Handbook of the History of Logic:

Mediaeval and Renaissance Logic

Volume 2

edited by Dov M. Gabbay and John Woods

CONTENTS

viiPrefaceDov M. Gabbay and John Woods

ixList of Contributors

1Logic before 1100: The Latin TraditionJohn Marenbon

65Logic at the Turn of the Twelfth CenturyJohn Marenbon

83Peter Abelard and his ContemporariesIan Wilks

157The Development of Supposition Theory in the Later 12ththrough 14th CenturiesTerence Parsons

281The Assimilation of Aristotelian and Arabic Logic up to theLater Thirteenth CenturyHenrik Lagerlund

347Logic and Theories of Meaning in the Late 13th and Early 14thCentury including the ModistaeRia van der Lecq

389The Nominalist Semantics of Ockham and Buridan: A ‘rationalreconstruction’Gyula Klima

433Logic in the 14th Century afer OckhamCatarina Dutilh Novaes

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505Medieval Modal Theories and Modal LogicSimo Knuuttila

579Treatments of the Paradoxes of Self-referenceMikko Yrjönsuuri

609Developments in the Fifteenth and Sixteenth CenturiesE. Jennifer Ashworth

645Relational Logic of Juan CaramuelPetr Dvořák

667Port Royal: The Stirrings of ModernityRussell Wahl

701Index

PREFACE

As modern readers will be aware, one of logic’s most fruitful periods filled thecomparatively small space from the mid-19th century to the third quarter of thecentury that followed. While classical mathematical logic remains securely situatedin the mainstream of the subject, alternative approaches arising from researchprogrammes in computer science and philosophy have also flourished. It speaksto the intellectual gravitas of mathematical logic that it should have dominatedutterly for a century and a quarter, but other developments have had longer runs,none more so than logic in the five centuries between the 11th and 16th. This isstaying power of formidable heft, one of the main reasons for which is the rich scopeof logical enquiry during this period. The same is true of modern symbolic logic.In the period of its exclusivity, it exhibited an agreeable complexity, with a reachthat extends from classical treatments of proof theory, set theory, model theory andrecursion theory, to variations that encompass intuitionist, modal, many-valued,relevant and dialogue logic, among others. No doubt this complexity is part ofthe explanation of the dominance of symbolic logic. If so, a similar explanationattaches to the staying power of mediaeval logic, whose range is easily as robustas its modern cousin. While the mediaeval tradition never abandoned the centralfact of the syllogism as its organizing focus, it subjects this focus to the creativetensions of adaptation, extension and creative reinterpretation. All in all, thelogicians of the middle ages rang the project of logic through virtually all thechanges that characterize modern logic, at times rivaling the new developments inconceptual sophistication and theoretical robustness. The coverage of mediaevallogic is striking, extending from treatments of logical consequence to the intricaterules of logical disputations, from amalgamations of preceding traditions, whetherAristotelian or Arabic, to the development of new insights into quantification, frominvestigations of meaning to the exploration of modal contexts, from enquiry intothe paradoxes to the stirrings of the logic of relations, and much more.

It is agreed that logic lost the vigour and high reputation achieved in the middleages, as the Renaissance emerged as Europe’s dominant intellectual and culturalforce, but it is wrong to say that logic was sent into an impotent retirement inthis period. It is more accurate to speak of hibernation, a period of quiescenceduring which logic was renewing itself for the challenge of a looming modernity.Astride the gap between Renaissance and the new world of learning is the work ofthe Port Royal logicians, included here for its role as a beacon. The Port Royallogicians disliked technical formalisms, and are in that respect the forbears ofmodern informal logic. But these same logicians did some of the best of the earlywork in probability theory, thus anticipating the rise of inductive logic.

viii Preface

It remains to be seen whether, on the score of intellectual power, methodologicalrigour and conceptual inventiveness, the present-day pre-eminence of logic willextend its reign another three hundred and twenty-five years. However we reckonthe probabilities, suffice to say that if the longevity of mediaeval logic is indeedbested by our descendants, that will have been an accomplishment of supremeimportance in the annals of human intellectual effort.

Once again the Editors are deeply and most gratefully in the debt of the vol-ume’s superb authors. The Editors also warmly thank the following persons:Professor Margaret Schabas, Head of the Philosophy Department and ProfessorNancy Gallini, Dean of the Faculty of Arts, at the University of British Columbia;Professor Michael Stingl, Chair of the Philosophy Department and ChristopherNicol, Dean of the Faculty of Arts and Science, at the University of Lethbridge;Jane Spurr, Publications Administrator in London; Carol Woods, Production As-sociate in Vancouver, and our colleagues at Elsevier, Senior Acquisitions Editor,Lauren Schultz and Mara Vos-Sarmiento, Development Editor. For their excellentadvice and support the Editors also owe a special debt of gratitude to MartinTweedale, Stephen Read, Jennifer Ashworth, Henrik Lagerlund and John Maren-bon.

Dov M. GabbayKing’s College London

John WoodsUniversity of British Columbia

andKing’s College London

andUniversity of Lethbridge

CONTRIBUTORS

E. Jennifer AshworthUniversity of Waterloo, Canada.ejashwor@watarts.uwaterloo.ca

Catarina Dutilh NovaesUniversity of Amsterdam, The Netherlands.cdutilhnovaes@yahoo.com

Petr DvořákAcademy of Sciences of the Czech Republic, Czech Republic.peterdvorak99@gmail.com

Dov M. GabbayKing’s College London, UK.dov.gabbay@kcl.ac.uk

Gyula KlimaFordham University, USA.klima@fordham.edu

Simo KnuuttilaUniversity of Helsinki, Finland.simo.knuuttila@helsinki.fi

Henrik LagerlundThe University of Western Ontario, Canada.hlagerlu@uwo.ca

Ria van der LecqUniversity of Utrecht, The Netherlands.Ria.vanderlecq@phil.uu.nl

John MarenbonTrinity College, Cambridge, UK.jm258@cam.ac.uk

x

Terence ParsonsUniversity of California, Los Angeles, USA.tparsons@humnet.ucla.edu

Russell WahlIdaho State University, USA.wahlruss@isu.edu

Ian WilksAcadia University, Canada.ian.wilks@acadiau.ca

John WoodsUniversity of British Columbia, Cananda.jhwoods@interchange.ubc.ca

Mikko YrjönsuuriUniversity of Jyväskylä, Finland.mikyrjo@cc.jyu.fi

THE LATIN TRADITION OF LOGIC TO 1100

John Marenbon

1 INTRODUCTION

The twelfth century, like the fourteenth, was arguably one of the great creativeperiods in the history of logic. The same is not true for period that precedes it,and forms the subject of this chapter: Latin logic in the early Middle Ages, up to1100, and the Latin tradition from Cicero to Boethius, Cassiodorus and Isidore, onwhich, along with some translations of Aristotle and Porphyry, it drew. It had nogreat logicians, but only influential ones, like Boethius, and outstanding philoso-phers, like Eriugena and Anselm, who were interested in logic. Yet it is worthstudying, for at least two, very different reasons. First, twelfth-century logicianssuch as Abelard worked in a tradition that continued from the earlier medievalone: the text-books were the same and the methods and questions asked wererelated. Knowing about the Latin tradition and the early medieval backgroundhelps in understanding and assessing their ideas. Second, although the early me-dieval logicians may not have innovated in the contents of their teaching, theyachieved something importantly novel with regard to the position of logic in thecurriculum.1

In the ancient world, logic had never been a central, or even mainstream, subjectin ordinary education. Educated Romans would have studied, above all, rhetoricand the literary classics — Augustine gives a vivid account of such an education inhis Confessions. But in the Middle Ages logic became a fundamental discipline forevery student who went beyond the elementary level of studying Latin grammar.This central placing of logic had its origins in the revival of learning in the Carolin-gian period: logic was given a position within the standard scheme of education

1At the beginning of each section and subsection, I give references to the main secondary workson the area. Parts of the chapter are based on a series of studies I have published on Boethiusand on early medieval logic over the last 25 years. I mention these as and where relevant in theseinitial lists, but I do not then repeat my reference to them, except where I wish to indicate somespecial discussion. Readers will, therefore, be able to find a fuller exposition of the views hereby consulting these more detailed discussions. But in many areas (for example, Eriugena andAnselm), I have reached different conclusions from those I previously argued, and even wheremy views have remained more constant, I have taken the opportunity to correct errors, add newideas and take account of the most recent scholarship. There has not been any previous attempt(outside short sections in general histories) to give a complete account of this long period inLatin logic, but the medieval part of was to some extent treated in [Van de Vyver, 1929; 1942;Lewry, 1981].

Handbook of the History of Logic. Volume 2: Mediaeval and Renaissance LogicDov M. Gabbay and John Woods (Editors)c© 2007 Elsevier BV. All rights reserved.

2 John Marenbon

which was new; the position was consolidated in the three centuries followed, andlogic continued to hold it until the end of the Middle Ages. By studying logic inthe early Middle Ages, therefore, we can hope to gain some understanding of howand why the subject had its special role within medieval education and thought.This aim calls for an approach rather different from that of most chapters in thishandbook. Consideration of the uses of logic and its connections with other sub-jects are as important here as the technicalities of logical doctrine. Indeed, thereis a sense in which the treatment here, just because it must fit into a handbookof the history of logic, must still remain over-theoretical and insufficiently histor-ical. What is most needed to illuminate the broadly human importance of thesubject in this period (and in the twelfth to sixteenth centuries) is a social historyof medieval logic, a type of study that has never until now been envisaged, letalone attempted. The following pages could be seen as prolegomena to part ofthat enterprise.

2 THE ANCIENT LATIN TRADITION

When historians, using the medieval terminology, speak of the logica vetus — thecorpus of ancient logical works used by Latin scholars in the early Middle Ages —they sometimes take it in a narrow sense to mean just the three Greek logical texts,Porphyry’s Isagoge, and Aristotle’s Categories and On Interpretation, which wereavailable in translation. From this perspective, it seems that the ancient Greektradition of logic, though in a very curtailed form, is behind the work of theearly medieval logicians. But, by the eleventh century, the logical curriculum —the logica vetus in a wider and more useful sense — consisted of six works: thethree ancient Greek texts, and three textbooks written early in the sixth-centuryby the Latin thinker, Boethius: treatises on categorical syllogisms, hypotheticalsyllogisms and on topical argument. Also attached to the curriculum, thoughmore peripherally, was a work on definition attributed to Boethius but in factby a Latin predecessor of his, Marius Victorinus, and Cicero’s Topics, along withBoethius’s commentary on it. And Boethius’s logical commentaries — two on theIsagoge and On Interpretation, one on the Categories — were the tools with whichthese three texts were studied. Other Latin logical texts had been influential inthe eighth to tenth centuries, although they had mostly lost their importance bythe eleventh: the Ten Categories, a paraphrase of Aristotle’s Categories from thecircle of Themistius, thought at the time to be by Augustine; Apuleius’s PeriHermeneias; and the sections on logic in the encyclopaedias of Martianus Capella,Cassiodorus and Isidore of Seville. For all these reasons, though much in earlymedieval logic goes back ultimately to Aristotle or to the ancient Peripateticsand the Neoplatonists who cultivated Aristotelian logic, they drew more directlyon a distinctively Latin tradition. It is here that we must begin. Boethius isthe central figure but, as the list of names above suggests, his predecessors andsuccessors should not be neglected.

First, one preliminary, verbal note. Many of the chapters or treatises discussed

The Latin Tradition of Logic to 1100 3

here are titled, not ‘On Logic’ but ‘On Dialectic’, and the logicians treated hereoften referred to themselves as ‘dialecticians’ (dialectici) rather than ‘logicians’.There certainly was a distinction that could be made, and was in some contexts,between ‘logic’ and ‘dialectic’ in which ‘logic’ stands for the study of demonstrativereasoning (and so the Analytics), and ‘dialectic’ for persuasive reasoning (and sothe Topics). Usually, however, in the period until 1100, the words were usedinterchangeably, with ‘dialectic’ as the more common, to cover the whole of logic.In what follows, I shall speak simply of ‘logic’, although the word used in thesources will often be dialectica. (For a rather different view, see [D’Onofrio, 1986]).

2.1 Before Boethius

The Latin logical works from before Boethius’s time divide into two groups: thereare Cicero’s Topics, Apuleius’s Peri Hermeneias, Marius Victorinus’s On Def-inition and Book IV of Martianus Capella’s On the Marriage of Mercury andPhilology, all of which have various links with each other, as will become clear,although they also, except for Martianus, provide independent glimpses of Greeklogic. There is also the Ten Categories, which unrelated to these other Latin works.

Cicero ([Huby, 1989; Long, 1995])

The earliest Latin logical text is also treatise in legal rhetoric. Cicero wrote hisTopics (‘Topica’) [Cicero, 1924] in 44 BC, and professes that he will explain thereto his friend Trebatius the doctrine of Aristotle’s Topics. In fact, the work reflectsthe Rhetoric as much as the Topics, and probably handbooks of rhetorical andPeripatetic doctrine even more [Long, 1995, 54-7; Stump, 1989, 57-66]. The subjectof the Topics is said to be the finding of arguments; as his examples show, Cicerohas in mind particularly the needs of an orator in the courts. The aim of argumentis seen in terms of its persuasive effect: it convinces someone of something that wasin doubt (§ 8). The tools for finding arguments are, as in Aristotle, the topics orloci. But whereas Aristotle’s topics are a proliferation of argumentative strategies,linked to his doctrine of the Categories, Cicero’s topics are a short list of types ofrelationships, consideration of which can help the orator to discover an argument.They include, for instance, genus, species, likeness, cause, effect, comparison. Forinstance, if the orator needs to show that the heir to a dilapidated house is notbound to repair it, he can argue that the case is similar to that of an heir to aslave, who is not bound to replace him if he has died (§15). All these topics andarguments are intrinsic, but the orator can also argue extrinsically, says, Cicero, byappealing to authority. The importance for logic of this very practically-oriented,rhetorically directed treatise lies in the evidence it gives of how Aristotle’s theoryof topics had been changed in later centuries, and in the use that Boethius wouldmake of it.

For historians of logic, the most important passage in the book is where (§§53-7) Cicero sets out the modi dialecticorum — which consist of an extended andslightly mangled list of the Stoic indemonstrables, expressed, not as the Stoics did,

4 John Marenbon

using numbers as propositional variables (‘the first’, ‘the second’), but rather ‘this’and ‘that’. In Cicero’s list, where there is some confusion because the examplesentences do not always match the vaguely given definitions, the first five modescorrespond roughly to the five Stoic modes, and Mode 6 is a re-formulation of Mode3; whilst Mode 7 is (§57) ‘Not this and that; but not this; therefore that’ — that isto say: ∼ (p&q);∼ p; q, an obviously invalid inference. (For discussion, see [Knealeand Kneale, 1962, 179-81; Hadot, 1971, 144-56]). This mistake suggests that,already by Cicero’s time, Stoic propositional logic was not properly understood(see below, p. 17).

Apuleius ([Sullivan, 1967; Londey and Johanson, 1987])By contrast with Cicero’s Topics, Apuleius’s Peri Hermeneias (‘On Interpreta-tion’ — but the Greek title, echoing Aristotle was deliberate and will be retained)written roughly two centuries later, is very straightforwardly a logical treatise, anexposition of Aristotelian syllogistic. Apuleius (c. 125 — c. 171) was a writer inRoman North Africa, most famous for his comic novel, the Golden Ass, but respon-sible too for a number of philosophical works, including an exposition of Plato’sthought (De dogmate Platonis). Although his authorship of Peri hermeneias hasbeen questioned, recent specialists accept it [Sullivan, 1967, 9-14; Londey and Jo-hanson, 1987, 11-15]. The treatise covers much of the material in Chapters 1-8 ofAristotle’s On Interpretation and in the Prior Analytics, excluding modal syllo-gistics. After treating the nature of propositions and their terms, and the squareof opposition, it goes on to explain the principles of the syllogism, giving both thedifferent moods and how the validity of the second and third figure syllogisms canbe demonstrated by reducing them to first-figure ones. Apuleius’s main differencesfrom Aristotle are that he casts syllogisms as inferences, rather than conditionals;he gives third-figure syllogisms in a different order; and he does not use letters asvariables to stand for predicates. He also stands out in the Latin tradition by histerminology, which is sometimes a very literal Latin version of the Greek — forinstance, a syllogism is a collectio. Not surprisingly, given his period, Apuleiusknows something of Stoic logic, but he takes the line about it common among thePeripatetics, condemning it (Chapter 7) without understanding it. For instance,he rejects the inference ‘If it is day, it is light; but it is day, therefore it is light’, onthe grounds that in the conclusion ‘it is light’ means that it is light now, whereasin the premisses, ‘it is light’ has a different meaning: it is asserted merely that itfollows that if it is day, then it will be light. This criticism shows a clear failureto distinguish between the propositional operator ‘if . . . then . . . ’ and the propo-sitional contents it links together: a failure, that is, to grasp the propositionalitywhich is central to Stoic logic.

Marius Victorinus ([Hadot, 1971])Marius Victorinus (c. 280-365) was a philosophically-educated pagan rhetoricianwho was converted to Christianity about ten years before his death and proceededto write on the Trinity. He had been one of the rare writers since Cicero to write

The Latin Tradition of Logic to 1100 5

on logic in Latin. Two of his logical works survive: a translation of Porphyry’sIsagoge (used by Boethius for his first commentary) [Hadot, 1971, 371-80] and OnDefinition (De definitione/definitionibus [Hadot, 1971, 331-62] that was wronglyattributed to Boethius in the Middle Ages. Victorinus also wrote a now lostcommentary on Cicero’s Topics (Reconstruction in [Hadot, 1971, 118-41]), whichis mentioned critically by Boethius in his own commentary on the same work, andfrom Cassiodorus we know that he wrote, just as Boethius would do, a treatise onhypothetical syllogisms. (See [Hadot, 1971, 323-7] for an assemblage of possibletraces of the treatise.) According to Cassiodorus, Victorinus also translated theCategories and On Interpretation and wrote a long commentary on it. But thereis no trace of these works, and it has been argued that Cassiodorus (whose textpresents problems: see below, subsection 2.3, pages 21–22) is misleading here[Hadot, 1971, 105-8].

Victorinus placed logic within the framework of rhetoric. Study of the Isagoge,Categories and On Interpretation led, not as in the Aristotelian organon, primarilyto syllogistic (in the Prior Analytics) and its use in demonstration (in the PosteriorAnalytics), but to the topics, as expounded by Cicero. And, for Victorinus — tojudge from his words as probably reported by Cassiodorus [Cassiodorus, 1937, 127]— it is the very fact that the Ciceronian topics presents arguments that are suited,not just to philosophers, but to orators, lawyers and poets as well, which makesthem so precious. On Definition and the (lost) treatise on hypothetical syllogismscan be seen as continuations of the commentary on Cicero’s Topics, since eachcorresponds to a part of Cicero’s text (definition: §§26-37; hypothetical syllogisms53-7) not treated in the commentary itself, which covers only half the work. OnDefinition draws extensively on Cicero himself in categorizing and explaining thedifferent sorts of definition — rhetorical definition, philosophical definition (whichis based on the five predicables: genus, species, differentia, proprium — i.e. anaccident that distinguishes a species, such as ability to laugh in humans — andaccident) and other types of definition, such as that from a thing’s parts, whichdoes not explain what the things are, but gives some understanding of them. It hasbeen suggested that here a work by Porphyry may have been the source. [Hadot,1968, I, 482-8]

The ‘Ten Categories’ ([Kenny, 2005, 128-33])

The Categorial Decem(Ten Categories), as it came to be called, probably owedsome of its early medieval popularity to the fact that it came to be attributed toAugustine. But it also deserved to be used, because it is an excellent work forbeginners in logic trying to understand Aristotle. The real author is unknown,but in a couple of comments (Aristotle, 1961, 137:20-1; 175:18-9) he makes clearthat he belongs to the circle of Themistius, the fourth-century philosopher andstatesman who was perhaps the last member of the ancient Peripatetic school.(Anthony Kenny has suggested that the author of the paraphrase might in fact beMarius Victorinus: [Kenny, 2005, 130-3].)

The paraphraser reveals his approach when (Aristotle, 1961, 148:33 — 149:2),

6 John Marenbon

excusing himself for not going further into the distinguishing features of the firstCategory, substance, he comments that ‘since they are clear in Aristotle himself,it seems superfluous to explain them, especially since this discourse does not aimto put down everything that the Philosopher said, but to recount in a simpler waywhat seem obscure to the untrained.’ In practice, this means that the paraphraseromits some of the more complex ideas and concentrates on providing an elegant,lucid exposition of the Categories. On the question that had exercised readers ofthe text since interest in it revived in the first century BC, whether it is aboutwords or things, the paraphraser manages to maintain a neutral position. Aristotlebegins — he says, following Themistius (Aristotle, 1961, 137:20 -138:1) — fromthe things that are perceived, but in order to discuss them he has to talk aboutboth the things that exist, and the things that are said, because what we perceiveis produced by what exists and cannot be demonstrated except with the aid ofwhat is said. What will follow must therefore be a ‘mixed disputation’.

Martianus Capella (E.L. Burge in [Stahl, 1971, 104-21], very unsatisfactory)Martianus Capella was a pagan, living in Roman North Africa either near thebeginning of the fifth century or c. 470 [Shanzer, 1986]. His one work is anencyclopaedia, in prose interspersed with verse passages, called On the Marriageof Mercury and Philology (De nuptiis Mercurii et Philologiae), because Books Iand II tell the story of the marriage of Mercury (divine reason) and Philology (thehuman soul), an allegory of the ascent of the soul to wisdom; Books III — IX[Martianus Capella, 1983] each treat one of the Liberal Arts. Book IV is devotedto logic, and Book V to rhetoric. Both books need mentioning, because in Book IVMartianus treats the material of the Isagoge, the Categories and On Interpretation,followed by a presentation of syllogistic based on Apuleius (cf. [Sullivan, 1967, 170-3]) and, near the end of the book, an account of what he calls the ‘conditionalsyllogism’, in which he presents a list of seven modes that are the same as Cicero’s,but he is unusual in, at one point, giving these seven modes in the traditional Stoicform, using numbers to stand for propositions (‘If the first, the second; the first;so the second’) [Martianus, 1983, 144]. Then, in Book V, Martianus goes into apresentation of the Topics, based on Marius Victorinus. It has been argued thatVictorinus originally incorporated Apuleius’s Peri hermeneias into his own work,and so Martianus is putting forward a thoroughly Victorine scheme of logic [Hadot,1971, 196].

2.2 Boethius

([Chadwick, 1981, 108-73; Marenbon, 2003, 17-65; Cameron, Forthcoming; Ebbe-sen, Forthcoming; Martin, Forthcoming])Boethius is the central figure in the ancient Latin tradition of logic. A smallpart of his importance is due to his continuing the tradition of Cicero and MariusVictorinus; the far larger part to his making — as a translator, a commentatorand a writer of textbooks — Greek Aristotelian logic available to the Latin world

The Latin Tradition of Logic to 1100 7

in far more breadth and depth than the glimpses which previous Latin texts hadallowed. Yet Boethius, though not himself outstanding, or even particularly good,at logic, was not a mere passive transmitter of other, more inventive logicians’ideas: he made what seems to have been a very deliberate choice among thecompeting theories, approaches and interpretations available to him, and in doingso profoundly influenced the style and contents of medieval logic.

Anicius Severinus Manlius Boethius was born c. 475-7 AD. Although he livedat a time when Italy was ruled by the Ostrogoths, Roman aristocrats like himwere free to enjoy their wealth, leisure and a limited local power. Fluent in Greekand in contact with the Greek intellectual world, Boethius chose to devote mostof his life to writing or translating works on arithmetic, music and, most of all,logic. His earliest work on logic, his first commentary on Porphyry’s Isagoge, datesfrom c. 500 and he continued to write mainly in this area until up to about 523,when he became closely and disastrously involved in the politics of the Gothicruler’s court. At one stage [Boethius, 1880, 79:9-80:9], Boethius announced hisintention to translate and comment on all of the works of Aristotle he could find,and Plato’s dialogues, as well as writing a book to show how the two philosophersare in fundamental agreement with each other. But, in fact, he devoted himselfto the logical part of this task and, in the last fifteen years of his life, he wasespecially occupied in composing text-books as well as commentaries. Althoughnot a priest, Boethius also became involved in the religious controversies of thetime, which divided the Catholics of Italy from those of the Eastern Empire. Hisfive short Theological Treatises (opuscula sacra) [Boethius, 1999] have a place inthe history of logic, because his use there of logical techniques would encouragemedieval readers similarly to see in logic a tool for theological speculation anddebate.

Not long after Boethius’s move to Theoderic’s court at Ravenna, he was accusedof treason and found himself imprisoned, awaiting execution. It was during thistime that he wrote The Consolation of Philosophy, the work by which he wouldbecome best known. Although the Consolation is not directly concerned withlogical questions, it ends with a discussion of God’s foreknowledge and futurecontingents that returns to some of the issues Boethius had raised in his logicalwritings.

We shall look at each area of Boethius’s contribution to logic in turn: as trans-lator, as commentator and as a writer of text-books.

Boethius the Translator

Boethius put the whole of Aristotle’s logical Organon (along with Porphyry’s Isa-goge: see below) into Latin, except for the Posterior Analytics. (Ed. in AristotelesLatinus [Aristotle, 1961; 1962; 1965; 1966; 1969; 1975].) He seems to have beenled into this task of translation by his work as a commentator. For the firstcommentary he wrote, on the Isagoge, he relied on an existing version by MariusVictorinus. But for his next commentary, on the Categories, he made his own

8 John Marenbon

translation, and he made a fresh translation of the Isagoge for his second com-mentary on it. Since Boethius’s commentaries, although rarely a word by wordexegesis, would often focus on a particular phrase, it was important to have a lit-eral translation, which to a considerable extent preserved rather than ironed outthe interpretative difficulties commentators puzzled over. Though elsewhere an el-egant stylist, Boethius translates very closely, often following the Greek syntax asfar, or further, than Latin idiom permits; and he translated with great care, usu-ally revising his versions at least once [See the prefaces in Aristoteles Latinus]. Inthe case of the Categories, the textual history as reconstructed by Minio-Paluello[1962; Aristotle, 1961, ix-lxiii] is very complicated and perhaps open to query:Boethius’s final version was combined at some time with another version, alsoprobably by Boethius, to form a composite version; the composite version, itselfvariously corrupted, was the one most usually used, but the original version ispreserved, with corruptions, in some manuscripts and can be reconstructed.

Boethius’s translation of the Organon remained the standard version, through-out the Middle Ages. Its accuracy and literalness made it possible for some me-dieval logicians to step out of the commentary tradition, transmitted by Boethiushimself, within which they studied Aristotle’s texts, and reach back to grasp Aris-totle’s own thought. But this return to origins was more a phenomenon of thetwelfth century than the early Middle Ages, a period in which the three Boethiantranslations then available (the Isagoge, the Categories, On Interpretation) had toshare their place, as will become clear, with a variety of other material.

The Neoplatonic Aristotelian Tradition ([Ebbesen, 1990; Sorabji, 2004])

As a commentator, Boethius was certainly dependent on the study of Aristotelianlogic that had been going on in the Neoplatonic schools of Athens and Alexandriafor two centuries. I shall sketch some of the main features of these philosophers’approach to logic, since this important area of logical history is treated no whereelse in the present Handbook (a mark of how little the ‘History of Logic’ servedup by and for logicians has to do with history?).

Although Plotinus, the founder of Neoplatonism, was hostile to many aspectsof Aristotelian logic, this attitude was not shared by Porphyry (c. 232-305), hiseditor and leading follower. Porphyry believed that the ostensible differences be-tween Plato and Aristotle could be explained by what we can label the ‘DifferentObjects Theory’: Plato was discussing the intelligible world, whereas Aristotlefocussed his attention on the world as it appears to the senses. He therefore in-corporated Aristotelian texts within the Neoplatonic curriculum, and he gave aparticular emphasis to Aristotelian logic, a field that seemed especially to interesthim. (See [Karamanolis, 2006]; but [De Haas, 2001], suggests by contrast thatPlotinus’s and Porphyry’s views were not very different.) From then on, logicwas studied enthusiastically in the Neoplatonic schools. Porphyry himself wrotean introduction (Eisagoge; latinized as Isagoge) to the Categories, which becameincorporated into the Aristotelian Organon as the first work to be studied in lateantiquity and the Middle Ages, as well as a short commentary on the Categories,

The Latin Tradition of Logic to 1100 9

and long commentaries, both lost, on this text and on On Interpretation. His im-portant follower, Iamblichus, produced a commentary on the Categories (also lost)and Boethius’s contemporary at the School of Alexandria, Ammonius (435/45 —517/26) seems to have concentrated on Aristotelian commentary. (See [Sorabji,1990; 2004], for an introduction to these commentators.)

Porphyry’s Different Objects Theory gave Neoplatonists a way to be thoroughlyAristotelian in logic (which was concerned with language, and language with theworld as sensibly perceived [Ebbesen, 1981, 133-70]), and he was certainly a keenreader of the greatest of the later ancient Peripatetic, Alexander of Aphrodisias.His Isagoge can be seen as fitting neatly into the Aristotelian Organon as an In-troduction, although modern assessments of its metaphysical commitments vary(compare [Porphyry, 1998] and [Porphyry, 2003]). Some later Neoplatonists, how-ever, did not follow the Different Objects theory so consistently. Although theAristotelian texts remained for them the basis of the logical curriculum and muchof their discussion concerned the type of issues Porphyry had raised, views of aPlatonic kind influenced their exegesis. For example, in his Categories commen-tary, now lost but witnessed through the commentary by Simplicius (early 6thcentury), Iamblichus seems to have taken advantage of the idea that the origi-nator of the Categories was Archytas, a Pythagorean whom he claimed Aristotlecopied, and he attempted to apply the Categories to the supra-sensible realitiesof Platonic metaphysics; and Ammonius, commenting on On Interpretation, triesto insert the teaching of Plato’s Cratylus that words are not merely conventionalsigns [Ammonius, 1897, 34:10–41:9].

Boethius and the Commentary Tradition

What was the nature of Boethius’s dependence on the Greek Neoplatonic com-mentators? According to James Shiel, it was total. Boethius simply found aGreek manuscript crammed with marginalia, themselves drawn from the writingsof several commentators. ‘The translation of these various marginalia and thearrangement of them into a continuous commentary according to the order ofAristotle’s words would seem to be Boethius’ only title to originality’, remarksShiel [1990, 361], even though he concedes [1990, 370, n. 83] that Boethius himselfcontributed expansions and references to Latin authors. Shiel founds his positionon the fact that Boethius’s commentaries are not based on any one known, Greeksource. Most specialists now reject his view [Chadwick, 1981, 129-31; Ebbesen,1990, 375-7], because it assumes the very point it claims to demonstrate, thatBoethius was incapable of making his own choice and arrangement of material.Even if his sources included manuscripts with marginal scholia — and it is a mootpoint whether any such codices existed at that time — there is no reason to thinkthat Boethius did not use them selectively, along with the complete texts of com-mentaries [De Libera, 1999, 164-8; Magee, 2003, 217].

Boethius, then, was not a mere translating machine. But nor was he an originalthinker in his logical commentaries. He was happy in general, just like his Greek

10 John Marenbon

contemporaries, to put down his own version of the views of his chosen authorities.It was mainly in making this choice that he could exercise his independence, and hedid so by selecting Porphyry above all as the interpreter to follow. The Categoriescommentary is close to the surviving shorter, question-and-answer commentary byPorphyry [Asztalos, 1993], and from Boethius’s own comments about his sourcesit is clear that his longer commentary on On Interpretation is by far the bestguide we have now to the contents of Porphyry’s lost commentary on this text.By choosing Porphyry, rather than any more recent Greek commentator, as hismain guide, Boethius ensured that his presentation of logic would be, by and large,faithfully Aristotelian, in line with the Different Objects Theory.

Boethius on the ‘Categories’ ([Asztalos, 1993])

Porphyry bore out his general approach to Aristotle with a particular theory aboutthe subject-matter of the Categories. Interpreters differed as to whether it is aboutwords or things. Plotinus had taken it to be about things and had been critical ofAristotle’s discussion, since it said nothing about the Platonic Ideas. Porphyry’sview, as expressed in his question-and-answer commentary on the work [1887, 90-1], was that the Categories is about language: it is about words of first imposition,which signify things, as opposed to words of second imposition (such as ‘noun’ and‘verb’) that signify other words and are treated in On Interpretation. The thingssignified are sensible particulars, since it is to these that people first of all attachnames; and the secondary substances, on Porphyry’s view, are concepts, universalsthat are abstracted from the particulars, not the Platonic Ideas. The Categories,then, and even the assertion in it that (2b5-6) ‘if the primary substances’ (that is,the sensible particulars) ‘did not exist it would be impossible for any of the otherthings to exist’ can be accepted since, in this extension of the Different ObjectsTheory, Aristotle is not concerned here with Platonic Ideas, but with universalsthat are mental concepts, gained by abstraction, and dependent for their existenceon the primary substances.

Boethius follows Porphyry’s question-and-answer commentary closely and re-produces his approach to the subject-matter of the Categories. He dramatizes thetheory by attaching it to a story about the origins of human language placed atthe very beginning of his commentary [Boethius, 1891, 159A-C], in which he tellshow, first, names of first imposition, such as ‘horse’, ‘branch’ and ‘two-foot long’were given their meaning, and then names of second imposition such as ‘verb’ and‘noun’. Boethius is fairly brief in his comments, because he says that he is writingfor beginners. Whether he ever wrote the second, more advanced commentarythat he promises [Boethius, 1891, 160A-B] is very uncertain: he may well havebeen reluctant to produce the type of non-Aristotelian, Iamblichan discussion hisdescription of it suggests [Marenbon, 2003, 23].

Boethius on ‘On Interpretation’ ([Magee, 1989; Lloyd, 1990, 36-75] a complex dis-cussion of Porphyrian semantics, which may underlie Boethius’s theories, [Cameron,Forthcoming; Sharples, Forthcoming])

The Latin Tradition of Logic to 1100 11

In commenting On Interpretation, Boethius again turned to Porphyry, especiallyin the second, more advanced commentary [Boethius, 1880] (the first commentary[Boethius, 1877] was designed just as an aid for beginners to a literal understandingof the text). He says so himself [Boethius, 1877, 7:5-9], and it seems very likelythat the very influential ideas on semantics and modality he puts forward weredeveloped by Porphyry in his detailed commentary, now lost.

At the beginning of On Interpretation, Aristotle says (to translate Boethius’sLatin version literally):

The things therefore which are in the utterance (in voce) are the marks(notae) of the passions that are in the mind, and the things that arewritten of those that are in the utterance. And just as the letters arenot the same for all, so the utterances are not the same; but what theyare primarily signs of, the passions of the mind, are the same for all,and the things too, of which these are likenesses, are the same. [16a1-8;Aristotle, 1965, 5:3-9; cf. Magee, 1989, 21-34]

As the commentary as well as the translation shows, Boethius takes Aristotle tobe presenting a semantics which is in many ways a mental language theory. The‘passions of the mind’ are the words of this language which, unlike written andspoken languages, is common to all humans, and these passions are in some waylikenesses of objects in the world.

To an extent, this is indeed Boethius’s approach. He speaks explicitly of mentaldiscourse (oratio) [Boethius, 1880, 30], and he believes that the thoughts thatare its simple terms are combined into complex thoughts that are true or false.There is, however, an important difference between Boethius’s thinking and astraightforward theory of this sort. When I utter ‘dog’ and you utter ‘dog’, weare speaking the same word in the sense that utterances are tokens of the sametype, in virtue of a physical resemblance between the sounds we produce, whicha native speaker would judge to be close enough to take us as uttering the sameword. What about my mental concept of dog and your one? For Boethius, theycan be called the same just because they both [Boethius, 1880, 21:18-22] originatefrom the same type of animal. We begin from sensory contact with some objectin the world, form a pre-conceptual image in our mind, on which the intellectworks in order to have a thought of it. It seems, therefore, that in Boethianmental language, in so far as it is a language, the individual words (‘dog’, ‘cat’,‘human’) are not imposed on objects, as in a natural language, but derive fromthem causally.

When he comes to Chapter 9 of On Interpretation, Boethius has to give hisreading of the much debated passage on future contingents. Earlier (17a1-4) Aris-totle had asserted the principal of bivalence: every proposition is either true orfalse. But it seems that, if propositions about future events are true, or are false,then no future events will be contingent. Suppose p states that a certain event Ewill happen tomorrow. If p is true, it seems that E must happen, and if p is false, itseems that E cannot happen, and so, whether p is true or false, E will not be con-

12 John Marenbon

tingent. One way out of the problem is to abandon bivalence for future contingentpropositions. Arguably, this was Aristotle’s strategy: so the Stoics thought, andsome modern scholars agree. Boethius, however, believes that Aristotle retainsbivalence, but avoids determinism by holding that future contingent propositionsare indefinitely, and not definitely, true or false.

What does Boethius understand by this position? (See [Kretzmann, 1998] fora different view.) He thinks that, when we assert or deny a proposition about afuture event without qualification, we are saying that it is definitely true or false,and we are thereby implying that the event will or will not happen necessarily. Inconsequence, any proposition of the type ‘CE will happen’, where CE is a con-tingent event, is false, because it asserts that a contingent event is not contingent.What the speaker should do is to say ‘CE will happen contingently’, in whichcase — so it seems, tying together the different elements of the theory — he isasserting the indefinite truth of ‘CE will happen’ [Boethius, 1880, 212-3]. In linewith this theory, when he discusses in this commentary the question of God’s fore-knowledge (not raised by Aristotle, but debated in the commentary tradition, aswitnessed by Ammonius), Boethius says that God knows that future contingentswill take place, but he knows that they will take place contingently, not neces-sarily [Boethius, 1880, 225:9-226:25]. It may be because even Boethius himselfrealized that his theory is inadequate as an explanation that, when he returned tothe problem of divine prescience at the end of his final work, the Consolation ofPhilosophy, he produced a different and far more ambitious solution (cf. [Huber,1976; Marenbon, 2003, 125-45; Evans, 2004; Sharples, Forthcoming]).

Boethius on the ‘Isagoge’: Porphyry’s Questions ([De Libera, 1999, 159-280; Maren-bon, Forthcoming-B])

Boethius could not, as he usually did, turn to a commentary by Porphyry whenhe wrote his two commentaries on Porphyry’s own Isagoge [Boethius, 1906]. Theearlier, in dialogue-form, was his first piece of writing on logic, dating from c.500; the later one (c. 510-5) was by far the most commonly studied of the twoat all stages of the medieval tradition. In fact, Boethius continued to show hisadherence to Porphyry’s approach, since in both commentaries he concentrateslargely on straightforward explanation of the ideas in the text, using materialsome of which is reflected in Ammonius’s commentary, the earliest surviving inGreek, written at much the same time as his own. One passage, however, ledBoethius and almost every commentator into a long discussion of a subject thatPorphyry explicitly refuses to treat here. Close to the beginning of the Isagoge[Porphyry, 1887, 1:10-13; Porphyry, 1966, 5:10-14 — Boethius’s Latin translation],Porphyry puts a set of questions about universals and how they exist (he uses theword hufistasthai, translated by Boethius as subsistere, but here it probably meansthe same as ‘exist’ [Porphyry, 2003, 40]) or do they consist only in pure thoughts?If they exist, are they bodies or incorporeals, and if they are incorporeals, are theyseparable or in perceptible things, existing about them? Porphyry himself says hewill not try to gives answers, because the subject is too deep for an introductory

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work.Boethius puts forward his fullest and most influential answer in his second

commentary. Even here, he is one sense loyal to the Porphyrian project, sincehe turns to one of Porphyry’s preferred sources, the great Peripatetic philosopherAlexander of Aphrodisias, from whom he says he has taken his position (cf. [DeLibera, 1999]). He begins with a powerful argument [Boethius, 1906, 161:14–164:2]which claims to show that universals do not exist, and any enquiry into them ispointless. The first premiss resumes Porphyry’s first question:

1. Either genera and species exist (sunt atque subsistunt) or they are formedby the intellect, in thought alone.

He then argues against the truth of the first disjunct of (1): -

2. Everything that exists is one in number.

3. Nothing that is common to many at the same time can be one in number.

4. Genera and species are common to many at the same time.

5. Genera and species do not exist. (2,3,4)

It follows, therefore, that

6. Genera and species are formed in the intellect, in thought alone. (1,5; dis-junctive syllogism)

But to hold (6), Boethius goes on to show, apparently entails a drastic conclu-sion for the enquirer. Some thoughts — call them ‘corresponding thoughts’ —correspond to how their object is in reality, some do not.

7. If the thoughts that, by (6), are genera and species are corresponding thoughts,then genera and species exist in reality in the way they are thought.

8. Genera and species do not exist in reality in the way they are thought. (5)

9. Genera and species are not corresponding thoughts. (7, 8; modus tollens)

10. Thoughts that are not corresponding are empty and false.

11. All enquiry into universals should cease.

Boethius does not, of course, agree with this argument, but one of the remark-able feature of his answer is that he accepts every stage of this argument up to(9). He simply denies (10), and therefore (11); the opponent’s argument, in themain, goes through, but without its sting. Boethius denies (10) by appealing tothe idea of (mathematical) abstraction. He explains [Boethius, 1966, 164:12–14]that when one thing is abstracted from another ‘the thing is indeed not as thethought is, but the thought is not however at all false.’ For example, a line cannot

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in fact exist apart from a body, but it is thought of in abstraction from any body,and this thought is not false.

Not only does the appeal to abstraction defeat the argument (1)–(11): it alsosuggests a way of explaining what universals are, which we could label ‘Neutral Ab-stractionism’. According to Neutral Abstractionism, particulars of a given specieseach have a nature or, as Boethius calls it here, a ‘likeness’ (similitudo), whichexactly resembles the likeness of any other member of the species. The species isconstituted by the thought which brings together these likenesses, and the genusby the thought that brings together the likenesses of the species. This solution isone of those Boethius puts forward.

At the same time, and without marking the difference, Boethius proposes arather different solution. He starts by explaining that the likeness ‘is sensibleto the senses when it is in the singular things, but it is intelligible in universalthings, and in the same way when it is sensible it remains in singular things; whenit is thought in the intellect (intelligitur) it becomes universal’ [Boethius, 1906,166:18-21]. Then he goes on to say — expanding this idea — that singulars anduniversals are two things in the same subject. Just as the same line is convex orconcave depending on how it is regarded, and so it can be considered two thingsin one subject, so there is the same subject (for instance, this human, John) forsingularity and universality. When John is perceived through the senses, amongthe things in which he has his existence (esse suum habet), he is a singular; butwhen he is grasped in thought (as a human), he is a universal [Boethius, 1966:23-167:7]. This solution differs from Neutral Abstractionism and might be called‘Realist Abstractionism’ since it suggests that the process of abstracting does notmerely provide a way of regarding a world that is made up only of singular things,some similar, some diverse, but that it allows people to grasp real universals,accessible only to thought. [Marenbon, Forthcoming-B].

Boethius’s Logical Treatises([Martin, 1991])

The short On Division (De divisione; probably 515-20) [Boethius, 1998 — withtranslation and commentary] stands somewhat apart from Boethius’s other logicaltreatises. Like much else in his logic, it is probably based on a work by Porphyry,prolegomena to a now lost commentary by him on Plato’s Sophist. Despite thePlatonic text, the approach is Aristotelian. Using the language and concepts ofthe Isagoge and Categories, Boethius explains the difference between accidentaldivision (dividing, for instance, humans in virtue of accidents of colour into black,white and medium) and intrinsic division. Intrinsic division is of a whole into parts,a genus into species and a word into its different meanings. In the twelfth century,when this treatise was studied most carefully, the section on whole-part divisionwas especially important. Questions about genera and species were treated morefully in the Isagoge, and on semantics in On Interpretation, but On Division wasalone in providing a brief introduction to mereology.

All of Boethius’s other logical treatises concern types of argument. Two ofthem, On the Categorical Syllogism (SC ) [Boethius, 2001] and Introduction to

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Categorical Syllogisms (ISC ) [Boethius, 1891, 761-94], present Aristotle’s doctrineof (non-modal) syllogisms. The relations between the two treatises are complex.SC has a first book devoted to preliminaries to syllogistic (as discussed in OnInterpretation), and a second book which contains a straightforward account ofsyllogistic itself. ISC has one book only, which covers in greater detail the groundtreated in SC, Book I. It seems to be Boethius’s attempt — left unfinished or mu-tilated in transmission — to rewrite and expand SC. Boethius has been accused[Patzig, 1968, 75-6] of making an innovation in presenting Aristotle’s theory of syl-logisms that made it less clear. According to Aristotle, the validity of first figuresyllogisms is evident. In his way of stating them, they read like, for example: ‘Abelongs to every B, B belongs to every C, therefore A belongs to every C’ — aformulation in which, just by looking at the first two premisses, the conclusion isobvious. When, as became usual, the syllogism is constructed using ‘is’ instead of‘belongs to’, the Greek commentators ensured that this transparency was main-tained by reversing the order of the premisses: for instance, ‘Every C is B, everyB is A, therefore every C is A.’ But Boethius loses the transparency by using aformulation with ‘is’ along with the Aristotelian order. In fact, this accusation isnot completely fair. It applies only to the way in which Boethius formulated hisexample syllogisms. When he uses letters for terms, he follows a Latin version ofAristotle’s Greek phrasing, such as ‘A is predicated of every B.’

Boethius is particularly fascinated by the theory of conversion, and he intro-duces an explicit discussion of how propositions with infinite names (that is, onesinvolving negations, like ‘not-man’ and ‘not-animal’) convert (ISC : [Boethius,1891, 780-5; Prior, 1953]). Moreover, he extends the theory of conversion tocases where truth is preserved only so long as the terms in the proposition beara certain relation to each other. For instance, ‘Every A is B’ does not convert to‘Every B is A’, but it does if B is a proprium, as defined in Porphyry’s Isagoge, ofA: ‘Every human is capable of laughing’ — ‘Every thing capable of laughing is ahuman being’ (ISC : [Boethius, 1891, 786B]).

On Hypothetical Syllogisms (De hypotheticis syllogismis) [Boethius, 1969] is afar more interesting work than SC or ISC. It represents a tradition of writing onhypothetical syllogisms that is found, otherwise, only in a brief scholium preservedin a tenth-century Byzantine manuscript [Bobzien, 2002]. Presumably there weresome other, now lost accounts of the area (we know that Marius Victorinus gaveone), but Boethius says himself [references are to the section divisions in Boethius,1969: I.1.3-4] that he is giving a fuller and more systematic treatment than any-thing he can find in the Greek, and there is every reason to accept this claim,certainly about the detailed working out of the theory in Books II and III (cf.[Striker, 1973]), but possibly even about Book I. Moreover, the treatise providesimportant, though negative, information on Boethius’s grasp of Stoic propositionallogic.

Hypothetical syllogisms are those in which one or both premisses are compound,rather than simple propositions. Boethius considers two types of compound propo-sition, those using the connective ‘or’ (aut, understood as exclusive disjunction)

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and those using ‘if’ (si/ cum). In practice, he concerns himself almost entirelywith ‘if’. Early in the work [I.3.6-7], he makes a distinction to which he does notreturn. There are two sorts of conditionals (hypothetical propositions using si orcum): accidental (secundum accidens) and those which have a consequence of na-ture (ut habeant aliquam naturae consequentiam). An accidental conditional is, forinstance, ‘If (cum) fire is hot, the sky is round’. Those which have a consequenceof nature are of two types. In one type the consequence is necessary, but does notrest on the positing of the terms (positio terminorum), as for example: ‘If (cum)it’s a human, it’s an animal’. The other type has a necessary consequence thatdoes rest on the positing of the terms, as for example, ‘If (si) there is an interpo-sition of the earth, an eclipse of the moon follows’. From the example he gives,the distinction that Boethius seems to have in mind is that, in a true accidentalconditional, the antecedent are both necessarily true, but the truth of the one isentirely unrelated to the truth of the other. In a natural conditional, the truth ofthe consequent is related to that of the antecedent, either by dependency wherethe conditional rests on the positing of terms — it is because there is an interpo-sition of the earth that the moon is eclipsed — or by relevance that is not causaldependency — something’s being a human gives us reason to say it is an animal,but Boethius would want to say that it is not because it’s a human that it’s ananimal, but rather, because it’s a mortal, rational animal that it’s a human. Thedistinction between accidental and natural conditional was one which would be-come enormously important in the history of Latin logic from the twelfth centuryonwards [Martin, 2005]. But Boethius does not dwell on it; his standard exampleconditional, ‘If it is day it is light’, seems to be a natural conditional resting onthe positing of terms,

Rather, Boethius wants to set out which hypothetical syllogisms are valid. Justas the theory of categorical syllogistic lists the different combinations that arevalid, so too hypothetical syllogistic offers a tabulation of valid inference forms.But the table is vastly more complicated. The simplest form of a hypotheticalsyllogism, where the major premiss involves just two terms, is exemplified by ‘Ifit is day, it is light. It is day. So it is light.’ Varying the quality of each ofthe two propositions making up the major premiss yields four types of syllogism.But the major premiss can involve three terms (for instance, ‘If, if it is A, thenit is B, it is C) or four terms (for instance, ‘If, if it is A, it is B, then if it isC, it is D’). Taking into account all the combinations of quality, and then thedifferent ways of qualifying them modally, the number of combinations reachesthe ten thousands (I.8.7), and far more if the propositions are quantified (I.9.2).But Boethius confines himself, wisely, to charting the non-modal, non-quantifiedcombinations — still a long and tedious task, that occupies Books II and III ofthe treatise.

It is tempting to see Boethius as setting out some variety of propositional logic.‘If it is day, it is light. It is day. So it is light’ looks very like an inference of theform ‘p → q, p; so q’. Yet it is clear that Boethius conceives himself as doing asort of term logic (and the same is true for the Byzantine scholium). Each of the

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propositions is of the form ‘It is (an) A/B/C. . .’, where ‘A’, ‘B’, ‘C’ stand forpredicates, and the conclusion follows — as in a categorical syllogism — becauseof the relation between these terms. One moment in the treatise brings out thispoint especially clearly. Boethius (II.2.3–4.6) has established that, if the majorpremiss is ‘If it is not A, it is B’, then, whilst ‘It is B’ follows when the minorpremiss is ‘If it is not A’, and ‘It is A’ follows if the minor premiss is ‘It is not B’,from the minor premisses ‘It is A’ and ‘It is B’, no conclusion follows. And yet,Boethius points out, in the nature of things from ‘If it is not A, it is B’ and ‘It isB’, it does follow that it is not A, and from ‘If it is not A, it is B’ and ‘It is A’, itdoes follow that it is not B. The reason (III.10.4) is that the major premiss will betrue only if ‘A’ and ‘B’ are immediate contraries — they are such that everythingis either A or B. If A and B are immediate contraries, then indeed if somethingis not A it is B, and if it is not B it is A. This line of thought makes sense only ifBoethius has the connections between terms, not propositions, in mind. As ChrisMartin has shown in his important study [Martin, 1991], whereas Stoic logic ispropositional, Boethius had no grasp of the very notion of propositionality; that isto say, he was unable to see negation or consequence as propositional operations.

Boethius is not, though, entirely removed from propositional logic. There aremoments, indeed, when he seems to come close to propositional logic, as when hegives two of the Stoic indemonstrables using, in Stoic fashion numbers to stand forpropositions: ‘if the first, then it follows that there is the second’, ‘if the secondis not, it follows necessarily that the first is not’ (I.4.6). In his commentary onCicero’s Topics, Boethius includes a long passage [Bk. V; Boethius, 1833, 355-9]discussing Cicero’s seven modes of inference. This passage may be linked, notjust to Cicero’s own text, but to the presentation found in Martianus Capellaand Cassiodorus, which seems to go back to Marius Victorinus. There is, nodoubt through Cicero, genuine Stoic influence at the basis of this list. But, well byBoethius’s time, as Anthony Speca has shown [Speca, 2001], the Peripatetic theoryof the hypothetical syllogism and Stoic propositional logic had become conflated,to the extent that Boethius (and possibly Marius Victorinus before him), readingCicero’s Stoic-based list of modes of inference, took them for modes of hypotheticalsyllogisms.

Indeed, there is one point here where Boethius makes clear just how far hewas from understanding Stoic logic (pace [Stump, 1989, esp. 19-22]). He knowswhat Cicero’s form of the third mode is, but he deliberately changes it [Boethius,1833, 362]. Instead of ‘Not: A and not B; A; therefore B’, Boethius puts: ‘Not:if A then not B; A; therefore B’ [Boethius, 1833, 356-7]. If this is translatedinto propositional calculus, it gives ∼ (p →∼ q); p; q, which is clearly invalid.Boethius explains, however, that in this mode it is assumed that A and not-B are incompatible. He understands ‘Not if A then not B’ as expressing thisincompatibility: to negate ‘If it is day, is not light’ is, for Boethius, to say that itcannot be the case that it is day without its being light. And so it follows that,if it is day, as the minor premiss states, it is light (cf. [Martin, 1991, 293-4]).Boethius is therefore, as shown by his very willingness to change the formula he

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inherited, trying to think about the meaning of these Stoic-derived formulas, butwithin the context of his own term-logic.

The strange character of Boethius’s hypothetical syllogistic comes out even moreclearly when he treats the negation of a conditional in On Hypothetical Syllogisms.Not realizing that his discussions should be construed as term logic, earlier com-mentators [Dürr, 1951; Kneale and Kneale, 1975, 191; Barnes, 1981, 83; cf. Martin,1991, 295-6] argued that Boethius thought the contradictory negation of ‘If p, thenq’ is ‘If p, then not-q’, rather than ‘Not (If p, then q)’ as in classical propositionalcalculus. Therefore, they concluded, he had a strange propositional system. But,as Martin puts it [1991, 279]: ‘The problem is not . . . that Boethius’ logic is notclassical propositional calculus but rather it is not propositional at all.’ Boethiusis in fact both much less strange in his underlying conception than he has been seento be, and yet at the same time more distant from contemporary logical models.Boethius’s account of the state of affairs that must be the case for a conditional tobe ‘negated’ or ‘destroyed’ is exactly the same as the contemporary logician’s ac-count of what obtains when a whole conditional is negated, but Boethius can onlyoffer his explanation, however tortuously, using term logic. For the conditional ‘IfA is, B is’ to be destroyed, we must show ‘not that A is not or B is not, but that,when A is posited, it does not immediately follow that B is, but that A can beeven if the term B is not’ (I.9.7). And even in his extended discussion of the validforms of hypothetical syllogisms, Boethius seems, whilst always working in termlogic, to be mimicking the results which would obtain in a propositional calculus,often employing various extra premisses that allow him to reach the results which,by means of examples, he has identified as the correct ones (cf. [Marenbon, 2003,53-55, 191]).

Boethius and Topical Argument ([Green-Pedersen, 1984, 37-81])

The remaining logical monograph by Boethius, On Topical differentiae (De topicisdifferentiis) (TD) [Boethius, 1990, 1-92; trsl. Boethius, 1978; Boethius, 1891,1173-1216] was written near the end of his life (c. 522-3), at a time when topicalargument became a central concern for him. Shortly before, he had written acommentary on Cicero’s Topics (TC) [Boethius, 1833; transl. Boethius, 1988]that is closely related to it, translated Aristotle’s Topics into Latin, and probablywritten a commentary on it, now lost.

Much as in the case of hypothetical syllogistic, Boethius’ work is the only sub-stantial survival from the late ancient tradition of topical argument as it haddeveloped after the time of Cicero. One of its principle exponents had been thefourth-century Peripatetic philosopher, Themistius. He and Cicero are Boethius’sspecial authorities, and one of the main aims of TD is to compare the apparentlydifferent lists of topical differentiae given by these two philosophers, showing thatthey really coincide.

In the way it is structured around a list of topical differentiae, the topical theoryBoethius presents clearly descends from Cicero, though Cicero had just called them‘topics’. Discussion of the topics is no longer, however, the mixture of law and

The Latin Tradition of Logic to 1100 19

rhetoric with logic that it had been five centuries before; the proof of this is whatmight seem to be the exception, the fact that in Book IV of TD, after devotingthe rest of the work to the logical topics, Boethius gives a separate treatment ofwhat are identified explicitly as the rhetorical topics. Topical argument has itsplace within logic as the discipline for finding arguments, whereas the PosteriorAnalytics teaches us how to judge them. Boethius thinks of an argument as aimingto decide to between the disjuncts of what he calls a question: ‘Either A is B orA is not B’. The argument will be a syllogism with one or other disjunct as itsconclusion. Finding the argument is therefore a matter of finding an appropriatemiddle term, from which a premiss can be formed with A, and a premiss withB, which yield syllogistically the desired conclusion. Topical theory does not,of course, provide a machine, into which the conclusion only need be fed for anargument to emerge. There could be no such machine. Rather, it provides amethod for arguers to search their stock of knowledge in the right way to come upwith an argument. Since the middle term is predicated of, or has as a predicate,the other two terms, what it designates must be related, even if negatively, towhat they designate. The scheme of differentiae systematizes the main categoriesof such relationships — categories such as, for example, part and whole, genusand species, more and less, signified and sign. Suppose [TD II; Boethius, 1847,1188C — the new edition and translation reproduce the column divisions of the1891 ed.] I want to show that human affairs are ruled by providence. I mentallyscan the list of differentiae and my attention is caught by that ‘from a whole’: itsuggests to me that what human affairs stand in relation to as a part to a wholeprovides me with the middle term I need. I know that the world is ruled is ruledby providence. But human affairs are a part of the world and so they too, I canconclude, are also ruled by providence.

As well as setting out the topical differentiae, Boethius lists for each a maximapropositio (‘maximal proposition’) — sometimes giving it in a variety of differ-ent forms. The maximal proposition is a statement putting in general terms thepattern of reasoning on which arguments rely which are made using the topical dif-ferentia in question. So, for the differentia ‘from a whole’ the maximal propositionis: ‘What is fitting to the whole, also is fitting to the part.’ When I argue,

12. The world is ruled by providence.

13. Human affairs are a part of the world.

so

14. Human affairs are ruled by providence,

I am giving a particular example of how what is fitting to the whole is also fittingto the part. The maxim has another role too, however. (12–14) is not a validargument, although it may seem to be (just about!) a plausible one. If, however,we add, as an extra premiss

13a. What is fitting to the whole, also is fitting to the part

20 John Marenbon

that is to say, the maximal proposition, the result is (or could be, with a littlere-expression) a formally valid argument.

This example illustrates a general rule in Boethius’s account of the topics: whenthe maximal proposition is added as a premiss, the arguments become formallyvalid deductions. But Boethius does not suggest that this is how maximal proposi-tions should be used. Rather, he says [TD 1185B-D; TC, Boethius, 1833, 280:24-7]that maximal propositions give arguments their force. His idea seems to be thata formally invalid argument such as (12–14) gains its force as an argument fromthe principle encapsulated in the maximal proposition: we are happy to accept(14) as following, in an informal way, from (12) and (13) because we accept andhave in the back of our minds the principle that what is fitting to the whole isalso fitting to the part. The strength of a topical argument will therefore dependon the strength of the underlying maximal proposition. Some maximal proposi-tions are analytic truths (for instance: ‘the cause of anything brings about what itcauses’ TD 1189C; ‘once the antecedent has been asserted, the consequent follows. . . ’ (i.e. modus ponens) TD 1198D). Some, like the one in the example here, aremuch vaguer statements of what is generally the case. Some, like the maximalproposition of the one topic considered to be extrinsic, ‘from judgement’ — ‘Whatseems so to all or to many or to learned people should not be contradicted’ (TD1190CD) — hardly even amount to useful argumentative rules of thumb.

Boethian Logic and its Survival

Boethius is by far the most important figure in the ancient tradition of Latin logic,but it is important to realize that the Boethian Tradition was not the only ancientLatin one. The logic of the earlier Latin authors, along with, or transmitted by,later encyclopaedic accounts, provided a separate tradition, which would be theone on which, more than Boethius, medieval logic depended in the period up to thelate tenth century. It is in the eleventh century that the Boethian Tradition beginsto dominate (See §4 below). The twelfth century was the Golden Age of BoethianLogic: the six works that formed the core of the logical curriculum were Boethius’smonographs and his translations of the Isagoge, Categories and On Interpretation,which were taught making extensive use of his commentaries. And the PriorAnalytics and Sophistical Refutations, also in his translation, began to be known.As a result of the introduction of the whole range of Aristotle’s writing and itsadoption, by the mid-thirteenth century, as the Arts course in the universities, andwith the development of the logica modernorum, branches of logic newly devisedby the medieval logicians themselves, Boethian Logic became less important inthe thirteenth and fourteenth centuries, although his translations continued to beused by all students of logic, and some outstanding theologians, such as Albertthe Great, Aquinas and William of Ockham, made some use of his commentaries.Moreover, On Division and TD remained part of the standard university logicalcollections — and commentaries were even written on TD in the thirteenth century.The monographs on categorical syllogisms were no longer useful now that the Prior

The Latin Tradition of Logic to 1100 21

Analytics itself was known, and the treatise on hypothetical syllogisms too wasforgotten [see Martin, 2007].

2.3 The Encyclopaedists

Between Boethius’s death and the late eighth century, no Latin writer worked onlogic in a serious and sustained way. But two accounts of logic written withinlonger encyclopaedic works would be important in the centuries following.

Cassiodorus

Cassiodorus (484/90–590) succeeded Boethius in his post at Theoderic’s court,and he probably had a hand in ensuring the preservation and transmission ofBoethius’s work. In 554, he retired to a monastery at Vivarium in southern Italyand wrote a handbook called the Institutions (Institutiones) [Cassiodorus, 1937;transl. Cassiodorus, 1946], which was widely read in the early Middle Ages. InBook II he gives short accounts of the seven liberal arts among which is logic (II.3.1-18). There are very summary accounts of the matter of the Isagoge, the Categoriesand On Interpretation (which is singled out for its difficulty). For all these, heuses Boethius’s translations [Courcelle, 1941, 80-3]. He then presents categoricalsyllogisms, following Apuleius [Sullivan, 1967, 173-7], definition, basing himself onMarius Victorinus, and topical argument, in which it seems he is following MariusVictorinus’s now lost work [Hadot, 1971, 115-41]. There is a list (II,13) of whathe calls ‘the modes of hypothetical syllogisms’: the phrase is Boethius’s, but thelist is closer (though not identical) to that given by Martianus Capella and so,probably, by Marius Victorinus.

At the end of the section on logic (II,18), Cassiodorus includes a list of those ‘bywhose efforts these things have come into the Latin tongue’. In the standard textof the Institutions, Marius Victorinus is credited with the major role — as trans-lator of the Isagoge, Categories and On Interpretation, the writer of monographson hypothetical syllogisms and definition and the commentator on Aristotle’s Cat-egories and Cicero’s Topics. Apuleius is mentioned for his categorical syllogistic,and Cicero, of course, for his Topics. Boethius’s role is reduced to that of com-mentator on the Isagoge and On Interpretation — despite the fact that it was histranslations of Aristotle and Porphyry which Cassiodorus had in fact used (andit is uncertain whether Victorinus did in fact translate the Categories and OnInterpretation, or comment on the Categories). In one textual tradition, however,the list is changed, and all the writings attributed to Victorinus are attributedto Boethius, even the commentary on Cicero’s Topics, where Victorinus and notBoethius seems to have been the source. A complex explanation involving an orig-inal draft and additions at various stages has been proposed to explain this strangedifference in the lists [Courcelle, 1941; Hadot, 1971, 105-9], but perhaps politicalfactors could provide a better explanation. Another feature of the pro-Boethiantextual tradition is that these manuscripts contain a series of additions of logical

22 John Marenbon

and other material, including extracts from Boethius’s On Topical differentiae.[Cassiodorus, 1937, xxv, xxxvii].

Isidore of Seville

Isidore, Bishop of Seville in the early seventh century and relentless collector offacts, was even further from being a logician in his own right than Cassiodorus. Hismost influential work, surviving in more than a thousand medieval manuscripts,is called the Etymologies (Etymologiae) [Isidore, 1983], and it is an encyclopae-dia which organizes its discussion around the etymologies, usually imaginary andsometimes fantastic, of words. It contains a short account of logic (II, 25-31) mostlyborrowed from Cassiodorus, sometimes with mistakes that show a compiler whodoes not understand his material. Thus the Apuleian account of categorical syl-logistic reappears, along with the same brief passage on hypothetical syllogisms,the account of definition and the topics. Isidore also takes some material fromMartianus Capella and Marius Victorinus’s On Definition, which he uses, alongwith Cassiodorus, in giving summaries of the Isagoge, Categories and On Inter-pretation. He also seems to be the first author to makes use of the Ten Categories,which would become popular two centuries later.

The Character of the Encylopaedic Tradition

At first sight, it would appear that, alongside the Aristotelian logical traditiontransmitted through Boethius, the encyclopaedists transmitted a more rhetorically-based tradition, going back to Marius Victorinus, in which Cicero’s Topics is thecentral text. The account in Martianus Capella is, arguably, strongly rooted inVictorinus, and Cassiodorus too seems to have looked to Victorinus, and Isidorefollows Cassiodorus. But there is also an emphasis on the Categories in theseaccounts, which would be taken up strongly by their medieval readers, and Mar-tianus Capella’s presentation works against a rhetorical conception of logic, bysimply placing the account of the topics in his presentation of rhetoric.

3 CAROLINGIAN BEGINNINGS

([Van de Vyver, 1929; Marenbon, 1981])

For a century and a half from the time of Isidore there seems to have been nostudy of logic in Latin Europe, and no writing about it, even third-hand. Logicwas re-discovered at the court of Charlemagne at the end of the eighth century.

3.1 Logic at the Court of Charlemagne [Marenbon, 1997]

There were two different strands of logical work among Charlemagne’s court in-tellectuals, one associated with the Anglo-Saxon Alcuin, the other with Theodulf,who came from Visigothic Spain.

The Latin Tradition of Logic to 1100 23

Alcuin as a Logician

Alcuin (d. 806) was educated at the Cathedral school of York and managed,from the 780s until he was made Abbot of Tours in 796, to gain a position and,ultimately, a good deal of influence, in Charlemagne’s court at Aachen. Amonghis compositions are text-books on grammar, rhetoric and logic. The one on logic,Dialectic (Dialectica) [Alcuin, 1863], written in the form of a dialogue betweenAlcuin and Charlemagne himself, can claim to be the first medieval work on thisdiscipline. In setting out these three linguistic arts of what came to be called the‘trivium’ as basic elements of education, Alcuin was, in a sense, merely followingthe lead of Cassiodorus, though unlike him neglecting the mathematical arts ofthe quadrivium. But in a preface to the three works, pointedly called On TruePhilosophy (De vera philosophia) [Alcuin, 1863, 951-76], Alcuin makes explicitlythe case for the liberal arts as pillars in an education that will finally lead to thetemple of Biblical wisdom (cf. [Marenbon, 1984, 172-4]). This was an educationalprogramme that Alcuin ensured was politically underwritten; Charlemagne’s roleas pupil and interlocutor in Dialectic is a flattering endorsement of the directionof royal policy.

Alcuin did not just help to place the arts of the trivium at the centre of medievaleducation: he helped to make logic the foremost among them. But from Dialectic,a text not only wholly derivative, but copied in the main — with one importantexception — verbatim from the encyclopaedic accounts of Cassiodorus and Isidore[Prantl, 1885, 16-19; Lehmann, 1917], perhaps with some use of Boethius’s firstcommentary on On Interpretation (queried in [Kneepkens, 1998]; but [Bullough,2004, 404] upholds its use), it is not easy at first to see how. Certainly not becauseof any logical thinking done by Alcuin himself: the one section for which there is noobvious source, Chapter XII on ‘Arguments’, is simple in the extreme and avoidsgiving even the summary accounts of types of categorical syllogisms or modes ofhypothetical syllogisms available in the encyclopaedias.

Yet Alcuin manages his material with a clear sense of his own particular purpose.In Isidore’s Etymologies, his main source, the presentation centres on logic as a toolfor devising and judging arguments: the section on syllogisms is the longest, andas in Cassiodorus it comes at the end of the work, along with the presentation oftopical arguments, punctuated by the discussion of definitions. Alcuin ends withhis treatment of material from On Interpretation, and, as mentioned, he gives avery simple and brief treatment of syllogistic. The emphasis of Dialectic in termsof space and detail falls on the exposition of the Categories. Here alone Alcuinturns to a non-encyclopaedic source, the Ten Categories, the intelligent paraphraseproduced in the circle of Themistius (see above, 2.1). The excerpts from it occupytwo fifths of the whole treatise. To judge from Dialectic, logic is above all aboutthe doctrine of the Categories.

There is every reason to believe that Alcuin would have been happy to leavethis impression. He believed that the Ten Categories was the work of Augustine,no less, and he wrote a prefatory poem for it which would accompany it in the

24 John Marenbon

manuscripts [Aristotle, 1961-1, I, 1–5, , lxxxvii] in which we learn that this ‘littlebook contains ten words which hold everything that we are able to perceive’. TheCategories are, therefore, a key to understanding the sensible world — and morethan that. In a letter dedicating his On the Faith of the Holy Trinity (De FideSanctae Trinitatis; finished 802) to Charlemagne, Alcuin professes the hope thatby his treatise he will convince

. . . those who have been judging as of little use your most noble inten-tion to want to learn the rules of the discipline of dialectic, that in hisOn the Trinity, St Augustine thought them necessary above all, whenhe showed that the most profound questions about the Holy Trinitycannot be explained except through the subtlety of the Categories.[Dümmler, 1895, 415]

Alcuin has in mind the passage in On the Trinity (V.2-5) where Augustine askswhether Aristotle’s Categories apply to God, and decides that, properly speaking,only the first, substance, does. In his own work, based in part on Augustine’s, thistheme is given pride of place in Book I. Just because, as he says in his prefatorypoem, the ten Categories provide a comprehensive classification of everything inthe sensible world, they are the perfect tool for understanding the distance be-tween God and his creation. Within a programme where studying the liberalarts, especially the trivium, is justified as providing the foundations for Christianwisdom, logic in particular is thus seen to have a special doctrinal role, once thecentrality of the Categories is recognized and their part in clarifying some of thecentral mysteries of the faith.

Theodulf of Orleans and the ‘Libri Carolini’

Theodulf of Orleans (d. 821) was another of Charlemagne’s court intellectuals.Mainly known as a poet, his part in the history of logic is due entirely to KingCharles’s Work against the Synod (Opus Caroli Regis contra Synodum or LibriCarolini) [Opus Caroli, 1998] — the official response from the Latins to the secondCouncil of Nicaea (787), composed between 790 and 793. Although issued in theEmperor’s name, the Work against the Synod has now been shown fairly surelyto be the work of Theodulf [Freeman, 2003, collecting her articles on this theme;Meyvaert, 1979, for a summary of the discussions]. It is only in one chapter (IV,23) that logic is employed, but here its use is concentrated. The aim is a simpleone: to show that the Greeks are wrong in contending that ‘to kiss’ and ‘to adore’mean the same thing. Theodulf chooses to make his critique of this (strikinglyweak) position the excuse for a lesson in, and display of, logic. He borrows fromBoethius’s first commentary on On Interpretation, and takes a long explanationfrom Apuleius about the truth-values of different propositions. Above all, he seesthe chapter as an opportunity to demonstrate his prowess in handling arguments,even though none of this complicated syllogizing is necessary, or even germane, foroverturning the Greeks’ position.

The Latin Tradition of Logic to 1100 25

Theodulf’s logical project differs from Alcuin’s in the emphasis it places onargument, and its lack of interest in the more metaphysically-inclined logic of theCategories. I once argued [Marenbon, 1997], using the chronology of Alcuin’s workestablished by his biographer, Donald Bullough [Bullough, 1991, 37; Bullough,1997, 581-2] that the first medieval logician was not Alcuin, but Theodulf. Butit turns out to be more plausible to retain the traditional dating of Dialectic to786-90 [Bohn, 2004], and there is evidence, in any case that Theodulf made useof it [Opus Caroli, 1998, 61; English version in Freeman, 2003, 88-9]. Despite thedifference in their main aims and interests as logicians, both Alcuin and Theodulfare alike in attaching logic to the official policy of the Carolingian Empire, as partof a scheme of Christian education and the defence of Christian doctrine. Betweenthem, Alcuin and Theodulf map out the three main ways in which logic would bevalued throughout the early medieval ages: as one of the Liberal Arts, themselvesaccepted as the beginnings of an ultimately Christian educational scheme; as atool in theology; and as a weapon in the fight against heresy.

Theodulf, Alcuin and Alcuin’s pupils

A merging of the approaches of Alcuin and Theodulf may be indicated by thecontents of the earliest surviving logical manuscript, MS Rome, Biblioteca PadriMaristi, A. II. 1, which belonged to an associate of Alcuin’s, Bishop Leidrad, whodied c. 814. Along with the Ten Categories, Porphyry’s Isagoge and extracts fromAlcuin’s Dialectic, it includes Boethius’s first commentary on On Interpretationand Apuleius’s Peri Hermeneias [Delisle, 1896]. The other piece of evidence thatsurvives about interest in logic at the turn of the ninth century very much reflectsAlcuin’s interests, perhaps because it is found in a set of passages connected withhis pupil, Candidus Wizo [ed., Marenbon, 1981, 151-66]. The logical pieces aremostly linked to the Ten Categories (I, XIV, XV), though one (XII) takes anAristotelian passage from the theologian Claudianus Mamertus, and another (XIII)may be taken from Boethius’s Categories commentary, though it can perhaps beexplained as an elaboration of Cassiodorus.

3.2 Eriugena and the Ninth Century

([Marenbon, 1981, 67-87])

John Scottus Eriugena, who worked in the 850s and 860s at the court of Charle-magne’s grandson, Charles the Bald, dominates the logic, as well as the philosophyand theology, of the ninth century. As in all his work, Eriugena’s logic shows astrange mixture between ideas that fit closely with the Latin tradition, and ideasthat are foreign to it, introduced by the fact that John learned Greek and wasdeeply influenced by Greek Christian Neoplatonism, combined with an intellec-tual temperament inclined to take such elements to their extremes. In order toappreciate this combination, it is important to place John in the context bothof his Latin predecessors and contemporaries, and the gloss traditions that be-

26 John Marenbon

gin shortly after his lifetime; and to look at John’s probably earlier glosses onMartianus Capella’s logic, as well as his masterpiece, the Periphyseon.

Macarius the Irishman and Ratramnus of Corbie on Universals ([Delhaye, 1950;Erismann, Forthcoming-A])

An interesting discussion about logic from the time of Eriugena survives in an un-usual setting. In the early 860s [Bouhot, 1976, 59], Ratramnus of Corbie addressedhis Book on the Soul (Liber de anima) to Bishop Odo of Beauvais [Ratramnus,1952]. The indexRatramnus of Corbie!Book on the Soul Book is directed againstan anonymous monk of Saint-Germer de Fly, with whom Ratramnus had beenin correspondence, and who claims to be expounding the ideas of his master, anotherwise unknown Irishman named Macarius. Their difference was over the un-derstanding of a passage in Augustine’s On the Quantity of the Soul (xxxii, 69),where the question is raised, but not resolved, of whether human souls are allone, are many or are one and many. Macarius and his pupil (it is impossible todisentangle their contributions), and even more decidedly Ratramnus, make theissue a logical one: what is the nature of universals?

Macarius’s position has been described as Platonic realism [Delhaye, 1950, 19-37] and as ‘hyper-Realism’ [Marenbon, 1981, 69]. In fact, it seems to be a rathercrude and incompl