Science and Speculation: Studies in Hellenistic Theory and Practice 052124689X, 9780521246897

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Science and Speculation Studies in Hellenistic theory and practice

edited by Jonathan Barnes Balliol College, Oxford

Jacques Brunschwig Université de Paris X-Nanterre

Myles Burnyeat Robinson College, Cambridge

Malcolm Schofield St John’s College, Cambridge

C am bridge U niversity Press Cambridge London N ew York Melbourne Sydney

N ew Rochelle

Editions de la M aison des Sciences de l’H o m m e Paris

Published by the Press Syndicate o f the U niversity o f Cam bridge The Pitt Building, T rum pington Street, C am bridge CB2 irp 32 East 37th Street, N ew Y ork, N Y 10022, USA 296 Beaconsfteld Parade, M iddle Park, M elbourne 3206, Australia and Editions de la M aison des Sciences de l’H om m e 54 Boulevard Raspail, 75270 Paris Cedex 06 © Maison des Sciences de l’H om m e and C am bridge U niversity Press 1982 First published 1982 Printed in Great Britain at the Pitm an Press, Bath Library o f C ongress catalogue card num ber: 82-4221

British Library Cataloguing in Publication Data Science and speculation: studies in Hellenistic theory and practice I . Science— H istory— Greece 2. Science, Ancient I. Barnes, Jonathan 509'.38

Q127.G7

ISBN o 521 24689 X hard covers ISBN 2 901725 47 3 (France only)

Contents

Préface Victor Goldschmidt Acknowledgements Introduction Jonathan Barnes Bibliographical note Chronological table I

The method of the so-called Methodical school of medicine Michael Frede Princeton University

page ix xvii xix xxv xxvii

i

2 Medicine, experience and logic Jonathan Barnes Balliol College, Oxford

24

3 Geometry and scepticism Ian Mueller University o f Chicago

69

4

Force et science des machines François D e Gandt C .N .R .S ., Paris

96

5 Observational error in later Greek science G. E. R. Lloyd King’s College, Cambridge

128

6 Astrology: arguments pro and contra A. A. Long University of Liverpool

165

7

The origins o f non-deductive inference M. F. Burnyeat Robinson College, Cambridge 8 On Signs David Sedley Christ’s College, Cambridge

9 Confirmation et disconfirmation Jean-Paul D u m ont Université de Lille III 10 La théorie épicurienne du droit Victor Goldschm idt Université de Picardie Indexes (i) Passages 327, (ii) General index 341, (iii) Index and glossary of Greek terms 349

193 239 273 304

In m em oriam

V I C T O R G O L D S C H M I D T ( 1914- 1981)

Ce volum e était sous presse lorsque nous avons appris la brusque disparition de V ictor G oldschm idt, le 25 septem bre 1981. Ce m aître discret et célèbre, d o n t chaque livre a fait date en France, avait accepté, avec beaucoup de sim plicité et de gentillesse, de “ p a tro n n e r” les travaux de notre C onférence, et d ’y participer activem ent. En prenant connaissance des textes q u ’il avait bien voulu nous confier, nos lecteurs p o u rro n t voir quelle place il y avait tenue. Ce q u ’ils ne p o u rro n t pas m esurer aussi directem ent, c’est l’effort d ’intelligence et d ’am itié q u ’il avait su fournir, pour com prendre et p ou r se faire com prendre, par delà les différences d ’âge, de langue, de form ation, de style intellectuel parfois. De m êm e, et plus généralem ent, on peut laisser parler p o u r elle-m êm e son oeuvre, dans son abondance et sa diversité. Il a écrit sur Platon, sur les Stoïciens, sur Epicure, mais aussi sur M ontesquieu, Rousseau, beaucoup d ’autres; la veille de sa m ort, il avait rem is à son éditeur le m anuscrit d ’un livre sur A ristote. Ces travaux exigeants et subtils, où la densité s’allie à la rigueur, sont com m e les essais d ’une m éthode q u ’il n ’a pas cessé de m éditer et d ’appro­ fondir. M ais il appartient à ceux qui o n t connu et aimé ce penseur probe et secrètem ent passionné, cet h o m m e intraitable et qui savait être exquis, d ’ho norer sa m ém oire et de tém oigner, s’ils le peuvent, de l’exem ple q u ’il leur laisse. J.B . J.B . M .F.B . M .S.

Préface

Le regain d ’intérêt p o u r la pensée hellénistique pourrait s’expli­ quer, de prim e abord, par des raisons m odestem ent philologiques. Q u an d H . U sener, en 1887, publie ses Epicurea, il prend soin, dès la prem ière page de la préface, de nous avertir que ce n ’est pas “ l’adm iration de la philosophie épicurienne” qui a m otivé son travail, mais seulem ent, “ ainsi q u ’il arrive à un g ram m airien ” , l’obscurité et les difficultés q u ’il avait rencontrées chez D iogène Laërce. C ’est à l’instigation d ’U sener que J. von A rnim entreprend sa collection des fragm ents stoïciens et, à son tour, nous prévient q u ’il s’est su rto u t attaqué à C hrysippe “ qui avait été négligé” auparavant. C et intérêt p h ilo lo g iq u e 'p o u r des textes insuffisam ­ m ent édités se m anifeste de nos jo u rs dans les entreprises, encore en cours, de refonte de ces deux recueils, et dans des éditions nouvelles, com m e celles de Polystrate, de Philodèm e, de D iogène d ’O enoanda, de Panétius, de Posidonius, etc. Il n ’y aurait donc là rien qui excéderait les exigences de l’érudition, pas plus, par exem ple, que dans la curiosité que suscitent, depuis quelque tem ps, les textes de basse époque, com m e la Seconde Sophistique, avec Libanius et Aelius A ristide, ou encore l’épopée tardive, avec Q u intus de Sm yrne ou N o n n o s de Panopolis. C ette explication, recevable en u n sens, serait m anifestem ent incom plète. L ’atten tio n accordée au jo u rd ’hui à la pensée hellénisti­ que est bien d ’ordre doctrinal, et c’est de cela q u ’il faut essayer de rendre com pte. S’agissant de philosophie, on pourrait y voir d ’abord une réaction contre le ju g em e n t de H egel, qui avait disqualifié le dogmatisme et le scepticisme com m e des doctrines de la “ conscience de soi”, com m e un “form alism e de l’entendem ent”, et y avait trou v é u n déclin certain par rap po rt à l’aristotélism e qui,

Préface lui, est une “ philosophie du concept” . Ce ju g em e n t a été inter­ prété, p lutôt que discuté, par M arx, dans sa dissertation sur La différence de la philosophie de la nature chez Démocrite et Epicure (1840). M arx essaie d ’éclairer, à la lum ière de la philosophie grecque, son p rop re présent. C o m m e après la m o rt d ’A ristote, on assiste, après la m o rt de Hegel, à l’apparition d ’une “ m édiocrité” , à l’entrée en scène de “ d em i-esprits” (polém ique contre les jeunes hégéliens, en particulier, Ruge). M ais, d ’autre part, les doctrines hellénistiques “ ne sont-elles pas les p rototypes de l’esprit rom ain [Hegel l’avait déjà dit], la form e sous laquelle la Grèce ém igre à R om e?” (com m e l’Athènes de T hém istocle a changé d ’élément): il s’agit, autrem ent dit, de transplanter la philosophie (qui, en tant que telle, est aussi indépassable après H egel q u ’elle l’a été après Aristote) de son élém ent traditionnel (la pensée pure) dans cet élém ent nouveau q u ’est la “ praxis politique et économ ique” (Löwith). O n ne saurait donc inv o q u er la dissertation de 1840 p ou r réform er le verdict hégélien et p o u r tro u v er un antécédent véritable de la faveur actuelle tém oignée à la philosophie p ost­ aristotélicienne. T o u t au plus, dans cet o rdre d ’idées, pourrait-on m entionner des auteurs m arxistes m ineurs qui essaient de tro u ver chez Epicure de quoi conforter le m atérialism e et l’athéisme, et tentent de tirer du cinquièm e chant de Lucrèce une philosophie du progrès et du sens de l ’histoire. Rien de to u t cela ne concerne, ni l’épicurism e, ni l’actualité de la pensée hellénistique. D e fait, l’intérêt renaissant, sinon pour cette pensée en général, du m oins p o u r celle des Stoïciens, est bien due à une réaction, non pas contre H egel directem ent, mais contre un de ses élèves, l ’historien de la logique C. Prantl. C ette réaction, com m e on doit le noter par parenthèse, est d ’ailleurs beaucoup m ieux fondée: alors que l’appréciation hégélienne des écoles hellénistiques garde une portée philosophique certaine et n ’a du reste jam ais été pro prem ent réfutée, le ju g e m e n t que Prantl a p o rté sur la logique stoïcienne tém oigne d ’une rem arquable incom préhension et ne constitue plus guère q u ’une curiosité historique. O r l ’initiateur de ce revirem ent est le logicien polonais J. -Lukasiewicz. D ans une série d ’articles, à partir de 1920 (réunis dans les Selected Works) et dans son ouvrage de 1951 sur La syllogistique d’Aristote du point de vue de la logique formelle moderne, il a cru tro u v er chez les Stoïciens la thèse de bivalence, u n calcul propositionnel avec des variables, des connecteurs binaires; ces résultats ont été confirm és et élargis

Préface

XI

(par une confrontation, en particulier, de la sém antique stoïcienne avec celle de Frege) par H . Scholz, I. M . B ochenski, puis dans les études de B enson M ates (Stoic Logic (Berkeley, 1953)), de W. et M . Kneale ( The Development o f Logic (O xford, 1962)). Il faut essayer de com prendre la signification et la portée de ces travaux dans Thistoire du stoïcism e et de son exégèse. Le stoïcism e, sans doute, n ’avait pas besoin d ’être découvert. C icéron et Sénèque en ont assuré la transm ission à travers le m oyen âge occidental; le X V Ie siècle voit renaître un néo­ stoïcism e, physique avec Pom ponazzi, éthique avec Juste Lipse, G uillaum e du Vair, C harron; plus tard, les idées de droit naturel et de religion naturelle s’appuient sur le stoïcism e, et l’élaboration de la conscience m orale m oderne, de Descartes à Kant, en passant par Spinoza, se conçoit difficilem ent sans l’im pulsion stoïcienne; cet élan ne s’est guère ralenti depuis lors: on en trouverait des tém oignages chez Schopenhauer et N ietzsche, chez T aine et Renan, chez E m erson et ju sq u e chez A. M alraux. Mais ce n ’est pas du to u t de cela q u ’il s’agit. Ce que découvre et inaugure la date de 1951 - date prise ici sym boliquem ent - c’est quelque chose d ’entièrem ent différent: la réhabilitation scientifique du stoïcism e, c’est-à-dire l’unique label qui puisse garantir sa valeur actuelle et lui m ériter l’attention de la pensée contem poraine. O n savait bien q u ’en dépit du ju g em e n t de K ant, la logique avait progressé depuis A ristote. Ce q u ’on croyait voir m aintenant, c’est que ces progrès avaient déjà été, sinon accom plis, du m oins ébauchés et anticipés par la logique stoïcien­ ne, si récem m ent et si vivem ent tenue en m épris. A u trem en t dit: la philosophie scientifique contem poraine, peu intéressée, en tant que telle, à l’histoire de la philosophie, venait d ’accorder à ce vieux systèm e son dignus intrare: le H u ro n avait fait son entrée dans la Société Royale. Les conséquences de cette p ro m o tio n sont considérables. Essayons d ’en indiquer seulem ent les plus apparentes. Le stoïcism e, le vrai, le scientifiquem ent valable et qui, seul, avait bénéficié de cette réhabilitation, c’était sa logique. D u coup, on était débarrassé de sa physique archaïque, avec ses thèses inacceptables, telles le fatalism e (le “ déterm inism e” , avait dit Lukasiew icz) ou le R eto u r éternel. D ébarrassé aussi de sa m orale pesante: on pouvait enfin avouer franchem ent que celle de l’épo­ que im périale ne saurait engendrer q u ’un “ ennui m o n u m en tal” , et

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déjà le “ suicide raisonnable” de Z énon ne paraissait guère raisonn­ able. D u point de vue de l ’exégèse: puisque la logique stoïcienne fournissait une confirm ation du calcul propositionnel et de la sém antique frégéenne, c’est donc q u ’il était légitim e, en retour, d ’appliquer à la lecture des textes stoïciens les acquisitions scien­ tifiques m odernes, c’est-à-dire, par suite d ’une conjonction dont il faudrait débrouiller les origines diverses: la logique sym bolique, la philosophie analytique et aussi la linguistique. L ’actualité du stoïcism e confirm ait donc ces disciplines, non pas seulem ent en tant que telles, mais en tant q u ’instrum ents exégétiques. Il n ’est pas étonnant q u ’à p artir de là, l’application en ait été faite à des textes non-stoïciens. En ce qui concerne l ’histoire de la philosophie: deux idées sem blaient se dégager de ces travaux. Celle de progrès, d ’abord, car m algré tous ses m érites, la logique stoïcienne n ’égale pas en perfection la nôtre. M ais l ’idée dé vérité éternelle to u t autant: il n ’y a pas eu progression continue, du P ortique aux écoles contem po­ raines, et cependant l’un et les autres tém oignent de la m êm e vérité. C ’est donc q u ’il y a, com m e o n a pu le dire, une logica perennis qui pourrait servir, au gré des auteurs, à fonder une philosophia perennis. L ’histoire, par là, si elle n ’est pas biffée com m e telle, n ’oppose donc aucune objection préjudicielle à une lecture im ­ m édiate, directe, des textes antiques, et nous autorise à ju g er ceux-ci d ’après n o tre standard de vérité. Il y a là com m e un retour à l’historiographie telle q u ’elle était pratiquée d ’A ristote à Hegel: depuis le positivism e et le développem ent des disciplines histori­ ques et philologiques, il avait fallu, en face d ’une doctrine du passé, se dem ander d ’abord ce q u ’avait voulu dire l’auteur; auparavant, et m aintenant de nouveau, il suffisait de se dem ander si elle était vraie. C ette entreprise est belle, sans doute; elle n ’est pas sans périls. Ce serait une question de savoir si le m o t de vérité se prend, de part et d ’autre, dans u n sens univoque, et si n o tre fonction de vérité peut s’accorder avec ce que les écoles hellénistiques appellent critère de la vérité. O n s’interrogerait de m êm e sur l ’idée que nous nous faisons, aujourd ’hui, de la philosophie par rap p o rt à 1’ “ art de v ivre” et à l ’idéal du sage; ou encore sur le scepticism e qui, certes, nous paraît im m édiatem ent accessible dans les gros traités de Sextus, mais qui, d ’abord, a été un m ode de vie p ou r P y rrh o n et

Préface

xiü

qui sera transposé dans l’école épicurienne com m e une technique en vue de l’ascèse des désirs. O n pourrait se dem ander encore si le traitem ent auquel nous soum ettons souvent les diverses thèses des doctrines ne renouvelle pas le procédé de la doxographie antique qui consistait à découper chaque doctrine en tranches bien distinc­ tes, en dogmata, alors que les stoïciens avaient conçu leur philo­ sophie com m e un ensem ble organique, com m e un système, dont toutes les thèses sont enchaînées les unes aux autres par l’exigence de Γimplication réciproque. Il n ’est pas sûr n o n plus que leur logique puisse être com prise isolém ent et en elle-m êm e, ce qui était peut-être l ’avis de Γ “ hérétique” H érillus de C arthage, alors que l’orth od ox ie de l’Ecole ne cesse d ’affirm er em phatiquem ent que la logique est une partie (et non un organon préalable et détachable) de la philosophie; on peut douter, enfin, que le form alism e m oderne soit bien pro pre à in terpréter une logique qui “ place au com ­ m encem ent la théorie de la représentation et de la sensation” (DL vu 49). Les travaux de Lukasiew icz ont placé la logique stoïcienne dans le collim ateur de l ’actualité. Le regain d ’intérêt p o u r la philosophie hellénistique en général est dû à d ’autres causes encore, m oins aisém ent décelables (négligeant ici des causes contingentes, com ­ m e la découverte des papyrus dont ont bénéficié su rto u t les études épicuriennes). O n ne peut guère hasarder là-dessus que des conjectures. La génération qui, après la m o rt de H egel, s’était dem andé com m ent il était possible de philosopher encore, s’est reconnue, on l ’a rappelé to u t à l ’heure, dans les efforts de la pensée post-aristotélicienne. Il sem ble q u ’à nous aussi, la philosophie hellénistique tende un m iroir, m êm e si nous ne prenons pas toujours plaisir à nous y regarder. N ous aussi som m es partagés entre le dogm atism e et le scepticisme, com m e entre deux p ropen­ sions q u ’il ne suffit pas de déclarer com plém entaires, parce q u ’elles ne définissent plus, com m e chez les Grecs, des positions philo­ sophiques claires: elles se jo ig n e n t souvent et parfois se confondent chez un m êm e auteur, mais elles restent en état de guerre perm anente parce que, plus que la réflexion sceptique qui, en un sens, est la philosophie m êm e, le dogm atism e est “ la chose du m onde la m ieux partagée” , encore q u ’il soit rarem ent avoué ni m êm e reconnu par les dogm atistes m êm es. Plus précisém ent encore: il y a deux tendances dans la philosophie hellénistique, qui

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ne s’épanouiront que plus tard, mais qui y sont dès l’abord présentes: le syncrétism e (bien avant q u ’A ntiochus ne le m ette en systèm e), à quoi correspond chez nous un certain oecum énism e qui n ’est pas seulem ent d ’ordre théologique; et le m ouvem ent, préparé par la propagande et la large ouverture des écoles, qui aboutira à la philosophie populaire (dont Sénèque, plus tard, sera le représentant le plus ém inent, com m e l’était, à notre époque, Sartre). Il y a autre chose encore. L ’époque hellénistique, par opposition à la période précédente, offre un trait paradoxal: alors que se m ettent en place, à l ’échelle m ondiale (mais régionale aussi bien, à A thènes, en particulier) des régim es m onarchiques et autocratiques (dictatoriaux, si l’on préfère, ou “ présidentiels”), on assiste (ce qui n ’était pas encore le cas, dans ces proportions, du tem ps des sophistes) à une véritable démocratisation de la philo­ sophie: d ’une autre m anière que l ’Académ ie et le Péripatos, les écoles hellénistiques (et cynique) essaim ent, se répandent dans toute l’oikoumenè, et proclam ent qire la philosophie est l’affaire de tous. Par contre-coup, la philosophie risque de tom ber au niveau des m ilieux où elle prétend m iliter: elle fait partie de la culture générale, prend la défense des “ opinions de la foule” (Polystrate) et m êm e, dans la Rhétorique de Philodèm e, professe son entier accord avec ces “ opinions” ; Plutarque transform e les “ notions com m unes” de C hrysippe en une philosophie du sens com m un. Il en résulte (en dépit du penchant de cette époque pour la spécialisation et po ur l’érudition) une espèce de p ro m o tio n de l ’usager, p o u r ne pas dire du consommateur: n ’im porte qui, à la lim ite, peut avoir des idées sur des questions philosophiques et, la rhétorique aidant, les exposer sans encourir le ridicule, discuter de plain-pied avec les grands ancêtres com m e avec des collègues ignares: Platon avait redouté le com bat avec Parm énide com m e un “ parricide” , mais Epicure traite sans façons D ém ocrite de “ bavard” et P y rrh o n de “ rustre ig n o ran t” . Q u an t aux génies créateurs qui, pas plus que de n otre tem ps, ne sont des philo­ sophes, mais s’appellent Euclide, A rchim ède, A pollonius, ils prennent leurs distances, et E ratosthène revendique le titre de savant (philologos), de peur d ’être confondu dans ce que Rousseau devait appeler la “ tou rbe philosophesque” . P ourquoi ce brusque intérêt p our les philosophes hellénistiques? Si c’est pour y retrouver n otre propre vérité - qui devrait se n o u rrir d ’elle-m êm e et n ’avoir pas besoin de se chercher des

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“ précurseurs” - ce serait un détour inutile ou, to u t au plus, un jeu de l’esprit. En réalité, cet intérêt est lui-m êm e, si l’on peut dire, intéressé, et m êm e vitalem ent intéressé, ainsi q u ’on le voit dans les efforts insistants p o u r présenter ces philosophes com m e les dignes successeurs d ’A ristote (ou, à l’inverse, dans une récente tentative de présenter Γ “ o n to lo g ie” d ’A ristote com m e une ébauche anticipatrice, encore que m alhabile, de la philosophie analytique). C o m m e on l ’a dit ailleurs: “ En égalant le P ortique à l’Ecole d ’A ristote, en le lavant du reproche de décadence, nous rédigeons en fait n otre propre apologie et, par une analogie tacite, tentons de nous persuader que la pensée du X X e siècle finissant pourrait elle aussi n ’être pas to u t à fait indigne des grands nom s qui l’ont précédée.” Les recherches sur la science et la philosophie hellénistiques peuvent donc se com prendre com m e un défi lancé à Hegel: prou ver que la m o rt d ’A ristote n ’a pas arrêté le progrès philo­ sophique, et que la m o rt de H egel (de H usserl et de Russell) ne doit pas nous em pêcher d ’avoir confiance en notre propre philo­ sophie. Ce n ’est pas la pensée des Grecs qui est en cause: c’est nous-m êm es. En ce sens, le thèm e apparem m ent historique de notre colloque po u rrait procéder d ’une visée authentiquem ent philosophique. V ictor G oldschm idt

A cknow ledgem ents

This book is the fruit o f a conference on H ellenistic philosophy and science held in Paris at the Collège Franco-B ritannique in the C ité U niversitaire fro m 2—10 Septem ber 1980. T he conference was a successor to the m eeting in O x fo rd w hose proceedings w ere published in Doubt and Dogmatism, ed. Schofield, B urnyeat and Barnes (O xford, 1980). Professor V ictor G oldschm idt presided over the discussions o f the participants: Jo nathan Barnes, Jacques B runschw ig, M yles B urnyeat, M aurice Caveing, François De G andt, Jean-Paul D u m o n t, Ferrucio Franco Repellini, M ichael Frede, Lorenz K rüger, A ndré Laks, G eoffrey Lloyd, T o n y Long, M ario M ignucci, Ian M ueller, M artha N ussbaum , E rik von Savigny, M alcolm Schofield, D avid Sedley, R ichard Sorabji, H einrich von Staden, Gisela Striker and M ario V egetti. All the chapters o f the book w ere presented originally as papers at the conference, and have been revised in the light o f the discussion, form al and inform al, and o f the subsequent correspondence w hich they provoked. It is a pleasure to thank all w hose help m ade the occasion a success, in particular the C ollège Franco-B ritannique for its hospitality, and the C entre N ational de la Recherche Scientifique, w hich gave m ost m unificent financial support to the conference. W e are also grateful to C .N .R .S . and to the Jo w e tt T ru st for grants tow ards secretarial costs incurred in preparation o f this volum e. j.B . J.B . M .F.B . M .S.

Introduction

JO N A T H A N BA RN ES

In the five hu n d red years from 300 b . c . to a . d . 200 G reek science m ade spectacular advances and G reek philosophy u nderw ent dram atic changes. P hilosophy and science, w hich m erge at their lim its, present one another w ith m utual challenges: scientific discoveries provide philosophers w ith new problem s o r add new dim ensions to old problem s (as m odern physics has sorely com pli­ cated the traditional philosophy o f space and time); philosophical issues m ay bear —or at any rate appear to bear —upon the w o rk o f the practising scientist (as sceptical doubts about explanation have affected research in econom ics). A nd again, questions broadly characterisable as ‘m eth o d o log ical’ are o f equal im portance, in their different ways, to philosophers and to scientists. H o w extensive and h o w im p o rtan t w ere such interconnexions betw een science and philosophy in the Hellenistic period (as those five hun dred G reek years m ay be labelled)? T hat was the general question w hich underlay the Paris C onference w hose proceedings are printed on the follow ing pages. A ny general answ er to that general question w o u ld be at best vacuous: the question m ust be divided and subdivided into ever m ore specific interrogatives before any w o rth w h ile answ ers can properly be expected; and it is plain that the specific questions are vastly m ore num erous than the chapters in the present volum e. These chapters seek to pose and to answ er a few o f those specific questions: w e hope that the sam ple is n ot w holly unrepresentative; b u t w e are well aw are - and, to tell the tru th, well pleased - th at very m uch m ore w o rk rem ains to be done. M edicine is n ot to d ay closely allied to philosophy: death, no doubt, offers sim ilar problem s to m etaphysicians and to physi-

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dans, and there is a subject called ‘m edical ethics’; but by and large m odern m edical m en do n o t seem to influence o r be influenced by m odern philosophy. T hings w ere otherw ise in the Hellenistic period. All the em inent doctors o f Greece, as G alen’s w ritings abundantly testify, w ere keenly concerned over philosophical issues, and especially over issues in m etaphysics and in epistem o­ logy. T h eir concern was not m erely an accidental piece o f intellec­ tual vivacity: it was as doctors that they cared about philosophical problem s; and their philosophical beliefs had a direct effect upon the ways in w hich they treated their patients. T he long and exciting disputes am ong the three great ‘schools’ o f m edicine - the Em piricists, the R ationalists, and the M ethodists - w ere at one and the same tim e philosophical and practical. T he doctors are discussed in tw o o f the follow ing papers. M ichael Frede gives an account o f the M ethodist school o f m edicine and show s how its adherents attem pted to discover a ‘th ird w a y ’ alongside the older paths o f E m piricism and Rational­ ism. Frede stresses the M ethodists’ search for sim plicity and their desire to rid their art o f the baggage w hich, in their view , it had uselessly accum ulated. (But it should n o t be tho u g h t that the M ethodists w ere unsophisticated as physicians.) T he M ethodists’ view o f their practice has evident affinities w ith certain parts o f P yrrhonian scepticism; and it m ight be said that they used philosophy to rid them selves o f philosophical ballast. Jo nath an Barnes discusses one episode in the argum ent betw een the Em piricists and the Rationalists: m edical know ledge, accord­ ing to the E m piricists, is purely a m atter o f ‘experience’, it is based entirely on observation and not at all on theory. B ut how does observation yield experience? and, m ore particularly, how many observations are required to give rise to experience?1Those questions - w hich have fam iliar descendants - m ust be answ ered by the E m piricist; yet, according to the Rationalist, they are unansw erable —and to prove their unansw erability he adduces, from the standard philosophical repertoire, a version o f the Sorites argum ent. M odern philosophers perhaps find m ore to interest them in the ‘h a rd ’ or m athem atical sciences than in the art o f medicine: problem s in logic and the foundations o f m athem atics, issues in o n to logy and the nature o f reality, questions about the attributes o f space and tim e, all are raised by the hard sciences. A nd we

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xxi

m ight w onder if the rapid developm ent o f the m athem atical sciences in the H ellenistic period had a sim ilarly stim ulating effect upon philosophy. As to m athem atics itself, there is, o f course, nothing to com pare to the w o rk sio f a Frege or a H ilbert; and the com m ents by Sextus Em piricus on m athem atics appear at first sight jejune. Ian M ueller argues, how ever, that Sextus w o n - o r at least did n o t lose - the battle he was engaged in: the m athem aticians o f the tim e w ere m athem atically gifted b ut philosophically confused (as were Frege’s m athem atical contem poraries) and Sextus’ criticism s, m ade exclusively from a philosophical point o f view and de­ veloped in an ad hominem fashion, clearly expose som e o f that confusion. T he ancient Sceptics did n o t offer a ‘philosophy o f m athem atics’, as A ristotle and the Platonists had done; b u t they did produce som e p ertinent criticism s o f the foundations o f contem porary m athem atics. François D e G andt is concerned prim arily w ith m echanics, and w ith the crucial concept o f ‘force’ as it is used in the pseudoA ristotelian Mechanics and by H ero o f Alexandria. H e finds the origin o f that notion - and hence the origin o f m echanics - in an earlier philosophical treatise: A ristotle’s Physics develops w h at De G andt calls a ‘topics’ o f m otion, and then uses that logicophilosophical construction as the basis for som e rudim entary -thoughts about m echanics. If we here find philosophy influencing hard science, w e m ust, alas, record that the influence was not benign. T he hard science o f astro n o m y reached a peak w ith the w o rk o f Ptolem y, at the end o f ou r period. A stro n o m y touches on philosophy at tw o places: at its highest level o f gerierality it m erges w ith philosophical cosm ology (a m erging m o st fam iliar from A ristotle’s de Caelo)\ at its m ost hum ble level - the level o f the collection o f em pirical data - it comes into contact w ith the philosophy o f perception. Geoffrey Lloyd discusses that second point o f contact: he details som e o f the observational problem s w hich faced ancient scientists in general and ancient astronom ers in particular; he show s to w h at extent they w ere aw are o f such problem s, and he indicates the various ways in w hich they attem pted to solve them . H o w does that bear on philosophy? A ccording to Lloyd, relatively little. As philosophers, w e m ight expect P tolem y and

xxii

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his fellows to have sh o w n som e interest in developing a general ‘theory o f e rro r’ to determ ine their dealings w ith unreliable data; b u t in fact they do no such thing. Again, the astronom ers - and the w riters on optics - often refer to various puzzles (illusions and the like) w hich the sceptical philosophers had used for their ow n ends; yet the scientists show no awareness th at there w ere philosophical m atters at stake, and the Sceptics do n o t refer to the scientific resolution o f their puzzles. (There is a m oral in that.) B ut astro nom y does bear up o n philosophical issues in another and m ore surprising fashion. T o n y Long rehearses som e scenes in the long tragi-com edy o f astrology. A lthough he argues that the early Stoics did n ot have th at passion for astrology that is som etim es credited them , he recognises that astrology becam e a topic o f philosophical discussion fro m the first century b . c . onw ards; and he gives som e account o f the standard argum ents used by sceptical philosophers against the pretensions o f the ‘C haldaeans’. B ut then w e find that P tolem y was an astrologer: his scientific astronom y, em pirically sound and m athem atically sophisticated, is at the same tim e the basis for a subtle and advanced astrological system . P tolem y defends astrology against philosophical attack in his Tetrabiblos: Long urges that the defence is adequate against its historical enemies; b ut he fears that P to lem y ’s victory m ay be Pyrrhic, if n o t Pyrrhonian. Q uestions o f scientific m eth o d are m ore often discussed by philosophers than by scientists: scientists do science, they do not discuss h o w to do it. M ost o f the ancient m aterial on w hat m ay broadly be term ed ‘m e th o d o lo g y ’ is, sim ilarly, to be found in the philosophers’ w ritings. O n e central question was the issue o f w hat w e call non-deductive inference: on the one hand, it seem ed plain enough to m ost thinkers that scientific advance depended, in part at least, up on the use o f reason - upon argum ent from data to theory, from the evident to the unseen; on the o ther hand, ordinary deductive logic - logic like A ristotle’s syllogistic or the Stoic calculus —was apparently inappropriate for such a function. W hat was required was an account o f non-deductive argum ent; and the m ain elem ent o f that account was the theory o f ‘signs’. T hree o f the papers in this b o o k are closely connected to the them e o f non-d ed uctiv e logic. M yles B urnyeat discovers the origins o f non-deductive logic in A risto tle’s account o f ‘signs’. He stresses the im portance o f ‘signs’ in Stoic theory, and discusses

Introduction

xxiii

their refusal to accept any logic that is not deductive. His exam ination o f the logical form o f a sign-inference concludes that their refusal is closely connected w ith the fact that the Stoics w ere never perfectly d e a r about the relationship betw een an argum ent and an assertion. D avid Sedley takes up certain them es in the Epicurean Phi­ lodem u s’ treatise On Signs. Philodem us contrasts the Stoic m ethod o f testing sign-inferences, w hich appears to suppose a logical or analytical connexion betw een sign and significate, w ith the Epicurean m ethod, w hich applies an inconceivability test that is nonetheless based up on em pirical observation o f similarities. (It m ig ht be m entioned th at there are close connexions betw een the Epicurean m eth od advocated by Philodem us and the practices o f the E m pirical doctors.) A t the end o f his paper, Sedley discusses the Epicurean notions o f ‘co nfirm atio n’ or ‘attestatio n ’ and ‘d isconfirm ation’ or ‘con­ testation’. T hose notions are subject to special scrutiny by JeanPaul D u m o n t. D u m o n t starts from Sextus’ presentation o f the Epicurean view , and then com pares it w ith the Epicurean texts them selves; he ends by suggesting that confirm ation and discon­ firm ation w ere intended to govern investigation o f the ‘m iddle area’ o f reality, an area bounded on one side by ‘m o n o valen t’ perceptual data and on the other by ‘p olyvalent’ states o f affairs rem ote in tim e or space. T he b oo k concludes w ith a paper by V ictor G oldschm idt on another aspect o f Epicurean epistem ology, or rather on its applica­ tion to the concepts o f law and justice. G oldschm idt attacks the traditional picture o f Epicurus as a crude conventionalist and utilitarian political philosopher. H e argues that Epicurus founds his theory o f justice on the co m m o n m an ’s concept o f fairness and abhorrence o f violent bloodshed; and so on principles firm ly rooted in h um an nature. Positive law is accorded validity only inasm uch as it passes the test o f conform ity to such prolëpséis, ‘p réno tio ns’ or ‘preconceptions’. T he requirem ent o f such a test, how ever, provides a m ore pow erful defence o f positive law than is available in the absolutist and objectivist theories o f law p ro p ­ ounded by Plato and the Stoics. T he contributors to this volum e are n o t always in agreem ent w ith one another; and none w ou ld claim to have said the last w ord on his subject. T he volum e is n o t a tidy, hom ogeneous, rep o rt on

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a com pleted project o f research; rather, it is a set o f pilot studies, unified by a co m m o n them e and a co m m on purpose: together, they hope to give som e idea o f the riches to be found in this area, and to indicate the exciting and challenging w o rk w hich rem ains to be done.

Bibliographical note

Texts and translations o f the philosophical authors w ho are discussed o r to w h o m reference is frequently m ade in this book are for the m ost part readily available. T he Loeb Classical Library offers editions, w ith original text and facing E nglish version, o f A ristotle, A u g u stin e’s City o f Cod, Cicero, D iogenes Laertius, Epictetus, Favorinus (in A ulius Gellius), Lucretius, Plotinus (E nneads ι-m ), Plutarch, Seneca and Sextus Em piricus. Som e o f these w riters are also available in French translation in the sim ilar B udé series. For Philodem us, On Methods o f Inference, see the edition w ith E nglish translation by Philip and Estelle de Lacy (Naples, 19782). O riginal texts o f the scientific authors discussed in the book are m ostly available in go od m o d ern critical editions. In the Leipzig T eub ner series are to be found, for exam ple, A rchim edes, A ristar­ chus, C leom edes, Euclid, Firm icus M aternus, G em inus, P roclus’ Hypotyposis and com m entary on Euclid, and P to le m y ’s Syntaxis and Tetrabihlos; and am ong the m edical w riters Caelius A ure­ lianus, Celsus, Galen (various sh o rt treatises) and Soranus (but m ost o f Galen has still to be consulted in the old edition o f C. G. K ühn (1821-33), despite continuing additions to the Corpus Medi­ corum Graecorum series, published in Leipzig and in progress since 1914). O f the m ain scientific w orks analysed in these pages the follow ing are available in English translation: T. L. H eath, The Works o f Archimedes (C am bridge, 1912) T. L. H eath, Aristarchus o f Samos (w ith text; O x fo rd , 1913) R. S. M acran, Aristoxenus, The Harmonics (w ith text; O x fo rd , 1902)

xxvi

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W. G. Spencer, Celsus, On Medicine, 3 vols. (Loeb edition; C am bridge, M ass, and L ondon, 1935-8) I. E. D rabkin, Caelius Aurelianus, On Acute and Chronic Diseases (w ith text; C hicago, 1950) T. L. H eath, The Thirteen Books o f Euclid’s Elements, 3 vols. (C am bridge, 1908) R. W alzer, Galen, On Medical Experience (includes Arabic text and fragm ents o f the Greek; O x fo rd , 1944) G. R. M o rro w , Proclus, Commentary on the First Book o f Euclid’s Elements (Princeton, 1970) R. C atesby Taliaferro, Ptolemy, The Almagest (Chicago, 1952) F. E. Robbins, Ptolemy, Tetrabiblos (Loeb edition; C am bridge, M ass, and L ondon, 1940) T he surviving Latin version o f P to le m y ’s Optics is edited by: A. Lejeune, L ’Optique de Claude Ptolémée (Louvain, 1956) In French translation is H e ro ’s Mechanica: C arra de V aux, Les Méchaniques otf l’Elévateur de Eléron d’Alexandrie in Journal Asiatique ix eme série, 1 (1893), 386-472 and 2 (1893), 152-269, 420-514 (includes A rabie text) N o te also the translations o f A rchim edes (C. M ugler, 1970-2) and G em inus (G. Aujac, 1975) in the B udé series, and o f M anilius (G. P. G oold, 1977) in the Loeb. U seful selections o f texts in translation m ay be found in I. T hom as, Greek Mathematical Works, 2 vols. (Loeb edition; 193941); T . L. H eath, Greek Astronomy (London, 1932); A. G. D rachm ann, The Mechanical Technology o f Greek and Roman Antiquity (C openhagen, 1963); M . R. C o h en and I. E. D rabkin, A Source Book in Greek Science (C am bridge, M ass., 19582), w hich also includes a fairly full (but n o w ageing) select bibliography. A select b ibliography o f secondary literature on the epistem olo­ gy o f the H ellenistic schools m ay be found in Doubt and Dogmat­ ism, ed. Schofield, B u rn y eat and Barnes (O xford, 1980). A bbreviated references to w orks by G reek and Latin authors are given in com m o n form s, m ostly those adopted in L id d ell-S co ttJo n es’ Greek Lexicon and Lewis and S h o rt’s Latin Dictionary (or alternatively the Oxford Latin Dictionary).

C H R O N O L O G IC A L TABLE

o 390-0340 B.c. Eudoxus 384-322 Aristotle 371-286 Theophrastus f l . c .350 Eubulides f i . c .325 Aristoxenus 344-262 Zeno o f C itium 341-271 Epicurus 323 Death o f Alexander 312 Zeno arrives in Athens 307 Epicurus founds Garden f l . c .300 Euclid Polyaenus D iodorus f l . c .280 Berosus f l . c .275 Aristarchus 0273 Arcesilaus becomes head o f Academy; institutes scepticism fl.c.270 Herophilus 262 Cleanthes succeeds Zeno as head o f Stoa fl.c.260 Erasistratus c. 287-212 Archimedes 0280-0206 Chrysippus 0232 Chrysippus succeeds Cleanthes f l . c . 22$ Eratosthenes f l . c . 2 1 0 Apollonius o f Perga f l . c .200 Philo o f Byzantium d . 200/175 Basilides fl.c.1 7 s Serapion C.200-C. 130 Philonides 153 Carneades’ embassy to Rom e 146 Rom e destroys C arthage and C orinth f l.c . 135 Hipparchus Dionysius o f Cyrene 129 Panaetius becomes head o f Stoa D eath o f Carneades 0155-075 Zeno o f Sidon

109 Death o f Panaetius f l .c . 100 D em etrius Lacon ?c. 90-80 Aenesidemus revives Pyr­ rhonism c.87 A ntiochus secedes from Academy 86 Sulla sacks Athens 0135-051/50 Posidonius c. i 10-040/35 Philodemus 106-43 Cicero r.55 Lucretius’ de K e r u m N a tu r a f i . c . s o Asclepiades Geminus d . 45 N igidius Figulus 44 D eath o f Caesar 31 Battle o f Actium f l.c . 10 Them ison f l . c . A . n . 30 Celsus Manilius c-4 B.C.-A.D.05 Seneca f l . c . 6 s H eron o f Alexandria Thessalus 69 Death o f N ero c .s o - c . 120 Plutarch 0 5 5 -0 1 3 5 Epictetus 0 8 1 -0 1 5 0 Favorinus 0 8 3 -0 1 6 1 Ptolem y f l .c . 125 Soranus M enodotus 121-180 M arcus Aurelius c. 129-c . 199 Galen f l . c . 1 7 s Cleomedes f l . c . 2 0 0 Sextus Empiricus 205-269/70 Plotinus f l . c . S3 5 Firmicus M aternus 354-430 St. A ugustine 410 Sack o f Rom e by Goths 410/12-485 Proclus 0450 Caelius Aurelianus

1

The m ethod o f the so-called M ethodical school o f medicine1 M ICHAEL FREDE

I. Introduction Later antiquity, as a rule, distinguishes three schools o f m edicine, the Rationalists, the Em piricists, and the M ethodists (cf. Galen, de Sect, ingr., chs i and 6; ps.-G alen, de Optima secta, i ii8 ff. K ühn; but also cf. ps.-G alen, Def. med. 14-17, x ix 353 K). W hat is at issue betw een these schools is the nature, origin, and scope o f medical know ledge. U sually their view s on this m atter are based on view s about h u m an know ledge in general; Rationalists, Em piricists, and M ethodists in m edicine tend to be Rationalists, Em piricists, or M ethodists concerning hum an know ledge and science quite generally (for the M ethodists cf. Galen, de Sect. ingr. 14,1 M arquardt). B ut it is only m edicine they are im m ediately concerned w ith, and hence they only argue their case for m edical know ledge. In m edicine the issue came to take the form o f the question ‘H o w does the doctor, in a particular case, k n o w h o w the patient is to be treated?’ A nd one particular w ay this question was form ulated was the follow ing: ‘W hich is the correct m ethod o f treatm ent?’ (cf. G alen’s de Methodo medendi). O bviously ‘m ethod o f tre a tm e n t’ here does n o t m ean the w ay one treats a patient, but rather the w ay in w hich one arrives at a certain treatm ent, i.e. the w ay one com es to think, or arrives at the conclusion, that a certain treatm ent is the rig h t treatm ent. T his is the sense in w hich w hat was at issue was the m ethod. A nd accordingly one talked o f a i. I am grateful for the generous help which I received in w riting this paper. Ift particular I w ould like to thank Jonathan Barnes, Geoffrey Lloyd, Don M orrison, and M ario VegettL

2

MICHAEL

FREDE

rational m eth o d and an em pirical m ethod. For the Em piricists claimed that it is all a m atter o f experience, that it is by experience that we have the general know ledge w e have, and that it is from experience that w e k n o w w hat to do in a particular case. T he Rationalists on the other hand claim ed that it is, at least in part, by reason that w e have the general know ledge w e have and hence k n o w w hat to do in a particular case (Gal. de Sect. ingr. i. T2ff. M ). In part they th o u g h t so because they assum ed that professional medical practice had to be based on scientific theory and that a scientific theory necessarily involved tru th s w hich could not possibly be k n o w n by experience. For they assum ed that a scientific theory had to account for the phenom ena in term s o f the underlying reality and that this reality included hidden natures, causes, and actions, n ot open to observation, b u t only accessible to reason, e.g. atom s, invisible pores, functions o f organs, or essences. T hus the rational m ethod involves the know ledge o f truths about non-observable item s w hich can only be obtained by reason (Gal. de Sect. ingr. 4. i8ff. M ). M ethodism arises in the first century a . d . in reaction to both Em piricism and Rationalism . It is a m ov em ent o f radical reform . T he dispute betw een Rationalists and Em piricists, at least by this tim e, is som ew hat academic; Galen som etim es even tells us (de Sect. ingr. 1. 12; 7.16; 12.12) th at they agree on the treatm ent, th o u g h they disagree on the m eth od w hich leads to this treatm ent. W e will hesitate to accept G alen’s claim that they agree on the treatm ent. For we k n o w fro m G alen’s ow n w ritings that there w ere significant differences in their approach to therapy. B ut presum ably in the de Sectis Galen tries to m inim ise the practical differences betw een the established schools o f the Rationalists and the Em piricists in o rd er to be in a position to characterise the innovations o f the M ethodists as w anton, unasked for, irresponsi­ ble departure from the established, respectable practice o f tradi­ tional m edicine. In any case, in the de Sectis he goes on to claim that the M ethodists, on the other hand, do n ot ju st disagree on the m ethod, but also object to the actual m edical practice o f Rational­ ists and Em piricists (de Sect. ingr. 12. 13ff.; 15.25fr.). A nd they object to their practice precisely because, in their view , it is fundam entally m isguided by a w ro n g m ethod, basically flawed by the lack o f the true m etho d (Gal. ibid. i2.9ffi). T hey conceive o f them selves as finally p u tting m edical practice on a firm , solid.

The method o f the Methodical school

3

reliable basis by providing m edicine w ith a safe, simple, scientific m ethod. T hey ju st call it ‘the m eth o d ’ (Celsus, prooem . 57), and them selves ‘the m ethodical ones’ (Gal. de Sect. ingr. 12.9; de Meth. med. X 76.2; 380.5 K). T he follow ing is an attem pt to characterise the new m ethod advocated by the m ethodical school at least in rough outline. M edicine, as conceived o f by the M ethodists, is supposed to be very sim ple. Life is long, and the art is short, a m atter o f about six m onths, they like to say, and thus w ith a few w ords m anage to outrage the representatives o f traditional m edicine in m ore than one w ay (Gal. de Sect. mgr. 15.6; 24.22; de Meth. med. x 5.2 K). T heir definition o f m ethodical m edicine bears the same character o f provocative sim plicity in expression and content. M edicine, according to the M ethodists, am ounts to no m ore than a ‘k n o w ­ ledge o f m anifest generalities’ {gnosis phainomenôn koinotëtôn), i.e. o f certain general, recurrent features w hose presence or absence can be determ ined by inspection (Gal. de Sect. ingr. 13.24; 23.1; de Meth. med. x 206. n K; ps.-G alen, de Opt. sectai 175. 18; 182.2 K). This characterisation obviously is m eant to em phasise the sim pli­ city and clarity o f m edicine, once w e have grasped the true m ethod, and th o u g h at first it seem s unduly sim ple, it turns out, on closer inspection, to am o u n t to an adm irably clear, concise, and econo­ mical su m m ary o f the M ethodist position. It is true that som e M ethodist characterisations o f m ethodical m edicine are slightly m ore com plex. B ut this is ow ing to the fact that this very general characterisation is supposed to apply n o t ju st to m edicine, b u t to any art w hatsoever (Gal. de Sect. ingr. 14.1). It thus reflects the M ethodist, as opposed to the E m piricist or Rationalist, conception o f the art o f m edicine as a true art. W hen the M ethodists w ant to distinguish m edicine from other arts they go on to specify the generalities w hich are the particular concern o f m edicine. Thus, standardly, they say that m edicine is k n o w ­ ledge o f m anifest generalities w hich are relevant to the aim o f m edicine (Gal. de Sect. ingr. 14. 1-7); som e o f them , am ong them Thessalus, a m ain exponent o f the school, m ore restrictively say that m edicine is the know ledge o f m anifest generalities w hich are proxim ate to and necessary for health (ibid. 14. 7ff. ; ps.-G al. de Opt. secta 1 172.7 K; Def. med. x ix 353.13 K). ‘M ore restrictively’, because it seems that Thessalus w ants to insist that although there also m ay be all sorts o f general features w hich are o f m ore or less

4

MICH AEL FREDE

rem ote relevance to the presence or absence o f health, the m eth od ­ ical d o cto r should not, and does n o t have to, occupy him self w ith these, for he know s the crucial features w hich are im m ediate­ ly relevant to the health o f a patient. B u t since w e are concerned w ith the m ethod, the M ethodist conception o f m edicine as a m ethodical art, we will concentrate on this very general character­ isation o f m ethodical m edicine. In fact, the follow ing will be no m ore than a first attem p t to elucidate the term s o f this character­ isation in som e detail. II. Indication Before w e start to consider the details o f this general characterisa­ tion, though, w e have to ask ourselves h o w this possibly could am o u n t to a characterisation o f m ethodical m edicine, o f the true m ethod. For, as w e saw above, the m eth o d is w h at is supposed to enable us to find the rig h t treatm en t for a patient. B ut this general characterisation does n o t seem to tell us anything at all about the w ay in w hich w e find out h o w to treat a patient. T he m atter is even m ore puzzling if w e take into account that the m anifest generalities the M ethodists are thinking o f w hen they give the very general characterisation, seem to be the various affections and diseases them selves (Gal. de Sect. ingr. 23. 2-12). B u t it is difficult to see, unless one is a philosopher, h o w the m ere know ledge o f a disease by itself could provide one w ith a know ledge o f its treatm ent. A nd yet this is w h at the M ethodists do w an t to m aintain. T h e very brevity and apparent deficiency o f their characterisation ju st serves to draw our attention to the point that all the d octor really has to k n o w are the affections and diseases them selves; k n o w in g th em he will also know their treatm ent; and to k n o w their treatm en t he does n o t have to k n o w anything but the affections and diseases them selves. B ut h o w is know ledge o f the disease by itself supposed to provide one w ith a know ledge o f its treatm ent? T h e M ethodists claim that the disease in itself is indicative o f its o w n treatm ent (Gal. de Sect. ingr. 12.14fr.; 13.13; 17.5ff.; de Meth. med. x 351.7 K; Med. XI V 677.12 K; ps.-G alen, de Opt. secta 1 125.2ff.; 164.iff. K). T o see w hat is m eant by this w e have to consider the M ethodist conception o f indication (endeixis). T h e n otion o f indication is n o t o f M ethodist origin. It com es into use in later Hellenistic

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epistem ology, m ost co m m o n ly to distinguish kinds o f signs and, correspondingly, kinds o f conditionals. R oughly speaking, som e­ thing A is a suggestive o r com m em orative sign o f som ething B, if w e k n o w fro m experience th at B obtains if A obtains. Thus, to use a traditional exam ple, the presence o f sm oke is a suggestive sign o f the presence o f fire. Som ething A, on the other hand, is n ot a suggestive, b u t an indicative sign o f som ething B, if w e kn o w , not by experience, b u t by reason that B obtains if A obtains. A n A tom ist, for exam ple, m ig h t regard the presence o f m otion as an indicative sign o f the presence o f void. T he application o f these notions to conditionals should be obvious (cf. Sextus Em p. P H 11 iooffi). if, then, the M ethodists claim that the disease itself is indicative o f its treatm ent, they obviously m ean to say that it is n o t by experience, as the Em piricists claim, that w e k n o w that a certain disease needs a certain treatm en t (cf. Gal. de Sect. ingr. 14.10-12). B ut it also turns out n o t to be a m atter o f reason in the w ay the Rationalists assum e, either (cf. ibid. I3 .i9 ff.). In fact, this, in a nut-shell, is the ultim ate source o f the difference betw een the three schools. T o see this m o re clearly, we have to take a closer look at the M ethodist use o f the n o tion o f indication. Sextus E m piricus (P H 1 240) tells us: ‘T he M ethodist in an undogm atic m anner also m akes use o f the term “ indication” to refer to the guidance w hich both natural and unnatural affections provide tow ards w h at seems to be (the) fitting (treatm ent) for them , as I pointed o u t in the case o f thirst, hunger, and the re st.’ He is referring back here to w hat he had said a few sentences earlier in P H 1 238: ‘As . . . the sceptic is guided by thirst tow ards drink, by hunger tow ards food, and thus w ith the rest, in a sim ilar fashion the m ethodical doctor is guided by the affections tow ards w hat is fitting for them , by constriction to dilation, ju st as som ebody tries to escape fro m condensation due to intensified cold by getting to a w arm spot. ’ A few lines further d o w n Sextus goes on to refer to the exam ple o f a dog w hich, pricked by a thorn, m oves to do w h at is indicated and rem oves the tho rn w hich is alien to its body. O n Sextus’ account, then, a disease is supposed to be indicative o f its treatm ent in the w ay in w hich h u n g er is indicative o f the need for food. If there is a relevant difference betw een affections like thirst and hunger on the one hand and disease on the other, it

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ju st seems to lie in the fact that it takes a do cto r to k n o w the diseases in the w ay in w hich w e all k no w thirst and hunger. T here is no suggestion that there is a relevant difference in the w ay in w hich affections and diseases are indicative o f w hat needs to be done to rem ove them . T he peculiarly M ethodist n o tio n seems to be that once one has recognised the affection or disease for w hat it is, it is im m ediately obvious w h at needs to be done; ‘im m ediately ob v io u s’ in the sense that it is neither a m atter o f observation, nor a m atter o f inference, if w e k n o w w hat needs to be done once we have recognised the disorder (cf. ps.-G alen, de Optima secta i I3 i.6 ff. K). T he Rationalists th in k that the m anifest state o f the body does n o t m ake it im m ediately obvious w hat needs to be done. For th em the m anifest state is indicative o f a hidden state w hich causes the affection or the disease. A nd it is only if w e k now this hidden state that w e k n o w h o w to treat the patient. T hus, for the Rationalist, know ledge o f the appropriate treatm ent on the basis o f the m anifest co n d itio n is a m atter o f inference, and indication is a relation betw een a m anifest and a non-m anifest state. M ore specifically, there is on the one hand the relation betw een the m anifest state o f the body and the underlying, hidden abnorm al state, and on the other the relation betw een this hidden state and the treatm en t indicated by it (and no t directly by the m anifest state). It is the distinctively Rationalist position that reason can grasp such relations (cf. Gal. de Sect. ingr. 2.3; 5.17; io .2 2 ff). Like the Em piricists the M ethodists reject such infer­ ences to and fro m hidden states; according to the M ethodists there is no need for such a detour via the non-m anifest (Gal. de Sect. ingr. 14.9-11). T he m anifest affection m akes it im m ediately evident w hat needs to be done; ‘im m ediately eviden t’ in the sense that we do n o t require the m ediation o f assum ptions about hidden states, but presum ably also in the sense that it does n o t take any chain o f reasons to see that constriction requires dilation and that dilation requires constriction. T he po int o f Sextus’ exam ples seems to be that the connexion betw een a state and w h at is indicated by it is so im m ediately obvious that even a dog ‘k n o w s’ im m ediately w h at is indicated; there is no inference involved. B ut the M ethodists, in claim ing that the affection by itself is indicative o f its treatm ent, also deny the E m piricist claim that the connexion betw een disease and appropriate treatm ent is ju st a m atter o f experience (cf. Gal. de Sect. ingr. 14.11-12). It does not

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take experience to k n o w that a state o f constriction requires dilation, that depletion asks for replenishm ent. These, if properly interpreted, are truths o f reason. B ut w e have to be careful n o t to rush to unw arran ted conclusions as to the sense in which they are supposed to be truths o f reason. T here is no reason, for example, to think that the M ethodists take them to be conceptually or analytically true. For all we know , the M ethodists m ay ju st insist that, w hatever the explanation for it m ay be, it is im m ediately obvious to com m on reason that som ebody w ho is suffering from constriction will find relief in dilation, that w e do n o t feel any need to justify such a claim by reference to past experience, that w e not only do n ot expect any counter-exam ple, b u t in fact do n o t see how there could be counter-exam ples (cf. Cels, prooem . 62-3; Gal. de Meth. med. x 208.1 off. K). Since know ledge o f w hat is indicated is n o t a m atter o f observation, nor a m atter o f experience, the M ethodists are w illing to say that it is a m atter o f reason. Thus on this point the M ethodists do side w ith the Rationalists against the Em piricists and grant that reason does play a constitutive role in m edical know ledge (cf. Celsus, prooem . 62). B ut at the same tim e they do not accept the dogm atic Rationalist conception o f the role reason plays in the acquisition o f m edical know ledge. T hey do n o t accept the Rationalist claims that reason can, and has to, grasp hidden entities to acquire the necessary m edical know ledge. T hey refuse to attribute to reason any obscure pow ers w hich w e w ould not have dream t o f in ordinary life. T hey are ju s t noting, in this and in other contexts, w hat seems to be an obvious fact, b u t w hich the Em piricists in their dogm atism do n o t w ant to recognise, that there are certain things w hich are obvious to rational creatures, th o u g h it does n o t seem to be by observation or experience that they are obvious. T o adm it, tho u gh , against the Em piricists, that certain things are obvious to reason, is n o t to adm it that they are obvious on the basis o f som e scientific theory constructed in accordance w ith the canons o f the rational m ethod or logic. T he M ethodists insist that it is obvious to reason that som ebody w h o is h u n gry needs som e food prior to, and quite independently of, any theory w hich w ould prove that and explain w h y this is so. In particular the M ethodist does n o t see h o w only a theory w hich operates in term s o f hidden, theoretical entities can m ake it really obvious, or evident, that som ebody w h o is thirsty needs to drink.

T he M ethodist is content to stay w ith w hat is obviously obvious rather than really obvious. Thus, in taking the view on indication he does, the M ethodist m erely tries to stay w ith the phenom ena. He does accept truths o f reason, b u t he does n o t accept the Rationalist canons for truths o f reason, w hich w o u ld com m it him to the assum ption o f hidden, theoretical entities. This, according to our ancient com m entators, is the fundam ental source o f the differences betw een the M eth o d­ ists on the one hand and the Em piricists and the Rationalists on the other (Gal. de Sect. ingr. I3 .i9 ff. and 14. t o f f ; Celsus, prooem . 57; ps.—Gal. de Opt. secta 1 119 K). A ccording to the M ethodists, then, the disease itself is indicative o f its treatm en t in the sense,that once w e are aw are o f the disease in the appropriate w ay it will also be obvious to us h ow it is to be treated. It is for this reason that the M ethodists can characterise m ethodical m edicine sim ply as know ledge o f certain m anifest generalities. W ith this in m ind let us tu rn to the characterisation itself. III. Generalities From w h at has been said it is clear that we have to pay particular attention to tw o features o f this characterisation: (i) it seems to be im p o rtan t for an understanding o f the m ethod that diseases are conceived o f as generalities and that they are conceived o f as manifest; (ii) obviously it is n o t any kind o f awareness o f a disease w hich gives us the know ledge o f its treatm ent; it m ust be the kind o f awareness the M ethodist d octor has; hence w e have to find out w hat kind o f know ledge the M ethodists are referring to. Let us then first consider w h y the M ethodists insist that m edical k n o w ­ ledge is know ledge o f generalities. ‘G enerality’ (koinotis) is a term o f dogm atic m etaphysics. It refers to a com m on, general, recur­ rent feature. As Sextus (PH 1 240) tells us, the M ethodists adopt this term , b u t use it, like all other term s, in an undogm atic m anner; i.e. they are w illing to talk o f generalities, bu t they do n o t m ean by this to co m m it them selves to the assum ptions involved in the dogm atic use o f this term . They do not com m it them selves to any particular m etaphysical view concerning the nature o f generalities, no r do they even com m it them selves to the m eta­ physical assum ption that there are such com m on properties or

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qualities. This is im p o rtan t, because it m eans that the M ethodists in talking o f diseases as generalities do n o t really com m it th em ­ selves to the existence o f diseases as separate entities. T he sense in w hich they are w illing to talk o f diseases as generalities is a perfectly sim ple and straightforw ard one: w e ordinarily say that tw o persons w ho suffer from pneum onia have the same disease, and in saying ‘the same disease’ w e do n o t com m it ourselves, let alone m ean to com m it ourselves, to the existence o f a universal called ‘p n eu m o nia’; all we co m m it ourselves to is that the tw o persons in question in certain respects are very m uch alike, so m uch alike that in this respect w e do no t care to distinguish betw een them . T hu s M ethodist talk about generalities is entirely based on ordinary talk about sim ilarity and likeness betw een objects (cf. ps.-G alen, de Opt. secta i i gi . ^f f . K, w here the point is explicitly m ade). O n the other hand the M ethodist also w ould not w ant to com m it h im self to the view that such com m on entities do no t really exist; i.e. w hen he explains his use o f ‘generality’ in term s o f the w ay w e ordinarily talk about the sim ilarity or likeness betw een objects he does n o t m ean to com m it him self to som e form o f nom inalism . It is in this n o n -co m m ittal sense, then, that the M ethodists talk o f ‘generalities’. W ith this in m ind let us return to o ur question: o f w h at im portance is it that diseases should be conceived o f as generalities in this sense? T his question has to be seen on the background o f a long tradition in G reek m edicine according to w hich treatm ent has to be individualised to do ju stice to the individuality o f the particular cases to be treated, none o f w hich is exactly like any other (cf. H ipp. Epid. i 23; de Vet. med. 20). T here are a large n um ber o f factors w hich are supposed to m ake a relevant difference to the particular case, and w hich hence have to be taken into account w hen one tries to decide on the rig h t treatm ent for the particular case. Rationalists, especially those under Stoic influence, tend to assum e that individuals have an individual nature or essence w hich has an effect on the fo rm and the course a disease takes (cf. Galen, de Sect. ingr. 5.20fr.; de Meth. med. x 209.4ff. K). In addition, there are differentiating and particularising factors like age, sex, con­ stitution, and habits o f the patient, the part o f the body affected, antecedent causes, the place and its climate, the season o f the year, and w hatever else m ay be relevant (cf., e.g., Galen, de Sect. ingr. ch.3). This view tended to be com bined w ith the view that

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know ledge, at least scientific know ledge, is o f the universal, whereas the individual and its condition are ineffable, i.e. cannot be captured by general notions, how ever scientific they m ay be (cf. Galen, de Meth. med. x 209.7 K; de Loc. aff. vm ii7 .6 f.; 339.13fT. K), and hence cannot be k n o w n scientifically. As a result it tended to be assum ed that diagnosis and treatm ent, though based on a scientific theory, cannot be m ore than a m atter o f artful conjecture (cf. Gal. de Plenit. vu 581. iff. K; de Sanit. tuenda vu 129.4fr. K; de Rat. cur. x i 285.10fr. K; de Meth. med. x i8 i.i7 f £ ; 206.5ff. K). H ence the classification o f m edicine as a conjectural art. T he M ethodists claim that m edicine as a w hole is a m atter o f firm know ledge (ps.-Gal. Med. xiv 684 K) and thus deny that treatm ent cannot b ut be conjectural. If m edicine is to be safe and reliable, treatm en t should be a m atter o f firm and certain k n o w ­ ledge. A nd th at it can be a m atter o f know ledge w e see, once we have grasped the true method*. For the fact that traditional m edicine does indeed proceed by m ere conjecture and that its representatives think that it cannot but be conjectural, is due to a m istaken conception o f the m ethod. A ccording to the M ethodists all these differentiating and individualising features are o f no relevance in determ ining the appropriate treatm ent. There is no need to take into account m ere sy m p to m s (ps.-Gal. de Opt. secta 1 162.9 ff; I0 3 .i2 ff.; 164.2fr.; I7 0 .i8 ff. K), sex is irrelevant (Soran. Gyn. p. 95, 4), so are causes (Celsus, prooem . 54; ps.-G alen, Med. x iv 683. 2 K; Gal. ad Pis. x iv 278. ir ; 279.4 K; Cael. A ur. Ac. in 45; 190), w hether hidden (Gal. de Sect. ingr. I7 .3 ff; Cael. Aurel. Chron. 1 4.83) or antecedent (Gal. de Sect. ingr. i 6 .i2 f f ; Cael. Aur. Ac. i i 187); there is no need to k n o w the part o f the body affected (Cael. A ur. Ac. 1 53; 11 148) or to take note o f the age, constitution, habits o f the patient, the season, the location and its clim ate (Gal. de Sect. ingr. 6 .io f£ ; 12.14fr.; i7 .7 ff ; 19.20fr.; de Meth. med. x 6 2 9 .14fr.; O n Med. E xp. p. 87F.; Cael. A ur. Ac. 1 157; Celsus, prooem . 65). As Galen puts it (de Meth. med. x 206.12 K), the M ethodists talk as if their patient was n ot an individual, but the universal m an. T h e M ethodists take the position that thirst is the same, w hatever the nature, age, sex, constitution, and habits o f the patient, the clime o f the place, the tim e o f the year, and there is one and the same treatm ent w hich is asked for, nam ely the adm inistration o f drink. A nd since this affection is a generality,

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w hich asks for one and the same treatm ent w henever it occurs, we do n o t even have to w o rry about the problem w hether individuals can be k n o w n scientifically or n o t and h o w w e can apply our general know ledge to the particular case; we do n o t have to w o rry that ou r theorem s only hold for the m ost part, because som e idiosyncratic feature o f a particular case m ay cause an exception to the genera] rule. T he rules hold w ith o u t exception, exactly because no account needs to be taken o f the various differentiating and individualising features. T hus they are tru ly scientific, firm and stable (Gal. de Meth. med. x 206.10; 208.10 K; de Cris, ix 657.18 K; Celsus, prooem . 62). Rationalists and Em piricists ju st confuse m atters by dragging in all these irrelevant factors. Hence it is not surprising that their theorem s should be hopelessly unreliable. At the sam e tim e it is n o t surprising that their doctrine should be excessively and needlessly com plicated and difficult to m aster, whereas the true m eth o d show s medical know ledge to be a rather clear and straigh tfo rw ard m atter. It has to be added, though, that - as Galen points out (de Meth. med. x 630 K) —the M ethodists do take into account differentiat­ ing features, after all, w h en it com es to adm inistering the indicated treatm ent; the differentiating features m ay, e.g., offer counterindications to certain ways the treatm ent m ight be adm inistered (cf. Gal. de Sect. ingr. 20.3fr.; 2 0 .i6ff.). In fact, to be precise, in order to determ ine the appropriate tim in g and dosage o f the indicated treatm ent, the M ethodist d octor in addition to the generality is also supposed to k n o w the stage o f the disease and its intensity (Gal. de Sect. ingr. i3 .i2 ff.; 26.2iff.; ps.-G alen, de Opt. secta i 162; 194; 211 K; Celsus, prooem . 55-6). IV . The manifest Some generalities, e.g. colours, clearly are m anifest, i.e. open to inspection. T here also m ay be hidden generalities, n o t open to inspection, b u t accessible only to reason. A nd som e o f them m ay be relevant to m edicine in the sense that tru th s about them m ay entail truth s about diseases and their treatm ent. This is w hy Thessalus, unlike m o st M ethodists, does n o t characterise the generalities m edicine is concerned, w ith as those w hich are relevant to the aim o f m edicine, bu t as those w hich are proxim ate and necessary. T he ones w hich one has to k n o w in m edical practice,

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the ones w hich im m ediately determ ine the treatm ent, are m anifest generalities. T h o u g h , then, the M ethodist grants that there m ay be hidden generalities relevant to the aim o f m edicine, he will only rely on assum ptions about obvious or m anifest entities, and m ore particularly only on those assum ptions about m anifest entities w hich them selves are obvious. B ut w hat does count as obvious or manifest? W e m ig h t think that those things are obvious or m anifest w hich one can perceive or perceive to be the case. A nd in the de Sectis Galen talks as if this was the M ethodist view (24. i2ff. ; 24.19fr.). B ut w e have already seen that the M ethodists also take truths o f reason to be obvious. A nd it seems that there is som e unclarity in G alen’s m ind as to w hether they think that generalities can be perceived (de Meth. med. x 36.5fr.; 38.5 K). T he author o f de Optima secta is quite unequivocal about this. H e tells us (1 175. i8ff. K) that by ‘m anifest’ the M ethodists here do n ot m ean ‘grasped by perception’. B ut w hat, then, distinguishes the M eth o d ist’s gener­ alities from the R ationalist’s hidden entities? T he claim seems to be that everybody can be taught to recognise these generalities by careful observation; one learns to ‘see’ them , develops an eye for them , w hereas no am ount o f training will teach one to recognise an atom or a com plex o f atom s as such. B ut w h y does the M ethodist insist that the d octor should restrict h im self to the m anifest? R ationalist physicians have p ost­ ulated the existence o f all sorts o f hidden entities. In each case it has turned out that there is som e reasonable d o u b t as to their existence, and there does no t seem to be any clear w ay to settle these doubts, once and for all (Cael. A ur. Ac. 11 8). M oreover, even given their existence, assum ptions about them seem to be a m atter o f endless speculation and controversy. T he M ethodist does not deny that such entities m ay exist and that one can have know ledge about them (Gal. de Sect. ingr. 14.14; Cael. A ur. Ac. 1 9). B ut since he is determ ined to provide safe m edical treatm ent, he refuses to rely on such controversial and speculative assum p­ tions. A nd since m edical theories are characterised by such assum ptions, he also quite generally refuses to rely on such theories for his practice. W hereas the Rationalists think that it is only in virtue o f these theories that medical practice can have a sound, scientific basis, the M ethodists argue that these theories fail to provide a reliable basis, because they them selves are co n tro ver­ sial.

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Fortunately, according to the M ethodists, there is no need to rely on such assum ptions and theories. For our know ledge of w hat is m anifest is entirely sufficient to determ ine the correct treatm ent for a disease. T hus, even if these assum ptions and theories w ere n ot controversial, b ut well established, know ledge o f them w ould be redundant and superfluous, as far as the aim o f m edicine is concerned (Gal. de Sect. ingr. 16.1 iff.; i8 .2 of£; de Meth. med. x 268.17 K; ps.-G alen, de Opt. secta 122.6ff. K). H ence the M ethodists refuse to accept physiology or anatom y as part o f the art o f m edicine (Gal. de Meth. med. x 9.10; 107. nfF .; 319.17; 349. i 6 a ; 928.5ff. K; Soran. Gyn. 6.6ff.). T h ey claim that others, in pursuing these subjects, go beyond the boundaries o f the art (Gal. de Meth. med. x 106.2 K; cf. Celsus, prooem . 64). In this refusal to rely on anything bu t the obvious and m anifest the M ethodists are taking the side o f the Em piricists against the Rationalists. B ut the M ethod ists’ position on the hidden and the obvious is n o t quite the same as that o f the Em piricists. T o start w ith, as w e have seen, the obvious for the M ethodists includes truths o f reason. In addition, the M ethodists accuse the E m p iri­ cists o f dogm atism because o f their attitude tow ards hidden entities. T he E m piricists tend to claim that such entities do not exist and that, even if they do exist, no th in g can be k no w n about them . T he M ethodist will n ot com m it him self on these questions; he ju s t observes that in fact n oth ing seems to be kn o w n about such entities. In keeping w ith this, the M ethodist does n ot claim that there are no true theories, o r that, even if there were, they could no t be know n. In fact, it seems that the M ethodist takes a m uch m ore positive attitude tow ards theories. It is tru e that he refuses to rely on theories for his practice, b u t this does n o t m ean that his interest in m edical theory is entirely negative o r critical. If w e look at Caelius A urelianus w e see a M ethodist author w ho n ot infrequently gives causal accounts o f diseases (cf Ac. 1 33; Chron. 11 125; v 109) and even refers to hidden entities like hidden dissolutions (cf. Ac. 11 172, adëlos diaphoresis; 217, occulta diaphoresis; cf. also Chron. in 19). G iven that he h im self refers to them in this w ay, w e have to assum e that he thinks that it is in perfect agreem ent w ith his M ethodism to consider such theoretical assum ptions w ith approval o f som e kind. T h at this is n o t an aberration on C aelius’ part we can see from the fact that even

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Soranus w ro te treatises on etiology and physiology. A nd from various passages in Caelius A urelianus (cf. Ac. π 28.147-8; Chron. IV 1 . 5 ) it is clear that Soranus th o u g h t that there is nothing w rong w ith having theoretical view s, as long as one keeps in m ind that they are purely speculative, and as long as one does n o t base o ne’s treatm ent on these views. Soranus him self tells us (G y n . 6.6ff. 1 ib .) that th o u g h anatom y is useless, it is good to k n o w it; for otherw ise people m ight think that one is rejecting it o u t o f ignorance. H e also acknow ledges that there is real anatom ical know ledge; after all, anatom y in good part is a m atter o f experience (Gyn. 6.8; 10.12; 12.3). W e m ay also assum e that the M ethodists think that it w o u ld be dogm atic to reject theories o ut o f hand w ith o u t having carefully considered them ; after all, one o f th em m ay tu rn o u t to be obviously true. Soranus also tells us o f b o th anatom y and physiology that, though they are useless, one should take account o f them ‘pros chrëstomatheian’ (G yn. 4-6ff.; 6.6ff. 1 ib'.). This suggests that know ledge o f these theories satisfies learned curiosity, is, as it w ere, an am enity o f life, a decorative orn am en t o f the educated person. Som ehow , tho u gh , I am inclined to think that there m ust be, according to the M ethodists, a m ore positive connexion betw een medical theory and the art practised by the doctor. Celsus obviously does assum e that there is such a positive connexion, and th o u gh he does n o t attribute this view to the M ethodists, there is at least som e faint reason to suppose that it does reflect the M ethodist position. H e says (prooem . 74): ‘T h o u g h I think that m edicine should be rational, I also think that one should take o n e’s instructions fro m m anifest causes, all hidden m atters being re­ jected, no t from the th o u g h t o f the practitioner, bu t from the art itself.’ T he point o f these lines seem s to be this: th o u g h the d octor in his practice should only be guided by w hat is evident, he also in his thinking, as opposed to his practice, should engage in medical theory. Celsus clearly thinks th at such theoretical activity is o f m ore than ornam ental value; for otherw ise he w o u ld n ot say that in his view m edicine has to be rational. B ut w hat reason is there to suppose that these rem arks reflect M ethodical thought? It seems to m e that the contrast betw een the art itself and the th o u g h t o f the practitioner, the restriction o f the art, bu t no t o f the th o u g h t o f the practitioner, to w h at is evident, and the insistence that treatm ent should be guided by the evident cannot b u t rem ind one o f the

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M ethodist position. M o reo ver it also seems that there are certain features o f M etho d ism w hich are m ost easily understood, if we assum e that the M ethodists allow ed theoretical speculation to have a positive influence on the art itself. For, if one thinks o f the n o n -co m m ittal attitude o f the M eth o d ­ ists tow ards theories, it does strike one that they w ould hardly have arrived at their central doctrine that all diseases are form s o f one o f three basic generalities (constriction, dilation, and the com bination o f both) if they had n o t been th o ro u g h ly influenced by Asclepiades’ rather speculative physiology. Asclepiades’ p h y­ siology was based on the assum ption that the b o dy is constituted by atom s and invisible pores. H e explained m any illnesses as ow ing to the constriction o f these invisible pores, som e as ow ing to an excessive flow th ro u g h them (cf. Gal. de Tremore vu 615.3ff. K; Cael. A ur. Ac. 1 6ff.; io6ff.), i.e. as due to dilation. The M ethodist position obviously is reached by tw o m oves: (i) they generalise the Asclepiadean position by assum ing that all illnesses are a m atter o f constriction, dilation, or a com bination o f both; (ii) but constriction and dilation in A sclepiades’ account are hidden states postulated by the theory; after all, invisible pores and atom s are paradigm s o f hidden entities only to be grasped by reason; thus the M ethodists have to leave it an open question w hether u n der­ lying the phenom ena there are hidden states o f constriction and dilation o f the kind postulated by Asclepiades; instead they assum e that there are m anifest states o f constriction and dilation, w hether or n ot underlying these m anifest states there also are correspond­ ing hidden states o f constriction and dilation o f the kind assum ed by Asclepiades w hich are the cause o f the m anifest dilation or constriction. T hus som etim es the M ethodists criticise Asclepiades for basing his account o f a disease on these hidden states (Cael. A ur. Ac. i 9). B ut there also is som e evidence that in som e sense M ethodists did accept A sclepiades’ view o f the reality behind the m anifest states o f dilation and constriction (Cael. A ur. Ac. 11 52; hi ιδρ ί.; Gal. de Temp, et virtut. simpl. med. xi 783. j f f K). If such a speculative view w ere ascribed only to T hem ison, w e m ig h t think that this was ju st further evidence that T hem ison had n o t yet m anaged to free h im self entirely from his Asclepiadean views and to take a consistently M ethodist position (cf. Cael. A ur. Chron. 1 50; IV 6). B ut the fact that Galen (l.c.) seems to attribute such views also to Thessalus m akes this explanation far less plausible. It rather

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seems that at least som e M ethodists saw the relation betw een A sclepiades’ theory concerning the hidden states and their o w n view concerning the corresponding m anifest states in the follow ­ ing way: if one was to speculate about such m atters they w ere w illing to accept A sclepiades’ account; this account seem ed so m uch m ore plausible than any other account, th o u g h this did not change the crucial fact that it still was only a m atter o f speculation; in fact, quite literally a m atter o f speculation, for the hidden entities involved in this account w ere called logotheorêta (i.e. to be seen by reason; cf. Gael. Aurel. Ac. i 105; 106; Chron. v 105), and ‘theoria', ‘theôrëtikos’ etc. n o t only cam e to be rendered by ‘specula­ tio’, ‘speculativus’, etc., bu t also to take on the sense o f ‘specula­ tio n ’, ‘speculative’ (cf. Gal. de Dogm. Plat. et. Hipp. p. 815 M ). B ut th o ug h it is ju st speculation, it does have tw o positive effects: first o f all A sclepiades’ theoretical speculation suggested som ething w hich was borne o u t by careful attention to the phenom ena; if it had n o t been for A sclepiades’ theôry w e m ight never have becom e aware o f the m anifest generalities. A fter all, it is extrem ely unlikely that by m erely looking at the phenom ena w ith o u t the guidance o f som e theory we w ou ld ever have realised that all diseases are form s o f the three generalities. N evertheless it was not speculation b ut observation w hich provided us w ith the k n o w ­ ledge o f these generalities. B ut speculation did help us to focus our attention in the rig h t direction. T his is one w ay in w hich m edical theory, th o u g h n o t part o f the art o f m edicine itself, m ay be m ore than a m ere o rn am en t o f the educated doctor. Secondly the theory, th o u g h n o t itself part o f m edical know ledge and irrelevant for treatm ent, does provide som e understanding and m akes sense o f our medical know ledge. T he reason w h y the M ethodist for his treatm ent will only rely on w h at is obvious is that it is only in this w ay that safe and reliable treatm en t can be guaranteed; for only w h at is m anifest can be k n o w n reliably. B ut is it really the case that the generalities the M ethodist claims to take his indications from are manifest? Galen repeatedly points o u t (cf., e.g., adv. Iul. $o.2ff. W enkebach) that the M ethodists them selves disagree in their definitions or charac­ terisations o f even the m o st basic generalities. If they w ere m anifest, Galen claims, there should be universal agreem ent on their definition. A t this point it m ay be useful to consider briefly the M eth od ists’

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attitude tow ards definitions. T he evidence on the m atter is som ew hat confused. In p s.-Soranus, Quaestiones medicinales §46, for exam ple, w e are told that whereas the Rationalists rely on definitions and the Em piricists on descriptions, the M ethodists use both. T he distinction betw een definitions and descriptions, horoi and hupotupöseis or hupographai, is part o f dogm atic dialectic (cf. DL vu 60). A definition specifies the essence o f som ething in term s o f the true theory, a description captures the notion o f som ething in pretheoretical term s accessible to everybody, e.g. by capturing the com m o n n o tio n or the ordinary m eaning o f a term . N o w som etim es w e are told about the M ethodists, in particular about Soranus, that they refuse to give definitions (cf. Cael. Aur. Ac. 11 142; 163). A nd given w h at w e have said, this is easily understood. D efinitions in the technical sense involve a co m m itm ent to a theory and to theoretical entities, a com m itm en t M ethodists reject. Caelius A urelianus, for exam ple, repeatedly rejects defini­ tions o f diseases because they m ake reference to hidden entities {Ac. i 9; π 8). N evertheless they often do give us definitions and talk o f them as definitions. B ut this apparent inconsistency is easily explained by their general policy to use dogm atic term s like ‘definition’, w ith o u t feeling co m m itted to the dogm atic theories and distinctions associated w ith these term s. T hus in this case they feel free to talk o f definitions, w hen in fact, from a dogm atic point o f view , they should be talking o f descriptions. So the M ethodists refuse to give definitions in the technical sense, bu t they do not refuse to give definitions in the sense o f descriptions. B ut the fact that they call these b o th ‘definitions’ and ‘descriptions’ has given rise to the confusion w e find in ps.-Soranus. If the M ethodists had m eant to give definitions in the technical sense the fact that different M ethodists give different definitions o f the various generalities w o u ld have raised a serious problem . For in the technical sense each kind o f thing can only have one definition. B ut once w e see that, from a dogm atic point o f view, the M ethodists are only giving descriptions, even if they them ­ selves m ay call them ‘definitions’, it no longer seems problem atic that they should offer different characterisations o f one and the same generality. For, obviously, one thing m ay be characterised in different ways. A nd even the fact that they disagree about the m ost suitable and appropriate characterisation no longer seems problem atic. For suppose that w e all m anage to focus our

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awareness on a certain phenom enon and that this phenom enon does stand ou t in ou r m ind w ith all desirable clarity; w e still m ight disagree as to h o w we should characterise it in such a w ay that others w ho are no t fam iliar w ith it know w hat to pay attention to and thus m ay com e to see it, too. M ethodist definition, and M ethodist language quite generally, does not pretend to be m ore than a pragm atic attem p t to draw our attention to the phenom ena, to help us to becom e aw are o f them in our ow n experience. This fam iliarity w ith the phenom ena is w hat counts; it can never be replaced by the m ere possession o f a phrase; how ever appropriate and precise the phrase m ay be it will never quite capture the phenom enon. O n e m ig ht object that if the generalities really w ere m anifest, they should be constituted by a set o f phenom enal features. A nd hence, if one had a clear awareness o f a generality, it should be possible to give a list o f its constitutive features, and hence a definition all M ethodists s h o u ld ‘be able to agree upon. B ut this presupposes that there is a set o f basic, sim ple phenom enal features such that all com plex phenom ena can be resolved into these sim ple features, and th o u g h this is an assum ption w hich philosophers th ro u g h o u t the ages have been very tem pted to accept, it is entirely speculative and dogm atic; the phenom ena them selves do n ot ju stify it. It is only w hen w e try to develop certain kinds o f epistem ologies that this assum ption seems to be attractive. T hus the fact that the M ethodists them selves disagree as to how the generalities should be characterised does n o t show that the generalities are not m anifest. W hat it does show is that som ething can be m anifest w ith o u t being im m ediately m anifest to every­ body. It does take som e training till the m edical generalities becom e m anifest to one w ith sufficient clarity. O therw ise we w ould not need any doctors. T his brings us to the third and last part o f the general characterisation o f m ethodical m edicine, the d o c to r’s know ledge. V. The doctor’s knowledge As w e have seen, the M ethodist position is very m uch influenced by the consideration that m edical treatm ent should not, and need not, be a m atter o f speculation and conjecture, as in fact it is in the hands o f Rationalist and E m piricist doctors. If w e restrict

The method o f the Methodical school

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ourselves to m anifest generalities our treatm ent will be a m atter o f firm and certain know ledge, based on o u r know ledge o f these m anifest generalities and thereby o f w h at they indicate. W hat, then, is it to k n o w these generalities and h o w do we com e to kn ow them ? It seems to be a safe assum ption that the kind o f know ledge o f generalities in question is supposed to involve the ability to recognise a generality w hen one comes across it. M oreover, it w ould seem to be an ability to recognise a generality, rather than an instance o f it. For w hat we are supposed to be aw are o f are the generalities them selves, and n o t instances o f them . This, in turn, suggests that the generalities them selves, rather than instances o f them , are the kind o f thing we can be fam iliar o r acquainted w ith, and th at w e can k n o w them in the w ay in w hich w e can k n o w other things w e are fam iliar w ith, like people, trees, colours, or pain. Presum ably it is significant that the term the M ethodists use in this connexion is ‘gnosis' , a term w hich suggests direct acquaint­ ance. M ere fam iliarity in this sense, though, does not suffice for the doctor. H e has to acquire a sufficiently articulate and clear notion o f the disease to have a clear indication o f its treatm ent. This he achieves by carefully observing the various diseases, by com paring them w ith each other, noting their sim ilarities and their dissim ilarities (cf. ps.-G al. Med. xiv 680.3 K; also consider C aelius’ differential diagnoses). In this w ay he learns to distinguish betw een the disease itself and sy m p to m s w hich tend to accom ­ pany it (Cael. Aur. Ac. 11 30), and slow ly he comes to see that the diseases them selves are ju st different form s o f the three basic generalities. A t this point everything falls into place; he can n o w clearly see the various diseases for w hat they are and know s their indicated treatm ent. T he M ethodist in acquiring know ledge o f the generalities and their treatm ent does acquire som e general know ledge. B ut, unlike the R ationalist’s or the E m piricist’s p u rp o rted general know ledge, the M eth o d ist’s know ledge is firm and certain, n o t subject to revision by future experience (Gal. de Cris, ix 657.18 K; de Meth. med. X 206.8-10; 208.10-11 K; Celsus, prooem . 62; cf. 63). N o w , one m igh t think that it is by applying this general know ledge to the particular case th at the M ethodist is supposed to kn o w w ith certainty how to treat the particular case. B ut it should be clear from w hat has been said that this w ould be an unm ethodical way

MICHAEL

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o f looking at the m atter. T h e M eth o d ist does n o t deal w ith a particular case, except incidentally; he deals w ith a disease, a generality, and n o t w ith an instance o f it. M oreover, once we k n o w the disease, and hence have the general k now ledge h o w to treat it, the awareness o f the disease will produce the th o u g h t how it is to be treated n ot by inference, but im m ediately. This is part o f w hat is m eant by ‘ind icatio n ’. T hus the question o f the application o f ou r general know ledge to the particular case and the question o f the validity o f logical inference does n o t even arise. This last point is n ot w ith o u t relevance, since, as w e m ay have suspected, the M ethodists also refuse to rely on logic and its various subdisci­ plines (Gal. de Meth. med. x 5.4-7; 30.iff.). T hey have no need for a theory o f p ro o f and inference and conspicuously refrain from presenting canonical proofs for their theses (Gal. de Meth. med. x 3 0 .iff.; 109.4ff. K; in Hipp, de vict. acut. C M G v 9.1.286.27fr.). Since, as w e already have seen, they reject definitions in the strict sense, they also have no use for a fogical theory o f definitions. N o r are they interested in the m eth o d o f resolution (cf. Galen, de Meth. med. x 30.2 K). O bv io u sly the M ethodist rejection o f logic also involves a rejection o f the Rationalist conception o f the role reason plays in m edical know ledge, since for the R ationalist logic defines the w ay in w hich w e com e to have know ledge by reason. In this respect, again, the M ethodists side w ith the Em piricists. It is in this sense, then, that the art o f m edicine, according to the M ethodist, does n ot involve m ore than the know ledge o f certain m anifest generalities. VI. Scepticism Given their em phasis on the necessity o f safe and certain k n o w ­ ledge and their claim to actually possess this know ledge, it comes as a considerable surprise w hen w e are told by Sextus Em piricus (PH i 236fr.) that o f all the m edical sects the M ethodical school is the one w hich is m ost attractive for a sceptic. Sextus does n o t say that the M ethodists are sceptics. B ut he does say that M ethodism is m ore in line w ith scepticism than E m piricism . A nd since E m piricism and P yrrh o n ean scepticism w ere closely associated w ith each other, so m uch so th at Sextus finds it necessary to explicitly reject their identification (PH 1 2 3 6 ff), the relation betw een M ethodism and scepticism , at least in Sextus’ m ind, m ust

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be very close. U nfo rtu n ately w e have no further evidence which explicitly links M ethod ism w ith scepticism . T here is a notice in Eusebius (PE xiv 5.6) w hich show s that som ebody called ‘M naseas’ took the kind o f interest in the history o f scepticism w hich w ould suggest that he him self was a sceptic; and it so happens that there also is a leading, w idely k n o w n M ethodist o f the sam e nam e; hence it is generally assum ed that the sceptical author m entioned by Eusebius is identical w ith the M ethodist, th oug h the basis for this identification is rather tenuous, especially in light o f the fact that the nam e ‘M naseas’ is n o t that u ncom m on. G iven that there is no other evidence w hich directly links M eth o d ­ ism w ith scepticism , one m ig h t be inclined to think that such sceptical leanings m ay have been peculiar to M naseas and his follow ers, especially since w e k n o w that M naseas had distinctive view s o f his o w n on other m atters, too (cf. Cael. A ur. Chron 11 97)·

B ut if one looks at the reasons Sextus gives for his association o f M ethodism w ith scepticism , all o f them tu rn out to rely on features w hich are characteristic o f M ethodism in general: their u ndogm atic use o f term s, the undogm atic attitude tow ards hidden entities, their letting them selves be guided by m anifest affections. A nd this suggests that Sextus is n o t thinking o f som e particular g roup o f M ethodists, or m istakenly identifying the position o f a particular group o f M ethodists w ith that o f the school as a w hole, but rather o f the school in general, w hen he links M ethodism w ith scepticism. T hus w e have to see w hether w e can find a w ay in w hich the general M ethodist position, as w e have outlined it above, m ight be th o u g h t to be com patible w ith som e fo rm o f scepticism . T he resolution o f the puzzle seems to m e to lie in the follow ing: w hen the M ethodists talk about certain know ledge, they again do so in an undogm atic m anner. W e do say in ordinary life that w e k n o w this or that for certain. It is in this trivial, ordinary sense that the M ethodists talk o f ‘certain k n o w led g e’. By doing so they do not have the slightest inten tion o f taking a position on the question w heth er there really is such a thing as certain know ledge, let alone w hether there could be such a thing as certain know ledge in the sense in w hich dogm atic philosophers claim certainty. T heir point rather seem s to be th at their R ationalist opponents in their attem pt to gain certain know ledge in the p h ilo so p h er’s sense not only seem

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to fail in that endeavour, b u t also fail to acquire know ledge in the uncontroversial ordin ary sense. It is because the M ethodists content them selves w ith vulgar know ledge that they have been able to gain at least th at m uch. This position is perfectly com pati­ ble w ith an unrestricted scepticism as to h o w things really are. For vulgar k now ledge is know ledge o f the phenom ena, o f h o w things appear to us. A nd the M ethodists do n o t lay claim to m ore. It is hardly an accident that Sextus, in his characterisation o f the M ethodist use o f indication (PH i 240), says that the affection guides us tow ards w h at ‘appears’ to be the fitting treatm ent. Thus even our firm and certain know ledge o f the indicated treatm ent is a m atter o f appearance. T h e M ethodist, like the sceptic, ju st follow s the phenom ena. O n e m ig ht object that a p ro p er ancient sceptic will n o t ju st refuse to rely on anything w hich is n o t a phenom enon, b u t that he will also n o t have as m uch as a m ere opinion on m atters hidden, w hereas the M ethodist, as w e have seen, does engage in theoretic­ al speculation and m entions theoretical view s w ith approval, th o u g h he refuses to base his practice on them . B u t it is n o t true that ancient sceptics quite generally reject any kind o f theoretical belief. T here is a w hole trad itio n o f Academ ic scepticism, o f w hich M etrodo ru s, Philo, C icero, Favorinus, and Plutarch are a part, w hich allows for the possibility o f theoretical or philosophic­ al beliefs. A nd this suggests th at if w e are to associate M ethodism w ith a particular kind o f scepticism , it m ay be w ith a b rand o f late Academ ic scepticism , rather than w ith P yrrhonean scepticism , as Edelstein has suggested (‘T he M eth o d ists’, Ancient Medicine (Balti­ m ore, 1967), 187). B ut ho w ev er this m ay be, there does n o t seem to m e to be any difficulty in understanding h o w the M ethodist claim to certain k now ledge could be com patible w ith a th o ro u g h ­ going scepticism . In fact, it is w o rth n o tin g that Sextus, th o u g h he carefully refrains fro m fully endorsing M ethodism as a sceptical position, does n ot give a single reason for this hesitation. This is all the m ore rem arkable, since in the preceding discussion (PH 1 2 1off.) Sextus had gone out o f his w ay to show in w hich respects the various positions w hich m ig h t be th o u g h t to be sceptical fall short o f true scepticism .

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VII. Conclusion Galen (de Sect. ingr. 12. I2ff.; 15.17fr.) gives us the im pression that if the M ethodists w ere right, there w o u ld have to be a radical change o f m edical practice. A nd this is an im pression w hich, it seems, the M ethodists them selves m eant to create. H ence, at first sight, we w ould seem to have a case in w hich a philosophical view has an enorm ous im pact on the actual practice o f an art. A nd it w ould be extrem ely useful to investigate in detail w hich effect these philosophical view s had on the actual practice o f medicine. B ut such an investigation, I suspect, w ould show that once we com e to M ethodist authors like Soranus the actual change in practice stood in no p ro p o rtio n to the revolutionary zeal w ith w hich Thessalus offended the medical profession w h en he set o u t to propagate the new m ethod. Thessalus had his to m b inscribed Ίatronikês, (Plin. N H 29.9). B ut it was largely traditional medical practice w hich happily survived, even under the guise o f M eth o d ­ ism.

0

]Vdedic^lie

, exp

e r ie n c e

and logic

JO N A T H A N BARNES

And he said. O h let not the Lord be angry and I will speak yet but this once'. Pcradventure ten shall be found there. A nd he said, I will no t destroy it for ten ’s sake.

1 turn now to tell you of what has become clear to me on reflexion and investigation, viz. that the examination of a thing very many times does not admit o f a final decision. Reflect upon my words and study them to see if I do an injustice or if I am a master o f the principles on which the proof is based, either as regards the opinion that I hold and am convinced of or as regards the things which they support and are convinced of. And that is that they say that a thing which has been seen only once is not accepted nor reliable, and similarly for what has been seen a few times. They think that a thing is only acceptable and reliable if it has been seen a great number of times - and moreover in the same manner on each of the times. Then I ask them concerning that which has been seen ten times whether it is included among that which has been examined a great many times; and their answer to that is No. Then I say to them: And that which has been seen eleven times? And they say No. Then I ask them also concerning that which has been Seen twelve times; and they say No. Then I say to them: And that which has been seen thirteen times? And they say this also has not reached that limit. I continue in this vein: I extend the question one by one until I reach a large number. The necessity for the respondent is inevitable: either he does not admit at any one time that the number has already reached the limit of that which is said to be a very large number; or, if he does admit it, he has already reduced himself at that time to the status of a laughing-stock, since he is asking that people allow him a number and a limit [?] according to a usage fixed by himself and an opinion contrived for himself. And the speaker might say to him: Why has what has been seen fifty times, for example, become as if it has been seen a great many times, and that which has been seen forty-nine times is not among that which has been seen a great many times? Your assertion is the assertion of one who asserts two mutually contradictory issues. And that is that you have affirmed that what has been seen once is not therefore acceptable or

Medicine, experience and logic

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reliable: then we see now that you have admitted that it is acceptable and reliable, because if what has been seen forty-nine times and in all those times has been unacceptable and unreliable has only to be increased by one time to become acceptable and reliable, then it is clear that in fact it ends up acceptable by one examination only. Then it must be, from that, that the examination o f the thing once - which has already been, from the beginning o f the issue, unacceptable and unreliable - has acquired at this time the power that, when it was added to the thing that was already unacceptable and unreliable, makes it acceptable and reliable. And if it is curtailed and removed, it makes the thing which was already acceptable and reliable unacceptable and unreliable. This, then, is what the Dogmatists argue against the Empiricists with regard to the examination o f the thing very many times; and they are arguments which ought to be remembered by heart and borne in mind. G alen’s treatise On Medical Experience, 1 from w hich that passage is taken, is a dram atic account, in dialogue form , o f the disputes betw een the E m pirical D octors and the D ogm atic or Logical D octors - disputes w hich ran on for several centuries and which dealt p rofoundly w ith num erous issues in the philosophy o f science. Galen w ro te the w o rk w hen he was a young m an o f tw enty: in his later Outline o f Empiricism he refers to it for a fuller discussion o f one o f the m ajor problem s faced by the Em pirical school: And just as the art as a whole is put together from several experiences, so again individual experiences of this sort are put together from many experiences. But this, viz. the question ‘from how many?’, is indeter­ minable, and falls into the puzzling argument which some call ‘soritical’. I have spoken more fully about that in another book which is entitled On Medical Experience.12 1. Apart from tw o short passages o f Greek, the treatise survives only in an Arabic translation. The Arabic is at tw o rem oves from the original, being a version o f an earlier Syriac translation o f the Greek; although the Arabic is not sufficiently literal to perm it a ‘back-translation’ into Greek, com parison w ith the surviving Greek fragments indicates that it provides a reliable account o f Galen’s argum ents. The Arabic has been edited and translated by Richard Walzer: Galen on Medical Experience (O xford, 1947). For discussion o f the text and content see W alzer’s Introduction, and also: R. Walzer, ‘Galens Schrift über die medizinische E rfahrung’, SB Preuss. Akad. Wiss., phil. hist. KI. (1932), 449-68; id., ‘U n o scritto sconosciuto di Galeno’, Rivista di storia critica dette scienze mediche e naturale 19 (1938), 258-65; K. Deichgraber, Die griechische Empiriker­ schule (B erün/Z urich, 19652), 400. T he passage quoted is found at Med. Exp. vn 8-viil I, pp. 96-7 W. I am indebted to Adam Bruce-W att o f Balliol College, w ho has been kind enough to check Walzer's translation against the Arabic and to suggest several im provem ents to it. 2. Suhf. emp. 38.12-17 Bonnet = p. 46 Deichgräber. The Outline survives only in a Larin translation, which is edited and faced by a Greek ‘back-translation’ in Deichgräber, op. cit. (n. 1).

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T he Em pirical D octors hold that the art o f m edicine is a congeries o f ‘experiences’, and that an ‘experience’ is m ade up o f m any particular observations; b u t the ‘soritical’ argum ent rehearsed in On Medical Experience threatens the central n otion o f an ‘experi­ ence’ w ith incoherence. T he concept o f ‘experience’ has a long history, going back th ro u g h A ristotle to the Presocratic philosophers.3 I shall not attem pt to w rite that history, n o r to give an account o f the precise w ay or ways in w hich the concept was u n derstood by the Em piricist doctors w h o took their sobriquet from it. I assum e that an ‘experience’ is a piece o f general know ledge (‘Pom egranates cure diarrhoea’),4 based upon a series o f particular observations (‘Pom egranates w ere good for D ion w hen he had diarrhoea’, etc.); and I assum e, further, that in the eyes o f the Em piricists the general know ledge was justified by its observational basis.5 In effect, then, the Em pirical doctors w ere com m itted to the accepta­ bility o f certain inductive inferences; and the ‘soritical’ argum ent — or the sorites, as it is n o w custom arily called —was used by the D ogm atists to cast d o u b t upon induction. T he argum ent betw een D o g m atist and Em piricist in On Medical Experience is not a literary fiction: Galen says that he is recording, in a m ore orderly form , a conversation w hich took place betw een tw o em inent physicians, Pelops (Galen’s o w n D o g m atist teacher) and Philippus;6 and Pelops and Philippus them selves claim to be

3. See, e.g., P. H. and E. A. do Lacy, Philodemus: on Methods o f Inference (Naples, 19782), 165-82. (The connexion betw een Empiricist doctors and Epicureans requires some exam ination.) 4. The know ledge may be universal (‘All sufferers . . . ’), but it need not be: experience, or general know ledge, is som etim es a m atter o f w hat happens as a rule (‘M ost sufferers . . . ’), or ά μ φ ιδόξω ς (‘For half the time, sufferers . . .’), or rarely (‘A few sufferers . . in w hat follows I shall usually have universal know ledge in mind; but m ost o f the argum ents are readily generalised to cover all varieties o f experience. 5. B oth assum ptions are questionable. (1) M any texts imply that ‘experience’ is no m ore than the possession o f num erous bits o f particular inform ation: no process of generalisation —and hence no inference - is involved at all. (2) Even i f ‘experience’ is general know ledge which arises from a m ultitude o f observations, it is not clear that the relation between experience and observations need be one o f inference: perhaps, rather, a m ultitude o f observations simply produces or causes a piece o f general know ledge. —Any discussion o f the nature o f medical Empiricism w ould have to look closely at those issues. I pass them by for tw o reasons: first, it is clear that sometimes and notably in Med. Exp. - the question o f justifying claims to general knowledge is upperm ost in the m inds o f the disputants; secondly, m y discussion o f the sorites is largely independent o f those“ issues. 6. See Galen, Libr. propr. xix 16-17 K (= Scripta Minora 11 97, 16-23).

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review ing a m uch older debate - Pelops’ case is ‘sim ilar to A sclepiades’ v iew ’, w hile P hilippus’ argum ent is to be th o u g h t o f as ‘laid dow n by a representative o f the Em piricists, M enodotus, if you like, or Serapion, o r T heo d o siu s’.7 T hus the argum ent I am about to consider actually exercised m edical practitioners, and considerations o f an abstract and logical nature w ere an integral part o f a debate w hich bore directly upon therapeutical practice and affected the welfare o f patients. T he sorites was no invention o f the physicians, n o r was it peculiar to m edical disputations. Elsew here, discussing the ques­ tion o f the tim e at w hich a disease m ay be said to com m ence, Galen observes that ‘for present purposes, we are n o t affected by the argum ent from little-by-little, w hich they also call soritical; for the puzzle arising from it is com m on to m any m atters o f everyday life, about w hich previous philosophers and doctors have talked and arg u ed ’ (de Loc. aff. vm 25 K). W ho were those doctors and philosophers? and h o w did they argue? W hat was the history o f the sorites? H o w w ere its puzzles solved? Before turning to those questions, I shall first attem pt to give a clear account o f ju st w hat constitutes a soritical argum ent.

I G alen’s D o gm atist presents his case inform ally, by posing a series o f questions: A re ten observations m any? are eleven? are twelve? . . . A nd other authors w h o parade soritical argum ents often do so in the same interrogative fashion. B ut w e can - and the ancients did - see a logical structure behind that dialectical façade. A reasonably form al account o f the argum ent can be found at the end o f D iogenes L aertius’ survey o f Stoicism, w here he lists the ‘puzzling arg u m en ts’ traditionally discussed in Stoic lo g ic.8 T he text o f D iogenes is corrupt; b u t the description o f the sorites can be rescued intact: It is not the case that two are few and three are not also; it is not the case 7. Galen, Med. Exp. n 3, p. 87 W. The elements o f the argum ent thus go back to the second century b.c. 8. For similar references to the sorites as a standard λόγος ά π ορ ος in Stoicism see: Cicero, Div. it iv 11; Gellius, 1 ii 4; Lucian, Symp. 23; Fronto, Eloq. p. 146 N aher = p. 140 van den Hout; M artianus Capella, iv 327.

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that these arc and four are n o t also (and so on up to ten thousand). B ut tw o are few: therefore ten thousand arc also.9

Strictly speaking, the arg um ent D iogenes describes contains 9,998 prem isses; b ut the figure o f 10,000 is a conventionally vast num ber, and no th in g hangs upon it: we m ay generalise and give the argum ent n prem isses, w here n will be p retty large. O n e o f the n prem isses is categorical (‘tw o are few ’, in Diogenes); the rem ainder are negated conjunctions, o f the fo rm rn o t b o th (P and not-Q )"1 (‘it is no t the case that tw o are few and three arc not also’). In m any ancient presentations o f soritical argum ents, w e find conditionals instead o f negated conjunctions, rif P, then Q"1 instead o f rn o t b o th (P and not-Q )"1; and, on the w eak interpreta­ tion o f ‘if . . ., then . . .’ w hich is custom ary am ong m odern logicians and was fam iliar to the ancients, rif P then Q"1is logically equivalent to rno t b oth (P and not-Q )"1. W e k n o w that C hrysippus w ould som etim es rew rite conditionals as negated conjunctions w hen he w anted to indicate that they w ere to have the weak in terp retatio n ;101and since D iogenes’ account o f the sorites is Stoic in origin, it is plausible to suspect the same m otiv ation here: the com pound prem isses o f soritical argum ents are conditionals, but weak conditionals —they are w hat m odern logicians call ‘m aterial im plications’ and w h at the Stoics knew as Philonian conditionals. In m y form ulation o f the sorites I shall adopt the overtly con­ ditional form o f the co m p ou n d prem isses; bu t I shall use the artificial sym bol ‘D ’, rather than the natural ‘i f . . ., then . . . ’, in order to m ake it clear that the conditionals are w e a k .11 It is w o rth observing that soritical argum ents are in no sense ‘w eaker’ w hen form ulated w ith m aterial conditionals or negated conjunctions than they w o u ld be w ere they form ulated by w ay o f som e to ugher conditional. O n the contrary, they are ‘stro n g er’, 9. DL vu 82. T here are lacunae before and after the passage quoted (see M enagius ad loc.); but there is no doubt that the passage describes the sorites. W ith Egli (U. Egli, Zur stoischen Dialektik (Basel, 1967), 8, 55), I read μυρίων and μύρια for δέκα and δέκα (cf. M vu 416-21); but 1doubt if E gli’s final < ό λ ίγ α έσ τίν> is needed. Sillitti’s proposal to insert a lot m ore into the text is based upon a m isunderstanding o f the logic o f the argum ent (Sillitti (1977), 77, 83). [Abbreviated citations refer to the bibliography at the end o f the chapter.] 10. See Cicero, Fat. vi 12. The Stoics generally preferred a strong interpretation o f ‘i f . . ., then . . . ’: full discussion in Μ. Frede, Die stoische Logik (Göttingen, 1974), 80-93. 11. The argum ent does not require form ulation in terms o f m aterial implication: it works for any conditional for w hich modus ponens holds good, i.e. for any conditional at all.

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inasm uch as their hypothetical prem isses assert less and are thus easier to sustain and harder to reject.12 Stated m ost generally, then, the logical structure underlying any soritical arg um ent will look like this: Pi

Pi 3 P2 P2 3 P 3

P n - 1 =5 P n

T here is n o thing rem otely esoteric o r obscure about that argum ent pattern; n o r —at any rate on the surface —docs there seem to be anything fallacious about the sorites. Rather, the argum ent pattern seems evidently valid; and even if its validity is n o t perfectly evident, it can be reduced to a p attern w hich m ust count as evidently valid if any arg um ent pattern does. For the first tw o prem isses yield, by the inference know n as modus ponens, the categorical prop osition P2\ P2 and the third prem iss yield, again by modus ponens, the categorical proposition P3; and so by a series o f modus ponens inferences, to P„ - how ever large n m ay happen to be. T he logical sim plicity o f the argum ent is to be em phasised. The sorites is often connected w ith, and held to produce puzzles for, the com plex inference pattern k n o w n as ‘m athem atical ind u ctio n’. 13 T h at m ay be so; but if it is so, it is n o t because the sorites has the form o f a m athem atical induction. If the argum ent produces puzzles for any inference pattern, it produces puzzles for 12. For criticism o f this paragraph (which was originally w ritten w ith Sedley (1977), p. 91 and n. 97 in view) see Sedley (1982), below p. 255 n. 41. 13. T h e rule o f m ath em atical in d u c tio n can be fo rm u lated as follow s:

Given (i), rF(o)n and (ii), rFor any n, if F(n) then /'·’(« + 1)"1 infer: rFor any n, F (tip Inform ally speaking, the principle behind the rule is this: if zero possesses a given property; and if the successor to any num ber has that property provided that the num ber in question has the property: then every num ber has the given property. For the connexion betw een this and modus ponens see e.g. D u m m ett (1975), 303-6.

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modus ponens·, if the argu m ent sheds do ub t on any principles o f logic, it sheds d ou b t on one o f the m ost sim ple and fundam ental o f all logical principles. N ex t, w e m ay observe th at each P, in the argum ent pattern will in fact be a singular propositio n ascribing a predicate to a subject, predicating ‘T( ) ’ o f a. T he specific structure o f the argu m ent is thus: Fax Fax D F ü2 Fa 2 D Fa 3

Fan- \ D Fan

A n argum ent o f that fo rm will be soritical provided that its subjects - the a/s - and its predicate - ‘F( )’ - satisfy certain undem anding conditions. First, the a/s. D iogenes’ text uses the num erals ‘2’, ‘3’, . . ., Τ ο,οοο’; b u t he is n o t talking about the numbers 2, 3, . . ., ro,ooo (it is nonsense to say that the n u m b er 2 is few). R ather ‘2 are few ’ stands for ‘tw o so-and -so’s are few ’ (as it m ig ht be, ‘tw o experiences are few ’), and is thus im plicitly general. If w e take D iogenes strictly, w e shall suppose that the a /s are always groups or sets o f things; b u t th at supposition is unduly pedantic, and it has the unw elcom e consequence that the m ost no to riou s o f ancient sorites (C arneades’ argum ents against the gods) are n o t soritical. T he subjects o f a sorites m ust form an ordered set:

iC'> T he use o f num erals in D iogenes’ general description o f the sorites need indicate no m ore than that the a/s are thus ordered. Secondly, ‘F( )’. D iogenes uses ‘few ’; the sorites in On Medical Experience can readily be form ulated in term s o f the predicate ‘few ’; and indeed the term ‘few ’ was standardly em ployed in ancient accounts o f the argum ent. B ut the sorites is n o t about fewness, and ‘few ’ is n o t the unique soritical predicate: ‘few ’ m ay

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be paradigm atically soritical, but the ancient texts provide us w ith plenty o f sorites w hich do n o t use ‘few ’. In D iogenes, then, ‘few ’ stands as the representative o f a general class o f predicate: how can that class - the class o f soritical predicates - be characterised? ‘F( )’ will be soritical, relatively to a given sequence o f subjects,14 < au ct2, ■ . ., an> , if it satisfies three conditions. First, ‘F( ) ’ m ust, to all appearances,15 be true o f αχ, the first item in the sequence o f subjects. Secondly, ‘F( ) ’ m ust, to all appearances, be false o f a„, the last item in the sequence o f subjects. Finally, each adjacent pair o f subjects in the sequence m ust, to all appearances, be indistinguishable w ith respect o f ‘F( ) ’; that is to say, given any tw o adjacent subjects, a, and α,+χ, it m ust be the case, to all appearances, either that ‘F( )’ is true o f b o th or that ‘F( )’ is false o f both. T he first o f those three conditions m akes plausible the categor­ ical prem iss o f soritical argum ents; for i f ‘F( )’ is true o f a\, then the proposition that Fa\ is true. T he second condition indicates that the conclusion o f the argum ent is false; for, if ‘F( )’ is false o f an, then the pro p o sitio n th at Fan is false. T he th ird condition validates all the hypothetical prem isses o f the argum ent: unless ‘F( )’ is true o f αχ and false o f ^2, the prop osition that Fa\ D Fa 2 is true; unless ‘F( ) ’ is true o f û2 and false o f a^, the proposition that Fa2 D Fa-2 is true; and so on, dow n to an- 1 and a„. T hus soritical predicates, and soritical argum ents, are paradoxical in the follow ­ ing sense: i f ‘F( )’ is soritical, then by the second condition it does 14. The qualification is necessary: CF( )’ m ay satisfy the soritical conditions for some sequences o f subjects but not for others. (‘Sm all’ m ight be soritical for the sequence < 1 ,2 ,3 ,. · ·, i,o o o > but n ot for the sequence < t , 100, 200,. . ., i,o o o > .) A predicate m ight be called unqualifiedly soritical if it satisfied the following condition: for any object, X, if ‘F( Y is to all appearances true o f x, then there is some sequence o f which X is a m em ber and for w hich ‘F( )’ is soritical. If a predicate is soritical relative to some sequence, does it follow that it is unqualifiedly soritical? 1$. T he phrase ‘to all appearances’ has caused some difficulty. The point is simply this: not every argum ent o f the logical form set out above is a sorites - not every predicate will produce puzzles if it is substituted for ‘F( ) ’ in the schema. Hence it seems necessary to give som e general characterisation, how ever vague, o f those predicates w hich do produce puzzles. Plainly, it will not do to say that ‘F( )’ is soritical if it is actually true o f al5 actually false o f an, . . . - no predicate could satisfy such conditions. Ï m ight have said that a j should be a ‘paradigm instance’ o f ‘F( )’ (cf. Carneades’ formula: εΐ δέ γε ήσαν θεοί, κ α ί ό Ζ ευ ς ήν α ν θ ε ό ς - Μ ιχ ι8 4); or that it should be ‘eminently plausible’ to predicate *F( )’ o f aj, etc.; or that ‘anyone w ould grant’ that ‘F( )’ is true o f ah etc. I hope that the general thrust o f these phrases is plain enough: ‘to all appearances’ has the same general thrust; and that is all that matters about the phrase. (It may be w orth adding that ‘to all appearances’ is used only in the characterisation o f soritical predicates: it is not a part o f those predicates themselves, nor does it appear in the premisses o f soritical argum ents.)

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not, to all appearances, hold o f a„, and by the first and third conditions taken together, it does, to all appearances, hold o f an. It is perfectly obvious that n o t-Farj, bu t evidently valid m oves from evidently true prem isses lead to the conclusion that Fa„. Soritical argum ents w ere som etim es called argum ents from ‘little-b y -little’;16 for they proceed little by little from palpable tru th to palpable falsity .17 B ut their standard ancient nam e was ‘so rites’:18 the G reek w o rd ‘sorites’ is an adjective cognate w ith the n o u n ‘soros’, w hich m eans ‘heap’ or ‘pile’; and the adjective was 16. ό π α ρ ά μικρόν λόγος: Galen, Loc. aff. vni 25 K; Med. Exp. xvi 2, p. 115 W; M 1 68-9; C hrysippus, Λ ογικά Ζ ητή μα τα , S VF 11 p. 106.9; DL vu 197; Plutarch, Stoic, rep. 1084AC; cf. Aspasius, in E N (C IA G xix) 57.5; Simplicius, in Phys. (C 1A G x) 1117.2; gradatim: e.g. Cicero, Ac. tl xvi 49; cf. Seneca, Ben. v xix 9 (paulatim). R üstow (A. R üstow , Der Lügner (Leipzig, iy io ), 77 n.2) argues that ό π α ρ ά μικρόν λόγος is a highly generic notion (‘Kleine U rsachen, grosse W irkungen’), o f w hich the sorites and the Liar are both specifications. Certainly, π α ρ ά μικρόν is used in logical contexts w here soritical argum ents are not in question (Rüstow cites Aristotle, Top. 169hl 1, 15; An.pr. 47b38); but the evidence shows, I think, that ό π α ρ ά (or: κατά) μικρόν λόγος was also used specifically o f the sorites. 17. Natura cavillationis quam Graeci σω ρίτην appellant haec est, ut ab evidenter veris per brevissimas mutationes disputatio ad ea quae evidenterfalsa sunt perducatur (Ulpian, Dig. i xvi 177; cf. Julian, ibid, xvii 65); ό . . . σω ρίτης σ οφιστικός έστι λόγος έκ τής π αρ ά μικρόν έρω τήσεω ς ά πά γω ν κ α τά την εκλυσιν τώ ν φ αντασιώ ν έπ’ άδηλον ή ψ ευδός έκφανές (Simplicius, in Phys. (C IA G x) 1177.2-4 = Scholiast to Lucian, vol. iv p. 254 Jacobitz). 18. In Greek, the standard nom enclature is ό σω ρίτης λόγος (or sim ply ό σωρίτης); ή σω ριτική ά π ο ρ ία and ή σω ρική ά π ο ρ ία are also found, in Sextus and in Galen. Latin authors norm ally use sorites. (The form soritam is found in the MSS o f Cicero, Hortensius, Fr. 26 G = fr. 60 S-Z: but the text should be em ended, w ith R üstow , to soritas.) Cicero, Div. 11 iv 11, proposes acervalis (sc. ratio) as a suitable Latin translation o f σωρίτης; but he adds that sorites is already well established in Latin so that there is no need for acervalis. (The w ord acervalis was apparently never taken up, although Latin w riters will often use acervus in connexion w ith the sorites.) W ords in -τ η ς are com m on in Greek: Buck and Petersen (C. D. Buck and W. Petersen, A Reverse Index o f Greek Nouns and Adjectives (Chicago, 1944), 544—73) list som e 4,500, o f w hich about 750 are in -ιτη ς. The term ination is ancient (e.g. όδίτη ς from H om er onw ards), and ‘its m ost com m on and probably oldest use was as an agent suffix’ (Buck and Petersen, p. 544). σω ρίτης is form ed from σωρός, ‘heap’ (cf. e.g. καμηλίτης from κάμηλος), and it is naturally taken in an ‘agentive’ sense: ‘heaper’, ‘accum ulator’. (For the adjectival use o f such ‘agentives’ c f e.g. οπλίτης.) A dm ittedly, som e w ords in - ιτ η ς are ‘agentive’ only in an extended sense, and others have no ‘agentive’ force at all (e.g. άσκίτης, a form o f disease; or φ αρμακίτης, which is apparently used exclusively as an adjective, usually in the sense o f ‘drugged’); b ut the general truth about -ιτ η ς term inations makes it reasonable to suppose that σω ρίτης was originally intended in the ‘agentive’ sense o f ‘accum ulator’. C hrysippus is the first author we know to have used the w ord σωρίτης; but it is plausible to think that it was coined by Eubulidcs to nam e his argum ent. Sedley (1977), 115 n. 132, points out that the titles o f the ancient paradoxes often have a double sense - ‘the έγκεκαλΰμμενος is a veiled argum ent about a veiled m an’. In the same way, the σω ρίτης m ay be seen as an accumulating argum ent about an accum ulating man: the argum ent adds premiss to premiss (or question to question) as the m an adds grain to grain.

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applied to the argum ent because the original soritical argum ent was about a heap or pile. ‘T here are som e D ogm atists and logicians w ho call the argum ent expressing this d o u b t a sorites, after the m atter w hich first gave rise to this question, I m ean the h eap .’19 T he original sorites is expounded as follow s in G alen’s Medical Experience: W herefore I say: tell m e, do y ou thin k that a single grain o f w heat is a heap? T hereu p o n you say N o . T hen I say: W hat do you say about 2 grains? For it is m y purpose to ask you questions in succession, and if you do n o t adm it that 2 grains are a heap then I shall ask you about three grains. T h en I shall proceed to in terrog ate you fu rther w ith respect to 4 grains, then 5 and 6 and 7 and 8; and I think y ou w ill say that none o f these m akes a heap. Also 9 and 10 and 11 grains arc n o t a heap. For the conception o f a heap w hich is form ed in the soul and is conjured up in the im agination is that, besides being single particles in ju x tap o sitio n , it has q uantity and m ass o f som e considerable size. . . . I for m y part shall not cease from continuing to add one to the n u m b er in like m anner, nor desist fro m asking you w ith o u t ceasing i f you ad m it that the quantity o f each single one o f these num bers constitutes a heap. It is n o t possible for you to say w ith regard to any one o f these n um bers that it constitutes a heap. I shall proceed to explain the cause o f this. If you do n o t say w ith respect to any o f the nu m bers, as in the case o f the 100 grains o f w heat for exam ple, th at it n o w constitutes a heap, b u t afterw ards w hen a grain is added to it, y ou say that a heap has n o w been form ed, consequently this q uantity o f corn becom es a heap by th e addition o f the single grain o f w heat, and if the grain is taken aw ay the heap is elim inated. A nd I know o f n o th in g w orse and m o re absurd than th at the being and not-being o f a heap is determ ined b y a grain o f corn. A nd to p revent this absurdity fro m adhering to you, y o u w ill n o t cease from denying, and w ill never adm it at any tim e that the sum o f this is a heap, even i f the n u m b er o f grains reaches infinity by the constant and gradual addition o f m ore. A nd by reason o f this denial the heap is pro ved to be non-existent, because o f this pretty so p h ism .20

T he sequence o f subjects is a series o f collections o f grains {a\ T he term 'sorites’ is long established as the English for σωρίτης. W c speak o f the M aster argum ent, not o f the 'kurieuon , o f the Liar, n o t o f the ‘pseudomenos’: w hy not translate σω ρίτης instead o f transliterating it? In the first version o f this paper, I used ‘heap’ and ‘heap-like’ for σω ρίτης (‘heaper’ w ould have been better); in a second version I tried ‘accum ulator’ and ‘accum ulative’. But although both translations have the m erit o f giving the sense o f σω ρίτης, they are aesthetically displeasing - and I am assured that they will not catch on. I have therefore reluctantly returned to orthodoxy, and now prefer ‘sorites’ and ‘soritical’. ty. Galen, Med. Exp. xvi 2, p. 115 W. Sillitti’s suggestion that the application o f the sorites to heaps o f grain may be postaristotelian is highly implausible (Sillitti (1977), 76 n. 2). 20. Galen, Med. Exp. xvn 1-3, pp. 115-16 W; cf. Aspasius, in E N (C IA G xix) 56.27-57.7.

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consists o f one grain, «2 o f tw o, and so on); and the soritical predicate is ‘. . . does n o t constitute a heap’. Y ou can never m ake a heap o f grain, how ever m any sackfuls o f w heat y ou pour out. Som e ancient texts say that soritical argum ents m ay proceed either ‘by adding’ o r ‘by su btracting ’.21 T he original sorites, as Galen reports it, proceeds ‘by adding’: each successive tf; is obtained by adding one grain to its predecessor. T he heap exam ple can also be presented in a ‘su btractin g’ form : let a\ be a collection o f 1,000,000 grains, 02 a collection o f 999,999 grains, and so on; and let ‘F( ) ’ be replaced by ‘. . . constitutes a h eap’. T hen the argum ent show s that even a single grain constitutes a heap —or, for that m atter, that a collection o f no grains constitutes a heap; and the reasoning proceeds by successively ‘sub tractin g’ one grain from the previous collection. In general, i f ‘F( ) ’ is soritical for , then ‘n ot-F ( ) ’ is soritical for ; and vice versa. A nd one o f each pair o f such soritical argum ents m ay be regarded as proceeding ‘by addition’, the other as proceeding ‘by su b tractio n ’. T he sorites w ou ld be little m ore than an am using con un dru m if only such relatively tedious predicates as ‘. . . does n o t constitute a heap’ appeared to be soritical. B ut in fact, as Galen says, ‘the puzzle arising from it is co m m o n to m any m atters o f everyday life’ (de Loc. aff. vm 25 K); and the a rg u m en t’s ancient exponents tricked it out w ith philosophical as well as w ith quotidian predicates. For according to what is demanded by the analogy, there must not be such a thing in the world as a heap of grain, a mass or satiety, neither a mountain nor strong love, nor a row, nor strong wind, nor city, nor anything else which is known from its name and idea to have a measure of extent or multitude, such as the wave, the open sea, a flock of sheep and herd of cattle, the nation and the crowd. (Med. Exp. xvi 1, p. 114 W) Cicero, tw o centuries earlier, had generalised the case: ‘the nature o f things has provided us w ith no know ledge o f boundaries so that in any case w e could determ ine h ow far to go; no r is this so only in the case o f the heap o f grain, from w hich the nam e derives; bu t in no case at all if w e are questioned by degrees - is he rich or poor? 21. E.g. Cicero, Ac. n xvi 49; Scholiast to Persius, ad vi 80, p. 35oJahn; Galen, Med. Exp. XVII 4, p. 1 16 W (‘I wish to capture you . . . from tw o sides’). There is no interesting difference betw een the ‘adding’ and the ‘subtracting’ arguments; if we are to believe Galen, the original sorites was an ‘adding’ argument.

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fam ous or obscure? are they m any o r few, great or small, long or short, broad o r narrow ? - do w e k n o w h o w m uch is to be added o r subtracted before w e can answ er definitely’ (Ac. 11 xxix 92). V irtually all predicates are soritical. A fter centuries o f com parative neglect, philosophers have re­ cently begun to pay serious attention to the sorites. Som e are w orried by the fact th at certain epistem ologically basic predicates are soritical. Take, for exam ple, the observational predicate ‘. . . is red ’. C o nstruct a band o f colour, dark red at the left-hand end and shading by degrees th ro u g h light red and orange to yellow at the right-hand end; and m ark o ff a series o f points, a\, a2 . . ., an, from left to right. N o w a\ is patently red; and an is patently n o t red. B ut any tw o adjacent points are indistinguishable in respect o f colour: if a, is red, then so too, to all appearances, is ai+\, and vice versa. Thus ‘. . . is red ’ is a soritical predicate; and all our colourpredicates — and, in general, all o u r observation predicates — are threatened by soritical parad o x .22 O th e r philosophers have considered predicates associated w ith ordinary m iddle-sized objects. Take, for exam ple, . . is a table’. Tables, w e know , are m ade up o f m illions o f m inute particles; and plainly if you rem ove ju st one particle from a table, w hat is left will still be a table. It is clear, then, that tables - and in general, all m aterial objects - provide us w ith m atter for soritical argu­ m ents: w e can show that a single atom is a table, if anything is a table — and hence conclude that there are no tables at all. O rd inary predicates o f everyday life are infected by soritical p arad o x.23 T he sorites m ust be taken seriously: the D ogm atical D octors w ere on to a good thing. II

Galen reports that soritical argum ents had been w idely discussed by ‘philosophers and d o cto rs’ before his time: the particular debate w hich he records too k place in about a . d . 150; but at that tim e the dispute betw een E m pirical and Logical doctors was already cen­ turies old, and the sorites had no d o u b t entered their debates at an early stage. A nd, as I have observed, the sorites is also found 22. See esp. W right (1975).

23. See esp. U nger (1979).

36 J O N A T H A N BARNES outside m edical contexts: it was closely associated w ith the Stoics, and it functioned as a pow erful w eapon in the battle betw een the Stoa and the Sceptical A cadem y; it was fam iliar enough, as we should expect, to philosophers o f other schools - to the Peripate­ tics and to the P yrrhonists. M o re interestingly, it was k n o w n outside strictly philosophical circles. H orace uses it in his m ocking attack on the laudatores temporis acti: old poets are best, b u t w ho counts as old? A poet w h o lived a century ago, perhaps; well then, let us subtract a m o n th fro m that century: surely a poet w h o lived that long ago was old? A nd subtract a further m onth; and a further m onth. All poets are old if any are; and o u r o pponent collapses, ‘overcom e by the argum ent o f the dim inishing h eap’.24 Persius urges som eone to ‘sell his soul for cash’: he doubles his m oney, trebles it, quadruples it - b u t w here should he stop? w hen will he be rich? Persius ironically com m ents: ‘W e have found som eone to put a lim it to y ou r heap, C h ry sip p u s’.25 In antiquity, the sorites was as n otorious as the L iar.26 T he discovery o f the sorites is usually ascribed to A ristotle’s contem porary, Eubulides:27 according to D iogenes Laertius, ‘he proposed m any argum ents in logic - the Liar, the Elusive M an, the Electra, the Veiled M an, the Sorites, the H orns, the Bald M an ’ (n 108). D iogenes does n o t actually say that Eubulides invented those argum ents;28 and som e scholars have attem pted to push the origins o f the sorites back a century or so, ascribing it to Z eno o f Elea.29 In his paradox o f the M illet Seed, Z eno argued that since a 24. Epistles π i 36—49; ‘the dem onstration is deliberately presented in terms o f hackneyed school logic’ (E. Fraenkel, Horace (O xford, 1957), 387 n. 2). (Tacitus, Dial, 16, asks the same question, ‘w ho are the old w riters?’, but docs not allude to the sorites.) 25. Satires vi 75-80; see the scholiast to line 80 (ed. Jahn, p. 350). Persius was a friend o f the Stoic C ornutus, w ho became his literary executor (see the ancient Life, ed. Jahn, pp. 233fr.). For ‘rich’ as a soritical predicate see e.g. Cicero, Ac. 11 xxix 92 (quoted above, p. 35); Aspasius, in E N (C IA G xix) 56.29—32; for the indeterm inacy o f the m oneygrubber’s desires see the passages cited by Jahn, p. 229. 26. See Appendix A. N o t every occurrence o f the w ord σω ρός alludes to the sorites: scholars regularly refer, e.g. to Tatian, adv. Graec. 27; but w hen he asks τί δ ’άν ώ φελήσειε λ έξις Α τ τ ικ ή κ α ί φιλοσόφω ν σω ρεία κ α ι συλλογισμών πιθα νότητες . . .; he means ‘a gaggle o f philosophers’, not ‘the sorites o f the philosophers’. Again, acervus is frequently used in Latin texts w ithout any reference to the sorites - though it is tem pting to see such a reference in passages like Horace, Epistles 1 vi 35. 27. O n w hom see D öring (1972), 102-14. 28. And in fact the ancients were not unanim ous about the authorship o f these paradoxes: some ascribed som e o f them to D iodorus (see DL 11 111), som e ascribed som e o f them to C hrysippus (see DL vu 187). - Abraham got there first: Genesis xvm 23-3 3. 29. See e.g. G rote (1867), 490 n.e.; Zeller (1922), 11.1 265 η.τ; Kräm er (1971), 59, 75; D öring (1972), i n . Contra e.g. Moline (1969), 393 n. 3; Sedley (1977), 112 n. 85; Sillitti

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bushel o f seed m akes a noise as it falls to the ground, any individual seed m ust also m ake a noise on falling. N o w it is certainly possible to get from Z e n o ’s prem iss (‘A bushel m akes a noise’) to his conclusion (‘A n individual seed m akes a noise’) by w ay o f a soritical argum ent. B u t our evidence, such as it is, indicates that Z eno did n o t proceed in that soritical fashion; rather, he derived his conclusion by the aid o f a principle o f p ro p o rtio n al­ ity that has n o th in g to do w ith the sorites.30 T h e M illet Seed is not presented in soritical form , and there is no reason to think that Z eno ever gave it a soritical tw ist: as far as w e can tell, Eubulides was the first m an to hit upon the sorites. D iogenes m entions the sorites as one o f seven paradoxes.31 A ccording to Sextus (M vii 13), Eubulides was exclusively interested in logic; and w e m ight well suppose th at for him the sorites was a logical puzzle and n o th in g m o re .32 A fter all, logical puzzles are captivating things: they divert party-guests, and they delight logicians even w hen they have no serious m oral to convey; and the evidence o f P lato ’s Euthydemus and o f A ristotle’s Sophistici Elenchi show s that puzzles o f that sort w ere found as entertaining in the fo u rth century b . c . as they are now . N evertheless, m any scholars have searched for a philosophical context w ithin w hich to set E ubulides’ p arad o x o latry .33 O f the

30.

31.

32. 33.

(1977), 393 n. 3. It has been suggested that the M illet Seed, though not soritical, gave Eubulides the idea o f the sorites (Moline (1969), 393 n. 3; Reale (1976), 67): the suggestion is attractive, but quite untestable. For the Millet Seed see Aristotle, Phys. 250119-22; Simplicius, in Phys. (C M C x) 1108. 18-28. T he ‘principle o f p ro portion’ Z eno relies upon is som ething like this·, if a w eight w makes a sound o f volum e v on falling a distance d, then for any n a weight w/n will make a sound of volum e vln on falling a distance d. (See further, below n. 43.) There is no suggestion that the seven paradoxes form ed a system atic set, nor that Eubulides generalised them (the occurrence o f the Bald Man alongside the sorites is good evidence that he did not - for the Bald M an is sim ply an instance o f a soritical argum ent, as later authorities recognised: e.g. Galen, Med. Exp. x x 3, pp. 124-5 W; Aspasius, in E N (C I A G xix) 56.32-4). See also Kneale and Kneale (1962), 1:4, who reduce the seven paradoxes to four. So, e.g., K. von Fritz, ‘M egariker’, RE Suppt. V (1931), col. 710; D öring (1972), 107. E.g. R itter (1828), 332 (a refutation o f das Werden); tienne (1843), 172 (an attack on ‘expérience’); G om perz (1905), 190 (‘a new pro o f o f the contradictory nature o f empirical concepts’); Gillespie (19 11), 234 (a refutation o f the Principle o f N onContradiction); Levi (1932), 483-4 (an attack on pluralism); Beth (1954) and (1964) (against A ristotle’s notion o f infinity); Kneale and Kneale (1962), 114 (‘it is incredible that Eubulides produced < th e paradoxes> in an entirely pointless way, as the tradition suggests. He m ust surely have been trying to illustrate some theses o f M egarian philosophy, though it may be impossible for us to reconstruct the debates in which he introduced them ’); M oline (1969) (see below); Reale (1976), 68 (‘against all doctrines that adm it plurality’); Sillitti (1977), 91-2 (against Plato’s m athematical analysis o f the sensible world).

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several suggestions that have been made, only one has even a m orsel o f ancient testim ony in its favour; and that is the sugges­ tion that we associate E ubulides’ sorites w ith som e aspect o f A ristotle’s philosophy. For Eubulides is k n o w n to have attacked Aristotle; and w hat is m ore natural than to suppose that he directed his paradoxes - in particular, the sorites - against an item o f A ristotelian th o u g h t?3435 N o w E ubulides’ attack on A ristotle was, so far as w e are inform ed, scurrilously personal: it is n o t k n o w n to have had any philosophical content at all.33 B u t the sorites is at least once connected w ith a piece o f A ristotelian doctrine. In the Nicomachean Ethics A ristotle observes that ‘it is n o t easy to determ ine by reason (logos) h o w far and to w hat extent a m an m ay go before he is b lam ew o rth y - for that is n o t easy in the case o f any other perceptible thing eith er’ (ii0 9 b 2 0 -2 ). In their notes on that sentence, Aspasius and the anonym ous co m m en tato r both refer to soritical argum ents: it is because o f the sorites, they say, that perceptible things cannot be determ ined by logos·, and hence perception - or, in the case o f feelings and actions, phronësis - m ust act as ju d g e and arb iter.36 Perhaps, then, A risto tle’s doctrine o f the M ean, w ith its deliberate refusal to specify precise conditions for virtuous and vicious actions, was the original target o f E ubulides’ sorites?37 Perhaps. B ut the com m entators do n o t say so: they do not m ention Eubulides o r im ply that the sorites had been originally directed against the M ean. (N o r do they state or im ply that A ristotle was aw are o f the sorites and recognised that it was directed against his d o ctrin e.38) M oreover, the sorites has no peculiar relevance to the specific point A ristotle is m aking. H e is stressing, as he often docs, that universal prescriptions can never offer m ore than ro u g h and approxim ate guides to action; 34. So, e.g., Henne, Beth, Moline (seen. 33). 35. See A ristodes, Fr. 2 Heiland = Eusebius, PH xv ii 3, 79ld; DL π 109; Them istius, Or. xxiii, 285c; Suda, s.v. φομβοστωμύληθρα; Athenaeus, 354c; cf. I. D üring, Aristotle in the Ancient Biographical Tradition (Göteborg, 1957), 373-88. Pace Moline (1969), 394, 394 n. 3, 399, Diogenes does not say that Eubulides got the better o f the dispute; he rem arks sim ply that ‘Eubulides actually was at odds w ith Aristotle and slandered him a great deal.’ 36. Aspasius, in E N (C IA G xix) 56.27-57.7; Anon, in E N (C IA G xx) 140.6-12. 37. So Moline (1969). But he allows, p. 395, that there may have been other Aristotelian doctrines under attack too. 38. Pace M oline (1969), 396.

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circum stances alter cases, and circum stances are indefinitely various. A philosopher m ay propose a n u m b er o f generalisations; bu t he m u st leave it to individual agents in individual circum ­ stances to determ ine w hat individual courses o f action they should take. T he sorites has no special bearing on that line o f th o u g h t, and I do n o t im agine that Eubulides th o u g h t it h ad .39 Som e later com m entator, perhaps Aspasius himself, was the first to connect soritical argum ents w ith the M ean. H ow ever that m ay be, w e m ay still w onder if A ristotle had any know ledge o f E ubulides’ argum ent, and if he th o u g h t o f it as part o f a philosophical m anoeuvre. T w o passages in A ristotle’s trea­ tises have been adduced in evidence. A t Physics 2 5 3 ^ 4 -2 6 A risto­ tle refers to ‘the arg u m en t about the drop o f w ater rubbing away the stone and g ro w in g plants dividing stones’. B o th A ristotle’s examples can indeed be reconstructed on soritical principles;40 and the w aterdrop exam ple was som etim es used by later authors as an illustration o f the sorites. (One drop can have no effect on a stone; if one has no effect, tw o cannot; and so o n .41) In his com m entary on the passage, Simplicius explicitly raises the question o f w hether A ristotle is adverting to a soritical argum ent: after a long discus­ sion he sides w ith A lexander, w ho took the argum ent to be based on a principle o f p ro p o rtio n - if a long sequence o f drops has a large effect, each individual drop m ust have had a proportionally sm aller effect.42 A nd A lexander is certainly correct: A ristotle’s answ er to the argum ent proves that he, at least, had nothing soritical in m ind; for he thinks that, like Z e n o ’s M illet Seed, it rests sim ply upo n a false principle o f p ro p o rtio n .43 T he second A ristotelian passage comes from the Sophistici Elenchi - and w e should expect to find the sorites in that w o rk if it was considered by A ristotle at all. Before quoting the passage, let 39. O f course, you can use a soritical argum ent in connexion w ith virtuous action: is giving away £50 generous? Yes. £49.99? And so on. But that is not an argum ent against anything specifically Aristotelian; and there is no peculiarly Aristotelian doctrine in E N to combat w hich Eubulides m ight specially have designed the sorites. 40. See e.g. Prantl (1855), 55. 41. See Simplicius, in Phys. (C lA G x) 1177.4-9. 42. Simplicius, in Phys. (C IA G x) 1197.35-1199.5. 43. Phys. 2 53bi4-2i is similar in both language and argum ent to Phys. 250319-28, where Aristotle discusses Z en o’s Millet Seed; and in both cases Aristotle argues that the error lies in a m istaken principle o f proportion. Simplicius’ discussion o f the waterdrop argum ent suggests that in antiquity the sorites had been assimilated to, or at least closely associated w ith, Z eno ’s Millet Seed and its congeners. (See above, n. 30.)

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m e observe that even if the sorites is to be found in the Sophistici Elenchi that will n o t give it any particular philosophical im p o rt­ ance or prove that Eubulides advanced it as part o f som e philo­ sophical cam paign: the Sophistici Elenchi is a book o f logical puzzles, som e serious, som e trivial; a few o f the puzzles are connected by A ristotle w ith philosophical issues, b u t m ost appear m erely as puzzles. If the sorites is there, its inclusion will be adequately explained by the sim ple fact that it is a puzzle. T he Sophistici Elenchi does n o t cite the sorites by nam e; b u t it has been discerned in the follow ing lines:4445 T hose w h o solve it by saying that every n u m b er is few m ake a sim ilar m istake to th at o f those w e have described; for if, th o u g h it does not follow , they o verlook this and say that a tru th is inferred (for every n u m b er is b o th m any and few), they m ake a m istake. (1 7 ^ 3 4 -7 )

A ristotle is discussing a sophism the conclusion o f w hich read: ‘E very n u m b er is b o th m any and fe w .’ W hat sophism has he in m ind? He tells us h im self a few lines earlier:43 All the follow ing sorts o f arg um ents depend on the accidental: ‘D o you k n o w w h at I am going to ask you?’, ‘D o you k n o w the m an w h o is approaching (or: the veiled m an)?’, ‘Is the statue yo u r w ork? (or: is the father-dog yours?)’, ‘A re few tim es few few ?’ For it is evident in all these cases that w h at is true o f the accident need n o t also be true o f the thing. ( 179a3 3—6)

T he arg um ent A ristotle alludes to at 1 7 ^ 3 4 -7 evidently started from the question ‘A re few tim es few few ?’, and led to the conclusion that every n u m b er is b o th m any and few. W hat is the connexion betw een that argum ent and the sorites? T he prem iss o f the argum ent (‘Few tim es few are few ’) has n othing to do w ith the soritical form ; the conclusion (‘Every n um ber is m any and few ’) is n o t a conclusion o f any k n o w n soritical argum ent; A risto tle’s classification o f the argum ent (it ‘depends on the accidental’) does n o t fit the sorites in any w ay. It is, adm ittedly, uncertain ju st w h at argum ent A ristotle alludes to at I79a3 5, and it is uncertain w h at the reflexions o f 1 7 ^ 3 4 -7 im p ly .46. B ut it is perfectly plain that the sorites is in no w ay referred to in those lines. 44. ‘This appears to be an unm istakable allusion to the Sorites’, M oline (1969), 399; '. . . Aristotele alluderebbe qui, inequivocabilm ente, proprio a quest’ ultim a form a del sorite pur senza nom inarlo esplicitam ente’, Sillitti (1977), 84; cf. Prantl (1855), 54 n 94. 45. N either Moline nor Sillitti appears to notice that I79b34~7 refers back to 179333-6. 46. The only evidence we have for the form o f the argum ent is found in pseudo-Alexander

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A ristotle, I conclude, either did n o t k n o w the sorites or else kept his know ledge to himself. In either case, there is no reason to look for a philosophical debate betw een Eubulides and A ristotle (or, I m ight add, betw een Eubulides and anyone else) based upon soritical argum ents and puzzles. Eubulides, I im agine, posed the puzzle in its original and particular form : he did n o t generalise it, and he did no t find any philosophical em ploym ent for it.47 A fter Eubulides, the m ost celebrated nam e associated w ith the sorites is that o f C hrysippus. N u m ero u s texts connect the puzzle w ith the Stoics in general or w ith C hrysippus in particular; the sorites becam e a standard part o f Stoic logical teaching; and it was doubtless its Stoic connexion w hich gave it such w ide currency in later antiquity. C hrysippus is credited w ith three books On Soritical Arguments against Words,48 and w ith tw o books On the Argument from w ho offers the follow ing expansion: π ά λ ιν ά ρά γε χά όλιγά κ ις άλίγα όλίγα; vat· άλλα μήν τα εκατόν π ρ ο ς τα δ εκά κις μύρια όλ ιγά κ ις έστ'ιν όλίγα ■τά εκατόν ά ρα όλίγα · άλλα μήν κ αί πολλά {in S E (C'JAG n 3) i6 i.i8 -2 o ). If we take that seriously, the argum ent moves from ‘ 100 are few times few compared to i o X 1 0 ,0 0 0 ’ to ‘ 100 are few times few ’; and that is the m ove which Aristotle stigmatises: it transfers a predicate from the συμβεβηκός (‘ιοο compared to 10 x 1 0 ,0 0 0 ’) to the π ράγμ α (ioo). B ut it is hard to believe that pseudo-A lexander’s interpretation is right: it makes the argum ent needlessly com plex and obscure. And it may be that pseudo-A lexander’s text is corrupt: Jim H ankm son suggests τά δ εκά κις δέκα for τά εκατόν πρ ός τά δεκάκις μύρια, which gives a simple and intelligible gloss on A ristotle’s text. ‘Few fews are few; ten tens are few fews; so too are few .’ Aristotle tackles the argum ent by attacking the first premiss; but instead o f simply dismissing it as false (few fews are som etim es but not always few), he brings the argum ent under the head o f π α ρ ά τό συμβεβηκός. I am not sure w hat he means; but perhaps it is this: ‘W hen you say “η X m are few ” you m ay be truly predicating “ are few ” o f the accident - it may be true that what is taken m times is few, ju st in the sense that m times is not m any times. B ut you cannot infer - as your argum ent requires - that “ are few ” is truly predicated o f the πράγμα, nm.’ The m en Aristotle m entions at 179034-7 ignore this error in the argum ent, and try to ‘solve’ the puzzle by adm itting that its conclusion is true: Aristotle criticises them for passing over the error, but he seems to im ply that he accepts their suggestion that the conclusion is true. If that is so, then he will no doubt explain how the conclusion can be true by reference to his notion o f the relational status o f ‘m any’ and ‘few ’ (see Cat. 5bi2-25). (For a different interpretation o f these passages see G. Colli, Aristotele: Organon (n.p. 1955), 1025-6.) 47. Was the sorites originally a serious piece o f logic or a divertissement? Grote (1867), 484, is sure that Eubulides offered his puzzles 'not to impose upon any one, but on the contrary, to guard against im position’. W ho told Grote that? We know nothing at all about Eubulides’ m otives. 48. DL vu 192. The title is puzzling: som eone had presum ably directed soritical arguments against w ords (φωναί); but who? and how? Sedley (1977), 91, plausibly suggests an Academic author (Arcesilaus?), and supposes that he was ‘led to question the validity o f Stoic term inology by exposing the lack o f adequate definitions’. B ut the title appears am ong C hrysippus’ w ritings on language, not am ong his logical treatises; and we should expect that the soritical argum ents had a linguistic rather than a logical target. (See below, n. 60, for a sorites in a gramm atical context.)

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Little-by-Little, to Stesagoras.49 N o d o u b t it was also discussed elsewhere in C h ry sip p u s’ volum inous w ritings: it was at least m entioned in the Logical Inquiries;50 and Plutarch records that in his Use o f Argument C hrysippus attacked ‘M egarian reasoning’, alleging that it had becom e ‘in part som ew hat clum sy, in part evidently sophistical’ (Stoic, rep. T03ÔF) - that w ould have been a suitable place for a few com m ents on the sorites. B ut w h y did C hrysippus b other w ith the sorites? and w h at had „ happened to the argum ent betw een the days o f Eubulides and those o f C hrysippus? A m o n g E ubulides’ pupils was A pollonius C ronus; and A pollonius tau g h t his skills, and bequeathed his derisive surnam e, to D iodorus, that éminence grise o f Hellenistic philosophy (DL 11 h i ) . D iodorus was a m aster o f paradox; he probably discussed the so rites,51 and he used som ething very like a soritical argum ent to sustain his paradoxical view s on m o tio n :52 we m ay well im agine that it was D iodorus w ho transferred E ubulides’ sorites from its original hom e in C hristm as-cracker eristic to the sober lecture-halls o f philosophy; and from D iodorus we m ay find tw o paths leading to the Stoa. First, we k n o w that Z eno, the founder o f the Stoa, studied for a tim e under D iodorus (DL vu 5), and that he h im s e lf‘used to solve sophism s and to order his pupils to learn logic since it was capable o f solving th e m ’ (Plutarch, Stoic, rep. 1 0 3 4 F ) . Logic was a part o f 49. DL vu 197. - The next title reads in the MSS: περί τών είς τά ς ύπολήψ εις λόγω ν καί ήσ υχά ζοντω ν π ρ ό ς Ό ν ή το ρ α β'. The text is scarcely sound, and tw o titles seem to have been conflated, (περί τώ ν είς τά ς ύπολήψ εις λόγω ν α '. < π ε ρ ί τώ ν > ήσ υχά ζοντω ν < λ ό γ ω ν > πρ ός Ό ν ή το ρ α β'?) Several scholars have supposed that the ή σ υ χά ζω ν is the same as the sorites (see Reid on Ac. n xxix 93; D öring (1972), 107; Sedley (1977), 113 n. 94; cf. M enagius on DL vn 197). The ήσ υχά ζω ν is m entioned also by Epictetus (Arrian, Epict. 11 xviii 18) and by Gellius, 1 ii 4; but neither author implies that it is the sorites under a different name - if anything, they suggest that it is a distinct argum ent, and from its name we should expect it to be a paradox connected w ith silence (The Silent Man). The only, and insufficient, reason for identifying it w ith the sorites is the fact that C hrysippus counselled ήσ υχά ζειν to those faced by soritical argum ents (below, pp. 49-54). 50. SV F i i , p. 106; see below, n. 68. 51. Fronto, Eloq. 14, p. 146 N aber = p. 140 van den H out, urged M arcus Aurelius to give up the frivolities o f dialectic: Discere le aulem ceratines et soritas et pseudomenus . . . hoc indicat loqui te quam eloqui malle . . . Diodori tu et Alexini verba verbis Platonis et Xenophontis et Antisthenis anteponis? F ronto’s rhetoric is vague: he does not say that D iodorus w rote about the sorites - but it seems a pretty safe assum ption that D iodorus did. - O n D iodorus see the brilliant paper o f Sedley (1977) (for the sorites, pp. 89-94), to which 1 am greatly indebted. 52. The argum ent in question is to be found at M x 112-17: it refers to heaps (cf. 114), and it is, in a loose sense, soritical in tone; but it is not, strictly speaking, a sorites.

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the Stoic curriculum from the beginning; and the study o f paradoxes was a part o f logic. Z eno will have heard o f the sorites, am ong other such puzzles, from D iodorus; and fro m the begin­ ning the sorites will have been an item in Stoic teaching. T he fact that C hrysippus was a logician w h o inherited som e o f the interests o f D iodorus w o uld in itself be a sufficient explanation o f his concern w ith the sorites: there is no need to seek any m ore profound m otivation for his w o rk on the paradox. B ut, secondly, there is in fact another, indirect, route by w hich the sorites m ay have im pressed itself u p o n C hrysippus. A rcesi­ laus, w ho converted the A cadem y to scepticism, had som e association w ith D iodorus: in the celebrated parody by A riston the Stoic, he was ‘Plato in front, P y rrh o behind, D iodorus in the m iddle’ - and D iodorus in the m iddle ‘because he used the logic o f D io d o ru s’.53 N o w Arcesilaus devoted m uch o f his energy to attacking Stoic epistem ology and the fundam ental Stoic concep­ tion o f ‘apprehensive p resen tatio n ’. If Arcesilaus b o th used D iodoran logic and attacked Stoic presentations, perhaps he used D iodoran logic in his attack on Stoic presentations; perhaps, m ore specifically, he used the soritical form o f argum ent w hich he had learned from D iodorus in order to reveal flaws in Z e n o ’s notion o f an apprehensive presentation; and perhaps, finally, that attack gave C hrysippus an u rgent philosophical reason for tackling the puzzles set by the sorites. T hat string o f perhaps’s m ay sm ack a little to o m uch o f conjecture. B ut the conjecture here can be backed up by evidence. In the course o f his discussion o f apprehensive presentation, Sextus adverts to an argum ent w hich b ro u g h t soritical arm o u r to bear u p on the Stoic conception. T he argum ent is com plex;54 but 53. PH I 234; cf. N um cnius, fr. 24 des Places ( = Eusebius, PE xiv v 13, 729b); DL iv 33. 54. M vu 401-35 considers the Stoic claim that 'apprehensive presentation’ is a criterion of truth; 415—23 contains one sceptical argum ent against the Stoics. The argum ent is this: ‘since apprehensive presentation attaches closely to (προσαρμόζεται) nonapprehensive presentation, apprehensive presentation will not be a criterion o f tru th ’ (415). Sections 4i6ff. are designed to show that apprehensive presentation does ‘attach closely’ to non-apprehensive presentation: the p ro o f starts, in 416, from reflexions upon C hrysippus’· attem pt to answer a soritical argum ent against apprehensive presentation; and in 418ff. a sorites is developed to prove the close attachm ent of apprehensive to non-apprehensive presentations. Thus there arc three distinguishable layers in 415-23: first, the sorites against which C hrysippus argued; secondly, C hrysippus' argum ent; thirdly, the sorites developed against C hrysippus in 4i5ff. In the text, I ascribe the first layer to Arcesilaus; it is tem pting to suppose that the third layer comes from Carneades. (See further, below n. 70.)

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for present purposes it is enough to cite a single line from it: ‘in the case o f the sorites, w h en the last apprehensive presentation lies next to the first non-apprehensive one . . C hrysippus and his school say t h a t . . (M v i i 416). C hrysippus h im self55 thus replied to a soritical argum ent directed against apprehensive presentation. It follows that that argum ent is at least as old as C hrysippus; and if we w an t an author for the argum ent, w h o is there but Arcesilaus?56 C h ry sip p u s’ interest in the sorites was overdeterm ined: as a logician, he will have found it a fascination in its o w n right; as an epistem ologist, he will have had it forced u p o n his attention by the sceptical attacks o f A rcesilaus.57 T he large question rem ains: how did C hrysippus attem p t to solve the sorites? B ut before answ ering that, let m e com plete this b rie f history o f the arg u m en t.58 A fter C hrysippus, the sorites is always closely associated w ith Stoicism; and the m ajority o f references to it are by Stoics or in Stoic co n tex ts.59 For all that, there is no evidence that any later At Ac. ii xvi 49—50, Cicero records an argum ent against apprehensive presentation which he calls a sorites. T he argum ent is quite different from the one at M v i i 415-23, and it is not in fact a sorites o f the sort described in m y Section I. C icero’s argum ent uses a single subject and an ordered sequence o f predicates: *Fj( )’ is to all appearances true o f a; ‘F„( )’ is to all appearances false o f where ‘ν ’ is the proper nam e o f som eone belonging to the same class as οί π ε ρ ί, always denotes either x and his colleagues or x alone - it does not mean :thc colleagues o f x ’. See S. L. Radt, ‘N och einmal Aischylos, N iobe Fr. 162 N 2. (278 M )’, Zeitschrift fiir Papyrologie und Epigraphik 38 (1980), 47—58. 5 6 . So e.g. Zeller ( 1 9 2 2 ) , 111.1, 5 2 0 n. 5; Sedlcy ( 1 9 7 7 ) , 9 2 . - Arcesilaus was an Academic: did the sorites receive anv Academic colouring? According to K räm er ( 1 9 7 1 ) , 7 5 - 6 , Plato’s T heory o f Principles, and especially his notion o f The Great and Small, had a bearing upon the Academic history o f the sorites; but I cannot see how that theory could have had any relevance to the sorites, w hich neither requires nor readily takes on any such metaphysical clothing (see Sedley ( 1 9 7 7 ) , 1 1 3 η . I 0 2 ; Glucker ( 1 9 7 8 ) , 3 4 n. 7 9 ) . W eische ( 1 9 6 1 ) , 6 9 , connects the rise oi the sorites w ith T heophrastus’ botany, which self-consciously avoids the use o f any precise concepts; but again, I do not see any plausible connexion there. 57. The Stoics themselves, as Plutarch observed (Comm. not. 1084 AC), used argum ents o f the same logical form as the sorites: that fact too, m ight have stimulated C hrysippus to attend to the problem s raised by soritical arguments* 58. Clem ent, Strom, v i 11.6, seems to im ply that T im on m entioned the sorites, among other paradoxes; if that is right, then the argum ent may have been a weapon o f early Pyrrhonian as well as o f Academic Sceptics. 59. I know o f no reference to the sorites in an Epicurean context.

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Stoic studied the argu m ent or attem pted to im prove u p o n C h ry ­ sippus’ discussion o f it - the sorites seems to have becom e a part o f the Stoics’ logical curriculum , b u t it does n o t seem to have been an object o f controversy w ithin the Stoa. Perhaps the later m en th o u g h t that C hrysippus had said the last w o rd on the subject. N o t everyone th o u g h t so: the D ogm atic D octors, w ho used the sorites against their E m pirical opponents, presum ably th o u g h t that soritical argum ents - or rather, that som e instances o f the sorites - w ere sound argum ents; at least, there is no reason to think that the D ogm atists w ere consciously advancing w hat they took to be incorrect argum ents. It is n o t clear w hen or h o w the sorites entered the m edical debates; b u t Galen suggests that the D octors w ere using it as early as the second century b . c .,60 and we m ay im agine that they learned o f it - as o f so m uch else - from their Stoic contem poraries. H ow ev er that m ay be, the later m em bers o f the Sceptical A cadem y th o u g h t little o f C h ry sip p u s’ reto rt to Arcesilaus. For Carneades explicitly disputed - indeed, m ocked - C h ry sip p u s’ teachings on the sorites (Cicero, Ac. 11 xxviii 91-xxix 92); and he him self b ro u g h t fo rw ard a celebrated series o f soritical argum ents. ‘Carneades p ro p o u n d ed certain argum ents in a soritical fashion, w hich his friend C litom achus recorded as being m ost excellent and conclusive’ (M ix 182). Sextus transcribes five o f C arneades’ argum ents, adding that there w ere m ore; their conclusion is ‘that there are no g o d s’, and Sextus construes them as general argu­ m ents for atheism . Cicero also reports C arneades’ argum ents, and m ore num erously; bu t he says that they w ere p ropounded ‘n o t in order to do aw ay w ith gods (for w h at could be less fitting for a philosopher?), b u t to prove that the Stoics explain n othing about the go d s’ (N D hi xvii 43).61 C icero is certainly rig h t about C arneades’ aim s:62 they w ere n o t positive and atheistical but negative; Carneades was engaged in an attack on Stoicism , and he 60. O n the date o f the argum ents o f Med. Exp. see above, p. 26. - At M I 68-9, Sextus uses a sorites against D ionysius T h rax ’s definition o f gram m ar; and in the same context ( M 1 72) he reports that Asclepiades had attacked the definition. But 1 think Sextus implies that Asclepiades’ attack did not involve the sorites. 61. See e.g. Vick (1902); Couissin (1941); dal Pra (1950), 14&-55· 62. Carneades appeals to Stoic doctrines to support the conditional premisses o f his argum ents, which are thus ad hominem; and in general, Carneades was given to ad hom inem -ad Stoicum - argum entation: see e.g. Cicero, Ac. 11 xlii 131 \D iv. 11 lxxii 150; Fin. II xiii 42. Sextus adapts Carneades’ argum ents - quite properly - to his own Pyrrhonian ends.

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felt able to use in his attack a w eapon that C hrysippus had hoped t o render obsolete. O ne o f the argum ents reported by C litom achus and transcribed by Sextus runs like this: ‘If the sun is a god, the day will be a god; for the day is n othin g else than the sun above the earth. A nd if the day is a god, the m o n th will be a god; for it is a collection o f days. And if the m o n th is a god, the year will be a god; for it is a collection o f m onths. B u t this is n ot so; nor, therefore, is the original supposition ’ (M ix 184). C arneades’ argum ents are som e­ tim es cited as paradigm s o f the soritical form ; but the one I have ju st quoted differs in certain w ays from a classical sorites.63 First, the subjects o f C arneades’ propositions do n ot form an o rth o d o x ordered sequence; for there is no obvious ordering relation that fixes the m em bers o f the sequence. In standard soritical argum ents the subjects can be im agined as points along a continuum , or as successive steps in a single jo u rn e y , or the like. In C arneades’ argum ents that is n o t so: his sets o f subjects are ordered, and there is an ordering relation (trivially so); b ut in a plain enough sense his subjects do not form a natural succession o f item s. Again, Carneades provides argum ents for at least som e o f his conditional prem isses — and different argum ents for different prem isses. In standard sorites, the conditional prem isses are n o t supported - and do n ot need to be supported - by argum ent; and if they were argued for, the argum ent w ou ld be quite general, applying equally to any adjacent pair o f subjects. T he fact that C arneades’ subjects are n o t a ‘natural succession’ perhaps explains w h y he uses different argum ents for different premisses; b u t it does n o t explain w h y he uses argum ents in the first place. It is tem ptin g to suppose th at the provision o f argum ents reflects C arneades’ response to C h ry sip p u s’ criticism o f the sorites: w hile rejecting that criticism as inadequate, C ar­ neades m ay have felt that it required him to m odify som ew hat the presentation o f his o w n soritical argum ents. In o rder to assess the m erits o f that suggestion w e m u st go back to C hrysippus and attem p t to discover his answ er to the soritical paradoxes. 63. O ne m ight also w onder if the subjects o f the constituent propositions o f the argum ents are individuals: by ‘the day is a g o d ’ does Carneades m ean ‘daytim e is a go d’ or rather ‘each day is a g o d ’? If the latter, then his argum ent contains universal propositions. And by ‘the m onth is a g od’ he surely means ‘every m onth is a g o d ’. But that is niggling: let us suppose that he does mean to provide an ordered set o f subjects, say the set: .

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III W hat should be said about the sorites? ho w is the paradox to be resolved? I shall first m ake a b rie f general rem ark about the m atter, then look at C h ry sip p u s’ discussion o f the paradox, and finally retu rn to m y starting-po in t and consider w hat the Em pirical D octors had to say about the sorites. If the conclusion o f an argum ent is false, there are in principle tw o things th at m ay have gone w rong: the argum ent m ay be invalid, its conclusion m ay fail to follow from its prem isses; o r the argum ent m ay be false, one or m ore o f its prem isses m ay fail to be true. A nd so it is w ith soritical argum ents; if the conclusion o f a soritical argum ent is false (if, for exam ple, it is false that 10,000 observations are few), then either the conclusion does no t follow from the prem isses or at least one o f the prem isses is false. (O f course, the arg u m en t m ay be w ro n g in b o th w ays at once: it m ay be b oth invalid and false.) A nyone w ho m aintains that (at least some) soritical argum ents are w ro n g by virtue o f being invalid I shall call a radical opponent o f the sorites: a radical oppon en t is com m itted to rejecting the validity o f modus ponens inferences; he m ay hold either that modus ponens is sim ply an invalid form o f reasoning, that from ΓΡΊ and rP D Q"1 w e are not entitled to infer rQ"1; or else that modus ponens m ust be restricted to certain types o f pro po sitio n (say to proposi­ tions w hich do n o t contain soritical predicates). In either case he will be involved in a radical reform ation o f classical propositional logic, and good luck to him . A nyone w ho m aintains that a soritical argum ent is w ro n g in virtue o f being false I shall call a conservative opponent o f the sorites: a conservative opponent m ay hold that all soritical argu­ m ents are w ron g, o r he m ay hold that only some are w rong; in either case he will have no quarrel w ith the logic o f the soritqs, but he will argue — differently in different cases —that in all or som e soritical argum ents at least one prem iss is false. C hrysippus w as, I assum e, an oppo nent o f the sorites: he th o u g h t he had solved the problem s it raised.64 B ut was he a radical or a conservative opponent? 64. The sorites rem ains an ά πο ρ ο ν in the Stoic handbooks; the Stoic Seneca refers to it as sorites ille inexplicabilis (Ben. v xix 9); and the obnoxious youth w ho alm ost ruined one o f Herodes A tticus’ dinner-parties claimed that ‘he alone could unravel the M aster and the Silent M an and the Sorites and other riddles o f that so rt’ (Gellius, 1 ii 4). B ut that

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T he Stoics offered a fourfold typology o f fallacy: ‘the dialecti­ cians say that an argum ent becom es inconclusive either because o f incoherence or because o f deficiency o r because o f being p ro ­ pounded in an incorrect form or by red un d an cy’.65 Soritical argum ents will no t have been accused o f redundancy: if they had been, the p rop onen t o f a sorites, m erely by om ittin g one o r m ore o f his prem isses, w o uld have been able to confront C hrysippus w ith an arg um en t he could n o t fault.66 N o m ore will the sorites have been accused o f incoherence: in ‘inco herent’ argum ents the prem isses are unconnected in content w ith one another and w ith the conclusion. (‘If it is day, it is light; w heat is being sold in the m arket-place: therefore D ion is w alk ing ’: P H π 146.) In the sorites, prem isses and conclusions are connected as closely as you could w ish. N o r, again, is C hrysippus likely to have argued that soritical argum ents w ere p ro p ou nd ed in a w ro n g form , or that they w ere not form ally valid; for, as Plutarch was quick to point out, the standard fo rm o f the sorites is th o ro u g h ly in accordance w ith Stoic principles o f logic: the Stoics explicitly recognised the general form as valid, and they m ore than once produced argu­ m ents o f that general fo rm .67 Is the sorites inconclusive ‘th ro u g h deficiency’? Sextus’ exam ple o f a deficient argum ent is this: ‘W ealth is either good or bad; it is not bad: therefore it is g o o d ’; and the Stoics’ objection is that the first prem iss is deficient - it should read: ‘W ealth is either g oo d or bad o r indifferent’ (P H π 150). Deficiency, in short, is a disease o f the prem isses o f an argum ent: it m arks a species o f falsity. It is hard to see in w hat w ay the prem isses o f a sorites m igh t have been regarded as deficient; b ut even if C hrysippus did so regard them , he w ould thereby assum e the position o f a conservative o pponent o f the argum ent and w ou ld n ot be taking a radical stance. If the sorites was accom m odated to the fourfold typ olog y o f fallacies, then it m u st have been placed under the head o f scarcely suffices to show that C hrysippus did not think he had solved the paradox - at very m ost, it show s that som e later Stoics still found the sorites puzzling. (And paradoxes may remain puzzling even when they are k now n to have been definitively solved.) 65. P H tt 146; cf. M vin 429: by ‘the dialecticians’ Sextus here means the Stoics (see M vm 4 3 5 )·

66. O n redundancy see J. Barnes, ‘P ro o f destroyed’, in M. Schofield, M . F. Burnyeat, J. Barnes (eds.). Doubt and Dogmatism (O xford, 1980), 164-75. 67. Plutarch, Comm. not. 1084AC; cf. e.g. Alexander, Fat. 207.5-21; 210.15-28.

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‘deficiency’; and w hether or n o t that was so it will n ot have been treated in a radical fashion. N o d oub t it is possible that C hrysippus took a radical position, and that the fourfold typology was post-C hrysippean and took no account o f his treatm ent o f the sorites; but there is, for all that, som e reason to suppose at the outset that C hrysippus was a conservative opponent. A nd now for the texts in w hich C h ry sip p u s’ stance is actually described. T here are three passages to consider:68 A nd if C hrysippus and his fellow dogm atists say that w hen the sorites is being pro p o u n d ed one should, w hile the arg u m en t is proceeding, stop and suspend ju d g e m e n t in o rd er n o t to fall into absurdity [how m uch m ore appropriate it is for us Sceptics to suspend ju d g e m e n t in such cases], ( P H 11 253) For in the case o f the sorites, w h en the last apprehensive presentation lies next to the first n o n -apprehensive presentation and is hard to distinguish from it, C hrysippus and his school say that in the case o f presentations w here the difference is sm all in this w ay, the w ise m an w ill stop and fall quiet (hësuchasei ) , b u t in cases w here it strikes him as greater, he will assent to the one as being true. (M vu 416) ‘B ut sorites are v icio u s.’ - T h en destroy them , if you can, lest they be harm ful; for they w ill be unless you are careful. ‘We have already been careful,’ he says; ‘for C hrysippus holds that w hen you are being 68. We m ight hope to find a fourth text in the Logical Inquiries o f C hrysippus himself; for they contain a b rief reference to the ‘little-by-little’ argum ent (S V F n, p. 106, 7-12). D avid Scdley has kindly allowed m e to publish his new reading o f the papyrus:

καί εως τίνος δεϊ ταΰ θ ’ ίιπακο·ύε[ι]ν παρέξει έπίστα σιν κατά τον παρά μικρόν λόγον. όμο[ί]ως [. . .] δεϊ πε ρί τής άποκρίσεως τεμεΐν, πι θανόν δε μη[. .] τοϋτο ύπά[ρ]χειν. T he first sentence is relatively clear: ‘And up to w hat point one should continue giving the same answers will cause perplexity in virtue o f the little-by-little argum ent. ’ The second sentence is problematical: there are tw o holes in the papyrus at crucial places; the sense o f the verb τέμνειν is uncertain (its occurrence in the booktitles at DL VII 197 is intriguing but unenlightening); and the second clause, π ιθ α νό ν δε . . . is doubtful in syntax and in sense. Sedley tentatively suggests όμοίω ς [δ’ et] δει for the first gap and μή[ of)] for the second. I incline to prefer C rön ert’s μηδέ for the second gap, and I w onder if τε μ ε ΐν . refers to finding a cut-off point along the a/s between F 's and n o n -F ’s. Thus the sentence w ould read: ‘And similarly, if you m ust make a cut-off point in your answer, but it is plausible that n ot even this is possible.’ T hat fits well (of course) with the view that I am about to ascribe to Chrysippus; but I do not offer the papyrus lines as evidence in favour o f the ascription. (I should add that further inform ation about the papyrus will not help: the reference to the sorites was very short, and the context surrounding the lines I have quoted deals w ith different paradoxes.)

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questioned step by step, e.g. as to w hether three are few or m any, you should fall quiet a little w hile before you com e to m an y ’ (that is w hat they call h esu ch a zein ). (C icero, A c . π xxviii 92)

Those three texts certainly do n o t contain all that C hrysippus said about the sorites; and indeed, since they w ere selected by enemies o f the Stoa - by P yrrhonists or Academics - , there is no reason to believe that they represent the best o f w hat C hrysippus said. B ut they are all that we have to w ork with. C hrysippus recom m ends us to ‘sto p ’ and to ‘fall q uiet’ w hile the soritical argum ent is in full flow. H e is thinking o f a sorites in its inform al, interrogative, version; and he m eans that at som e stage in the questioning w e should sim ply refrain from giving any answer. ‘Is a\ F?’ Yes. ‘A nd aoT Yes. . . . ‘A nd atV Silence. (In the form al version o f the argum ent, the questions are replaced by hypothetical propositions; and in term s o fth a t version C hrysippus recom m ends us to refuse to assent to one or m ore o f the hypothetical premisses: if the question ‘A nd cp?’ should be passed over in silence, then the prem iss rF (M l2,m ,s!2,t) » (M ,2 m ,sl2 ,t)

La prem ière justification est d ’ordre expérim ental. A ristote prend l’exem ple des haleurs qui tirent un bateau. U n seul des haleurs s’épuiserait inutilem ent, s’il espérait faire parcourir au bateau la fraction de parcours qui correspond à la puissance d ’un seul hom m e. La pro portionn alité n ’est donc pas satisfaite. Ces exceptions ont aussi une portée théorique essentielle. Aris­ tote répond à un arg um en t de Z énon, q u ’on pourrait considérer com m e le p ro to ty p e des sorites qui auront tant de faveur dans les

Ιθ8

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siècles su iv an ts.11 U n boisseau de m il fait du bruit en tom bant, mais il se peut q u ’un grain isolé qui tom be ne fasse aucun bruit, parce q u ’il ne réussira pas à m ettre en m ouvem ent, m êm e très lentem ent, l ’air que le boisseau entier avait ébranlé.12 La solution réside dans la n o tio n d ’être en puissance: une force peut n ’exister q u ’en puissance tant q u ’elle ne s’est pas fondue dans une force plus grande qui l’englobe et l’actualise. Le m ot dunamis, dans ce texte, désigne donc à la fois le m oteur (“ puissance” m otrice) et un certain m ode de réalité (l’être “ en puissance” ). La réponse d ’A ristote à Z énon nous oblige à saisir cette double dunamis com m e une n o tion unique. Il faut envisager la virtualité com m e une force: l’être en puissance est tendu vers l’acte, et p rod uit de ce fait un m ouvem ent; il faut, dans l ’autre sens, voir en la force une virtualité, et adm ettre que la force peut ne pas passer toute entière dans son effet, q u ’il y a un seuil à la force, ou plutôt un seuil au rap port force/corps à m ouvoir, seuil en deçà duquel la force reste purem en t virtuelle. Le livre vu de la Physique s’arrête brusquem ent après l ’énoncé de ces règles de p ro p o rtio n n alité.13 N ous ne savons donc pas à quelles 11. Voici com m ent Simplicius (in Phys. (C IA G x ) 1108.18) rapporte l ’argum ent de Zénon: “Par ce m oyen il résout l’argum ent de Zénon l’Eléate, que celui-ci avait proposé à Protagoras le sophiste. “ D is-m oi, Protagoras, est-ce q u ’un seul grain de millet fait du bruit lorsqu’il tom be, ou le m illième d ’un grain?” Et com m e Protagoras disait que cela ne fait pas de bruit, “mais le boisseau de m illet fait-il du bruit ou non lorsqu’il tom be?” ; com m e l’autre répondait q u ’il fait du bruit: “ n ’y a-t-il pas assurém ent un rapport entre un boisseau de millet et un grain ou m em e le millième d ’un grain?” ; et com m e l’autre reconnaissait q u ’il y a un rapport: “ n ’y aura-t-il pas assurém ent les mêmes rapports des bruits entre eux? Car tels sont les [corps] qui font du bruit, tels sont aussi les bruits. P uisqu’il en est ainsi, si le boisseau de m illet fait du bruit, un seul grain ou le millième d ’un grain tera du bruit aussi.” C ’est ainsi que Zénon proposait son argum ent.” 12. La portée de ces restrictions apparaît mieux si on les confronte avec d ’autres raisonnem ents d ’auteurs anciens. Par exemple H éron d ’Alexandrie applique très strictem ent un principe de proportionnalité entre la force et l’effet, à propos de l’enfoncem ent du coin. Il va ju sq u ’à affirmer, contre l’évidence sensible: “Je dis que toute percussion, m êm e très faible, peut m ouvoir tout coin” (Les Mécaniques ou l ’élévateur, π ï5, trad. Carra de Vaux, journal Asiatique (1893), 118). Il postule ainsi que le phénom ène obéit à une loi linéaire de variation, ju sq u ’à l’absurde. 13. Aristote ne donne pas de justification en faveur de ses règles de proportionnalité. Elles ne sont appuyées ni par un rappel et une discussion des opinions admises, ni par une argum entation inductive, ni par une réduction à des vérités antérieures plus fon­ damentales. Faut-il supposer q u ’il considère ces règles com m e découlant évidem m ent de ce que chacun m et sous le nom de force et de m ouvem ent? Au couple d ’opposés force-résistance doit correspondre le couple espace-tem ps (cf. Alain: l’espace, marque de ma puissance, le temps, m arque de m o n impuissance )?? O n pourrait m ettre cela sous form e proverbiale: “ à grande puissance, long parcours” , mais “ une grande résistance fait durer les choses” . . . . La notion com m une de vitesse, connue et utilisée

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fins elles ont été form ulées. C ependant il existe plusieurs autres passages où A ristote présente et utilise de sem blables règles, dans des argum entations relatives au m ouvem ent. Par exem ple, en de Caelo i 7 (274^7) A ristote pose le principe suivant pour un m o uv em ent d ’altération: Un moteur égal, agissant en un temps égal, modifie quelque chose d’égal, et un moteur plus petit en un temps égal modifie quelque chose de plus petit, et un moteur plus grand, quelque chose de plus grand, cela autant que l’exigera la proportionnalité, c’est à dire tel qu’est le moteur plus grand par rapport au plus petit. Ce principe est très proche des règles que nous avons examinées, mais il est plus faible ou plus vague. Il perm et ici à A ristote de rejeter l’hypothèse d ’un corps infini: Par conséquent l’infini ne sera mû par aucun moteur limité en aucun temps . . . l’infini en effet n’est dans aucun rapport vis-à-vis du fini. (275am) D e m êm e, dans le passage du de Caelo qui a été invoqué plusieurs fois, l’argum entation est dirigée contre l’idée d ’un corps “ sans poids” . E tant donné que “ ce qui est plus petit et plus léger est mû davantage par la m êm e puissance” , il en résulterait que “ ce qui est sans poids parcou rrait une distance qui dépasse toute distance” (de Caelo ni 2, 275aio). Le de Motu Animalium contient un raisonne­ m ent m oins explicite, mais analogue, qui s’applique à la situation de la terre en repos au centre du m onde: Si quelqu’un arrivait à surpasser le repos de la terre par la puissance du mouvement, il est clair qu’il réussirait par ce mouvement à l’écarter du centre. Or il est clair que la vigueur, dont la terre tire sa puissance, n ’est pas infinie; la terre en effet n ’est pas infinie, donc non plus son poids. (MA 4, 699b 14-17) Par conséquent il est possible, au m oins en principe, q u ’existe un m ouv em ent capable de déplacer la terre. C o m m e dans les textes précédents, la pro portio nnalité du m oteur et du m û est utilisée de m anière indéterm inée, vague et non quantitative. C ’est sim ple­ m ent une affirm ation de principe qui assure q u ’il y aura une certaine proportionnalité, du m oins tant q u ’on reste en présence de term es finis. dans la Physique, perm et de com biner espace et temps. Q u ’Aristote ne justifie pas ses régies, c’est peut-être un indice que l’idée lui semble assez banale. Cependant il est le seul auteur de l’Antiquité, à ma connaissance, à avoir exprim é cette idée aussi précisément.

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Le m êm e raisonnem ent est em ployé pour réfuter la possibilité d ’un m ou vem en t dans le vide (Phys, iv 8). O n notera une variante im portante et riche de développem ents: cette fois le m û n ’est pas un autre corps, mais le m ilieu lui-m êm e, l’espace traversé qui fait obstacle au m ouvem ent, Le Tableau ni m et ce raisonnem ent en parallèle avec les quatre term es de Phys, vu 5. T ableau ni: C om paraison de Phys, Phys,

vu

Phys.

IV 8

5

m o teu r corps en dép lacem en t,

(phenomenon, haros, sörna) p o id s

vii

5 et Phys. iv 8

m û m ilie u trav e rsé,

lo n g u eu r corps

(to di’hou, to sôma empodizon)

ré sista n t

lo n g u eu r

tem p s tem p s

vitesse

Le m o teur est cette fois le corps en m ouvem ent, le m û est le milieu, et les m êm es proportionnalités doivent continuer à jouer: si le corps en m o uvem en t et la longueur parcourue restent les m êm es, le tem ps sera prop ortio n nel à la résistance du m ilieu (kata tën analogian tou empodizontos sômatos, 2i5b2). Ce principe est énoncé en vue de l ’application suivante: dans le vide les pro ­ portionnalités ne peuvent subsister, “ car le vide n ’a aucun rap port par lequel il excède le corps, to u t com m e le rien vis-à-vis du n o m b re ” (2 i$ b i2 ). U n e nouvelle fois, A ristote utilise les p ro ­ portionnalités du m ou v em en t dans le seul b u t d ’écarter les caslim ites, et de bannir les entités dém esurées, sans rapport. D ans le m êm e passage, A ristote exprim e le principe général qui le guide dans des cas de cette sorte: P o u r le dire en bref, o n vo it clairem ent la cause de ce qui se passe ici: c’est que, d ’un m o u v e m e n t à un m ou v em en t, il y a, chaque fo is , u n rap p o rt (hoti kinëseôs m en p ros kin êsin pasës esti logos). (21639)

La proportionnalité est donc, avant tout, une propo rtio n nalité de principe. O n ne fait aucune allusion à des m esures effectives, à des assignations de grandeur, à des rapports précisém ent déterm inés qui pourraient, selon les situations particulières, rem plir la place des term es. O n se contente d ’affirm er q u ’il doit y avoir p ro ­ portionnalité et donc rapport; cela exclut par conséquent les cas où une proportionnalité serait im possible, parce que l’un des term es ne pourrait entrer en rap p o rt avec l’autre. C ette exigence que les term es en présence soient finis est to u t à fait fondam entale dans la pensée d ’A ristote, et elle est liée à la notion plus générale d ’u n ord re et d ’une nature. C ’est la possibilité

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m êm e d ’une nature qui est en cause, ainsi que la possibilité de la connaissance. Par exem ple, il est absurde de parler d ’un repos d ’une durée infinie, auquel succéderait sans justification un m ou vem ent, et cette absurdité est la conséquence d ’une thèse générale relative à l’ord re et à la finitude dans la nature: 11 n ’y a rien de déso rd o n n é dans les choses qui sont par nature et conform es à la nature; car la nature est, en toutes, cause d ’ordre. O r l’infini n ’a aucun ra p p o rt vis-à-vis du fini, et to u t ordre est rapport. (Phys, vin I , 252a! i)

Parce q u ’il y a une nature, et donc un certain ordre, le dém esuré ou le sans-rapport sont exclus. Les fondements de la mécanique antique (I): Archimède et Héron Il est grand tem ps d ’aborder le deuxièm e versant de notre ques­ tion: cette analyse du m o u vem en t a-t-elle inspiré le développem ent de la science des machines? J ’ai déjà cité au début l’étonnant tém oignage de Simplicius à propos de Phys, vu 5: C ’est en vertu de cette p ro p o rtio n n alité entre le m oteur, le m obile et le chem in parco u ru , q u ’A rchim ède a com posé l’in stru m en t destiné à peser et appelé charistion. (in Phys. (CIAG x) 1110)

Ce docum ent ne nous est m alheureusem ent pas d ’un grand secours, d ’abord à cause de sa date très tardive (vers 500 ap. J.C .). En second lieu, on discute toujours sur la nature de l’instrum ent évoqué: le dernier au teu r14 qui ait abordé le problèm e considère le m o t charistion com m e la transcription d ’un vocable arm éno-persan qarastun, qui désignerait quelque chose com m e le chad ou f du M oy en -O rien t . . . - et personne ne croira q u ’A rchim ède ait inventé le bon vieux procédé du chadouf! D ’autre part on peut se dem ander si Simplicius évoque un écrit théorique d ’A rchim ède, ou sim plem ent donne sa prop re explication à propos d ’un instru­ m ent construit par A rch im èd e.15 Enfin il n ’est pas im possible que 14. K. Jaouiche, Le livre du Qarastun de Thâbit ibn Qurra (Leiden, 1976), 11-13. A partir du m ot charistion ou quarastun, D uhem avait forgé toute une généalogie fantastique autour d ’un imaginaire C haristion ou H ériston (identique au fils de Ptoléméc?); cela l’avait notam m ent empêché de reconnaître l’originalité de l’ouvrage de T habit ibn Q urra (cf. Origines 1, 79-93, 11, 301-10). 15. Il faut noter aussi que l’Antiquité tardive a beaucoup prêté à Archimède, spécialement dans le dom aine des mécanismes. Cf. le Kitâh Arshimïdas f i 'amal al binkamât, On the Construction o f Water-clocks, ed. & transi, by D. R. Hill (London, 1976).

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Simplicius invoque ici un ouvrage perdu d ’A rchim ède (par exem ­ ple le péri Zugôn m entionné par Pappus). D ans les ouvrages d ’A rchim ède que nous possédons, il n ’y a en tous cas rien qui ressem ble à un raisonnem ent inspiré des règles d ’A ristote. Les propriétés des leviers et des centres de gravité sont dérivées d ’un ensem ble de postulats où le m o u v em en t n ’intervient nullem ent. Le raisonnem ent repose sur la com binaison du poids et de la distance au p o in t d ’appui: N o u s d em andons que des poids égaux s’équilibrent à des distances égales, et que des poids égaux à des distances inégales ne s’équilibrent pas (...) (et nous dem andons que) si des poids sont en équilibre à certaines distances et que l’on ajoute à l’un des deux poids, les poids ne s’équilib­ ren t plus, m ais il y ait inclinaison du côté du poids auquel on a ajouté. (A rchim ède, E quilibres P lans, Postulats i et n)

En com m ençant de cette m anière, A rchim ède prend sim plem ent com m e point de départ la propriété fondam entale du levier. D uhem décrit la dém arche d ’A rchim ède en ce dom aine com m e une “ m éthode de d ém o n stratio n ” , mais non une “ m éthode d ’in v en tio n ” (Origines i 12): les principes du raisonnem ent sont “ cueillis à la surface des phénom ènes, et non pas déracinés du fond m êm e des choses” (ib.). Par opposition à ce style archim édien, une dém arche inspirée d ’A ristote devrait rem o n ter en deçà des pro­ priétés du levier, et chercher la cause de ces phénom ènes dans les relations entre la force m otrice et les autres param ètres du m o uve­ m ent. C ette m éthode d ’explication aurait d ’ailleurs l’avantage de rassem bler plusieurs sortes de phénom ènes sous des principes com m uns: les lois des corps flottants, peut-être m êm e celles des projectiles, pou rraien t dépendre des m êm es hypothèses fon­ dam entales qui régissent les leviers, les poulies et les plans inclinés.16 A u contraire la théorie d ’A rchim ède n ’est nullem ent une enquête sur les causes des phénom ènes m écaniques. C ’est m êm e à peine de la physique, p lu tô t une géom étrie des poids, assez proche de ce qui deviendra la géom étrie barycentrique: on associe à chaque point de l’espace un n o m b re positif, que l’on peut appeler “ m asse” , ou de to u t autre n o m .17 Les règles d ’A ristote énoncées en Phys, vu 5 n ’o n t rien à voir avec cette sorte de théorie. 16. Il me semble que c’est très exactem ent l’entreprise de Galilée. 17. La traduction de C. M ugler, dans l’édition de la C .U .F . des Belles Lettres, masque cet aspect en ajoutant le m ot “ suspendu” dans les formules com m e “ des poids égaux à des distances inégales” (je tiens ces remarques de P. Souffrin).

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L ’ouvrage de H éro n d ’A lexandrie, Les Mécaniques, 18 qui ne nous est parvenu q u ’en version arabe, est assez différent par son style des Equilibres Plans d ’A rchim ède. H éron analyse diverses situa­ tions m écaniques concrètes, et cherche la cause des phénom ènes en term es dynam iques. Il trouve cette cause dans les propriétés des cercles concentriques, et réduit les autres machines sim ples19 au cas des cercles: “ Le levier qui m eut les corps graves opère par le m êm e cause qui agit dans les deux cercles” (Les Méc. 11 9, p. 109), “ la balance se ram ène aussi au cercle . . . ” (ib., p. t u ) , “ le treuil n ’est pas autre chose que deux cercles concentriques . . . ” (ib. π 10, pp. T il-1 2 ). Mais si l’on exam ine de plus près les lignes où il expose le principe initial de toute son argum entation, on s’aperçoit q u ’en réalité les cercles concentriques ne sont pas le véritable point de départ. L ’équilibre de poids suspendus à des roues concentriques de largeur différente est justifié par un appel au principe de la balance: si en b et c sont suspendus des poids égaux, “ il est évident que les cercles ne penchent ni d ’un côté ni de l’autre, puisque les deux poids z et i sont égaux et les distances ba, ac égales” (ib. 11 7, pp. 106-7).

Si un poids bien choisi t est suspendu en e, et q u ’il y a équilibre, dans ce cas: Le rap p o rt du poids t au poids z sera égal au rap p o rt de la distance ba à la distance ae. Ainsi la ligne be jo u e le rôle d ’un fléau de balance m obile au to u r d ’un point de suspension qui est le point a. A rchim ède a déjà 18. Traduction citée n. 12 ci-dessus, ou extraits in: Drachm ann, The Mechanical Technology o j Greek and Roman Antiquity (Copenhagen, 1963). 19. L'analyse de l’enfoncem ent du coin est en fait isolée du reste du raisonnem ent (Les Mécaniques π 14 et 15, pp. 118-21).

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F R A N Ç O I S DE G A N D T

donné cette p ro p o sitio n dans son livre sur l’équilibre entre les poids. Il est évident, p ar là, que nous pouvons m o u v o ir un corpes très lourd avec une très faible puissance, lorsque, étant donnés deux cercles concentriques et un grand poids appliqué à un arc quelconque du grand cercle, le rapport de la ligne issue du centre du grand cercle à la ligne issue du centre du petit, est plus grand que le rap p o rt du grand poids à la faible puissance qui le m eut. La faible puissance l’em porte alors sur le grand poids. (L es M écaniques il 7, pp. 107-8, cf. D rachm ann, pp. 61—3)

C ’est donc le p rod u it du poids par la distance au point de suspension qui sert ici de concept fondam ental. N ous som m es clairem ent dans la lignée d ’A rchim ède, que H éro n cite d ’ailleurs expressém ent, se référant presque certainem ent aux Equilibres Plans. Les rayons des cercles sont considérés com m e cas particulier de leviers ou de balance. H éro n reconnaît d ’ailleurs l’artifice de son raisonnem ent lo rsq u ’il analyse les autres m achines simples et arrive au cas de la balance: “ la balance se ram ène aussi au cercle, cela est évident, puisque le cercle est une sorte de balance” (ib. p. i n ) . La réduction des m achines au cercle n ’est q u ’une apparence, que H éron lui-m êm e dissipe en rem arquant à la fin de cet exposé: Je rem arque p o u rta n t que [ces m achines] se réduisent encore plus directem ent à la balance q u ’au cercle; on a vu en effet que les principes de la dém o n stratio n des cercles ne nous sont venus que de la balance, (ib. Π 20, p. 127)20

P ourquoi, dans ce cas, avoir feint de com m encer par les cercles concentriques? P eut-être H éron a-t-il voulu se conform er à l ’u­ sage, puisque, dit-il, les Anciens com m ençaient par ce qui concerne les cercles (ib. p. 108; D rachm ann, p. 63). Ce peut être une allusion aux Questions Mécaniques, d o n t nous parlerons plus loin, et dans lesquelles les cercles concentriques sont en effet le point de départ de toute la théorie des m achines. H éro n en tous cas n ’a reproduit q u ’en apparence une sem blable dém arche: le fondem ent de toute son argum entation est archim édien. C ependant H éron ajoute, après son explication des cinq m achines, une rem arque d ’im portance capitale: C et in stru m en t [= l’élévateur à roues dentées] et toutes les m achines de grande force qui lui ressem blent sont lents, parce que plus est faible la puissance com parée au poids très lourd q u ’elle m eut, plus est long le 20. Drachm ann (Mechanical Technology, Si) traduit: “ But I think that their shape is nearer to that o f the balance than to the shape o f the circle, because in the beginning the first explanation o f the circles came from the balance.”

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tem ps que dem ande le travail. Il y a u n m êm e rap p o rt entre les puissances et les tem ps. (L es M éc. 11 22, pp. 131-2; D rachm ann, p. 85)

H éron m on tre alors en détail com m ent cette proportionnalité sc retrouve dans différents cas. Ainsi sur un palan, ou sim plem ent sur une poulie m obile, il y a aussi “ ralentissem ent de la vitesse” (D rachm ann tradu it par “ delay” , p. 88): si l’appareil est com posé de cinq poulies dans lesquelles passe une corde unique, et que l’on veuille élever un poids d ’une lon g u eu r hc, il faudra “ faire glisser cinq cordes [= cinq m orceaux de la m êm e corde] de la longueur de l’intervalle bc” (ib. π 24, p. 135). A u trem en t dit la m ain qui tire la corde ainsi dém ultipliée doit aller cinq fois plus vite que le poids qui est élevé. La m êm e différence des vitesses a lieu dans les cas du

levier, du coin et de la vis (ib. 11 25-8, pp. 135-7)· Ainsi “ le rap p o rt des tem ps est le m êm e que le rap p o rt des puissances” (11 28; D rachm ann, p. 89): c’est-à-dire que c’est le m êm e rapport, mais inversé. U n e petite force peut m o u v o ir un poids cinq fois plus grand, à condition d ’aller cinq fois plus vite. H éron énonce ainsi, com m e par u n rem ords tardif, l’invariance du p ro d u it p o id svitesse dans un m écanism e. M alheureusem ent il n ’en a pas fait le principe de sa théorie m écanique, com m e ce sera le cas chez N ew to n , Galilée et sans doute T h ab it Ibn Q u rra .21 21. N ew ton, Principia·*, Scolie des Lois, p. 26; Galilée, Les Mécaniques, Ed. N az., 11 156-60; T hâbit ibn Q urra, in: Jaouiche, Le Livre du Qarastun, 149.

Les fondements de la mécanique antique (II): les Q uestions M écaniques C ’est précisém ent ce principe, que H éron énonce a posteriori, que D uh em a cru reconnaître dans l’argum entation des Questions Mécaniques, et q u ’il considère com m e une conséquence des règles de prop o rtio n n alité de Phys, vu 5. Voici com m ent D uhem illustre son idée sur l’exem ple du levier, en réponse aux objections de G. Vailati: C o n s id é ro n s u n le v ier o ù la p u issan ce est A et où la résistan ce est B ; cette résistan ce se tr o u v a n t à u n e certain e d istan ce d u p o in t d ’ap p u i, su p p o so n s q u e la puissan ce A la pu isse m o u v o ir et lu i faire d éc rire en u n te m p s D l’arc C; elle p o u rra é g a le m e n t [p ar su ite des règles d e P h y s , v u 5] m o u v o ir le p o id s B ! 2 , placé à u n e d istan c e d o u b le d u p o in t d ’ap p u i, car d an s le m ê m e te m p s D , elle22 lu i fera p a rc o u rir l’arc 2 C. Il fau t d o n c la m ê m e puissan ce ( is c h u s ) p o u r m o u v o ir u n certain p o id s, placé à u ne certain e distan ce d u p o in t d ’ap p u i, et p o u r m o u v o ir u n p o id s m o itié m o in d re placé à u n e d istan c e d o u b le . D e là o n tire a isém en t la ju stific a tio n de la th é o rie d u lev ier d o n n é e d an s les Q u e s t i o n s M é c a n iq u e s . O r c’est bien cette ju stific a tio n q u e se m b le in v o q u e r A risto te lo r s q u ’il d it à l ’ap p u i de sa d é m o n s tra tio n : “ si b ie n q u e g râce à la m ê m e v ig u e u r, le m o te u r q u i est d a v a n ta g e élo ig n é d u levier se dép lace d a v a n ta g e ” . ( O r ig i n e s , 11, 292—3 )23

Selon cette exposition des fondem ents de la théorie des m achines, ce n ’est donc plus, com m e chez A rchim ède, la distance au point d ’appui qui intervient d ’abord, mais p lu tô t le chem in parcouru: parce que B et B I2, dans le m êm e tem ps, parcourent des chemins C et 2C, ils o nt “ m êm e puissance” et peuvent tous deux contrebalancer A qui parcourt un arc E. Le fait que les distances telles que O B soient en rapport inverse des poids est alors une conséquence. 22. Je co rrige une faute d ’im pressio n. 23. E n fait D u h e m p arv ien t à une p o sitio n plus nuancée à la fin de la m ê m e n o te annexe au to m e il des Origines de la statique (pp. 300-1). M ais il ne sem ble pas s’ap ercevo ir que cela c o n tred it sa thèse d ’ensem ble.

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Pour D uhem , ce raisonnem ent est une application des règles de Phys, vu 5. O n aurait dans le cas présent: (M ,m ,s,t)-------- » (M ,m /2,2s,t) c’est-à-dire: (A ,B ,C ,t) -------- > (A ,B ! 2,2C,t) O n notera d ’abord un point im portant: le tem ps peut à volonté être pris en considération ou passé sous silence, puisq u ’il s’agit de systèm es m écaniques liés. U n e p o rtion du systèm e ne peut se m o u v oir sans entraîner le reste, et tous les déplacem ents sont contem porains. O n p o u rra donc ici faire jo u e r à volonté soit la vitesse, soit la distance parcourue, sans que cela fasse aucune différence.24 La difficulté fondam entale est la suivante: q u ’avons nous appelé M dans le cas présent? quel rôle jo u e A dans (A ,B ,C ,t)? q u ’est-ce que D u hem désigne par ischus (la puissance)? En réalité D uhem a utilisé ce term e en deux sens différents: une fois p our désigner A to u t seul (“ la puissance A ”), et une autre fois p our désigner la com binaison du poids A , de l ’arc parcouru E et du tem ps t (“ 11 faut donc la m êm e puissance . . . ” ). N o tre écriture (A ,B ,C ,t) n ’est pas correcte; il faudrait écrire l’égalité des produits poids-vitesse:

ce qui pourrait s’écrire en résum é: Puissance de A = Puissance de B = Puissance de B /2 Le m o t ischus, puissance, désigne alors une grandeur com posée, qui se trouve être invariante dans le systèm e m écanique considéré. D onc ischus sera soit la force seule, soit la force com binée avec une longueur. Le texte cité de D uhem n ’est pas explicite à ce sujet, mais en se rep ortan t au début du m êm e ouvrage (Origines 1, 6-7), on voit nettem en t que la puissance est, selon D uhem (et selon les choses m êm es, si j ’ose dire), le p roduit du poids par la vitesse ou 24. A Descartes, qui se piquait de bannir la vitesse des considérations mécaniques, Leibniz rétorque: “ Ainsi il est étonnant que M. Descartes a si bien évité l’écucil de la vitesse prise pour la force., dans son petit Traité de Statique ou de la force m orte, où il n ’y avait aucun danger, ayant tout réduit aux poids et aux hauteurs, quand cela était indifférent . . . ” (Essay de Dynamique, Phil. Sehr, vi, 218). O n notera que non seulement la vitesse peut être remplacée ici par le chem in (le chemin vertical en toute rigueur), mais que les anciens ne distinguaient pas entre poids et masse, si bien que la grandeur composée dont il est question ici peut être explicitée soit com m e travail F X L soit comm e quantité de m ouvem ent M.V. D ’où certaines confusions . . .!

par le déplacem ent (cf. texte cité p. too). Le véritable invariant n ’est donc plus ici le poids ou la force, mais une certaine grandeur com posée: le p rodu it du poids par la vitesse (ou la longueur parcourue). C ’est cet invariant com posé que D uhem appelle “ puissance” (ischus). Il faut sous entendre alors que les règles de p ro p o rtio n n a­ lité du m o uvem en t o n t été réécrites sous une form e appropriée: M = m . s/t L’expression com plexe à droite est la m esure (et la définition?) du term e de gauche. Si on l’applique à la figure ci-dessus, on s’aperçoit q u ’il faut écrire deux fois cette form ule com plexe: de chaque côté du levier se trouve un certain p ro d u it m.s/t. Il n ’y a plus équilibre entre un m oteur et un m obile, ou une force et un fardeau, mais entre deux “ puissances” com posées. Le m o teu r et la résistance sont chacun le p rod uit d ’une résistance par une vitesse. D uhem sem ble sous-estim er une telle différence conceptuelle entre la “ puissance” utilisée dans la Physique et la puissance d o n t il parle (et d ont il croit que parlent les Quest. Méc.). Il néglige les détours intellectuels nécessaires p o u r définir et m anipuler de telles grandeurs com posées. Il connaît p o u rtan t certains des m éandres par où o nt chem iné des notions com m e la “ gravitas secundum situ m ” au M oyen Age, ou le “ m o m e n to ” chez Galilée et après lui. C ependant une certaine prudence s’im pose. N ous avons vu com bien la relation énoncée par A ristote est souple et m êm e protéiform e. D ’autre part les Anciens m anipulaient assez aisém ent des pro portio ns com posées, qui leur tenaient lieu de nos énoncés algébriques. U ne form ule com m e M = m.s/t, qui paraît assez raffinée, exprim e une certaine loi de variation, que les Anciens auraient pu percevoir et utiliser, sans la form uler aussi co m m odé­ m ent. La seule réponse décisive consiste dans une étude attentive des Questions Mécaniques. Les lignes que cite D uhem : H ô s t ’a p o tes a u të s isc h u o s p l e o n m e ta s tê s e ta i to k i n o u n to p l e i o n to u h u p o m o c h lio u a p e c h o n .

Si bien que grâce à la même vigeur, le moteur qui est davantage éloigné du levier se déplace davantage (85ob5) sont la fin d ’une dém o n stratio n relative au levier, et reprennent d ’autres propositions presque littéralem ent identiques (85ob6 =

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84Ç)b20 = 848b3). C ’est dans les pages précédentes que l’essentiel s’est jo u é, lors du préam bule et de la prem ière question (“ P o u r­ quoi les grandes balances sont-elles plus précises que les petites?” ). La suite des trente-cinq questions fournira une sorte de cham p d ’application au schém a fondam ental qui a été établi au début. L’auteur affirm e avec la plus grande netteté cette dépendance logique: Les p ropriétés de la balance (ta p é ri ton zu g o n ginom ena) se ram ènent au cercle, les propriétés du levier se ram ènent à la balance, et presque tout ce qui concerne les m o u v em en ts m écaniques se ram ène au levier. (848312)

Le cercle est donc le “ principe de toutes les m erveilles” de la m écanique (847bi6, 848312). Rien d ’étonnant à cela, puisque le cercle est lui-m êm e une sorte de m erveille; il est l’u nion des contraires, il jo in t ce qui se m eu t et ce qui dem eure (847b2o), le concave et le convexe (b2$), le m ouv em ent vers l’avant et le m o uvem ent vers l’arrière (84834) (car lorsque le cercle tourne, deux points diam étralem ent opposés se m euvent de m ouvem ents opposés). C e m orceau de rhéto riq ue sur les m erveilles et les contraires m e paraît déplacé ici, et peu digne de la sobriété d ’A ristote. D ’ailleurs le Philosophe avait rem arqué ces propriétés du m o u v em en t circu­ laire, et les avait m en tionn é d ’une m anière beaucoup plus brève et sèche. La Physique n o tam m en t évoque l’union du repos et du m ou vem ent dans la sphère en ro tatio n (V II1 9 , 205b7 et V 19, 240329) ainsi que la différence des vitesses des points selon leur éloigne­ m ent du centre (v n o , 240b 15). C e thèm e capital des Quest. Méc. est donc déjà présent dans l ’oeuvre d ’A ristote. (Je ne prétends po u rtan t pas que le cercle ne puisse nullem ent être un sujet d ’étonnem ent, je considère no tam m en t que la seule form ulation du paradoxe des roues concentriques dans la 24e question m écani­ que, 855324, tém oigne d ’une m éditation assidue et pénétrante sur les propriétés surprenantes des cercles en rotation.) A près ces rem arques sur le cercle, illustrées par la description de plusieurs cercles qui s’entraînent l’un l’autre, l’auteur énonce le prem ier des 35 problèm es, concernant les balances, puis il reprend im m édiatem ent le fil de son argu m en tatio n précédente: Le principe de cela est la question de savoir pourq uo i, sur le cercle, la ligne qui est plus éloignée du centre est transportée plus vite, tout en étant m ue par la m êm e force, que la plus petite qui est plus près. (848b2-5)

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La différence des vitesses selon la distance au centre n ’est donc pas acceptée com m e u n fait géom étrique, elle requiert une explication qui devra se placer sur un terrain dynam ique: une m êm e force obtient des effets différents. C ette différence de vitesse selon la distance au centre est due au caractère com posite du m o u v em en t circulaire: La cause de ces choses est que ce qui décrit un cercle est transporté selon deux m o uv em en ts (pheretai duo p horas). (848bio)

Il est donc indispensable d ’étudier la com position de m ouvem ents en un m o uvem ent unique, ou p lu tô t ce que cela signifie que d ’être “ transporté selon un certain ra p p o rt” (en logôi tint). (8 4 8 h li) C ’est ici que l ’auteur insère sa dém onstration assez rem arquable du principe de la com position des m ouvem ents uniform es (c’est la prem ière occurrence, historiquem ent, de cette loi). Le rapport qui est p ro p re au déplacem ent proposé est représenté par le rappo rt des segm ents latéraux: Estö gar ho logos hon pheretai to pheromenon, hon echei hë AB pros tin Α Γ (848bi4). Le rap p o rt de AB à Α Γ est le rappo rt du déplacem ent (tes phoras ho logos). Si l ’on prend une fraction quelconque du déplacem ent total, on trouvera toujours des com posantes latérales dans le m êm e rapport, qui form ent par conséquent un petit parallélogram m e sem blable au grand; une m êm e diagonale convient donc à tous ces parallélog­ ram m es successifs. Si au contraire un corps est transporté selon deux m ouvem ents qui n ’ont aucun rapp o rt déterm iné pendant un intervalle de tem ps m êm e très petit (ean en mêdeni logôi pheretai duo phoras kata mêdena chronon, 848b26), le déplacem ent ne s’effectuera pas sur une droite. C ar si c’était une droite, on po u rrait en faire la diagonale d ’un parallélogram m e, et le “ rap p o rt des côtés” serait le rap p o rt selon lequel serait transpo rté le m obile (anankê ton ton pleurôn logon pheresthai to pheromenon, 848b29). O n retrouve ainsi le cas du cercle et des trajectoires curvilignes. Si un m obile est p orté selon deux déplacem ents dont le rap p o rt ne reste pas déterm iné pendant u n tem ps fini (ce que l’auteur désigne par “ en aucun rap p o rt pendant aucun tem p s” ), cela engendrera une courbe (848b34). L ’auteur rend m anifeste cette absence de rap p o rt dans le cas du déplacem ent sur un cercle, en m o n tran t que l’arc de cercle n ’est pas la diagonale qui correspondrait à deux segm ents rectilignes:

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Soit le cercle Α Β Γ, que son so m m et B soit tran sporté en direction de Δ; il se trou v era à u n m o m e n t vers F. O r, s’il avait été tran sp o rté dans le rap p o rt qui est celui de Β Δ à Δ Γ, il aurait été transporté sur le diam ètre ΒΓ. B

Δ

L ’auteur “ d é m o n tre ” ainsi que le rap p o rt des deux com posantes n ’est pas un rap p o rt déterm iné, qui resterait constant pendant un intervalle de tem ps si petit soit-il. D ans cette m êm e phrase, si on la lit bien, se trouve déjà indiqué un élém ent capital de to ute la discussion (qui a échappé à plusieurs traducteurs ou com m entateurs). O n peut déjà lire ici en quel sens le cercle doit être conçu com m e la résultante de plusieurs m ouve­ m ents ou forces: B est d ’abord poussé vers Δ, et parce q u ’il est fixé au cercle, il est contraint par quelque autre influence à se déplacer vers Γ. L ’im pulsion rectiligne initiale (que l’on peut concevoir com m e tangentielle, ou norm ale au rayon - c’est peut-être ce que signifie la phrase précédente, assez obscure) a été déviée par une autre influence. A cet endroit l’auteur pose l’axiom e qui sera le principe fon­ dam ental de son argum entation: D e deux corps transportés grâce à la m êm e vigueur, si le prem ier est déto u rn é davantage, l’autre m oins, il est raisonnable de considérer que celui qui est davantage déto u rn é sera m û plus lentem ent que celui qui est m oins détourné. (84936)

“ D é to u rn e r” traduit le grec ekkrouein (heurter hors de sa voie), un m ot q u ’A ristote utilise en plusieurs endroits (cf. de Sensu 7, 557ai5: “ le m o uvem ent le plus grand détourne toujours le plus p etit” ; Phys, vin 8, 204aio). O n a ici, com m e dans la Physique, une règle de proportionnalité du m ouvem ent, mais assez différente. Les term es en présence ne correspondent à aucune des rangées du Tableau 1. C ependant cet

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énoncé n ’est pas incom patible avec les autres. O n pourrait m êm e adm ettre que la “ gêne” , l’influence “ pertu rb atrice” désignée par le verbe ekkrouein, doit être considérée com m e une variante de la résistance venue du m ilieu ou du fardeau à tran sp o rter (cf. Tableau iii). Le couple vigueur/gêne correspondrait alors au couple m o te u r/m û de Phys, vu 5. L’auteur tente de préciser quelle est cette influence perturbatrice qui contraint le point extrêm e du rayon à suivre un m ouvem ent curviligne: Parce que le so m m et du plus petit rayon est plus près de ce qui dem eure im m obile que le som m et du plus grand, et q u ’il est p o u r ainsi dire tiré en sens opposé vers le centre, ce so m m et sera transporté plus lentem ent. (849311-14)

C ertains com m entateurs ont parlé d ’une force centrale ou d ’une attraction. Ce sont des rapprochem ents intéressants, mais l ’auteur est plus réservé ou plus vague: il essaie sim plem ent de caractériser l ’influence qui détourne et incurve le m o u v em en t rectiligne initial. Le verbe “ tirer en sens o p posé” traduit antispân (tirer à soi, tirer en sens contraire), qui n ’est nullem ent un m o t exceptionnel. Q uel­ ques lignes plus bas, on pourra d ’ailleurs constater que ekkrouein et antispân sont accolés com m e des term es presque synonym es (849331). U n autre m o t notable est em ployé, le verbe kratein (vaincre, m aîtriser): Parce a u ’il est plus près du centre qui le tire en sens contraire, il est vaincu davantage. (849319)

Dans ces m êm es lignes, l’auteur com m ence à caractériser les deux com posantes du m o uvem ent curviligne en les désignant com m e “ celle qui est conform e à la n atu re” et “ celle qui est contraire à la n a tu re ” . O n peut gloser sur ces dénom inations. Il me sem ble que l’interprétation la plus probable est celle-ci: il est question des arcs de cercles que décrivent les bras de la balance, donc la figure ci-après doit être tournée de 900; le point B porte un poids do nt le m o u v em en t naturel est dirigé selon la verticale tangente au cercle en B; au contraire le m o u v em en t contre nature s’oppose à ce prem ier m ouvem ent, le gêne et contraint le corps à se déto urner en direction du centre. (La figure du V at.G r. 253 est conform e à cette interprétation; cf. F. Krafft, cité n. 26, p. 29.) La question est reprise en term es géom étriques, afin de pro u v er que, sur u n petit cercle, l ’influence perturbatrice est plus forte.

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B

O n considère des cordes de longueur égale, inscrites dans des cercles différents. Le segm ent qui sépare la corde de l ’arc de cercle (le “ sinus-verse” , ou ce que les m édiévaux et N e w to n appelleront la “ flèche” de l’arc) est plus petit dans le cas du plus grand cercle. Ici YB est plus petit que X Z . C e théorèm e assez raffiné n ’est pas dans Euclide, m ais on peut le dém on trer en utilisant le troisièm e livre des Eléments (la puissance des points Z et Y par rappo rt à leur cercle respectif): ΖΘ2 = Z X X Z M et Υ Ω 2 = Y B X YE. O n a par hypothèse ΖΘ = ΥΩ et donc Z X :Y B = Y E :Z M . M anifestem ent Z M < YE Par conséquent Y B < Z X . (Cf. Heath, Mathematics in Aristotle (1949), 233.)

L’auteur conclut (après une incise qui em piète sur la suite): Le déplacement selon la nature est égal, et le déplacement contre nature est plus petit (sur le plus grand cercle); en effet BY est plus petit que ZX. (849b2) L’intérêt exceptionnel de ce raisonnem ent réside dans la traduc­ tion géom étrique des deux m ouvem ents qui engendrent le cercle. L ’auteur perçoit clairem ent la notion de courbure d ’un arc, et la m anipule de m anière féconde, en com parant les com posantes tangentielles (mesurées par une corde constante) et les com ­ posantes centrales (mesurées par le sinus-verse). Je ne connais pas

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d ’exem ple qui atteigne ou surpasse cette perspicacité avant le de Vi centrifuga de H uygens et les travaux de N ew to n . Le tem ps est ensuite in tro d u it dans le raisonnem ent (il sem ble que l’auteur parvient à séparer le raisonnem ent strictem ent géom étrique qui précède et le raisonnem ent ciném atique ou dynam ique). Puisque la com posante contre nature est plus petite sur le grand cercle, le point B ira plus loin que Ω. C ’est l’application exacte du principe énoncé plus haut: le m ouvem en t le m oins gêné, à force égale, parcourra plus d ’espace. La suite du texte m e paraît m oins convaincante. Voici quel me sem ble être le raisonnem ent: on sait que l’extrém ité B est soum ise à une gêne m oindre, p o u r une force tangentielle égale, et que par conséquent ce point, dans son m ouvem ent, dépassera Ω. J u sq u ’ou ira-t-il? il suffit de voir que les deux cercles sont semblables, et que les com posantes tangentielles et norm ales doivent toujours rester proportionnelles. Aussi l ’auteur introduit-il le principe suivant: Il faut q u ’il y ait pro portio nnalité, les m ouvem ents selon la nature étant entre eux com m e les m ou vem en ts contre nature. (8 4 ^ 5 )

C ’est de cette m anière qu’il déterm ine la position du point H (les segm ents H K et KB sont sem blables aux segm ents ΘΖ et Z X ). Q u o iq u ’il en soit de ce dernier passage,25 l’analyse qui précède est assez claire: la déflexion vers le centre est m oindre dans le cas d ’un grand cercle. Le m ouvem ent initial est donc m oins gêné, et l ’espace parcouru sera donc plus grand dans le m êm e tem ps. N ous som m es m aintenant en m esure de com prendre pleine­ m ent le texte que D uhem invoquait en faveur de sa thèse: Grâce à la m êm e vigueur, le m o te u r qui est davantage éloigné du point d ’appui se déplace davantage.

Il n ’est nullem ent question d ’un p roduit poids X vitesse. La “ v ig u eu r” en question est l ’im pulsion rectiligne (venue du poids pour le cas présent). C ette puissance aura un effet plus grand si le 25. G. Lloyd m ’a suggéré de le lire de la manière suivante: il faut que B se soit avancé plus loin que le point Ω, car en Ω on aurait des m ouvem ents naturels égaux (ΥΩ = ΖΘ) et des m ouvem ents non-naturels inégaux (BY est plus petit que X Z), ce qui est impossible à cause de la proportionnalité entre les deux cercles (le rapport entre m ouvem ents naturels doit être le m êm e qu'entre m ouvem ents non-naturels). La difficulté essentielle du passage m e semble être la suivante, en termes peut-être trop modernes: quelle est la variable fondamentale dont dépendent les autres? Dans le passage précédent on calculait les déflexions pour une m êm e composante tangentielle, et ici on aboutit à une m êm e vitesse angulaire; com m ent est-ce possible?

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point d ’application est plus éloigné du centre, parce que sur un grand cercle la déflexion est m oindre, com m e l’auteur l’a exposé m agistralem ent. L ’enchaînem ent logique des argum ents est donc le suivant: 1 une m êm e force engendre u n m ou vem ent plus rapide si elle est m oins gênée; 2 sur un cercle, la force qui pousse en direction tangentielle est d ’autant plus détournée q u ’elle est plus près du centre; 3 donc une m êm e force s’exerçant à l ’extrém ité d ’un rayon de cercle produira un m ouvem ent plus rapide (ou plus grand dans le m êm e tem ps) si elle est plus loin du centre du rotation; 4 de là résultent les propriétés des roues concentriques (treuils, engrenages), puis celles des leviers, des balances, etc. Sur les points essentiels nous som m es donc obligés de contre­ dire D uhem (et ceux qui l’ont suivi): (a) le principe du raisonnem ent des Questions Mécaniques n ’est pas la m esure de la force par le p rod uit poids-vitesse; (b) ce raisonnem ent n ’est pas une application des règles de p ro­ portionnalité énoncées par A ristote en Phys, vu 5. Il reste que l ’axiom e énoncé - une m êm e force produira un m ouvem ent plus rapide si elle est m oins gênée ou m oins détournée - est très voisin des règles de Phys, vu 3 (notam m ent si on adm et que le rap p o rt poids-résistance du m ilieu peut être interprété com m e un rap p o rt force-résistance ainsi que je l’ai fait dans le Tableau in ci-dessus). O n est alors inévitablem ent conduit à reposer la question: les Questions Mécaniques auraient-elles pu être écrites par A ristote lui-m êm e?26 Je ne m e sens pas capable de trancher cette question. C ependant j ’apporterai plusieurs argum ents contre l’authenticité (à part l’ém erveillem ent excessif du prologue, dont j ’ai parlé plus haut): 1 L orsqu’il énonce ses règles de proportionnalité des m ou ve­ m ents, A ristote ne m e sem ble pas orienter son enquête vers des m esures effectives et des applications pratiques, m ais p lu tôt vers la solution de certaines apories d ’ordre philosophique ou cos­ m ologique. 26. Fritz Krafft consacre une partie de son ouvrage Dynamische und Statische Betrachtungs­ weise in der Antiken Mechanik (Wiesbaden, 1970) à prouver l'authenticité des Quest. M é c et récem m ent P. Louis, dans une com m unication orale, a affirmé sa conviction que cet ouvrage est d ’Aristote.

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2 L ’étude de la com position des m ouvem ents dans les Quest. M éc., qui aboutit au principe du parallélogram m e, et la n otion m êm e de “ rap p o rt du déplacem ent” , m e sem blent absentes du corpus aristotélicien. 3 La décom position du m o u v em en t circulaire dans les Quest. Méc. m e sem ble très neuve par son habileté, unique m êm e dans l’A ntiquité, et elle paraît contredire la thèse aristotélicienne selon laquelle le m o u v em en t circulaire est l’un des m ouvem ents simples. Fritz K rafft27 allègue en sens inverse un passage très b ref de la Physique (vn 2,244a!): “ La rotation est com posée de traction et de poussée” ; mais cette indication ne m e sem ble nullem ent aussi féconde que ce qui est proposé dans les Quest. Méc. : A ristote se contente de dire que p o u r faire to u rn er une roue, il n ’y a q u ’à la pousser par un côté et tirer les parties diam étralem ent opposées, alors que les Quest. Méc. décom po­ sent chaque arc de cercle en un élém ent norm al et un élém ent tangentiel (cf. schéma).

Il y a là en tous cas une m ine de travaux à faire: quelle que soit leur origine, les Questions Mécaniques m ériteraient une étude très approfondie, plus détaillée et plus précise que ce qui a été fait ju s q u ’ici. Conclusions La thèse de D u h em était séduisante, parce q u ’elle proposait une vue assez sim ple et harm onieuse du développem ent de la m écani­ que, et q u ’elle m aintenait en dépendance étroite la théorie des m achines et l’analyse philosophique du m ouvem ent. Sans vouloir proposer une autre reconstruction d ’ensem ble, je suggérerai quel­ ques traits qui m e sem blent se dégager d ’une lecture de H éron. O n peut distinguer en effet trois aspects (ou trois couches) dans son argum entation: 27. O p . cit. (n.26), 64.

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τ H éron reprod u it par politesse une dém arche im itée des “ anciens” , où les cercles concentriques sont le point de départ. 2 II considère com m e plus satisfaisante et plus rigoureuse une dém arche archim édienne, où le concept fondam ental est le p ro d u it p o id s-b ras de levier (ou force-bras de levier). 3 Enfin il rem arque, après coup et com m e en passant, que dans les m achines le p ro du it poids—vitesse (ou force—vitesse) est in­ variant. Si les “ anciens” q u ’il évoque avaient lié l’étude des cercles concentriques avec l ’invariance du pro d u it poids-vitesse, H éron n ’aurait pas présenté les aspects (1) et (3) de m anière indépendante et sans y attacher la m êm e valeur. C ette présentation indique clairem ent, à m o n avis, que personne n ’avait encore choisi ce pro d uit com m e point de départ de la théorie des m achines. Galilée, d ’ailleurs, usera de nom breuses précautions et fournira bien des justifications lo rsq u ’il introduira ce p ro d u it sous le nom de momento. C ’est que la n otion n ’était nullem ent un bien com m un de la tradition, connu et appliqué de longue date. L ’oeuvre d ’A rchim ède a donné un to u r entièrem ent nouveau à cette théorie, et sans doute a exercé une grande fascination sur ceux qui l ’o n t connue et com prise. Le raisonnem ent de H éron tém oigne de cette influence. C ependant des recherches de nature plus dynam iques, com m e celles des Questions Mécaniques et de la Physique, ne pouvaient rester enferm ées dans le cadre trop strict des Equilibres Plans. Les savants du M oyen Age et de la Renais­ sance rep ren d ro n t cette enquête sur les causes des phénom ènes m écaniques, renouant avec les spéculations d ’A ristote sur le m o u v em en t.28 28. A insi T h â b it ibn Q u rra raisonne à p artir d ’un p o in t de dép art d y n am ique: il définit la p ro p o rtio n en tre puissances de m o u v e m e n t (v i r t u s m o tu s ) de différents po in ts co m m e la p ro p o rtio n en tre les espaces q u ’ils p arco u ren t dans le m êm e tem p s (M o o d y & C lagett, T h e M e d i e v a l S c ie n c e o f W e i g h ts (M adison, 1952), p. 90 lignes 37-41, et p. 92 lignes 8 6 - 9 4 ; Jaou ichc, o p . d t . ( n . 1 4 ), 147). Il d éd u it l ’équ ilib re de la balance à bras ég aux de l ’égalité de la “ puissance de m o u v e m e n t” des p o in ts (M o o d y -C la g e tt, p. 94; Ja o u ich e a u n texte très different). 11 est intéressan t de rem arq u e r que l ’au teu r arabe a pu s’inspirer d ’u n tex te parfois attrib u é à E uclide, le L i b e r d e p o n d e r o s o e t le v i, qui repose su r des défin itions très voisines de P h y s , v u 5: “ O n n o m m e corps égaux en v ertu ( v i r t u s ) ceux qui p a rc o u re n t des espaces égaux en des tem p s égaux au sein du m ê m e air ou de la m êm e eau. C e u x qui p arco u ren t des espaces ég aux en des tem ps différents so n t dits différents en force ( fo r titu d o ) ; et celui qui a le plus de v ertu est celui q u i a m is le m o in s de te m p s .” (M o o d y -C la g e tt, p. 26.) C e tex te est u n e version m od ifiée et enrichie du pap ier présenté en S eptem bre 1980 à Paris. Les qu estio n s et su g g estio n s des p articip an ts m ’o n t été très précieuses, p articu ­ lièrem en t celles de J. B ru n sc h w ig , M . C av ein g , G. L loyd. Je rem ercie égalem ent G. G. G ran g er et A. S ego nds p o u r leu r critiqu e détaillée.

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O bservational error in later Greek science1 G. E. R. L L O Y D

T he u ntru stw o rth iness o f perception is one o f the oldest them es in G reek philosophy, as the fragm ents o f H eraclitus, Parm enides, M elissus, Em pedocles, A naxagoras and D em ocritus testify. A lready in the Presocratic period the positions adopted and the objections stated differ. For exam ple, H eraclitus said b o th that ‘eyes are m ore exact witnesses than ears’ (fr. io ia ) and that ‘eyes and ears are bad witnesses for m en if they have souls that do n o t understand the language’ (fr. 107). M elissus in a fam ous argum ent starts from the supposition that ‘w e see and hear co rrectly ’ and ends by contradicting it: ‘w e did n o t see correctly’ (fr. 8). Em pedocles w ro te darkly about the n arro w palamai spread th ro u g h the lim bs (fr. 2) th o u g h also instructing his hearer to ‘consider w ith every palamë in w h at w ay each thing is clear’ (fr. 3). A ccording to A naxagoras fr. 21, reported by Sextus, it is ‘because o f the w eakness’ (o f the senses) ‘that w e are n o t able to ju d g e w hat is tru e ’, and Sextus and Galen provide us w ith our evidence for D em o critu s’ distinction betw een w hat is nomdi and w h at eteêi (fr. 9, fr. 125, cf. fr. 11). T he philosophical analysis o f perception m akes considerable advances w ith Plato and A ristotle, n ot that they agreed on that analysis, and the argum ents about its status continue in Hellenistic philosophy, w ith bo th Stoics and Epicureans allotting to aisthêsis a basic role in their epistem ologies, w hile the Sceptics attacked it as a criterion o f w h at exists. Thus the ten A enesidem an m odes i . I am m ost grateful to all those w ho took part in the discussion o f this paper in Paris and to those w ho have corresponded w ith m e since, and especially for the com m ents of Jonathan Barnes, Jacques Brunschw ig, Ian Mueller, M artha N ussbaum , Heinrich von Staden and Gisela Striker.

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reported in Sextus all exploit differences in phantasiai in different ways in order to recom m end suspension o fju d g e m en t, and m any draw on exam ples relating to sense experience. B y Sextus’ tim e a w ide variety o f exam ples had becom e familiar, even co m m o n ­ place (w hether they had originally been used to indicate the radical unreliability o f perception or m erely the m uch w eaker thesis that perception is som etim es deceptive). T hey include the to w er that appears square close to, but ro u n d fro m a distance (PH 1 118), the oar that looks bent in w ater, b u t straight o u t o f it (PH 1 119), the body that is light w hen im m ersed in w ater, b u t heavy in air (PH 1 125) , the m arble that looks yellow in a block, b u t w hite w hen planed (PH 1 130), the distortions o f shapes in concave or convex m irrors or w h en the eyeball is pressed (PH 1 47-9), the tro m p e l’oeil effects o f paintings (PH 1 92, 120), the sheen o f doves’ necks (PH i 120), the honey that tastes b itter to the jaundiced (PH 1 101) and the m uch m ore puzzling because very largely fictitious2 cases o f w hite things appearing yellow to the jaundiced (PH 1 44, and 126) or blood-red to those w ith eyes suffused w ith blood (PH 1 44, 126, cf. 101) - as well as m any others. All o f this is well know n and needs no elaboration. The problem that this paper addresses relates n o t to the philosophers’ epistem ological debates as such, but rather to the question o f w hat 2. The notion that sufferers from jaundice see things yellow persists in nineteenth- and early tw entieth-century text-books on clinical diagnosis, though it loses ground as notes o f caution arc sounded. The first edition o f Jam es Finlayson’s Clinical Manual (London, 1878), 151, remarks: ‘ Yellow vision (xanthopsia) is observed in certain cases o f jaundice, but it is rare, at least in a highly m arked form; it is occasionally produced by santonine \sic\ adm inistered internally.’ The first edition o f H erbert French’s A n Index o f Differential Diagnosis o f Main Symptoms (Bristol, 1912), 840, has: ‘X anthopsia, or yellow vision, may occur in jaundice or in poisoning by santonin, amyl nitrite, cannabis indica, or picric acid’, but in the fourth edition (1928), 926, this becomes: ‘Xanthopsia . . . has been said to occur in jaundice . . ., but it is hardly ever m et w ith in practice’ (a rem ark still repeated in the tenth edition, 1973). The tw elfth edition o f the Textbook o f Medicine o f Sir John Conybeare and N . W. M ann (Edinburgh, 1957), 350, has: ‘X anthopsia, or yellow vision, which is very rare, is not dependent on the degree o f jaundice, but is probably a toxic effect on the retina’, but this is dropped from the thirteenth (1961) and subsequent editions. M any medical dictionaries continue, however, to carry references to xanthopsia in connexion w ith jaundice, for example the tw enty-second edition o f Stedman (1972), the second edition o f B utterw orth (1978), and the fourth edition o f B lakiston’s Gould Medical Dictionary (1979), none o f which stresses rarity o f occurrence. The repetition o f this idea is remarkable testim ony to the tenacity and conservativeness not ju st o f popular belief but o f medical opinion. Mr. W. N . Mann, w ho confirm s that he has not encountered a case o f xanthopsia in jaundice, has rem arked to m e (personal com m unication) that it is striking that the m atter has not been tested by a post m ortem exam ination o f jaundiced subjects to establish w hether the media o f the eye (aqueous, vitreous) and/or the lens is discoloured.

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effect, if any, these or sim ilar argum ents and objections m ay have had on those w ho actually engaged in scientific investigations in the m ain areas o f ancient phusikê. T o w h at extent w ere the philosophers’ doubts about the reliability o f perception picked up or reflected either in the theoretical or m ethodological pronounce­ m ents, or in the actual practice, o f Greek scientists? T he field is a vast one and I fo rth w ith enter tw o m ajor disclaimers. First m y investigation is lim ited tem porally: I shall largely ignore the form ative period o f Greek science, up to A ristotle, and concen­ trate on the m ore developed scientific inquiries o f the postA ristotelian period. Secondly, w ithin post-A ristotelian science I shall focus m ainly on the exact sciences - w here the problem s o f either the inaccuracy or the inexactness3 o f the observational data m ight be th o u g h t to take their sharpest form . This in turn is my excuse for using w h at I w ould be the first to insist is a crude distinction betw een ‘philosophers’ and ‘scientists’. M any indi­ vidual Stoic, Epicurean and Sceptic philosophers m ade a co ntribu­ tion to cosm ology or to other areas o f ancient natural philosophy. T he inquiries I am chiefly concerned w ith are w hat A ristotle called the m ore physical branches o f m athem atics, especially astronom y, optics and acoustics, w here the running was m ade by specialists, or if not by specialists at least by m en w ho m ostly - so far as we know —w ere no t engaged in w hat was the central preoccupation o f H ellenistic philosophy, nam ely ethics. O u r first task is to review the evidence for an awareness o f the possibility o f observational erro r and to distinguish betw een the different types o f such erro r that arc recognised. W e have next to discuss how the difficulties thus identified w ere m et, the different responses or reactions to the problem s o f the inaccuracy or the inexactness o f the observations. M y final section will return briefly to the question o f the com parison and the contrast betw een the them es that dom inate the philosophers’ epistem ological de-

3. Greek ά κρίβ εια som etim es connotes exactness or precision, sometimes accuracy. The distinction we draw between precision in the sense o f ‘the degree o f refinement with which an operation is perform ed or a m easurem ent stated’ (as W ebster puts it) and accuracy in the sense o f ‘degree o f conform ity to some recognised standard value’ or ‘value accepted as true’ w ould have to be made in Greek by contrasting ά κρίβ εια with όρθότης, correctness, or ά λή θεια , truth (cf. e.g. Ptolem y, Syntaxis in 1, 1 i 200.15f.). As W ebster also observes, how ever, exactness, precision and accuracy are often used loosely and interchangeably.

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bates on the one hand, and those that represent the chief concern o f the practising scientists on the other.

I We m ay begin by attem pting a ro u g h typo lo g y o f the various sources o f error in observation that Greek scientific w riters appear to recognise, and the first and m ost obvious o f these is error arising sim ply from the negligence o f one kind or another on the part o f the hum an observers them selves. In such contexts as the law and historical research,4 the reliability - including the tru th fu l­ ness - o f eye-w itness accounts had long been recognised as open to question. Sim ilarly in natural science the w riters occasionally flatly deny that w hat is said to have been observed has indeed been observed. O ne notable passage in w hich A ristotle, for instance, does so is in his discussion o f the alleged link betw een the sex o f the offspring and the side o f the body from w hich the male seed comes. A t G A 7όζΆ2ζ{{. he reports that som e claimed that w hen one testicle was excised the resulting offspring w ere all o f the same sex, and he then continues: ‘b u t they lie; starting fro m w h at is likely, they divine w h at will happen, and they presuppose that it is so, before they see that it is in fact so ’. Similarly Galen in his frequent com bative m oods often accuses his opponents o f lying in their accounts o f w hat they have observed. In On the Natural Faculties Asclepiades is said to have done so in claim ing that urine does n ot reach the kidneys, b ut passes in the form o f vapour direct from the region roun d the vena cava to the blad d er,5 and in On Anatomical Procedures Erasistratus is accused o f fabricating a report o f w hat happens w hen a tube is inserted into an artery to test w hether the pulse continues distal to the insertion: Galen, w ho obtained the opposite result to Erasistratus, concludes by rem ark-

4. Similarly in geography, Ptolem y, for instance, draws a contrast betw een the unreliabil­ ity o f travellers’ reports on distances and locations and the determ ination o f those (acts by astronomical m ethods, although some o f his confidence in the use, for example, of differences in the recorded times o f eclipses is misplaced (Geography I 4 . 12.4fr. Müller). 5. Nat. fac. i 16, Scr. min. m 150.3fF. (11 67.6fr. K), reading κοίλην with Helmrcich, rather than κοιλία ν (with K ühn, though contrast ‘cavae venae’ in K ühn’s Latin translation). Cf. a further m ore general accusation that some o f his opponents describe w hat they have never seen in dissection as if they had seen it accurately, at de Placitis Hippocratis et Platonis vin i; C M G ν 4 4 ,2 4^ ι . 3ι ff-, ν 650.1 iff. Κ.

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ing ‘so great is the tem erity o f som e w ho m ake rash statem ents about things they have never observed’.6 In other cases the truthfulness and honesty o f the observers are n o t challenged, b u t their care and skill are called in question. T he need for care and skill is m entioned in general term s by A ris­ toxenus, for exam ple, w hen he contrasts the study o f m usic w ith that o f geom etry. H e notes that w hile ‘the geom etrician m akes no use o f his faculty o f sense-perception’, for the student o f m usic, on the other hand, ‘exactness o f sense-perception is a fundam ental requirem ent. For if his sense-perception is deficient, it is im possi­ ble for him to deal w ith those questions that lie outside the sphere o f sense-perception alto g eth er.’7 H ere A ristoxenus’ point is not, or n ot only, the obvious one that the student o f musical harm onies should n o t be deaf, b u t rather, or in addition, that he should not be, as w e say, tone deaf. ‘It is by hearing that we ju d g e the m agnitudes o f the intervals’, and ‘we m ust therefore accustom ourselves to discrim inating particulars exactly’. W hereas the geom etrician does no t ‘in any degree train his sight to discrim inate the straight line, the circle or any other figure, such training belonging rather to the practice o f the carpenter, the turner or som e other such handicraftsm an’, the student o f m usic, by contrast, m ust indeed have a trained ear.8* O bservation requires ju d g em e n t or discrim ination, and for this experience is necessary. 6. Anat. admin, vn r 6 (it 648.2fr. K), cf. also A n in arteriis natura sanguis contineatur ch. 8 (ιν 734.2ft'. K). Erasistratus evidently used the test to show that the arteries are dilated because they arc filled, not filled because they are dilated, although he believed that w hat they are filled w ith, in their natural state, is pneuma, not blood. Galen held that the arteries have a natural pow er o f dilating, but that they derive this from the heart. Whereas Erasistratus claimed that the pulse distal to the ligatured tube continues, Galen countered that if the tube is fitted and bound accurately the part o f the artery distal to the ligature ceases to pulsate. As C. R. S. Harris, The Heart and the Vascular System in Ancient Greek Medicine (O xford, 1973), 378fr. points out, the experim ent was repeated m any times by later anatom ists, notably by Harvey, w ho rem arked on its difficulty and inconclusiveness as a m ethod o f testing how the pulse in the arteries is to be explained: in fact the result will depend largely on how the tube is fitted and ligatured. 7. Harm. 11 33 (translation adapted from Macran). Cf., for example, D idym us’ com pari­ son and contrast betw een music and geom etry in Porphyry, in Harm. 28.9ft., Düring. 8. Harm. ibid. A lthough Ptolem y disagrees w ith Aristoxenus on certain fundamental epistemological issues, notably in that he insists - against Aristoxenus - that reason is m ore trustw orthy than hearing as the ju dge o f small intervals (e.g. Harm. 1 to, 21.25ft*., Düring), he shares A ristoxenus’ tendency to appeal to w hat the ‘musical m an’ has to say about harmonies, e.g. Harm, in 1, 85.13 ft*., cf. 1 i t , 25.5ft*., 1 15. 37·i2 · Evidently in acoustics, as in astronom y, it was som etim es recognised that different observers will get different results: see, for example, Porphyry, in Harm. 18.12ft*., Boethius, de Inst, musica 1 9, 195.23ΓΓ. (and cf. below n. 12).

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A ristoxenus here has som e inkling, perhaps, o f a p o in t w e are all fam iliar w ith in scientific education, notably b u t n ot exclusively in the context o f the use o f scientific apparatus such as the m icro­ scope or the telescope (let alone m ore sophisticated instrum ents), nam ely that to som e degree the student m ust be taught w h at he sees. Similarly in astro n o m y the unsatisfactory nature o f m any o f the observations carried o u t by the earlier Greek astronom ers is often m entioned by P tolem y and was evidently rem arked on already by H ipparchus, although it is n o t always clear on precisely w hat grounds he considered them to be unreliable. Thus in Syntaxis in i, i i 203.7ff. P tolem y refers to observations o f the sum m er solstices m ade by the associates o f M eto n and E uctem on and after them by those o f A ristarchus, and he says that they w ere carried o u t ‘in a rather ro u g h and ready fashion’ (holoscheresteron, 203.14, cf. also 205.i5ff.), ‘as H ipparchus also appears to have th o u g h t’. Again in vii 1, I ii 2.22ff., P tolem y reports that H ipparchus first ‘conjectured rather than affirm ed’ the precession o f the equinoxes ‘since he had found very few observations o f the fixed stars before him , those being ju st about only those recorded by A ristyllus and T im ocharis and these w ere n o t undisputed n o r th o ro u g h ly w o rk ­ ed o v e r’ (oute adistaktois out’epexeirgasmenais, 3·4ί·). Similarly Ptolem y for his o w n part notes that m ost o f the ancient observa­ tions he had to d raw on for his planetary theories had been recorded both ‘inattentively and at the same tim e in a rough and ready fashion’ (anepistatös hama kai holoscherös, ix 2, 1 ii 209.5ff.).9 By them selves such passages suggest m erely that som e later Greek scientists w ere conscious o f the need for care and accuracy in observation, o r at least that they w ere concerned to present them selves as sticklers for accuracy in observation, and that they found fault w ith som e o f their predecessors on that score. B ut we can go a good deal further than this. T he astronom ers, especially, specifically refer to and discuss a n u m b er o f particular difficulties and obstacles to exact observation. W e m ay distinguish broadly betw een problem s that arise fro m the conditions under w hich the object is to be observed or from the nature o f the object itself, and those that relate to the m eans or m eth o d o f observation, for 9. Cf. iv 9, i i 327.24fr., w here he insists that one should not be ashamed to introduce corrections to old hypotheses, and to one’s ow n, as surer observations become available.

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exam ple in the use o f instrum ental aids, although this distinction cannot always be firm ly draw n. A prim e exam ple o f the first kind o f problem is atm ospheric refraction or, m ore generally, any type o f interference arising from atm ospheric conditions. A lthough P tolem y discusses atm os­ pheric refraction at som e length in his Optics (v 23ff.), he does not m ake system atic corrections for refraction in the Syntaxis. B ut not only Optics v 23f f , but also a passage in C leom edes’ On the Circular Motion o f the Heavenly Bodies illustrate h o w refraction was som etim es taken into account. In C leom edes, for instance, it was appealed to, adm ittedly hesitantly, as one o f a variety o f possible explanations for certain ‘paradoxical’ lunar eclipses, w hen both sun and m oon are seen above the horizon at the same time. ‘N evertheless,’ Cleom edes w rite s,10 ‘having regard to the m any and infinitely various conditions w hich naturally arise in the air, it w ould n o t be im possible that, w hen the sun has ju st set, and is under the horizon, we should receive the im pression o f its n o t yet having set.’ A fter m entioning a n u m b er o f other possibilities he proceeds: ‘For if a gold ring is pu t into a drinking cup o r other vessel, then, w hen the vessel is em pty, the object is n o t visible at a certain suitable distance, since the visual current (pneuma) goes right on in a straight line as it touches the brim o f the vessel. But w hen the vessel has been filled w ith w ater up to the level o f the brim , the ring placed in the vessel is now , at the same distance, visible, since the visual current no longer passes straight on past the brim as before, but, as it touches, at the brim , the w ater which fills the vessel up to the brim , it is thereby bent, and so, passing to the b o tto m o f the vessel, m eets the ring there. Som ething similar, then, m ight possibly happen in a m oist and th o ro u g h ly w et condition o f the air, nam ely that the visual ray should, by being bent, take a direction below the horizon, and there catch the sun ju st after setting, and so we receive the im pression o f the sun’s being above the h o riz o n .’11 M oreo ver even if, in the Syntaxis, P tolem y does n o t take refraction as such into account, he occasionally there rem arks adm ittedly rather confusedly —on the possibility o f distortions in 10. Cleom edes π 6, 222.28ft. Ziegler. M y translation is adapted from that in Heath, Greek Astronomy (London, 1932). 11. Cleomedes II 6, 224.1 iff. A. Lejeune, L'Optique de Claude Ptolémée (Louvain, 1956), 225 η. 9, collects other ancient references to the trick w ith the ring in the cup.

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the appearance o f objects view ed near the horizon. In 1 3, 1 i 11.2o ff., he says that heavenly bodies appear larger w hen they are near the horizon, and at 13.3ff. he explains this as due not to their being closer to the earth (w hich they are not), but to the evaporation o f the m oisture that surrounds the earth (an effect w hich he claims is sim ilar to the increased apparent size o f objects seen in w ater). A gain in ix 2, 1 ii 2 09.i6f., he rem arks generally that the appearances o f planets are difficult to determ ine because o f differences both in atm ospheric conditions and in the eye-sight o f the o bservers,12 and at 210.3fr. he suggests that ‘the same angular distances appear greater to the eye near the horizon, and less near the zenith, and so for this reason it is clear that they can be m easured som etim es as greater and som etim es as less than the real angular distance’. T he sam e chapter o f the Syntaxis, ix 2, m entions tw o other types o f difficulty. B oth the stations and the first and last appearances o f planets are, P tolem y says, hard to establish w ith precision. As for the first and last appearance o f a planet, the trouble here is that w ith the last appearance, for instance, the exact position o f the planet disappears w ith the planet itself (209.13fr.) and he adds that observations o f the planets m ade w ith reference to a fixed star at a great angular distance are ‘hard to calculate and subject to g u essw o rk ’ (209.2of.). As for the stations, their exact tim e is difficult to obtain since the p lan et’s local m otion rem ains im perceptible over m any days before and after the stationary point (209.y ff). A precisely sim ilar difficulty arises in determ ining the solstices, w hen the su n ’s position rem ains little changed over a period o f days. In in 1, 1 i 203.12fr., he rem arks on the greater accuracy o f equinox observations, and in 11 5, 1 i io o .2 2 ff., in discussing the ratios o f the su n ’s shadow at the solstices and equinoxes, he further notes that at the w inter solstice the end o f the shadow is difficult to determ ine, although he does n o t specify how the ‘e n d ’ is to be defined n o r distinguish um bra and penum bra. M oreo v er in this context he also rem arks that the problem about obtaining the length o f the shadow at the equinoxes was that the equinox had to be determ ined indepen­ dently. 12.

Cf. VIII 6, I ii 2 0 3 .1 5 f r ., where Ptolem y again draws attention to the problem s of atm ospheric conditions and to the discrepancies between different observers attem p­ ting to determine, for instance, the heliacal risings and settings o f heavenly bodies.

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O u r second group consists o f problem s that arise n o t so m uch in w hat was observed as in the m eans or m eth o d by w hich it was observed, for exam ple in the use o f particular sighting aids or other instrum ents. T he use o f such aids is certainly n o t confined to a stro n o m y .13 In P to le m y ’s account o f h o w to m easure the am ount o f refraction betw een different m edia (air to w ater, air to glass and w ater to glass), for instance, there is a description o f the p rotrac­ tor-like disk to be used to obtain the angles o f incidence and o f refraction.14 T he smallest interval m arked on the disk is one degree, and consonantly w ith this the results are given in degrees or h alf deg rees.15 Sim ilarly in his Harmonics, i 8, i6 .3 2 ff., Ptolem y has a n u m ber o f rem arks to m ake about the difficulties o f obtaining exact data concerning harm onies by using clarinets or pipes or by attaching w eights to strings: it is only on the kanön that the ratios can be sho w n reliably, th o u g h he has reservations about this too (cf. ii 12, 66.6ff.). It is, how ever, again in connexion w ith astronom y that Greek scientific instrum ents w ere m o st fully developed. A lthough the use o f sim ple sighting aids such as the g n o m o n or u p rig h t rod goes back long before the beginnings o f G reek astronom y, from the tim e o f E udoxus, at least, w e have good evidence that a n u m b er o f prom inent G reek astronom ers paid considerable attention to the developm ent o f astronom ical in stru m e n ts.16 T h e exact nature o f E udoxus’ ‘spider’, m entioned in V itruvius (ix 8), is disputed: the controversy has been given a new im petus by the reconstruction recently undertaken by M aula and others on the basis o f archaeological finds at C n id u s.17 A rchim edes in an im p o rtan t text in the Sand-Reckoner describes the dioptra he used to obtain the angular diam eter o f the sun and rem arks on a difficulty that was n ot confined to instrum ental observations, nam ely that the eye itself is not a point, b u t has a certain m ag n itu d e.18 Passages in 13. Already in the P h i l e b u s , 55Eff., for example, Plato rem arked that some τέχνα ι are m ore exact than others, partly because o f their use o f instrum ents. 14. O p t i c s V 8, 227.5fr. Lejeune. 15. Cf. further below , p. 151 and n. 56. ιό. There arc brief surveys o f ancient astronomical instrum ents in D. R. Dicks, ‘Ancient astronomical instrum ents’. J o u r n a l o f t h e B r i t i s h A s t r o n o m i c a l A s s o c i a t i o n 64 (1953-4), 77-85, and D. J. de S. Price, ‘Precision instrum ents: to 1500’, in A H i s t o r y o f T e c h n o l o g y H i, ed. C. Singer and others (O xford, 1957), 582— 619. 17. See E. Maula, ‘The spider in the sphere: E udoxus’ Arachne’, P h i l o s o p h i a 5—6 (1975-6), 225—57. 18. S a n d - R e c k o n e r ch. 1, 11 224.2fr., c f further below, pp. 154 f. Cicero ( R e p . 1 xiv 21-2, T u s e , i XXV 63) further reports that Archimedes constructed a mechanical m odel or orrery to represent the m ovem ents o f the sun, m oon and planets.

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Ptolem y m ake it clear that H ipparchus described an im proved version o f the dioptra, the so-called ‘four-cubit ro d d io p tra’ (Syntaxis v 14, 1 i 417. iff.), k n o w n in som e later w riters sim ply as the H ipparchan d io p tra ,19 and that H ipparchus was also familiar w ith the equinoctial (or equatorial) arm illary, a ring m ounted in the plane o f the equator from w hich the equinoxes could be determ ined. In Syntaxis hi 1, 1 i 194.231!., 196.8ff., tw o passages are quoted from H ipparchus’ lost w o rk On the Precession o f the Tropical and Equinoctial Points w here references are m ade to observations m ade on the bronze ring set up in the Square Hall in Alexandria. As for P tolem y him self, apart fro m the four-cubit rod dioptra and the equinoctial arm illary, four other m ain instrum ents are referred to in the Syntaxis, the m eridional arm illary, the plinth or quadrant, the parallactic ruler and the arm illary astrolabe.20 He gives quite detailed instructions concerning the construction o f each o f the last four as well as for the d io p tra.21 H e notes, for instance, in connexion w ith the arm illary astrolabe that the concentric rings m ust be accurately turned and that the convex outer surface o f each o f the inner rings should exactly fit the concave inner surface o f the one above (Syntaxis v 1, 1 i 351.12fr., 2 1ff., 352. iff.). A gain in his description o f the parallactic ruler he stipulates that the rods should be ‘n o t less than four cubits lo n g ’ and thick enough to be rigid (v 12, 1 i 403.9fr.). M oreover this concern to provide accounts o f the astronom ical instrum ents used continues, rem arkably, in later w riters such as T heon o f A lexan­ dria, Pappus and Proclus, w ho in som e cases go beyond the description in the Syntaxis and afford us supplem entary inform a­ tion on the instrum ents in question. Thus Pappus rem arks that Ptolem y did not specify the dim ensions o f the rings o f the astrolabe and gives a figure o f a cubit for the largest, outerm ost rin g ,22 and Proclus devotes several extended passages in his

19. See, for example, Proclus, Hyp. 120.21 and 126.14. Hero devoted a short treatise to the construction and use o f the dioptra. 20. A lthough Ptolem y docs not mention the plane astrolabe in the Syntaxis, it has been thought likely that he refers to it as the ‘horoscopic instrum ent’ in the Planisphaerium ch. 14, II 249.19ff. (see, for example, O . Neugebauer, ‘The early history o f the astrolabe’, Isis 40 (1949), 240-56, and A. B. Drachm ann, ‘The plane astrolabe and the anaphoric clock’, Centaurus 3 (1953-4), 183-9). 2 1 . See Syntaxis I 12 (1 i 64.12fr.); I 1 2 (66.5fr.); v 1 2 (403.9fr); and V 1 (351.5fr), respectively; and on the dioptra, v 14 (417.1fr). 22. Pappus, in Plot. Synt. v, 4.4fr, 6.6ff, Rome.

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Outline to the construction and use o f the m ain astronom ical instrum ents.23 T he advantages to be gained from the use o f such observational aids were, in som e cases, considerable, even th ou gh (1) that point should not be exaggerated,24 and (2) the extent o f their actual deploym ent is controversial.25 Thus P tolem y explains, in Syntaxis V i, i i 353.Tiff., how the arm illary astrolabe can be used to give the ecliptic coordinates o f any heavenly body. T he instrum ent had first to be set w ith reference to a k n o w n point - the sun, if it is the m oon that is being investigated, or the m oon itself or a b rig h t star, for any other heavenly bo dy - b ut once that was done, the astrolabe enabled distances b o th along the ecliptic (i.e. in longi­ tude) and n o rth and south o f it (i.e. in latitude) to be read off directly, instead o f having to be determ ined from observations o f the object’s position in relation to the zenith and the horizon. A m ong his particular claims are that he used this in stru m en t (1) to establish the positions o f the stars for his star catalogue in Syntaxis vu and v m ,26 (2) to obtain better data concerning the positions o f M ercury (here the problem was that m ost o f the fixed stars are rarely visible at a distance from the sun equal to M ercury’s, b ut this difficulty could be circum vented by taking a fix on m ore distant stars w ith the astrolabe, ix 8, 1 ii 270.iff.) and (3) to do so for the m oon. In this last case his account o f the stages by which his lunar m odel developed is circum stantial. Previously the only accurate data w ere those obtained from lunar eclipses. ‘T he other kinds o f ob serv atio n ,’ he says in Syntaxis iv 1, 1 i 265. i8ffi, ‘that depend either on its course w ith respect to the 23. P roclus, Hyp. ch. 3, 42.5-54.12; ch. 4, 126.13-130.26; ch. 6, 198.15-212.6; and cf. also 7 2 .20f'f., l l O ^ f f . , I20.15ff. 24. C f. A. A aboe and D . J. de S. Price, ‘Q ualitativ e m easu rem en t in a n tiq u ity ’, in L ’aventure de la science I (Paris, 1964), 1-20, w h o rem ark th at the characteristic ty p e o f m easu rem en t d ep end ed n o t on in stru m en tal perfection b u t on the choice o f crucial p h en o m en a, a lth o u g h in insisting on the co m p arativ e im precision o f ancient in stru ­ m en ts th ey , fo r th eir p art, ten d to play d o w n the im p ro v e m e n ts in the data th at w ere obtainab le, and o b tain ed, by th eir use. 25. See especially the recent exchanges betw een R. R. N e w to n , The Crime o f Claudius Ptolemy (B altim ore, 1977) and ‘C o m m e n ts on “ W as P to le m y a fraud?” by O w en G in g erich ’, Quarterly Journal oj the Royal Astronomical Society 21 (1980), 388-99, and O . G in g erich , ‘W as P to lem y a fraud?’. Quart. Jour, o f the Roy. Astr. Sec. 21 (1980), 253-66, and ‘P to lem y revisited, Quart. Jour, o f the Roy. Astr. Soc. 22 (1981), 40-4. 26. Syntaxis v n 4, 1 ii 35.11fr., and cf. vu 2, 13.15fr. P to lem y gives the lo n g itu d es and latitud es in degrees and fractions o f a degree, using seven sim ple fractions, ^ J f |, J i.e. 10', 15', 20', 30', 4 0 ', 45 ' and $o': thus finer d iscrim ination , b elo w 5', is n o t attem p ted .

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fixed stars, or on instrum ents [he does not specify w hich], or on solar eclipses, can all be very deceptive because o f the m o o n ’s parallaxes.’ B ut w hile his first m odel for the m ovem ent o f the m oon - in w hich he follow ed H ipparchus closely - is based on eclipse data, he returns to the problem in v 2 and rem arks on certain discrepancies he had discovered betw een the predicted and the observed positions o f the m o o n by using the arm illary astrolabe described in v 1. ‘In general, observing in this way . . ., we found that the distances o f the m oon in respect o f the sun som etim es agreed w ith the calculations m ade according to the hypothesis w e have expounded, but som etim es differed and disagreed w ith them , at tim es by a little, at tim es by a great deal’ (1 i 354.2offi). C arry in g out w hat he describes as a ‘progressively m ore com plete and m ore m eticulous exam ination’, he found that at conjunctions and at full m oons there was little or no discrepancy w ith w hat was predicted by the m odel based on eclipse data. But w hen the m o o n was in the first o r third quarter, and at the same tim e m idw ay betw een the apogee and the perigee on the epicycle, the discrepancies betw een the predictions and w hat was observed w ere appreciable. N o w as already noted, the truthfulness o f P to lem y ’s claims not ju st about the use o f the astrolabe but about all the observations he said he u n d erto o k is currently - and n o t for the first tim e27 - at the centre o f controversy. W e shall com e back to the issue later, but for the m o m en t w e m ay rem ark that there are im portant differ­ ences betw een the three particular cases w e have referred to. W hatever the grounds for scepticism about the first - P to le m y ’s claims concerning the construction o f his star catalogue28 - the M ercury and M o o n exam ples differ from it in that an issue o f theory, indeed the sim plicity o f his w hole astronom ical m odel, is at stake. These have in co m m on that they are the tw o instances w here he m ade radical m odifications to his usual epicycle27. J. B. J. D elam bre, especially, raised the issue in his Histoire de l’astronomie ancienne, 2 vols. (Paris, 1817), e.g. ï x x v ff., 183 and 11 264. The idea that Ptolem y’s star catalogue was plagiarised from an earlier astronom er, namely Menelaus, was already suggested by Arabic astronom ers: see A. A. Björnbo, ‘H at Menelaos aus Alexandria einen Fixsternkatalog verfasst?’, Bibliotheca Mathematica, D ritte Folge 2 (1901), 196-212. 28. It is agreed on all sides that he was here building on earlier w ork, especially the star-catalogue o f H ipparchus. O n the thesis that all that Ptolem y has done is to take earlier observations and to adjust them for precession, I entered some caveats in Magic, Reason and Experience (C am bridge, 1979), 183-4, but compare also now Gingerich, ‘Ptolem y revisited’, op. cit. (n. 25).

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eccentric m odel, in b o th cases introducing an extra circle in addition to the epicycle and the deferent.29 T he very com plexities that he th o u g h t necessary w ould appear to be quite gratuitous unless they are a response to w h at he perceived to be m ism atches betw een the sim ple m odel and some em pirical data (how ever and by w hom soever these w ere obtained).30 This does not, to be sure, prove that his account o f his procedures is correct. B ut it is striking, at the least, that he chose to represent w h at he claims as better em pirical data as the result o f the use o f his m ost sophisti­ cated instrum ent. B ut although im p rov em ents in the quality and the range o f the available data w ere som etim es attributed, by the Greeks th em ­ selves, to the developm ent o f astronom ical instrum entation, the use o f instrum ents was far from u nproblem atic and there is good evidence that in som e instances, at least, this was clearly recog­ nised b o th by H ipparchus and by Ptolem y. T he discussion o f problem s connected w ith the determ ination o f the length o f the year in Syntaxis III i provides the m ost striking illustration o f this and is w o rth considering in som e detail. P tolem y first points out that H ipparchus drew a clear distinc­ tion betw een w h at w e should call the sidereal year (m easured by the sun’s return to the same fixed star) and the tropical year (m easured by the su n ’s retu rn to the same solstitial or equinoctial point), the latter being less than 365? days, the form er m ore, the difference betw een them being due to the phenom enon o f the precession o f the equinoxes (1 i i9 i.2 o ffi). B u t Ptolem y also notes that H ipparchus suspected that the tropical year m igh t n o t be constant, th o u g h he adds that he was h im self sure, on the basis o f the successive observations o f the solstices and the equinoxes that he had m ade, that this was n o t the case (194.3ffi). For w e find them differing by no im p o rtan t am o u n t fro m the additional quarter day, b u t som etim es by ju s t about as m uch as it is possible to be in error due to the construction and position o f the instrum ents. For w e guess from the considerations that H ipparchus adduces that the error 29. For an account o f the M ercury and M oon models, see, for example, O. Pedersen, A Survey o f the Almagest (Odense, 1974), 159ÎT., especially 192!!., and 309ff. 30. Cf. Gingerich, ‘Was Ptolem y a fraud?', 26if.: ‘Ptolem y m ust surely have put credence in som e specific observations here, or he w ould not have ended up with such an unnecessarily com plicated m echanism for M ercury.’ (In the same article, at p. 257, Gingerich produces a table that indicates very clearly the im provem ents in accuracy Ptolem y obtained in his revised lunar model).

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w ith regard to the inequalities belongs rath er to the observations. For after he had first set o u t, in O n the Precession o f the T ropical and E quinoctial P oints, the su m m er and w in ter solstices that seem ed to him to have been observed accurately and in order, he h im self agrees that the discrepancy in th em is n o t so great th at the inequality o f the yearly period is recognised. For he co m m en ts on them thus: ‘it is clear, then, from these observations th at the differences o f the years have been very small. B u t as regards the solstices I do n o t despair o f m y and A rchim edes’ being in erro r both in observation and in calculation even up to the fourth part o f a day. B u t the irreg u larity o f the yearly periods can be accurately apprehended fro m observations m ade on the bronze ring set up in A lexandria in the so-called Square Hall, w hich - it is agreed - indicates the equinoctial day as that in w hich its concave surface begins to be lit up on the opposite side’ (i i 194.10-195.9).

W e m ay conclude from this that H ipparchus was well aw are o f the difficulty o f obtaining precise determ inations o f the solstices and that he envisaged the possibility o f an error o f up to six hours arising from one o r other or b oth o f tw o distinct sources, nam ely (1) in the observations and (2) in calculation.31 P tolem y then cites a n u m b er o f specific observations o f autum n and spring equinoxes m ade by H ipparchus, from which it em erges that H ipparchus did n o t sim ply average his results. The spring equinox data yielded no evidence o f a discrepancy w ith the value o f 3654 days for the tropical year. T he au tum n equinox data, how ever, gave values that varied from 365! days to 365 days 4 hours. H ipparchus settled, it seems, for a figure o f ^ t h o f a day less than 365! days for the tropical year, b u t the procedure he used is n o t described. P tolem y follow s up the observational difficulties on his o w n account at 196.2iff. It is possible, he says, for there to be an erro r o f up to a q uarter o f a day n o t only in solstice observations, b u t also in equinoctial ones. T here will be an error o f that m agnitude if the position or calibration o f the instrum ents deviates from the true by a m ere 6 m inutes o f arc.32 A nd the error could be greater still w here the instrum ents are n o t corrected according to the observations them selves, w here, for exam ple, they have been fixed on foundations and an unnoticed shift has taken place in their placem ent. ‘A nd one can see this, ’ he rem arks (197.17ff.), ‘in the case o f the bronze rings in the palaestra in our 31. O bservation and calculation are again distinguished as possible sources o f error at SytUaxis iv n , i i 339.13fr., for example. 32. Price, ‘Precision Instrum ents’, 587, notes that an error o f 6 m inutes corresponds to a shadow m ovem ent o f about ύ m m in a 2-cubit instrum ent.

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w hich are supposed to be in the plane o f the equator. For so great is the distortion in their position, and especially in that o f the bigger and older one, w hen we m ake o u r observations, that som etim es their concave surfaces tw ice suffer a shift in lighting in the same equinoxes.’ A gain a sim ilar observation m ay be ascribed already to H ipparchus, since P tolem y says that at a particular spring equinox (in 146 b . c . ) w hich occurred in the m o rn in g (i.e. sunrise) on a particular date, H ipparchus recorded that the ring in A lexandria was lit up on both sides equally at the fifth h o u r ‘so that the same equinox differently observed differed by about five h o u rs’ (ip b -iff.).33 W hat H ipparchus took to be stronger evidence for the variation he suspected in the length o f the tropical year came from calculations based on eclipse data. B ut here P tolem y first com ­ plains that this involves already assum ing the su n ’s position as given (i98.2off.) and then protests that the results obtained are far m ore likely to be due to other factors than the alleged variation in the tropical year. ‘For it w o u ld seem m ore possible either th at the distances o f the m o o n at the eclipses w ith respect to the nearest fixed stars had been estim ated in a rather ro u g h and ready fashion, o r that the calculations either o f the m o o n ’s parallaxes for the sighting o f its apparent positions o r o f the su n ’s m o v em en t from the equinoxes to the m iddle o f the eclipses had been obtained either not truly or n o t exactly’ (200.9-16). P tolem y ends this part o f his discussion by stating th at he is satisfied that there is no variation in the tropical year, b u t he emphasises that the actual length o f the tropical year is hard to determ ine. It is slightly less than 365! days, b u t the am o u n t less is so small that it rem ains indistinguishable for m any years. The extra am ount can only be perceived by taking an extended period o f tim e. H ere, as elsew here in determ ining periods o f return, it is necessary to use observations spaced o u t over a long period. ‘The period o f return will be obtained as nearly exactly as possible the longer the tim e betw een the observations com pared’ - for this will have the effect o f m inim ising the erro r due to the ‘w eakness’ o f the observations them selves (202. ioffi). city

33. O n how this m ight be the effect o f refraction, for example, see F. Bruin and M . Bruin, ‘The equator ring, equinoxes and atm ospheric refraction’, Centaurus 20 (1976), 89-111, and N ew ton, The Crime, 85. It is striking that this is referred to as one o f the ‘exact’ observations, Syntaxis m 1, 1 i I96.5f., indeed ‘m ost exactly’ observed, 204.21.

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In the detail it provides concerning the inaccuracy o f in stru ­ m ents and the errors that m ight arise in their use, this chapter o f the Syntaxis is exceptional. Y et the general m essage it conveys about the unreliability o f som e o f the observational data obtained w ith the instrum ents available is one that P tolem y reiterates often enough in the body o f the w ork. Thus he alludes to the difficulty o f obtaining an accurate figure for the variation in the apparent diam eter o f the m o on at perigee and at apogee by direct m easure­ m ent w ith the dioptra in Syntaxis v 14 (1 i 4 i7 .2 2 ff.).34 In the same chapter (4i6.2off.) he also rejects as unsound any attem p t to establish the angular diam eter o f the sun or m o o n by m eans o f the w ater-clock, that is by m easuring the tim e taken by the sun or m oo n to rise o r set or pass som e given point - a m ethod that is actually used in C leom edes 11 1 (ΐ3 ό .2 ό ίϊ.) w h o m entions a figure of o f the orbit, or 28'48", for the angular diam eter o f the sun thus obtained. Proclus com m ents (H yp. ch.4, 124.7ff.) that such a m ethod was, in P to le m y ’s view , quite w orthless, first because the hole o f the clepsydra gets stopped up, secondly because the quantity o f w ater that flow s out in a night or a day is not necessarily an exact m ultiple o f the quantity taken at the rising, and thirdly because it is inexact to take the chord as equal to the arc it su b ten ds.35 T he m ore general difficulty here - and it was a m ajor one for all G reek astronom y - was that o f accurate tim e-keeping, especially at night, for even th o u g h im provem ents had been m ade to the w ater-clock, no tab ly by the in tro d u ctio n o f the constant-head w ater-clock by C tesibius o f A lexandria, the m argin o f e rro r was still wide. O n e cautious au th o rity estim ates that ancient astro­ nom ers could tell the tim e at n ig h t to an accuracy o f w ithin ten m inutes,36 w hich will correspond to betw een tw o and three 34. Ptolem y states first that the sun’s apparent diam eter does not vary appreciably (as Pedersen, A S u r v e y , 208, notes, ‘this tells us som ething about the quality o f the instrum ent, since we know that the solar diam eter varies between 32' 36" and 31 ' and 31"’) and then that the m o o n ’s diam eter at apogee equals the sun’s (Ptolem y appears not to know , or to ignore, the phenom enon o f annular eclipses o f the sun). H e then c a l c u l a t e s the m oon’s diam eter at perigee from eclipse data. As B. R. Goldstein notes, ‘The Arabic version o f P tolem y’s P l a n e t a r y H y p o t h e s e s ’, T r a n s a c t i o n s o f t h e A m e r i c a n P h i l o ­ s o p h i c a l S o c i e t y 57 (1967), 11, in the P l a n e t a r y H y p o t h e s e s ‘the apparent diam eter given for the M oon indicates that Ptolem y has taken his lunar m odel as accurately measuring the size as well as the distance o f the M o o n ’ - despite the difficulties this involves. 35. Cf. Sextus, M v 7 5 ff, and Ptolem y, T e t r a b i b l o s hi 2. 36. Dicks, ‘Ancient astronomical instrum ents’, 84; cf. J. K. Fotheringham , ‘The probable error o f a w ater-clock’, C R 29 (1915), 236-8, and 37 (1923), 166-7.

degrees in the m o tio n o f the stars on the celestial equator. In line w ith this, no actual recorded observation in P tolem y is m ore precise than to w ith in one-sixth o f an hour. T here is no need to em phasise that w hile such a level o f im precision in keeping tim e was a m ajor im pedim ent in astro­ nom y, it m ust have represented an even greater obstacle to attem pts to determ ine the exact speed o f m oving terrestrial objects.37 A lthough tow ards the end o f antiquity we do have rough and ready tests proposed by Philoponus in order to check the effect o f an increase in w eight on the tim e taken for a falling body to traverse a given distance, for exam ple, it should be noticed h o w his results are set out. T hus in the fam ous passage in w hich he objects to certain o f the theories he ascribes to A ristotle, in Phys. 6 8 3 .t8 ff, w hat Philoponus says is sim ply that ‘if you let fall at the sam e tim e from the sam e height tw o w eights that differ greatly, you will see that the ratio o f the tim es o f the m otions does n ot correspond to the ratio o f the w eights, b u t that the difference is a very small one’. A lth o u g h elsew here in his discussion he refers to som e specific w eights and specific tim es purely for illustrative purposes,38 no attem p t is m ade to report precise results o f actual tests, and in part the reason for this, no doubt, is the obvious one that to obtain exact results for the tim es o f fall o f different w eights w ou ld have been extrem ely difficult w ith the tim ing devices available.39 Finally, as a coda to this b rie f and highly selective discussion o f G reek awareness o f difficulties in obtaining precision and accuracy in the observational data, I m ay m ention a rather different case from outside the exact sciences. This concerns the controversy over the value o f dissection, w here the Em piricists argued against their D o gm atist opponents that dissection is useless, n ot ju s t on the general grounds that any inq uiry into w h at is hidden and obscure, ta adëla, is useless, bu t for the extra reason th at no thing can be learnt concerning the living b od y from the exam ination o f the dead - n o r indeed fro m the exam ination o f a living body 37. Yet as A. K oyré pointed out, e.g. in Metaphysics and Measurement (London, 1968), goff., especially 93, the tim ing instrum ents used by Galileo in his discussion o f the problem o f free fall are not m arkedly superior to those available in the ancient world. 38. E.g. in Phys. 68i.3off., 682.25^., 083.13fr. 39. This is not to deny, how ever, that other m ore general factors have also to be taken into account: thus little attem pt is m ade even to specify weights, though there was no technical obstacle to this.

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opened in vivisection. As Celsus reports the argum ent, it was that ‘w hen the body had been laid open, colour, sm oothness, softness, hardness and all sim ilars w ould n ot be such as they w ere w hen the body was untouched . . . N o r is anything m ore foolish, they say, than to suppose that w hatever the condition o f the part o f a m an ’s body in life, it will also be the sam e w hen he is already d e a d .’40 Here, although there is no question o f the problem being the difficulty o f obtaining m athem atical precision, the awareness o f the possibility that the very m etho d that had to be used in undertaking the observation m igh t involve a distortion or change in the object observed is rem arkable, even tho u gh the evaluation o f that possibility was disputed. II

T he next part o f our inquiry concerns how G reek scientists attem pted to deal w ith, or h o w they responded to, the types o f inaccuracy o r inexactness that they recognised in the data at their com m and. In som e cases the problem s could be m inim ised, if not com pletely overcom e. D oubtful observations could be repeated: the need to base conclusions on as m any observations as possible is stated on occasion by P to lem y .41 T he astronom er w ho was aware that the faulty construction or positioning o f instrum ents could be a source o f error w ould be wise to check both, even th o u g h this was no doubt often om itted: in Syntaxis in x, 1 i 197.1 iff. (cf. above p. 141), P tolem y even suggests that equatorial arm illary rings should be corrected for each set o f observations. Again the problem s encountered in using one m ethod m ight be obviated by checking the results w ith another. T he use o f alternative m ethods to obtain a result is a feature o f the discussion o f the length o f the tropical year in Syntaxis, hi 1 (w here he cites both direct observa­ tions o f solstices and equinoxes and results arrived at by calcula­ tion on the basis o f eclipse data) and o f that o f precession in Syntaxis vii 2 and 3 (w here he uses b oth declination shifts from w hich differences in longitude can be calculated and then also values for the longitudes them selves, obtained from observations o f the occultations o f stars by the m o o n ).42 40. Celsus, de Medicina, prooem . 41Γ, Spencer’s translation. 41. E.g. Syntaxis m 1, I i t93.2lff., v 14, 4 2 t.14ft., and cf. v 2, 355.5ff. 42. I ii itj.Sff and 25.13fr., cf. further below, pp. I47ff. C f also above, pp. 138f., on obviating the problem o f lunar parallax by using lunar eclipse data, iv 1, 1 i 265.15fr

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In som e instances, at least, the effect o f observational inaccuracy can be m inim ised by taking observations separated by a consider­ able interval. W e have seen that in hi 1 (1 i 202.12ff., above p. 142) P tolem y points out that this is, in general, the best w ay to ensure accuracy in the calculation o f periodic retu rn s.43 In practice, in his discussion o f the m o o n ’s latitudinal m o v em en t in iv 9 (1 i 328.iyff.), for instance, he even draw s on B abylonian data going back to the eighth century B.c. Sim ilarly in his account o f each o f the planets he aims to correct the figures for their periodic returns by taking observations w ith a long tem poral base. T hus although he starts w ith a rough figure for the cycle o f anom aly (synodic period) o f Venus, nam ely that five such cycles correspond to eight E gyptian years o f 365 days, he uses observations separated by nearly 4 T 0 E gyptian years to obtain a m ore exact figure. T he first o f these is an observation recorded by T im ocharis in 272 b .c ., the second one o f P to le m y ’s o w n in a . d . 138. D ividing the total n um b er o f degrees travelled by the total n um b er o f days betw een the tw o observations P tolem y arrives at a figure for the mean daily m ovem ent in anom aly w hich he states to six sexagesimal places.44 This give a synodic period o f 583 days 22 hours 24 m inutes, or 583.933 days,43 w hich com pares very closely w ith the m odern value, according to Pedersen, o f 583.92 days. W e should be under no illusions as to w here the exactness o f the figures in his tables o f m ean m o tio n comes from : the sexagesimal long division I referred to can be carried o ut to any n u m b er o f places you like, and that Ptolem y took it to six places m erely reflects the degree o f precision he th o u g h t he needed for his m od el.46 T he second key point is this: the accuracy o f the tw o observations them selves does not have to be very great, provided they are separated by a 43· From Syntaxis vii 3, 1 ii 18.iff., it is clear that H ipparchus’ initial doubts concerning precession reflected the shortness o f tim e that had elapsed between such reliable earlier observations as he had to draw on (those o f Tim ocharis especially) and those he undertook himself. W ith this device to ensure accuracy in astronom y, one m ight compare the observation m the Aristotelian Mechanica, ch. 1, 848biff., that larger balances are m ore accurate than smaller ones. 44. As I pointed out in Magic, 194, we obtain a figure o f 361 591125“ 49lv 8V51vl, as against the figure o f 36' 59" 25111 53lv n v 28vl given by Ptolem y. Unless Ptolem y has simply m ade a slip, this suggests that he rounded a value or used a procedure that otherwise differs from our own. 43. Pedersen, A Survey, 426, how ever, gives 383.98 days. 46. This, like other such figures, is not the ‘abus de calcul’ that T annery called them: cf. O. N eugebauer, A History o f Ancient Mathematical Astronomy, 3 vols. (Berlin and New York, 1975), I 35.

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considerable length o f tim e. P tolem y gives the time o f the observa­ tions in hours and fractions o f an hour, and the longitudinal position o f the planet in term s o f fractions o f a degree. B ut both im precision and error will have only a negligible effect w hen spread over a period o f several centuries. T hus a com bined erro r in longitudinal position o f the planet o f one w hole degree will only affect the figure for the daily m otion in anom aly in the third sexagesimal place. In his calculations o f the tw o m ain periodic returns for each o f the planets w e can see exactly h o w P tolem y proceeded and ho w the effects o f observational inexactness and inaccuracy could be, and very largely w ere, countered. In practice the accuracy o f his figures for these returns is very great - to w ithin 0.002% in every case. T here is certainly no need, in this case at least, to suppose w ith D elam bre and N ew to n , that Ptolem y is engaged in a m assive confidence trick, that he is — as N e w to n p u t it — the m ost successful fraud in the h isto ry o f science.47 O n the other hand w e are often n o t in such a favourable position to reconstruct his procedures n o r to establish the likely m argins o f erro r w ithin w hich he aim ed to w o rk . A t a nu m ber o f points there are lacunae in ou r evidence concerning b o th his data and his calculations. His drive to su pp ort and confirm his theories (and m any o f those he to o k over fro m H ipparchus) is everyw here apparent - and o f course in no w ay surprising. That, in the process, he discounted som e o f the evidence available to him is clear. T he question is rather the extent and the m otivation o f this discounting. Som e further specific test-cases will help to th ro w som e light on the subject, even if, in m any instances, we cannot hope to arrive at clear and definitive answers to our questions. It is n ot reassuring that, w hile he tells us from tim e to tim e that he will select the m ore accurate o f his predecessors’ observations, these also often happen to be the ones that corroborate his theory. N o torio usly, in his discussion o f precession in Syntaxis v i i 2 and 3 , he first records a variety o f data concerning shifts in declinations, bu t then uses ju st those cases that produce the result he w ants, the figure o f ‘very nearly’ i° in 100 years that had som e authority from H ipparchus (though it was probably his low er lim it for preces­ sion) and that had obvious convenience for the calculation o f the 47. N e w to n , The Crime, 379; D elam b re, Histoire, 1 x x v ff. and 11 2 jo ff.

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effects o f precession over extended periods. Y et this is n o t the patent fraud that N e w to n believes, provided w e are rig h t to insist that the conversion o f declination shifts to longitudinal m ovem ents was both m ore com plex and less exact than the application o f a sim ple m athem atical fo rm u la.48 M oreover in this case he at least records a fair spread o f data, including the data that D elam bre and N e w to n used to suggest he was forging it, and one o f the chief weaknesses o f their charge o f m assive fraudulence is that they provide no explanation o f w hy, if P tolem y was cooking the books, he should have included the evidence from w hich his deceit could be deduced. T h e very inclusion o f such evidence - o f data that do not exactly fit his results - was taken by D reyer, for one, as testim ony to P to le m y ’s bona fides.49 B ut if he is here n o t plain dishonest, he is, nevertheless, by m odern ideals, extraordinarily tolerant o f e rro r.50 A lthough, as I said, we do n o t k n o w exactly h o w he converted declination data into longitudinal m ovem ents, we can be sure that if he used the data for all the eighteen stars he cites he w o u ld have obtained an average value for precession that is appreciably higher than i° in t o o years. T he average for the set as a w hole w hich is obtained by applying the m o d em form ula for conversion is som e 47" a y ear.51 Even for the six stars for w hich Ptolem y gives a calculation o f the longitudinal m ovem ent, the average is som e 38'' a year. It is true that, having cited his declination data, he proceeds: ‘w h at is required will be even clearer to us from the follow ing observa­ tio n s’ (1 ii 2 5 .i3 f.), and he then gives som e longitudinal m ove­ m ents obtained directly from observations o f the occultations o f certain stars by the m o o n (which o f course u n fortunately presup­ pose his m odel for the m oon). These give values for precession that are, in general, far closer to his figure o f 36" a year:52 they 48. Cf. Lloyd, M a g i c , 195ft’. 49. J. L. E. D reyer, O n the origin o f P tolem y’s catalogue o f stars’, M o n t h l y N o t i c e s o j t h e R o y a l A s t r o n o m i c a l S o c i e t y 78 (1917-18), 347. 50. We should, how ever, emphasise the w ord ‘ideals’ and recognise that it was not ju st in the ancient w orld that scientists often fall short o f these in practice: see further below, n. 59. 51. See, for example, A. Pannekock, 'P tolem y’s precession’, in V i s t a s i n A s t r o n o m y 1, ed. A. Beer (London and N ew Y ork, 1955), 03f. 52. Ct. R. M ercier’s conclusion, that ‘the value 36" per annum w ould follow from soundly observed occultations if they were reduced in the way indicated by Ptolem y’, Review of R. R. N ew ton, A n c i e n t P l a n e t a r y O b s e r v a t i o n s a n d t h e V a l i d i t y o f E p h e m e r i s T i m e , in B r i t i s h J o u r n a l f o r t h e H i s t o r y o f S c i e n c e T2 ( 1 9 7 9 ) , 2 1 1 - 1 7 , at 2 1 6 .

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range from 30 45' in 379 years, i.e. 35" 37'" a year, to 10' in 12 years, i.e. 50" a year, th o u g h that last figure is appreciably higher than the next highest figure (30 55' in 391 years, or 36"4"' a year) and is based on a far shorter tim e span than any other o f the com parisons. T h e average value for this second set o f data is 38" 45"', if w e include the 50" case, or 35" 56"' if w e exclude it. T he conclusions w e m ay d raw from the occultation data m ay be expressed in the fo rm o f an alternative. Either P tolem y is discount­ ing nearly 3" per year - rounding d o w n 38" 45'" to 36" - or he discarded one apparently aberrant value and then discounted a m ere 4'". In either event he does n o t specify his procedure: in particular i f one observation has indeed been discarded as unreli­ able, he docs n o t indicate this. T u rn in g back to the declination data, w e m ay rem ark that Ptolem y does n o t set o u t his w orkings in such a w ay that we can see precisely w hat m argin o f error he allow ed him self (as opposed to the erro r w e can establish that he m ade). B ut the im portant points are these: first he was evidently satisfied that the data confirm ed his figure o f i° in too years well enough, and yet, secondly, the inaccuracy o f his result cannot, in this case, be attributed m ainly to the observations them selves, for they could have yielded a value for precession m uch closer to the one arrived at by m odern com p utatio n for his epoch o f 49" 52'" a year. The fairly gross inaccuracy, in this instance, m ust, then, stem largely from a com bination o f the m ethod o f conversion used and the m argin o f erro r w ith in w hich he was w orking. W e are in no position to apportion the inaccuracy betw een these tw o sources, b u t there is obviously a distinct possibility that he .was, in practice, allow ing him self a far w ider m argin o f erro r than that w hich appears from his o w n figures for the occultation data. In his planetary theory the problem o f reconstructing his data is even m ore severe. In his discussion o f the individual planets he cites either the absolute m inim um , or very close to the m inim um , n u m b er o f actual observed positions necessary in order to extract the param eters o f his m o d el,53 som e 17 particular observations for 53. O n the potential accuracy o f ancient planetary models, w ith an appropriate selection of parameters, see, for exam ple., S. E. Babb, ‘Accuracy o f planetary theories, particularly for M ars’, Isis 68 (1977), 426-34. Cf. Gingerich, ‘Was Ptolem y a fraud?’, 255fr., who has particularly emphasised the superiority o f Ptolem y’s parameters to his cited observations.

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M ercury, n for V enus and 5 each for M ars, Ju p iter and Saturn. T he aim is to exp ou n d the m odel and to determ ine its param eters, b ut the con frontation betw een m odel and data is kept to a m inim um . H e m akes little or no effort to test his m odel against fresh data, that is data no t used in deriving the param eters in the first place. W e k n o w that m any o f his specific observations are inaccurate,54 and w e can follow him step by step in his interpreta­ tion and use o f such data as he does record, including his frequent recourse to roun din g adjustm ents o f various kinds, b o th in the purely m athem atical features o f his calculations (as for exam ple in the conversions o f chords to arcs and vice versa and in renorm ing procedures) and in his ro u nd ing o f observational data. B ut while we can be certain that he has been drastically selective in his presentation o f th at data, he does n o t indicate the principles on w hich he m ade that selection no r even show that he had any such clearly th o u g h t ou t principles at all. Again, the magnitLide o f the rounding adjustm ents he allows h im self can be as m uch as 2% o f the value concerned.55 B ut h o w m uch greater latitude he allow ed him self in the w orkings that he does n ot present can, o f course, only be guessed. H e is clearly confident (and w ith som e reason) that his theories w o rk well on the whole. N o d o ub t he w o uld be absolutely right n ot to abandon his m odel except in the face o f seriously discrepant data - thoirgh ( t ) w e should distinguish betw een abandoning the m odel and revising particular para­ m eters, and (2) w e have noted th at he does revise his m odel quite drastically in tw o cases, nam ely those o f the M o o n and M ercury. It rem ains the case, how ever, that w e are left largely in the dark on just how far he has discounted discrepant evidence in the data available to him . H o w ev er selected and interpreted, the observational data set out in P to lem y ’s chapters on the individual planets have this m o d ­ erately reassuring feature that m any o f them do no t yield results 54. See, for example, A. Czwalina, ‘Ptolemaeus: Die Bahnen der Planeten Venus und M erkur’, Centaurus 6 (1959), 1-3 s; cf. N ew ton, The Crime, 266 and 307, and Gingerich, ‘Was Ptolem y a fraud?’, especially 26off. 55. As, for example, in the roundings he evidently allowed him self in determ ining the distances o f the equant o f Venus from the centre o f the deferent circle and from the earth, see Neugebauer, A History, 1 154, and other examples given at 177fr., 91, 127 and I97f. R ounding adjustm ents are an equally prom inent feature o f Ptolem y’s discussion o f planetary distances in the Planetary Hypotheses: thus in the calculation for M ercury in 1 § 5, the fraction — is first rounded to 8, and that figure is used in a further fraction — w hich is itself then rounded to f .

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that exactly fit the theory. T he situation in his Optics is quite different, at least if w e m ay tru st the extant Latin version o f the A rabic translation o f his treatise. T here, w hen he presents w hat he claims as the results o f detailed experim ents to determ ine the am ounts o f refraction fro m air to w ater, from air to glass and from w ater to glass, these results have clearly already been adjusted to tally w ith the underlying general th e o ry .56 T o be sure, he signals the approxim ate nature ol the results by the term ‘very nearly’, engista. As already noted, the p ro tracto r he used was m arked w ith degree intervals and his results consist o f tables giving angles o f refraction in degrees and h alf degrees. Y et although the errors in these values cannot be com puted exactly (since w e cannot repeat P to lem y ’s experim ents w ith precisely the sam e m aterials he used), even on the m ost favourable interpretation they range, in all three sets o f results, higher than three quarters o f a degree.57 H ere, then the observations have been interpreted before they are recorded. Indeed som ething sim ilar happened far m ore frequently, if less noticeably, in the dom ain o f acoustics. In the extensive ancient reports o f the results o f real or pu rp o rted experim ents investigat­ ing the m ain concords o f octave, fifth and fourth, those results are invariably presented in the form o f ratios that exactly correspond to w hat acoustic th eo ry dem anded —and they do so even w hen the tests referred to could n o t conceivably have yielded anything like those results.58 56. All three tables tally exactly w ith a general law that takes the form r = ai — bi2, w here r is the angle o f refraction, i the angle o f incidence and a and b are constants for the m edium concerned (the angle o f incidence in Ptolem y’s term inology is that from the eye to the perpendicular o f the refracting surface). This law is, how ever, now here stated in the Optics. 57. The best fit that can be obtained for Ptolem y’s values for the refraction betw een air and w ater, and betw een w ater and glass, in each case involve an error o f m ore than i° in at least one o f the eight values set out in the table: for that between air and glass the error is still over 50h 58. This is clearly true o f the tests that purported to reveal the principal harmonies from weighing ham m ers and m easuring jars with different quantities o f w ater, where in each case the test as reported does not yield the result claimed: the sources are listed in Lloyd, Magic, 144 n. 95. W hile both these stories are fictitious, there is this difference betw een them that the ham m ers are given, while Pythagoras is represented not as first getting jars to give the harm onies and then measuring the water, but as w orking back from the result he expected: he poured predeterm ined quantities o f w ater into the jars and then ‘confirm ed’ that these gave the harmonies. T hat perception cannot attain to exactness in ju dging harm onies is repeatedly emphasised in the acoustical writers, for example Ptolem y, Harm. 1 1, 3 .iff-, i6 f f , 1 2, 5.12F; Porphyry, in Harm. 16.13Γ., 17.6fr., 18.7fr. From outside the dom ain o f the exact sciences we m ay note Galen’s tenacity in sticking to his anatomical and physiological doctrines and his insistence that

These last tw o exam ples from optics and acoustics show that, in certain circum stances, G reek scientists dealt ruthlessly enough w ith the discrepancies betw een their data and their theories: they sim ply ignored th e m .59 Y et that should n ot lead us to discount entirely all those protestations o f carefulness in observation that w e review ed earlier. T he contrast betw een P to le m y ’s Optics and his Syntaxis is as im p o rta n t as the sim ilarities betw een them . W hat they have in com m on, is that in b o th m any results, o r w hat are claimed as such, are introduced w ith the qualifying expression engista - very nearly. B ut the difference is that, unlike the Optics, the Syntaxis does not, as a w hole, present results that have already been tailored to m atch the theory precisely. T he problem there is no t that discrepant observational data are corrected, in a bid to obtain perfect fit w ith the theories, but rather that they are tolerated - along w ith a very b road tolerance o f other sources o f im precision in the purely m athem atical part o f the calculations. W e have discussed various types o f ancient response to the problem s o f inaccuracy or inexactness in the observational data. B ut one further possibility has yet to be m entioned. It was, o f course, open to the ancient scientist to m eet the problem by bracketing, that is by attem ptin g to obtain upper and low er lim its betw een w hich the desired value m u st fall. In fact w e find several ancient scientific treatises in w hich certain results are stated n o t in term s o f exact figures, b u t in term s o f such upper and low er lim its.60 T hree o f the best k n o w n such w orks are A ristarchus’ On only repeated observations will count as counter-evidence to them. Thus at A m t. admin. I n (n 278,i4ff. K) he says: ‘if ever, w hen you are dissecting a limb, you see som ething that contradicts what I have w ritten, recognize that this happens infrequent­ ly. D o not prejudge m y w ork until you yourself have seen, as I have, the phenom enon in m any exam ples’ (trans. Singer). 5y. Yet the ancient Greeks were not, o f course, alone in this. From the 20th century we m ay cite G. H o lto n ’s recent study o f the dispute betw een R. A. M illikan and F. Ehrenhaft on the results o f oil-drop experim ents in The Scientific Imagination (C am ­ bridge, 1978), ch. 2. D espite M illikan’s em phatic, italicised, claim that what he was presenting ‘is not a selected group o f drops but represents all o f the drops experim ented on during 60 consecutive days’, it is clear from his laboratory notebooks that he selected favourable experim ents and discarded unfavourable ones: see the series o f M illikan’s notes set out by H olton, 68 and 70-1, for example: ‘Very low Som ething w ro n g ’ [N ovem ber 18, 1911] . . . ‘This is alm ost exactly right and the best one I ever had ’ [Decem ber 20, 1911] . . . ‘Exactly rig h t’ [February 3, 1912]. ‘Som ething the m atter . . [February 13, 1912]. ‘A greem ent poor. Will not w ork o u t’ [February 17, 1912]. ‘Publish this Beautiful one . . [February 24, 1912], and on March 15, 1912, ‘Error high will not use’. O ther striking examples from astronom y and other fields are m entioned by Gingerich, ‘Was Ptolem y a fraud?’, 254 and 263F 60. T he notion o f approxim ation to a lim it is fundam ental to the Greek m athematical m ethod o f exhaustion, where, for instance, the area o f a curvilinear figure such as a

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the Sizes and Distances o f the Sun and Moon, A rchim edes’ Measure­ ment o f the Circle and his Sand-Reckoner. H ow ever, although all three o f these treatises share the characteristic I have m entioned, there are im p o rtan t differences in the w orkings in the three cases. A rchim edes’ Measurement o f the Circle, w hich arrives at a value for π stated as ‘less than 3^ b ut greater than 3^’, is purely geom etrical and involves no m easurem ent w hatsoever. H e first proves that the ratio o f the diam eter o f the circle to the perim eter o f a circum scribed çô-sided polygon is greater than 46735 : 14688, from w hich it follow s, given that the circum ference o f the circle is less than the circum scribed polygon, that the ratio o f the cir­ cum ference to the diam eter is less than 3], and he then show s, sim ilarly, that the ratio o f the diam eter to the inscribed 96-sided polygon is less than 6336:2017!, from w hich it follow s that the ratio o f the circum ference to the diam eter is greater than 3^. A ristarchus’ On the Sizes and Distances is, again, geom etrical th ro u g h o u t the deductions in the body o f the treatise, but (unlike the Measurement o f the Circle) this incorporates as part o f the initial hypotheses certain values for observable data, nam ely hypothesis four that ‘w hen the m o o n appears to us halved its [angular] distance from the sun is then less than a quadrant by one-thirtieth o f a q u ad ran t’ (i.e. 87°), and the n otorious hypothesis six that ‘the m o o n subtends one fifteenth part o f a sign o f the zodiac’ (i.e. 20). U sing these hypotheses, A ristarchus proves geom etrically that, for exam ple, ‘the distance o f the sun from the earth is greater than 18 tim es, b u t less than 20 tim es, the distance o f the m o o n ’ and that ‘the diam eter o f the sun has to the diam eter o f the earth a ratio greater than that w hich 19 has to 3, b u t less than that w hich 43 has to 6’. H ere w e have astronom ical conclusions, yet the lim its w ithin w hich the values arrived at fall are sim ply the result o f the assum ptions as set o u t.61 In A rchim edes’ Sand-Reckoner also w e find a m athem atical circle m ay be determ ined by inscribing successively larger regular polygons. It should, how ever, be noted that, despite the conventional English name for the m ethod, in the Greek view the area was, precisely, not exhausted: the circle was not identified with the inscribed polygon. A nother context in which approxim ation techniques were well established is in the extraction o f square roots, discussed for example by Hero, Metrica i 8, 18.22ff., on w hich see T. L. Heath, A History o f Greek Mathematics, 2 vols. (Oxford, 1921), II 323ff., and cf. n 51-2 on A rchim edes’ approxim ation for "vGj in Circ. Proposition 3, I 236.12ff. 61. He does, how ever, refer to w hat is perceived when he proves, on the basis o f his assum ption about the angular diam eter o f the m oon, that the arc o f the shadow is not perceptibly different from a great circle (Proposition 4).

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problem tackled using inequalities. His aim is to show that the num ber o f grains o f sand that the universe w ould hold is less than a given n u m b er w hich is expressible w ithin the notation he develops in the treatise for the expression o f very large num bers. T hus he takes an upper or a low er lim it for a variety o f values w hich he needs to use, choosing always a lim it well beyond w hat he takes to be likely in order to m ake his problem m ore difficult. He assumes, for instance, that there will be n o t m ore than 10,000 grains o f sand in a p o p p y seed o f diam eter not less than ^ th o f a finger breadth. H e also assumes an upper lim it for the circum fer­ ence o f the earth that is ten tim es the value he believes to be approxim ately correct (not greater than 3,000,000 stades, as opposed to about 300,000 stades), although it turns out that he was not cautious enough in his upper lim it for the ratio o f the diam eter o f the sun to that o f the m oon. Earlier astronom ers had all put the diam eter o f the sun at a value o f less than 20 tim es the diam eter o f the m oon. A rchim edes says that ‘in order that the tru th o f m y propo sition m ay be established beyond dispute’ (11 220.26f.) he will take a figure o f not greater than 30 tim es the diam eter o f the m o o n - although this is, o f course, still a drastic underestim ate. N o w w hile m ost o f the other lim its taken are not directly related to his ow n observations, the upper and low er lim its he obtained for the angular diam eter o f the sun quite definitely are. In a passage 1 have m entioned before, he describes h o w the dioptra is to be used to obtain this angular diam eter and he rem arks, for instance, on the problem that arises because the eye is not a point but has a certain m agnitude. If, how ever, the eye is assum ed to be a point located at the end o f the dioptra, this will give an upper lim it for the angular diam eter o f the sun, w h en the sun itself is com pletely covered by the disk on the dioptra (226.3 f f ) . T o obtain the low er lim it, tw o conditions m ust be fulfilled: first the disk on the dioptra m ust be m oved so that it ju st fails to cover the sun; then allow ance has to be m ade for the m agnitude o f the eye itself by substituting for it a second disk w hich is at least as big as the eye62 and m easuring the angles to it rather than to the end-point o f the dioptra itself (222.22ffi). T he result o f his investigation is not a single approxim ate value for the angular diam eter o f the sun, but 62. H ow this is to be done is set out at π 224.i6ff.

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an upper lim it o f yjgth o f a rig h t angle (just under 32' 55" 37'") and a low er one o f ^ t h o f a right angle (or 27'). T he use o f bracketing and o f inequalities can, then, be illustrated not ju st in G reek m athem atics b u t also in certain contexts in astronom y. This is, w e m ight think, precisely the technique that Greek astronom ers could and should have adopted w herever they w ere in doubt about the accuracy o f the observational data them selves. Y et the occasions on w hich they did so are rare. T here is som e evidence that in his attem pt to determ ine the value o f precession H ipparchus aim ed to establish a m in im um figure, for w hen P tolem y quotes from H ipparchus’ w ork On the Magnitude o f the Solar Year in the Syntaxis (vu 2, 1 ii is .iç f f .) the result H ipparchus reached is expressed as ‘n ot less than [a shift of] y^th o f a degree a year’. P tolem y him self gives upper and low er lim its for the obliquity o f the ecliptic in the chapter (1 12) w here he attem pts a determ ination o f its value, nam ely betw een 230 50' and 230 52' 30". Yet in his calculations he adopts E ratosthenes’ and H ip par­ chus’ result o f §5 o f tw o right angles, i.e. 2 3°5i'2o". Elsew here too - for all the repeated references to the approxim ate nature o f his results - he does n o t w o rk w ith upper and low er lim its for doubtful values as a general rule. B ut the - or rather a —reason is n o t far to seek. If, instead o f w orking w ith specific values for the rate o f precession, for the length o f the tropical year, for the obliquity o f the ecliptic, for the latitude o f A lexandria and various other fundam ental param eters in his system , P tolem y had on each occasion tried to w o rk w ith upper and lower lim its for all those values, the com plexity that this w ou ld have introduced into his calculations w ould have been quite unm anageable. T he p oint is w o rth spelling out a little. Take any one o f these param eters, for instance the value o f the tropical year. Instead o f settling on a specific figure (365 + j days ) it w ould have been preferable to have attem pted - as A rchim edes does for the angular diam eter o f the sun in the Sand-Reckoner - to determ ine the upper and low er lim its w ith in w hich the value fell and to proceed w ith those figures. T he sam e goes for the other fundam ental values I specified. B ut then consider the problem s that w ould have faced P tolem y in attem pting to determ ine the param eters o f his m odels for each o f the planets. V enus’ m odel, for exam ple, is constructed largely by using positions at w hich it is at m axim um elongation from the sun: but these presuppose the su n ’s position as given -

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not directly observed, b u t calculated according to the tables w hich incorporate P to le m y ’s figure for the length o f the tropical year. Indeed for each o f the planets one o f its tw o m ain m otions is directly linked to the su n ’s m ovem ent. In the case o f V enus and M ercury the centre o f the epicycle rem ains on a direct line from the earth to the m ean sun. For the three outer planets the line jo in in g the position o f the planet on the epicycle to the centre o f that epicycle rem ains parallel to the line jo in in g the earth to the m ean sun. T hus in the tables o f planetary m otion, for Venus and M ercury the table o f m o tio n in longitude exactly repeats the table o f the su n ’s m ean m otion in longitude, and for the other three planets the sum o f the m o v em en t in longitude and that in anom aly is equal to the m ean m o tio n o f the sun in longitude. T he m odel o f the sun’s m otio n perm eates, in fact, the w hole analysis o f the m otion o f each o f the planets. M oreover P tolem y is evidently perfectly well aw are o f how certain fundam ental assum ptions underpin the w hole o f his astro­ nom ical theory. T hus his in tro d u cto ry rem arks in B ook hi (1 i 190.15ff. ) show that he is absolutely clear b o th that his account o f planetary m otions presupposes his solution to the problem o f the m otion o f the sun, and that his account o f the m o o n also does so. A gain he points out, as we have noted, concerning H ip p archus’ w o rry about a possible variation in the length o f the tropical year, that his calculations from lunar eclipses already assum e the su n ’s position at the eclipse, and so cannot be obtained independently o f assum ptions about the su n ’s m ovem ent (m 1, 1 i 198.20fr.).63 B ut if the deductive articulation o f his theories in m ost cases effectively ruled out using upper and low er lim its for the m ain fundam ental param eters, w e m ay n o w retu rn to the m ore p rob­ lem atic question o f the view s he m ay have held on the m atter o f the basis on w hich approxim ations could be tolerated. H e is certainly explicit at particular points about particular sources o f either inaccuracy o r im precision. W e saw that he rem arked that errors o f up to a q uarter o f a day are possible in determ ining solstices and equinoxes (above pp. 140-1). A gain in v 10 (1 i

63. Thus at I99.9ff. Ptolem y rem arks that the sun’s positions at the middle o f the eclipses are obtained from the spring equinoxes, from the sun’s positions the m o o n ’s are derived, and from the m oon’s those o f the stars: cf. also 200. gCi. Equally sightings with the astrolabe frequently presuppose the position o f the sun or m oon.

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400. i off.) he com m ents that a difference o f four m inutes o f arc or o f an eighth o f an ho ur is n o t surprising in observations o f the m o o n ’s m ovem ent. M ore generally, at vn 3 (1 ii 18.14ff.) in his discussion o f precession he speaks o f discrepancies w hich can be neglected as ‘the result o f the observations them selves’, although he does n ot specify their m agnitude. If we go over his w orkings we find m any approxim ations - usually signalled as such - both in his observations and in his calculations, and in one notable chapter (iv 11, i i 338.5ff.) he goes over H ip p arch u s’ w orkings to show w here certain errors have occurred w hich influenced his figures for the ratio o f the m o o n ’s epicycle to its deferent. T h e corrections P tolem y here introd uced range from 9 to 56 m inutes in tim e and from 9 to 36 m inutes o f arc in the su n ’s m ovem ent. C learly his expectation o f the level o f accuracy obtainable in eclipse data is far higher than for solstice and equinox observations, and he explicit­ ly notes that errors o f this m agnitude are above the ‘chance’ errors that m ight be expected in such an investigation (344.8ff., cf.

347.14#.)· B ut w hile this all adds up to excellent evidence o f an awareness o f the approxim ate nature o f his results and to im plicit notions o f the lim its o f tolerable erro r in particular contexts, n o t even the m ore explicit passages can be said to am ount to anything like a general theory o f error. T o begin w ith, rather than regularly setting o ut the w hole o f a bo dy o f data and then arriving at a result by averaging the w hole set, for exam ple,64 he far m ore often w orks w ith selected data, that is data from w hich som e item s have already been discarded, b ut the basis for such discarding is intuitive. Thus he n o t only tolerates, but frequently positively recom m ends, the selection o f the ‘m ost accurate’ data. It is, to be sure, understandable, in his term s, to attem pt to exclude observa­ tions that m ight bias or distort the results,65 and w e have found that he som etim es identifies a particular source o f inaccuracy or difficulty that casts d oub t on results found by a particular

64. In one context, how ever, the notion o f an average value is com m on enough: it is fundamental to the idea o f the mean m otion o f a heavenly body, clearly stated in an elem entary text such as Gem inus, xvm 19. 65. Thus it is clear from Syntaxis ix 2, 1 ii 213. iff., that in his planetary theory he preferred to w ork, so far as possible, w ith observations o f the planets taken at contact or in close proxim ity w ith the stars or the m oon, these being, as he puts it, the ‘m ost undisputed observations’.

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m eth o d .66 Y et elsew here the basis on w hich he considers som e observations to be m ore reliable than others is not m ade explicit and there is an evident possibility o f circularity - the observations are ju d g ed accurate because they confirm the theories (H ippar­ chus’ o r his ow n) and the theories are accepted on the grounds that the ‘b est’ observations confirm ed them . Again, although he distinguishes broadly betw een errors in the observations and errors in m athem atical calculations, he does not usually discuss w here im precision can be obviated (for exam ple by taking the calculation to further sexagesim al places), and w here it cannot (for instance because o f the lim its o f resolution o f the observations). N o r does he, in general, draw attention to the points in the w orkings w here im precision will have far-reaching consequences and the points w here it will not, even though he m ust constantly be exercising his ju d g em e n t on that issue. Inter­ polation and extrapolation procedures in the use o f tables o f arcs and chords and o f tables o f periods o f return are not m ade explicit, and although this m ay som etim es be because som e procedures could be taken to be well k n o w n to practising m athem aticians, that can hardly always be the case. A pproxim ations are extrem ely com m on, b ut although in particular cases we can determ ine their m agnitude, w e lack any general statem ent o f the principles on w hich they are to be allowed. We end this section w ith som ething o f a paradox. P tolem y is em phatic, in the opening chapter o f the Syntaxis (i i 4.7ff., 6 . n f f ) , that the inquiry he is about to engage on — w hich he there calls ‘m athem atics’ - is to be contrasted w ith both theology and physics on the grounds that - unlike them - it is capable o f yielding certain and unshakeable know ledge. Y et in practice the entire discussion in the bod y o f the w o rk is steeped in inexactness.67 Yet that is not its weakness: or rather it is n ot always a m ark o f its weakness, but on the contrary, at certain ju n ctu res at least, associated w ith one o f 66. A lthough he som etim es implicitly recognises what we should describe as systematic errors, he does not explicitly contrast these and random ones. Again he has a term for ‘significant’ or ‘notew o rth y ’ difference, ά ξιόλογος δ ια φ ο ρ ά (see, for exam ple, l i 347.14ff., and cf. 194. i t , 197.1, 400.12; and compare Harm. I 4, 9.23F.), but employs, o f course, no procedure that corresponds to a test for significance. 67. Inexactness is not, to be sure, incom patible w ith a claim that certainty is, in principle, and on particular issues, obtainable. B ut we may contrast the claims for βεβαιότης in 1 I w ith the acknowledgem ent o f the lack o f βεβαιότης in, for example, IX 2 (e.g. 1 ii 20S.22) and cf. ΧΙΠ 2, 1 ii 5 3 2 .1 2 fr.

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its strengths. For in astro n o m y it is only w ith reference to inevitably m ore or less im precise observational data that the elegant and rigorous geom etrical theory can be applied to the explananda - and P to le m y ’s Syntaxis, after all, is the first extant text to carry this ou t in detail. T he w eakness here lies, rather, in the silence w ith w hich P tolem y passes over the general issues connected w ith the ap proxim ation techniques he used and the errors he allow ed - th o u g h to speak thus is to speak from the point o f view o f ideals that w ere n o t to be expressed, let alone adopted, for m any centuries.

ill Finally, w e m ay retu rn briefly to the question o f the com parisons and contrasts betw een points m ade in the philosophers’ epistem o­ logical debates and the w o rk o f practising scientists. Evidently the scientists are concerned often enough, in certain contexts, w ith the unreliability o f perception. B u t equally evidently the issues they raise are n o t those o f the types that figure m ost pro m in en tly in the philosophers’ debates. N o n e o f the exam ples that I listed at the beginning from Sextus68 is ever m entioned —so far as I k n o w —in a practical scientific context as a source o f radical confusion. O n the contrary, several stock exam ples are cases w here som e o f the scientists w ere in a position to offer an adequate account o f som e aspects at least o f the m ore or less unfam iliar phenom enon popularly th o u g h t o f as puzzling or problem atic. This is true, for exam ple, o f puzzles about the w eights o f objects in different m edia, w here the sam e object is heavy in air. but light in w ater (as m entioned by Sextus at P H 1 125). A rchim edes’ w o rk in hydrostatics rem oves the paradoxical feature o f this. T he fam ous principle enunciated in proposition seven o f On Floating Bodies B o o k 1 enables the w eight o f an object in air to be related to its w eig h t in any fluid. It enables one to predict, for exam ple, w h at a b o d y fully im m ersed in w ater will w eigh from its w eight in air to g eth er w ith the w eight o f the corresponding volum e o f w ater. It is true that the p o in t in the Sixth m ode, reported by Sextus, is that there is a ‘m ix tu re ’, as he puts it, 6 8 . It is, however, notable that when Sextus comes to attack άστρολογία in M v iff., he

takes as his prim e target Chaldaean genethlialogy and explicitly contrasts this w ith the w ork o f Eudoxus and Hipparchus.

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form ed by the com bination o f the external object and the accom ­ panying conditions under w hich it is apprehended, and insofar as the m oral is that there is no such thing as w eight per se, but only w eights in given m edia, the scientist can and m u st agree w ith the sceptic. B ut the scientist will draw no radical sceptical conclusions about w ithho ldin g ju d g em e n t from this, for he will insist on, and be content w ith, the point that w eights in different m edia are perfectly investigable.69 Similar points apply also to som e o f the optical exam ples in Sextus. T he oar that looks bent in w ater (PH i 119)70 and the effects o f concave and convex m irrors (PH 1 48-9) do n o t lead the student o f optics to epochë. Rather, it is recognised that optics enables illusory appearances to be explained.71 Thus the exact am ount o f the bending o f the oar is som ething that can be m easured and predicted. T o be sure, the phenom enon did not receive an adequate physical explanation (in term s o f the velocity o f light in different media) in antiquity. Y et ancient w riters on optics w ere confident that the phenom ena o f refraction w ere subject to general laws, even if they did n o t state the sine law itself. T he exact m easurem ent o f angles o f refraction betw een tw o w ell-defined m edia was in principle - and som etim es in practice72 — no more difficult than the exact m easurem ent o f angles o f reflection. As for concave and convex m irrors, w riters o f specialist treatises on catoptrics73 as well as students o f optics in general w ere in a position to specify the fundam ental principles o f reflection that applied to every plane or spherical reflecting surface. P to le m y ’s Optics provides n o t ju st a statem ent o f such principles, but sim ple experim ental corro b o ratio n o f them , b oth for plane and for spherical convex and concave m irro rs.74 Such know ledge o f optical principles could be used, and was

69. C o m p a re also th e series o f atte m p ts m ade in an tiq uity to d eterm in e w h e th e r air has w eig h t in air, A ristotle, C a e l . 3 11b8ff., Sim plicius, in G a e l, y io .iq ff . (referring to P to le m y ’s inv estig atio n ) and 7l0.29ff. (rep o rtin g S im p liciu s’ o w n results). 70. T h is w as a stock exam ple, appearing in a w id e v ariety o f auth ors: for a list o f references, see R. Schöne, Damianos Schrift über Optik (B erlin, 1897), 29 n. 9. 7 T . See, for exam ple, P ro d u s , in Eue. 40.9ff. 72. C o n tra st, h o w e v e r, the m u ch m o re p ro b lem atic case o f atm o sp h e ric refraction, w here, precisely, th e m edia and th eir b o u n d aries are n o t w ell defined. 73. See, for exam ple, H ero , Catoptrics, e.g . ch. 5, 328.9 f f , chh. 8ff., 332.8ff. and cf. ‘E u clid ’, Catoptrics, ch. 1, 2 8 6 .2 iffi, ch. 29, 338.7ff. 74. See P to le m y , Optics hi 6 7 , 120.8ff.; Ill 9 7 f f, 131.14fr.; iv iff., 147.2ff.

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used, to produce startling or apparently paradoxical effects. These are, indeed, m entioned by H ero in the opening chapter o f his Catoptrics as one o f the aims o f his in q u iry ,73 and in ch. 18, for instance, he show s h o w ‘to place a m irro r so that anyone approaching it sees neither his ow n im age nor that o f another but only w hatever im age one selects’.7 76 B ut the essential point is that, 5 how ever startling they m ay seem to the bystander or victim , such effects depended, for their production, on knowledge on the part o f the individuals w h o set them u p .77 They had to have a firm enough grasp o f the principles o f optics and kn o w w hat they w ere doing. A dm ittedly the point at issue in Sextus at P H i 48-9 is that animals w ith different shaped eyes m ay sec things differently, and in P H 1119 that position m ay m ake a difference to h o w an object appears. As in the w eight exam ple, the latter is certainly a point that m ay be agreed, except that the scientist will no t go on to draw any radical sceptical conclusions about the suspension o f ju d g e ­ m ent. O n the contrary, the firm er his understanding o f the law s o f reflection and refraction, the less inclined the student o f optics will be to draw sceptical m orals, the m ore confident he will be concerning the investigability o f the phenom ena. T hus in the second book o f the Optics Ptolem y goes th ro u g h a long list o f illusory phenom ena and is able to give satisfactory accounts o f m any o f them : so far from concluding from such cases that sight as a w hole is deceptive, he insists on the contrast betw een the exceptional and the norm al case.78 T he types o f problem s concerning perception that trouble the scientists relate less to sight or hearing as such and in general, than to particular obstacles to observation that arise in p a rticu la r. circum stances. General points, about the need o f the observer to be skilled, and careful, are m ade, bu t they are to be understood w ithin the fram ew ork o f the investigation in question. T he astronom er, for instance, as w e have seen, m ay be concerned w ith the distorting effects o f certain atm ospheric conditions; he should be aw are o f possible faults in the construction and positioning o f instrum ents, o f errors that m ay arise in the tim ing o f observations, 75. H ero, Catoptrics, ch. I , 318.cjff. 76. Hero, Catoptrics, ch. 18, 358.1fr. 77. C f., m ore m undanely, the aims o f σκηνογραφ ία, see, for example, Proclus, in Eue. 40.19, and Dam ianus, 28.1 iff. 78. See, for example, Ptolem y, Optics 11 134h, 8o.3ff.

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in estim ating w ide angular distances,79 and so on. C ertainly the m ove to sim plify and idealise the problem s investigated is com ­ m on in Greek, as in all, science, and this m ove often, even norm ally, involves discarding som e o f the perceptible phenom ena as irrelevant to the inquiry. T here are already certain such idealisations in A ristotle, as for exam ple in his being prepared to treat o f point sources o f light in his discussion o f haloes and the rain b o w .80 T he study o f the lever involves discounting the effects o f friction (as w e call it),81 and the principle o f the absence o f elasticity o f fluids is encapsulated in Postulate I o f A rchim edes’ On Floating Bodies. T he assum ption that the earth is as a point in relation to the fixed stars is com m on in astronom y;82 for the purposes o f his discussion o f the longitudinal m ovem ents o f the planets P tolem y explicitly leaves out o f account their deviations in latitude;83 and m any other exam ples could be given. B ut it is one thing to discount som e o f the perceptible data as irrelevant;84 it is quite another to discount them all as unreliable. T o be sure, the latter m ove is m ade in certain contexts w ithin one strand o f a Platonising tradition. For Plato himself, it was tho u g h t, astro­ n o m y should be reduced to a branch o f geom etry, acoustics to num ber-theo ry . B ut A ristoxenus is clear that such a reduction is 79. Cf. also the problem o f estim ating very small angles, a difficulty present in Ptolem y’s discussion o f determ ining the apparent and true angular diameters o f the planets, P l a n e t a r y H y p o t h e s e s 1 § 5 and cf. § 7. 80. M e t e o r , m ch. 3, 373a6ff., ch. 5, 375b 19Œ See further G. E. L. O w en, ‘A ristotle’, in D i c t i o n a r y o f S c i e n t i f i c B i o g r a p h y 1, ed. C. C. Gillispie (New Y ork, 1970), 256fr. 8τ. As in Archimedes, O n t h e E q u i l i b r i u m o f P l a n e s . The tendency to discount or minimise the effects of friction is also a feature o f the discussion o f the actions o f the simple machines, for example in H ero, M e c h a n i c s 11 21 (wheel and axle), 23 (compound pulley), D i o p t r a 37 (cogged wheels). Cf. also the discussion o f the problem o f friction in connection w ith the analysis o f forces acting on weights on an inclined plane, Hero, M e c h a n i c s 1 23; cf. Pappus vm 9, 1054.4ff. 82. At S y n t a x i s 1 6, 1 1 20.5fr., Ptolem y argues for this: cf. also Euclid, P h a i n o m e n a . Proposition 1, 10.12ff, Cleomedes 1 11, 102.23fr. Com pare the assum ption that the earth is as a point in relation to the m o o n ’s o r b i t , in Aristarchus, O n t h e S i z e s a n d D i s t a n c e s , H ypothesis 2 —which discounts lunar parallax - and contrast the assumption that the circle in which the earth moves round the sun is as a point in relation to the fixed stars, in A ristarchus’ heliocentric theory, as reported in Archimedes, S a n d R e c k o n e r , ch. 1, ii 218.13 ff. 83. S y n t a x i s ix 2, 1 π 2 H .2 iff. He comes back to the problem o f m ovem ent in latitude in S y n t a x i s xiii. 84. The attem pt to isolate the operative variables is a feature o f the stories purporting to describe Pythagoras’ investigation in acoustics, however fantastic their other elements m ay be (see above p. 151 and n. 58), and it is also an aspect o f the m ethods used by the Alexandrian engineers, according to Philo, B e l . 50, in their attem pts to im prove the construction o f catapults.

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foreign to acoustics: ‘som e o f those [predecessors] introduced extraneous reasoning, and rejecting perception as inexact fabri­ cated rational principles, . . . a theory utterly extraneous to the subject and quite at variance w ith the phenom ena’.85 Again although Proclus, m any centuries later, began his Outlines w ith a pious reference to P lato’s recom m endation that the true philo­ sopher should bid the senses good-bye and concern him self w ith the study o f ‘slow ness its e lf and ‘speed itse lf ‘in true n u m b e r’, the w hole o f the rest o f his w o rk deals w ith the investigation o f the visible m oving objects in the sky. Idealisations and sim plifications there m ay be, indeed m ust be. B ut the key question, w h eth er or no t it was m ade explicit, was, rather, w hich perceptible phenom ena to discard. T hose that rem ained, that provided the explananda of the science in ques­ tion, had to be as com prehensive and reliable as possible, and considerable efforts w ere expended, at least in certain quarters, to achieving that end. T h e tru stw orthin ess o f perception in general was n ot the m ain issue in the exact or the natural sciences: the problem s related, rather, to particular contexts and to the particular circum stances o f an inquiry. T he w riters w e have been studying often show quite a keen sense o f w here, in their particular subject, the practical problem s o f securing a reliable data-base lay. T hey exercise, on occasion, som e ingenuity in m eeting or getting round the difficul­ ties, and they are, at least som etim es, careful to em phasise the approxim ate nature o f approxim ate results. T he lim itations o f such m ethodological discussions as they engage in are, how ever, apparent. W hile first-order recognition o f particular problem s and. difficulties is com m on enough, second-order analysis o f the issues connected w ith erro r and approxim ation procedures is rare, that is notably o f such questions as the interpolation and extrapolation techniques to be used, and o f the m ethods to be applied to extract results from sets o f discrepant data —w hile there is little or no use at all, o f course, o f a cluster o f concepts associated w ith probabil85. Aristoxenus, Harm, π 32, cf. also Boethius, de Inst, musica 1 10. Porphyry, quoting Ptolem y o f C yrene at in Harm. 23.25ft., 25.26ft'., suggests that for the Pythagoreans when reason (λόγος) and perception (αΐσθησις) are in conflict, the latter is to be rejected, and in fact the Pythagoreans denied that the interval form ed by an octave plus a fourth (i.e. 8:3) is a concord because it did not fit their ideas o f the simplicity o f the ratios o f the num bers to which concords m ust correspond.

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ity in the statistical sense,86 let alone a theory o f error o f the form fam iliar since Gauss. O n these and sim ilar questions, no t m uch awareness, let alone sophistication, is show n by practising Greek scientists.87 In this respect, they could have done w ith being better epistem ologists and philosophers o f science. Y et it is n o t as if they could have learnt m uch on m any o f these topics from the usual epistem ological discussions in contem porary philosophical w rit­ ings: for if the points about the problem s connected w ith erro r and probability w ere n o t m ade in science, they cannot be said to have been part o f the philosophical debate either. 86. The developm ent o f this notion has been studied by I. Hacking, The Emergence of Probability (Cam bridge, 1975); cf. also S. Sam bursky, O n the possible and the probable in ancient Greece’, Osiris r2 (1956), 35-48, Ο . B. Sheynin, ‘Early history o f the theory o f probability’, Archive for History o f Exact Sciences 17 (1977), 207-59, and on its application in astronom y in particular, Sheynin, ‘M athematical treatm ent o f astronomical observations (A historical essay)’, Archive for History o f Exact Sciences 11 (‘973), 97-126. 87. N or, as we have said, by other scientists for m any centuries.

6

Astrology: argum ents pro and contra A. A . L O N G

O n e o f the special sciences which Sextus E m piricus attacked was astrology. F rom a m od ern view p oint it m ay seem surprising that he regarded astrology as w o rth y o f serious refutation alongside such subjects as gram m ar, m athem atics, and music. B ut in later antiquity, th ou gh there was considerable opposition to astrology by philosophers, its defendants could include scientists o f the first rank, m o st n otab ly the astronom er Ptolem y. A rg u m e n ts for and against the m ain principles o f the subject have a continuous history from the second century b . c . up to the tim e o f St A ugustine. O tto N eugebauer, the greatest living autho rity on ancient astronom y, is a good guide to the right historical perspec­ tive: [ts actual dev elo p m en t [i.e. horoscopic astrology] m ust be considered as an im p o rta n t co m p o n en t o f H ellenistic science . . . T o G reek philo­ sophers and astronom ers, the universe was a w ell defined structure o f directly related bodies. T h e concept o f predictable influence betw een these bodies is in principle n o t at all different from any m odern m echanistic th eo ry . . . C o m p ared w ith the b ackground o f religion, m agic, and m ysticism , the fundam ental doctrines o f astrology are pure science . 1

Fortunately the validity o f astrology is n ot m y them e. 1 shall be concerned rather w ith three stages o f a com plex debate, w hich began w ith Stoics and Academ ics and continued into N eo p lato n ­ ism and C hristianity. Follow ing som e historical prelim inaries, Part II will be ‘the controversy according to C icero’, w hich establishes the chief foundations o f later argum ent. In Parts III and I. The Exact Sciences in Antiquity (Harper T orchbook edition = reprint o f original 2nd ed., N ew Y ork, 1962), 171.

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IV I will consider P to lem y ’s defences o f astrology, and his success in m eeting Sceptical criticism as represented by Cicero, Favorinus, and Sextus Em piricus, glancing for com parison at M anilius. Finally, in Part V, som e later developm ents will be sketched: the positive argum ents o f Firm icus M aternus, the qualified criticisms o f Plotinus, and the attacks o f A ugustine.2

I. Historical preliminaries T he experts seem to agree that horoscopic astrology or genethlialogy, based u p o n the position o f planets in the zodiacal signs, was virtually u n k n o w n or neglected in Greece before the third century B . c . 3 Little can be inferred from a disapproving com m ent about Chaldaean predictions, attributed to E udoxus by Cicero (D iv . π 87), and a statem ent on their ‘m ost am azing science’ (theöria) predicting individuals’ lives (as well as weather) - ascribed to T heophrastus by Proclus (in Tim. 285F).4 T he earliest k n o w n horoscope is B abylonian, o f 410 b . c .; but the earliest Greek horoscope is a relief in N o rthern Syria signifying an event o f 7 July 62 b.c:., the apotheosis (or coronation by Pom pey) o f A ntiochus I o f C o m m ag en e.5 A firm er datum for G reek fam iliarity w ith Babylonian astrology is the history o f B abylon w ritten in Greek in

2. I h ave been greatly helped b y the indispensable w o rk o f A. B ouché-L eclercq, L ’astrologie grecque (Paris, 1899). Its m ain th em e is astrological th e o ry and practice, b u t ch ap ter 16, ‘L ’astro lo g ie dans le m o n d e ro m a in ’, discusses philosoph ical responses to astro lo g y o n pp. 5 70—609. O th e r sections o f this chapter consider astro lo g y in relation to R o m a n society and also the attitu d e o f the early C h u rch . F or m o re recent w o rk on technical aspects o f astro lo g y see especially W . and H . G. G undel, Astrologoumena (Sudhoffs A rchiv, Beih. 6, 1966); F. B oll, Kleine Schriften z . Sternkunde des Altertums (Leipzig, 1950); and for texts o f h o roscopes, O . N eu g eb a u er and Η . Β . van H oesen, Greek Horoscopes (Philadelphia, 1959). F or general b a c k g ro u n d see P. M . Fraser, Ptolemaic Alexandria (O x fo rd , 1972), I 435-9 , n 629-36; F. C u m o n t, Astrology and Religion among the Greeks and Romans (D o v er ed itio n o f th e origin al 1912 cd ., N ew Y o rk , i960); E. R. D o d d s, The Greeks and the Irrational (B erkeley and Los A ngeles, 1951), 245L, 2 6 1G ; A .J . F estugière, La révélation d ’Hermès Trémegiste (Paris, 1944-54), 1 89ÎL, S. D ill, Roman Society from Nero to Marcus Aurelius L o n d o n , 19052), 45, 446fr. 3. B ouché-L eclercq, op.cit. (n. 2), 37ff.; C u m o n t, op. d t (n. 2), 3 iff. (w ho th o u g h t the G reeks befo re A lex an d er th e G reat k n e w o f astro lo g y b u t w ere to o scientifically d isc rim in atin g to p ay h eed to it); N eu g eb a u er, op. dt. (n. 1), 188. 4. O n these passages see B o u ché-L eclercq, op. cit. (n. 2), 27, 62 11.3; C u m o n t, op. cit. (n. 2), 31; N eu g eb a u er, op. cit. ( n .i), 187F 5. N eu g eb a u er, op. cif. (n. 1), 187; H . D ö rrie , Der Königskult des Antiochus vom Kommagene im Lichte neuer Inschriften-Funde, Abh. der Akad. Der Wiss. in Göttingen, P h il.-h ist. Kl. 3, 6o (1964), 201-7.

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about the year 280 by the B abylonian B erosus.6 Berosus settled on the island o f Cos, and his w o rk certainly gave an account o f B abylonian astrology w hich stim ulated further research. In the Natural Questions hi 29.1 (cf. Stoic H eraclitus, Horn, alleg. 53) Seneca reports connexions posited by Berosus betw een uni­ versal conflagrations and deluges and the m ovem ent o f the planets. ‘E arthly things will burn w hen all the planets w hich no w m ove in different orbits com e together in the sign o f Cancer, and are so distributed in the sam e path that a straight line can pass th ro u g h all their spheres.’ In the Stoic theory o f ekpurösis the ‘w orld conflagration’ occurs w hen the planets return to the same position they occupied at the beginning o f cosm ogony (Nem esius, S V F π 625). T he theories o f Berosus are sufficiently sim ilar to suggest that he or doctrines like his m ay have been taken up enthusiastically in the early Stoa. B erosus’ dates are attractively close to Z e n o ’s later life in Athens. A ccording to Cicero, Z eno said that the aether is god; that a ‘rational principle’ (ratio) w hich pervades all nature is furnished w ith divine pow er; and that this p o w er belongs to the stars, and to the years, m onths, and seasons (N D 136). All this, together w ith the general principles o f Stoicism , m ight incline us to regard Zeno as strongly sym pathetic to B abylonian astrology. B ut caution is necessary. T he Stoic concept o f universal ‘sy m p ath y ’ was to becom e the first axiom o f philosophical astrology and is constantly stated by M anilius (e.g. 1 247-54, π 6 o -8 i). T here is every reason to think that Z eno him self established this principle o f Stoic cosm ology, so fundam ental to the causal theory and ethical doctrine. N o doubt, too, he and his successors eagerly drew upon all available support for natural signs w hich reveal the ordered nature o f the cosm os and provide m aterial for living accordingly. In Stoicism the existence o f the gods requires the validity o f divination.7 B ut no texts actually associate Z eno or Cleanthes w ith astrological divination;8 and the only evidence w hich seems to give C hrysip-

6. V itruvius 9.4; Josephus c. Apion 1.129: see Bouché-Leclercq, op. tit. (n.2), 36fF.; Neugebauer, op. tit. (n. 1), 157. 7. Cicero, Div. 11 41 (S F F 11 1193); ibid. 1 82-4 (SK F It 1192). 8. Plutarch records the story that Cleanthes w anted Aristarchus impeached for his ‘im piety’ in m aking the earth rotate against a stationary sky, de facie 923A ( S F F 1 500). B ut this implies nothing about astrology.

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p u s’ belief in horoscopes is the fam ous argum ent in C icero’s de Fato concerning the analysis o f the conditional: ‘If som eone is born at the rising o f the D o g Star he will n o t die at sea. ’9 T he context in w hich Cicero states this conditional, as a paradigm case o f astrological principles, is concerned w ith the m odalities o f state­ m ents referring to the future, and C h ry sip p u s’ disagreem ent w ith D iodorus C ronus. Cicero w ants to develop a contradiction be­ tw een C h ry sip p u s’ claim that w hat will never happen m ay still be possible and his sup p o rt for divination, since divination appears to exclude the possibility o f Fabius’ dying at sea if he was born at the rising o f the D og Star. For C icero ’s purpose any prediction, expressed as a conditional, w o u ld serve. C ertainly, from the de Fato on its ow n, one could suppose that C h ry sip p u s’ defence o f divination rested in part upon astrology; and the w eig ht o f m o d ern scholarship has im pressed upon us the decisive role o f the Stoics as defenders o f a stro lo g y .10 B ut in the de Divinatione itself the predictions w ith w hich C hrysippus is linked are exclusively oracles and dream s. It was on these, and n o t on astrology, that he w ro te his tw o books dealing w ith divination (i 6 ) . T he case for divination, set out by Q uintus in B o ok I, m entions astrology only in passing at the very end, and the nam e associated w ith it there is Posidonius (130). C icero ’s counter-argum ents in B ook 11, ow ing m uch to C ar­ neades, focus equally on dream s, oracles, and portents interpreted by augury. B ut he does include one passage (87-99) on ‘Chaldaean apparitions’ (Chaldaeorum monstra) setting o u t and then seeking to dem olish the principles o f astro lo g y .11 N o th in g in B ook 1 corresponds to this. H e prefaces it by saying that Panaetius is the

9. Fat. vi 12-viii 16. O n the evidence o f actual Greek horoscopes the example is anom alous in w orking from the position o f a fixed star. Greek horoscopes were regularly cast w ith reference to the position o f the planets at cardinal points, m id-heaven, etc. (see the m aterial in N eugebauer and van Hoesen, op. cit. (n. 2)). 10. All the standard books insist on the central im portance o f the Stoics in the Greek assimilation o f astrology, but Bouché-Leclercq is honest enough (op. cit. (n. 2), 33) to adm it the difficulty o f assessing the influence o f astrology on Stoicism. T he older authorities were w riting at a tim e w hen it was fashionable to see Posidonius’ trade-m ark everywhere, e.g. C um ont (op. cit. (n. 2), 47fr. 11. Chaldaeorum monstra is plainly a pejorative expression. ‘Chaldaean’, i.e. Babylonian, is one o f the stocknam es for astrologer. It does not exclude Greeks, see Bouché-Leclercq, op. cit. (n. 2), 546. As early as the late third/early second century B.c. Ennius could speak o f astrologos (the Greek w ord) alongside Latin w ords for other kinds o f diviners, Cic. Dio. i 132.

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only Stoic w ho has rejected astrological predictions (88); and he concludes his prim ary criticism s w ith the question: ‘D o you observe that I am n o t stating C arneades’ argum ents b u t those o f the Stoics’ president, Panaetius?’ (Din. 1197). W ithin this section m ention is m ade o f D iogenes o f B abylon (90), w ho succeeded C hrysippus as head o f the Stoa. He, says Cicero, gave qualified su pp ort to astrology, holding that predictions o f dispositional characteristics could validly be given b u t n o t particular details o f an individual’s future life. Since Cicero explicitly drew on Panaetius, n o t Carneades, for his p rim ary refutation o f astrology it seems probable that astrolo­ gy was at m ost a m in o r topic in C arneades’ m any argum ents against C hrysippus on divination. C ertainly that is n o t the only possible explanation for C icero’s use o f Panaetius here; for he is obviously enjoying the o p p o rtu n ity o f setting one Stoic against others. B ut the general conclusion seems to m e inescapable: astrology was at m ost a subordinate feature o f the earliest Stoic interest in d iv in atio n .12 T he m ost likely explanation o f this is historical. If Bouché-Leclercq and other experts are right, the Greeks did n ot sim ply take over Babylonian astrology. B ouchéLeclercq (p. 61) th o u g h t that the final form o f the G reek zodiac was n o t reached before the tim e o f H ipparchus, m id second century b . c . Later research seems to show that the artificial division into tw elve equal segm ents o f th irty degrees was already in use in B abylonia in the fo u rth cen tu ry .13 B u t N eugebauer agrees that ‘the evidence for direct borro w in g s from Babylonian concepts rem ains exceedingly thin. T he m ain structure o f the astrological theory is undou bted ly H ellenistic.’14 If this is correct, it helps to explain w h y astrology becam e o f substantial interest to the Stoa fro m the m id second century b . c .,

12. As Dodds acutely notes (op. cit. (n. 2), 262 n. 57), ‘earlier Stoics’ (i.e. than Diogenes o f Babylon) ‘had perhaps not thought it necessary to express any view, since Cicero says definitely that Panaetius (Diogenes’ im m ediate successor) was the only Stoic who rejected astrology, while Diogenes is the only one he quotes in its favour’. See also Schiche (n.34 below). But in the obscure train o f thought at Cic. Fat. iv 8 C hrysippus is probably being supposed to claim that astrorum adjectio does apply to all terrestrial things. 13. Neugebauer, op. cit. (n. 1), I 0 2 f . T he earliest extant Greek text which divides the ecliptic circle into 3 6 0 degrees is the Alexandrian Hypsicles’ Anaphorikos ( O n Ascen­ sions’), a w ork o f the later second century b . c . , see Fraser, op. cit. (n. 2 ), I 4 2 4 . 14. Op. cit. (n. 1), 170.

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the period o f H ipparchus, b ut n o t apparently earlier.15 Greek astrology differs from early B abylonian in its concern w ith ordinary individuals’ horoscopes. T he calculation o f birth tim es, planetary angles and aspects, and the relevant degree o f the zodiac was a h ighly com plex task. D evelopm ents in Hellenistic astronom y seem to have been a prim e determ inant o f the theoretical founda­ tions o f horoscopic astrology w hich also drew heavily on standard concepts o f later G reek physics.16 In short, the system as w e know it in M anilius and later w riters was probably a creation o f the second century B .C ., if n o t later. This seems the m o st econom ical explanation o f the virtual silence o f C hrysippus and Carneades, the qualified approval o f D iogenes o f B abylon, the opposition o f Panaetius, and the w holesale support o f Posidonius. I say ‘w holesale su p p o rt’ o f Posidonius. B u t even this putative fact m ay be based m ore on the convenient assum ptions o f m odern scholars than on hard evidence. C ertainly A ugustine, follow ing Cicero presum ably (but no t in ou r Cicero), calls him ‘m uch given to astro lo g y ’;17 and he attacks him for holding that sim ultaneous illness o f tw o brothers pointed to their being bo rn and conceived under the same configuration o f planets. Posidonius was w illing to cite connexions betw een celestial and h um an events as evidence for universal ‘sy m p ath y ’. 18 B ut no technical details o f astrology are linked w ith his nam e. Is that only the accident o f transm ission? P osidonius’ general approach to divination seems to have been an open-ended interest w hich fell short o f claim ing a causal conne­ xion betw een celestial or other natural events and particular hum an fortunes. H e believed that valid predictions could be m ade from ‘signs in n atu re’ (D iv . i 129). B ut w hat w e m ay call ‘h ard ’ astrology claim ed m ore than th is.19 T he ‘aspects’ o f the planets w ithin a zodiacal sign w ere n ot ju st indications o f an individual’s 15. This is the date favoured for the first appearance o f the influential Egyptian records fabricated under the names o f Nechepso and Petosiris, see Bouche-Leclercq, op. cit. (n. 2), 563Γ.; Fraser, op. cit. (n. 2), 1 436F It also fits the time proposed for the oldest extant star catalogue recorded in the w ritings attributed to H erm es Trism egistus, cf. N eugebauer, op. cit. (n. 1), 68, 171. 16. T hough D iodorus Siculus, w riting in the latter part o f the first century B.c., found Babylonian astrology vastly superior to Greek thought, 2.29, 17. Civ. Dei j 2 = Ft 14 Edelstein-Kidd. 18. Cf. Cic. Div. π 33ÎÏ., Fat. iii. 5. 19. 1 will distinguish, during this paper, between ‘hard’ astrology, which claims that heavenly bodies are both signs and causes o f hum an affairs, and ‘so ft’ astrology which regards heavenly bodies only as signs o f hum an affairs w ithout also attributing a causal role to the heavenly bodies; see below on Plotinus.

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destiny b u t efficient causes o f it. Posidonius does not claim this in any o f our evidence. H e th o u g h t it w o rthw hile to note connexions ‘even if the causes could n o t be fo u n d ’ (Div. 11 47). T his is Q u in tu s’ procedure in Cicero, D iv. 1: he insists tim e and again that he is interested in investigating occurrences w hich arc possible evidence o f divination, w hatever m ay be their causal explanation (e.g. 13, 16, 23, 35). If even Posidonius was n o t a dyed in the w ool defender o f technical astrology w e can better understand w hy the subject was treated sketchily and dism issively by Cicero. H e concentrated his attack on the Stoics’ supp ort for other form s o f divination, passing over, one presum es, his fam iliarity w ith N igidius Figulus, the m ost fam ous contem porary R om an expert on astrology.20 B y the tim e o f the later Pyrrhonists and Plotinus astrology was too pow erful to be dism issed as ‘incredible rav in g ’ (Div. 11 90). B ut the explanation o f this p o w er belongs to the social history o f the early R om an em pire rather than to approval o f astrology by serious thinkers. Silver age Latin literature is stuffed w ith lurid references to portents; and the im portance o f astrology extends from grass roots superstition to im perial addiction'.21 Y et even Seneca, o u t­ side the tragedies, endorses astrology only once or tw ice, and then in vague general term s.22 Epictetus ignores it, but criticises people’s reliance on augury, w ith o u t denying the validity o f divination (D iss. 11 7). M arcus A urelius, th o u g h he seems to have had a tam e astrologer, follow s Epictetus in criticising those w ho resort to divination w hen they have the innate resources to live well (Med. 11 13). If Tacitus is reliable, the general run o f Stoics o f the first century b . c . explicitly rejected astrology as the basis o f their determ inism , w hich was derived from ‘the principles and linkages o f natural causes’.23 M anilius and others claimed the 20. Cicero refers to Figulus’ interests in ‘occult’ arts in the introduction to his translation of Plato’s Timaeus. 2 1. E.g. Tiberius, Suetonius 6-9. 22. Bouché-Leclercq (op. cit. (n. 2), 552 n.3) cites Prov. 5.7, consol, ad Marciam 18.3, but builds his case on the m ore dubious claim, ‘com m e stoïcien, Sénèque croyait à l’astro­ logie’. In iVQ Seneca’s interest in predictive pow ers concentrates on lightning (n 32ff.), though he digresses to augury and astrology (11 32.7-8). He accepts stellar influences on hum an affairs but questions the astrologers’ ability to specify them. 23. Principia et nexus naturalium causarum, Atm . 6.22. The context is T iberius’ astrological prophecy o f G alba’s principate. Tacitus does not explicitly identify the determinists, w ho do not derive ‘destiny from the planets’ (fatum e vagis stellis), as Stoics. B ut that identification is implied by the ethical views he ascribes to them.

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Stoics as allies. B ut the m odern consensus on unqualified Stoic sup po rt for astrology has alarm ingly frail foundations.

II. The controversy according to Cicero H ere is C icero ’s account o f ‘Chaldaean genethlialogy’: They say that the starry circle, which the Greeks call zodiac, contains a power such that each single part of that circle moves and changes the sky in a different way according to the positions of all the stars in these and the neighbouring regions at any time; and they say that that power is modified by the planets, either when they enter that very part of the circle containing someone’s birth, or that part which possesses some familiarity (coniunctum) or harmony (consentiens) with the birth sign they call these triangles and squares. For since with the time of year and seasons such great changes of the sky take place at the approach and withdrawal of the stars (i.e. planets), and since the sun’s power brings about the effects which we see, they think it is not only plausible but also true that howsoever the atmosphere is modified so the births of children are animated and shaped, and by this force their mentalities, habits, mind, body, action, fortune in life and experience are fashioned. (Div. π 89 )

This is ‘h ard ’ astrology (see 11.19 above), b u t p retty crudely expressed.24 Cicero is aw are that horoscopes are determ ined both by the sign o f the zodiac, u n d er w hich so m eo n e’s b irth falls, and by the aspects o f the signs and their relations to the planets. B ut his one attem pt to state a technical point goes astray. It was standard doctrine that the triangular aspects o f the signs, w orked o u t by dividing the tw elve divisions into four equilateral triangles - e.g. Aries, Leo, Sagittarius - are ‘h arm o n io u s’ (sumphônoi) and parti­ cularly beneficent.25 B u t it was equally accepted that the quadratic aspects, established by inscribing three squares w ithin the circle, w ere ‘d isharm on io u s’ (asumphönoi) and m aleficent.26 Cicero how ever seems to equate fam iliarity (coniunctum, Gk. sunoikeiôsis), w hich covers b o th h arm onious and disharm onious aspects, w ith h arm on y (his consentiens presum ably rendering sumphönos), a basic confusion. B ut for all its deficiencies, C icero ’s account does contain the 24. After reaching this conclusion I found I had been anticipated by A. S. Pease in his edition o f Div. 497-9. 25. See Bouché-Leclercq, op. at. (n. 2), 169. 26. Ibid. Γ70.

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single m ost pow erful reason w hich the astrologers could cite in their ow n favour, and cite it they did ad nauseam. T h e sun brings ab ou t visible effects o f fundam ental im portance to the earth; and those effects coincide w ith different positions o f the planets at different tim es. Since the atm osphere is directly affected by celestial pow ers, w e are to infer th at it also transm its less evident influences w hich control h um an births and fortunes. (This point is developed w ith infinitely m ore sophistication by Ptolem y.) C icero ’s critical com m ents establish points against astrology w hich recur constantly in subsequent argum ents. H e begins w ith the problem o f tw ins (11 90), a difficulty for astrology developed at great length by A ugustine (civ. Dei vi 2 -6 ).27 T w ins have sim ilar appearance (forma), bu t their lives often take very different courses. U nlike A ugustine, Cicero leaves it to the reader to infer w hy tw ins are a fundam ental difficulty for astrology. His point seems to be the inconsistency o f sim ilar appearances and different fortunes. T w in s, being b o rn at alm ost identical tim es, look like a good exam ple for astrologers w h o can explain their sim ilar appearances by reference to the influence o f sim ilar atm ospheric and celestial conditions. B ut it should then follow , according to astrology, th at their subsequent lives will take sim ilar courses. Yet this is disproved by historical exam ples.28 C icero’s second objection is astronom ical (11 91). T he astrolo­ gers take the m o o n ’s conjunctions w ith the planets as observable evidence o f causes w hich control people’s births. B u t we know from m athem atics that the m oon, w hose light is b o rro w ed from the sun, is very close to the earth by com parison w ith its distances from M ercury, V enus and the sun, and that the rem aining planets together w ith the heaven itself are vastly distant from the sun. ‘W hat contact then over the alm ost infinite distance can extend to the m o o n o r rather to the earth?’ This argum ent, w hich 1 will call relative distances, looks rather good at first glance. T h e astronom ical facts are broadly accurate 27. Cicero (loc. cit.) says it was the problem o f tw ins which persuaded the Stoic Diogenes o f Babylon that astrology could predict only natural character and aptitude, not the specific circumstances o f a future life. 28. N igidius Figulus had an answer to this challenge: the heavens m ove at such speed that even a tiny interval o f tim e (such as that separating the birth o f twins) makes a vast difference to the planetary relationships in the zodiac, Augustine, civ. Dei. vi 3. This prom pted the obvious rejoinder, how could such a fleeting m om ent be grasped by the astrologer?, Favorinus ap. Aul. Gell, xiv 1.26.

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and the treatm ent o f the m o o n as categorically sim ilar to the planets is no do u bt a w eakness o f all astrology. T he sheer distances o f the planets from the earth also present a challenge w hich the astrologer can reasonably be expected to answ er. It is perhaps then surprising th at this arg um en t is n o t repeated in the principal later attacks on astrolo g y.29 N eith er Favorinus n o r Sextus uses any version o f it. T he question o f the earth ’s distance from certain heavenly bodies docs arise in G em inus and in P lotin u s.30 G em inus denies that any ‘effluences’ from the sphere o f the fixed stars reach the earth (17.16), and he also denies that the planets as well as the fixed stars can cause the earth to g ro w h o t (17.38). B ut he adm its that planetary effluences do fall upon the earth, and he raises no special difficulties about the m oon in relation to the planets. His rem arks, m oreover, are only m arginally significant since their context is not horoscopic astrology but the influence o f heavenly bodies on the w eath er.3132 P lo tin u s’ criticism s are m uch m ore barbed. R ecognising that the planets are far below the stars w hich form the zodiacal signs he finds it ridiculous that the planets should differ in their disposi­ tions tow ards m en according to their positions in the zodiac (11 3.3). He tartly dismisses the w hole theory o f planetary aspects, and is particularly effective in handling the m o o n ’s relations w ith the planets: As for their statem ent that the m o o n w hen she is full is good in conjunction w ith a particular planet, b u t bad w h en she is w aning, the reverse w o uld be true, if this sort o f thing is to be adm itted as possible at all. For w hen she is full in relation to us she w o u ld be dark in the other hem isphere to the planet w hich stands above her . . . It w ill m ake no difference w hatever to the m o o n h erself w h at phase she is in since h a lf o f her is alw ays illum inated, (π 3 .5 P 2

These points are closer to C icero ’s objections, b u t they do n o t tu rn on the question o f the planets’ distance from the earth, n o r on the m o o n ’s relative closeness to the earth. Plotinus, it seems to m e, is arguing w ith m uch greater insight into the nature o f astrology, 29. But cf. Anon. H crm ippus 2.44, cited by Pease in his edition o f D iv. ad loc. 30. Gem inus was probably C icero’s contem porary, see G. Aujac’s Budé edition o f the Eisagöge (Paris, 1975). 31. Thus 1 fail to understand how E. Pfeiffer could think Panaetius was G em inus’ source, Studien zum antiken Sternglauben (Leipzig, 1916), 59. 32. Transi. A. H. A rm strong, Loeb ed.

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and his criticism s are m o re telling because they are m ore precise. As P tolem y and M anilius m ake clear, an im p o rtan t feature o f the m o o n ’s conjunction w ith planets, for casting horoscopes, lay in the m etho d it provided for establishing the degree o f the zodiac to be taken as a starting point for establishing the planetary influences on the birth. Wc must then take the syzygy most closely preceding the birth, whether it is a new moon or a full moon . . . and . . . we must sec what stars rule it (sc. the degree) at the time of the birth. ( Tetrab. hi 2, pp. 231-3 Loeb cd., cf. Manilius 2.720ff.) For this purpose the relevance o f the m o o n ’s relationship to the planets is geom etrical. T he m o o n ’s relative closeness to the earth and its problem atical contact w ith the planets do n o t seem points w hich dam age the astrology in the w ays that Cicero m aintains. If his blow s here are glancing ones this m ay explain w h y little use was later m ade o f his argum ent from relative distances. C icero ’s third arg u m en t m ay be called the relativity o f earthly locations (D iv . 11 92-3). M uch o f it is loosely expressed b u t the essential claim am ounts to this: the astrologers say that the births and subsequent fortunes o f everyone born at the same tim e are the same, wherever they are horn. B u t elem entary astronom y show s that the risings and settings o f the planets do n o t occur at the same tim e in all places. G iven the astrologers’ doctrines about celestial influences they m u st adm it th at people b orn at the same tim e can have different natures on account o f the constant variation o f the horizons. B ut this is inconsistent w ith their thesis that those born at the sam e tim e, no m atter w here they are born, are born under the same celestial conditions. This arg u m en t is repeated by later Sceptics, in slightly different form s. Favorinus insists that C haldean observations can have no validity outside their o w n region (Aulus Gellius χ ιν 1.7-11): although it is obvious that the astrologer’s stars cause different w eather at the sam e tim e in different places they claim that in hum an affairs the stars alw ays show the sam e face w herever they are view ed from . Sextus Em piricus uses relativity o f earthly places in giving his ‘m ost conclusive’ argum ent, as he calls it, against the possibility o f establishing an accurate horoscope (M v 83-5); ‘a sign o f the zodiac does not appear to all at the same tim e . . . b u t that w hich seems to one set o f people to have risen appears to others to be quite beneath

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the earth . . . Such relativity (or latitude dependence, as w e w ould say) is evident from the fact that certain o f the fixed s ta r s . . . do not appear to the inhabitants o f every region at the same tim e. ’ As B ouché-Leclercq points o u t (pp. 581 ff.), this argum ent, from the relativity o f places, was probably irrelevant even to B abylonian astrology; for on tablets w e find such inscriptions as: ‘if the m oon is visible on the 30th, a good om en for Acadia, b ut a bad one for Syria’. As an objection to Greek astrology, as represented by M anilius or Ptolem y, it misses the m ark com plete­ ly. B oth w riters distinguish sharply betw een stellar determ ination o f nations and horoscopes o f individuals. A ccepting the enorm ous regional differences betw een parts o f the earth, they explained these by reference to a highly com plex set o f different planetary and zodiacal influences. T hus, according to Ptolem y, all nations fall under four quarters o f the heavens, determ ined by the four triangular relations o f the zodiac (11 3, p. 129 Loeb ed.). These quarters in tu rn w ere subdivided geographically and astronom i­ cally so that, for instance, B ithynia is situated in the south w est o f the north-eastern quarter. Its inhabitants, being in the quarter o f Cancer, Scorpio and Pisces, w hose co-rulers are M ars, Venus and M ercury, are ‘exceedingly depraved, servile, toilsom e, w orthless . . . ’ (ibid. p. 149). M anilius actually accepts the relativity argu­ m ent, and w rites: ‘there are as m any w orlds as there are parts o f the w orld, ju s t as the stars shine u p o n the specific regions to w hich they have been allocated and shed their clim ate on the nations that lie ben eath’ (4.741-3). Place as well as tim e is a fundam ental co-ordinate o f G reek astrology, and the treatm ent o f it occupies m uch o f the second book o f P to le m y ’s Tetrabiblos. Since later authorities on G reek astrology did n o t accept the prem iss o f C icero ’s objection concerning their indifference to earthly locations, w e m ay account for his p oin t either as due to ignorance on his part (as B ouché-Leclercq does, pp. 58of.), or as a purely dialectical ploy. Ignorance will hardly excuse Favorinus and Sextus. B ut this w o u ld no t be the first tim e in G reek philosophy w hen an op po n en t m isrepresents his target in order to score a point. It does seem increasingly clear, at all events, that C icero k n ew very little about G reek astrology in its developed form . It is also probable that the highly developed ethnology and regional geography in P tolem y w ere the outcom e o f challenges to astrology to explain the com m o n characteristics o f one ethnic

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group and their differences from others. C icero ’s next set o f objections is o f particular historical interest precisely because P tolem y w ent o u t o f his w ay to respond to m any o f them . For C icero astrology offers a com plete and irreducible explana­ tion o f everything concerned w ith the birth, behaviour, character and fortunes o f a person. In that case, he argues, astrologers insanely ignore the enorm ous changes to the sky bro u g h t about by changes o f the w eather, w hich can vary greatly betw een adjacent regions (Din. 11 94). D isallow ing the w eath er’s influence on people’s births, they insist on the utterly obscure m odification o f the sky by the m o o n and stars. F urtherm ore, the astrologers’ celestial causation totally fails to explain the obvious im portance o f genetics and parental influence. In addition, the tim e o f birth cannot be relevant to the life som eone lives since people b o rn at the same m o m en t have different dispositions and lives and fortunes - ‘u nless,’ he adds, ‘w e suppose that no one was con­ ceived and b o m at ju st the same tim e as A fricanus’ (11 95). F urtherm ore, according to astrology, it w ould no t be possible, as it evidently is, to change and im p ro ve by m edicine or training, defects w ith w hich som eone is bo rn (11 96). Finally, geographical variation is a m uch m ore effective candidate than lunar contact for causing the enorm ous physical and m ental differences betw een nations. A fter detailing these objections Cicero concludes by rejecting the vast antiquity - 470,000 years - o f B abylonian re­ cords concerning births (and, presum ably, celestial data, 11 97).33 All these points, Cicero im plies, w ere m ade by Panaetius. He him self p u rp o rts to supplem ent them by four further objections w hich m any scholars suppose to derive from C arneades.34 The first tw o o f these pick up one o f his previous argum ents and develop it, in effect, as a dilem m a: m any people, presum ably not born under one and the sam e star, m ay have a com m on death, as in the battle o f Cannae. B ut equally, there can hardly be only one star under w hich som eone o f unique character, such as H om er, 33. The supposed antiquity o f the observations was a key item in the astrologers’ argum ents; cf. Bouché-Leclercq, op. cit. (n. 2), 574, for other evidence. 34. For C icero’s sources see Pease’s edition o f D ip., p. 26. In a w ork know n to m e only via Pease, Schiche, De fontibus librorum Ciceronis qui sunt De Dip. (1875), argued that Cicero drew on Panaetius because, in the absence o f an early Stoic defence o f astrology, the Academic Sceptics had not provided the contra arguments. For reasons given above I think this m ay well be correct in general. B ut it is probable, as m any have held, that C icero’s concluding argum ents have Academic background.

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was born. So, he im plies, astrology can neither account for an individual’s birth n o r his death. C orrespondingly, it fails to m eet the fact that individuals b o rn at different tim es m ay have the same destiny, and that those b o rn at the same tim e differ in their fortunes (11 97). T his argum ent, one o f his strongest certainly, I will retu rn to. A further objection, w hich turns up again in Favorinus (Aulus Gellius 14.1.31) and A ugustine (civ. Dei v 7), concerns animals. T heir fortunes should also be revealed by astrology, says Cicero, which w ould be absurd .3536Lastly, Cicero achieves a rhetorical flourish by noting that horoscopes are refuted every day, such as those predicting to the trium virs that they w ould each die at hom e in glorious old age (n 99). W e have n o w surveyed C icero’s w hole case against astrology. His opening objections seek to be technical, b ut suffer from lack o f know ledge, at least w hen set against M anilius and Ptolem y. The subsequent argum ents, tho ug h dialectical, are m ore pointed and, perhaps for this reason, appear to have been m ore influential. (Their effectiveness m igh t be evidence o f their Carneadean au­ thorship.) In order to assess them , historically and conceptually, it seems best n o w to let P tolem y him self have the floor. This m ay enable us to ju d g e som e o f the developm ents in astrology, w hich philosophical controversy stim ulated; and it will provide us w ith the context for evaluating the objections o f Favorinus and Sextus Em piricus, P to le m y ’s near contem poraries. III. Ptolemy’s defence o f astrology Seldom , one could say from our ow n perspective, have k n o w ­ ledge, intelligence, and rhetorical skill been m ore m isused than in the opening three chapters o f P to lem y ’s T e t r a b i b l o s H e begins m odestly by stressing the inferiority o f astrology to astronom y in our sense o f the term (1 1, pp. 3-5 Loeb ed.). A strology does not establish the certainty w hich can be attained in our pure observa­ tion o f heavenly bodies. In A ristotelian fashion Ptolem y contrasts the ‘w eakness’ and ‘un certain ty ’ o f enm attered things w ith the

35. Augustine (loc. cit.) says that som e astrologers met this point by giving horoscopes of animals! 36. T he Tetrabiblos has Syrus as its dedicatee, like the Syntaxis, but astrology is not m entioned in the astronomical work.

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everlasting invariance o f the objects the astronom er studies.37 But this concession is n o t sufficient to render astrology impossible: evidence show s that m ost events, taken quite generally, m anifest the causal p o w er o f the surrou nd ing heavens. Som e have charged astrology w ith being com pletely incom prehensible on account o f its particular difficulties (cf. Sextus, M v 95); others have criticised it as useless on the grounds that (im plying, ‘assum ing its predic­ tions tru e ’) one cannot escape things that are know n. Ptolem y proposes to answ er these objections, by discussing the possibility and utility o f astrology. U n derp in n in g his entire cosm ology is the A ristotelian theory o f five elem ents, crucially m odified by the Stoic belief that the m ovem ents o f the aithër directly affect the sublunar elem ents w ith w hich it is in contact (1 2, pp. 5—7 Loeb ed.). A risto tle’s distinction betw een the heavens and the sublunar region influences P to lem y ’s epistem ology, as w e have seen. B ut, as an astrologer, he cannot entertain a physical th eory w hich underm ines the unity o f the cosm os. W hen it com es to explaining the behaviour o f the five planets and the sun and m o on he uses the A ristotelian theory o f elem entary qualities for quite un-A ristotelian purposes: assum ing that the p rim ary pow ers in the heavens are heat, from the sun, and m oisture, exhaled from the earth, P tolem y identifies the su n ’s causal efficacy w ith heating and drying (the A ristotelian properties o f fire), and the m o o n ’s w ith m oistening and heating (the Aris­ totelian properties o f air). T he tw o planets, Jup iter and Venus, share in the sam e pow ers as the m oon; this nature accounts for their being regarded as beneficent. M ars and Saturn m anifest extrem es o f dry heat and dry cold respectively; they are thus opposed to the beneficent planets. M ercury, ow ing to its nearness to the sun and the m oon, som etim es has the po w er to dry and at other tim es the p o w er to m oisten (1 4, pp. 35-9 Loeb ed.). This sym m etrical th eo ry o f elem entary pow ers and com bina­ tions (based u p o n unargued inferences from the planets’ relative positions) enables P tolem y to dem ythologise astrology and to

37. T he same point is m ade in the preface to the Syntaxis where, with reference to Aristotle, Ptolem y distinguishes the different sciences (ed. Heiberg (Leipzig, 1898), I p. 5 lines 7ff.); but, in un-Aristotelian vein, he rates the certainty o f the results m athem atics achieves above those o f theology. Physics too for Ptolem y is ‘conjecture’ (eikasia) rather than ‘know ledge’ (katalëpsis) ow ing to ‘the instability and obscurity ot m atter’ (ibid. p. 6 lines n ff.).

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relate diurnal and seasonal changes to the elem ental effects o f the sun, m oon, and planets. T h e theory is also presupposed in his basic argum ent concerning the possibility o f astrology. W e are to envisage a universe in w hich the pow er o f the eternal aithër penetrates to and changes the entire mass o f sublunar fire and air surround ing the earth, w hich elem ents in tu rn encom pass and change earth, w ater, and all the contents o f the earth (i 2, pp. 5-7 Loeb ed.). P tolem y offers three pieces o f celestial evidence, in decreasing orders o f obviousness. First, the sun in conjunction w ith the surrou nding heaven is constantly ‘disposing’ (diatithësi) things on the earth, and its regular heating and cooling effects etc. accord w ith the order o f its positions in the zenith.38 Secondly, the m ovem ents o f rivers, the tides, and the life cycles o f living things are ‘sym pathetic’ to the m oon, w hich, being the nearest heavenly bo dy to the earth, distributes to it ‘the greatest effluence’. So far so good, the sceptic m ay say. N o w comes the third and dubious claim. B ut note P to le m y ’s skill in m aking it. W ith an unobtrusive ‘an d’ (te) he m oves to the m ovem ents o f the fixed stars and planets (1 2, p. 6 Loeb ed., 4 lines up). ‘Soft’ astrology (see n. 19) is handled first: these m ovem ents effect very m any ‘indications’ (iepisëtnasiai, the technical w ord) o f hot, w indy, or snow y w eather . . . N ext, w ith studied vagueness, w e get the ‘h a rd ’ astrology: ‘and further, their aspects to one another, as their contributions com e together and m ix together, produce very m any varied changes’ (p. 8 Loeb ed., lines 1—4). N o w , tw o genitive absolutes linked by men and de: ‘on the one hand, the pow er o f the sun is dom inant for the general arrangem ent o f quality, b u t the rem ain­ ing heavenly bodies assist or oppose in particular respects’ (ibid. 4- 7) ·

T h e logic and antitheses are beguiling. Y ou m ust grant the obvious p o w er o f the sun. As for the m oon, w hose terrestrial influence yo u have already conceded, she is cleverly relegated to the de clause, as one o f the loipa, the ‘rem ain in g ’ heavenly bodies. B ut another antithesis subdivides these lesser lights o f auxiliary pow er: ‘the m o o n m ore obviously and continuously, as in its new ,

38. N ote the Stoic adverbs expressing cosmic order, tetagmvfiôs and akolouthos (middle o f Loeb p. 6).

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quarter, and full phases, the stars (i.e. planets) over longer intervals and less distinctly, as in their appearances and occulta­ tions and approaches’ (ibid. 7-11). Is it intellectual honesty or rhetorical skill w hich accounts for P to le m y ’s evasions here? T he to u g h em pirical argum ent has vanished, leaving only ‘very m any varied changes’, th ro u g h the planets’ interactions, and the relative ‘o b scu rity ’ o f their auxiliary role as astrological appendages clinging uneasily to the pow ers o f the sun and m oon. This chapter has a long w ay still to run. B ut fro m n o w on P to lem y ’s case will rest on rhetoric and dialectic. W e are asked to grant, w ith farm ers, sailors, laym en and animals as our su p p o r­ ters, that the births o f living things conform to the tem poral state o f the heavens (1 2, pp. 8-11 Loeb ed.). True, the sailor’s experience o f the w eather in its relation to the heavens is a fallible source for predictions. ‘B ut if a m an know s precisely the tim es and places o f all celestial m ovem ents, and if he know s at least such potential effects as the su n ’s heating and the m o o n ’s m oistening, and if he is capable o f distinguishing the specific quality resulting from the m edley o f everything, then w hat is to prevent him from being an infallible w eather forecaster?’ (paraphrase o f pp. 10-11 Loeb ed.). ‘W hy too should he n ot be able to perceive the general quality o f an in dividual’s idiosyncrasy from the state o f the heavens at the tim e o f his birth? For instance, his generic type in body and so u l.’ A nd w hy should he n o t be able to perceive ‘w hat will happen to him at different tim es’, th ro u g h the beneficial or adverse characteristics o f ‘this kind o f heaven for this kind o f m ake u p ’ (1 2, pp. 12-13 Loeb ed.). P tolem y rem arks that the possibility o f astrological know ledge is established by such considerations (loc. cit.). He then m akes a n u m b er o f im p o rta n t disclaim ers. H e grants to the critic that inexpert practitioners have given currency to the belief that even correct predictions depend upon chance. Proper astrology, m oreover, has been besm irched by vulgar soothsaying, as hap­ pens too w ith philosophy. B u t his strongest defence is his greatest concession. H e adm its that even the expert is likely to m ake m any m istakes (1 2, pp. 14-15 Loeb ed.). This is due b o th to the sheer m agnitude o f the undertaking, b u t also to the only approxim ate relationship betw een the ancient configurations o f the planets, w hich form ed the basis o f the ancients’ records, and the present

state o f the heavens. H ere then, in the data o f astrology, w e are offered grounds for erroneous predictions. Finally Ptolem y restores o u r faith in his scientific integrity by utterly disclaim ing com plete causal efficacy for the findings o f astrology (i 2, pp. 16-19 Loeb ed.). It turns out that, in his view, the state o f the heavens at b irth is only the m ost pow erful o f a w hole range o f im p o rtan t co n trib u to ry factors. These include genetics: a horse begets.a horse, and a m an begets a m an, under the same celestial conditions. G eographical differences, nurture, and custom s also contribute to the particular w ay o f life. A strology then, th o u g h necessary, is far from sufficient to explain all the details o f som eone’s life. B ut, in spite o f its fallibility, it is a divine art, and w e should be grateful for w hat it can provide. T he astrologer is quite entitled to base his predictions on any additional m aterial from ethnology, geography, education, etc. In the th ird chapter o f Tetrabiblos 1 Ptolem y m akes the task o f the critic still m ore difficult. His principal subject here is the utility o f astrology, b ut the argum ents w hich he uses to establish this also help to answ er som e o f the standard criticism s o f the a rt’s general rationale. A strology, he claims, is useful because know ledge o f the future is one o f the m in d ’s goods, and that know ledge has a practical application to an individual’s bodily constitution (1 3, pp. 20-1 Loeb ed.). T he criticism o f astrology for being superfluous fails to recognise that fore-know ledge o f necessary events makes for m ental health by inducing equanim ity (pp. 22-3 Loeb ed.). But P to lem y ’s m ost effective defence draw s on the earlier adm ission that astrology doesn’t establish com plete and absolute causal laws. Celestial causes are n o t like irrevocable divine im peratives such that no other cause can counteract them (pp. 22—31 Loeb ed.). O w in g to the difference betw een the im m utable heavens and the changeable nature o f earthly things, celestial m ovem ents provide only ‘first causes’. These are o f the form , such and such will happen if no th in g con trary counteracts. First causes necessitate effects only if n oth ing stronger intervenes. T hus, on the basis o f celestial conditions operative at so m eone’s birth, in conjunction w ith that p erso n ’s constitution, an astrologer m ay predict a disease i f no natural preventive m easures are taken. T he thesis that astrology identifies predisposing conditions enables P tolem y b o th to defend its utility as a quasi-m edicinal art,

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and to m eet the objection that its predictions underm ine hum an precautions. His astrologer does n o t advance exceptionless gener­ alisations, bu t gives reasons for expecting certain occurrences. As to the supposed difficulty o f vast num bers perishing at the same tim e (C icero’s C annae exam ple), P tolem y takes the occurrence o f natural or h u m an disasters to show that the celestial causes o f general effects are always m ore pow erful than those w hich affect individuals in isolation (11 1, pp. 118-19 Loeb cd.). Follow ing this principle he discusses astrology in its application to nations (Book 11) before he treats the horoscope o f individuals (Books m -iv). Even on the evidence o f this b rie f study it should be plain that Ptolem y, or his sources, have a conception o f astrology w hich explicitly rebuts the principal criticism s found in Cicero. C icero ’s arg um en t concerning the relativity o f earthly locations is coun­ tered by the distinction betw een national and individual celestial influences, and the insistence that geographical and ethnic differ­ ences are the strongest effect produced by different celestial conditions. By denying that astrology identifies com plete causal conditions for an individual’s life P tolem y underm ines C icero ’s criticism o f the om ission o f genetics and nurture. B y m aintaining that astrological predictions are conditional on the absence o f countervailing causes P tolem y is able to accom m odate C icero ’s evidence for the am elioration o f congenital defects. T h e im p o rtan t dilem m a - different lives ensue on births at the same tim e versus co m m o n deaths follow ing births at different tim es - is answ ered im plicitly. P to le m y ’s insistence on the effect o f non-celestial causes, and his claim that general effects have stronger celestial causes than individual characteristics, enable him to provide som e answ er to m ost p roblem cases that could be advanced against him . H e adm its that m any predictions are b o u n d to fail. H e does not b o th er to answ er the problem o f tw ins or anim al horoscopes. IV . Favorinus, Sextus Empiricus, and Manilius It seems highly likely that P to lem y ’s astrology, b o th in its technical details and in its buttressing against criticism , m anifests developm ents o f the tw o hu ndred years separating him from Cicero. I am n o t in a position to pronounce on the subject o f his sources. B ut his indebtedness to Posidonius, stressed by n in eteenth-century scholars, seems highly dubious. O n technical

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details P tolem y and M anilius, one hundred years earlier, appear to agree in the m ain. B ut M anilius’ cosm ology is m uch m ore decisively Stoic, and his astrology, as w e shall see, invites the kind o f objections w hich P tolem y took pains to avoid. P to le m y ’s opening chapters, w ith their theoretical points and defences against criticism , probably contain a good deal o f w ork that is his o w n .39 Support for this view can be derived from Sceptical criticism . T he Sophist and Academic, Favorinus, m ay have been too old to read the Tetrabiblos.40 C ertainly his criticism s o f astrology are close to Cicero, w hich has persuaded m any scholars that they derive from com m on A cadem ic m aterial. Like Cicero, Favorinus takes astrology to prom ise that every detail o f h um an life is controlled by the stars. H e ridicules the assum ption that hum an affairs are analogous to tidal m ovem ents in their causal connexion w ith heavenly bodies (xiv 1.4). Passing over M anilian and Ptolem aic treatm ent o f the astrology o f nations he uses C icero ’s objection concerning the relativity o f earthly locations (xiv 1.7 10). H e repeats the C iceronian dilem m a concerning the lack o f congruence betw een different lives w hich begin at the same tim e, and com m on deaths o f those b orn at different tim es. T he problem o f tw ins and anim als com es up again. B ut several new objections are m ade. W hy sho u ld n ’t there be m ore planets than those w hich have been observed? —a good, and as it turns out, correct point (xiv 1.11-12). Even if one concedes only the existence o f the visible stars and their visibility from all locations, astrology requires an im possibly long tim e for its observations to be effective: records are based on the correlation betw een celestial m ovem ents and hum an affairs, bu t the same celestial m ovem ents will no t recur for an alm ost infinite n u m b er o f years (xiv 1.14-18). (Ptolem y, as has been m entioned, acknow ­ ledged the inexact correspondence betw een ancient records and 39. A case for Posidonius as P tolem y’s source for his opening chapters o f Tetrab. was stated by F. Boll, Studien über Claudius Ptolemy (Leipzig, 1894), >3 iff. T hough accepted by m ost subsequent w riters it seems to me to be a conspicuous example o f the fallacies o f treating intellectual history by the m ethods o f stem m atology. Such parallels as Boll cites betw een Cicero etc. and Ptolem y do not justify the supposed influence o f Posidonius. 40. O u r evidence for his opposition to astrology comes from Aulus Gellius who sum m arised a lecture he heard Favorinus deliver in Greek at Rome, xiv 1.1-2. For his and P tolem y’s dates see n. 46 below.

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the contem porary state o f the heavens ( Tetrab. 1 2, pp. 14-15 Loeb ed.)·) A nother new p oint concerns the relation betw een stars at the tim e o f conception and those at the tim e o f b irth .41 Favorinus very reasonably assum es that the celestial configurations at these tw o tim es will differ, and infers that this im plies tw o different fortunes for the same individual (χ ιν 1.19). Ptolem y, how ever, denies the prem iss o f the objection, m aintaining that a child is naturally born under a configuration sim ilar to that governing its tim e o f conception (in 1, pp. 224—7 Loeb e d .).42 Favorinus includes a n u m b er o f n o t very im pressive dialectical objections, w hich I pass over. H e does how ever touch on a point w hich Sextus develops at m uch greater length - the difficulty o f grasping the m o m en t o f the horoscope. It appears that astrologers had responded to the problem s over tw ins by claim ing that no tw o people are b o rn at exactly the sam e m o m e n t.43 Favorinus seeks to ridicule the n o tion that m en could grasp the tiny intervals o f tim e w hich allegedly cause such great differences in the arrangem ents o f the heavenly bodies (xiv 1.26). (Ptolem y ack­ now ledges the practical difficulty o f determ ining the canonical degree o f the zodiac, b ut offers lengthy instructions about this w hich are n ot m entioned by the critics (m 1-2, pp. 222-35 Loeb ed.).) T aken generally, Favorinus’ objections show little m ore ac­ quaintance w ith M anilian or Ptolem aic astrology than do the argum ents o f C icero. Sextus Em piricus, w ritin g perhaps sixty years later, is a m ore effective critic. In his norm al fashion he lets his opponents first develop their position, and his exposition -of this is m ore detailed and technically proficient than the sum m aries o f other sceptics. A ccording to the Chaldaeans, he says, ‘sym ­ p a th y ’ betw een earthly and celestial things effected by ‘effluences’ from the latter m akes the ‘seven stars’ efficient causes o f all affairs o f life, w ith co-operation from the signs o f the zodiac (M v 4-5). This then is ‘h a rd ’ astrology w ith o u t any o f P to lem y ’s concessions regarding non-celestial causes.

41. Cf. Augustine, civ. Dei v 5. 42. If Augustine (loc. cit.) is to be believed, Posidonius had already made this claim in reference to a particular pair o f twins. 43. See Bouché-Lcclercq, op. cit. (n. 2), 588-9.

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Sextus proceeds to outline quite accurately the basic doctrines o f aspects and cardinal points etc. His refutation is divided into tw o parts: a b rie f survey o f w hat he calls ‘long-range objections’, and a m uch longer attack ‘at close q uarters’ (ibid. 43—8, 50-106). T he detailed criticism is largely focused on the im possibility o f estab­ lishing an accurate horoscope. Sextus m ethodically exposes the problem s o f defining the m om ent o f birth or conception, the m arvellous absurdity o f the signalling system used to alert the observer o f the sky that the birth has occurred, and the difficulty o f establishing the rising star in the zodiac.44 Som e o f the stock objections we have noted already are later developed, but only Sextus exploits the absurdity o f associating hum an characteristics w ith the m yth o lo g y o f the zodiac (v 95-102). This sum m ary does no t do ju stice to all his argum ents. B ut though they contain points w e have no t m et before, their principal target is hardly Ptolem aic astrology but som ething m uch m ore prim itive. At this point M anilius can help us to evaluate the interaction betw een philosophy and astrology. If Ptolem y has taken trouble to protect astrology against the standard argum ents, the same can only in p art be said o f M anilius. He does have answers to the argum ents about the relativity o f earthly locations (4.696fr.); and his guidelines for establishing a horoscope look better than the crudities attacked by Sextus (3.203-509). B ut he is still vulnerable to m any o f the stock criticisms. H e repeatedly m akes the stars responsible for every circum ­ stance o f hum an life (e.g. 3 .57ffi). H e makes w ild claims about the infallibility o f astrological predictions (2.132). H e sees no problem in asserting that ‘tiny m ovem ents o f the sk y ’ cause enorm ous changes o f fortune (1.53-7), and that records are based on observations o f the stars’ return to their appropriate positions (1.58ft.). B oth o f these claims are attacked by Favorinus (Aulus Gellius X I V 1.15, 26). Like Ptolem y, M anilus uses the obvious effects o f sun and m oo n as evidence for the validity o f astrology in general, conceding the rem ote distance o f the planets and their unobvious causal pow er (2.82, 4 .8 6 9 ^ ). U nlike Ptolem y, his general thesis is underpinned no t by a physical theory o f elem entary properties, bu t by a Stoicising deism w hich treats m an 44· Ptolem y himself com m ents on the fallibility o f the instrum ents used by astrologers (including the w ater-clock attacked by Sextus, M v 75-7) apart from ‘horoscopic astrolabes’, 'I'etrab 111 2, pp. 228-31 Locb. cd.

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as an im age o f god, seeking h im self am ong the stars (4_886ff.). M anilius constantly insists that ‘fate rules the w o rld ’ (fata regunt orbem, 4.14). H e blandly attributes hum an vice and virtue alike to the sky w ith o u t seriously facing problem s about m oral responsi­ bility (4.108-18). H ere then we have ‘h a rd ’ astrology w ith a veneer o f philo­ sophical colouring. It is difficult to believe that Stoic philosophers can have adm ired M anilius’ proficiency. A gainst such a crude fatalism as M anilius defends m any o f the argum ents o f Cicero, Favorinus, and Sextus do well enough. If M anilius is typical o f ancient astrology - and the evidence suggests he was b etter than som e - P to lem y ’s achievem ent, or m isplaced ingenuity, m ust gain ou r respect. B ut perhaps the ‘h a rd ’ astrologer w ould say that P to le m y ’s skill in answ ering the critics was bo u g h t at to o high a price. H e has m ade it difficult to refute astrology, b u t his disclaim ers are so extensive that they seem to m ake it dispensable. V. Some later developments I m ust pass over the influence o f P to lem y ’s Tetrabiblos in antiqui­ ty. T he later N eoplatonists to o k it seriously and com m entaries on it w ere attributed to P o rp h y ry and P roclus.45 B ut here I shall confine m y self to Plotinus. P lo tin u s’ attitude tow ards astrology is com plex. As a Platonist he defends the organic unity o f the physical universe, and is quite w illing to grant the stars som e causal influence on hum an affairs. B ut such theoretical su pp ort as he m ight appear to lend to astrology does n o t prevent him from being an acute and strong oppon ent o f its o rth o d o x claims. In his early treatise O n D estiny’ (m 1) he totally rejects the n o tion that the stars are causes o f everything ( h i 1.5-6), b ut he does show sym pathy for ‘so ft’ astrology (see n. 19 above): W e m ust rath er say th at the m o v em en t o f the stars is for the preservation o f the universe, b u t th at they p erfo rm in addition another service; this is that those w h o k n o w h o w to read this so rt o f w ritin g can, by looking at th em as if they w ere letters, read the future fro m their patterns, discovering w h at is signified by the system atic use o f analogy, ( h i 1.6 transi. A rm stro n g , Loeb ed.) 45. See Boll, op. cit. (n. 39), 127.

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T he m eth o d is rather lam ely exem plified by the high flight o f a bird w hich m ig h t be said to indicate heroism . H aving ju st rejected any decisive role for the stars as causes, Plotinus has hardly prepared us for the cryptographic function w hich he does concede to th e m .46 H e returns to the subject m ore fully in the later essay, ‘O n w hether the stars are causes’ (11 3). H ere his attack on ‘h a rd ’ astrology is m u ch m ore closely integrated w ith basic doctrines o f his ow n. B ut he again accepts the stars as signs, on the Platonic principle that the parts o f the w orld organism all contribute to the w hole (11 3.7). ‘T h ey signify everything that happens in the sensible w orld , b u t do o th er things, the things w hich they are seen to d o ’ (11 3.8). Y et this is no t all, for Plotinus. He rem inds us o f statem ents from the Republic and Timaeus concerning P lato ’s astronom ical interpretations o f fate and the passions bestow ed on the soul by the lesser gods = the heavenly bodies (11 3.9). ‘These statem en ts,’ he says, ‘bind us to the stars, fro m w hich w e get our so u ls.’ B u t this apparent concession to astrology is equivocal, since only ou r descended nature is thus affected. T he unem bodied, transcendent self is no t b o u nd up w ith stellar influences. As for our com posite nature, the im p o rtan t thing is to identify the relevant causes. T he heavens can contribute to certain hum an states, e.g. physical strength, a farm er’s success, but they are irrelevant to m any circum stances, such as inherited w ealth, fame, occupation (11 3.14). O verall P lo tin u s’ position seems to be a w eakened version o f Ptolem aic astrology, b u t w ith o u t any com ­ m itm en t to its technical doctrines or interest in horoscopes. O u tsid e philosophical debate little note was probably taken o f Ptolem aic or Plotinian refinem ents. T he m easure o f P to lem y ’s sophistication is clearly seen w hen w e com pare his handling o f objections to astrology w ith the efforts o f Firm icus M aternus

46. For his critical rem ark s P lo tin u s seem s to be considerab ly in d eb ted to the Sceptical tra d itio n o u tlin ed above; b u t the first p art o f m 1.6 also recalls (th o u g h w ith a different em phasis) P to le m y , Tetrab. I 2, pp. 1Ô-19 L oeb ed. T h ere is no direct evidence that P lo tin u s read P to lem y , b u t n o th in g in th eir relative dates excludes this. E. L am m e rt (RE s.v. P to lcm aiu s 6 6 , x x m 2 ( 1 9 5 9 ) , col. 1789) places P to le m y ’s life b etw een a . d . 83 an d 161. T h a t h e w as active b etw een the years 127 and 147 is settled by astron om ical o b se rv atio n s in the Syntaxis and the date o f th e Canobic Inscription, L am m e rt col. 1788. T h u s P to lem y an d F avo rinus w e re m o re o r less direct co n tem p o raries, F av orin us being b o rn in the 80s a . d . and livin g o n b ey o n d 143, see W. S chm id, R E ad loc. vi 2, cols. 2079-81.

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w hose eight book tract called Mathesis was w ritten in the fourth century A.D.47 F irm icus’ w o rk frequently recalls M anilius but he follow s P tolem y in answ ering objections to astrology before he expounds the system (1 2). His m ain lines o f defence are a curious com bina­ tion o f deist cosm ology and rhetorical adaptation o f the objections to his ow n advantage. Like P tolem y he acknow ledges the difficul­ ty o f getting definite results (13.2). B ut this does n ot invalidate the principles o f astrology. T he science should n o t be blam ed for erroneous horoscopes, w heth er their cause is the m inuteness o f the relevant degree o f the zodiac, the enorm ous speed o f the stars’ orbits and the inclination o f the heavens, o r ignorance in the practitioner. O u r bodily constitution m akes it difficult for us to acquire know ledge o f the divine. B ut o u r m inds are parts o f the divine m ind, m ediated to us by the stars (1 3 .4 & 1 5 .1 1 ). Since we have been proved capable o f discovering the tim es and orbits o f planetary m ovem ents, w hy should it be th o u g h t harder for us to define their terrestrial effects? (1 4.11). Critics object that astrology cannot explain the obvious physical and m ental characteristics w hich a w hole nation shares in com m on (1 2. i). Firm icus (perhaps taking a hint from P to lem y ’s introduc­ tion) adm its that celestial m ovem ents as such do n o t construct the basic physical constitution o f hum an beings; this is due to the m ixture o f the four elem ents as organised by divine providence (1 5.6). B ut the stars are responsible for all our secondary characteris­ tics, colours, shapes, custom s, etc. C ertainly the critic can fill a theatre w ith m en w h o are all black Ethiopians; but he m ust then adm it that every one o f them is physically distinguishable from his fellows. So the properties o f individuals are n o t reducible to a lim ited n u m b er o f ethnic types. As for its religious and m oral consequences astrology, accord­ ing to Firm icus, encourages w orship o f the gods by acknow ledg­ ing o u r relationship to the stars (1 6). T he critic objects that it underm ines m orality by m aking the stars, and n o t o u r wills, responsible for virtue and vice.48 B ut, Firm icus seems to say, that 47. T he standard Latin text is that o fW . Kroll and F. Skutsch (Teubner ed., Stuttgart, 1897 repr. 1968). T here is an English transi, b y j. R. Bram, Ancient Astrology. The Mathesis o f Firmicus Maternus (N ew Jersey, 1975). 48. ‘H ard5 astrology, like determ inism o f w hich it is a species, was open to the obvious objection that it negated the freedom o f the will, see Favorinus ap. Aul. Gell, xiv 1.23; Plotinus in 1.5; Augustine, civ. Dei v 9.

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is h ow things ate: ‘n o th in g is in o u r p o w e r’ (i 9.3). C hance is seen to prevail everyw here, as sh o w n by the unjust fortunes o f the good and the prospering o f the wicked. Serious Stoicism had m ade an honest attem p t to ju stify the same m aterial w ithin a providential w orld. B ut Firm icus, like M anilius before him , sees no apparent problem in com bining rationalist theology w hich m akes m an a divine m icrocosm w ith stellar causation w hich pays no heed to hum an deserts. T he appeal that astrology could exert is show n by the fact that A ugustine dabbled in it as a young m an .49 B ut by the tim e he came to w rite the City o f God he th o u g h t otherw ise. A strology is n o w equally repu gn ant to him , w hether it m akes the stars causes o f our actions independently o f divine will, o r treats the stars as divinely m andated to determ ine h u m an lives, or conceives them as sim ply obeying G o d ’s com m ands (civ. Dei v 1). B ut philosophers, he observes, have another w ay o f stating the relevance o f the stars’ position, treating this n ot as a cause o f hum an affairs b ut as a sign. Plotinus is one obvious candidate for A u gu stin e’s rem arks here. As a thesis such ‘soft’ astrology is m o re acceptable to A ugustine; but, he asserts, it has always failed to explain the diversity in the life o f tw ins (loc. cit.). As w e have seen, this p roblem w ent right back to the earliest recorded controversies, and A ugustine im pli­ citly recognises this by criticism o f Posidonius w hich he probably found in Cicero, perhaps in m issing sections o f the de Fato.50 Parts o f A u g ustin e’s argum ent are already found in Aulus G ellius’ sum m ary o f Favorinus (xiv 1.19, 26), and m any other objections included in the C ity o f God (v 1-7) belong to the same tradition o f Sceptical criticism .51 Such antiquarianism , due in part presum ably to the sources he used, is characteristic o f A u g u stin e’s m ethods as a controversialist. T here is no evidence that he to o k account o f 49. See Peter B row n, A u g u s t i n e o f H i p p o (London, 1969), 57L 50. D i v . D e i v 2, v 5, see above p. 173. A. Schmekel makes a good case for A ugustine’s draw ing upon parts o f C icero’s d e F a t o w hich are missing from our m anuscripts o f that w ork, D i e P h i l o s o p h i e d e r m i t t l e r e n S t o a (Berlin, 1892; repr. Hildesheim , 1974), 163ff. Less persuasive, to m y m ind, is his argum ent that missing parts o f the d e F a t o rather than the fully extant d e D i v i n a t i o n e were A ugustine’s principal Ciceronian source for argum ents against astrology. His attem pt to make astrology as such the object o f C icero’s critique in the surviving d e F a t o up to 20 is quite unconvincing, as A. Yon has show n, C i c é r o n . T r a i t é d u d e s t i n (Paris, 1950), xx n .i. 51. Further evidence o f the persistence o f that tradition is seen in Photius’ account (cod. 223) o f the attack on astrology by one D iodorus o f Tarsus (fourth century a .d .). See C. Schäublin, R h e i n . M u s . 123 (1980), 51-67, w ho also finds traces o f the influence o f Alexander o f Aphrodisias d e F a t o in D iod orus’ work.

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P to lem y ’s refinem ents or even knew them . H eredity and en viron­ m ent, causes w hose im portance P tolem y adm itted (see above p. 182), are the positive w eapons A ugustine uses to refute astrologic­ al explanation o f the sim ilarity and differences o f tw ins (v 2). A ugustine has tw o surprises, tho ug h , to rem ind us th at his prim ary concern is theology. H e adm its that astrologers often give true predictions, bu t the explanation o f this lies in the pow er o f evil spirits and n o t the art o f h o roscopy (v 7). Secondly, he tem pers his praise o f C icero ’s refutation o f astrology by accusing him o f denying fore-know ledge to god: Cicero m istakenly feared that divine fore-know ledge w ould underm ine freedom o f the will. B u t even astrology is preferable to a denial o f g o d ’s fore­ know ledge (v 9).52 Conclusion P lato’s astral theology and Stoic determ inism and pantheism are doctrines w hich helped to give astrology a theoretical foundation w ithin the G reek philosophical tradition. Som e Stoics and som e Platonists too k astrology seriously, b u t it was not a subject w hich m attered greatly even to them up to the tim e o f Plotinus. O n the w hole the philosophers w ere hostile, especially Epicureans and Sceptics. A strology is im p o rtan t to later G reek philosophy largely because o f the sceptical argum ents it provoked. These began in the second century b . c . w ith Panaetius, probably under the stim ulus o f Carneades. B ut astrology seems to have been only a m inor item in C arneades’ critique o f C hrysippus on divination; and even Cicero treats it briefly and rather perfunctorily. T he argum ents he records w ere probably developed before astrology had obtained a secure place in the G raeco-R om an w orld. B ut they continued to be repeated by critics up to the tim e o f A ugustine. Dialectical rather than technical, they are effective against the prim itive versions o f astrology w hich offers itself as a com plete explanation o f terrestrial events. A strological w riters 52. ‘Multo sunt autem tolerabiliores, qui vel siderea fata constituunt, quam iste qui tollit praescientiam futurorum’, p. 203. 3-5 cd. 2 D om bart i (Leipzig, 1877). Actually Cicero does no t explicitly com m it him self to this awful heresy in Div. or de Fato. W hat incensed Augustine, and w hat he builds upon, are various dialectical argum ents in Cicero, such as Div. π 41 w here Cicero m aintains that the existence o f the gods does not entail (contrary to the Stoics) the validity o f divination, and his claiming as dubitable the proposition that the gods know the future, ibid, 106.

IÇ2

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s u c h as M anilius and Firm icus M aternus m ade only half-hearted

efforts to m eet them . B ut P tolem y w ent m uch further in defend­ ing astrology against the standard criticism . His disclaim ers and m odifications (together w ith the qualified criticism o f Plotinus) are perhaps the high points o f a protracted debate m ost parties to w hich took up entrenched positions.

7

The origins o f non-deductive inference M . F. B U R N Y E A T

God, as we know , did no t leave it to A ristotle to m ake m en rational. B u t he did leave it to A ristotle to m ake philosophers take account o f the fact th at there is m ore to m en ’s rationality than the ability to construct syllogism s. T he ability to reason from signs, or m ore generally, the use o f evidence, came to be a central topic in the H ellenistic ph ilo so ph ers’ discussions o f rationality, and it was A ristotle w ho first proposed an analysis o f the n o tio n o f sign (.sëmeion). His treatm ent set b o th a precedent and a standard o f accom plishm ent for his successors. So it is w ith A ristotle that we should begin. T he n otio n o f sign itself is o f course virtually as old as the G reeks’ habit o f giving grounds or evidence for their assertions. T he term ‘sëmeion m ay be found in tragedy, in the orators, in the historians, in the m edical w riters, in the philosophers. R eporting the illegal burial o f Polyneices, a sentry says, ‘T here w ere no signs o f any beast o r dog having com e and m auled the b o d y ’ (Soph. Ant. 257-8). N ear Heracleia is a place ‘w here they n o w show the signs o fH e ra c les’ descent to H ades’ (Xen. Anab. vi 2.2). An orator pleads, ‘D o n ’t seek any o th er test o f m y good will b u t the signs furnished by m y present co n d u ct’ (Andoc. 2.25). T he accused argues that the fact that a m an was n o t stripped is n o t a sign that he was no t m urdered for his clothing (A ntiphon 1 2.5). A ny num ber o f persons m arshal grounds for a claim by saying ‘H ere are the signs for it’, or w ords to that effect (e.g. A ristoph. Nub. 369; D iog. Apoll, fr. 4; H ipp. V M 18.1—2; Isoc. Paneg. 86; PI. Theaet. 153A), w here the signs w hich follow are as likely to be abstract and argum entative as concrete and observational. T here is no fixed preference for using ‘sëmeion’ o f observable things or

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observable states o f affairs, any m ore than there is in the English usage o f ‘sig n’ for ‘a token or indication (visible or otherwise) o f som e fact or quality’.1 In any one o f the exam ples cited ‘evidence’ w ould be as good a translation as ‘sig n ’. G iven this background, w e naturally assum e, w hen first A risto­ tle and then later the Stoics propose an analysis o f sign, that it will be a technical analysis o f a n o tion in co m m o n use, n o t the stipulation o f a technical concept. W e expect no restriction on the range o f things that can serve as a sign or evidence o f som ething, for existing usage displays none. It is not even correct to say that a sign is w h at w e w o uld call em pirical evidence for som ething. O ften this is so, b ut in the Elcatic tradition, w hen P arm enides’ ‘signposts’ (sëmata, fr. 8,2) becam e M elissus’ signs (sëmeia, fr. 8,1), they w ere intended to give dem onstrative p ro o f o f an inescapable conclusion. Likewise in Sextus Em piricus it is regularly reported that dem onstrative p ro o f is one species o f sign (PH π 96, I22, 131, 134; M vm 140, 180, 278, 289, 299). If so, i f ‘sig n ’ covers any kind o f ground, evidence, or reason for believing som ething, including dem onstrative evidence, w e m ig ht expect that a rough, general first sketch o f the n o tio n as it functions in everyday discourse could take the follow ing sim ple form : For X to be a sign or evidence o f Y requires (i) that X should be evident or m anifest to us in som e appropriate w ay, (ii) that it should be evidence o f som ething else in that Y can be inferred from it. T he task o f the technical analysis w o uld then be to explain the relationship betw een X and Y w hich sustains and justifies the inferring o f the second fro m the first. Let us see h o w far A ristotle fulfils these expectations. II T he official account is Prior Analytics B 27. A ristotle’s starting point is n ot so m uch the ordinary m an ’s n o tio n o f simeion as the inferences to w hich it is applied. People say,1 2 for exam ple, ‘She is pregnant because she has m ilk ’, ‘W ise m en are good, for Pittacus is g o o d ’, ‘She is p regnant because she is sallow ’.3 T he form s o f 1. Oxjord English Dictionary s.v. ‘sign’, italics mine. 2. Cf. ού λέγουσι. . . . λαμβάνουσι 7oaty-2o, 6ε6είχ4α ι ο ϊο ντα ι 22. 3. By contrast, the examples in the closely related discussion in Rhetoric I 2 m ake an explicit claim that one thing is sbneion o f another, e.g. ‘If som eone were to say it is a sign that the wise are just, that Socrates was wise and ju s t’ (13 57811-13).

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inference exem plified in these unstudied locutions are all capable, A ristotle thinks, o f w inning tru th s.45B u t none o f them is form ally valid as they stand and, m ore im p o rtan t, w ith m any o f them no plausible filling o u t o f the reasoning will be form ally valid either. Let us use the phrase ‘the reconstruction o f an inference’ to include everything that is involved in supplying unexpressed assum ptions and arranging prem isses and conclusion in proper logical fo rm .3 T hen A ristotle sees his chief task in A n. Pr. B 27 as that o f sorting his examples into those that do and those that do n o t adm it o f a form ally valid reco n stru ctio n .6 A risto tle’s only m eans o f exhibiting form al validity was syllo­ gistic, so w ith som e strain (e.g. adm itting singular term s) syllogis­ tic has to serve.7 T hus for the m ilk exam ple w e supply ‘All w ho have m ilk are p reg n a n t’,8 and continue ‘This w om an has milk; therefore, this w o m an is p reg n an t’, to get the form ‘All B are A; this C is B\ therefore, this C is A ’ - a valid first figure syllogism . By analogous procedures the Pittacus exam ple becom es ‘Pittacus is good; Pittacus is wise; therefore, all the wise are g o o d ’, to w hich A ristotle ascribes the form o f an invalid third figure syllogism . 4. άλιγθές μέν οΰν έν α πα σ ιν ύ π ά ρξει το ις σημείοις (70337-8) is open to tw o interpretations: (a) that ju st given, according to which these forms o f inference are respectable m ethods (in a sense yet to be elucidated) o f reaching true conclusions; (b) a deflating interpretation according to w hich the point is som ething that can be said of any inference w hatsoever, valid or invalid, respectable or otherwise, that its conclusion may be true. I defer defence o f (a) over (b) until the picture it yields has taken shape. 5. For deductive argum ent Aristotle gives his ow n account o f this process at An. Pr. A 32-42. H e calls it ά νά γείν, άνα λΰειν είς τα σχήματα, reducing or resolving an argum ent into the figures, and it includes am ong other things the specification o f missing premisses (47313-20). It is im portant here that reduction to syllogistic form does not mean show ing that the argum ent is in fact already a syllogism in disguise (cf. esp. 47322-40, Alex, in A n. Pr. 344.9fr.), any m ore than reducing a second figuré syllogism to the first figure means show ing that it was a first figure syllogism all along (cf. G ünther Patzig, Aristotle’s Theory o f the Syllogism (Dordrecht, 1968), 134-7, 185 n. 11). In both cases, although in different ways, one recasts the original argum ent into a form the validity or invalidity o f w hich is already know n and thereby determines the validity or otherw ise o f the original. A fortiori to undertake the reconstruction o f a sign-inference in the m anner o f B 27 is not to claim that the inference is or is m eant to be a syllogism already. 6. Rhet. 13 57ha 2-3 confirm s that this was the project: ‘In the Analytics we have defined them m ore clearly and stated w hy some o f them are valid (συλλελογίσμενα), others invalid (ασυλλόγιστα)’. 7. The chapter should not be listed as an exception to the exclusion o f singular terms from syllogistic, as by Patzig, op. cit. (n. 5), 4—5. Rather, syllogistic is applied to material it was not originally designed to handle, as happens also w ith ‘the practical syllogisin’. 8. By the letter o f A ristotle’s instructions at 70315-16 and 23-4 we get ‘All w ho have milk are pregnant’ here, and ‘All w ho are pregnant are sallow’ later. But he surely means ‘All w om en (hum an females) w ho . . . ’ on both occasions: cf. κύουσαν 70313, κυοΰσ α ις 70a2i. O n extra-logical aspects o f the milk example, see n. 30 below.

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Finally, ‘All w ho are pregnant are sallow; this w o m an is sallow; therefore, this w o m an is p reg n a n t’ has the form o f an invalid second figure syllogism . T aking these exam ples to be representa­ tive enough to cover all reasoning from signs (7oai 1-13), A ristotle concludes that the only exam ples w hich can be m ade form ally valid are those w ith a first figure reconstruction (70328-37). Since the second and th ird figure reconstructions are invalid, in the other cases the conclusion reached m ay be true, b u t it does not follow necessarily (70333, 37) from the prem isses set o u t in the recon­ struction. I w an t to argue th at it should be perfectly plain that the purpose o f this technical exercise is not to reject the inferences w hich do not adm it o f a form ally valid reconstruction. T he invalidity is to be noted and appropriated for the classification and understanding o f certain co m m on and useful inferences o f ordinary life. W hen the technical w o rk is done, A ristotle reserves the w o rd ‘tekmêrion for use in connexion w ith exam ples w hich do adm it o f form ally valid (i.e. first figure) reconstruction, leaving it open w hether ‘sëmeion’ should collect the rest (those w ith second and third figure recon­ structions) or should continue to stand as the genus o f w hich tekmêrion is one species (70b 1-6).9 This is hardly to dism iss sëmeion as no m o re than an invalidity. It is an act o f linguistic regim enta­ tion w hich finds its ju stification in the claim (70b2—3) that for ordinary parlance that w hich m akes us k n o w som ething is the tekmêrion o f it, or in the claim (Rhet. i3 5 7 b 7 -io ) that ety m o lo g i­ cally ‘tekmêrion connotes conclusiveness. These tw o contentions, w hether correct or incorrect about the usage o f ‘tekmêrion , 10 belong together and the im plied contrast surely is correct, that the evidence indicated by sëmeion need n o t be conclusive enough for know ledge. Som eone w h o infers that a w o m an is pregnant from the fact that she is sallow docs n o t k n o w that she is pregnant; but

9.

140334-5 seems to think the A n a l y t i c s decided for the first alternative: ‘It is clear from the A n a l y t i c s that every s ë m e i o n is invalid (άσυλλόγιστον)’ (cf. 1402b 13—20). R h e t . !357b4-5 is better: using ‘sign’ in the generic sense, Aristotle remarks that the invalid class o f sign has no specific name. 10. Incorrect even for A ristotle’s ow n usage o f the w ord, to judge by the passages listed in Bonitz, I n d e x A r i s t o t e l i c u s s . v . N o r has the distinction Aristotle makes between t e k m ê r i o n and s ë m e i o n any basis in earlier rhetoric: see L. Radermacher, A r t i u m S c r i p t o r e s (Vienna, 195t), 214-15. O n the other hand, the form ula for t e k m ê r i o n in the pseudo-Platonic D e f i n i t i o n s 414e! is ά π ό δ ειξ ις ά φανοϋς. R h et.

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his belief is reasonably based on a useful piece o f evidence (7oa2i-2 takes it as true that sallowness is a concom itant o f pregnancy: in case o f doubt, substitute m o rn in g sickness). T here are different grades o f evidential su p p o rt and A ristotle explicitly states (7ob4~6) that inference th ro u g h the first figure, i.e. from a tekmërion, is the m ost reputable (endoxotatonf1 and the m ost true (malista alêthes), i.e. the m ost productive o f true conclusions. This im plies that the inferences reconstructed in other figures do have som e, th o u g h a lesser, claim to reputability and tru th .1112 Recall H eracles’ descent to Hades and the signs listed earlier: they w ere evidence b u t n o t all o f th em w ere conclusive evidence. A risto tle’s thesis in A n . Pr. B 27 is that they w ou ld be conclusive evidence (tekmëria), sufficient for know ledge, if and only if a true universal generalisation (cf. 70330) can be supplied to give the inference a valid first figure reconstruc­ tion. W hat, then, is a sign according to A ristotle? T he question m ay be answ ered at tw o levels. T he non-technical dictionary defini­ tion, so to speak, w hich A ristotle gives at 7027-9, records sim ply that one thing (state o f affairs, event), X , is sign o f another, Y, being the case or having com e about if and only if, given that X is the case or th at X came about, Y is the case o r has com e about before or after X . This am ounts to saying that X is a sign o f Y if and only if, given X , Y’s being or happening (earlier o r later) m ay be inferred. It gives no guidance on the question w ith w hat w arrant or assurance it m ay be inferred - that investigation comes elsew here in the chapter —but it does recognise that the sign is not the bare fact as such that she has m ilk (that Pittacus is good, that she is sallow), b ut th at fact as the basis for an (actual or possible) inference to som ething further. T he point is highlighted w hen the non-technical definition supports (gar in I.7) a logician’s technical

11. O n the im portance o f translating ένδοξος by ‘reputable’, ‘respectable’, I agree with Jonathan Barnes, 'A ristotle and the m ethods of ethics’, Revue Internationale de Philo­ sophie, 133-4 (1980), 490-511. 12. For w hat it is w orth, som ething like this interpretation is know n to the subsequent rhetorical tradition. Alexander N um enius (2nd cent, a . d .) expounds Aristotle as calling X a tekmërion o f Y when Y invariably follows X, and a shneion o f Y w hen Y follows on m ore or fewer occasions than not (for ‘few er’ the example is ‘If he is a grave-robber, he will find treasure’) (Rhetores Graeci, ed. Walz v 406-8, vu 765—6). W ithout express reference to Aristotle, Quintilian, Inst, v 9, offers a m ore sophisticated version o f the same line o f thought.

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explication o f w hat a sign is (7036-7): protasis apodeiktikê,)j a prem iss for an inference o r a proposition used to show som ething. A pro po sition used to show som ething is a proposition asserted as true, so A ristotle is n o t m oving as far from ordinary language as he m ight seem to be doing w hen he construes the sign as a proposition rather than a thing (state o f affairs, event) w hich is or happens. O rd in ary G reek and ordinary English license b o th ‘X is a sign o f . . . ’ and ‘ That.p is a sign o f . . w ith the choice repeated for the b lan k s.1 14 B ut given the point w e have been em phasising, 3 that signs belong in inferences, it is m uch clearer to proceed in term s o f propositions. T h at is w hy I called 7037-9 a definition but 70a6~7 an explication, in other w ords a ‘construal . . . w hich is intended to replace a fam iliar b u t vague and am biguous n o tio n by a m ore precisely characterised and system atically fruitful and illum inating o n e’.15 T he full explication o f ‘sign’, how ever, is this: protasis apodeiktikë ë anankaia ë endoxos, a proposition, either necessary or rep u t­ able, used to show som ething. T h e further characterisation ‘either necessary or reputable’ sounds, puzzlingly, like a com m ent on the m odal status o f the propo sitio n itself. B ut w hat w e need to com plete the technical explication is a com m ent on the w arrant w hich the sign-proposition, as w e m ay call it, confers on the conclusion inferred from it: ‘I call those signs necessary (anankaia) 13. α ποδεικτική in its relaxed sense (cf. SE i67b8, G C 333824, Metaph. 10258113) which can prescind not only from the standards o f the An. Post, notion o f dem onstrative p ro o f from necessary premisses, but also, when as here Aristotle is discussing rhetorical argum ent, from the standards o f logical validity (e.g. Rhet. 1396234-81 and n. 29 below). Pace W. D. Ross, Aristotle’s Prior and Posterior Analytics (O xford, 1949), 501, this α ποδεικ τική is not the same as συλλογιστική: for the premiss is asserted as true. Ross also goes w rong (ibid. 500) in saying that the premiss states a connexion betw een tw o characteristics; it states the presence o f one characteristic, on the strength o f which another is inferred. Semeion as defined = prem iss/state o f affairs premissed for an inference (yoa6~9) should be distinguished from the use o f the term later in the chapter to denom inate, by a natural extension, the sign-inference itself (70a24—5, 7-8, 7ob4). The latter seems to be the only sense recognised by M ario M ignucci, Aristotele: gli analytic: primi (Naples, 1969), 722-4, for he speaks throughout o f the sign as having the form ‘p because q . Lastly, βούλεται είνα ι (70a6) has called forth som e unnecessari­ ly fanciful suggestions: it sim ply indicates ‘quo quid per naturam suam tendit’ (Bonitz s.v.).

14. See the examples p. 193 above and compare LSJ s.v. σημειον w ith O E D s.v. ‘sign’ or ‘evidence’. This is surface gram m ar and settles nothing about w hat we call the question o f logical form. 15. Carl G. Hem pcl, Aspects o f Scientific Explanation (New Y ork & London, 1965), 489. 1 w ould m odify the above diagnosis if evidence em erged that Aristotle has in view a thesis to the effect that ‘That p is a sign o f . . . ’ gives the underlying logical form o f ‘X is a sign o f . . . ’.

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from w hich a syllogism can be constructed (ex hön ginetai sullogismos)’, sc. a valid syllogism in w hich the conclusion follow s necessarily from the conjunction o f the sign-proposition w ith the true generalisation supplied in the reconstruction (Rhet. 135705—6; cf. 140332-15). T hus ë anankaia e endoxos anticipates the distinction A ristotle will draw and defend betw een tekmëria and other sig n s.16 Som e evidence is conclusive. G iven that she has m ilk, it is necessary that she is p regnant (cf. Rhet. 1 3 5 7 ^ 4 -1 6 ); it is to the highest degree a respectable thing to believe (endoxotaton, 7obs). M ore often evidence is n o t in this w ay conclusive or sufficient for know ledge. It m erely m akes a conclusion a respectable or rep u t­ able thing (endoxon) to believe. T h at com pletes m y account o f Prior Analytics B 27. If the interpretation is correct, it w ould be churlish n ot to hail the chapter as a pioneering start to the study o f non-deductive lo g ic.17 B ut to back up this conclusion I need to set it in a w ider context and quell an alternative in terp retatio n 18 according to w hich A r­ istotle m eans us to th ink that, w h en an inference fails the test o f syllogistic validity, it fails as an inference tout court, i.e. it has no probative force w hatsoever. In that case all there is to be said about argum ents fro m signs other than tekmëria is that they are bad argum ents. T he m oral will be: so m uch the w orse for the rhetorical contexts in w hich such argum ents a b o u n d .19 16. Ross, o p . c i t . (n. 13), 500, agrees, likewise Philoponus, i n A n . P r . 481.7-9. J. Padus, A r i s t o t e l i s O r g a n o n c u m c o m m e n t a r i o a n a l y t i c o (Frankfurt, 1597), 264, translates ' p r o p o s i ­ t i o n e m d e m o n s t r a t i v a m , s i v e n e c e s s a r i o s i v e p r o b a b i l i t e r d e m o n s t r e t ' . T he proposal of Heinrich Maier, D i e S y l l o g i s t i k d e s A r i s t o t e l e s 11 (Tübingen, 1900), 481 n. 2, to excise α να γκ α ία as a gloss is m otivated only by the thought that the message is already conveyed by αποδεικ τική , i.e. M aier m istakenly (n. 13 above) reads into the latter term elements o f the A n . P o s t , notion o f dem onstrative proof. If α να γκ α ία com m ents not on the m odal status o f the premiss but on its inferential connexion w ith the conclusion, the same m ust be true o f ένδοξος, ένδοξος matches δ ε δ εϊχ ϋ α ι ο ί ο ν τ α ι 70a22, and this, not ‘dem onstrates w ith probability’, is w hat ' p r o b a b i l i t e r d e m o n s t r e t ’ m eant w hen P adus wrote. 17. We have been discussing sign-argum ents in term s o f form al rather than o f deductive validity, but Aristotle does not allow for argum ents w hich are deductively valid but not formally valid, e.g. ‘Socrates is m arried, therefore Socrates is not a bachelor’. This is only to be expected given his thesis that all deductively valid argum ents can be show n to be syllogistically valid; syllogistic validity is one type o f form al validity. One o f A ristotle’s fefemënoM-arguments m ight be thought to come into the missing category: ‘He is ill, for he has a fever’ ( R h e t . 1357b 15). But Aristotle treats it on a par w ith ‘She has given birth because she has m ilk’. 18. Interpretation (b) in n. 4 above. 19. T he m ost determ ined advocate o f this view is Pacius. He contrasts the third figure example, where som ething follows, viz. ‘Some o f the wise are g oo d’, though not the universal conclusion draw n (μηδέ πρ ός τό πρ άγμ α τόν συλλογισμόν, 70232), w ith the

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N otice first th at if syllogistically invalid inference from signs is to be condem ned w ith o u t reprieve, a good deal else goes w ith it. T he chapter we have been discussing is part o f a project begun at A n. Pr. B 23: We must now state that not only are dialectical and demonstrative deductions [sullogismoi in the broad sense defined in An. Pr. 24bi8-2o] effected by way of the aforesaid figures [i.e. are reducible to syllogisms in the narrow sense defined by the figures: a thesis already argued, csp. An. Pr. A 23], but so also arc rhetorical ones and in general any persuasive argument,20 whatever its procedure. For all conviction comes about either by way of deduction or from induction (epagöge). (68b9—14) T he project is to show that syllogistic is a universal test o f logical validity. T h at is the m eaning o f ‘All these argum ents are effected th ro u g h the figures’; it is n o t the absurd claim that rhetorical deductions are already in syllogistic form . Likewise, I suggest, it is by w ay o f p ro m o tin g syllogistic as a universal test o f logical validity th at in B 23 A ristotle goes on to a syllogistic reconstruc­ tion o f induction (epagöge), finding that the conclusion follows necessarily only if an extra condition is satisfied, over and above w hat is given by the prem isses o f the syllogism itself. T he extra second figure case, w here tw o affirmative premisses yield neither the conclusion drawn nor any other (the argum ent is always and in every way refutable, 70234-5). O n the basis o f this exegesis, which so far as formal validity is concerned is perfectly correct, he explains the rem ark at 6gbs6—y: ‘For this reason also this [the second] is the only figure from which no sign can be obtained’. He does not inquire why, if this is the right interpretation, Aristotle does not exert him self to say, either in An. Pr. B 27 or in the Rhetoric, that the truth o f ‘Pittacus is go od’ is unobjectionably a third figure sign that som e o f the wise are good. Conversely, once 6 ^ 3 6 - 7 is recognised as a gloss (F. Susemihl in Jahresbericht, über die Fortschritte der dassischen Aîterthumswissenschajt 42 (1885), 1$, follow ed by Maier, op. cit. (n. 16), 487 n. 2, Ross, Mignucci), irrelevant to its context and derived from a Pacius-type interpretation o f 70334—5, it should be a question w hy Aristotle speaks in B 27 as if there were signs in the second figure, only not syllogistically valid ones. T o this question Philoponus, in An. Pr. 481.28-30, 482.10-12, returns the em barrassed answer that the invalid examples Aristotle uses are merely illustrative (π αρα δείγμα τος χάριν), i.e. illustrative o f what a second or third figure sign-argum ent w ould be like if there were any. A m ore m odern representative o f this kind o f view is George Grote, Aristotle (London, 18802), 203: ‘in the second figure, the conclusion . . . is altogether suspicious’. C ontrast T heodorus Waitz, Aristotelis Organon (Leipzig, 1844), 1 537 ad 70229: ‘quod vero in reliquis [figuris cogitur], quum solvi possit et redargui, nihil quidem habet necessarii, sed veri simile est’. F. A. Trendelenberg, Elementa Logices Aristoteleae (Berlin, 18929), 119 and Maier op. cit. (n. 16), 487, also incline m y way. 1 cannot tell w hich side Ross or M ignucci are on: they seem not to confront the central question at all. 20. π ίσ τις here is not ‘any attem pt to produce conviction’ (Ross), ‘any form o f persuasion’ (A. J. Jenkinson in the O xford Translation), but excludes arm -tw isting, playing on the em otions, and suchlike (cf. Rhet. r 354a 11—18, 135524-8); A ristotle’s thesis only makes sense as a thesis about reasoned, argum entative inducem ents to believe som ething.

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condition is that the enum eration o f species falling under the genus w hich is subject o f the conclusion m ust be com plete.21 N o w , if A ristotle condem ns syllogistically invalid sign-inferences, because they are syllogistically invalid, he o u g ht equally to condem n inductive argum ent, even in the favourable circum stance o f com plete enum eration, and a fortiori in the m ore com m on case, w hich includes m any o f his o w n inductive argum ents, w here this extra condition is n o t satisfied. N o such condem nation is uttered in B 23 or elsewhere. O n the contrary, A ristotle regularly treats induction as a respectable, indeed essential, source n o t m erely o f conviction b ut o f kn o w led g e.22 M uch the sam e story can be told o f the analysis in B 24 o f argum ent fro m exam ple (paradeigma), i.e. extrapolation from one particular case to another. A ristotle offers a tw o-stage syllogistic reconstruction, the first stage o f w hich is exactly parallel to the third figure sign-argum ent in B 27.23 T hat is, from a form al point o f view it com m its the fallacy o f Illicit M inor. B ut there is no t a w o rd to im ply that rational persons will eschew exam ple, and it w ould be a foolish politician w ho did so: ‘Exam ples are the m ost suitable for deliberative speaking, for it is by conjecturing from past events that w e ju d g e the fu tu re’ (Rhet. 1368329-31). T h e tru th o f the m atter, I believe, is that A ristotle does think that syllogistic is a universal test o f form al or deductive validity, b ut he does no t think that form al or deductive validity is the only test o f w hether an argum ent is intellectually respectable or has a justifiable claim on rational m inds. V arious form s o f inference are in use and enjoy good standing w ith those w hose business it is to argue a case. Let them be classified, reconstructed in syllogistic form , and tested for validity: then w e shall see ho w far their

21. For details, see Ross’s com m entary on the chapter. There is no need to be troubled by Ross’s com plaint (op. cit. (n. 13), 50) that Aristotle here identifies induction w ith the one type o f induction, perfect induction, which alone can be cast in the form o f a valid syllogism. It cannot and he does not. Jaako Hintikka, ‘Aristotelian induction’, Revue Internationale de Philosophie 133-4 ( ï 980), 422—39, is a m ore recent treatm ent o f A«. Pr. B 23 which also fails to confront squarely the invalidity o f ό έξ επαγω γής συλλογισμός (68b15). N ote the.strain on syllogistic when Aristotle has to assign a term -letter C to the sum o f the species in order to represent the enum eration as a premiss in syllogistic form which is convertible if and only if the enum eration is complete. Any substitutioninstance o f the converted premiss w ould have a disjunctive predicate. 22. For discussion, see m y ‘Aristotle on understanding know ledge’, in Aristotle on Science: ‘The Posterior Analytics', ed. Enrico Berti (Padua, 1981), 118-19, i26ff. 23. For details, see R oss’s com m entary on the chapter.

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strength is strictly logical (‘irrefutable if tru e ’, A n . Pr. 70329—30, Rhet. I357bi7), h o w far and w here it leaves ro o m for an opponent to counter-attack by objection or refutation. T h at is the project, and A risto tle’s Rhetoric show s h o w useful it is for the practice o f p ropo un ding argum ents and replying to the argum ents o f one’s adversary in judicial and political debate. M ost o f the argum entform s assem bled in the Rhetoric are taken to be open to objection or refutation (cf. esp. 1402b 12-03333).24 D ebate about hum an affairs is a trial o f argum entative strength in w hich the outcom e is decided n o t on necessities alone b u t on likelihoods (i402b32-4; cf. T357a22-31). If these form s w ere pruned to m eet the requirem ents o f syllogistic validity, A ristotle’s attem pt to build an intellectually respectable rhetoric w ould cru m ble.25 I conclude that the w ider context o f Prior Analytics B 27 confirm s the interpretation given earlier. N o t only is the very 24. It is for this reason th at 1sêmeion can designate a topos for charging o n e ’s o p p o n e n t w ith ‘app arent e n th y m e m e ’, reasoning th at is n o t really p ro b ativ e (Rhet. 1 4 0 ^ 9 -1 4 ) . See the sensible co m m en ts o f Sally R aphael, ‘R h eto ric, dialectic and syllogistic arg u m en t: A risto tle ’s position in “ R h e to ric ” i - n \ Phronesis 19 (1974), 160. T h e sam e exp lanatio n applies w hen rhetorical sig n -arg u m en ts appear u n d er the fallacy o f affirm in g the co n seq u en t at SB I0 7 b i-I2 , p u t parallel to exam ples like this: ‘Since it happ ens that the earth becom es d renched w hen it has rained, if it is d ren ched, w e supp ose it has rained, th o u g h this is n o t necessarily tru e ’. N o te the ‘w e ’. T h e o n ly m istake A risto tle aim s to exp ose here is th at c o m m itte d by p eople w h o th in k th at so m e th in g follow s necessarily w h e n it docs n o t (i0 7 b 2 —3). A glance th ro u g h B o m tz ’ Index s.v. σ η μ εΐο ν will sh o w that A risto tle him self, w h e n n o t talk in g logic, freq u en tly m en tio n s signs and p ro p o u n d s sig n -arg u m en ts w hich h e is m o st u nlikely to consider logically conclusive.

25. There is a complication. Nearly all m y references to the Rhetoric have been to the tw o sections o f that w ork w hich refer to and make use o f Prior Analytics B 27. These are I357a22-b25, which presents the same triple division o f sign-argum ents as A n. Pr. B 27 but less formally, w ith the invalid examples classified in terms o f w hether the argum ent moves from the m ore general term to the m ore particular or in the reverse direction; and I402bi2-03ai6, which discusses refutation in terms o f the same scheme. T hey are the only tw o sections w hich presuppose syllogistic and they contain all but one (i350b9) o f the Rhetoric's five references to the Analytics. I am persuaded by the thesis o f Friedrich Solmsen, Die Entwicklung der Aristotelischen Logik und Rhetorik (Berlin, 1929), now powerfully reargued by Jonathan Barnes, ‘P ro o f and the syllog­ ism ’, in Aristotle on Science op. cit (n. 22). (cf. esp. 51-2 n. 5$), that they are in fact later insertions into a w ork which otherw ise know s the dialectic o f the Topics and has some conception o f apodeictic but none o f syllogistic. The critique o f Solmsen by Raphael, op. cit. (n. 24) is an interesting discussion o f difficulties in A ristotle’s attem pt to analyse persuasive reasoning in term s o f deduction and induction, but it does not meet the central point, which is that only tw o detachable sectons o f the Rhetoric are familiar with A ristotle’s attem pt to analyse deductive reasoning in term s o f syllogistic. The same is true o f the otherw ise helpful defence o f the unity o f the Rhetoric by William M. A. Grimaldi, Studies in the Philosophy of Aristotle’s Rhetoric (Hermes Einzelschritten 25, W iesbaden, 1972). M y ow n view is that Aristotle w ould not have inserted the new material if he had thought it destructive o f his original project, and I have argued that the technical analyses o f An. Pr. B 23, 24, 27 are not inimical to that project either.

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n o tio n o f form al validity A risto tle’s invention: he has further seen that there are respectable argum ents w hose probative force does not derive from their form al validity, because they are in fact invalid. I call this a pioneering advance because it is the decisive insight prior to w hich no one will think to ask about w hen an argum ent w hich is form ally invalid is nonetheless a good argu­ m ent and w hen it is a poor one, or about h o w the good specim en can m ake a rightful claim on rational m inds. A ristotle does not address these questions.26 B ut he left the subject poised for further developm ent by any successor w ith the logical acum en to discern the challenge that they pose. H e also left som e indications as to w h at m ight be gained by taking up the challenge. Prior Analytics B 27 concludes w ith an appendix (yobyff.) on the logical requirem ents for setting up a science o f physiognom ies, a system atic m eth o d o f inferring m ental characteristics in hu m an individuals from bodily features taken as their ‘signs’.27 T his m ay strike us today as an u n p ro m is­ ing field o f application for a logic o f evidence, b u t the idea o f an application is there nonetheless, and in fact the general form o f the problem is both interesting and com plex. It is a problem about establishing a one to one correlation betw een tw o item s so as to infer a co m m o n cause and then using the correlation to argue from one item to the o ther in a significantly different case.28 T he goal is to provide a th eory w hich will yield generalisations for the reconstruction o f such inferences as ‘H e is a cow ard because his eyes are w eak and blinking and his m ovem ents constrained’ (cf. [Ar.] Physiogn. 8o7b5-i2). W e shall retu rn to physiognom ies later. M eanw hile, a conne­ xion betw een signs and o ur overall view o f hum an rationality is m ade in the first chapter o f the Rhetoric, the treatise w hich aims to study the full range o f everyday reasoning, w hether it be rigorous

26. D epending on how late we place the breakthrough to syllogistic (see Barnes, op. cil. (n. 25)), we m ust reckon w ith the possibility that he simply did not have the tim e or the inclination to rew ork the Rhetoric. Had he done so, it m ight have changed the course of history. 27. For elucidation see Ross ad loc. and R. Förster, Scriptores Physiognomonici (Leipzig, 1893). 28. Similar logic can be seen at w ork in de Div. 463022-31. Aristotle considers some examples where the com m on cause o f a sign and the event it signifies is prevented from bringing about the event: in such cases you have a sign o f som ething which was im m inent but which did n ot in fact happen.

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or ‘relaxed’,29 and including as one im p o rtan t division reasoning from signs. T he in tro d u cto ry apologia for that study contains the rem ark that reasoning in defence o f o n e’s case or point o f view is m ore characteristic (mallon idion) o f m an than physical self-defence (i355a38-b2). Again, ‘All m en share in som e w ay in both [rhetoric and dialectic]; for all up to a certain point endeavour to criticise o r u phold an argum ent, to defend them selves or accuse’ (i354a3-6). G od did n o t w ait in vain. Indeed, w ith so m uch spelled o ut for the first tim e in the history o f th o u g h t, and m ore projected, it is easy to overlook som e im p o rtan t om issions. T w o m atters in particular rem ain untouched w hich will be at the centre o f later philosophical discussion and w hich w ou ld have been well w ithin the com pass o f A ristotle’s pioneering start. O ne thing that is m issing is any discussion in this context o f the covering generalisation w hich m akes a sign into a tekmërion, reconstructable in the form o f a first figure syllogism . So long as it is a true universal propo sition (70a3o), the conclusion follow s necessarily, bu t w e m ig ht w ant to raise questions about the epistem ic or the m odal status o f this universal. A ristotle’s o w n exam ple ‘All w ho have m ilk are p reg n an t’ show s one o f the problem s that can arise. As stated, it is in fact (like so m any philosophers’ examples) false, n o r is it all that easy to say precisely w h at general tru th it is that one relies on in m aking the inference ‘She is p regnant because she has m ilk ’.30 W ould it m atter if one was m ore certain o f the inference than o f the exact specification o f 29. Cf. Rhet. i396a34-bi: έάν τε άκριβέστερον εάν τε μαλακώ τερον συλλογίζω νται. A ristotle’s acknowledgem ent o f a ‘relaxed’ συλλογίζεσθαι fits neatly w ith the interpretation 1 have been defending. I w ould connect it w ith his characterisation o f that m uch m isunderstood object, the enthym em e, as συλλογισμός τις, which o f course does not mean ‘a kind o f syllogism ’. But enthym em e is too large a topic to em bark on here. 30. Since the example (like so m any philosophers’ examples) is repeated interm inably in the subsequent literature, it is w orth a brief note. First, Aristotle uses γά λα for colostrum as well as milk proper (G .-4 776320-5, H A 583334); let us do likewise. Second, concerning animals in general Aristotle believes that it is only a for the m ost part truth that pregnancy is a necessary condition for lactation; some animals have been know n to produce milk w ithout getting pregnant (H A 522a2ff.). T hat means we m ust at least have ‘All hum ans w ho have milk are pregnant’ rather than ‘All w ho have milk are pregnant’ (cf. n. 8 above), and we had better waive m odern reports that in certain parts o f the world hum an grandm others are induced by suckling to give milk. Third, Aristotle is quite capable, w hen it pleases, o f giving us the different inference ‘She has given birth because she has m ilk’ (Rhet. 1357b 15-16). Accordingly, we should not cite nursing m others, let alone wetnurses, as counter-exam ples to the An. Pr. inference: Aristotle is thinking o f a context in which the wom an has not yet given birth to the infant she is carrying, and she or the doctor infers that she is carrying one from the signs given by a m ilky secretion in the breasts. The problem (left as an exercise for the

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the covering generalisation? T here m ay be a weak spot here for later sceptical p robing - o r alternatively, for fruitful philosophical exploration. T h e other n o tew o rth y absence is com pensated for by Ross w hen he reports the connexion betw een sign and w hat it signifies as ‘a connection b etw een a relatively easily perceived characteristic and a less easily perceived one sim ultaneous, previous, or subse­ quent to it’, referring to 7 0 a8 -io (the non-technical definition) w hich, how ever, contains absolutely no thing corresponding to the contrast I have italicised.31 It m ay be tem pting to suppose that A ristotle m ust have som ething o f the sort in view (he is presum ­ ably com m itted to it by ‘apodeiktikë’), but in fact the chapter makes explicit com m ent on the epistem ic status o f a prem iss once only, and then n o t on the sign prem iss itself but on a prem iss added in the reconstruction: in the Pittacus exam ple people om it to state ‘Pittacus is w ise’ because it is co m m o n know ledge (70319—20; cf. Rhet. i357a20-22). As w ith the covering generalisation, so also on this point, A risto tle’s account o f signs m akes no use o f epistem ic notions. Has he m ade a decision o f principle to keep the logic o f evidence separate, or as separate as possible, from the epistem olo­ gy or use o f evidence? T he contrast w ith later developm ents (see below )32 is so striking (and R oss’s m isperception of the text so natural) that one could easily think so. At any rate, this looks to be the only substantial point on w hich A ristotle has failed our initial expectations (p. 194 above). H e has analysed, or at least given an explication of, the ordinary m an ’s notion o f sëmeion, and has done p retty fairly by it. H e has p ut no restriction on the range o f things that can serve as a sign or evidence. (For exam ple, for all he says to the contrary, pregnancy could be a sign o f lactation.) B ut although he has distinguished evidence w hich is sufficient for know ledge from evidence w hich is not, he has n o t exactly m atched our initial, rough characterisation o f ‘sign’. For he has n o t required, n o r even m entioned, that the sign proposition, stating the evidence for som ething, m ust itself be evident or k n ow n. O n the other hand, insofar as the study o f knowledgeable reader) is to form ulate conditions C such that ‘All hum an females who have a m ilky secretion in the breasts and w ho meet conditions C are pregnant’ comes out true. 31. Ross, op. cit. (n. 13), 500. 32. And w ith his ow n account o f argum ent from example, w here the example has to be better know n than the case extrapolated from it: An. Pr. 68b 16, Rhet. I3 57b29~30.

sign-argum ents has b ro u g h t him w ithin reach of the idea o f a non-deductive logic, he has gone m o m entously beyond those sim ple first expectations. In section IV w e shall com pare and contrast the Stoic approach. B ut first, because o f the nature o f our source m aterial on Stoic signs, there is w o rk to do to gain the right to m ake the com parison and to set the term s in w hich it should be made.

Ill T o establish the reality o f signs, the Stoics assert: It is n o t u ttered speech b u t internal speech by w hich m an differs from irrational anim als; fo r crow s and parrots and jay s u tter articulate sounds. N o r is it by the m ere fact o f having im pressions, as such; for they too receive im pressions. T he difference is that m an has im pressions arising fro m inference and com bination. T his am ounts to his possessing the idea o f consequence (akolouthia) and directly thereby grasping the concept o f sign. For sign is itself o f the sort ‘If this, then th a t’. T herefore, the existence (huparchetn) o f signs follows from the nature and construction (,kataskeuë) o f m a n .33 (Sextus E m piricus, M vm 275-6)

This is a rem arkable passage. Ju st h o w rem arkable em erges w hen w e supply, from the reprise later in Sextus’ discussion (M vm 285—6), the extra prem iss w ith o u t w hich the argum en t is no argum ent at all: m an is providentially constructed {pronoëtikôs kataskeuasthai) ,34 W e only have one o f the prem isses in the claim that ‘the ability to think (to discourse w ith oneself), to fram e concepts and to draw inferences is part o f m an ’s n a tu re ’;35 or 33. M y translation here owes m uch, and n ot ju st the stolen phrases, to the translation and elucidation by A. A. Long, ‘Language and thought in Stoicism ’, in Problems in Stoicism, ed. A. A. Long (London, 1971), Syff., w ho rightly says that crucial parts o f the Loeb translation o f R. G. Bury are meaningless. T w o points o f difference deserving notice: (1) Long renders xfj άπλή μόνον φ α ντα σ ία in a m anner (‘in virtue o f simple presentations’) which suggests a species o f φ αντα σ ία - as it were, Lockean simple ideas. B ut it is surely the generic φ αντα σ ία as such, φ αντα σ ία simpliciter. (2) Long’s translation com m its him to tw o views he does n ot really hold: (a) that ά κο λο υθία is (exclusively) logical consequence, for he translates it so; (b) that signs are conditional propositions, for he makes the penultim ate sentence read ‘For signal itself is o f the follow ing form: “if this, then th at’” (similarly Bury). B oth points await discussion, so I have been as noncom m ittal as the Greek allows. 34. It is this extra premiss which assures us that the argum ent is Stoic. T he argum ent is destroyed by the wilful em endation o f Kayser (Rhein. Mus. N .F. 7 (1850), 187): νοητικώ ς for π ρ ο νο η τικ ό ς. 3j. Long, op. cit. (n. 33), 87. But the only textual basis on which to extract a claim about fram ing concepts as such, as opposed to the tw o concepts mentioned, is φ α ντα σ ία

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better, that it is the distinctively hum an aspect o f his nature, constitutive o f his rationality. A nd this claim itself is hardly news. It is the Stoics’ inheritance fro m Plato (thinking as internal discourse - Theaet. 1 8 9 E - 1 9 0 A , Soph. 263e) and from A ristotle, w hose position was already, as w e have seen, that the philosophic­ al account o f hum an nature m ust include reasoning o f every sort, including reasoning from signs. W hat is original to the Stoics is the appeal to providence and the argum ent built up on it: M an is providentially constructed. M an is a reasoning, inferring creature, w hich m eans, first and forem ost, that he draw s infer­ ences from signs. T herefore, there m u st in reality be the conne­ xions that reason takes itself to be discovering. If nothing is objectively evidence for anything else, m an is poorly equipped for the w o rld he has to live in; w hich cannot be so if his cognitive equipm ent (kataskeue) is the end ow m en t o f providence. It is a bold argum ent. Sextus is entirely ju stified w hen he points o ut (M vin 285-6) that its conclusion, the existence or reality o f signs, is a good deal less controversial than the prem iss w hich invokes providence to establish it. T h a t’s ju s t bullying, he says (.sphodra biaiori). B u t I hazard the opinion that A ristotle could not afford to be so sceptical. His Physics is founded on the no less bold contention that the fundam ental concepts needed for the un der­ standing o f nature are to be obtained by a probing exam ination o f the ideas o f the ordinary m an and a handful o f previous seekers after tru th .36 T he ideas have to be clarified, m ade consistent and

συνθετική. In w hich case it will not be enough (ibid. 109 n. 54, followed by John M. Rist, ‘Z eno and the origins o f Stoic logic’, in L e s S t o ï c i e n s e t l e u r l o g i q u e , ed. J. B runschw ig (Paris, 1978), 392) to cite DL vii 52-3, w here κ ατά σΰνθεσιν is only one m ode o f concept form ation am ong six, illustrated by the unprom ising example of c e n t a u r . M uch as one feels that the m ore general claim would be in place here, can συνθετική stand tor it? DL’s six modes are pretty clearly o f unequal im portance and are cut dow n to a list o f four (including c o n j u n c t i o = σΰνθεσις) at Cic. F i n . m 33; and cf. c o n s t r u i t describing concept form ation as such as Cic. A c . 11 30. But a simpler and more likely interpretation, given one brief phrase, is that o f Gerard Verbeke, ‘La philosophic du signe chez les stoïciens’, in Brunschw ig, o p . c i t . (above), 408: ‘L’hom m e . . . est capable . . . de passer d ’un élément à l’autre et d ’associer différents éléments; il possède une im agination discursive (μεταβατική) et synthétisante (συνθετική).’ In other w ords, it is distinctive o f hum an thought to be able to draw inferences and ‘put tw o and tw o together’. Cf. Epict. D i s s . 1 6.10 and n. 83 below. 36. See esp. Book i and G. E. L. O w en, ‘Tithenai ta phainom ena’, in A r i s t o t e e t l e s p r o b l è m e s d e m é t h o d e , cd. S. Mansion (Louvain, 1961), repr. in A r t i c l e s o n A r i s t o t l e 1, ed. Jonathan Barnes, M alcolm Schofield, Richard Sorabji (London, 1975); also G. E. L. O w en, 'Aristotle: m ethod, physics, and cosm ology’, 1n D i c t i o n a r y o f S c i e n t i f i c B i o g r a p h y , cd. C. C. Gillespie (N ew Y ork, 1970). Key texts include i88b26-i89aio, I9ia23ff.

generalised. B ut the large assum ption (contrast N ew to n ) is that this is the place to start. W hat assurance do w e have that m a n ’s m ind and nature are so attuned to each other? O nce the epistem o­ logical question becom es a m ajor issue —a typical Hellenistic developm ent - Stoic providence (w hich is not, o f course, an agency outside nature) seems the answ er closest to the spirit o f the Platonic-A ristotelian tra d itio n .37 T hus the concept o f sign com es to take a central place in the H ellenistic version o f the established conception o f m en ’s rational­ ity. W hat has happened to the concept o f sign (semeion) to enable it to bear this role? W hat exactly has been p roved to be real if it is established that signs are real? T he passage before us m ig h t suggest the follow ing answ er. Signs are conditional propositions o f the form ‘If this, then th a t’, so the argum ent establishes the real existence o f a class o f propositions. This is quite certainly w rong, doubly so, and it is w o rth seeing w hy. First, a p roposition in Stoic doctrine is an im m aterial lekton, a m ere ‘sayable’, and does n o t exist. A long w ith place, tim e and the void, the lekton defies a celebrated Platonic axiom in that it is som ething b u t n o t a thing th at is (exists); it m erely subsists w ith or underlies o u r th o u g h t.38 A dm ittedly, various passages (ours am ong them and others m ore polem ical) have been th o u g h t to m ake it difficult to accept this official categorisation as the w hole story, b u t I can bypass the com plexities o f that issue39 if I can show that it has no relevance to the passage we are exam ining. I offer tw o reasons, each o f w hich seems to m e sufficient on its ow n. (a) T he conclusion o f o u r passage is that signs huparchein, and this does not contradict the conclusion o f the sceptic’s argum ent 37. By this I m ean that it develops, how ever aggressively, the teleology o f the faculties w hich Aristotle could have used to justify basing science on τα ένδοξα: see Barnes, ‘Aristotle and the m ethods o f ethics’, 505fr., for an argum ent to this effect constructed from Aristotelian materials but not, Barnes admits, explicitly unrolled in any Aristotelian text. O n Stoic providence, the m ost illum inating w ork I know is J. Mansfeld, ‘Providence and the destruction o f the universe in early Stoic th o u g h t’, in Studies in Hellenistic Religions, ed. M. J. Vermaseren (Leiden, 1979), 129-88. 3 8 . Plato: Rep. 4 7 8 B , Parm. 1 3 2 B C , Theaet. 1 8 8 E - 1 8 9 A , Soph. 2 3 7 C D . τι not ov: P H 11 8 6 - 7 , Μ X 2 1 8 , S V F π 3 2 9 - 3 5 (the separation o f τι from ov in the case o f imm aterial things encapsulates a neat escape from num erous Platonic difficulties). T he status o f the lekton: τη ήμετέρα παρυφ ισ ταμ ένου δ ια ν ο ία Μ vin ΐ 2 , κ ατά λογικήν φ αντα σ ία ν ύφ ισ τάμενον Μ vm 7°> D L νπ 63. 39- fo r references and a very full discussion, see Long, op. cit. (n. 33).

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that signs me einai (275, ju st before m y quotation begins) unless huparchein = einai. B ut it is quite clear w h at it means in the context o f this debate to say that signs einai or that they do not. T he rival theses are that nothing is a sign o f anything (e.g. vin 279) and that at least one thing is a sign o f another (e.g. vm 278). T h e ontological status o f propositions them selves is not the p rim ary issue at all.40 (b) T he second reason w hy the ontological status o f propositions them selves has no bearing on the present passage is that it w o uld reflect badly on providence. M erely to ensure the real existence o f a w hole lot o f propositions w ould leave open the possibility that they are, one and all, false. W hat is needed for the hu m an m ind to be in tune w ith the w orld is that som ething should actually be evidence for som ething, n o t that there should be a ‘sayable’ to th at effect. N o w for the second m istake in the w ro n g interpretation w hich the w o rd ing o f our passage m ight suggest. Signs are n o t con­ ditional prop o sitio n s.41 T he official Stoic account states, ‘A sign is a proposition w hich form s the antecedent in a sound conditional, being revelatory o f the consequent’ (M vm 245).42 N o t the w hole conditional bu t its antecedent is the sign. B u t getting that right is only a prelude to the serious problem s. G ranted that the passage should n o t be read as equating signs w ith conditional p ro p o sitio n s,43 does it say or im ply that signs are expressed only in conditional propositions, as antecedents thereof? 40. N ote that I do not say it is not an issue. Sextus brings it in, polemically, at M vm 257fr. (cf. P H π 107), w ith the argum ent that, sign being a species o f kkton, the existence or reality o f the first presupposes that o f the second, which may he disputed. This looks like a scandalous departure from the question set for debate, but it is in fact an excellent example o f the sceptic m ethodology. Sextus operates on the basis that you are not entitled to any assertion w hich makes a truth claim, no m atter how mundane, unless you can justify it, w here this will include giving a philosophical elucidation and defence o f the concepts involved in or presupposed by your claim, to the point where no further questions remain. Empirical, scientific and philosophical justification are seen as continuous w ith one another in a way that is foreign to m odern philosophy. There are large and im portant issues here, which I hope to discuss elsewhere (‘The sceptic in his place and tim e’, forthcom ing). 41. Contra e.g. V. Brochard, ‘La logique des stoïciens’, Arch. Gesch. Phil. J (1892), cited from his Etudes de philosophie ancienne et de philosophie moderne (Paris, 1954), 231; M ignucci, op. cit. (n. 13), 722; Rist, op. cit. (n. 35), 396. 42. Long, op. cit. (n. 33), 84-5 with n. 21, m isreports this text, w riting ‘a true antecedent proposition . . .’ As we shall see, it is a nice problem ju st where in the proceedings the truth o f the antecedent comes in. 43. Alternatively, if it is so read, it should be judged inaccurate on the point or misleadingly condensed.

If one m eans to speak o f a sign, does one have to start out w ith the w ord ‘I f ’?44 T hat cannot be rig h t either, or else p ro o f w ould not be a species o f sign. T he standard explanation o f the claim that p ro o f is a species o f sign points to the fact that in a dem onstrative p ro o f the premisses serve to reveal, i.e. give know ledge of, the conclusion (PH π 131, 134; M vin 140, 180, 299). T he conjunction o f the prem isses is a sign o f the conclusion (M vm 277). It is thus by a sort o f m eto n y m y that p ro o f com es to be classified under ‘sign’. T he official genus o f p ro o f is logos, i.e. argum ent, i.e. prem isses plus conclusion (e.g. M vm 301, in such close p ro xim ity to the claim at 299 that the genus o f p ro o f is sign that we m ust suppose the tw o classifications are n o t th o u g h t to be at variance w ith each other and try to understand them accordingly). Strictly, n ot the w hole p ro o f but its prem isses m ake the sign. T he m etonym ous classifica­ tion is best explained at M vm 140: it is by participation in sign, i.e. it is because the prem isses are a sign o f the conclusion, that a p ro o f serves to reveal its conclusion. Proof, it seems, derives its revelatory character fro m that o f sign. But now , a p ro o f does n o t begin w ith the w o rd ‘I f ’ (save per accidens). T o every argum ent (hence to every proof) there corres­ ponds a conditional proposition w ith the conjunction o f the a rg u m en t’s prem isses as its antecedent and the conclusion o f the argum ent as its consequent, and Stoic logic declares that the argum ent is valid if and only if the associated conditional is sound (PH π 137). B u t th at fam ous contribution to logical theory presupposes a clear distinction betw een an argum ent, w hich is a sequence or ‘system ’ o f propositions (PH 11 135-6), and a con­ ditional, w hich is a single com plex proposition (DL vu 68-9). In a p ro o f in w hich the prem isses are a sign o f the conclusion they are not enclosed w ithin a conditional. It follows that, even if every sign is a proposition w hich form s the antecedent o f a sound conditional, it should n ot be Stoic doctrine that the proposition counts or serves as a sign only w hen it occurs as the antecedent in a sound conditional. R ightly read, our passage ought to claim an im p o rtan t association betw een signs and conditionals (an associa­ tion related to the association betw een p ro o f and conditionals); it

44. Cf. Long, op. cit. (n. 33), 86: “ Ί ί smoke, . . . ” not sm oke as such is the signal’.

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should not im priso n signs w ithin the conditional fo rm o f express­ ion. W e m ust labour ou r w ay th ro u g h one m ore thicket and then (I trust) a light will daw n. It is generally assum ed that tw o kinds o f sign are recognised by the Stoics, the com m em orative (hupomnëstikon) sign and the indicative (endeiktikon) sign. It is controversial w hether b o th are m eant, or only the second, w hen it is said that a sign is a proposition w hich form s the antecedent o f a sound conditional, being revelatory o f the consequent.45 In due course I will argue that both are m eant. T he im m ediate problem is that w hen the distinction betw een the tw o kinds o f sign is explained, it turns ou t that signs o f both kinds are observable, w hich no lekton could ever be. T here should really be no dispute about th is.46 T he com ­ m em orative sign is (by definition) som ething observed in con­ ju n ctio n w ith w hat it signifies, as sm oke is observed in conjunc­ tion w ith fire (P H π ioo; M vm 152). T he indicative sign is not som ething observed in conjunction w ith w hat it signifies, b u t the reason for this is that w hat it signifies is unobservable (M vm 154). T he sign itself, by contrast, m ust be im m ediately evident, as w hen blushing is a sign o f sham e (M vm 173) or the m ovem ents o f a p erso n ’s body a sign o f the soul w ithin (M vm 154—5). T he distinction is expressly tailored (PH 11 99; M vm 151, 156) to an epistem ological distinction betw een tw o classes o f non-evident object. T he com m em orative sign is for getting know ledge o f things w hich are tem porarily (pros kairon) non-evident, as e.g. the city o f A thens happens not in present circum stances to be evident to us now . T h e indicative sign is for getting know ledge o f things w hich are naturally (phusei) non-evident, one im p o rtan t category o f w hich com prises internal states o f the hum an body, e.g. the presence o f ‘intelligible p o res’ in our flesh th ro u g h w hich sweat

45. Both according to Jacques Brunschwig. ‘P ro o f defined’, in Doubt ami Dogmatism, cd. Malcolm Schofield, Myles Burnyeat and Jonathan Barnes (O xford, 1980), 147 with 132-3, 134 n. 22. Indicative signs only according to Jonathan Barnes, ‘P ro o f des­ troyed’, ibid. 179-80 (they are disputing the extension o f the concept o f revelation, which is one part o f the official account o f sign). 46. Pace Long as quoted n. 44 above, taking issue w ith Benson Mates, Stoic Logic (Berkeley & Los Angeles, 196t2), 14, w ho had said, correctly, that the discussion o f com ­ m em orative and indicative signs, as Sextus presents it, is compatible w ith the view that signs are physical objects.

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flows (cf. also M vm 219-20); but rem em ber that for Stoic m aterialism psychological states like sham e are bodily as well. A ccordingly, ju s t as the thing signified is a n o n -evident object or condition, so in these exam ples and m any others w hat is spoken o f as the sign (com m em orative or indicative) is a thing (state o f affairs, event) observed, no t a proposition w hich is an abstract object o f th o u g h t. A t this point it m ay be suggested that the problem is unreal. T here is n o hard evidence that the distinction betw een indicative and com m em orative signs goes back to Stoic sources, indeed no explicit form ulation o f the distinction before the tim e o f Sextus E m p iricu s.47 M y reply is that the distinction as Sextus discusses it, and the term in o lo g y in w hich it is cast, m ay well be late and m ay ow e as m uch to m edical as to philosophical circles,48 but that a corresponding distinction w ith the sam e or sim ilar function is firm ly em bedded in Stoicism at least as far back as C hrysippus. First, it is indisputably a Stoic thesis, presupposing their princi­ ple o f conditionalisation, that the prem isses o f a p ro o f are a sign w hich reveals the conclusion; Sextus’ interw eaving o f the topics o f sign and proof, w ith the same exam ples recurring (see below ), m ust reflect Stoic sources. A nd w e k n o w that, for the p ro o f to be 47. Roughly contem porary w ith Sextus are Ps.-Galen, D e f . m e d . xix 396, 12 Kühn = Karl Deichgräber, D i e g r i e c h i s c h e E m p i r i k e r s c h u l e (Berlin, 1930), fr. 81, Ps.-Galen, H i s t . p h i l . in Diels, D o x o g r a p h i G m e c i (Berlin 6 c Leipzig, 1929), 605, 10-18. There are o f course num erous medical passages which presuppose the ideas here form ulated (see e.g. Dcichgräbcr, o p . c i t ., fr. 78, 80 and pp. 308!!.), and Sextus says ( P H 11 121) that controversy about the indicative sign had already started before his time. For a challenging critique o f the tradition o f attributing the distinction to the Stoics, see David Glidcien, ‘Skeptic sem iotics’, in R i v e r s i d e S t u d i e s i n A n c i e n t S k e p t i c i s m , ed. D. Gliddcn (forthcom ing); also Sedley’s paper, C hapter 8 below. It should be noted, however, that the m ost substantial o f the above references, Ps.-G alen H i s t , p h i l . , starts w ith the dialecticians’ (i.e. Stoic logicians’) definition o f sign as the antecedent o f a sound conditional, and then proceeds imm ediately to distinguish indicative and com m em orative signs, as if the distinction belonged quite com fortably with the definition. 48. Sextus says that the indicative sign is a concoction o f the dogm atists ( P H 11 102) or, m ore expansively, o f the dogm atic philosophers and Logical physicians ( M vm 156-7). This meagre testim ony hardly suggests medical priority; nor, as ju st seen (n. 47), does Ps.-G alen H i s t , p h i l . , w hom Diels, o p . ci t . (n. 47), 246-52, judged to be using a Stoic source. T he prom inence o f medical examples in Sextus’ discussion o f signs, w hich is som etim es thought to betray medical priority, seems to me neither here nor there: medical examples are equally prom inent in A ristotle’s discussions ol signs, as is rightly emphasised by G. Preti, ‘Sulla dottrm a del αημεϊον nella logica stoica’, R i v i s t a C r i t i c a d i S t o r i a d e l l a P i l o s o f i a 11 (1956), 5-16. I am inclined to think that w hat Sextus is discussing is the philosophical version o f a distinction which in the medical literature leads an independent and quite complicated life o f its own.

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a valid proof, the conditional in w hich the conjunction o f prem is­ ses stands as antecedent to the conclusion as consequent has to be a necessary truth; it m u st satisfy the strong criterion o f soundness called sunartësis (‘co n n ex io n ’ or ‘cohesion’), w hich the general consensus o f m o d ern scholarship associates w ith C h ry sip p u s.49 B ut secondly, no one w h o reads th ro u g h the first book o f C icero’s de Divinatione w ill d o u b t that the Stoics have a mass o f theory concerning a type o f sign w hose conditional expression could not possibly m eet this stro n g criterion. In divination, as in m edicine, o ur know ledge o f w h at is a sign o r evidence o f w h at grow s ou t o f a long record o f observed and rem em bered conjunctions, gradual­ ly corrected for erro r (D iv . 1 16, 24-5, 109, 127). T hat there are such divinatory signs for us to learn and use the Stoics establish by an arg u m en t fro m divine providence w hich is sim ply a m ore elaborate and specialised version o f the argum ent w e have been discussing (Div. 1 82-3, 11 101-2; cf. DL vn 149); and this argum ent is expressly attrib u ted to C hrysippus, D iogenes o f B abylon and A ntipater (Div. 1 84, 11 101). N o w , given th at there is in any case independent evidence that C hrysippus was keen to distinguish betw een a strong (sunartësis) conditional, w hich states a necessary connexion, and a w eaker (Philonian or m aterial) conditional to be em ployed w hen the form er is in ap p ro p riate,50 and given that the de Divinatione’s signs (observed item s like entrails and cocks crow ing) obviously go w ith the w eaker conditional, all w e need to com plete the four-part jig saw puzzle is to find th at other observed item s, such as blushing (an exam ple used by Cleanthes: S V F 1 518, n. 86 below ), are supposed to stand in a necessary connexion w ith that w hich they are a sign of. T his w e shall find shortly. Thus the distinction betw een tw o types o f conditional leads naturally to a correspond­ ing distinction betw een tw o types o f observed sign. W e shall need som e term in o lo g y to m ark the latter distinction. Since we know 49. References and discussion in Michael Frede, Die Stoische Logik (Göttingen, 1974), 80-93, 119-21; Barnes, op. cit. (n. 45), 169-72. 50. The main evidence is C ic. Fat. 1 r-r6 , where the discussion is firmly based in divination. For other references and discussion o f complications, see Frede, op. cit. (n. 49), 80-93; Richard Sorabji, Necessity, Cause and Blaine: Perspectives on Aristotle's Theory (London, 1980), 74-8; Sedley in C hapter 8 below; for another context where Chrysippus made im portant use o f the distinction, see Barnes in C hapter 2 above and m y ‘Gods and heaps’, in Language and Logos, cd. M. Schofield and M Nussbaum (Cam bridge, 1982).

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o f none that C hrysippus used, we m ig ht as well call it the distinction betw een ‘indicative’ and ‘co m m em o rativ e’ signs, adding scare-quotes w hen w e m ean to speak o f the Stoic original o f the distinction w hich was later so called.51 So the problem rem ains o f squaring the account in term s o f propositions w ith the definitions o f the tw o kinds o f sign, reflecting as they do everyday talk about the condition o f the entrails being a sign o f an abundant hay crop (an exam ple from Cic. D iv. II 30) or blushing a sign o f shame. B ut I subm it that we have now assem bled enough m aterial to see that both this problem and our earlier difficulties dissolve as soon as w e recognise that there are tw o levels in the Stoic account o f signs, as there w ere in A risto tle’s. T he distinction betw een ‘co m m em o rativ e’ and ‘in­ dicative’ signs, and the explanation o f each o f them , corresponds to the non-technical definition o f A n . Pr. 702.7-9. T he statem ent that a sign is a propo sitio n w hich form s the antecedent in a sound conditional, being revelatory o f the consequent, corresponds to the logician’s technical explication at A n . Pr. 7036-7.52 T h at is our first gain from setting the Stoic account o f signs side by side w ith A ristotle’s: in order to be rid o f an issue w hich has caused m uch perplexity in the scholarly literature, all we need to see is that in the m ove from the non-technical level to the technical the ordinary m an ’s idiom ‘X is a sign o f Y’ is replaced by logician’s talk o f propositions - A ristotle’s recom m endation is accepted by the Stoics because it is a prerequisite for analysing the inferences in w hich signs essentially b elo n g.53 B u t o f course the Stoic analysis will use propositional logic rather than syllogistic. 51. A distinction between inference to the unobserved and inference to the unobservable is im portant for the Epicureans also: Philodem us, de Signis 37.25—30. 52. As textual signs o f a two-level approach I w ould cite: (a) the harsh abruptness o f the transition (οφεν καί) from non-technical to technical and back again at P H π t o i- 2 (but see further n. 57 below), (b) M vin i4off. finds it possible to discourse at length against the theory o f indicative signs w ithout bringing in materials from the technical explication, the critique o f w hich is delayed until 245, one hundred sections later, (c) W hen the explication is finally brought in, it is actually described by Sextus as a piece o f their technologia (vm 257; cf. 87, 435). (d) Μ vm 254-6 appends to the technical explication a lucid w arning against the confusion involved in thinking that one can carry over to the technical level the tem poral categories appropriate at the non­ technical level (cf. n. 68 below). I should m ake it clear, however, that by talking o f tw o levels 1 mean nothing m ore elaborate or sophisticated than we have already found in Aristotle. 53. In their case (cf. n. 45 above) it is not out o f the question that they have additionally in view' a thesis about the underlying logical form o f ‘X is a sign o f Y’. For they do have things to say about the logical form o f ‘X is the cause o f Y’: see Michael Frede, ‘The

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T hus the m ilk exam ple returns, b u t A risto tle’s universal gener­ alisation ‘All w h o have m ilk are p reg n a n t’ gives w ay to the conditional ‘If she has m ilk in her breasts, she has conceived’ (PH η 106; M vin 252).54 W e surm ise that, as the A ristotelian recon­ struction o f this exam ple too k the fo rm o f a first figure syllogism (Barbara), so the Stoic reconstruction is a p ro o f in the form o f their first indem onstrable (modusponens)·. ‘If she has m ilk in her breasts, she has conceived; she has m ilk in her breasts; therefore, she has conceived’. A nd this very argum ent duly turns up in the discus­ sion o f p ro o f (M vin 423). Sim ilarly, the ‘intelligible p o res’, w hich are a stock illustration o f the sort o f thing w e need the indicative sign for (P H 11 98; M vm 146), recur in the frequently cited p ro o f ‘If sw eat flow s th ro u g h the skin, there are intelligible pores in the flesh; b u t the first; therefore the second’ (PH 11 140-2; M vm 306, 309). These pores, m oreover, are clearly stated to be a necessary consequence o f their sign, on broadly conceptual grounds (PH 11 142; M vm 309).55 T h a t is one earlier desideratum secured (p. 213 above). N otice also th at reconstruction in modus ponens allows, indeed it requires, the sign p ro p ositio n ‘She has m ilk ’ to be able to appear as an independent assertion, outside the conditional o f w hich it is the antecedent. T h ereb y a second desideratum is secured and confirm ed (p. 210-11 above). C an we go fu rth er and suggest that th e Stoics agree w ith A ristotle that this is the m ode in w hich sign p ropositions ordinarily appear? It seem s from Sextus’ exposition that w e can. N o t one o f the concrete exam ples in Sextus (either com m em orative o r indicative) has the ordinary m an asserting o r th inking a conditional. O n seeing a scar, one says, ‘T here was a w o u n d there before’ (PH π 102; M vm 153), not: ‘If this m an has a scar, he has had a w o u n d ’. T he p ro p o sitio n w hich form s the consequent o f the conditional appears as an independent assertion, presupposing the same status original notion o f cause’, in Doubt and Dogmatism, op. cit. (n. 45), esp. 229-34, Jonathan Barnes, ‘Ancient scepticism and causation’, in The Skeptical Tradition, ed. M . F. B urnyeat (forthcom ing). 54. The reader may im agine extra-logical reasons for changing the conclusion from ‘She is pregnant (κύει)’ to ‘She has conceived (κεκύηκεν)’. Cf. n. 36 above. The conclusion in ps.-G alen Hist, phil., loc. cit., is ‘She has given birth (τετοκυΐά έστιν), as at Ar. Rhet. I3 5 7 b i5 -i6 , w hich confirm s Diels’s view (n. 48 above) that Ps.-G alen is not simply copying Sextus. 55. Sec further Brunschw ig, op. cit. (n. 45), 135-6, 153; his emphasis on ‘preconception’ (πρόληψις) as the backing tor the conditional here can be further supported by the polemical context P H it 198-203, even though the consequent there is n ot non-evident.

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for the proposition form ing the antecedent. A gain, on observing a m an w o u n d ed in the heart w e foretell that death will com e (M vm 153), not: ‘If this m an is w o u n d ed in the heart, he will die’.56 Thus far the exam ples are o f ‘co m m em o rativ e’ signs, so perhaps the conditionals are m issing because the technical explication and modus ponens reconstruction are n ot m eant for them , only for the ‘indicative’ sign (cf. p. 211 above)? B u t no, these very conditionals tu rn up am ong the exam ples used in a separate context later w hen the discussion has turned to the technical Stoic explication (M vm 252-6; cf. P H i i 106).57 It is the same w ith ord in ary life exam ples o f the indicative sign. W e reason, ‘W hat produces such m ovem ents as these is a p o w er w ith in the p erso n ’s b o d y ’ (M vm 155), not: ‘If a body m oves thus and so, it has a soul’. The consequent o f the conditional is asserted as the conclusion o f an inference. A nd, o f course, as o u r exam ple o f a p ro o f in w hich the conjunction o f the prem isses is a sign o f the conclusion w e have ‘If m otion exists, void exists; m o tio n exists; therefore, void exists’, 56. The same holds o f both indicative and com m em orative examples in Ps.-G alen Hist, phi!., loc. cit. In m ore polemical vein M vm 269-71 aligns illiterate farmers and navigators w ith irrational animals in order to m ake it plausible that one can make use o f weather signs and the like w ithout indulging in conditional judgem ents. 57. Unless Sextus is irresponsible in his choice o f examples, this should settle the dispute between Barnes and Brunschw ig (n. 45 above) in favour o f the latter. When Sextus says that he will confine his discussion to the indicative sign (PH π I 0 2 , M vm 156), it is not necessary (pace Barnes, ‘P ro o f destroyed’, 180 n. 23) that all Stoic material in w hat follows should pertain exclusively to that; the general technical theory o f signs is naturally sum m oned in defence o f the sign which is under attack (cf. 11. 40 above). B runschw ig, 147, is right to emphasise that the definition which speaks o f the antecedent revealing the consequent is presented as the definition o f sign in genera] at M vm 243, P H 11 104; and he too readily concedes that PH 11 101, exceptionally, makes it the definition o f indicative sign. For here, I think, he should have recognised the hand o f our m utual acquaintance ‘Lector Sublogicus’ (cf. B runschw ig, 155-6 n. 51), or at any rate a textual puzzle. The w ording o f the definition is identical at P H π 101, 104; M vm 245, 250, 2 7 2 ; Ps.-Galen, Hist. phi!. 605.10-11 Diels; but for one variation to be discussed later (p. 222-3 below) and but for the addition at P H 11 101 o f ένδεικτικόν, oddly separated from the noun σημειον. At the very least ένδεικτικόν is an intrusive gloss, explaining (correctly) τούτο το σημειον. But ο ρ ίζο ντα ι τούτο τό σημείον is just as troublesom e, im plying as it does that the Stoics are identical w ith the people who wield the term inology o f indicative and com m em orative signs (καλοΰσιν, ioo; cf. p. 212 above). T he w hole sentence όθεν κ α ί ό ρ ίζοντα ι τούτο . . . λήγοντος is at best parenthetical to its context, a prem ature intrusion o f a technicality which is shortly going to be reintroduced, as if for the first time, at 104. I believe that we have no choice but to excise the whole sentence, follow ing Paul N atorp, Forschungen zur Geschichte des Erkenntnisproblems im Altertum (Berlin, 1884), 142-4; W erner Heintz, Studien zu Sextus Empiricus (Halle, 1932), 46-51; J. Mau in the revised Teubner edition o f 1958. But others have tried to defend the text (e.g. O tto Rieth, Grundbegriffe der Stoischen Ethik (Berlin, 1933), 181-90; Glidden, op. cit. (n. 47)), and it will be sufficient for m y argum ent to insist that the sentence be set aside as too problem atic to be used in evidence.

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n ot the associated conditional ‘If, if m otion exists, void exists, and also m o tio n exists, then void exists’ (M via 277). O n ly after the official explication o f sign has been introduced do w e m eet ‘If she has m ilk in her breasts, she has conceived’, and the like (M vm 252 w ith 244; P H π 106 w ith 104). T he contexts w here sign (‘com ­ m em o rativ e’ or ‘indicative’) and significate appear unasserted inside a conditional are ju st those contexts w here the discussion is at the technical level. T h us fro m the organisation o f Sextus’ discussion, from the m anner in w hich he presents his exam ples, and above all from the requirem ents o f modus ponens reconstruction, it w ould seem to be the logician w ho brings o u t that the ordinary m an ’s sign-inference relies essentially on the soundness o f the associated conditional. T he conditional ‘If this, then th a t’ gives explicit expression to the connexion o f consequence (akolouthia) w hich the inference uses.58 Like A ristotle’s universal generalisation, it belongs m ore to the technical reconstruction o f the inference than to the everyday language o f the d o c to r’s consulting room . T his brings us back to our passage. It is the voice o f a logician turned m etaphysician (very Stoic, and a bit o f a bully) w hich argues that, since m an is prone to m ake inferences, providence w ould have equipped him badly for the w orld he has to live in unless the associated conditionals w ere really and truly reliable. For that is w h at he is saying w hen he concludes ‘Hence, signs exist’, changing n o t the subject b ut the level o f his discourse. His m eaning is not: there are antecedents in the aforesaid conditionals (= ‘sig n’ as explicated). B ut rather: certain em pirically observable item s (viz. those w hose existence or occurrence is asserted w h en a sign-proposition is taken o u t o f its conditional and used to show som ething) really are evidence for w hat is inferred from them (= ‘sig n’ as non-technically defined).

IV It was once said, ‘La théorie des signes n ’a pas d ’analogue chez A risto te.’59 I hope th at by n o w the analogy betw een A ristotle and 58. Akolouthia can be used for the relation o f antecedent and consequent in any sound conditional, not ju st those that arc logically true: M vm t o f f , Frede, op. cit. (n. 49), 81-2 (cf. n. 33 above). 59. Brochard, op. cit. (n. 41), 231.

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the Stoa is looking sufficiently close to suggest that a com parative assessm ent w ou ld be b o th m eaningful and rew arding. W e shall find that the assessm ent leads to qualifications and a change o f emphasis in the analogy, as so far draw n, w hich m akes com pari­ son possible. O ne im p o rtan t m atter w hich A ristotle is clear about is that the sign-inference is an argu m ent (enthym em e, A n . Pr. 70a!0, i.e. a rhetorical apodeixis, Rhet. 135536) in w hich an inferential particle joins tw o independently asserted propositions. This is especially evident in the exam ple ‘W ise m en are good, for Pittacus is g o o d ’, w here surface gram m ar presents prem iss and conclusion as dis­ tinct statem ents. A risto tle’s other exam ples use locutions o f the form ‘q because p ’, w hich have the surface gram m ar o f a single com plete statem ent, but his w hole approach determ ines that these shall be construed, like the Pittacus exam ple, as expressing an inference o f the form ‘p, so q’. B oth the sign-proposition and w hat is inferred from it are asserted as true. D id the Stoics appreciate the point as clearly as Aristotle? W e have so far given them the benefit o f the doubt, b ut it took a bit o f w o rk (pp. 215-17 above). Was our effort a mistake? W e m ay approach this question by w ay o f another. T he disadvantage o f illustrating ordinary language sign-inferences by locutions o f the form ‘q because p ’ is that ‘because’ can introduce considerations (o f causality, explanation, etc.) other than the purely inferential. A ristotle is no t m isled, bu t for clarity w e m ight prefer a locution such as ‘Since p, q’ w hich presents q as inferred from p w ith n o thing fu rth er either stated or im plied. A nd it so happens that the Stoics also take the trouble to distinguish betw een ‘Since p, q’ and ‘q because p ’. T he follow ing is reported from the A rt o f Dialectic o f one C rinis (DL vu 71-4):60 ‘Sincep, q’ is true if and only if (1) ‘Ifp then q’ is true, (2) ‘p ’ is true; ‘q b ecau sep ’ is true if and only if conditions (1) and (2) hold and also (3) ‘If q then p ’ is false (the idea, presum ably, is that ‘because’ im plies an 60. Possibly a pupil o f Archedem us o f Tarsus, hence second half o f the second century r . c . So von Arnim , R E s.v. ‘K rin is\ on the strength o f Epict. Diss. m 2,15, which in fact only says that he read Archedem us, not that he was his pupil. But the passage does indicate that it was easier to rem em ber the story that Crinis died of fright at the noise made by a falling mouse than to rem em ber the name o f the man about w hom the story was told. I.e. he is the very type o f undistinguished Stoic, whose book w ould be a school handbook rather than an original contribution to logical theory; that w ould be w hy his definitions are picked for citation (cf. DL vil 62, 68, 76 as well as 71-4). We can presum e that his material is reasonably orthodox.

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explanatory dependence o f q on p, a relation w hich o u g h t to be asym m etrical - cf. A r. A n. Pr. B 16). N o w , has this contrast anything to do w ith the study o f signs? W ould a Stoic be w illing to accept ‘Since p, q as the canonical representation o f a signinference? Som e Stoics clearly w ould, at least for purposes o f discussion, if it is Stoics w ith w h o m Philodem us is debating in de Signis, for ‘Since p, q' is the m ost co m m o n form o f sign-inference illustrated th ere.61 Sextus is no help on the point, since in fact he never spells ou t an exam ple fully enough to need either ‘because’ or ‘since’ or any other inferential particle (cf. p. 215-17 above).62 Let us be cautious, therefore. For the m o m en t let it be a m ere hypothesis o f our im agination th at a Stoic w o u ld w ant to accept ‘Since p, q’ as the canonical representation o f a sign-inference. Then, I think, w e are b o un d to observe that the Crinis analysis treats ‘Since p, q as a single com plex proposition, called ‘subconditional’ (parasunëmmenon).63 T o assert a subconditional is equivalent to asserting a conjunction o f the fo rm ‘p and if p then q’; and a m an w h o does that has n o t yet carried out an inference. N o inference takes place unless he proceeds to assert q. So m uch the w orse, you m ay say, for the suggestion that the subconditional has anything to do w ith sign-inferences.64 B ut let 61. See Sedlcy in C hapter 8 below for the identification o f Philodem us’ opponents as Stoics and its connexion with the form ‘Since p, q\ 62. I do not think this is accidental. Sextus intends to emerge from the discussion with nothing left for the sceptic but the com m em orative sign, and that only after it has been shorn o f the idea that it provides a reason for som ething. If he avoids writing, e.g. ‘This man has had a w ound because/sincc he has a scar’, he can leave the example intact and represent the ordinary life use o f com m em orative signs as mere associative habit such as m ay be found in irrational animals (M vm 269-71). This m atter is well discussed by Glidden, op. cit. (n. 47), although I am not convinced by his using it to argue that the indicative and the com m em orative sign are not the com plem entary pair they seem to be. True, habit does n o t pair w ith indicative sign-inference, but Glidden agrees that Empirical medicine accepts the inferential status o f the com m em orative sign. If Sextus does not, he diverges from the usual understanding o f com m em orative sign, preferring the M ethodic approach as he describes it at P H 1 236-41 (on which see Michael Frede, C hapter 1 above). This explains how Sextus can countenance including in his polem ic against the indicative sign a num ber o f argum ents which appear to some com m entators (w hether rightly or w rongly we need not decide) to underm ine reasoning from signs as such: Sextus seeks to underm ine all reasoning as such. 63. Presum ably the prefix π αρα - is added to suggest it is a derived or secondary type o f conditional; cf. παρώ νυμος. 64. Frede, Die Stoische Logik (η. 49). ιοο, remarks that the παρασυνημμένον seems not to have any im portance in Stoic logic; but a reader w ho looks up his useful references to w hat later gram m arians have to say about the conjunction ‘since’ finds them all, to a greater or lesser extent, influenced by the Crinis style o f analysis.

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im agination persevere a w hile longer. O ne solution w hich tw en­ tieth-century experience m ight offer our im aginary Stoic, could he have foreseen it, is a distinction betw een the content o f an assertion stricto sensu and w h at it presupposes. Instead o f holding, w ith Crinis, that ‘Sincep, q asserts the conjoint tru th o f ‘p ’ and ‘If p then q \ the rig h t answ er, it m ig h t be suggested, is that ‘Since p, q’ asserts the tru th o f ‘I f p then q on the presupposition that the tru th o f ‘p ’ is already g iv en .65 T he speaker w ho uses the w o rd ‘since’ rather than ‘i f ’ is (understood to be) presupposing - so that he does no t n o w need to assert - that the case w here ‘p ’ is false is ruled out. W ould som e such account as this fit ‘Sincep, q’ to be the canonical representation o f a sign-inference? If the question seems anachronistic, dem anding m ore pronoia than even Stoic w isd o m can aspire to, it m ay nonetheless open our eyes to one o f those divergencies in term in o lo g y and form ulation w hich Jacques B runschw ig has tau g h t us to see as a sign that the birth o f im p o rtan t logical notions is a slow process o f refinem ent, not a sudden em ergence o f fully arm ed w isdom . B runschw ig discerned in Sextus three distinct, progressively refined accounts o f p ro o f.66 I can n o w reveal that they are preceded by three distinct, progressively refined attem pts to form ulate a definition o f sign to m atch. T o see this, w e m ust attend carefully (follow ing B ru n sch w ig ’s example) to differences betw een the P H and the M versions o f the Stoic theory. ‘A sign is a p ro positio n form ing the antecedent (kathêgoumenon) in a sound conditional, being revelatory o f the con seq u en t.’ So begins the technical section at M vm 245. T he next m atter is to select one o f the com peting sets o f tru th -co n d itio n s for the conditional; the Philonian conditions (m aterial im plication) are selected, w ith o u t argum ent. These being set out, they yield three cases in w hich the conditional is sound (T D T, F D F, F D T). B ut reference back to the initial definition tells us that a sign ought to be a tru th w hich establishes, i.e. reveals, another tru th (24p).67 65. See T eun A. van Dijk, Text and (Context: Explorations in the Semantics and Pragmatics of Discourse (London and N ew Y ork, 1977), 68 ff., 2o6ff; Claudio Pizzi, ‘“ Since” , “ Even if” , “ As i f ” , in Italian Studies in the Philosophy o f Science, ed. Maria Luisa Dalla Chiara (D o rd rech t, 1980), 73-87.

66. The next five paragraphs are offered as an appendix to Brunschwig, ‘P roof defined’, op. cit. (n. 45), draw ing persuasive effect from it and contributing in return some support to its main contentions. 67. εί τό σημεϊον άλη θές είνα ι δει κ α ί ά λη θοΐ'ς π αρασ τατικόν. The point is brought in as som ething already determ ined by the definition, and in fact π αρα σ τατικόν is a

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So w hen it is said that a sign is a proposition form ing the antecedent (kathëgoumenon) in a sound conditional, we shall have to understand (deêsei akouein) this in the n arro w er m eaning ‘the antecedent (kathëgoumenon) p ro p o sitio n in a conditional w hich both begins w ith a tru th and ends w ith a tru th ’ (250) T he full definition is finally reached by dividing the conditional so speci­ fied into the case w here the antecedent (hëgoumenon) is revelatory o f the consequent and the case w here it is n o t (250-1) - the technical Stoic definition o f sign, unlike the A ristotelian, has an epistem ic com ponent. T h e antecedent m ust be evident and m ust give us know ledge o f a non-evident consequent, w h eth er this be the non-evidence o f things that are by nature unobservable (‘indicative’ sign) or that o f things that are tem porarily beyon d the reach o f observation (‘co m m em o rativ e’ sign). W e are n o w ready to draw the conclusion: ‘A sign, therefore, m ust n o t only be the antecedent (hëgoumenon) in a sound con­ ditional, that is (sic), one w hich b o th begins w ith a tru th and ends w ith a truth, b ut m ust also possess a nature such as to reveal the consequent’ (252). T he com m ents ‘w e shall have to u n d erstan d ’ and ‘that is’, together w ith the back-references at 248, 249, 250, give the gam e away. T his is a definition by division designed to elucidate and m ake m ore precise a pre-existing definition, in very m uch the style that B runschw ig revealed in the M vm discussion o f p ro o f.68 T he term ino logy confirm s it: the original definition uses ‘kathëgoumenon for ‘antecedent’, w hile the com m entary on it uses the standard term ‘hëgoumenon’. Janâcek’s index show s that ‘kathëgoumenon’ occurs in Sextus only w hen he is reporting or referring directly to this very definition (M vm 245, 248, 250, 256, 268, 271, 272, 265, 269). synonym for έκκαλυπτικόν: M vni 392 with PH 11 178; M vm 314, vn 85-6; Brunschwig, op. cii. (n. 45), 146-7; Barnes, op. cit. (n. 45), 165 n. 7. 68. W here precision is concerned the mam im provem ent is signalled by ‘we shall have to understand’, viz. that a sign is a true antecedent (cf. n. 42 above). Additionally, how ever, an appendix (254-6) to the division proper berates ‘some people’ for not appreciating that in the scar-w ound example, for instance, while the w ound itself is past and gone, the m an’s having had it is present, not past (cf. (d) in n. 52 above). The proposition ‘He has had a w o u n d ’ is ju st as m uch a present truth as the sign for it, ‘He has a scar’. The definition o f sign is then expanded to include the point that a sign is always a present sign ot a present thing, where ‘present’ (said o f a proposition) presum ably means ‘true in the present’. This extra refinement, which Sextus exploits at 272, docs not really belong in the definition o f sign. Its im portance lies in another direction: in the denial that a present thing is ever the sign o f som ething in the past (254), we see one Stoic at least claiming that the underlying logical iorm o f ‘X is a sign o f Y ' is given by 1That p is a sign that q (cf. n. 15., n. 53).

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It rem ains to com m ent on the choice o f the Philonian conditions for the soundness o f the sign-conditional. T he choice is presented as a deliberate choice from the m any available (245; cf. M vm 428 and the list o f four sets o f soundness conditions at P H 11 110-12). T he intention m ust surely be to fix the m inim al, m ost general conditions for signhood, so as to cover ‘co m m em o rativ e’ as well as ‘indicative’ signs (cf. pp. 211-14 above). For the exam ples in this indubitably Stoic discussion include tw o (scar—w ou n d , heart puncturing—death, 254—5) w hich are paradigm atic for the com ­ m em orative sign (PH ii 102; M viii 153), as well as the indicative m ilk exam ple (252).69 W hen w e tu rn to the definition o f sign at P H π 101 and 104 we sight a bird o f greater rarity still: a sign is a proposition w hich is prokathëgoumenon in a sound conditional, being revelatory o f the consequent.70 T he term ‘prokathëgoumenon evidently presupposes ‘kathëgoumenon’, so th at the P H definition, like the M definition by division, is posterior to the original definition. ‘Prokathëgoumenon m eans, we are told (P H 11 106, τ ι 5). ‘T he antecedent (hëgoumenon) in a conditional w hich both begins w ith a tru th and ends w ith a tru th ’. In oth er w ords, the P H definition encapsulates the results o f M v m ’s clarifying w ork: the tru th o f the antecedent is built into the definition o f sign fro m the outset. W here the M vm division laboured to em bed the sign-proposition in a conditional satisfying ju st those conditions that Crinis associates w ith ‘Since p, q , the P H π account handles the same m aterial w ith noticeably greater assurance and ties it all up in a new ly appropriated term o f art. B ut w hy choose the prefix ‘pro-’ for this term inological innova­ tion? ‘Kathëgoumenon’ (lit. ‘leading clause’) already indicates the proposition w hich com es first in the conditional and ‘guides’ you

69. T hat the m ilk exam ple ranks as indicative, pace Rieth, op. cit. (n. 57), 182, Sedley, C hapter 8, n. 8, is established by Ps.-Galen, Hist. phil. 605, 15-18 Diels. This m ust reflect the traditional classification because the w riter or his source seemingly fails to notice that changing the conclusion to ‘She has given b irth’ (n. 54 above) makes it express an observable event. Having conceived is a state internal to the hum an body and so counts as naturally non-evident, requiring an indicative sign (p. 211 above). 70. The occurrence o f ‘prokathëgoumenon’ at Ps.-Galen, Hist, phil 605.11, is due to a correction by Diels (misleadingly attributed in his apparatus criticus to Prantl) to bring a corrupt text into line w ith P H 11 101. T he MSS read έν ΰγ ιεϊ συνημμένον κ αί ήγοΰμενον. Prantl, Geschichte der Logik im Abendlande (Leipzig, 1855), 1 609, corrected συνημμένον to συνημμένω, but left κ αί ήγοΰμενον, for which καθηγούμενον seems a m ore likely correction than D iels’s προκαθηγούμενον. If so, the Hist. phil. passage aligns itself w ith M vm rather than with PH n.

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to the proposition w hich follow s.7172 T he only thing for ‘pro-’ to add is th at the tru th o f the antecedent precedes the conditional ju st as k now ledge o f the tru th o f the antecedent is supposed to precede any use o f the conditional to gain know ledge o f the consequent (PH 11 115-20). This suggestion is speculative. ‘Prokathëgoumenon m ay be no m ore than a term b o rro w ed from a verb o f ordinary language for a technical purpose. B u t if the b o rro w in g does bring som ething o f its ordinary language m eaning w ith it, the addition o f ‘pro-’ can only serve to em phasise that the antecedent is like a guide leading from ahead.12 W e are, it seems to m e, close to the th o u g h t that a sign-conditional presupposes the tru th o f its antecedent. A nd this w o u ld be an additional m otive for tu rning to ‘Sincep, q as an econom ical and appropriate expression for the sign-inferences on w hich so m uch analytical effort has been spent.73 W e m ay add that the difference betw een ‘i f and ‘since’ had been under discussion since T heophrastus, w hose explanation was that people use ‘since’ w hen the antecedent is n o t only true b u t also evident and u n d isp u ted .74 In m odern term s, w e m ig h t say that T heophrastus has ‘since’ contributing to speaker’s m eaning, Crinis to sentence m eaning (truth-conditions), while extending the P H presuppositional analysis to ‘Since p, q w o u ld connect it w ith pragm atics. It seems clear that ‘since’ is the focus o f a problem . W e see w h at the problem is w hen w e see w here all three o f these analyses go w ro ng. Q u ite sim ply, none o f them catches the argum entative force w hich m akes ‘Since p, q’ the expression o f an inference. All three analyses leave q so far unasserted. T hey locate the difference

71. As signs are guides to w hat is not im m ediately evident, so the wise man can guide (kathêgeisthai) the unw ise in the art of life (M xi 247); the Stoic logician w ould not be unaw are o f these w ider resonances w hen choosing his technical term inology. Cf. kathêgeisthai in M vrn 265, 269. 72. C f previous note. PH11 116 fin. employs the verb prokathêgeitai in a m anner consistent w ith this line o f interpretation. 73. This conclusion chimes perfectly with Sediey’s suggestion in C hapter 8 that the subconditional ‘Sincc p, q came into prom inence in connexion w ith signs during the period betw een C hrysippus and the Stoics attacked in Philodem us’ de Signis, with Antipater, whose contribution to an obscure chapter in Stoic logic we are about to discuss, possibly (but here I hesitate) playing some role in its prom otion. 74. Simplicius, in Ar. de Cael. 552.31-553,22, assuming that the substance o f the explanation derives from the first book o f T heophrastus’ Prior Analytics, to which Simplicius refers at the end as having given ‘the explanation o f this usage’. If so, it looks as though in the ancient w orld Gricean conversational implicatures preceded Strawsonian presuppositions.

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betw een ‘Since p, q’ and ‘If p, q’ in the fact that the antecedent o f the form er is so m eh o w asserted as true, and they fuss about to find a w ay (speaker’s im plication, conjunction, presupposition) in w hich the antecedent o f a conditional can acquire assertorie force. B ut this is both insufficient, as leaving q unasserted, and doom ed to failure, because there is no w ay in w hich the antecedent o f a conditional can acquire assertorie force. T h e m istake, how ever, lies no t in thinking that ‘p ’ in ‘Since p, q’ is asserted, w hich is correct. T h e m istake is to think that ‘Since p, q is a conditional o f any shape or form , w hen it is in fact an expression o f the inference i ) 7; p, so q . /D T his m istake, if the Stoics m ade it, is o f far-reaching signifi­ cance. It m ay seem outrageous to suggest such an error, given that the distinction betw een arg u m en t and conditional lies at the very core o f Stoic logic (p. 210 above). B u t a distinction w hich is quite clear in one type o f context m ay get lost in another, and unfortunately, the hypothesis that the Stoics saw a sign-inference as som ehow m ore like a conditional proposition than an argum ent w ould explain quite a lot m ore than the uneasy dealings w e have ju st surveyed. V (1) T he point about ‘Sincep, q and ‘q becausep ’ (for w hich Crinis proposes the sam e style o f analysis) was that they have the surface 75. I regret having to take a stand here on a debatable and complicated issue. For a contrary view, see van Dijk, o p . c i t . (n. 65), and, on ‘because’, Frege, ‘O n sense and reference’, in T r a n s l a t i o n s f r o m t h e P h i l o s o p h i c a l W r i t i n g s o f G o t t l o b F r e g e * ed. Peter Geach and Max Black (O xford, i960), 76-7; Gilbert Ryle, ‘“ If” , “ So” , and “ Because” ’, in his C o l l e c t e d P a p e r s 11 (London, 1971), 234—49 (but ‘because’ has extra complications o f its own). T he question is w hether ‘since’ m arks the occurrence o f an inference or functions as a tw o-place sentential connective. Consider any sentence o f the form ‘If p , then since r, q \ it seems clear that r is asserted and that its truth is a necessary condition for the truth o f the w hole (if the w hole is to be assigned a truth-value). This w ould be inexplicable if Crinis was right about ‘since’, or even if (as has been suggested to me) he was partially right in that he fixed the truth conditions but left out the force or function o f ‘since’; for inside a conditional the latter should be suspended (whereas r is asserted) and C rinis’ truth conditions do not yield the result that the truth o f r is necessary for the truth o f the whole. T he m oral is that ‘Since r, q’ is not a unit for assertion, as comes out also in the fact that ‘Ifjj, then since r, q’ is equivalently and indeed m ore perspicuously rendered ‘Since r, then if also p , q ’ (a form frequent in Philodem us, d e S i g n i s ) . But 1 am aware that m ore needs to be said, e.g. about ‘since’ in o r a t i o o b l i q u a , and that comparisons should be made w ith ‘for’, ‘so’, ‘and so’, ‘and consequently’, etc. (See the material collected in van Dijk). It m ust suffice lor this occasion to indicate what difficulties a full defence o f Crinis w ould have to overcom e. T he only certainty is that no historical Stoic had the resources to overcom e them . (I am m uch indebted to Jonathan Barnes and M ark Sainsbury for discussion o f this issue.)

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gram m ar o f a single com plete statem ent. H ence the tem ptation to construe them as a special sort o f conditional. B ut the other side o f that coin is that, if you yield to the tem ptation, you then face the problem o f w h at to say about A ristotle’s locution ‘q, for p ’, or the equivalent ‘p, so q’, or any o th er w here surface gram m ar suggests w e have tw o distinct statem ents jo in e d by an inferential particle. If these do the same jo b as ‘Since p, q \ and the latter is not an argum ent, will you say that ‘p, so q’ is n o t an argum ent either? Stoic o rth o d o x y was that indeed it is not. O n e prem iss does not m ake an argum en t (M v i i i 4 4 3 ; P H 11 1 6 7 ; Alex, in Top. 8. iqff.; in A n. Pr. 1 7 . i off. ; Apuleius, de Int. 1 8 4 . 1 9 - 2 3 ) . W hy not? It follow s im m ediately from the Stoic definition o f argum ent (logos) as w hat is constructed from prem isses (plural) and conclu­ sion (to sunestëkos ek lêmmaton kai epiphoras, M v i i i 3 0 1 ; cf. P H 11 T3 5, C rinis apud DL vu 7 6 ) that som eone w ho says ‘p , so q’ has not yet constructed an argum ent. A ccordingly, the o rth o d o x view , as Sextus expresses it, is that there are no one-prem iss argum ents, w hile a heretical view cham pioned by A ntipater m aintains that one-prem iss argum ents can be constructed (dunasthai sunistasthai, M v i i i 4 4 3 ) . E xam ples to illustrate A ntipater’s position include ‘Y ou see, so you are alive’ (Apuleius), ‘Y ou are breathing, so you are alive’,76 ‘It is day, so it is lig h t’ (Alexander). These are distinguished,77 b o th by the definition o f argum ent and by A lexander (in A n . Pr. 2 2 . 2 3 - 4 ) , from the category o f ‘u n m eth o d i­ cally conclusive’ argum ents like ‘a is equal to b·, b is equal to c; therefore, a is equal to c’, that is, valid argum ents w ith plural prem isses b ut requiring supplem entation to get them into the canonical form o f a Stoic syllogism ;78 here the addition o f the conditional prem iss ‘If a is equal to b and b is equal to c, then a is equal to c is needed, n o t to m ake the argum ent valid, still less to m ake it an argum ent, but, as the term inology show s, to m ake it ‘m ethodical’, i.e. form ally as well as deductively valid. 76. It m ay be significant that Q uint, hut. v 9.6 cites this example to illustrate tekmêrion, i.e. A ntipater’s concerns m ay well have included the place o f sign-inferences in the theory o f argum ent (we know that he w rote about signs: p. 213 above, Cic. Dip. 1 123). After all, w hy should he choose this type o f example (there is no good reason to doubt the reports that he did) rather than, say, examples o f contraposition ‘If p then q, so if not-g then not-p’ (cf. Frede, op. cit. (n. 49), 118-19)? O n the other hand, the next example on the list does not have the non-evident conclusion required o f a sign-inference (M vm 250-1), so sign-inference cannot have been his sole concern. 77. Pace Mates, op. cit. (n. 46), 66 w ith n. 37; Ian Mueller, ‘Stoic and Peripatetic logic’, Arch. Gesch. Phil. 51 (1969), 175. 78. O n λόγοι ά μ εθόδω ς περαίνοντες, see Frede, op. cit., (n. 49), 121-4.

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N o r are A ntip ater’s exam ples like the A ristotelian enthym em e, argum ents w hich are invalid w ith o u t supplem entation (Alexan­ der, in Top. çhçff., does b ring in the enthym em e, b u t as a distinct item for com parison), for it is co m m o n g ro u n d to b o th parties in the dispute that they are exam ples w here q follow s o f necessity from p (Alex, in A n . Pr. 17.26-18.1; in Top. 9.5-8). Ju st this, indeed, sets the problem . A lexander argues against A ntipater that even though ‘It is light.’ follow s o f necessity fro m ‘It is day ’, it is not redundant to add ‘If it is day, it is lig h t’, and one m ust add it to m ake an argum ent w hich is n o t deficient b u t com plete (in Top. 8.29-9.5; cf. plena conclusio in A puleius).79 B ut if the extra prem iss is no t needed to ensure that the conclusion holds o f necessity, the only further thing it can be needed for is to ensure that the conclusion holds o f necessity because the prem isses hold: a com ­ plete argum ent requires n o t only prem isses such that the conclu­ sion holds o f necessity but, in addition, prem isses such that the conclusion holds o f necessity because the prem isses h o ld ,80 w here the ‘because’ explains n o t w h y the fact is so b u t w hy one m ust accept that the fact is so (Alex, in A n. Pr. 17.22-4; Philop. in A n. Pr. 35-i8ff.). Thus w h at the Stoic o rth o d o x y denies is that, given a m an w h o is breathing, he is thereby sh o w n to be alive, i.e. ju st in virtue o f the bru te fact that he is breathing. R ather, he is sh o w n to be alive by his breathing taken in conjunction w ith the fact that if he is breathing, he is alive, i.e. w ith the fact that there is a connexion betw een his breathing and his being alive.81 W hat the conditional adds is an explicit m en tio n o f the connexion; ‘conne79. W hen Alexander says that in the example λείπει τι ή ένδεής ό λόγος κ αι ό συλλογισμός (notice the coupling o f Stoic and Peripatetic term inology), 1do not think he is putting the example into the Stoic category o f argum ents that are unsound by reason o f deficiency (PH n 150; M vm 434), for this fallacy is defined as a lack in one of the premisses (e.g. ‘W ealth is cither good or bad’ appears instead o f ‘W ealth is either good or bad or indifferent’), not as a lack o f one o f the premisses; as Jonathan Barnes remarks in C hapter 2, the fallacy o f deficiency is a species o f hilsity in the premisses. 80. For this as a Stoic thesis, together w ith its Aristotelian precedent and its m odern revival in the ’logic o f relevance’, see the illum inating discussion in Barnes, ‘P ro o f destroyed’, op. cil. (n. 45). 8 1. Alexander at this point shifts into Peripatetic gear and supplies ‘Everyone who breathes is alive’, explaining that it is only because this further fact is know n and taken for granted by us all that ‘You are breathing, so you are alive’ ever seems to be an argum ent (in An. Pr. 17.18-24; in Top. 8.23-9). But throughout his discussion he rims Stoic and Peripatetic logic in harness (we rem arked one effect o f this in n. 79 above), and we shall find reason to suppose that a Stoic w ould supply, in the first instance, a singular conditional (p. 233 below) and that he w ould not think o f it as a further fact (p. 228 below).

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x io n ’, indeed, is the literal m eaning o f the standard Stoic term for ‘conditional’, sunëmmenon (Latin conexum). W e have seen that the claim that ‘It is day, so it is lig h t’ is n o t a com plete arg um ent and the claim that ‘If it is day, it is light; it is day; therefore, it is lig h t’ suffers from redundancy are the tw o opposite sides o f a single dispute; w hich explains w hy, w hen Sextus m entions the dispute, it is to dragoon A ntipater into bearing witness to the sceptic accusation that even the first indem on­ strable, that leading light o f Stoic logic, is guilty o f redundancy.82 B ut if w e w ant to k n o w w hat A ntip ater’s exam ples are, on the o rth o d o x view th at they are deficient as argum ents, the only assistance w e get is A lexander’s statem ent (in A n. Pr. 17.25-33) that the concept o f follow ing necessarily from is w ider than the concept o f follow ing syllogistically from . T hat m uch he finds in the A ristotelian w o rk he is com m enting upon (An. Pr. A 32). N o t so the illustration he gives o f the point, nam ely, that in a sound conditional such as ‘If it is day, it is lig h t’ the consequent follows necessarily but not syllogistically from the antecedent. This surely is to fuse arg um en t and conditional statem ent in the m ost disastrous m anner. O ne could find no better illustration o f the dangers o f the pervasive Stoic habit o f using the notion o f follow ing or consequ­ ence (akolouthein, hepesthai) to cover both the relation o f the consequent o f a conditional to its antecedent and the relation o f the conclusion o f an argum ent to its prem isses.83 It is indeed hard to see, given this fusion o f ‘p, so q’ w ith ‘I f p, then q’, w hat ‘If it is day, it is lig h t’ can add to ‘It is day, so it is light’. If the addition is no t redundant, as o rth o d o x y insists, it can only be because, as ju st n o w suggested, it helps to exhibit in perspicuous form the connexion betw een the m aterials already given. This brings us back to signs. It has em erged that the Stoic 82. Specifically, A ntipater is made to rebut C hrysippus’ defence that w ithout its condition­ al premiss, alleged to be redundant, the first indem onstrable is no argum ent at all (for a reconstruction and assessment o f the sceptic accusation, see Barnes, op. cit. (n. 45)). N o doubt that was n o t his real intention. Frede, op. at. (n. 49), 118-19, suggests, plausibly, that he may have m eant to point a parallel w ith ‘unm ethodically conclusive’ argu­ ments: if these do n o t need supplem entation to be valid argum ents (p. 223 above), the same should apply where a conclusion follows from a single premiss. 83. Alex, in An. Pr. 373.31-2, actually asserts that Ί fp , then q' means the same as lq follows from C om pare the m ove from inferential consequence to conditional in the argum ent from providence discussed in section III. And while looking back at that argum ent, notice that συνθετική, which troubled us in n. 33, is not preceded by the definite article and therefore describes the same φ αντα σ ία as μεταβατική: consequence and connexion arc tw o sides o f the same coin.

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logician will think o f the technical reconstruction o f a signinference, n o t in the A ristotelian way as filling out an enthym em atic argum ent, bu t as m aking an argum ent w here strictly speaking there was none before, only the m aterials for one. Regardless o f the locution he starts from , be it o f the form ‘If p, then q or ‘Since p, q’ or ‘p, so q’, the m aterials he has to w ork w ith are invariably a conditional and its antecedent, the latter having been asserted in conjunction w ith the conditional o r som ehow presupposed as true. So invariably the argum ent comes out as an argum ent in modus ponens. Modus ponens requires, as w e said earlier (p. 215 above), that the sign proposition be able to be unconditionally asserted, but perhaps w e can understand n o w w h y it was hard w o rk in section III to extricate Stoic signs from the conditional form o f expression. W here A ristotle supplies a universal gener­ alisation ab extra, the Stoic logician finds his conditional already present in the ordinary language locution from w hich he starts. In this sense, the gap betw een the technical and the non-technical levels is less, hence less evident, than it was w ith A ristotle. In another sense, how ever, the gap is greater, for it is the gap betw een assertion and argum ent. (2) A curious confirm ation o f this diagnosis m ay be found in the Stoic approach to physiognom ies. A ristotle, as w e saw, took physiognom ies to be a m atter o f em pirical investigation and inference. C leanthes discerned instantly, from the m anner o f his sneeze, that a ro u gh -lo ok in g fellow was in fact a hom osexual effem inate, thereby vindicating Z e n o ’s claim that a m an ’s charac­ ter can be grasped (katalëpton) from his appearance (DL vn 173). Let us agree that the story, w heth er fact o r fiction, is em inently plausible. People often can tell ju st by looking. T he question is, does this ‘telling’ have an inferential basis, even if it is n o t one that the person could form ulate? I w ant to suggest that the Stoic answ er to this question is ‘Yes and n o ’. Recall that one o f the functions o f the ‘indicative’ sign is to give us inform atio n about other people’s m ental states (blushing is a sign o f sham e and in general bodily m ovem ents o f the soul w ithin). We reason (logizometha), w rites Sextus (M vm 155), ‘W hat produces such m ovem ents as these is a pow er w ithin the p erso n ’s b o d y ’. Yet perhaps in a way this is hardly reasoning at all, for Sextus also w rites th at the indicative sign has a peculiar

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nature such that it practically84 speaks right out loud to signify the presence o f soul (ibid. 154; cf. P H 11 ι ο ί ) . 85 (C haplin’s silent m ovies w o uld be an excellent illustration.) T he logical content o f this characterisation will concern us later. In the present context the story about Cleanthes suggests that w e m ig h t connect it w ith a surprising doctrine o f C hrysippus that b o th feelings like pain or fear and virtues or vices o f character can be perceived along w ith people’s appearance (Plu. Stoic, rep. 1 0 4 2 E F ; cf. Comm. not. 1062c).86 It is n o t supposed that everyone is equally good at this kind o f seeing87 - Cleanthes nearly failed the challenge, while there is independent evidence that w ith practice and fam iliarity the Sage can tell differences, betw een tw o eggs for exam ple, that the u n tu to red eye cannot see (Cic. Ac. 11 56-7). B ut the very concept o f a know ledgeable seeing seems to override the distinction betw een direct observation and inference w hich for m any philo­ sophers is the epistem ological analogue to the distinction betw een assertion and argum ent. It is true, and im p o rtan t for the overall assessm ent o f Stoicism, that various m o dern philosophers have m ade a strong case for recom m ending that w e should be sceptical about the epistem olo­ gical distinction betw een direct observation and inference, w here other m inds are concerned if no t as a sh o rt-cu t pregnancy test. B ut the recom m endation does n ot carry over into logic: the distinction betw een assertion and argum ent is fundam ental and unassailable. 84. μόνον ούχί: the hectoring note is typically Stoic —compare M vu 257. 85. Cf. Cic. de Orat, m 222: ‘Action is as it were the body’s speech’ - from a passage which w ould repay detailed study, as w ould the further material collected as ‘Prolegom ena’ in Förster, Scriptores Physiognomonici, op. cit. (η. 27)· 86. I am grateful to Paul Sanford for calling m y attention to this reference and the Cleanthes story. I fear that Cherniss in the Loeb edition mistranslates τα π ά θ η έστιν α ισ θ η τά συν το ϊς είδεσιν οιον λύπη κτλ. w hen he makes C hrysippus hold that mental affections are perceivable ‘along w ith their species’ (viz. pain, fear, etc.). C om pare ή μ οχθ η ρ ία τού ή θ ο υ ς ά να π ίμ πλησ ι τό είδος at Plu. Comm. not. 1 0 7 3 B , έξ είδους at DL vu 1 7 3 , and ά πο τού είδ ο υς in S V F ι 204 (quoted below n. 96). It should be clear in any case that Chrysippus is advancing a claim about other m inds (he is not addressing the problem o f self-knowledge which Plutarch develops as an objection), and since the passage is direct quotation from C hrysippus, α ισ θητά followed by εστιν α ϊσ θ εσ θα ι shows that he really does mean ‘perceive’; i.e. this is not simply Stoic materialism claiming that the items in question are bodily. Indeed, Cleanthes (SV F 1 518) used the fact that blushing is a sign o f shame and pallor o f fear (rubore atque pallore testetur) as a premiss from w hich to argue for that materialistic thesis. 87. 1 take it that hv perceives y’ in the enriched sense Chrysippus introduces here entails (i) A' observes som ething which is a sign o f y \ (ii) ‘y itself is unobservable’ in the sense o f ‘observing’ used in the definition o f indicative sign (p. 211 above). The idea is that x perceives y through its sign.

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U nfortun ately, it is all too characteristic o f the Stoic cast o f m ind to treat the tw o cases as parallel, or even (so deep and ineradicable is the tendency to fuse epistem ology and logic) as tw o aspects o f a single issue. G oing further, it is perhaps n o t too bold to suggest that b o th the Epicurean and the Stoic epistem ologies are a perfect m atch or m odel for their respective universes. Epicurean episte­ m ology is inferential th ro u g h and through, starting w ith inferen­ tial and com binatorial operations on m ental im ages —the ‘ato m s’ o f the m ind. It is w orlds aw ay from the Stoic em phasis on seeing and grasping connected w holes. For the Stoic, the visible and the invisible are connected in a th o ro u g h g o in g , organic unity gov­ erned by the cosm ic reason. M an is part o f the system , hence providentially endow ed w ith reason. We com e into h arm o n y w ith nature w hen reason fuses w ith sense-perception to grasp the connexion (sunëmmenon) o f the visible w ith the invisible as a unitary w hole. T o begin w ith, the connexions m ay be a m atter of inferential reasoning, b u t w e can learn to see them as naturally as we see fear in a m an ’s face. ‘G od has b ro u g h t m an into the w orld to be a spectator of h im self and o f his w orks, and n o t m erely a spectator, but also an in terp reter’ (Epict. D m . I 6. T 9 ) . 88 (3) T he issues explored under (1) and (2) pertain alm ost exclusive­ ly to the ‘indicative’ sign, w hose conditional expression states a necessary truth. W e m u st n o w broaden the inquiry to take in the ‘co m m em o rativ e’ sign, picking up from the diagnosis reached at the end o f the discussion under (1) (p. 228 above). For we have still to m en tion the m o st im p o rtan t consequence o f all. Modus ponens argum ents are always form ally valid. So if, for the reasons given, in the Stoic reconstruction sign-inferences invari­ ably com e ou t as argum ents in modus ponens, there will be no room for invalid form s in their logic o f evidence. T ry A ristotle’s 88. The inspiration for these w ider vistas is once again Jacques Brunschwig: see his ‘Le modèle conjonctif, in Les Stoïciens et leur logique, op. cit. (n. 35), 58-86. Cf. also Verbeke, op. cit., in the same volume, w ho rightly emphasises (esp. n. 45) that the main thrust o f Sextus’ argum ents against signs is to force the Stoics into a dilemma the very posing o f which destroys their conception o f an organic unity: either sign and significate are apprehended together, in which case there is no revelation o f the second by the first, or they are not, in which case apprehension gets no further than the sign and again there is no revelation o f the other. T here are further connexions, I believe, w ith the m atters discussed by Claude Im bert, ‘Stoic logic and Alexandrian poetics’, in Doubt and Dogmatism, op. cit. (n. 45), 182-216; cf., in particular, her reference (184 n. 7) to the arts and sciences as new form s o f perception (Cic. Ac. π 31; Flu. Demetr. 1) and her discussion (200) o f m y Epictetan peroration.

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inference from sallowness to pregnancy. ‘Since she is sallow, she is p reg n an t’, Stoically construed, invokes the w ro n g conditional. ‘Since she is pregnant, she is sallow ’ gets the inference the w ro n g w ay round. T h e conditional w hich w ould apply the empirical content o f A risto tle’s ‘All w ho are pregnant are sallow ’ to the Stoic reconstruction is ‘If she is pregnant, she is sallow ’, but if one relies on this as the basis for inferring her inner condition from the colour o f her face, one m ust be prepared to tolerate an argum ent w hich cannot be m ade form ally valid.89 T o people w ho think in the m anner I have been trying to describe, the idea o f a nondeductive logic is bound to seem absurd. O n their analysis, signs are conclusive (the reconstruction is a form ally valid arg u m en t in modus ponens), i.e. tekmëria, sufficient for know ledge, or they are n ot signs at all. T he Stoics are o f course aw are that in ordinary life w e are prepared to call som ething a sign w hich is n o t in this w ay conclusive. B u t they rem ain unim pressed: ‘W hat can be m ore absurd than to say, “ This is a sign (signum) o r p ro o f (argumentum) o f that, and I therefore follow it, b u t it could be that w h at it signifies is either false or no th in g at all?” ’ (Cic. Ac. 11 36). A rationale for this radical sounding claim can be constructed by p utting together a passage from Sextus (M vm 201-2) w ith a passage from P hi­ lodem us (de Signis ι . ι —20), as follows: (i) Take any sign S w hich is ‘c o m m o n ’ (koinon) to tw o things X and Y - for exam ple, a m an ’s fall from w ealth to p o verty m ig h t be evidence o f his having lived a life o f dissipation, b u t it m ight equally be evidence o f his having m et w ith disaster at sea (S, X, Y are repeatable event-types, n o t tokens). C onsidered in abstraction from the circum stances o f a particular case, S is no m ore evidential o f X than it is o f Y. T h a t m uch should be uncontroversial. B ut (ii) suppose that Y is or involves the absence o f X. T hen S is no m ore evidential o f X than it is o f not-X , in w hich case it is n o t really a sign (of X) at all. We only treat it as one because we are im plicitly relying on further inform atio n about the particular circum stances w hich w e do n ot (perhaps could not) fo rm u late.90 T aking this line 89. Cf. A ristotle’s rain inference, n. 24 above. 90. The last sentence is m y ow n gloss, (i) is from Sextus, (it) from Philodem us, but (ii) is already implicit in Sextus’ rem ark (M VIII 202) that X and Y cannot coexist. O n the Stoic use o f ‘com m on’ here, see Sedlcy, C hapter 8. It has nothing to do either w ith the distinction Sextus makes at M vm 143 betw een tw o senses in w hich the term ‘sign’ is used, generally (koines) to cover com m em orative as well as indicative sign, and

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o f th o u g h t further, one could restore som e respectability to the unrigorous everyday use o f ‘sig n’ by construing it as a three-term instead o f a tw o -te rm relation: S can be a sign o f X for a person A and a sign o f Y for person B if A and B have learned to respond to different features o f the circum stances in w hich 5 occurs - only there m ust in principle be an explanation for their ability to infer, correctly w e are to understand, different things from the same ‘sign’ (just as there is an explanation for the different effects that fire has on different m aterials), and the g ro un d o f the explanation will lead us to the sign strictly and properly so called.91 Be that as it m ay, so far as (i) and (ii) are concerned it is vital to appreciate that, w hile the argum ent requires that any genuine signrelation instantiate an exceptionless, circum stance-independent generalisation, it does n ot require that the generalisation be itself a necessary truth. Philodem us reports his opponents as thinking that the inference ‘This m an is good because he is rich’ is unsound because the generalisation ‘All rich m en are g o o d ’ is false. H e does n o t have them say, in the passage under considera­ tion, that it is unsound because the generalisation is c o n tin g en t.92 particularly (idiös) o f the indicative alone, or with the physiognom ic contrast between com m on and peculiar sign: in physiognom ies com m on signs are perfectly good signs but only o f com m on qualities, w hich is not w hat physiognom ies is interested in (|Ar.J Physiogn. 805b20, 8o8b3i). 91. I offer this as a reconstruction o f the otherw ise inexplicable concession made by the people w ith w hom Sextus is debating in M vm 192-202 (the context from which (i) is taken), the concession, namely, that an indicative sign m ay signify (sc. correctly) different things to different people. This is o f course flatly incom patible w ith the usual understanding o f the indicative sign, as Sextus gleefully dem onstrates at 201 = (i). So either Sextus is playing distinct theories against each other or the sense ot ‘sign’ has changed. It is obvious that the sense o f ‘sign’ (and ol ‘com m em orative’) has changed when the people concerned go on to say that com m em orative signs —here exem pli­ fied, uniquely, by conventional signals - may mean different things in different com ­ m unities, it being a m atter for legislation and custom to decide w hat they shall mean (193; cf. 200, 202). My suggestion gives point both to the comparison with the effects o f fire (cf also the emphasis on learning at 204-5, 243) and to the analogy with conventional signals, w hich clearly do call for a three-term analysis; for it is as an analogy that the latter is introduced at 193, not as the plain truth about com m em orative signs which Sextus purports to be left w ith at the end o f the debate (202). 92. Here I m ust register a disagreem ent w ith a main thesis o f the fine interpretation ol de Signis advanced by D avid Scdlcy in C hapter 8. Modal term s occur in 1 6, 14, 16, but they can quite well be taken to refer to necessitas consequentiae (likewise fieri potest at Cic. Ac ii 36), as they m ust be so taken in ta. 8 .15 and often. It is im portant that the example here, ‘This m an is good because he is rich’, is the sole example in the de Signis which has the typical look o f a Stoic sign-inference. The only other examples involving singular propositions are Epicurean examples o f the type ‘If Plato is a man, Socrates also is a m an’ (12.20, 14.27-8). The bulk o f the discussion concerns the Epicurean m ove from a local generalisation like ‘All m en in our experience are m ortal’ to an unrestricted generalisation such as ‘All m en are m ortal’. Both for this m ove and for the move

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T hus the rejection o f ‘c o m m o n ’ signs, the insistence that genuine signs are ‘peculiar’ fidiori) to ju st one significate, is quite com pati­ ble w ith the Stoics having m aintained a version o f the distinction betw een indicative and com m em orative signs. T hat distinction will show up as a difference in the m odal status o f the generalisa­ tions instantiated by ‘indicative’ and ‘com m em orativ e’ signconditionals respectively. Let us start from a typical pair o f exam ples, (a) ‘H e is blushing, so he is asham ed’; (b) ‘He has a scar, so he has had a w o u n d ’. T he Stoic reconstruction form ulates each o f these as a modus ponens argum ent from a singular conditional:93 (a) ‘If he is blushing, he is ashamed; b ut the first; therefore the second’; (b) ‘If he has a scar, betw een singular propositions the Epicureans claim n e c e s s i t a s c o n s e q u e n t i a e (e.g. 8.25, 12.33-13.i, 14.15-28, 32.38-33.8), meaning by this that it is inconceivable that the premiss be true and the conclusion false (14.15-28, 33. i-to ). B oth sides agree, though not necessarily for the same reason, to use the form ‘Since /;, q \ Consequently, for the Stoic the question w hether the Epicurean inference is cogent either is (regarding ‘Since p , q as a type o f conditional - so perhaps 3.27-8, 35, 32.34fr.) or depends upon (regarding ‘Since p , q in m ore typically Epicurean style as an inference - so perhaps 2.37) the question w hether by Stoic standards the conditional ‘If p , then q ' is a necessary truth - for him, the test o f any argum ent claiming n e c e s s i t a s c o n s e q u e n t i a e is whether the associated conditional is necessarily true. The conditional in question has a form which it will be convenient to write, ‘[(x)h Fx —* G x ] —» [(x) Fx —* G x ]\ w here ‘(x)h · · ·’ may be read ‘for any object x in our experience here . . . ’ (π α ρ ’ήμίν). The Stoic first offers his opponent a conditional w hich is necessary but only because its consequent is tautologous: Ί Μ η Ρχ Gx] —» [(x) (Fx & Gx) —» G x]’ (3.11-13). T hen he offers '[□ (x)h F x —* Gx] —* [(x) F x —* Gx] (3.31-5, following Sedlcy’s interpretation), which in effect reduces to ‘13 p —* p ’; for if ‘(x)h F x —* G x ’ is itself necessary, our subscript ‘h ’ is redundant —local conditions are irrelevant if it is qua m en that men are m ortal. In this w ay, f o r t h e S t o i c the question in dispute reduces to the question w hether ‘If som ething is a man, he is m ortal’ is a necessary truth, while f o r t h e E p i c u r e a n it looks as though the only sign-inferences his opponent will allow are inferences from, via and to a necessary connexion established by the ‘elim ination’ m ethod which Sedley shows to be a test for s u n a r t ë s i s . This is true o f the Stoic’s view o f the inferences the Epicurean is interested in, but it does not follow that it is true o f the Stoic’s view o f his ow n sign-inferences. Thus at 14.3ff. (cf. 32.36—33.1, 36.22-5) the Epicurean takes the Stoic to be m aintaining both (a) that the only genuine signs are ‘peculiar’ signs, and (b) that the only way these are established is by the elim ination method, i.e. s u n a r t ë s i s . But when we check back to 1.1—20 (to which 14.311. is explicitly replying), we find (a), but no unam biguous evidence o f (b). If it fits better w ith Sextus’ evidence to read the modal terms in 1.1-20 as referring to n e c e s s i t a s c o n s e q u e n t i a e , as above, and if, as I have been arguing, we can explain the E picurean’s supposing them to require that every sign-conditional be necessary as due to the fact that the Stoic does demand a necessary connexion for every E p i c u r e a n sign-inference, then (ii) can stand as in the text above - provided, o f course, it can be integrated into a plausible overall interpretation which gives the Stoic a coherent theory. 93. Singular conditionals are standard in the reconstructions given by Sextus ( P H 11 106; M vin 252-5, 271, 423) and are obligatory if the argum ent is to have the form o f the first indem onstrable. T o formalise the instantiation step would require predicate logic; it is not surprising that w e hear little about it (the clearest example is the instantiation o f an astrological generalisation at Cic. F a t . 12).

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he has had a w ound; but the first; therefore the second’. T he logic o f the tw o exam ples is the same. Epistem ologically, m oreover, each has one categorical prem iss w hich is taken to be established by observation. It is the conditional prem isses w hich differ: in (a) a strong (sunartêsis) conditional w hich states a necessary truth, in (b) only the w eak Philonian conditional. H ence the conditional in (a), w hile o f course it entails the corresponding Philonian conditional, instantiates a generalisation ‘If som eone blushes, he is asham ed’ w hich can be k no w n to be true a priori, on broadly conceptual g ro u n d s.94 T he conditional in (b), on the o ther hand, can only be k n o w n to hold on the strength o f a contingent generalisation linking scars to w ounds which w e have antecedently established by observation and m em ory. This, indeed, is an outcom e w e could have foreseen long ago, w hen the Philonian tru th conditions for sign-conditionals w ere com bined w ith the epistem ic requirem ent that the antecedent be revelatory o f the consequent. If k no w in g the tru th o f the antece­ dent is to lead us to k n o w the tru th o f the consequent, then w e m ust already k n o w that the conditional is sound, independently o f k no w ing the truth-values o f its constituents. T he Stoics expressly stipulate that ‘If p, then q’ is not a sign-conditional if it can be know n to be sound by the Philonian criterion sim ply from its being evident th at p and evident that q (M v i i i 250-1). This raises no problem w ith the conditional in (a), w hich is itself necessary, so that the tru th o f the antecedent can o f itself (‘by its ow n n atu re’) tell us that the consequent also is true (cf. P H 11 ιο ί; M vin 154). B ut w ith (b) there is no option but to say that it is on the strength o f an antecedently know n generalisation that the singular con­ ditional is k n o w n to be true. N evertheless, so long as the generalisation is indeed a true, exceptionless generalisation,95 the prop osition ‘He has had a w o u n d ’ will be established conclusively and o f necessity —the necessitas consequentiae o f the A ristotelian tekmërion. In effect, the

94. Cf. n. 55 above and Sedley, C hapter 8 below. For the purposes o f our discussion we need not w orry about w hether the alleged necessary truth is one. 95. The scar-w ound connexion is so regarded as Cic. Inv. 47, Q uint, hist, v 9.5; likewise the heart puncturing—death connexion: Philod. Si#h. 1.35-2.2, Q uint, hist, v 9.5, Galen, Subfig. emp. ch. 6, in Deichgräber, op. cit. (n. 47), 58, 18-20; and tiie sm oke-fire connexion: Philod. Sign. 36.2-8, Cic. Part. or. 34, Philop. in Ar. de Au. 31.31-2.

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Stoic thesis is that the only legitim ate sèmeion is a tekmërion96 —that is the burden o f the arg u m en t about ‘c o m m o n ’ and ‘peculiar’ signs. T he upshot is that Stoic logic guarantees to Stoic epistem ol­ ogy that the only w arran t w hich one proposition can confer on another is the w arran t o f conclusive proof. A ristotle’s idea that there arc different grades o f evidential support is rejected. If one does n o t have grounds w hich m ake it absolutely necessary that q, one has no grounds at all, and had better keep quiet w ith ju d g em e n t suspended. A nd this, as everybody know s, is exactly w hat the Stoic Sage is m eant to do. N o d o u b t true exceptionless contingent generalisations are hard to com e by, and harder in divination than in m edicine, which is one reason for the prom inence in these discussions o f m edical and sem i-m edical exam ples.9697 B ut the providential ordering o f the w orld, in w hich everything is connected w ith everything, guaran­ tees that they are there to be found and that m an has the cognitive capacities to find them . T he know ledge w hich can diagnose these signs (the m edical m etaphor is revealing) belongs to the Stoic Sage; he is the one true diviner (S V F m 605). The rest o f us, w ho are n o t Sages, are prone to error: w e take som ething to be an exceptionless contingent generalisation w hen it is not, or we miss a relevant difference betw een tw o circum stances o f its application (C ic. D iv. i 118, 124), B ut in principle it is possible for a divinatory generalisation to stand as certain, and it is enough to prove the existence o f divination if it happens ju st once that w e are in a position to say, ‘C hance cannot have played even the slightest part in this p red ictio n ’s com ing tru e ’ (Div. 1 124-5). O ne sound principle is sufficient to prove the existence of the art. M istakes and quacks, how ev er num erous, no m ore prove the contrary than they do in the field o f m edicine or navigation (Div. 1 24). A fter all, w h at we take to be a necessarily true generalisation m ay be w ron g also. T h e tex tb o o k exam ple illustrating the Stoic definition o f the persuasive (pithanon), ‘If som ething gave b irth to som ething, she is its m o th e r’ (DL vii 75), is a universally quantified conditional 96. Hence the unA ristotelian coupling ‘signum [= σημειον] aut argumentum \ ~ ιεκ μ ή ρ ιο ν]’ as alternative expressions for one thing in the passage quoted from Cic. Ac. π 36. Similarly, ‘signa et notas’, Cic. Div. 1 127. And to revert once m ore to physiognom ies, consider S V F i 204: ‘T he Stoics hold that the wise man is graspable by perception from his appearance in the m anner o f a tekmërion (τον σοφόν αίσθησει καταληπτόν ά π ό τοϋ είδους τεκ μη ριω δω ς)’. 97- C f. η. 48 above.

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M . F. B U R N Y E A T

precisely designed to bring hom e to people the fallibility o f their conceptual intuitions (they have to be rem inded that a bird is not the m other o f its egg).98 If this is correct, the difference in m odal status betw een strong and weak conditionals does not autom atically bring w ith it a difference in epistem ic status. Philonian conditionals m ay be no less certain than sunartêsis conditionals. This is obvious w here the Philonian conditional is entailed by a sunartêsis conditional, or w here antecedent and consequent are both evident in their o w n right (M vin 251). B ut w e have ju st confirm ed that it holds equally o f Philonian generalisations (universally quantified m aterial conditionals).99 W hat the m odal difference does mean is that the certainty in the tw o cases has different grounds: in the one case we consult ou r ‘preconceptions’, 100 in the other observation and m em ory. We need the second because w e arc hum an: only God can see things w hole and grasp the entire interconnected sequence o f past, present and future (Cic. D iv. 1 126-7). It is only w hen the second m etho d too has failed us that w e m ust resort to generalisa­ tions that are only ‘for the m ost p a rt’ true (Div. 1 126). This third type o f generalisation brings us finally back to A ristotle. T he picture thus far has been that the logic o f ou r reasoning is always deductive. W hat varies is the source o f the m aterials from w hich ou r argum ents are constructed. A ccordingly, the thesis to be defended has been that for the m ost part a good diviner is right about w hat he takes to be a true exceptionless generalisation (Cic. D iv. i 25,118, 124-5). T hat is quite different from the m ore A ristotelian topic - draw n, it should be noticed, from Posidonius (125) —o f generalisations w hich them selves hold only for the m ost part or about w hich one can be certain o f no m ore than that

98. For a context in which this point about our fallibility in making conceptual claims is crucial, see m y ‘Cods and heaps', op. cit. (n. 50). 99. T o the references already given, add Cic. Div. 1 109. I thus side w ith Barnes, Chapter 2, against Sedley, C hapter 8, in refusing to align the Philonian conditional w ith the epistem ological category o f the pithiinon. Nonetheless, I believe that what Sedley calls ‘a m ode o f thought not strictly governed by logic’ is recognised - and deplored - in Stoicism, but as a third category, to be introduced shortly. Replacing Sedley’s two categories by three and shifting the material he collects on the pithation into the third is an essential part o f m y strategy for vindicating for the Stoics a distinction between ‘indicative’ and ‘com m em orative’ sign. 100. Cf. n. 55, n. 96 above. This is not to say, as Sedley appears to say, that a necessary conditional is analytic in the m odern sense. Stoic necessities are as substantive as A ristotle’s.

The origins o f non-deductive inference

237

they hold for the m ost p a rt.101 G iven a generalisation o f this third type (im agine that ‘Sallow w om en are preg n an t’ is an example), w hat is the status o f the singular conditional w hich instantiates it in a particular case? D oes it presuppose that w e can form ulate, and have elim inated, the kinds o f exception to w hich it is liable (cf. p. 231 above)? W ith w hat assurance or probability can we draw the conclusion that she is pregnant from her sallow features?102 W hat role is played in such inferences by background know ledge o f the circum stances in w hich the generalisation is applied? Such ques­ tions as these could have led a Stoic-trained logician to develop a non-deductive logic w ith a different, and perhaps m ore prom is­ ing, structure than A ristotelian logic could provide (cf. p. 231 above). B ut it is quite clear, I think, that all inquiry in this direction was spurned by the establishm ent figures o f Stoic philosophy. T he Stoics recognise that w e voyage th ro u g h life follow ing, for m uch o f the tim e and even in the m atters m ost vital to our welfare, n othing better than th e pithanon: that w hich w e happen to find convincing o r persuasive. We ow e it to providence that, for the m ost part, we get aw ay w ith it, B ut to the extent that we rely on the pithanon, w e are fools, creatures o f unreason, failing abysm ally to use correctly the rational faculties w ith w hich providence has endow ed u s .103 T here is no logic to be discerned here, only persuasion. A nd indeed, it is to the art o f persuasion, as represented by the rhetorical treatises o f a Cicero or a Q uintilian, that w e m ust look if we w ant to study the later history o f A ristotle’s distinction betw een conclusive and lion-conclusive signs. B ut w hen w e com pare these w orks (the m ost sophisticated discussion is in Q u in t. Inst, v 9) w ith A ristotle’s Rhetoric, it is all 101. T he difference is obscured by Sedley’s talk (Chapter 8, n. 38) o f astrological rules as ‘fallible’. 102. Even signs sufficient for know ledge can be explicated in term s o f ‘for the m ost part’ connexions according to the Rhetorica ad Alexandrum, i43ob3off. 103. It is here that I w ould bring in Sedley’s brilliant exposition o f Philodemus, de Signis 7.26-38. T hat the concept o f the pithanon is not a concept o f evidence or reasonable grounds for belief, hence not a concept o f probability in the m odern sense, is a thesis for which I argue at length in ‘Carneades was no probabilist’, in Riverside Studies in Ancient Skepticism, ed. David Glidden (forthcom ing), while accepting that a more hospitable attitude to the pithanon becomes widespread in the first century B.C.; the general shift at that time towards ‘soft’ philosophy may also be the context in which to view Posidonius’ concession to ‘for the m ost p art’ connexions in divination.

238

M . F. B U R N Y E A T

too obvious that their authors are n o t logicians. N o r are the Epicureans m uch interested in logic (in the p ro p er sense o f form al logic), although they have som e good things to say about w h at it takes to establish a generalisation on inductive grounds, and they quite rightly charge the Stoics w ith paying insufficient attention to confirm ation th e o ry .104 All th ro u g h the Hellenistic period serious logic is the preserve o f the Stoic establishm ent (the political im age is perhaps not inappropriate), w hich m eant, as I have tried to explain, that the w hole m assive w eight o f the Stoic system stood against any fu rth er developm ent o f A ristotle’s pioneering start. W ith this last result we have com e full circle. If one believes that an adequate philosophy o f science m ust find a place for nondeductive as well as for deductive logic, one will conclude that, as logicians, A ristotle was a better friend to the sciences than Z eno and C hrysippus. If A risto tle’s w isdom in these m atters dis­ appeared into the rhetorical tradition, rather than being taken up and developed by philosophers or scientists, a large share o f the blam e m ust rest w ith the au th o rity o f Z e n o ’s w o rk On Signs (DL vu 4) and the Stoic trad itio n g en erally .105 104. See Sedlcy’s account in C hapter 8. 105. The length o f this paper is a response, I hope a productive response, to the difficulty o f som e o f the issues raised at the conference discussion and to an extrem ely penetrating set o f criticisms from Jonathan Barnes. I am grateful also for com m ents on the first draft from T heodor Ebert, D avid Glidden, Jonathan Lear and an audience at Stanford U niversity. In preparing the final version I had the advantage o f being able to consult D avid Sedley’s contribution in C hapter 8, to which 1 am enorm ously indebted even w here I have favoured a different view'.

8

O n Signs

DAVID SEDLEY

l . Philodemus, de Signis W ith the appearance in 1978 o f Philip and Estelle De Lacy’s second edition o f Philodem us, de Signis, one w hich unlike its predecessors is based on adequate papyrological in fo rm a tio n ,1 the tim e is ripe for renew ed discussion o f this w o rk and its place in Hellenistic philosophy. Its real title is Philodem us, On [. . .] and Signinferences. T he m issing w o rd m ay be phantasiai, ‘im pressions’, or phainomena, ‘appearances’, b u t this need n o t concern us now i. P. and E. D e Lacy, Philodemus, On Methods oj Inference (Naples, 1978i.2). M arcello Gigante, director o f the C entro Internazionale per lo Studio dei Papiri Ercolanesi, generously supplied the editors w ith the readings o f the papyrus, and to this end was able to call upon the expert papyrological assistance o f Francesca Longo Auricchio and Adele Tepedino Guerra. Previous editions and discussions had relied mainly on the 19th-century facsimiles: T. Gom perz, Herkulanische Studien 1: Philodem über Induktions­ schlüsse (Leipzig, 1865); F. Bahnsch, Des Epicureers Philodemus Schrifi Π ερί σημείων και 31211.31

Iso crates 128 128

Call.

27

317η·49

Paneg. 86

193

Jo sep h u s Apion I 129

3211.17

L a c ta n tiu s Inst. i xvi ir-1 7 V xvi 2-4

L u ciliu s 1305 L u c re tiu s I 3 2 9 -4 5 370-83 384-97 5841Ï*· Ö35—920 III 1-30 216-93 IV 110-28 129-42 176-216 4 0 9 ff. 722-48 V 526-33 1019-27 I I 17 1143 1143-60 VI 703-11

M a rtia n u s C ap ella IV 327

27η. 8

M elissus fi. 8

128, T94

N e m esiu s de Nat. hom. 38, 277 M

4411.54 32111.68

L u c ia n Symp. 23

171

16711.6

J u lia n Dig. L xvii 65

M a rcu s A u re liu s Π 13

2711.8

5 4 Π.7 7

269 269 269 31511.45

270 30811.19 27211.76 268 268 269 298η.io6 269 270, 27011.72 31511.42 31811.57 31811.56 3 I 511-43 27011.72

N u m e n iu s f i. 24

4311-53

Pappus V4 6 vin 9

Ι37Π.22 Ι37Π.22 i02n.8i

P a rm e n id e s fi. 8

194

P h ilo Bel. 50

Ι 0 2 η. 84

P h ilo d e m u s D m 14 de Signis I. 1-20 12-19 19-2.25 3 5 - 2 .2 2. 36 - 3 -4 37

M an iliu s I 5 3 -7 5 8 ff. 2 4 7 -5 4

π 60-81 82 132 720ff. in 57ff. 203-509 IV 14 108-18 696ff. 869ff. ' 8 86ff.

186 186 167 167 186 186 175 186 186 187 187 186 186 187

107

3. 10-12 11-13 27-8 3 0 -5 4·

5-13 5. 33-6 6. 1-32 32-7.5 7 - 5 -6 26-38 3 3 -4

8. 1-13 7-IO 2T—9.8

3 1811.54 231, 23311.92, 243 242η. 9, 244 249 2 3 4 η . 95 247 2 3 3 η . 92 247 2 3 3 η . 92

23311.92 2 3 3 Π.9 2 , 244, 258 258

247,

258

243

258 241

237η. 1 0 3 , 248-9, 248η . 25 252 272η.76 201 200

de S ig n is

(cont.)

25 32-9.3 9- 3

8-11.8 II. II 13-14 26-12.36 12. T-I4 7-12 14-31 20 26

13. 14.

15·

16. 17. 19. 20. 21. 28.

38 38 - 3 3 -8

1-10

21-36.7 24-32 33 - 3 4 -2 9 35 - 3 4 -5 50 34. I iff-

3 6 - 2 -7 7 -1 7

232η.92 288η.6ο, η.6τ

17 - 37-1 2 2 -5

23311.92 272η.76 242η.8

36-33·I

22-32 2 2 - 3 6 .7 26 3 5 - 3 6 -2

257

257

34 35

1 5 -3 5 2 1 -3

2 5 9 , 265

246

33-13.1 1-8 26 2 -1 1 2-27 3 ff. II-I4 15-28 27-8 13-16.1 19-28 28—16. I 29-17.II 8 -1 1 12-19 36-20.4 31-21.16 12-16 19 45

3 5 - 2 -3 4 -2 9

245

3 2 -6

29. 4ff. 4—16 19-24 30. 33-311 3 3 - 3 1 -3 6 31. 1-8 6-32.2 8-17 32. 8-10 8-13 24-7

33-

2 9 - 3 5 -4

23311.92 262 262 240η.5 242η.8 241

37- 1-38.8 1 -2 4 6 -9 7 1 2 -2 4

243 257 2 3 3 Π-92 259 23311-92

232η.92 249

272η. 76

2 4 -9 3 6 -7

38. 22-32

259 247, 258 259

6in.84 272η.76 240Π.3 200 24211. 8 200 26ο 272 2 4 m .7 23311.92 260, 2 6 m .54 264 246η.20 28311.42 257

256 246 241

R h e t.

i 253-1-254-17 254-25-36 2 5 9 -3 7 - 8

32211.74 32211.70 3 2 2 Π.7 3

257

258 258 6 ιη .8 4 247 6 ιη .8 4

272η.76 288η.6ο, η .6ι 28411.46 2 4 0 Π.3 258, 265η.6ι 2 4 0 Π.3 2 0 2 Π.5 5 202 263η . 57 26211.55 26ο, 202η. 55 2 0 2 , 26211.55 263η . 57 2 7 2 η .76 233Π-92, 240η. 5 288η.6ο, 289η.63 233η.92 288η.6ο, 28911.63 233η.92 23311.92, 246η. 19, 257> 200 258 258 258

P h ilo p o n u s in A n . P r .

31.31-2 35. i8ff. 481.7-9 28-30 482.10-12

23411-95

226 Ι 9 9 η .i6 20011.19 200η. 19

in P h y s .

681.30fr. 682.25fr. 683. 1 3 f r i8ff.

144η.38 1 4 4 0 -3 8

1440.38 144

P h o tiu s B ib i.

cod. 223

19011.51

P la to C r ito

52D

317η.50

*D ef

414E

196η. IO

P arm .

132BC

208η.38

Phd.

IOOAB

2 5 9 0 -4 9 285η . 49

P h ile b .

2 5 9 Π-49

55E

267η. 68 13611.13

Rep.

P o rp h y ry

3 3 6

d

3 0 5 1 1 .8

A b s t.

3 5 8 E -3 5 9 B

3 0 5 0 .3

478B

2 0 8 1 1 .3 8

527A

7 6 η . 12

602c

2 7 9 1 1 .2 8

I

2 0 8 1 1 .3 8

263 E

207

16.13-14 17. i6ff. 18.7ff. 18.12ff. 23-25 25.26 28.9

Th t. 153A

193

1 8 8 E -1 8 9 A

2 0 8 η .38

1 8 9 E -1 9 0 A

207

305η. το, 312- T3, 316, 3 i8 n .55, 319» 32411.78

in H a r m .

Soph. 237D

7“ 12

I5in.58 i5 in.58 15 m . 58 13311.8 163η. 85 163η.85 Ι32Π.7

P ro c lu s in E u c l .

P lin y

4 0 . 9 ff.

NH 2 9 .9

23

P lo tin u s

Il

m

3 .3

174

5

174

7 -9

188

14

188

1 .5 -â

1 8 7 , i 8 8 n . 4 6 , i; 48

40.19 77.15-78.8 89.15-18 100.6-10 14-19 n o . 18 117.7-8 125.14-18 198.6-9 199.3-200.3 215.22-3

ι6οη .7ΐ i 6 m .7 7 7 6 η .12 7 7 n - 13

80 79 76η. 12 76η.12 73

76η.12 70Π.12, 92 70η.ΐ2

H yp.

P lu ta rc h

42.5-54.12 72.20ff. n o .3 ff. I20.15ff.

a d v . C o l. I I2 IA

2950.95

II2 3 B

2 9 7 η .100

II2 4 A

D

21

5 θ η .ό 9

I 2 4 . 7 ff. 126.12-130.26 14 198.15-212.6

3 1 3 1 1 .3 8

C o m m . n o t. 1062c

229

1063A B 1073B

5 3 Π-7 5 2 2 9 Π .8 6

1 0 7 8 E -1 0 8 1 C

84

1 0 8 0 E -1 0 8 1 A

85

1084A C

4 4

7

,

143

138η . 23 Ι 37Π .Ι9 138η.23

in T i m .

285F Π .5

138η.23 138η . 23 138η.23 1 3 8 η . 23 I 37H.19

4 8

η.

6 7

ι66

P to le m y G eog.

de Fac.

I6 7 η .8

923A

2 3 0 Π .8 8

S to ic .rep. 1034A C

F IO 3 6 A

DE F

Ι 3ΙΠ-4

H a rm .

D e m e tr .

I

I 4 .12.4ff.

3 2 η . ιό 42

2 5 0 Π .2 8 2 5 1 1 1 .3 0 42

IO 3 9 C

4 4 η . 54

IO 4 2 E F

2 2 9

IO 4 7 C

S o n .6 9

IO 5 5 F

2 5 0 Π .2 8

I i ,3 2,5 4,9 8,16 n 12,66

15Μ.58 Ι 5 ΐη ·58 158η.66 136 136

O p tic s

n

80 134 III 67 97 131

ιό ιη .7 8 ιό ιη .7 8 ιό ο η .7 4 ιό ο η .7 4 ιόο η .7 4

Optics (cont.) IV i

16011.74 13611.14 134

V 8

23ff. Planisph. 14, π 249

13711.20

Plan. Hyp. 15 7

16211.79 162η.79

8,

270

XIII 2,

532

Tetrab. 179-82, 185, i88n.46 182 179 183 176 176 185 14311.35, 175, 18611.44

I 2

3 4 Il I

3 4 III 1 - 2

2

Syntaxis I I,I 1

158

4 6

158

3i

I I

135

6,

13 20

135 16211.82

III I ,

190

156

191

140

193 194

14511.41

196

137, 141- 2 , 142η . 33

S c h o lia st to P e rsiu s

197

I4I,

ad

198

142 , 156

S c h o lia st to L u c ia n 254 Jac. 3211.17

137 , 140- 1, 15811.66 145 , 15811.66

Vi

80

15611.63

Seneca

130η . 3 , 135 , 142

Ben.

202

T4 2 , 146

203

1 3 3 , 1.35 14211.33

IV I ,

265

133 138 , 14511.42

9,

327 328

1 3 3 n -9 146

338

157 14111.31

339

V

34η.21, 3011.25

xix 9

32n. 16, 4711.64

cons. Marc. 18.3

I

Ep. 118.12-16

53n .75

II III

32.7-8 2 9 .1

347 351

137 , 13711. 2 1 , 138

Provid. 5-7

352 354

137 139

S ex tu s E m p iric u s

355 400

14511.41

M

10,

156- 7 , 15811.66

Ϊ 2,

403

137, 137 η . 21

Η,

417 421

1 3 7 , 13711.21, H 3

V 1,

2,

VII I , I ii

2 3

14511.41 133 133

I 21 40 45 68-9 72 III

18

4, v i n 6,

35 203

IX 2 ,

208

15911.67

209 211

1 3 3 , 135 ι ό 2η . 83

94

213

15 711-95

13

13811.26

3=

J5 18

155 14611. 4 3 , 1 5 7

19

14511.42

25

14511. 4 2 , 148 138η .26 Ι3 5 Π .ϊ2

Ι 7 Ι Π .2 2 l

67

Ι7 ΙΓ 1 .2 2

22-8 28 29-36 35-6 37-57 60-4 82 83-91

2,

7I I I .22

NQ

157 157 , 15811.66

344

197η.12, 237 234n-95 22511.76

IV p .

199

205

IT,

Q u in tilia n 9 9-5 6

V

200

204

138 15911.67

84

76 24711.23 288η.s8 3211.16, 45η.60 45η.6o 247η.23 86 74 »7 84

78-81

V“>

T

O

GO

»7 74 75 74, 76 24711.23 82η.20

Index locorum M (cont.)

202

1 5 9 1 1 .6 8

219-20

4~5

185

4 3 -8

186

5 0 -1 0 6

186

244 2 4 4 -7 1 245

' iff.

7 5

ft·

Ι

4 3 Π .35

2310.90 212 217 256 209, 2 Ι 0 η .36, 220, 221 222

7 5 - 7

1 8 6 0 .4 4

248

8 3 -5

1 7 5 -6

249

220

95

179

2 Ι 0 Π . 56 , 221

Μ O T o‘ 4

186

250 250-1

2 8 8 1 1 .5 8

251

252

31

37

7 4

2 4 7 1 1 .2 3

8 5 -6

2 2 1 1 1 .6 7

1 4 1 -8 9

2 0 5 ff.

164

2 4 4 η .14

1 7 4-5

250

2 .5 2-5 254 2 5 4 -6

339

221

22511.76, 234 236 2 1 5 , 2 1 7 , 221, 222, 24211.8, 255 2 ΐ 6, 23311-93 2 4 2 η .8 2 Ι 4 Π . 5 2 , 2 2 Π1. 6 8 , 2 22 , 2 4 3 0 . 11

190

29711. ι ο ί

256

221

191

2 7 7 Π .2 0

203

2 7 9

257 2 5 7 ff-

2 0 3 -1 5

2 6 4 1 1 .6 0 , 2 7 6 - 9 2

21411.52 20911.40 221, 2 2 3 η . 7 1 , 25611.43

205

2 7 4

Π.7

210

2 7 9

η

21 I

207

Π.3

0

2 1 I-1 6

2

2 5 7

2 29η . 84

265 268 269 269-71 271 272

3 6 9

29711. 10 2

2 7 5 -6

200

3 9 5

2 4 7 0 .2 3

210,

4 0 1 -3 5

4 3 1 1 .5 4

4 1 4 -2 1

2 55

.2 7

Ö3 ff.

416

4 4

4 9

277 278 279 289

4 1 6 -2 1

2 8 η .9

299

4 1 8 -2 0

5

9

2 6 8 , 2 9 6 1 1 .9 8

,

θ η .7 θ

12

2 θ 8 η .3 8

60

2 4 7 1 1 .2 3

70

2 θ 8 η .3 8

8 7

2 1 4 0 .5 2

I I 2 ff.

2 1 7 η .58

US

5 0 1 1 .6 9

300-15 301 303-13 306 309 314 316^36 321 323 324 329 330

221

221, 22311.71 21611.56, 219 221, 23311-93 21611.56, 221, 22111.68 217

1 94 , 2°9 209 194 1 94 , 210

24211.8 22 5

24211.8 215 215

22111.67, 27611.18 29311.76 27611.15

140

1 9 4 , 2 1 0 , 2 1 4 0 .5 2

1 4 1 -2 9 8

24 1

143

2 3 1 1 1 .9 0

146

2 1 5

15 1 -2

211

1 5 2 -5

2 5 5

I53

215, 210, 222

154

2 2 9

2 3 4

1 5 4 -5

211

350 364 392

155

2 ΐ6 , 228

423

2 1 5 , 2 3 3 0 -9 3 ,

156

2 1 1 , 2 1 6 1 1 .5 6 , 2 4 1 0 . 8

222

1 5 6 -7

2 1 2 1 1 .4 8

428 429

164

2 4 7 0 .2 3

173

21

1 7 6 -9 1

2 4 1 1 1 .8

3 3 8 -9 348 ,

I,

2 5 5

180

194, 210

i 9 2 —2 0 2

2 3 2 1 1 .9 1

2 0 1 -2

2 3 1

, 2 4 4 0 .1 2

434 43 5 443

ix 139 182 184

2 8 8 η .57

2 9 3 η . 76

27611.18, 29411.81 2 8 8 η .57

2 4 6 η .22, 24 7 η .23 204 50 Π.6 9

2 8 8 η .57 2 2 ΙΠ .0 7 256η

48η. 6 j 2 2 6 η . 79 4811.65, 2Τ4Π.52 225, 243η. ίο 25311.36 45 3 m. 15 ,

46

.43

M

(c o n t.)

I I 5-20

223

258-64

84

116

2 2 3 η .72

313

2 4 7 η . 23

12 1

2 1 2 η .47

3 5 7

2 4 7 0 .2 3

122

1 9 4

406

2 4 7

13 1

1 9 4

» 210

1 3 4

1 9 4

= 210

1 3 4 -4 3

2 4 2 η .8

13 5 - 6

210, 225

407 X

II

η

.23

8ο - I

2

7

218

4 2 η . 52

219

2θ8η.3$ 26 4

1 3 7

210

219-20

2 8 4 0 .4 6

140-2

2 1 5

219-22

2 5 9 0 .4 9

236

2 4 7 0 .2 3

267

1 4

■

2 55

2 4 7 0 .2 3

146

4 8

269

2 4 6 η . 2 2 , 2 4 7 η ·2 3

150

48

270

2 4 7

153

4 4

2 4 7 0 .2 3

1 0 7

225, 243η· ίο

2 2 3 η . 71

178

2 2

198-203

2

XI 9 0 247

η

.23

PH η ·2 8

I 32

2 7 9

4 4

129

4 7 - 9

129,

92

129

IO I

129

118

1 2 9

II9

129,

120

129

125

1 2 9

126

129

130

1 2 9

181

2 9 7

2 1

Off.

ι6ο,

,

2 9 3 4 9

,

5 4

15

9 8

η

.3

2 4 7

Π.2

ΙΟΙ

2 4 7

η

130

2 4 7 η ·2 3

1 3 7

2 0 4

ιό ι

7

3

.23

159

S im p lic iu s in Cael. Π -7

1

28311.40

234

4 3

238

Π.7

4 0

, 299η.

107

7 1 0 . 14fr.

16011.69 ιό ο η

2 9 7 η . 103

ff.

.6 7

253

22

η

ΙΠ

2 2 4

, 2 7 9 Π .2 8 ιό ο ,

. 55

Ι 5Π -55 5811.81

m

227

2 3 6

16 1

η

2 2 9 - 5 9

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216

II

242η. 8

1

142

.6 9

in Cat. 2 4 .1 3 -2 0

. 53

5

θ η .ό

9

20

1 2 4 . 3 3 -5

7 6

5

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7 6 η . 12

in Phys.

240

5, 8, 2 2

55

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1 108. i8 ff.

3 7 η .30,

ιο 8 η .

8 6 —7

2 0811.38

I I 10

ιο ο η .8 ,

m

96

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32η. ιό

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1 1 7 7 .2 -4

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98

215

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η

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9 9

211

looff.

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101

222,

Ι Ο Ι —2

2 1 4 0 .5 2

102

2 Ι2 Π .4 8 , 2 1 5 , 2 ΐ 6 η . 57,

Ι ΐ 2 4 5

2 2 9

,

,

2 3 4

, 242η. 8

104

2

104-16

256

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215, 216, 217, 222,

107

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7

,

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, 222,

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23311

,

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,

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222, 2 5 6 η

III

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114-15

283η

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222

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5

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3911-42

S o p h o cles Ant. 257-8

222, 255 i

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193

o r 475

276η. ι6

496

2 7 6 η . 16

S o ran u s Gyn. 4 .6

14

6 .6

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8

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, Η

index locorum Gyn. (cont.) 10.12

12-3 *Quaest. med. 46

14 14

Dial. 16

341

3611.24

T a tia n

17

adV. Graec. 27

3611.26

S to b aeu s Ed. i 153-5 167 π 7 S tra b o XIV ii 20

T h e m istiu s 8511.26 8411.25 253n · 37

94

Suda s.v. ρομβοστωμΰληθρα 3811.35

Oral. 23,285c

38η.35

T h e o g n is 743-56 823-4

31611.46 31611.46

U lp ia n

Dig.

L xvi 177

32η.17

S u e to n iu s Tiberius 6-9

17111.21

16711.6

X enophon

T a c itu s Ann. vi 22

V itru v iu s IX 4

17111.23

Anab. VI ii 2

193

(ii) G E N E R A L IN D E X * abstraction, in geom etry, 70, 80, 92 Academy, sceptical, 22, 36, 45, 17711.34, 241, 318; under Arcesilaus, 4111.48, 43, 44η.56 accuracy, όοη.83, 142η. 33 An horoscopes, 185-6, 189; obstacles to, 133-45; lack of, in observation, 130, 132-3, 157-8, 161-2; due to conditions, 134-5, 161; inadequate instrum ents, 136-44, 145, 161, 18611.44; calculation, 141, 142, 157, 158; imprecise tim e-keeping, 143—4, 161; or to m ethod o f experim ent itself, 144-5; ™ ancient records, 181-2, 184-5 acoustics: concerned w ith phenomena, 162-3; accurate observation in, 132, 1 5 m .58; instrum ents, 136; interpretation o f data, 151; Pythagoras’ acoustics, 16211.84; see also harm onics, music Aenesidemus, 264, 292-3, 299; ten modes, 128-9 affections (pathë): criterion for Cyrcnaics, 277, 297; and for Epicureans? 276, 297, (relation to evidence) 280; relation to

exterior cause, 277-8; affections in medicine, 4, 5-6, 10—11 Alexander o f Aphrodisias, 39, 225-7 analogy: in concept-form ation, 78 w ith n.14, 90; in inference, 90-1, 242, 256, 28111.35, 289; see sim ilarity m ethod anatom y, 13, 14, 15111.58; use of experim ent in, 131, 1320.6; dissection/vivisection, 144-5 Anaxagoras, 270, 309; on perception, 128 Anaxarchus, 309 angle, 72, 76η. 12; o f reflection, 160; of refraction, 136, 151, 160; problem s o f m easurem ent, 162 w ith n. 79 antecedent, in a conditional: sign as, 209-17, 220-4, 228; hëgoumenon, 221; kathegoumenon, 220—1; prokathëgoumenon, 222; ‘antecedent’ sign, 262η.55, 26311.57 antimarturêsis, 285—91; see also ouk antimarturêsis Antiochus o f Ascalon, 241, 265-7 Antipater o f Tarsus, 213, 241; on one-prem iss argum ents, 225-7, 243

* The editors are grateful to Catherine O sborne for valuable assistance w ith the preparation o f this and the follow ing indexes.

342

General index

A pollodorus, 74-5, 77, 840.25 Apollonius C ronus, 42 A pollonius ofPerga: on geom etry, 73, 79, 8ο, 92, 93-4 appearances, conflict of, 2710.75, 273, 278-9, 297-8; see also experience, observation, phenomena apprehension, see katalëpsis apprehensive presentation, see phantasia (katalêptikë) approxim ation, m ethods of, 152η.60, 152-6 Arcesilaus, 43-4 Archedcm us ofT arsus, 218η.60 Archimedes, 100, 111-12; astronom y, 136, 141; geom etry, 153; hydrostatics, 159; m athematics, 153-4; mechanics, i n - 1 2 , 113-14, 116, 127 argum ent: deductive, 1950.5; non-deductive, 193-238; inductive, 200-1; one-prem iss, 225-7, 243; deficient, 48, 2260.79; enthym em e, 20211.24, 204η.29, 2i8, 226, 228; redundancy, 48, 227; paradoxes, 32η. 16, 3211.18, 36, 37-8, 42-3, 440.58; little by little, 3211.16; sorites, 27-35, 36-64, 107-8, 253, 255, (argum ent for conditional premisses) 46, 53; Millet seed, 36-7, 39, 107-8; argum ents for and against astrology, 172—92; against geom etry, 72-92; against gods 45-6; see also p ro o f Aristarchus, 133, 153; heliocentric theory, 162η.82, 167η.8 Aristippus o f Cyrene, 308 Aristotle, 162, 207, 246, 309, 310; logic, 195-203, 274-6; on future contingents, 275, 301; onjustice, 305, 317, 320; know ledge o f sorites argum ent, 38—41; scientific m ethod, 207-8; philosophy o f mathematics, 70-1, 72η.4, 77, 8o, 83—4, 86; mechanics, analysis o f m otion, 98-111, 112, 116-2 ôpassim, 1275011 physiology, 131 ; analysis o f perception, 128; on signs, 193-206, 214, 217-25 Aristoxenus: on accurate observation, 132 w ith n. 8 Asclepiades, 27, 450.60, 265; on physiology, 15-16; abuse o f observation, 131

assent: induced by thepithanon, 250; assent to premisses o f sorites argum ent (C hrysippus’ theory), 50-6 astrology, xxii, I 5 9 n . 6 8 , 165-92, 254; relation to Stoicism, 167-72; ‘h ard’, i.e. w ith causation, 170η. 19, 170-1, 172, i8o, 185, 187; ‘soft’, i.e. signs w ithout causation, 170η. 19, i8o, 187-8, 190;

argum ents against astrology, 172-8, 183-7, 188, 190-1; for astrology, 178-83, 188-90; utility of, 182-3 astronom y, xxi-xxii, 96-8, 133-59; use o f observation, 132η.8, 133-59; by means of instrum ents, 136; namely: armillary astrolabe, 137, 138-9; equinoctial armillary, 137, 145; m eridional armillary, 137; bronze ring, 137, 141-2; dioptra, 136, 143, 154; H ipparchan dioptra, 137; gnom on, 136; orrery, 136η. 18; parallactic ruler, 137; plinth/quadrant, τ3 7 ;‘spider’, 136; m ethod o f approxim ation, 153-5; contribution to astrology, 170, 173-4 atm ospheric conditions: interference in scientific observation, 134-5 atom s, 2, 15, 890.33, 90, 91, 230, 257, 2620.56, 271-2; atom ic swerve, 2720.76 attestation, see epimarturêsis Augustine: on astrology, 170, 173, 178, 190-1 Babylonia: astrology, 166-7, 169 balance, 97, 113-14, 119, 122, 125, 1270.28 Basilides, 93 Berosus, 167 body: term inology 74 w ith n.9; geometrical solid, 72, 74—7; physical body (distinction from m athem atical body), 75-7; as object o f m otive force, 102; floating body, 112, 159-60; falling body, 144 Caelius Aurelianus: on the non-evident in medicine, 13-14, 17 Carneades, 283, 321; argum ents against gods, 45-6; against astrology and divination, 168—70, 177, 191; on the pithanon, 250; on C hrysippus’ solution to sorites argum ents, 45—6, 54-6 causation: in medicine, 2, 10, 13-14; in mechanics 98, 112; in astrology, 170-3, 182-91 passim; causal relationship in sign and w hat is signified, 261 Celsus, 145; on medical theory, 14 centre o f gravity, 112 certainty, 158 w ith n .67, 255, 276; see also know ledge Chaldaeans, see astrology change: Aristotelian analysis of, 101-3, 109; confined to body, hence absent from m athem atical entities, 75, 76η. 12 character: predictions in astrology, 169, 172, 173η.27 Chrysippus, 36η.28, 84: reply to sorites argum ent, 41-4, 47-56; to Dem ocritean cone problem , 85-6; on signs, 212-14; on sunartesis, 245, 248; use o f the pithanon, 251—3; on physiognom ies, 229; on future

General index conditionals, i68; belief in astrology?, T 6 7 - 8 , T 70, 191

Cicero: on astrology, 1 6 8 - 7 8 , 1 9 0 η . 5 0 circles: in mechanics o f H ero, 1 1 3 - 1 4 , 1 1 9 , 1 2 0 - 5 , I 2 7 (concentric) 1 1 3 , 1 2 7 Cleanthes, 1 6 7 w ith n. 8 , 2 2 8 - 9 Cleomedes, 1 4 3 ; on atm ospheric refraction, 13

+

clepsydra (water clock): lack o f precision, 143-4, i86n.44 Clitom achus, 45-6 Colotes, 313 composition: in geom etry, 82; in mechanics, com position o f m otion, 1 2 0 -6

conception, tim e of: im portance in astrology, 185 concepts, form ation of, 78-81, 90, 91, 206-7 w ith n.35 conditionals: sunêmmenon, (Stoic) 227, 275, 284, (Epicurean) 2 8 m .35, 283-5, 289; ‘Philonian’ (material implication?), 28, 213, 220, 222, 234, 236, 245, 253-6; ‘sunartêsis’ (strict implication?), 213, 23211.92, 234, 236, 245—6, 248, 253-6; conditionals referring to the future, 168, 254; conditional premisses (in sorites), 28, 46; signs as conditionals or as antecedents o f conditionals, 5, 206, 208-TO, 212, 214-17, 22O-4, 228, 234, 255; subconditional, 219, 223η.73, 243; presupposition, 220-4, 228 cone problem , D em ocritean, 85-6 confirm ation, see epimarturêsis conflict: o f appearances, 2 7 m .75, 273, 278-80; o f alternative explanations, 271, 300 consequence: in inference, 206η.33, 217, 227, 245~6; in m ethods o f verification, 263-4,283 contact: in geom etry, 82, 84-5, 87-8 contract: in theory o f justice, 315-19 conventionalism: in theory ofjustice, 304, 315-19, 322 cosm ology, xxi, 130; Stoic, 167 Crinis, 218-19, 223 criterion o f truth, 4311.54, 263, 273-8, 291-303 Ctesibius o f Alexandria, 143 Cyrenaics, 277, 297 definitions, 16-18, 20, 258-9; geometrical, 72-7 D em etrius Lacon, 94-5, 240, 264, 288 Dem ocritus: cone problem , 85-6; on perception, 128, 297 dem onstration, 218; see p ro o f (demonstrative)

343

descriptions, 17 determ inism : and astrological predictions, 179, 187, 189 w ith n .48, 190, 191, 254 D idym us, 13211.7 dimensions, in definition o f geometrical body, 75-6, 77 D iodorus Cronus, 36n.28, 42, 293, 301; on future conditionals, 168 D iodorus Siculus, 170η. 16 D iodorus o f Tarsus, 190η.51 Diogenes ofB abylon, 169, 170, 17311.27, 213, 241 Diogenes Laertius: on the sorites argum ent, 27-8, 36-7 Dionysius o f Cyrene, 241, 249, 258 D ionysodorus, 94 w ith n.6 diseases, 4, 5-6, 8, 19, 20; as generalities, 8-T i, 19 dissection, 1 3 m .5, 144-5; vivisection, 145 distance: in Epicurean epistem ology, 283, 291-2, 298; displacement: in A ristotle’s mechanics, 98, ιο ί- n passim, io8n. 13; in [Aristotelian] Mechanica, 116, 118, 120, 123,124 divination, 167-72, 213, 235; Posidonius on, 170 dogm atist, in medicine, 25-7, 45;seeafio rationalist doxa, see opinion earth: m ovem ent of, 109, i6yn.8; treated as a point, in astronom ical calculations, 162 w ith n.82 eclipse, I3 in .4 , 301; lunar, 134; use o f eclipse data in astronom y, 139, 142, 14311.34,145 w ith n .42, 157 ecliptic, obliquity of, 155 effort, in mechanics, 97, 98; see force efficiency, mechanical, 98η.2 elements: Aristotelian theory of, 179 elim ination m ethod, in sign-inference, 242-56, 257η.46, 258-63, 286-91; not equivalent to contraposition, 245; but related to anairein in Aristotle, 246; relation to ouk antimarturesis, 263-72 Empedocles, 270; on perception, 128 em piricist philosophy, 70, 259; relation w ith m athem atics 70-2, 89 E m piricist school o f medicine, xx, 1-7 passim, 13, 17, 20, 25-6, 57-65, 144 endoxa, io 8 n .i3 , 207-8 energy, exchange of, 980.2 Ennius, l68n. 11 Epictetus, 171 Epicureans, 4411.59, 73η.6, 74-5, 76η. 12 238; scientific m ethodology, 263-72; epistem ology, 128, 230, 276-303; on signs, 2140.51, 232η.91, 239-72; on

344

General index

Epicureans ( c o n t.) perception, 128; logic, 273-303; truth values, 275, 300-1, (concerning the future) 301-3; theory ofjustice, 304—26; definition o f body, 76; attacks on geom etry, 79, 89, 91-2, 92-5; on infinite divisibility, 89-91; and on astrology, 191 Epicurus, 7311.6, 294—6; criterion, 277-8, 297; on m ethods o f verification, 263-72, 276-83; on geom etry, 79, 84η.24, 8ç, 93; against infinite divisibility, 89-91 e p i m a r tu r ê s is , 263, 266, 273-6, 276-83, 291-2, 293; a procedure o f verification, 283; w ith respect to the evident, 266, 280; also in legislation, 321 epistem ology, 4-5, 43-4, 77, 255; and problem s o f observational error, 130-1, 159-64; and use o f evidence, 205; and signs, 206-38, 239-72; and observation/inferencc, 228-30; Stoic epistem ology, 78, 128, 230, (and the p i t h a n o n ) 250; Epicurean, 128, 230, 276-303 e p i ta s is , in concept-form ation, 80-1, 9111.36, 92 equinox, 133, 135, 156, 157; precession of, 139η.28, 140, 145, 146η.43, 147- 9, 151, Τ55, 157; in calculation o flcn gth o f year, 140-2, 145 Erasistratus: fabrication o f observational material, 131-2 Eratosthenes, 74, 155 error, xxii, 130-1, 213; in scientific results due to: dishonesty, 131-2, 147-8; incom petence, 132-3, τ61 ; failure to take account o f experim ental conditions, 133—5, 161; inadequate instrum ents, 136-44, 145, 161, i8 6 n .44; imprecise positioning o f instrum ents, 141—2, 145, ΐόι ; imprecise tim e-keeping, 143-4, 161; im precise calculation, 141, 142, 157, 158; system atic error recognised, 15811.66; but theory o f error absent, 157-9, 163-4; responses to problem o f error, 145—59; by broad toleration o f error, 148-51, 156-9; selective use o f evidence, 147-52, 157; and adjustm ent o f data, 149-51; error in astrology, 181-2, 186; error in judgem ent concerning appearances (Epicurean theory), 268, 274 ethics, 304-26; Stoic, 167, 311 Eubulides: use o f sorites, 36-41 Euclid, 72-4, 77, 82-3, 92-3, 123 E uctem on, 133 Eudem us, 94 E udoxus, 136, 159η.68, i66; ‘spider’, 136 w ith n. 17 e u l o g o n , se e probable

Euripides, 316 evidence: in science: acquisition of, 128-59; selective use of, 147-52, 157; adjustm ent of, 149-51; in sign-inference, 193—238, 257; in epistem ology, e n a r g e i a , 26611.65, 274, 276, 280; criterion for Epicurus, 277-8; basis o f operations o f verification, 292; relation to k a t a lë p s is , 282; se e a lso observation, experim ent, error, signs, te k m ê r i o n

evident, 6, 11-18, 57; confirm ed by e p i m a r tu r ê s is , 266; signs as evident things, 194,205-6, 211, 221, 243, 263-4 exact sciences, 130, 131—64; s e e a ls o acoustics, astronom y, mechanics, optics example, argum ent from , 201 experience: in medicine, xx, Ch. 1 p a s s i m , 24-6, 57η. 80, 6o-5, 252; particular or general, 26, 60—1; in form ation of concepts, 78; empirical generalisation, 252-3; in sign-inference, 257, 260-2, 265-72; relation to logic, 64-5; experience o f m athem atical objects, 79; sensory experience, 70, 128-9, 273; as criterion, 274—8, 291-303 experim ent, 132, 144, 151, ιόο; eye-witness accounts of, 131, 132η.6 fate, 98, 187, 188; s e e a ls o determ inism Favorinus, 174, 175, 178, 183-7, i88n.46 Firmicus M aternus, 188-90 force, 97, 99; in mechanics o f Aristotle, 98-100, ιο ί - n ; o fH e ro , 113-15,· 162η. 8i; o f [Aristotelian] M e c h a n i c a , 116—26; virtual force, 108 freew ill, 191, 271; s e e a ls o fate, determ inism friction, 162 w ith n. 81 future: prediction of, 165—9 2 p a s s i m ; foreknow ledge of, 191; m odalities of, 168; future contingents, 276η. 17, 283; neither true nor false, 274—5, 301—2; s e e a ls o determ inism , providence Galen: on earlier philosophy, 128; on medical schools, 1-4; on M ethodist medicine, 4-23 p a s s i m ; on medical experience, 24—7, 131—2, 15111.58; on the sorites argum ent, 24-35, 57-65 gears, cogged wheels, 114, 125, 162η. 81 Gem inus, 174 generalities, 8 -1 1, 15; evident, 3, 4, 8, τ ι - i 8; know ledge of, 18-20 geography: use o f evidence, 13 in .4; geographical location, in astrology, 175-6, 182, 184, 186; in legislation, 323-4 geom etry: contrasted w ith music, 132 w ith n.7; attacks on geom etry, 72-92, 92-5; geometrical objects, 70η.2, 88; body,

General index 75-7; definitions, 72-7; limits, 84-5; approxim ation to limit, 152η.60, 153; π, 153; relational problem s in geom etry, 81-3, 91, 92; solutions: Aristotelian, 83-4; Stoic, 84-6; non-Euclidean geom etry, 71; barycentric geom etry, 112 gods: in Stoicism, 167; possession o f foreknow ledge, 191; argum ents against Stoic gods, 45-6 harmonics: accuracy in, 1510.58; use of scientific instrum ents, 136; see also music, acoustics heap, 32η. 18, 33; see also sorites hedonism: in Epicureanism , avoidance o f pain, 308 Heraclitus, 270; on unreliability o f perception, 128 H erm archus, 305, 312—15 Herm es Trism egistus, 170η. 5 H ero o f Alexandria: on geom etry, 74η.9, 70, 79; on mechanics, io 8 n .i2 , 713—5, 126-7; on the dioptra, 1370.19 Hesiod, 370, 376 H ipparchus, 139, 147, 155, 157, 1590.68, 169, 170; use o f observation in astronom y, 133, 740-2; use o f ‘four-cubit rod dioptra’, 137; equinoctial armillary, 137; determ ination o f length o f tropical year, 140-2, 155, 156; star catalogue, 139η.28 history: use of observational evidetice, 73 7; unscientific, 319 hoist, 114 Horace, 36, 311, 313, 319 horoscopes, 166-92passim·, horoscopes o f individuals, 170, 183; accurate determ ination of, 185, 186 Hypsicles, 93-5, 169η. 13 illusions, 129, 134—5; employed by Sceptics, 159-61; b ut explained by science, 160-1 inclined plane, ri2 , 762η.87 incorporeals, 85, 86n.28; dimensions as incorporeals, 75 indeterm inacy: in answer to sorites, 58-64 indication, 4-8, 20, 22; see also signs (indicative) individuals, 46n.63; in medical experience, 9 -1 1, 61-2, 63; but not knowable, 10 indivisible magnitudes, 74, 83, 84 induction, 26, 6ln.84, 62, 78η.14, io8n.i3; in Aristotle, 200-7; in sign-inferences, 242, 252-3, 256-72; vitiated by isolated phenom ena, 249; perfect induction, 201 w ith n.21; m athem atical induction, 29 w ith n.13

345

in f e r e n c e , 6, 2 0 , 2 6 η . 5, 6 i - 2 , 7 8 , 9 0 ,

274η. 5 7 ; non-deductive, xxii-xxiii, metabasis, 78η. 14; elim ination m ethod, 242-56, 2570.46, 258—63; sim ilarity m ethod, 249, 252-3, 256-63; from empirical generalisation, 252-3; presupposition, 220-4; ‘insofar as’, 258-9; modus ponens, 2811.71, 29-30, 47, 56, 58, 215-17, 228, 230-1; inference to other m inds, 228-9 infinity: in mechanical proportion theory, 109—17 ; o f universe or possible worlds, 270, 299-300; infinite divisibility, 91, 94~5 instrum ents, scientific: use of, in optics and harm onics, 136; in astronom y, 136—40 (see astronom y); in astrology, i86n,44; imprecision of, 138η.24, 141-4, 145, 18611.44 interval: musical, 132, 163η.85; of m ovem ent or change, 102, 103, 106; in geom etry: closed, 81; open, 82, 86 jaundice: effects on perception, 129 w ith n.2 judgem ent: as source o f error, in Epicurean epistem ology, 268, 274; suspension of, 49, 50η.70, 54, 129, ι6ο, 161 justice: Epicurean theory of, xxiii, 304-26; contributes to the good life, 309-10; basis in nature, 31t, 322; in com m unity, 312; contract theory, 317-19; see also law juxtaposition (parathesis), 82, 85, 88, 90 kcüalêpsis, 281-2; relation to enargeia, 282; see also phantasia (katalëptike) know ledge, t, 255, 276; medical, C h .i passim, 26, 61-2; m athematical, 70-2, 78; scientific, 158 w ith 11.67, 161 ; by induction, 201; from signs, 221 language, 41η.48, 2o6, 313, 318 law: legislation, 310-15; in conform ity w ith constitution, 320; differing in different regions, 318, 320, 323—4; educational value, 324; evidence in law, 131; see also justice laws: astrological, 254; o f mechanics, 97, 99-100, 10811.12, 120; o f optics, 160 least, 74, 75η. 10; see also m inim al part lekton, 78, 208, 209η.40 lever, 112-14, 775, 116, 178, 125, 762 limit: in geom etry, 75η. 10, 81-8; approxim ation to, in scientific m ethod, 152-6 line: definitions of, 72, 73-4; concept-form ation, 78-81; attacks on, 78-81, 87-8; straight lines, 72-3,

346

General index

line (cont.) 76η. 12, 8 i-2 ; relation to points, 81-2, 87; generation of, 86—7 logic, 7, 27, 42-3, 47, 64-5; Aristotelian, 274; Peripatetic, 22611η. 79 and 81; syllogistic, 195-7, 200-203; Diodoran, 42-3; Stoic, 28, 48, 214, 218-19, 275; Epicurean, 273-303; non-deductive, xxii—xxiii, 193—238; logic o f ‘since’, 218-24, 243; o f ‘insofar as’, 258—9; o f sorites argum ents, 27-35, 37; m any-valued, 630.87, 275, 300; alternative, 64 Lucretius, 308, 315, 319 machines, simple, 91, 112-16, τ 18-19, I2 5. 16211.81 magic, 97η. I man: rationality of, 193, 206—8, 230; providentially constructed, 189, 206-8, 230; hum an nature, as basis for law, 3II-I5

Manilius, 167, 170, τ7 τ, 175, 176, 183-7 M arcus Aurelius, 171, 307 m athematics, xxi, 158; and empiricism , 70; and rationalism , 70-1; and m entalism, 72η.4; m athematical body, 75-7; objects, 70, 71; know ledge, 70-2; truth, 71; m ethod o f approxim ation to a limit, 152η.60; applied mathematics, 130 mean m otion, 15711.64 mechanics, xxi; background to m odern science, 96-8; origins in Aristotelian mechanics, 98-100, 1 0 1 -in ; developm ent in Archimedes, 111-12; H ero o f Alexandria, 113-15, 127; IAristotelian] Mechanica, 116—26 medicine, xix-xx, 1-23, 240-1; schools of, X X , 1—3, 25; medical experience, 24—7, 61-5, 252; medical practice, 14, 23, 27; signs in medicine, 5-16, 47, 212 w ith n. 48, 213, 235, 241; pregnancy, signs of, 194, 195, 204 with n.30, 205, 2150.54, 231; views on xanthopsia, 12911.2; astrology as paramedical art, 182-3 M egarian school, 301 Melissus: on perception, 128; sêmeia, 194 M enelaus o f Alexandria, 13911.27 metabasis, see transference M ethodist school o f medicine, xx, 1-23, 21911.62; distinction from other schools, 1-3, 5, 8; relation to scepticism, 20-22 m ethodology, scientific, xxii, 130-1; ‘m ethod’ m medicine, 1-3; observational m ethod, 131-45, 146; distortion inherent in m ethod, 144-5, responses to m ethodological problem s, 145-59; use o f alternative m ethods, 145; selection o f

evidence, 147-52, 162; methodological discussions, 163; m ethods o f falsification and verification, 268—71, 273—303 Meton, 133 m inim al part, 74, 84, 86, 89—91, 93—4 m ixture (kräsis), 84, 85, 88 Mnaseas, 21 m oon: phases of, 300; treatm ent of, in astrology, 173-5, 180-1, 186 m otion, 42, 81, 87, 144; in mechanics, 112; A ristotle’s analysis, 98—100, ιο ί—i t ; m otion in a void, 110; in a circle, 119-20; circular and curvilinear m otion, 120-6; com position o f m otion, 120-6; m otion requires void, 259—60, 262, 263—4, 269, 274-5 music: contrasted w ith geom etry, 132 w ith n.7; role o f sense-perception in, 132; see also acoustics, harm onics nature, 970.1; order in, 98, I I I , 167 Nechepso and Petosiris, 170η.15 Neoplatonism , 720.4, 187 Nigidius Figulus, 171, 1730.28 non-contestation, see ouk antimarturèsis non-evident: the non-evident in medical theory, 2, 6-8, 11-16, 22, 144; signs o f the non-evident, 5, 211-12, 221, 2220.69, 243, 263-4; tem porarily non-evident or non-evident by nature, 211, 221; tested by ouk antimarturèsis, 266, 284-5; and antimarturèsis, 273-4, 276, 285-91; other minds, 228-9; void, 263 observation: in medicine, xx, 6—7, 12, 19, 26, 27, 57, 60-63, 144-5; in exact sciences: error, xxi, 130, 142, 157, 158; dishonest, 131—2, 147—8; incom petent, 132-3; observational problem s due to conditions, 133-5, 161; instrum ents, 136—44, 16 1; m agnitude o f eye, 136, 154; used (or not) by Ptolem y, 139—40; responses to observational error, 145-59 opinion (doxa), in Epicurean epistem ology, 282; true or false, 278-80, 300; m ethods o f verification, 279-92 optics, 134-5, 151, 154, 160-1 ouk antimarturèsis, 263-72, 273-6, 283-5; a m ethod of verification (not discovery), 268-72; with respect to the non-evident, 266, 280, 283; by consistency or consequence, 266-7, 283-5; a sufficient condition o f truth, 268—9; also in legislation, 321 Panaetius, 168-9, 170, 1740.31, 177, 191 Pappus, 7411.9, 76η. 12, 112, 137 paradox, 37-8, 42-3, 44η.58

General index parallax, lunar, 162η. 82 parathesis, see juxtaposition Parm enides, 194 Pelops, 26—7 perception, xxi, 12, 38, 57, 58, 6011.83, 78, 276; unreliability of, 128-31, 139-64; but regarded as criterion o f tru th by Epicureans, 263, 273-8, 291-2, 297-303; despite conflicting appearances, 273, 278-9, 297-8; perception o f geometrical objects, 79; o flim its, 86, 92; perceptible m inim um , 90, 91, 92; rôle o f perception in study o f music, 132 w ith nn.7 and 8; see also observation, experience Peripatetic school, 241, 265, 297 Persius, 36 persuasion, 200 persuasive, see pithanon phantasia, 277η.22; relation to external cause, 277-8; and to truth, 278-9; phantasia katalëptikë, 43-4, 49, 52, 278 phantasma, in Stoic theory, 277-8 phenom ena, 2, 8, 16, 18, 22, 96-7, 98; as starting point for science, 207-8; scientific explanations o f phenomena, 139-61, 163; plurality o f explanations countenanced by Epicureans, 269-70, 300-1; rôle in Archim edean mechanics, 112; in ouk antimarturësis, 266—72, 284-5; isolated phenom ena (freaks), 249 Philippus, 26-7 Philodem us, 219, 231-2, 239-72, 282, 283, 306, 321-2 Philonides, 94 Philoponus, 144 phronësis, 38, 6011.83 physiognom ies, 203, 228-9, 2310.90 physiology, 13, 14, 15, 131, 1510.58 pithanon, 235, 2360.99, 237, 25(^3, 261; three senses of, 250 planets: planetary theory, 133, 135, 149-51, 155-6, 157η.65; observation o f planets, 135, 138, 146-7, 1570.65; possibility o f additional planets, 184; planets in astrology, 166-8 9 Plato, 191, 207, 2650.63, 2670.68, 27011.73, 310; on fate, 188; onjustice, 305, 317; philosophy o f m athematics, 70-1, 7211.4, 76η. 12, 77; on perception, 128, 162-3; Timaeus, 7411.8, 77, 188 Plotinus, 171, 174-5, 187-8, 192 Plutarch: on D em ocritean cone problem , 85- 6; on Epicurean m ethodology, 295-6; on m inim al parts, 84—5 point: Greek term inology, 73, 74 w ith n.7; definitions of, 72, 73-5; attacks on, 81-3, 8 6- 7; problem s o f relation, 81-4, 87; particularly' contact, 82, 84—5

347

political theory, 304-26; Stoic cosm opolitanism , 307; the city not central in Epicurean concerns, 307; participation in public affairs, 309-10, theory o f justice based on com m unity, 312-15, 321; changes o f constitution, 321 Polyaenus, 83-4 Polybius, 307, 319 Polystratus, 322 pores, 2, 15, 211, 215 Porphyry, 187 Posidonius, 75η. 10, 7ön.i2, 77η. 13, 168 a n d n .io , 183, 184η.39, 185η. 42, 190, 237η. 103; support for astrology, 170-1 possibility, 301-3 potentiality, 108, 301 precision, see accuracy preconception: in sign-inference, 215η.55, 258; in theory ofjustice, 317, 320, 325-6 presentation, see phantasia Presocratic philosophers, 128, 270 privation (sterêsis), 78, 80, 92 probability theory: absent, 163-4 probable, 23711.103, 251; see also pithanon Proclus, 76η. 12, 79, 92-3, 137-8, 143, 163, i

87

projectile, 112, 120 prolepsis, see preconception proof, 20, 220; a species o f sign, 210, 212, 215; dem onstrative p ro o f (apodeixis) 194, 1980.13, 199η. i6 proportionality, 37, 39, io8n. 12; in A ristotelian physics, 98—9, 100, 103, 105—II; in mechanics o fH e ro , 115; in [Aristotelian] Mechanica, 116—25 propositions, ontological status of, 208-9 Protagoras, 108n.11, 297 Protarchus, 93—4 providence, 189, 190, 206-8, 213, 2270.83, 23 5

Ptolem y: on observational problem s, 145—7; ° n observation in astronom y, 133-5; on astronom ical instrum ents, 137-44; and error resulting from them, 140-4, 145, i86n.44; selection o f evidence, 147-52, 157; tolerance o f error, 148-51, 156-9; approxim ation, 155-6, 157; on music, 132η.8, 136; on astrology, 173, 175, 176, 178-83, 184-92 pais/m; star catalogue, 138, 139 w ith n .28; was Ptolem y a fraud? 138η.25, 139-40, 147, 148

pulley, 97, 112; mobile, 115; com pound, I 02n. 81; block and tackle, 115 puzzle, 27, 37; see also paradox Pyrrho: influenced by gym nosophists, 308 Pyrrhonian scepticism, 20, 36, 44η. 58, 58η.8 i, 17 1, 175, 184, 308

348

General index

Pythagoras/Pythagoreans, 15in .58, 16211.84, 163η.85 quantity, 59; in Aristotelian analysis o f change, ιο ί, 102 rationalist philosophy, 259; relation w ith ' m athematics, 70-1 Rationalist school o f medicine, xx, 1-17 passim·, see also dogm atist reason, 5, τι, 12, 38, 58; in medicine, 2, 6, 7; in acoustics, 1320.8, 162-3; divine reason, in Stoicism, 167; logos endiathetos, 206 reflection, principles of, 160 refraction: in different media, 136, 151, 160; in optical illusions, 160; atm ospheric, 134-5, 142η.33 resistance: in definition o f body, 76, 80; in mechanics, 98, io 8 n .i3 , n o , 116, 122 Scepticism, 36, 191; attacks on perception, 128-9; relation to medical schools, 20-2 screw, 115 security: the aim o f legislation, 309-10, 324 Seneca, 167, 171 Sextus Em piricus, 292-3; on earlier philosophy, 128; on M ethodist medicine 5-23 passim·, on argum ent, 225; on sorites argum ent, 43—6; on deficient argum ent, 48, 226η.79; on proof, 220, 293; on geom etry, 69-92; on astrology, 15911.68, 174, 175, 183-7; on signs, 194, 206-17, 219, 220-34, 241-2; on the criterion o f truth, 263-7, 276—81; on the unreliability o f perception, 129, 159-61 signs, xxii-xxiii, 5; as evidence, 193-4; in non-deductivc inference, 194-238, 239- 72; in astrology, 187-8, 190; in medicine, 5-16, 47, 212-13, 235, 241, (signs o f pregnancy) 194-5, 204-5, 215, 231; in physiognom ies, 203, 228-9; A ristotle’s analysis, 193-206, 214, 217-18, 237; Stoic analysis, 206-38, 2 40- 72; relations to conditionals, 206-17, 220-34, 242; reality of, 206-9, 217; Epicurean analysis, 239—72; com m em orative/indicative, 5, 211—17, 219-22, 228-36, 241; com m on/peculiar, 231, 233, 242-4; things or propositions? 208-12, 243 sim ilarity m ethod: in sign-inference, 242, 256-63, 288, 289; includes ‘analogy’, 256-7: ‘insofar as’ premisses, 258-9 Simplicius, too, 108n.11, i n simulacra, 268-9, 2770.22, 279, 299 Socrates, 309, 320 solid, geometrical, 74; see also body

solstice, 133, 135, 156, 157; observation of, in calculating length o f year, 140-1, 145 Soranus: on medical theory, 13-14 sorites argum ent, 25-7, 107-8, 253, 255 w ith n.41; account of, 27-35; name, 32η. 18; history, 35-46; in Z eno ofElea? 36-7, 39n.43, 107-8; Eubulides, 37-41; Aristotle? 38-41; Arcesilaus, 43-4; Stoicism, 27η.8, 28, 36, 41-5, 47η.64, 253; answers to, 47—65 speculation, 16-18 speed (velocity): in mechanics, 117η.24, 119—20; in A ristotle’s account o f m otion, 101-11 passim; reduction of, 115; m easurem ent of, 144; velocity o f light, t 6 o ; angular velocity, 12411.25 Speusippus, 7611.12 stars, fixed: in astrology, 167, 16811.9, 174, 176, 180 sterêsis, see privation Stoicism, 74-5; epistem ology, 78, 128, 230, 250, 297; signs, 194, 206-17, 218-38, 240-56; on perception, 128; causation, 98, 167; m aterialism , 75, 22911.86; geom etry, 75-8, 83-7; concept-form ation, 78-80; astrology, 167-72, 183-4, 187, 191; logic, 27, 28, 4in.48, 48, 210-17, 218-19; use o f sorites, 270.8, 28, 36, 41-5, 470.64; account o f fallacy, 48-9; ethics, 167; account o f virtue, 53 subconditional, see conditional suffering: an evil to be avoided, in Epicureanism , 308-10 sun: angular diam eter of, 154-5; size of, 300; rôle in astrology, 172-3, 180-1, 186 sunartësis, see conditionals surface, 770.13, 81, 85-6; definitions of, 72, 73- 4, 76η. 12 suspension ofjudgem ent, see judgem ent syllogistic, 195-7, 200-3, 274; practical syllogism, 1950.7 sym pathy, cosmic, 167, 170, 185 Tacitus, 171 technology, 96-127, 97η. i; technological devices, 97, i n - 1 2 ; charistion, 100, i n ; catapult, 162η. 84; scientific instrum ents, 136-44; see also machines, simple tekmêrion, 22511.76, 231, 235; in Aristotelian analysis o f inference, 196, 204, 234; conclusiveness, 196 tension, 76η. 12 Them ison, 15 Theognis, 316 T heon o f Alexandria, 137 T heophrastus, 166, 223

General index theory: in medicine, xx, 2, 7, 10, 13-16, 17, 20, 22, âin .8 5 ; adjustm ent o f evidence to theory, in science, 149—52, 157-8 Thessalus, 3, 15, 23 time, 81; in mechanics o f Aristotle, 98, 101-11 passinr, o f Hero, i i 5 ; o f [Aristotelian] Mechanica, 116-17, 124; in astronom ical observations, 144, 147; inaccuracy o f tim e-keeping, 143-4. i86n.44 Tim ocharis, 146 T im on, 44η.58 trajectory: curvilinear, 1 2 ^ 4 ; o f atomic swerve, 2720.76 transference, in concept-form ation, 78, 86 tranquillity, Pyrrhonian, 308 treatm ent, in medicine, 1-10 passim truth, 130η.3, I95n.4, 197, 220, 202, 267, 268-9, 297-8; correspondence, 274; criterion of, 430.54, 263, 273-8, 291-303; relation to th e pithanon, 250—1; necessary truth, in proof, 213; truth values in Epicurean logic, 275, 300 twins: problem atic in astrology, 173 with n.28, 184, 185, 190-1 unification see m ixture

349

utilitarianism , in theory ofjustice, 304-5, 312-15, 322 virtue, 38-9, 53; life according to virtue, a requirem ent for pleasure, 308-9 void: m otion in, n o ; p ro o f o f existence of, 216-17, 259-60, 262, 263-4, 269, 274-5 wedge, το8η.ΐ2, 113η. 19, 115 w eight, 97-8, 144; in Aristotelian mechanics, 99-111 passim·, in A rchim edes'm echanics, 112; hydrostatics, 159-60; in H ero o f Alexandria, 113-15, 162η.81; in [Aristotelian] Mechanica, 116—26; puzzles about, 159-60 windlass, 125 w ord, see language Z eno o f C itium (Stoic), 42-3, 167 Z eno o f Elea: Millet seed argum ent, 36-7, 39n .43, 107-8 Z e n o o fS id o n (Epicurean), 76η.12, 92-5, 240, 258, 26ο, 264η.6o zodiac, 169; signs of, i68n.9, 172; m ythology of, 186

(iii) IN D E X A N D GLOSSARY O F GREEK TERM S References are to occasions on w hich the Greek term is noted or discussed; for further detail and analysis consult the General Index under the given translation. Translations in brackets do not appear in the General Index, but w here relevant the transliteration o f such term s does appear. άδηλον adèlon non-evident 144 ά διάσ τα τος adiastatos (unextended) 73 ά δικειν adikein (com m it injustice) 305, 323 α ϊσ θησ ις aisthësis perception 6on.83, 128, 1630.85, 276 ακολουθία akolouthia consequence 2o6n.33, 2170.58, 263, 283 α κρ ίβ εια akribeia accuracy 6on.83, I3cn.3 αλήθεια alëtheia truth 130η.3 ά να ιρ εϊν anairein elim ination 246 α να λο γία analogia analogy, proportion 780.14, 90, Iio , 2 8 m .35 ανασκευή anaskeuê elim ination 242,2620.55, 263-4, 286-90 α ποδεικ τική apodeiktikë (dem onstrative) 198η. 13, 199η. ι6, 205 ά π ό δ ειξ ις apodeixis dem onstration, dem onstrative p ro o f 218 αστρολογία astrologia astrology 159η. 68 α σφ άλεια asphaleia security 310 άσώ ματον asömaton incorporeal 85 α τα ρ α ξία ataraxia tranquillity 308 ά φ α ίρ εσ ις aphairesis abstraction 92 βάρος

baros

w eight

101

3 5°

Index and glossary o f Greek terms

βεβαιότης βλάπτειν

bebaiotës btaptein

γνώ σ ις

gnôsis

certainty (do harm)

know ledge

15811.67, 2760.15 305, 323 3, 19

διάστημα diastema interval, distance δ ια φ ω ν ία diaphonia conflict 27T δόξα doxa opinion 278-80 δύναμ ις dunamis force 101, 102

283

έκπύρω σ ις ekpurösis (conflagration) 167 έλάχιστον elachiston least, m inim al part 74,7511.10 εμ π όδιζον empodizon resistance no ένάργεια enargeia evidence 266η. 65 ενδειξις endeixis indication 4 ένδοξα endoxa (reputable opinions) 208η. 37 ένδοξος endoxos (reputable) 197 w ith n . n , 198 ένω σις henôsis unification 88 έξ ίσου ex isou 72 w ith η. $ επαγω γή epagégë induction 200, 20in .21 έπίμαρτύρησ ις epimarturêsis (attestation) 263 έπισ ημ ασ ίαι episëmastai indications 180 έπ ίτα σ ις epitasis (intensification) 80-1, 98η. 3 επ οχή , επ έχειν epochë, epechein suspension o f judgem ent ετεή i'teëi (in reality) 128 εύλογον eulogon probable 251 ηγούμενον ήσ υχά ξειν

hëgoumenon hêsuchazein

antecedent 221, 222 (to keep silence) 420.49, 49, 50

θεω ρητικός theorëtikos (speculative) θεω ρία theöria speculation 16, 166 ίδιον ισ χύς

idion ischus

540.77, 160

16

peculiar (of signs) 23111.90, 233, 242 force 101, 102, 117-18

καθηγούμενον kathëgoumenon antecedent 220-1, 222 κανώ ν kandn (naonochord) 136 κ ατά ληψ ις katalëpsis (apprehension) 255, 281-2 κοινόν koinon com m on (of signs) 231,243-4 κοινότης koinotës generality 3, 8 κρά σ ις basis m ixture 84 λεκτόν λόγος

lekton logos

λόγος άπορος

(thing said) 208 reason, proportion, argum ent logos aporos

puzzle

μετάβασις metabasis transference μηχανή mëchanë (machine, ruse) νόμω nomoi (by convention) νοούμενα nooumena concepts

38, 6011.83, 6in,85, n o , 163η.85, 225 27η.8,'4711.64

78 97η. i 128 78

ο ι π ερ ί hoi peri 440.55 όρθότης orthotës accuracy 130η.3 όροι h oro i definitions 17 ούκ άντιμα ρτύρη σ ις ouk antimarturësis (non-contestation)

263

Index and glossary o f Greek terms oil μάλλον

ou mällon

(no more)

351

69

πάθος pathos affection 22911.86, 276 παλάμη palante (device) 128 π α ρ ά δειγμ α paradeigma example 201 π α ρ ά θ εσ ις parathesis juxtaposition 85 π α ρ ά μικρόν para mikron little by little (of argument) 32η. 16 παρασυνημμένον parasunêmmenon subconditional 219 with nn.63 and 64 π είρ α peira experience 252 π ιθ α νό ν pithanon (persuasive) 235, 237 πίσ τις pistis persuasion 200n,20, 27611.1$ προκαθηγούμενον prokathëgoumenon antecedent 222 w ith n.70 πρ όλη ψ ις prolepsis preconception 215η.$5, 2$8, 320 π ρ ο νο η τικ ή ς pronoëtikos (providentially) 206 σημείον

sêmeion

point, sign

73, 74 w ith n.7, 193-4, 196, 198η. 14, 20211.24, 23511.96, 24011.2 σημείωσις sëmeiôsis sign-inference 240 w ith n.2, 262 σ κη νογραφ ία skënographia (scene painting, perspective) 1610.77 στερεόν stereon solid 74 στέρησις sterësis privation 78 στιγμή stigmë point 73, 74 w ith n.7 συλλογιστική sullogist ike syllogistic 19811.13 αυνάρτησις sunartësis connection (in conditionals) 213 συνημμένον sunëmmenon conditional 22211.70, 227, 230, 28111.35, 283-4 σΰνθεσις sunthesis synthesis (in concept-form ation) 78, 20711.35, 2270.83 σώμα sôma body 74n.8 σω ρίτης soritës sorites argum ent 32η. 18, 32-3 σω ρός söros heap 320.18, 33, 36η.26 τεκμήριον tekmërion (conclusive evidence) τέρα τα terata (freaks) 249 τέχνη technë (science) 13611.13 ΰ π ο γρ α φ α ί υπ οτυπώ σ εις

hupographai hupotupôseis

descriptions descriptions

196, 23511.96

17 17

φ αινόμενα phainomena phenom ena, appearances 239 φ αντα σ ία phantasia (presentation) 129, 20611.33, 239, 24011.2, 27211.22 φ άντασμα phantasma (presentation) 277-8 φ ρόνησις phronësis (practical intelligence) 38, 6011.83 φυσική phusikë (natural science) 130 φωνή phone w ord 410.48