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Medieval Logic

Albert of Saxony, Quaestiones Circa Logicam: Twenty-Five Disputed Questions on Logic by Michael J. Fitzgerald (Dallas Medieval Texts and Translations: Peeters Publishers) This translation of Albert of Saxony's Twenty-five Disputed Questions on Logic brings to English readers an important fourteenth-century logician's contribution to the analytic core issues in philosophy. Many of these issues are still actively discussed today. Albert treats issues such as the nature and scope of logic; the meaning and reference of terms; self-reference; logical difficulties with possessive, non-designating, and fictitious terms; mental terms and relative pronouns; logical problems with propositions, such as quantity, truth, falsity, conversion, and verification; the scope of denials and modal notions; Aristotle's category theory; and the existence of universals. The book is intended to appeal to all those who are interested in the late medieval contribution to those discussions. Included with the translation, translator's notes, and introduction are an appendix containing two sophisms that treat part-whole relations, a glossary of Albertinian terms, an index of key rules, sophisms, and theses, and a table of parallel passages in Albert's other logical works.

Albert of Saxony is also known by the names Albert of Halberstadt, Albert of Rickmersdorf, and Albert of Helmestede. Albert referred to himself as Albert of Helmestede when he signed the procurator's book of the English-German nation of the University of Paris upon his election as procurator of that nation on 19 November 1351.1 He is also sometimes called Albert the Little (Albertus parvus), or occasionally Little Albert (Albertutius), pert- aps in an attempt by his critics to suggest that he was a minor or unoriginal thinker, or more probably in an effort to distinguish him from Albert the Great (Albertus Magnus), the teacher of Thomas Aquinas and important thirteenth-century thinker.2 Because of the possible negative connotations of "little Albert" Marcus Benevento, the 1496 editor of William of Ockham's Expositio aurea—a work that Marcus also interspersed with Albert's Quaestiones in artem veterem—felt obliged to say, "Although he is called 'Little Albert,' he ought to be considered the greatest Albert in logic and philosophy,"3 and not a minor or unimportant thinker.

Unfortunately, not much is known about the details of Albert's early life and education.' Since Heidingsfelder's 1922 article, the year 1316 is often given for his birth, but there is no historical evidence to corroborate that date.' Indeed, it is based on a misunderstanding on Heidingsfelder's part.' Albert was most certainly born before 1331, and was the son of Bernard Rich (Rike in German, Dives in Latin), in the village of Rickmersdorf (modern-day Velpke), in Saxony near the town of Helmestede.7 His father was almost certainly not a nobleman but a wealthy peasant farmer.' His brother John was likewise a master of arts in the English-German nation at Paris, serving as rector of the University in 1363.9

Albert's early studium generale training probably took place in Halberstadt and Magdeburg, possibly even in Erfurt, but clearly not in Prague. If his more advanced education was in fact at Magdeburg, then he probably would have been familiar with William of Ockham's Summa logicae very early in his academic career. There is a Cambridge University manuscript of Ockham's Summa logicae (Cambridge University, Gonville & Caius Coll., MS. 464/571), which is one of the best copies of that work; it was in fact prepared in Magdeburg by one Conrad of Nipeth in 1341. However, the early historical record of Albert's education and life is just not clear. Although he may have been studying at the University of Paris as early as 1345, the earliest known record of him there is 7 March 1351, when he determined under Master Adalbert Ranconis (Albert of Bohemia), a master in the English-German nation at Paris who was from the village of Jezov (Ericinium) in southern Bohemia, near Tábor. Until 1971, Albert of Saxony was frequently confused by medieval scholars with his master, Albert of Bohemia. One example of this confusion is that many scholars considered Albert of Saxony to have been rector of the University in 1353, and then again in 1355. But in fact, it was Albert of Bohemia who served as rector in 1355, and was responsible for the famous prohibition of 10 December of that year against masters giving ad pennam lectures to their students, that is to say, practically dictating word for word to the students. It was only with the publication of J. Kadlec's study of Adalbert Ronconis in 1971 that the identity of Albert of Bohemia with Adalbert Ronconis became firmly established." Albert of Saxony was himself rector of the University of Paris only once, in 1353.

Albert remained a master in the English-German nation in the faculty of arts at Paris during his entire academic career, that is, between 1351 and 1362. As far as we know, he never became a theologian, and continued lecturing in the arts faculty until 27 November 1362, when he seems to have disappeared from the university rolls. His whereabouts between then and 1364 still remain a mystery, although he may have been lecturing at Erfurt or Magdeburg, or perhaps inspecting his prebend at Mainz. He was summoned to Avignon in 1364 by Pope Urban V, who charged him with the task to found the University of Vienna. Later that year we know that he was with Prince Rudolph IV of Austria in Prague, attending a debate over the Immaculate Conception of the Blessed Virgin. He founded and was the first rector of the University of Vienna in 1365, and was appointed bishop of Halberstadt on 21 October 1366, by Pope Urban V. Having been enthroned as bishop on 2 February 1367, Albert became embroiled in the tumultuous ecclesiastical and political affairs of his diocese until his death in Halberstadt on 8 July 1390.

Albert's master, Adalbert Ronconis, determined on 8 November 1344 under Master John de Wezalia/Wesalia in the English-German nation at Paris, and in 1346 became a master of arts in the English nation. Adalbert was procurator of the English-German nation in October of 1350, and again in February of 1351. He went on to the faculty of theology, was a bachelor of theology in 1363, doctor in 1365, and became a canon of St. Vitus Cathedral in Prague in 1366. Adalbert, who was known for having ecclesiastical reformist tendencies, personally possessed an autographed copy of Richard FitzRalph's De paupertate Salvatoris. Adalbert, in fact, says of himself that he was known as "the second FitzRalph" (secundus Armachanus) at Paris. He died in Prague in 1388, just two years before Albert of Saxony.

John de Wesalia, the master of Adalbert Ronconis, determined in the English-German nation at Paris, under an early Scottish popularizer of Ockham's views in the Parisian arts faculty, Walter Wardlaw." Walter Wardlaw likewise determined in the English-German nation at Paris in May or June of 1340, under another famous Scottish Ockhamist, John Rathe, the socius critic of the theologian Gregory of Rimini. Thus, the Ockamist influence of the English German nation on Albert was quite strong.

Albert's Works and their Significance

Albert's philosophic writings amount to some 26 works, which survive in over 300 manuscripts and 50 incunabular editions. None of them is on theology." Given these statistics, it is astonishing that of the total 26 works, only about 10 have ever been printed at all and only about half that number exist in modern critical editions. Most of what is known about his philosophic views derives from his commentaries, and questions on logic and natural science. Other areas of his thought remain to be discussed.

His major works fall into two categories: commentaries and questions on Aristotle's works, and other miscellaneous works. His works on Aristotle include commentaries and questions on the Categories, On Interpretation, the Physics, On the Heavens and Earth, On Generation and Corruption, On Meteors, On the Senses, the Parva Naturalia, the Topics, the Prior and Posterior Analytics, On the Soul, Economics, Politics, and the Nicomachean Ethics.

Besides the commentaries and questions on Aristotle's works, Albert's most famous other works include his great logical work, An Extremely Useful Logic (Perutilis logica), which was frequently used and copied. He also wrote a long logical tract On Sophisms, treating some 255 problematic propositions; questions on the Isagoge of Porphyry; a tract treating Proportions, in the vein of Thomas Bradwardine; a tract on Squaring the Circle; a set of Questions on the Ancient Art [of logic] (Quaestiones in artem veterem); and a separate selected set of Twenty-Five Questions on Logic (Quaestiones circa logicam), translated in this volume.

Albert's logical and philosophic ideas were heavily influenced by the views of earlier fourteenth-century English thinkers, in particular William of Ockham, Adam Wodeham, Walter Burley, William of Heytesbury, Thomas Bradwardine, Richard Kilvington, Roger Swyneshed, Richard Billingham, and perhaps Robert Holkot and William Crathorn. The views of these English thinkers were most likely transmitted to him through the masters in the English-German nation. Albert incorporated many of the quasi-mathematical views of the early fourteenth-century Mertonians—especially those of Thomas Bradwardine, William of Heytesbury, and Richard Kilvington—into his own solutions of the many logical sophismata he treated. Albert's obligation theory also shows that he is clearly aware of the views of Roger Swyneshed and Richard Billingham on the matter. Moreover, even though Albert vigorously argues against Burley's ontological realism concerning the ontological status of universals, he shows a marked preference for Burley's logical treatment of syncategorematic expressions (that is, logical operators) and inference relations (consequentiae). Unlike Ockham, both Albert and Burley see the inference relation between the premises and conclusion of an argument, its consequence relation (consequentia), as a sort of logical "first principle" upon which all other argumentation ultimately rests—including Aristotelian syllogistic theory. They both seem to be struggling with clarifying what we would today call the "corresponding conditional statement of an argument," and are among the earliest of the medieval logicians who were beginning to absorb Aristotelian syllogistic theory within the more encompassing framework of a theory of inference. All that Albert has to say about terms, arguments, fallacies, and other logical "processes" (broadly construed so as to include various sorts of non-deductive inferences, like induction or abduction) must be seen in light of his views on inferences (consequentiae). For example, in these Twenty-Five Disputed Questions on Logic, Albert writes:

As far as the first issue is concerned, it should be known: Conversion is an inference between two categorematic propositions with their terms transposed. Notice I say "inference" (consequentia), for unless there is an inferential sign between the converse and the convertend in converting a proposition [for example, "therefore" or "then"], or at the very least an inferential sign should be assumed to be there, there will not be a conversion. It is required that there be an inference in order to convert a proposition. From the inference of conversion, certain other inferences are proven, namely syllogistic ones, as is shown in Book I of the Prior Analytics.

Likewise, in the very first question of the same work, he gives an example of his view concerning the breadth of the discipline of logic. He says:

Having made this distinction between theoretical and practical knowledge; I defend the following thesis: Logic is practical knowledge. This is proven: Logic considers deduction, induction, and other forms of argumentation, as well as division, definition, and other acts of reasoning, for the purpose of reasoning well in the other branches of knowledge.''

It should be clear from the above remarks that as far as Albert is concerned, the discipline of logic embraces much more than mere Aristotelian syllogistic theory, and is certainly not an attempt to reduce all the various kinds of logical argumentation to Aristotelian syllogistic. Logic as a discipline deals with all "acts of reasoning." It develops various concepts and rules for making deductive and non-deductive inferences, in order to help us get on with natural science and natural philosophy. In fact, he holds the discipline of logic in such high esteem that he is reported to have said, "Logic is the knowledge that frees a person from illusions that seem to be but are not, suppresses errors, hears the truth, and gives the right light to observation."

In his discussions of Aristotle's views on physical and celestial motion, Albert defended a variety of the famous "impetus theory" of projectile motion, which is generally credited by later historians and philosophers of science with helping to undermine Aristotelian authority in physics and celestial mechanics, and paved the way for the Copernican, Keplerian, and Galilean achievements of modern science. Albert is a paradigmatic example of the penetration of the logical and physical views of the post-Ockham English philosophers into the Parisian arts faculty, as well as an example of a new shift in medieval semantic and epistemological discussions. Thus, he is at the fourteenth-century forefront of those who reject cognitive or semantic intermediary entities to explain the perceptual apprehension of physical objects and the signification of terms and propositions. Albert expanded and developed William of Ockham's mental act theory of concepts, which was left mostly undeveloped in Ockham's late works. Albert's view, concerning the natural mental language of pure thought, was that concepts themselves as epistemic or semantic items are nothing but the mind's act of being operationally engaged with physical objects. His view of the ontological structure of concepts, and his view on the nature of the sphere developed in his De sphera, both seem to have been influential for the great theologian and cardinal, Peter of A419 These late medieval views of Albert and Peter are remarkably similar to the core views developed in contemporary discussions of "reliabilist" epistemology. Albert certainly seems to be one of their earliest medieval predecessors. In fact, Albert's view that signification is representation seems to have become the standard definition of signification for the famous fifteenth-and sixteenth-century Parisian nominalists, such as Peter Tartaretus, Hieronymus Pardo, Antonius Sylvester, Thomas Bricot, Ferdenando Enzinas, Juan de Celaya, Domingo de Soto, and John Major, who either studied or lectured there in the arts faculty. In fact, Albert's views on natural philosophy were much more widely known in the fifteenth and sixteenth centuries than either those of John Buridan or Nicholas Oresme. Indeed, Leonardo da Vinci's library contained his own copy of Albert's Questions on the De caelo, with marginal notes in da Vinci's own hand. Likewise, the young Galileo had a copy of Albert's De Caelo Questions in his personal library, and was also familiar with Albert's cosmological views.

Leaving aside his contributions to the history and philosophy of science, which have been thoroughly discussed in Sarnowsky's Theorie der Bewegung, what I take to be Albert's major contribution to the analytic core issues in philosophy is his semantic grounding of a Burlean theory of logical inference, that is, a view of logical inference which absorbs Aristotelian syllogistic and demonstrative theories as its proper logical parts, within a coherent nominalist metaphysics, epistemology, and philosophy of language. Albert's views are only just beginning to be studied in any detail today, and it is my hope that this translation will help contribute to a greater recovery and study of his views.

Fourteenth-Century Philosophic Disputations

Very little is known about the practice of formal disputations in the arts faculty, relative to disputations in the faculty of theology. There appear to have been at least two sorts of arts disputations that were conducted on a regular basis: disputed questions (quaestiones disputatae)`and sophisms (sophismata). The disputed questions given in the arts faculty at Paris should not be confused with the "questions on whatever/by whomever" (quaestiones quodlibetales/quolibetales) which occurred in the theology faculty on solemn occasions. The former developed out of various logico-grammatical problems raised by a "reading" (lectio) by an arts master from an approved text. For example, in the course of a reading by a master from the text of Peter of Spain's Summae logicales, a question on the nature of terms might arise, something like: Is every term written, spoken, or mental? Such a question might then give rise to a disputation.

Disputations took place both privately between a master and his students, and publicly or "solemnly" at an event that replaced regular classes at the university and was attended by the larger university community. The latter practice was eventually codified by university statute, which prescribed that masters would hold a certain number of disputations at various times of the year, sometimes as frequently as once a week. Most scholars agree that the process came to be divided into two sessions. In the first session, supporting and opposing arguments for a given thesis or question were brought forward and, in a preliminary way, clarified and determined by a student serving as the respondens under the supervision of the master. During the second session, the master himself would make the "determination," that is to say, give his answer and respond to all the opposing arguments. Some disputed questions we have in written form are clearly taken from different stages in this process: they are either a report (reportatio) of the first day's session, some abbreviation of the debate as a whole, or they reflect the master's answer and response to opposing objections, and were redacted after the second day's debate.

The formal structure of the disputed question under consideration in a disputation was fairly well fixed by Albert's time. Generally, the issue to be treated was stated as precisely as possible in the very title of the question (titulus quaestionis), always beginning with the expression, "Whether ..." (utrum), for example, "Whether every proposition is true or false." Next came some arguments in favor or against the question given, depending upon which the master intended to refute. These were either arguments actually defended by some contemporaries or, perhaps, positions not defended by anyone but which needed to be examined. These arguments were usually introduced by formulas like: "It is argued/It seems that it is so/not so" (Et arguitur/videtur quod sic/ non). The arguments presented at this point were eventually rejected by the master conducting the dispute. Arguments "in opposition" (in oppositum) were raised next, and sometimes may have amounted to only lip service to some authority, or perhaps merely a brief quote from Aristotle was given. Next the master's strategies for answering the main question were explicated, if necessary; for example, he answered the question by proposing to divide it into "articles" (articuli), drawing "distinctions" (distinctiones), or giving "theses" (conclusiones) that would be necessary to respond adequately to the question posed. The distinctions at times may have been simply common ones that everyone conversant with the issue knew, and that had to be acknowledged before the final solution to the question could be given. The theses stated by the master were generally not intended as being inferred from arguments presented earlier in the dispute, but were generally followed by some sort of proof by the master. At this point, additional arguments could be introduced by a real or fictitious opponent against a thesis of the master, beginning with expressions like, "You might say/someone might say ..." (Dicares tu/Aliquis diceret ...). Perhaps even a series of such arguments and replies would be examined and rejected. There was no set number of such back-and-forth discussions. (There are some good examples of such "point-counterpoint" discussions in Albert's questions 7 and 22 in this volume.) Then, the master would begin to resolve the matter and give his position—that is, his "determination" (determinatio)—of the question, usually introducing it with stock formulas like, "I respond/It is responded" (Responded Respondetur/Respondendum est). After the Master's solution to the question, each of the arguments given at the beginning of the question in favor of the question or rejecting it were systematically reintroduced and each refuted in turn with the formulas: "To the arguments ..." (Ad rationes); "To the first ..." (Ad primam ...), etc.

An early fourteenth-century account of such academic disputations maintains that public discussions of disputed questions or sophismata were pretty rowdy affairs on occasion:

That disputations were not always without danger can be seen from the statutes threatening to exclude students who demonstrate by "clamoring, hissing, making noise, stone-throwing by themselves or by their servants and accomplices, or in any other way." Even the most technical reports of medieval disputations can sometime be relieved by glimpses of the tumult of actual disputation. Thus Matthias of Gubbio, trying to give an orderly account of his opposition against the opinions of Hervaeus Natalis concerning the nature of logical relations, is interrupted by someone: "But before I come to the fourth point, somebody shouts against me with a loud voice: You deny such relations, I certainly deny yours." Certainly, disputations did not proceed as solemnly as the written redactions might make us believe.

Perhaps one of the reasons for this chaotic atmosphere was that the arts faculty at Paris, unlike universities elsewhere, was divided into four "nations": French, Norman, Picard, and English/German. Each student swore allegiance to his own nation, and to no other. John LaMonte tells us:

Each nation had its own elected proctor and the proctors of the nations elected the rector, who was the administrative head of the entire university. The student pledged his loyalty to his nation and to its officers and the nation became the center of his academic life. From evidences found in the sermons and court records, the nations were often on bad terms with each other and conflicts which often ended in free-for-all fights were not unknown among them.

William Courtenay also points out that in 1339 statutes were passed to regulate the conduct of students and masters at public discussions of issues raised in all the various faculties' lectures and disputes. He states:

One of the issues addressed by almost all the faculties in the University was a concern over the disintegration of classroom discipline, proper dress, and behavior, and magisterial control over teaching. Lectures and disputations in Arts, Medicine, and Law were being interrupted by whistling and foot stamping, or by contentious questions and comments from bachelors, masters, and others who had not received permission to speak.

By the time Albert was at Paris in the mid-fourteenth century, there were most likely no English students studying there. The Hundred Years' War, which began in 1337, had raged for fourteen years prior to any historical record of Albert's being at Paris. There was great animosity between England and France during this period. Increasingly, the only English philosophic presence felt in the Paris arts faculty was from continental allies, which itself must have provoked much philosophic difficulty among the various nations. William Courtenay and Katherine Tachau explain:

In 1339-1341, the English Nation at Paris had no English masters and probably no English students. Hostilities between France and England made Parisian study too difficult for the few English students Paris had been able to attract in the previous decade. The same circumstances discouraging the attendance of Englishmen encouraged growing numbers of Scots to study at Paris, where until 1341 their king was resident as the guest of his French allies. The composition of the English nation was about equally divided among Scots, Germans, Dutch and Scandinavians.

By the end of the fourteenth century the English-German nation became simply the German nation.

As far as we know, the structure of sophismata disputations more or less followed those of the more general disputed questions. Medieval sophismata were philosophically problematic sentences, rather than patently silly utterances, which were felt to require close analysis in order to avoid making fallacious inferences in logic. Modern analogues of medieval sophismata, that is to say, modern problematic propositions that require further analysis to avoid various logical difficulties, are propositions like the familiar Fregean example, "The morning star is the evening star," and the famous Russellian proposition, "The present king of France is bald."

The Twenty-Five Questions on Logic that I have translated here are based primarily on the reportatio tradition of the actual disputation, although one manuscript—Vat. Lat. Urbinato 1419—suggests that Albert later reworked and expanded at least some of the arguments in these questions. I believe that the actual disputation was conducted by Albert at Paris sometime between 1356 and 1362. The scribe of the oldest known copy of these Questions, MS. L.79 in the Archive of the Prague Castle, dated 1366, claims that he is copying from a "report" of Albert's Disputed Questions prepared by Peter Claus, who was at Paris at that time. I do not know whether this Peter Claus was Albert's personal secretary or just someone assigned to record the disputation being conducted.

Thomas Bradwardine, Insolubilia edition, translation and introduction by Stephen Read, series editor Philip W. Rosemann (Dallas Medieval Texts and Translations Series, 10: Peeters) Read's introduction, edition, and translation familiarize us with the roots of the medieval discussion of the insolubles in Aristotle's works, and with the more immediate context of Bradwardine's treatment, in particular his refutation of the views of contemporaries such as Walter Burley. The appendices include material that post-dates Bradwardine, yet shows clear signs of its dependence on the prince of the natural philosophers, as Ralph Strode called him half a century later. On the other hand, Professor Read's introduction brings Bradwardine's solution of the problem of insolubles into direct dialogue with modern logic, represented by the theories of figures such as Alfred Tarski, Saul Kripke, and Frederic Fitch. What is fascinating here is that the univocity of logical language, its quasi-mathematical precision, appears to render such a dialogue relatively uncomplicated. In cases where thinkers from different periods do not adopt such logical language, it is much more difficult to offer mutual translations of their systems of thought, which remain more closely tied to metaphors, literary genres, and other non-philosophical factors. Philipp W. Rosemann.

The fourteenth-century thinker Thomas Bradwardine (c.1290-1349) is well known in both the history of science and the history of theology. The first of the Merton Calculators (mathematical physicists) and passionate defender of the Augustinian doctrine of salvation through grace alone, he was briefly archbishop of Canterbury before succumbing to the Black Death in 1349. This new edition of his Insolubilia, Thomas Bradwardine, Insolubilia, made from all thirteen known manuscripts, shows that he was also a logician of the first rank. The edition is accompanied by a full English translation. In the treatise, Bradwardine considers and rejects the theories of his contemporaries about the logical puzzles known as insolubles or paradoxes, and sets out his own solution at length and in detail. In a substantial introduction, Stephen Read, Professor at the University of St. Andrews, describes Bradwardine's analysis, compares it with other more recent theories, and places it in its historical context.  Thomas Bradwardine, Insolubilia is accompanied by three appendices, the first of which is an extra chapter found in two manuscripts (and partly in a third) that appears to contain further thoughts by Bradwardine himself. The second contains an extract from Ralph Strode's Insolubilia, composed in the 1360s, repeating and enlarging on Bradwardine's text; and the third consists of an anonymous text that applies Bradwardine's solution to a succession of different insolubles.

The volume is the tenth in the series Dallas Medieval Texts and Translations under the general editorship of Philipp W. Rosemann, University of Dallas. The Dallas Medieval Texts and Translations series pursues an ambitious goal: to build a library of medieval Latin texts, with English translations, from the period roughly between 500 and 1500, that represents the breadth and variety of medieval civilization. The series is open to all subjects and genres, ranging from poetry through philosophy, theology, and rhetoric to treatises on natural science. Works published in the Dallas Medieval Texts and Translations are unexcerpted and unabridged.

This tenth volume of the series, a href="http://www.amazon.com/Thomas-Bradwardine-Insolubilia-Medieval-Translations/dp/9042923172/wordtrade-20-20"> Thomas Bradwardine, Insolubilia, contains a late medieval logical text, De Insolubilibus, which dates from the 1320s. The best known example of an insoluble is the liar paradox, the statement: "I am lying." What is the truth-value of such a proposition? If it is true that I am lying, then I am lying in the very statement, "I am lying," so that I am in fact not lying. But if I am not lying in saying that I am lying, then I am speaking the truth and so I am lying. It is easy to see why the medievals termed such self-referential logical paradoxes insolubles.

As described in the Introduction to Thomas Bradwardine, Insolubilia, while at Oxford and when chancellor of St. Paul's Cathedral in London in the late 1330s and 1340s, Bradwardine composed the robust defense of the Augustinian position published in his De causa Dei (On God's Cause): salvation comes not from good acts but from the grace of God, by which alone acts can be good. In the 1340s, Nicholas Aston referred to him as doctor profundus, the term by which he was known to posterity.

Reads interest is in Bradwardine's time as a regent master in arts at Oxford in the early to mid-1320s. It was at this time that he composed his logical masterpiece, De insolubilibus, as testified by the Madrid manuscript: "Here end the Insolubles of Master Thomas Bradwardine of England, teaching master at Oxford."' Tradition associates Bradwardine with Walter Burley, as do many of the manuscripts where their works appear together. Burley was a member of Merton College, although he had been studying theology in Paris since 1310. Readers will find that Burley's views on insolubles are the main focus of attack in the early pages of Bradwardine's treatise.

The treatise, written in Latin, was edited by Marie-Louise Roure in 1970. That edition was based essentially on just one manuscript, Erfurt Octavo 76. Roure knew of three others, and says that "a second manuscript (Venice Z 301), in a difficult hand, partly illegible, has, however, allowed us to make some corrections." Roure's text, although a welcome addition to available editions of such texts at the time, has many corrupt and unreliable passages. Thomas Bradwardine, Insolubilia is based on all thirteen known manuscripts.

In addition, two manuscripts contain an extra thirteenth chapter, although whether that chapter is authentic is open to doubt. Nine of the manuscripts attribute the work explicitly to Bradwardine, and of the remaining four, three are incomplete, while the last attributes it to master Thomas of England. None attributes it to anyone else. Bradwardine's inimitable style in his famous works is also found unmistakably in the Insolubilia.

Fleming speaks of the geometrical precision of Bradwardine's presentation of his arguments. Generally, his works open with a preface stating a problem, the need to deal with it, the procedure to follow, and an announcement of the contents of the chapters. Then come a description of terminology, definitions, divisions, suppositions, and conclusions. Following what he notes was Aristotle's approach, he first rejects erroneous opinions, then sticks faithfully to his plan.

Read's presentation of Thomas Bradwardine, Insolubilia combines a historical-philological with a contemporary logical approach. The preservation of these medieval texts is the valuable accomplishment of this series; taken together, they provide a window into the medieval mind.

On the Purity of the Art of Logic: The Shorter and the Longer Treatises by Walter Burley, translated by Paul Vincent Spade (Yale Library of Medieval Philosophy Series Yale University Press) is the first complete English translation, from the Latin, of medieval philosopher Walter Burley's handbook of logic. The work circulated in the Middle Ages in a shorter and a longer version, both translated here and fully annotated. Burley is revealed as both an innovator and a conservative who used new techniques of logical and semantical analysis to defend traditional views.

Walter Burley (or Burleigh) was a slightly younger contemporary of John Duns Scotus (c.1266‑1308) and a slightly older contemporary of William of Ockham (c. 1285‑1347). Although nowadays he is discussed mainly in connection with intellectual currents at Oxford University, he also studied and taught at Paris for some sixteen years or more. If today the generally educated reader does not know him as well as the more familiar figures of Scotus and Ockham, it is not through any fault of Burley’s. He was an important and influential philosopher in his own day, and a prolific author. One recent biographer describes him as "a man of impressive energy and versatility, whose literary output was markedly more extensive than that of any other individual of the early fourteenth‑century group of thinkers produced by Merton College, Oxford."

On the Purity of the Art of Logic  is a good place to see both the similarities and the differences between Burley and Ockham. There are two very different redactions of this work, the Shorter Treatise and the Longer Treatise. The relation between the two is uncertain and complicated, but what appears to have hap­pened is something like this: Burley began with what has survived as the Shorter Treatise. An introductory outline at the beginning of this version indi­cates that it was intended to cover most of the main divisions of the logic of the day." But only a small part of this project was completed: (i) a discussion of general rules of inference, and (ii) a treatment of syncategorematic terms. Then Burley apparently set the project aside.  Eventually he returned to it, but seems to have rethought his original plan.

For although the later Longer Treatise picks up where the Shorter Treatise had left off (with a discussion of the theory of "supposition"), it then continues with material that departs completely from the original outline: a discus­sion of "hypothetical" propositions, 18 and various kinds of reasoning based on them. Moreover, large sections of the Shorter Treatise are repeated verbatim in the Longer Treatise, indicating that the latter should not be thought of as simply the completion of the former, even under a revised plan. The result is that we are left with two treatises that plainly are closely related to one another and to some extent overlap, even though they in no sense form a neat unity.

The Shorter Treatise shows no awareness of Ockham's Summa logicae, which was written probably by c.1323 and which makes clear use of Burley's own treatise De suppositionibus, from 1302. By contrast, parts of the Longer Treatise are definitely directed against Ockham's semantic theories as found in his Summa logicae. The obvious conjecture, then, is that Ockham's Summa logicae was written between the two versions of Burley's On the Purity of the Art of Logic and was what prompted Burley to return to his earlier project and defend his own more traditional semantic views against Ockham's attacks?'

The two versions of Burley's On the Purity of the Art of Logic, therefore, not only provide us with the logical views of a major fourteenth‑century thinker; they also put us in a better position to identify and assess Ockham's own contribution to logic and semantic theory.

The translations are based on the only complete edition of Burley's treatises, corrected by Spade on the basis of one of the surviving manuscripts. The book also includes an extensive introduction, explanatory notes, a table of corresponding passages between the two versions, a select annotated bibliography, and three indexes. A contemporary of John Duns Scotus and William of Ockham, Burley was active at the universities of both Paris and Oxford. He became one of the most important figures in the transformation of medieval logic and semantics that took place in the early fourteenth century. Burley used new tools and techniques of logical and semantical analysis, yet in many cases he used them in defense of traditional views, such as a realist metaphysical theory of "universals."  On the Purity of the Art of Logic shows both these sides of Burley-the innovator and the conservative-as well as some of the ways in which his views corresponded or clashed with those of William of Ockham.

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