scattered throughout the Galenic . text, ·was gathered under five headings: /. Galen's Introductory Remarks; II. Logic of Propositions; 111. Aristotelian Term Logic; IV. Other Classes of Syllogisms; V. Applied Logic. Owing to the limited size of the volumes of this series, published under the sponsorship of Father I. M. Bochemki , 0. P. , it is impossible to publish here the whole result of the inquiry. Accordingly, we have selected for presentation our Introduction - tearranged as Part One in several short chapters - and the most important portion I of our examination of Galen's Dialectic, dealing with the logic of propositions. The latter section is divided into three parts. A brief conclusion completes the essay. It is traditional to attribute to Galen an eminent position in the field of logic, hut rarely do we find specific reasons assigned for this eminnce. The composition of this dissertation has, for me, definitely determined Galen's position in -

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the history of logic. It is hoped that it will serve a similm; purpose jov others. Here I wish to acknowledge briefly personal indebted· ness. I deeply UfJfJrec:iate the philos()phical course at the Pontifical Institute Angelicum ·which has made possible this study. To my professors and to all who have generously aided me in the composition of this work I offer m y sincere thanks. I am fJarti cularly grateful to Father I . M. Boc:henski, 0 . P. , who has been of great assistance by his wise counsel and patient direction. I gladly acknowledge my obligations to lJ;ll my .friends ; to me alon e are chargeable the errors wlzich critical ( .:amination may discover. ]AM E S

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w.

S T AKEL U M ,

c. M.

BIBLIOGRAPHY

SOURCES l. Manw;cript: HIBLIOTHEQUE NATJONALE PARIS, SuPP LEMENTUM GRAEC.UM, CooEx 635, folia 3v-l2r. Galen' s Introduction to Dialecti.c .

2. Edition8 and Translations of Galen ' s Wo rks: Dialectica. gt·a ece eel. M. Mina s, Pari s, 1844. lnstiJutio Logica , e d. C. Kalhfleisch, Lip s iae, 1896.

GALEN:

N atural Fru:ulries , transl. A.

J.

Brock , London- N .

Y. , l928 .

Opcrn Omnia , t:d. Aldus Manuliu s, Ven e tiis, 1S25. OpPra Omn in (Mcdit·o rum graecoruru ope ra), e d. C. C. Kuhn, Lips iae , 1821-30. Scripr.a Minora, cd. Lip s iae, 1884 . :-1 . Otlwr ,.,Jir i 011.~

J.

M.an1uard1, I. Mu e lle r, G . Helmreich,

:

ALBEHTU .'-' MAGN U'-' ( S.) : () JWI"fl Omnia , I'd. ;\. Bourgon c l , Parisiis,

1890-9. AL E\ :INDER APHHOil i'-'IA'-' : In A ri.~totdi .~ A naly ti.contnl Priorum librum I Comnwntari.um , e d. M. Walli es, Bct"Oiini, 1883.

-

In

. - lristoteli.~

TntJi cornm librus

ul'lo

Comnwnlariwn, eel. M.

Walli es, B erolini , l89l. AMMO N I U~ :

In Aristnlc!is Analvt.iconun. Priorum libru111 T Commt~ntarium , e rl. M. \Vallics; Bl'rolini , 1899.

APOLLONIUS Dv :-;c oLU~: Grmnmntici Gmeci, e d. R. Schn e ide r t'l G. U hlig, Lip siaf', 1878. APULEIUS: De Philosophia Libri , ed. P. Thoma s, Lip siae , 1908. -

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ARISTOTifLES: Opera Omnia , ed. Academia Regia Borussica, ex recognitione I. Bekkker, Berolini, 1831. ARNIM, I. AB: Stoicorum Veterum Fragmenta. Lipsiae, 1923. AULUS GELLlUS: Attic Nights, tran s!. 1927.

J. C. Rolfe, London-N. Y.,

AVERROES : Aristotelis St:ugiritae Omnia, qnae extant Opera ... Averrois Cordubensisitu' n Co nmwntarii, Ven etii s, 1:152. BoETHIUS: De Syllogismo Categorico; De Syllogisnw flypothetico; ln Topica Cireronis Commentarium, (Patrologia c cursus completus, Series Latina, ed . J. P. Migne, vol. LX1 V), Parisi is, 1891. Comm£•ntarium in librum A ristotelis Peri 1-lermeneias, Second Edit ion , ed. C. Mei ser, Lipsiac, 1880.

CICERO: De Natura Deorum, Academica, trans l. H. Rackharri, Loudon-N . Y. , 1933. DAVID: Prologem ena ct 1II Por [}hyrii A. Busse, Berolini, 1904.

r~(/ gogpn

Com m cntarium, ed.

DIOGENES LAERTJUS: transl. R. D. Hicks, London-N. Y., 1925. ELIAS: In Porphyrii Tsagogen Pt Aristotelis Catego rias Commentnria, ed. A. Busse, Berolini, 1900. EPICTETUS: Di.ssertations, transl. W. A. Oldfather, London-N. Y ., 1926. EuDEMUS: ed. T. W. Mullack (Frngnwnla Philosoplwrum Graecorum, vol. III), Paris, 1860-81. MARTIANUS CAPELLA: ed. A. Dick, Lip siac, 1925. MICHAEL: In Parva Natu.ralia Conunentaria, ed. P. Wendland, Berolini, 1903. PHILOPONUS: In Aristotelis Analytica Priorn Cummentnrium , ed. M. Walli es, Berolini, 190:1. PLATO: Opera Omnia, cd. C. E. C. Schneider, Pari siis, 1833. PJ"UTARCHUS: Mornli.n, ed. G. N. Bernanlakis, Lipsiae, 1888-96. PRJSCIANUS: OpPra, ed . A. Krehle, Lipsiae, 1819. SEXTUS EMPIRICUS: trans I. R. G. Bury, London-N. Y.,

19:~3-1936.

Outlirws of Pyrrlwni.mz , vol. I. Against Logiciam, vol. II (i. e., Against Mat hemal icians, VII and VIII). Against Physicists, vo l. III (i. e., and X). .

Aga in ~t

Mathematicians , IX

Against Ethicists, vol. III (i. c., Against il!fathematicians , XI). -

VIII -

SrMPLIClUS: In Aristotelis de Coelo Commentarium, ed. J. L. H e iberg, Berolini, 1894. STEPHANUS: In librum Aristotelis de lnterpretatione Commentarium , ed. M. Hayduck, B erolini , 1885 .

I, Commentarium in Aristnt:elis libros Peri He rm eneias et Postcriorum Analyticoru.m, e dit io L eonina , Romac , 1R82.

THoMAS AQUINAS , S.: Opera Omnia , vo l.

Sancti Thonw e Scri ptum super Libros Sententiarum, cditio nova, c nra R. P. Mandonnet, 0 . P. , Pari siis, 1929.

WORKS DAREMBERG , \..: Galien co t1.~idi> n!

n mllltl'

Philosoplw , Paris, JR48.

BocHENS KI , I. M ., 0 . P.: Elementa Lo,~irrte GrrH'cae , Roma e, 19::\7. BHOCHA RD , V.: Rt11des d e Phi/oso11hie A nr ienne et de Philosophic Moderne , 11 ew e dition , Pari s, 1926. CAMPBELL, D.: Arabian Mcdici.ne and its lnf/11encc AgPs, London, 1926.

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the Middle

CHAUVET, E.: ],ogiqu e de Gahen , Pari s, 1882.

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La PlrilosnphiP d('s 111edecins GrN·s. Pat·i s, 1886.

FESTUGIERE, A. J. e t FABRE, P .: Le Monde greco -romain au temps de Notre-Seigneur, Paris, 1935. FINLAYSON, J.: Two Bibliographical Denwn s tration .~ , Glasgow, 189S. J AEGER, W. : A ristodc , lt·a n s l. R. Robinson, Oxford, 1934. J ANET, P. c t SEAILLES, G.: fh~toire de la Philosnphic, 15th Edition,

Pari s, 1932. JoH GEN!->EN , J . : A TrPfltist'

of

l' onnul l-ogi1· , Co penha gen-Londott,

1931. KALBFLEI SCH , C.: Ulwr C alf'll ' s E inleitung i11 Dit' Logik (Jnhrbiicher fiir r-lns sisclll~ Philologie, Snppl. 23), Leipzig, -1897. KE YNES, H. J. N.: S tudif's nnd Exercises in Formal Logic , 4th f'dilion rCJHi ntcd , Louilon, 1928. KUMI-.E ,

F., S. J . : fnstitution es llistoriae Philo.wphi-aP , Romac,

1923. LE WI S, C. L. anrl LA NGFO IW , C. H.: Sy mbolic togic, N. Y.-London,

1932. L UKAS IEWICZ , J.: Zur Ct'.w-·hicht f' der A u.~.~ agen1ogil.- (Erkenntnis), B an d S, H eft 2/ 3, L e ipzig, 1935. IX -

O ' LEARY , DEL.: A rabic Thought and its Place tn Histor y , London, 1922. OwEN, 0. F.: Organon , London, 1885-7.

J. F.: Th e R elation of Har vPy to his Pred ecessors and es pecially to Gnlen , (The L a ncet), Lond o n , 189 7.

PAYNE,

PHA NTL , C.: Geschichte der LogiJ.: im A bendlonde, L e ip:.:i g , L927.

Ross, W. D.: Th e lll orks of A rist,otle, vol. I, O xford , 1928 . ScHOLZ , H. : Geschichte d er Logik , B erlin, 193 1. S MITH , SIR W.: Dictionary of Greek nnd Rom.a.n B iograph,, · M y thology, London, 1870 .

1111tf

STEBBJ NG, L. S. : A M.oclern Introdu ction to Logic, 2nd e di1i o n , Lo n don , 193~. SYLVESTEH MA URUS : Aristot eli.~ Opem Omnia , e el. F. Ehr lc, S. Pari siis , 1885 .

J .,

THORNDIKE, L.: History of Magic and Ex,wrinu'll.trd Sc iell.ce , N. Y., 1923 .

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Galen , th e man and his times , (Scic11tifi c Monthl y), Jan . 192:: .

TREND ELENBURG , A. :

Ct~s c hi c ht e

der /(ategorienlehre, B erlin , 1846.

T URNER , W.: Histon · of Philosuph_y , B os ton , 1929 . lTEBERW EGS, F . : Grundriss dt>r Gesr·hir ht e tier l ' hil o.~o f> hi e, vo l. I , h e r au sgegeh f' n vo n Dr . K a rl Praec hte r , B e rlin , 1926 . WHIT EH EAO , A. 1\ . and H u ~ S ELL B. : l'rinciJJia Math('fnatico , 2nd editi on r e print e d , London, 1927. WHIGHT, J.: Galen , his mentality Monthly), Aug. , 1922.

and co.m wlogy,

(Sc ientific

ZELLER, E.: Outlines of the Histor y of Gmek l'hilosoflh v, L o ndon , 1892.

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ABBREVIATIONS Pa ge ami lin e rcfcr encPs (c. g., 20.14) una cco mpani ed by '' A ristot/, , A nalvtint l'riora " « Ari.~ t otle, /), Categoriis " « Ari.stotle, De lnt

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CONTENTS v

PREFACE . BIBLIOGRAPHY ABBREVIATIONS

Vll :XI

P ART ON E I N TRODUCTION

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I. IMPORTANCE oF sEc.oNo CENTURY LoGic II. LIFE OF GALEN III. BRI EF H1 s TOHY OF PRE-GALEN IC. FoRMAL Loe1 c

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IV . Loc 1c

CHAPTER

))

Ol"

GA LEN

1 3

9 14

PART TWO HYPOTHETICAL PROPOSITIONS I NTRODUCTION CHA PTEH I. NoTION AND DIVI SION OF PnoPOSJTIOl'll . (A) Stoic Doctrin e : (1) No tion; (2) Divi sion. (B) Galelli c Doctrine: (1) Hypotlwtical Propos ition s; (2) Divi sion of Hypothe tical Proposition s >' II. OPPOSED PROPOSITIONS. (A) Stoic Doctrine . (B) Galenic Doctrin e: (1) Comple te Oppositiou (the Excluding Alternative); (2) In comp lete Opposition; (3) The N ot-excluding Alternati ve; (4) Origin of Galen 's D octrine of Opposition ; (5) Nam es of Proposition from Opposition >> III. CoNDITIONAL PnoPOSJTJONS . (A) Stoic Doctrine . (B) Gal eni c Doctrin e: (1) Con sequen ce jn Gen era l ; (2) Divi sion o[ Co nsequen ce: (a) Com pl ete Co nsequ ence, (h) In compl ete Co nse- - XIII -

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quence; (3) Origin of Galen's Conditional Proposition; (4) Names of Conditional PIOposition . IV. CoPULATIVE PROPOSITIONS. (B) Galenic Doctrin e

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S u MMARY oF PART Two

43

(A) Stoic Doctrine.

55 59

.

PART THREE HYPOTHETICAL SYLLOGISMS (i()

I NTRODUCTION

I. TH E SYLLOGISTIC MoD ES

CHAPTER

OJ' CHRISIPPUS. (l) Th e Five Inde mon s trab le Syll ogism s ; (2) Tenninolo gy: (a) Directing Principl e, (h) Tropicon, ( c) Assumptio n , (d) Pre mises, ( e) Co nclu sion, (f) Modes; (3) N umbe r of lnd e m o n strabl es according Lo Gal e n

11. 01'POSITJON SYLLOGISMS .

n

)l

61

(l) Syllogi sm s from Comp lete Opposition: (a) Exclud in g A lt e rnative of Two M e mbe r s , (b) Excluding Alt e rnative of More Than Two M e mbe r s; (2) Syllog is m s from Incompl e t e Oppositi o n : (a) Two Memhcrs , (h) More Than Two M embers; (;{) Sy ll o ~i s m s fr o m "'l"ot-exc ludin ~r AlternaI ives

TTL

J)

C o i\ UITIONA I. SY LLOGI SMS. (l) SyJio gi sm s from f:omplet c f:on se q uen ce; (2) Sy ll o~i s m s from Incomple te Conse qu e n ce

67

~" /_

77

IV. CoPULATIV E SY LLOGISMS

Su MMARY OF PAHT THREE

Stl

PART FOUR E(JUIV ALE NCE AND CONVERSION

Rl

INTHOOUCTIOJ\ CHAPTEH >>

I. EQUIVAL ENCE

8~

II. CoNVERSION. (l) Conve r sion of (2) Conversion o[ Syll ogisms

Pmposition s ; 84

SuMMAHY oF PAnT Fou R

89

CoNcLUSION

90 92 94

GLOS SAHY I NDEX XIV

DEO SUMMAE VERITATI

PART

ONE

INTROD UCTION

CHAPTER

J

lMPORTANCE OF SECOND CENTURY LOGIC The >"t Ud ) of the fo nn a l logic of tl11' ~eco nd ce ntury A . D. is undeniabl y interes tin g and fr ui lfu l. Sig nifica nce a llaches to it as a field of inquir y, not becau se of any originality among second ·c entury lo g ic~ ia n s, who seem to hav e lwe n nwre compile rs and commentators, but because the seconcl century I wr·i ters are the only ex ten sive witnesses of th e grea t epoch i111rn ediately precedin g : the span from the third century B. C. to th e fir st· cent ur y A. D. , without doubt a period in which logic was most studiou sly -c ultivat ed , but of wh ich , unfortunately, all the more ancient p o~t - Ari stot elian writings ha ve been lost. The importance of the lcgic of the second cen tury is not I i 111 i tecl solely to its hi storical funct ion of epitomizing its predecessors. It has, in turn , its own influence on its successor s. The centuries followin g, from the third to th e sixth, offer nothing n ew in the field of logic; so that those things which the Scholasti cs received from antiquity, partieularly through th e medium of Capella , Boethius and the Arabian s, have me c.liately come from seco rul ce ntur y writers. Scholasti c logic manifestly depend s uot onl y o u the logic of Ari s lollt~ hut a lso

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on that of the Stoics , especially as developed by the Stoics to the form which we find in the second century A . D. Scho lastic logic contains a kind of Peripatetic and Stoic synthesis, in which th e form er e lem e nt prevail s, but in which the latter is quite evident , especially in the doctrine concernin~ the h ypothetical syllogism. H ence appears the doubly instructive ·char acter of second century logic: it completes our knowledge of post-Ari stotelian logic (third ce.ntur y B. C. to second century A. D.), and aid s our und ers tanding of the remote origin of Scholastic logic. In second centur y logic three outstanding writer s challenge attention: Alexander Aphrodisias, Sextus Empiricus anrl Claude Galen. Each has his peculiar characteristic. Alexander , a rigid Peripatetic, denies the value of Stoic logic; Sextus, a Skeptic, exposes and refutes a logic almost exclusively Stoic; Galen, having severely examined the logic of both schools, form s his own eclectic syst em. The present study exclusively concerns Galen's system , as it is fo und in his Introduction to Dialectic. Little h as been wr itten concerning the lof!ic of Galen, the scholarly ph y ~ i cian of P ergamus , alth o ugh there exists an immense bibli ography of his medical works. In view of th e striking r es ults of philosoph ical r esearch in the past half century, a monograph on Galenic logic, published in 1882 by Emmanuel Chauvet, ' no longer suffices. Moreover, the re. cent evolution of the history of logic demands an up-to-date monograph. With the ho_IJ e of imm edi a tely ful fill ing this need , we offer th e present exposi tion of the Logic of Galen, in which we propose , fir st to describe in a systematic order th e doctrine found in his Introdu ction to Dialectic ; secondly , to estim ate in order to discover its originality or historical precedent, Galen 's teaching according to its doctrinal anJ histor ical value ; and , lastly, to draw conclusions as to it~ influence on sub sequent generation s.

' CHAUVIdical guardian of the son of th e E mpero r Ma rcus Aurdiu;; . whi le tlr e la tter was campaigning along the Danube. Dur ing thi s period Galen compo5

10

12

Kuhn , V, 4l.Hi and XIX, :i9.4 . Kuhn , V, 41.11. • Kuhn, XIX, 59.8. Kuhn, XIX, 43 .6. ' Kuhn, X, 609 .8 and XIX, :i9.9 . " Kuhn, X, 609.10. '" Kuhn , II, 217.14. " Kuhn , XIII, 599.6 ff. '" EncyclopPdin Britannica . 14th vol. IX , p. 973h. 1

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E dition ,

London ,

1929,

se$1 many works, both medical and philosophical. His extraordinary skill as a physician merited for him the title of « won·. derworker. )) He was also called the « narrator of marvels, » in con sequence, no doubt, of hi s unrivalled facility in lectnrin (! and arguing. Alexander Aphrodisias, according to Arabic testimony, nicknamed him « mule' s head » because of " His harshness, at times even bitterness, iu controversy is evident in all hi;; works. Hi s reputation aroused the envy of other ' practitioner~, and his criticisms provoked the enmity of his opponents. He was ridiculed by other phy sicians on account of his attachment t ave gone to Aristotl e . "" H is attachm ents, however , d o not I· reve nt him from critici sin~ his h eroes, when h e d eems cen~ ure in order. De veloping his system , he sought in his naturally lo gical way to r edu ce ever ything to gen eral principles . Thi s simplification h e effec ted in dialectics in regard to d em on stra tion b y reducing all ar gum ents to gen er a l axioms, "" and especiall y b y es ta blish ing th e Geome tri c Proof as the most exac t of d e mo nstrations . "' T o ol, tai n like re,; uJt,.; in medicine, it seems he woul d hegiu wit h a pr incip le ar rived at by a stra nge comb in a tion of d ed ucti o n a nd observation , ano th en woul d veri fy h is formul a ted conclusions by experiment. A nd alm os t in variabl y, through the sh eer force of hi s natural endowm ent , h e attained the ultimate obj ect in view , although .by an indirec t path )>;indirect , that is, for a n ex perim ental science . "·' Th e gen eral charac te ri sti cs ma nifes t.. d in G al e n 's oth er worl.; s are f ound in the lntrorlu ct,ion to Oialectic . ·' " /( uhn , ll, L79 .10 ; X, 609. 1:1 . "" Ku.hn , IX, 842.2; X, 29 .3; Xlll, 116.8, and 887 .1 rr. "" Kuhn, X, 159.12. "' Ku.hn , II, 189.5. " " ZEL L EII , E.: Outlini'S of tlrl' 1-listorv uf (;rl' l' l> l ' hilo.w ph)" , London , 1892, p . 299 . ::s

:l,l

42 .7 ff.

'" Kuhn , XIX, 47 .1 5. 5 a SM ITH, S IR W.: Dictio nar y of GrPI''' 111111 Ho11wn Biograph y and M y tholog:v , London , 1870, voL I , p . 210b. "" Kalbfleisch , p. 688 H.

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CHAPTER

III

BRIEF HISTORY OF PRE-GALENIC FORMAL LOGIC

From the beginniug we must bear in mind that Galen·~ Introduction to Dialectic i~ essentially formal logic; that is, it is mainly a treatise ou the valid forms of syllogisms, whicl1 1 St. Albert the Great calls the « formalia )) of the syllogism. We may describe formal logic as that scienc~ which examines the formulae of aq.rumentation valid for all matter. Therefore, formal lo:~ic con;.;iden; all the formulae employed by any system, regardles;; of the theory of knowledge on which it is built. Fully to tmderstand the Introduction to Dialectic it is necessary to appreciate not qnly the general diversity, hut also the special points of conflict, between the two logical systems, the Peripatetic and the Stoic, which we find treated therein. As far as we know, Aristotle introduced formal logic. lt was not, manifestly, an instantaneous invention. 'An analysis of the Organon proves it the evolution of years, as Jaeger has well demonstrated, " Galen seems to have been unaware of this fact. Aristotle, developing the logical metlwds of his master Plato, evolved more completely in Topica and De Sophisticis Elenchis the dialectic method, · which has disputation as its sole objective. This dialectic proof waioi founded on (( opinions ( svoo£a) generally accepted by eve1 S. ALBERTI MAI;NJ: Opera Omnia, ed. A. Bourgonet, Parisiis, 1890-9, Liber I Priurum Analvticnrum, p. 460a. 2 JAEGER, W.: Aristotle, transl. R. Robinson, Oxford, 1934.

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ryone, or by the majority, or by t~e ·p hilosophers. )> • Topica ('t61to~, .places) · is a collection of general rules useful in disputations. Scholz says: Lukasiewicz, p . 119. -· Alex. in APr., 372 .29. "

2 1

These metaphysical a·n d psychological rlifff"rences are well d eve loped by V r, that is, th e logic of propositions.

" Galeni lnstitut i~ Logica, ed. Caro lu s Kalbfl ei s~h , Lipsiae , l R96.

'" Uber Gnlen ' s E'i,nleitun g in ,Pie Logik , v on KA UL KA LB)cthrbuch er fiir clns,~isc h c Philologie. Snpp l. 2~ , Le ipzi g, 1897, p. 68 1-708 . " A RN IM , I. All: Sto icorum V t•terum f'r ag tllt'/1111. Lips ia e, 192 3, vol. n , p . 83.4 ; alsu t uka,~ i ew i cz. p . 11 7.

F L EISC H :

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PART TWO

HYPOTHETICAL PROPOSITIONS INTRODUCTION Gal en 's presentation (_If Stoic logic is the least systematic part to th e Introduction to Dialectic . His exposition is neither complete nor in full accord with Stoic tradition. It i:- preferable, for obvious r easons, to present Stoi c dialectic f'ys tematicall y, as is the practice toda y. This procedure was 1 al so th e custom of th e Stoi cs, who expl ain ed the wh ole d octrine of h ypothetical syll ogisms in a sys tema ti c ord er. They began with simple proposition s (anAIX &;twj.let.-ra), pr oceeded to compound proposition s (oux anAIX &~ tWj.lCXTet.), and f rom tlw~e latter formed their syllogism s (A6yot), The order of treatment in this division of our inquiry will be that of the Stoics. We shall exatiline the material. under four heads : (l) the Notion and Di vision of Stoic Proposition s, (2) Opposed Proposition s, ( 3) Conditional Proposition s, and ( 4) Copulative Propositions. This. order will assist u s to obta1 n a clear und er standing of th e somewhat unfamiliar Stoic dialecti c. Since G al en 's explanation is at times incompl :'t e, it will be n ecessa r y to have r ecourse to the primary fonts of Stoic doctrine, Sex tus Empiri cus and Diogenes Laertius. These authors wer e not Stoics, hut th eir pi·esentations of Stoic doctrine are considered r eliabl e . Also, since Galen 's d octrine frequ ently differ s from Stoic doctrine, in each chapter we shall examin e fir st th e Stoic teachin g and th e n Gal e n 's t"xplanatioB. 1

Diog . Lrwrt .. VII, 189 ff.

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17

CHAPTER

I

NOTION AND DIVISION OF PROPOSITION

A. Stoic Doctrine.

1. Notion . Diogenes Laertius defines and describes a proposition as « that which is either true or false, or a thing com plete in itself, capable of being denied in and by itself; as Chrysippus says in his Dialectical Definitions: A provosition is· that which in and by itself can be denied or affirmed; for example, ' It is da y ' , ' Dion is walking '. The Greek word for proposition (&~{w!-la), is derived from the verh &~toliv, signifying acceptance; for when you say ' It is day ', you seem to accept the fact that it is day. Now, if it really is day, the proposition before us is true; but if it is not day , it is false. >> ' A proposition, an interrogation, and an inquiry differ from one another, he continues, as do the following types of expressions: imperative , adjurative, optative, hypothetical (6noS·2nx6v) and vocative . ((For a proposition is that which we assert when speaking, and it is either false or true. >> " Then follows an explanation of solVe of th'~ above-mention~d terms, but, unfortunately, «hypothetical >> is not explained. > I;Iypothetical expressions are neither true nor false, because they are not propositions. It is important to note that, although the early Stoics knew the term > ' or > to signify > in regard to son1ething which possibly might be true , but which is assumed without proof as a

"' 12.7 arid 17.13. " 7.12: favo~ aAAo 7tpo~:cicrc:wv €crn v €v at> ( xtX-&' fm6&sow ). '" He also · uses « by 27 assumption )) ( s~ {mo&sosw by sub sequ ent philosoph er s, beca u se they are the fundam ents of sy llogisms found ed on th e (( general opinions or beliefs or acceptations of me u. )) Such propositions cannot h e denton strated; they are sim ply assumed. 2 . Di vi!>ion of Hypothetical Proposition!>. « Since in things there ar e three differ ences, th e fir st accordin g to the opposition (!-!ax·~) in thin gs never existing together, the second according to the consequence ( axo),ou&CtX ) in things always existing together, and the third in things sometimes existing togeth er but sometimes not existing together , all those which have neither n ecessary consequence nor opposition constitute the copu lative proposition ( OUj-!7tS1l),syj-!8vov a~CWj-!tX ) . "" Gal en makes this statement late in his trea tise,

"!; Sext. Emp . Pyrr. , I, 79. 27

Sext. Emp. Pyrr., II, 20, and Nlath ., VIII, 34:~. "' Sext . Emp. Pyrr., I, 168 and 173. "' :13 .19 : cptii>v yixp oiJcrwv otacpopwv zv -rot~ 7tp6.yf-Lacrt, l.tt'X~ f-LEV -r1)~ xa-rix -r·~'l f-LXX1JV Z7tl -rii>v fl-1JOETCO-re cruv tmxpz6nwv, hir-a~ oz -r1)~ xa-rix -r·~v cho),ou{Hxv E7tl -rw v ad (O"UV lJTCIXpx6v-rw v, i:ptl::"f)~ oz -r1), xai. scrtt ta tOUtOt This definition indicates, that the proposition expresses two facts which cannot coexist, and by. the existence or non-existence of one fact the respective non-existence or existence of the other fact is. necessitated. The sense of his words coincides with the Stoic definition of the excluding alternative. Therefore , Galen rightly adds later: « Excluding alternative (ots~SU''(f.LSVov) is the more proper expression for the propositions which we said are called disjunctive propositions because of the conjunction ' or ' (~-cot); but it makes no difference if you say ' or ' ( ~) with one or two syllablee ...

r

• 33.20 Gt·eek text given on page 23, note 29. 7.17: o:[ u, tho:v f)-rot (-L"f} onoc;; e:!vo:t fJ OV'tOc;; (l"f} e£vo:t, oto:tpe-rtxo:L 9

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for they mean one and the same thing. >> '" Thus far we find Galen's doctrine fully in agreement with that of the older Stoics. But, when Galen further discusses opposition between propositions, innovations begin to appear. H e tells us that « opposition (!lax·~) possesses the common property (xo tv6v) 11 that the opposed things do not coexist; >> and of opposed things some are simply insociable, whereas others add to the 'notion of insociability the note that one member must exist. In making the ,c ommon property or distinctive characteristic of opposition simply the insociability of th e propositions , Galen is no longer speaking solely of the Stoic excluding alternative, but of opposed propositions in general. In the genus of opposed things, we are told, all have the common property of not being abl e to coexist, and there is added the differentiation that of some things which cannot coexist one must exist, whereas in other things which cannot coexist it is not necessary that either one exist. According to this differentiation there is a twofold division of opposition: namely, a) complete opposition (1:cAEta !lcXXYJ) and b) incomplete opposition ( sA.A.m'lJ£ !lcXXYJ).

l. Complete Opposition (cEA.s{a !lcXXYJ) or the Excluding Alternative (o tE ~EUY!lsvov). Complete opposition, Galen says, occurs when the members are insociable and one must exist. " « I have thought proper to give to propositions according to complete opposition the appellation of excluding alterna13 tive; >> for example, « Either it is day, or it is night. )>

-

8.17: o1xc.totEptx o€ ~crtt AE~t~ tb OtE ~wyp.€vov tot~ ci~ twp.txcrtv, &~ 01) AOVOtt OttxtpEttxa~ 1tpodcrc.t~ Ecptxp.EV ovop.:X~ccr&txt, ota tOU YJ"tOL cruvUcrp.ov - ottxcp€pc.t oE ouoEv 'fJ ' ota p.t&~ cruHtx~ij~ Hym f) ota (f) ) tot~ > " for example, « Dion is not in both Athens and Corinth. )) Here 'an inconsistency in apparent in Galen. In a proposition designated > we exp ect to find the conjunction How ever , becau se h e present s a clear notion of the not-excl.uding alternative, for hi s precision h e deserves much credit. The definition of Aulus Gellius shows how vague was the notion in other mind s : ·> Unlike Gellius ' s definition , Galen' s is very clear: The not- excluding alternative is a proposition ~hich states that one member must be true hut the others may al so be true; it i s false only in the one r'

23

PL U TARCH :

Nloralia, ed. G. B ernardaki s, Lipsiaeo: 1888-96,

1059e. "' 33.11. 25

AuLus GELLIUS:

N. Y., 1927, XVI,

VIII,

Attic Nights, trans!. J. C. Rolfe, London14.

-37-

instance in which all the members are false. Apollonius 26 subscribes to this definition; and Galen uses the term in the same way in his other works. " If this proposition was known to the early Stoics, they did not use it. Probably it is a development of the later Stoics und er Peripatetic .influence. The earlier Stoics would argue that, since the conjunction > properly signifies only the excluding alternative, some other expression must be employed to indicate the present-day rul e, which requires us to em ploy another expression to convey the excluding alternative sen se; for exa mple , tx"Ctxov OUf.L7tE7tAeyp.€vov) for this proposition , and employ~; instead the term cc incomplete opposition >> (sA),m~~ f.LtXXYJ). Finally, Galen' s not- excluding alternative could have beeu suggested by th e notion of Aristotle's sub -contrary op· position. Proposition s suo-contrarily opposed ,c anno t both be fa lse; other w i ~;e their contradictories would both he true. 39 Sometimes two s uh-con traries may both he true . We must look lo th e material of th e proposition to know when both m embers are true, for th ey may both be true in contingent m a tler , although not in n ecessary matter. As we hav e seen, in Galen's not- excludin f! alternative it is al so n ecessary to look to th e matter in order to interpret correctly the con· junction « or , >> for we ca nnot follow the general Stoic interpretation that > (cuz ~psnxxt). '" Th e Stoics called their one proposition from opposition > " The conditional propo:::itiou I f' preci sely d efin ed by the following matrix of truth:

1

Sex/ . Emt'· Math. , Vlll, 109-lll.

" C ICERO : Academ icn, transl.

H. ]{a ekhalll , LonJun-N. Y.,

19:23, II, 143 . Sext. Emp. !'Hath. , VIII, ll2. ·• Sext . Emp. Pyrr., II, 104 ff. and Math. , VIII, 113 H. • Ding. Laert. , VII, 81. '' Sext. limp. P yrr. , II, 104 ff. 3

-

44· -

If the antecedent is

and the co n seq uen t i s

th e conditional pr o positi on i s

True

True

True

True

Fal se

False

Fal se

Tru e

Tru e

F alse

False

Tru e

The conditional proposition is, according to thi s d efinition, true in every case except wh en it begins with truth a nd ends with fal sehood. The conditional proposition, it may b e observed h e re, is yuite different from inference, which i s a noth er kind ol Stoic proposition. The conditional (ouVIJI111SV0'1) states that one thing implies another. It assigns no r eason or cause . This proposition i s well adapted to formal logic, because the material of the proposition may Le compl e tely ignored without losing au y of th e deductive value of th e proposition. Th e i 11 f ere nee (r:~p ~uU'I IJ 1-l ll ~ V O 'I )7 on th e contrary, must n ecessaril y r ega rd th e rnalle r of th e proposition. « According to Crinis in hi s Art u/ Dialectic, an infe r e ntial proposition is one which is introdu ced by th e conjuncti o n ' since ' ( ~7ts() and consi sts of an initial proposition and a con settu e nl ; for example , ' Since it is da y, it is light. ' Th e conjunction guarantees that the second follow s {rom the fir st and that th e fir st is r eall y a fact. >> « An inference is tru e wh en , startiu g from a truth , i t l' nd r,; in a consequ ent (from thi s truth) ; · for exampl e, ' Since il i~ d ay, lhl' "un is ove r th e earth. ' But it is fal se wh e n it l' iLl• e r starts from a fal sehood or tlot~ii not e nd in a con seque nt (from th e anteced ent) ; for exampl e, ' Since it is ni ght, Dion is walking, ' if thi s he said in th e da y- tim e . )) ' Onl y as an infer ence the last exampl e is d ecl a r ed fal se . It is true if we sul1stitnte > ( s~:s(). But Galen tells us that > Th e distinction of the Stoics in the use of these conjunctions was well known. For Galen, however. apparently there was no distinction in form between concl!tional propositions and inferences. Here we shall t' Xam ine hi s divisions of consequence. Whether he indicated coni"_e qu ence by th e conjunctional form or hy the ma. terial of the propositions, we shall see later. 14

15

2. Division of Consequena. The difficulty of und er standing Galen's teaching on consequence increases when he introduces his divi sion s. Consequence (axo),ou·iHa), he says, is ((either com1-1lete ( -rs),s[a) or incomplete (s)J,my); ). » 1 • This distinction is brought forth rather late in the Introduction; nor does he give a clear exposition of the nature of these two clivi sious. We are forced, therefore, to gather an explanation from his examples and not from definition s. As a wotking distinction the following appears to be sa ti sfactory: We have complete consequence when there is only one member ir1 the consequent; for example, « If it is 13 11 15 16

33.21. Cf. page 45. 8.22. C:f. pal-\e 34.16.

:w,

note 10, for Greek trxt.

-

47 -

day, the sun is over the earth. » We have incomplete consequence when there are two or more members in the consequent; that i s, the consequent is a not-excluding alternative; for example, « If Alcibiades knew justice, he either learned it from another , or di scovered it himself. >> Nothing doctrinally stated by Galen can be brought forth to support thi s interpretation; hut th e illu stration s that h e employed consciously to exe mplify incomplete conseq uence are all conditional s with a consequent of more than one m~ mb er. Unfortunatel y, h e specifically designates none of his ex a111pl~ s as complete consequence . . However, a deep er meaning presumably attaches to thi s tlistinction. It see ms that compl e te con sequence mean s equiva lence; that is, that two propositions so related imply each other. When th e fir st is present, the second also is present; and wh en the second is present, the fir st is present likewise . On the other hand , incomplete consequence appears to ht>/ the ordinary conditional proposition ; tha L is, th e a ntect•clt>n t always implies the consequ e nt , but tlw con SNflH' IIt d ol",.; not always impl y th e anteced c11L. . The arguments in support of thi ~ th eor y ar e dr awn from th e following compari son of th e exampl es used h y Galen. Wlwu he speak s of the differ e nce b etween the Stoics ; who r egard only the word s or the external form of a proposition , and th e P e ripatetics, who r egard not the words hut the ~ i f; ni ­ fication of the words or th e matter of th e pro position , he sa ys : In this statem ent he seems to indicate an analogy or eve n an equivalence, on the one hand, between complete opposition and complete con sequence with the first member w~ gative , and , on the other hand , be tween incompl e te opposition and incomplete consequence with the second member negative. We can hardly suppose that Gal e n , who was skill ed in the u se of equivalent propositions, '" e mployed the sam e kind of consequence as equivalent to two very different kind s of opposition. Probably h e is speakin g of two different kind s of consequence , even though be does n ot employ the names complete and incomplete in this in stance. Besid es, the words complete (t~/,~{cx) and incomplete ( 2/J,m~£ ), which he e mploy s to designate the divi sions of both opposition and conseq uence, would seem to indicate that th ey are resp ectivel y r e lated in some way. There is also the parallel in his r-;taternent that « things according to opposition never ex ist to ~f'L h er , >> wh er eas « things according to consequence alwa yR ex i~t toge th er. >> l111rnediately , of course, the objection will be rai sed tbat consequence in ge ne ral mean s that ((things always exist togeth er >> and in complete consequence , accord ing to our hypothesis, mean s that > Indeed, at first sight thi s explanation app ears inconsistent. But, if we r ecall that in complete opposition it is necessary that > whereaR in incomplete opposition « it is not n ecessary that one l1e tru e, lnll if one is tnw , th e oth er is fal se, » the difficult y van ishes. For tht ~ n WP can pa:-; il y perce ive th at, " 9.8: !crov os 1} otatpE'tL'X.YJ np6-cacrt~ ouva -.:a t -cip -.:owunp ),6ytp ' d 1-dl 1j[.L€pa Ecr-.:[, vu~ EO""tLV', t.lv EV O"XYJ[.LCX"tL AE~EW~ O"UV1] [1[1EVq> ),Ey6!lE'IO'I, ocrot [.LEV -cat~ cpw vat~ f16vov npocr€zoucrt, cruV'Y]flflEVov Cl'IO[lci~oumv, ocrot OE 't1) cpucrEt "tWV 1tPCXYf1tX"tW'I, OtEsEUYflE'IOV. wcrau-.:w; OE xed 'tC cOtOU"tO V ElOO> , In external form thes e propositions are exactly the sam e a s th e Stoic copulative; hut they are not th e same for Galen. To his mind a copu lative proposition is one in whi,ch between the connected members th~re is « neith er necessary consequence nor n ecessary opposition . >> The prese nce of con sequence or opposition is known from the mater .ial of the proposition. The only requi site for the Stoic copulative ii-i that the me mhers he connected by the conjunction c1 and. » Gale n "eem~ Lo he indicating thi s difference consciously when he says: H According Lo incomplete op position it is customary among the Greeks to . speak thus: ' Dion is not hoth in Athens and in Corinth, ' and · in all such propositions of 'i ncomplete opposition there will he

).

3 AULUS GELLIUS: A ttic Nights, lrans1. J. C. Rolfe, LondonN. Y. , 1927, XVI, vm, 9. ·• G. Zu; LIARA: S11mma Philosophica , Editio XVI, Paris, 1919, vol. I , Dialectica (24), p. 98. 5 33.23. Cf. page 23 , not e 29, Ior Greek t ext.

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this indicative word; but if you say by other words things which have neither consequence nor oppos,ition to one another, we shall call this kind of proposition a conjunctive ( OUfHtS7t/,syf-L8vov ), as in the proposition ' Dion walks and Theon disputes '; for these things, having neither opposition nor consequence, are explained as copulatives. Wherefore, when we deny them, we say the proposition is either a nega6 tive combination or a negative copulative. >> Obviously, according to Galen's mind, the negative copulative ( &7tocpanxov OUf-L7tS7t/,syflSVov) the iricomplete opposition(sAAt7t'f/~ f-L6.z·~) are not the same. Here , especially, it is most apparent that Galen is not following the formalism of the Stoics. If the negative copulative had meant for him what it meant for the Stoics, namely, a proposition of the form « Not both ..... and .... , >> he would have seen immediately that this class of propositions includes his incomplete opposition. It also includes the much larger class of propositions in which there is no opposition between the members , although their union is denied by the form «Not both .... . and ..... , >> as in the proposition « It is not true that Dion walks and Theon di sputes. >> According to the Stoics, the conju nction « and >> signified that the members were joined in the proposition; the negative (( not both ..... and ..... )) meant the d enial uf the union of the members in the same prop osition. For them there was no question of whether the members were joined on account of consequence, or separated on account of opposition. Here it is evident that, although Galen externally presents the Stoic copulative proposition s exactly , he really is not following the traditional Stoic doctrine.

6

10.9.

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SUMMARY OF PART TWO

We have seen that Galen presents Stoic compounrl propositions under the title of (&vcm6ostx'tot), that is , evident axioms. From th ese > with the utmos t exactness and formal rigor, were deduced other A6yot. Concernin g th e fiv e indemonstrable modes of Chrysippus Galen says : < icall y important, th e followers of Chrysippus called them the « fundaments )) (-rpo7tlxa). On them, indeed , th ey built th eir whole >ctly valid. Employing his f~xample of complt'Le opposition of more than two members, we have the two following syllogisms: Dion, or walks, or sits, or reclines, or runs, or stands; but Dion walks; therefm·e , he neither 8its, nor reclines, nor run.~. nor .~lands; 5Jlld

Difm or walks, or sits, or redines, or runs, or stands; but hP nor sits, nor reclines, nor runs, nor stamls ; therefore, Dion wa.lks.

'*

" 13.2: nf.c:t6vwv o~ cwv p.o:xop.evwv ovcwv bd p.·J1v cc:f.c:!o:~ l)cot yc: €v 6napxc:tv E1n6nc: should have said « the conclusion will be a not-excluding alternative (7ttxptxo ts~euyp.svov) of these . » Since no special name or numbe r is given to the no texcluding alternative syllogism , we may conclude that Galen would include it und er the general class of syllogi sms from opposition.

7

16.11.

-·- 71 . -

CHAPTER

III

CONDITIONAL SYLLOGISMS

1. Syllogisnis from Complete Consequence. > , he shows that it is possibl e from it Lo conclude all four of the above-mentioned morl es; but he a rids: « Because it is not always thus, » (i. e ., not in all conditional syllogisms is it possible to conclude in four mod es) According to Galen , as we saw, the opposition is only in the matter of the proposition, not in the formula « Not both ... and ... >> Therefore, he rejects all syllogisms from negative copulatives in which there is not also opposition. in the material of the propositions. Syllogisms which are built on material opposition he includes among his syllogisms from incomplete opposition. ' Naturally, by thus ·changing the notion of the third indemonstrable, Galen greatly restricted the syllogisms possible in this class. According to the Stoics, any propositions could be connected by the negative copulative formula , and from the affirmation of the truth of one member it was possible to conclude the denial of the other. But, according to ~alen's limited third inJemonstra-

33.24-34.10. " 34.24.

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78-

ble, a syllogism is possible only when there is incomplete opposition in the material expressed by the members of the compound proposition. Here it is quite apparent that Galen completely neglects the formalism of the Stoics. He is consider ing not the conj unction s but the matter of the propositiOns. Therefore, h e r ejects th e third indemonstrable, since, as h e co ntends, this syllogi sm is not from a negative copulati ve proposition, but from opposed propositions. His syll o~ i s rn is the same as the disjunctive syllogi sm of elassica! lo gic.

-

79-

SUMMARY OF PART THREE

In his doctrine on Stoic syllogisms Galen concisely presents a formal study of the five indemonstrable syllogi sms of Chrysippus. Except in regard to the third indemonstrabl e, that is, the negative copulative syllogism, he fol1ows rigorously the formalism of the Stoics in developing the syiJogistic modes. H e supplements these four modes with his own disjunctive mode from incomplete opposition , tl~t · not-excluding alternative mode. and tlw syllogi !irn R from excluding alternative and disjunctiv e propositiom of more th an two m ember:,:.

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PART FOUR

EQUIVALENCE AND CONVERSION

lNTRODUCTlUN In this final part we present Galen's Joctrine ou (1) Equivalence anJ (2) Conversion. .Equivaleuce pertains only to propositions. Conversion is applieJ Ly Galen Loth tu propositions and to syllogisms.

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CHAPTER

I

EQUIVALENCE

When he treats compound proposltwns and the syllo . gisms developed from them, Galen occa!'ion ally introduce:" examples of equi-valent compound propositions to clarify hi~ statements. Although he does not specifically explain the equivalence of propositions, we ·may gain so me notion ol his teaching by gathering here some of his many example.~ of equivalence. In this matter Galen seems to have been au incomparable master for his time. He wrote a special treat1 ise, Concerning Equivalent Propositions. He shows that he considered the subject highly important, for he frequently exhorts his readers to be well versed in equivalent pro2 positions. There is some doubt in regard to the ancient signification of the term « equivalent propositions >> (too~t>VtX!-LOtlOCY..l 7tpo-ccioEt£ ). Did it mean propositions identical in sense, or simply equivalent proposition s ? Today logicians distinguish sharply between the two. It appears that Galen did not make a distinction; at least, he did not employ it. Since his examples always include. propositions which are equivalent Lut have not the same sense, presumably he understood the word in this sense. The term is also used similarly by Alexander Aphrodisias. " 1

24.22. 24.20. " Alex. in APr., p. 84.13 and 15. 2

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From Galen's numerous examples we select the three following equivalences : The proposition > is pronounced equivalent to « If it is not night, it is day. >> ,, Here the excluding alternative is said to be equival~nt to a conditional proposition with a negative antecedent. Thi s equivalence is true only according to our interpretation of Galen's complete con sequence in a conditional proposition. Again, the proposition is equivalent to « Tf Dion is in Athens , he is not in Corinth »; that is, the di sjunctive proposition is equivalent to an incomplet,e consequence with a 5 negative consequent. Finally , th e proposi tion > is equivalent to « H Alcibialles knew justice, he kn ew it eithe r having learned it from another or having di sc oven~ d it himself. >> " He•·e Galen matle a slight error. H e would h~ve been more precise, if for the second proposition he had substituted: (( If Alcihiades did not know justi ce havin g learned it from another, he knew it having discoveretl it himself. » Th en he would hav e had a copulative proposition with a not- excluding alternativf' in th e second member , which is equivalent to a conclitional proposition with a negative copulative antecedent and a positive copulative consequent.

4

9.8.

9.18 . • :38 .4 ff.

0

~

83-

CHAPTER

II

CONVERSION

l. Conversion of Propositions. Intimately connecteJ with his teaching on equivalence is Galen's doctrine on th e conversion of propositions. He thoroughly und erf'tood the conversion of all classes of proposition.s, and in the Introduction he gives many exact conversions. It is important to keep in mind that for Galen only equally true propositions convert by a change of the ord er 1 of the sentence . He di stinguishes b etwee n transposition (tivCJ.r:npo:p~) and conversion in rh e strict sen se (&vnoL:po:p~). Transposition is the mere change of the order of the members of a proposition, in which the truth-value of the original proposition is not necess~rily preserved. Conversion is the change of the order of the members of a proposition , in which the truth-value of the original vroposition is preserved. Therefore , (( converted propositions are equally true , whereas transposed propositions are not equally true. )) " Galen has been much mi sunderstood in regard to this distinction. Necessarily, since he uses conversion in refer1

14.11. This doctrine is only negatively stated in I he Introduction. It is definitely develop ed by Galen in De Simplicium Medicamen torum Temperamentis ac Qualtatibus, Lib. II, ch. III, Kuhn, XI, p. 465.12: o1 &ntatpecpov-rE~ oux o1 &vaatpecpovtE~ &H·~).ot~. ).6yot auva). Y}&dwnot . ' Cf. JANET, P. et G. SEAILLES : Histoire de la Philosophic, 15th Edition , Paris, 1932, p . 574: r< A propos des equipollentes, 2

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ence to the conversion of conditional propositions, the term avnaTpo'f'~ must also signify contraposition, for this latter is th e only correct conversion in conditional propositions. In the transposition of the proposition « If it is day, j t is light, >> Galen did not transpose « if >> with its proper member; instead , h e transposed it in this manner: > Although his transposition in this example is false , nevertheless it is . in conformity with hi s statement that > Without doubt, he regarded the transposition of compound propositions as a process parallel to that of categorical propositions; and, thus, he ·Concludes that, as the latter are not always equal1y true, so the 1 former are not always equally true. Sextus effects the tran sposition of the above-cited proposition by tran sposing with its proper m e mber in this manner : cc It is ligh L, if it is day. >> • Galen's conversions of conditional propositions conform to the ordinary teaching and are well executed. « Conversion , )> he says, is effected > H e understands that transposition enters into th e conversion of th e conditional proposition , for h e transposes in this example: >

' Sext. Emp. Math., VIII, llO. ' 14.1.') : Y.CGta · p.tnot ta>; ~o that the same syllogi~ti c mod e results when we convert a 10 h ypothetical syllogi sm. Applying thi s doctrine to the conve rsion of th e conditional propo;;ition and the syllogism , we ge t the following: ORIGINAL SYLLOGISM

If it is day, it is light ; hut it is day ; th erefore , it is light,. CoN v~: HTEn ~YLLOGIS tvt

If it is da y . i1 is light; hut it is not light ; therefore , it is not day. The cotn'torlt'd ,; yllof!;i c: m i:-o tlw :-o t-'cond rnode of the conditimt al syllnl-\i sm , for tltr cott ;.; equcnl i:-o dt>ni ed in th e assumption and it proves the negation of th e antecedf'nt . The demon strability of the second conditional mode seems to h e what Gal en ha ~ in mind when he says that this mode i s not strictly inde mon:o;trahl e : . 7.

.l 6. 7: x.al -co[v ~.Jv c!H:;mp -ca ), ~1-11-la-ca cr•JvaA 'Y]a-eue'tat x.a-ca -cYjv xn~cr-cpo'f'~v, o:)'t(u x.al :ot ; hut hi !' ex planation s are not Stoical, hecau se he follow:-; the Peripate ti c practice of examinin g th e matter of the proposition s, instead of th e Stoic custom of considering only the conjunctionr;. To th e traditional Chrysippian propositions h e adds th e di sjunctive afHl the not- excluding altemative proposition s. His Introdu ction is al so one of th e ea rli es t source" for the doctrine on equivalence and co nversion of compound proposition s. Although hi s interpretation of Stoic proposition :; is not strictl y formal , Galen's prese ntation of the hypoth e ti ~al syllogi sms is in accord with th e most ri gid Stoic formalism. He cl early ex plain s th e unfamiliar Stoic terminology per tin ent to sy llogi sms, and he accepts four of th ~ five tradition a l indemonstrable formula e. These h e supplerneuts with the disjunctive and the not- excl udin g alternativ e syllogisms. H e comple tes the treatm ent of th e Stoic sy llogism with hi ;; ex traordinary doctrine on th e conv er sion of hypothe tical syllogism s. Galen's teac hing on th e logic of propositions is a comple te r ecord of the state of Stoi c logic in th e second century.

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He not only summarizes the doctrine of the centuries immediately preceding but indicates the direction actually followed by subsequent logicians. His tendency to interpret Stoic logic according to Peripatetic principles finds its culmination in classical logic. As this tendency so to interpret Stoic Iogie became more and more pronounced, the logic of the Stoa declined more and more until , having eventually lost its distinctiveneRs a~ a branch of dialectics, it was completely absorbed into Peripatetic logic. He proves himself beyond all doubt an independent thinker and not a mere compiler, for the logic of propositions comes from his hands colored by the touch of his originality. The study of this elementary logical treatise makes us strongly desire to know some of th e more extensive work s of Galen, the great logician, who has giVen us The Introduction to Dialectic.

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9L-

GLOSSARY

&.xoAou&ia, cons ctlu e nce, 23, 44, 4 7 ; eHm~c;, &.., incomplete COilSef(UeJlC(, l 4 7 1 52. taAda &.., complete consequence,

47, 51.

proposttwn, proper di sjunction, 24, 27, 30, 35, 62, 71. otatpe'ttx6c;,, di sjunctive, 29, 41,

48. OtA~[-L!J.O!:'tOt

&.va7tOOetX'toc;,, indemostrabl e , 61.

cruUoytcr!J.ot, twopt·emi se sy Jlogism s, 86.

&.vacr'tpicpatv, to tra-n s pose, 85 n. l ; &.vacr'tpocp~, transposition, 84.

eL7tep, if in faet, 43.

~ntxaicr6-at,

EAAm~c;,,

to oppose, to COJI· tradi , t, 39, 40 n . 1 ; &.v'ttxd!J.eVa, contradictories, 26.

&.ntcr'tpicpatv, to convert, 85 n . J ; &.ntcr'tpocp~, , c onv e r sion,

&.~wuv, to ace e l'te ,

84.

18; a7tAOUV simple propositio-n, 18, 19; oux a7tAo uv &.., compoud proriosition, 19.

&..,

a1tAo uc;,, s imple, 17, ~2.

bavciwc;,, contt·arily, 40 n. l. £voo~oc;,,

r e o. tin g on opinion s, probable , 9.

E7td, since, 4 7. E7tecr&at, to follow (logi c ally ), conclud e _ E7tO[-LeVOV 1 co nclusion, 46. lmcr't~!J.'Y), scie n ce,

&7tAwc;,, simpl y, 33. '

'

inco111ple t c; s e c &.xo),ou{Ha a nd !J.ax-~-

18.

&.~tW!J-0!: 1 proposition,

.

a1, if, 43 , 47 .

tX7tOOet~tc;, , demon stration,

22.

?.mcpopli, conclusion, 65 .

&.7tocpa'ttx6c;,, negativ e , 41, 58, 62.

1), or, 29.

&.px~, pt·inciple,

~Ye!J.O'Itx6c;,,

10.

Oethapoc;,, second; oautapov, con sequent, 43. ota~wyvuvat, to oppose , desjoin, exclude. Ote~WY!J.EVXV ( &. ~1w­

(1a),

excluding

alternativ e

10

!J.O'I tx6v, 63. ~YOU!J.eVOV 1

directive, 63 ; ~ya­ direc ting principle, ant eced ent,

61.

-Y)'tot, or, 26, 29.

92-

43, 46,

ZcroouwxfJ.Erv, to be equal, equivalent, 82. xotv6~,

common . I!(.Otv6v, co mmon property, 30.

A~yetv, to follow logic.ally. AYjyov, conseque nt, 43, 46, 61.

syllogism, 61.

1-L~Xsa{}at,

to be co ntrat y, 39;

f1tXXOf1EVa, contraries, 26.

23, 29. eAAt7tY}~ 11·, incomplete, 30, 41-58; "tEAELa !1·, complete, 30, 48 .

7tpo"tacrtialet:tic method, 9; proof, 22.

Imprope r (int·omplt•tf') ,

Diog•'tws l.aertius, H, 18, 20, 27, 14, 65.

Tncompletc, ~ef' alternativf' and t:.o nst'quence .

DiH,I'ting principle•, G:L

Ind emonstrable, 12, 20, 23, 61, 65; numher of, 65.

Di~junctivt· , ~~·t·

proposition , 28, :H; allt·rnativt•.

[ndieation , 22.

Dopuntists, :l:.L

Infere nce, 19, 4.'>, 47.

Elias , '14

lnstll'iahility,

11.

2.

E picltelus, 6:3 .

:w.

[uterrogative, 18.

95-

.Iaeger, W., 9.

Philo , 44, 52 .

.Janet, P., 84 n. 3.

Philoponus, 4, 64 .

Kalbfleisch, C., 5, 16, 77 n. l.

Place, Hl.

Keynes, ./. , 62 n. 2.

PllttO , 9, 14.

Log ic, Aristoteliam, 9; formal defined, 9; hi story of, 9; modal, 10; logi c of terms, 12, 22; of propositions, 12; Stoic,

Plutarch,

ll.

:~7.

Positi vism, 13.

Prantl ; C., 15. Prem ise, 64.

Lukasiewicz, ./., 13 n. 23, 13, 16 n. 11, 52.

Principles, 10, 22.

Marcus Aurelius, 4.

Prisciwws , 20 n. 9.

Material

of propos itions, 24, 39, 52, 72, 77.

2 1,

MathemaLi(:al m ethod , lO, 14. Matrix of tmth, 28.

R eductio ad imposs ihil e, 22, 87.

Michael , 14 n. 2.

Repugnalll:c, 39:

Minas, M., 15.

Rule, 13.

Mitigated-reali sm , B.

Sch.e n eit!er , H.,

Mode, 65, 68, 87.

:n.

Sc holastics, 1, 57.

Negati ve I:OJHilative, 35, 56.

Scholz , H. , 10.

Nicon , 4.

Science , 10.

Not-excluding, see alternative.

Seailles, G., 84 n. 3.

Opinions, 9, 23. Opposition , Galenic, 30; division of propositions, comp l ete, 30, 35; two m embers, 31, more than two, 32; incomplete, 33, two m embers, 34, 35, more than two m ember s, 34; not-excluding alternati ve or fal se opposition, 35, 37; nam es, 41; or igin , 38. Stoic, 23, 26. Syllogisms, 72.

o.·, 20, 26,

Proposition, definition, 18; Galen 's divis io n, 2 1, 23; h ypoth etical , 17, 21. Stoic division, simpl e, 17, not-simple of compound, 17.

36.

P eripatetics, 2, 9, 19, 38.

Second, (consequ e nt), 43. s(~:t tu s

Empiricus, 2, 19, 22, 27, 43, 44, 55, 64, 85.

Sheffer, H. , 35 n. 20. Since, 45, 4 7 f.

Ste plumus, 14 n . 2. Stoics, 2; logic of, 9 ff; see pro · position~ and syllogism s. Subcontrary opposition, 41.

Suidas, 5.

96 -

Symbols, 12; Aristotelian, 12; Stoic, 12. Syllogism, 60; Aristotelian or categorical, 10, 22; Stoic or hypothetical, II, 12; conditional, 92; copulative, 77; opposition, 67.

Thomas, St., 55 n. 2. Transposition, 84. Tropicon, 63. Two-premise syllogism , 86. Vel, 36.

Terminology of Stoics, 43, 46, 6:).

Words, 13.

Terms, 46 .

Zeller, E., 8 n. 32, 15.

Theophrastus, HI, 14, 54.

Zeno, 11.

Thesis, 13.

Zigliara, T., 57 n. 4.

Working principle, 22.

Supf• rinnuu penni ssu .

IMPRIMATU R Rumae di e lO mai 1940.

AL.

THAI;I.IA ,

Arch. Caes. VicesgerP/IS .

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