Medieval Science, Technology and Medicine

Lapidaries

Lapidaries are books of information about the properties and virtues of precious and semi-precious stones. Each entry in a lapidary usually tells of the color and origins of the stone, as well as its medicinal, magical, moral, and protective properties. Lapidaries are sometimes independent works and sometimes form part of more wide-ranging encyclopedic compilations. In both cases lapidaries are often found in close proximity to herbals because, as is commonly claimed, God has given virtues to herbs, to stones, and to words. Lapidaries were very popular throughout the Middle Ages, especially in the fourteenth and fifteenth centuries, and they appear in hundreds of medieval and early modern manuscripts. As late as the seventeenth century, lapidaries containing both traditional lore and newer information from world exploration continued to be printed and widely copied in manuscript form.

The origins of the medieval lapidary are in classical writings, Arabic writings, and biblical exegesis. Most prominent among the classical works is Book 37 of the Natural History compiled by Pliny the Elder (23–79 C.E.), which was an authoritative source of information about stones throughout the Middle Ages. Pliny was the major influence on two other well-known compilations that had a great influence on later medieval lapidaries, the first-century Wonders of the World (Collectanea Rerum Memorabilium) by Solinus, and the sixth-century Etymologies of *Isidore of Seville. From the medical tradition of the classical world, the most important lapidary is the Damigeron (named for its alleged author), a first-century Greek work translated into Latin, probably in the fifth century. It was the basis for the De Lapidibus of Marbode of Rennes (d. 1123), which has a predominant influence on later medieval lapidaries. From the Arabic tradition the most important sources are Latin translations of two eleventh-century works, De congelatione et conglutinatione lapidum, originally the work of *Ibn Sina (Avicenna), and Secretum secretorum, which was translated into Latin twice and then into the vernacular languages. The exegetical sources are commentaries on the lists of jewels found in scripture: the breastplate of Aaron (Exodus 28: 17–20, 39: 10–14), the lamentation of the King of Tyre (Ezekiel 28: 13), and the foundations of the New Jerusalem (Revelation 21: 19–20).

Marbode’s lapidary initiates a flowering of the lapidary tradition, both in Latin and in the vernacular languages. Four encyclopedic works of the thirteenth century incorporate lapidaries, all of them indebted to Pliny, Isidore, and Marbode, and are major contributions to the tradition: The Purposes of Things (De finibus rerum) by Arnold of Saxony, The Properties of Things (De proprietatibus rerum) by *Bartholomaeus Anglicus, The Nature of Things (De natura rerum) by *Thomas of Cantimpré, and The Great Mirror (Speculum maius) by *Vincent of Beauvais. In the same century the renowned scholar *Albertus Magnus compiled The Book of Minerals, for which he borrowed material from the lapidaries of Thomas, Arnold, and Marbode.

Vernacular lapidaries also begin to flourish in the thirteenth century. However, a work from outside this tradition, the Old English Lapidary, compiled between 950 and 1050, is certainly the earliest vernacular lapidary. Spanish and French versions of Marbode are extant in manuscripts of the twelfth century, and versions in those languages and in Italian circulate regularly from the thirteenth century onwards. *Alfonso X the Wise, king of Castile and Leon (1250–1284), encouraged production of numerous lapidaries, the best known of which organizes stones under the twelve signs of the zodiac. Still other French lapidaries are produced in significant numbers in the thirteenth and fourteenth centuries, and several were, in turn, translated into English. Among the most interesting is a late-thirteenth-century lapidary produced for a King Philip, probably Philip IV the Fair (1285–1314), which treats the stones in Aaron’s breast-plate and in Revelation. It circulated widely, to judge by the eleven known manuscripts, and was twice translated into English in the fourteenth and fifteenth centuries. It is related to a lapidary found in the French Sidrac, a late-thirteenth-century encyclopedic work that also enjoyed a wide circulation. Both Bartholomaeus Anglicus’s encyclopedia and the Secretum Secretorum were translated into numerous European vernaculars, which assured a wide audience for their information about stones.

The dissemination of information about stones is evident in a variety of medieval writings. In romances the heroine almost unfailingly presents a ring to the hero as he is about to set off on his adventures. In that ring is a magical jewel, usually of unspecified nature, which protects the hero in battle. In Wolfram von Eschenbach’s Parzival, Gahmuret, father of the hero, dies because goat’s milk is poured on his helmet of adamant, causing it to become as soft as a sponge. In the romances of Alexander the Great, his victory over the forces of Darius put him in possession of a land strewn with precious stones. In some versions Alexander finds the tomb of Ninus, the Assyrian king, which is carved from a single amethyst. In the Middle English Prose Alexander, after burying Darius, Alexander ascends to the throne of Cyrus by means of seven stairs, five of them made of precious stones, the properties of which are set forth in great detail, just as they appear in lapidaries. English medical treatises sometimes incorporate information about stones for their medicinal and other values; often these are simply entries taken from any of the popular lapidaries. A popular item concerns the use of jet: when placed in bed with a sleeping woman, the stone forces her to reveal her secrets to her husband. Household inventories show the value placed on the virtues of stones, particularly those that can indicate the presence of poison in foods. A particularly interesting archeological discovery is the fifteenth-century Middleham Jewel, found in 1985 after having been buried for centuries near Middleham Castle in Yorkshire, England. It consists of a sapphire set into a lozenge-shaped container for a holy relic. This container, inscribed with liturgical verses and two names for God commonly used as charms, unites the virtues of stones and the virtue of words with imagery of the Nativity of Jesus and of the Trinity. The Middleham Jewel provides an excellent context in which to understand the influence of the lapidary, which reveals to mankind useful mysteries of the Creator’s creation.

See also Magic and the occult; Mineralogy

Bibliography

Albertus Magnus. Book of Minerals. Translated by Dorothy Wyckoff. Oxford: Clarendon Press, 1967.

Bahler, Ingrid and Katherine Gyékényesi Gatto, eds. The Lapidary of King Alfonso X the Learned. New Orleans: University Press of the South, 1997.

Evans, Joan. Magical Jewels of the Middle Ages and the Renaissance Particularly in England. Oxford: Clarendon Press, 1922.

Fery-Hue, Françoise. La tradition manuscrite du Lapidaire du roi Philippe. Scriptorium (2000) 54: 91–192.

Jones, Peter Murray, and Lea T. Olsan. Middleham Jewel: Ritual, Power, and Devotion. Viator (2000) 31: 249–290.

Kitson, Peter. Lapidary Traditions in Anglo-Saxon England: Part I, the Background; the Old English Lapidary. Anglo-Saxon England (1978) 7: 9–60.

———. Lapidary Traditions in Anglo-Saxon England: Part II, Bede’s Explanatio Apocalypsis and Related Works. Anglo-Saxon England (1983) 12: 73–123.

Marbode of Rennes. De lapidibus. Edited by John M. Riddle. Wiesbaden: Franz Steiner Verlag, 1977.

Riddle, John M. Geology. In Medieval Latin: An Introduction and Bibliographical Guide. Edited by F. A. C. Mantello and A. G. Rigg, 406–410. Washington, D.C.: Catholic University of America Press, 1966.

GEORGE KEISER

“Latin Averroists”

Latin Averroism is a historiographical category that originated in the foundational work of the nineteenth-century French scholar Ernest Renan. Also sometimes known as radical or secular *Aristotelianism, it refers to the outlook of certain medieval and Renaissance natural philosophers who were inspired by the works of Averroes (*Ibn Rushd), a twelfth-century Islamic legist, physician, and philosopher from al-Andalus who wrote numerous commentaries on Aristotle. In the traditional account that stems from Renan’s work, Averroists are defined by their support for monopsychism, a term coined by Gottfried Wilhelm Leibniz, the eighteenth-century German philosopher, that refers to the belief that the human intellect is separate and numerically one, that the world is eternal, and that philosophical truths are independent of theological truths (the so-called doctrine of double truth). These positions were regarded as controversial because of their incompatibility with ecclesiastical positions and were at times censured, as for example in the *condemnation of 1277. Nevertheless, Averroes’ commentaries continued to be a prominent source for those interested in Aristotle until the mid-seventeenth century. The broad influence of his commentaries in the Latin West gave rise to his moniker “The Commentator.”

Accounts of Latin Averroism have emphasized its prominence at the end of the thirteenth century in Paris, where scholars such as *Siger of Brabant and *Boethius of Dacia discussed Averroes’ works and at times adopted or adapted his positions, and in fifteenth-century Bologna and Padua, where prominent professors of philosophy such as Nicoletto Vernia, Gaetano of Thiene, and Agostino Nifo grappled with his works. While these individuals identified themselves with some aspects of the Averroist tradition, they by no means represent its entire scope. The use of Averroes’ works as a guide to Aristotle was widespread from the time of their initial translation into Latin in approximately 1230 until 1630. The thorough expositions of his long commentaries and the conciseness of his middle commentaries and epitomes, which rendered a large number of Aristotle’s writings more intelligible, recommended his works to scholars. Furthermore, his stated goal of revealing the literal intent and mind of Aristotle was admired and emulated by his proponents. Nevertheless, his writings provoked scorn among others throughout Europe during the same period. *Thomas Aquinas, Ramon Llull, and Petrarch were among the scholars who wrote polemics against Averroes or Averroists.

While Averroes maintained a readership throughout the late Middle Ages and into the Renaissance, the translation of his commentaries came in two waves. The first wave took place in the first half of the thirteenth century and is associated with the work of *Michael Scot, William of Luna, and Hermann the German, who translated some fifteen commentaries on logic, ethics, and natural philosophy from Arabic into Latin. The Arabic versions of many of Averroes’ commentaries were no longer available soon after his death. Thus the second wave of Latin translations, which were printed a number of times by the Venetian Giunta press, used earlier Hebrew translations as the source for nineteen new Latin translations.

Perhaps the most notable position of Averroes and Latin Averroists was the contention that the active and passive parts of the rational soul were numerically one. This was based on interpretations of Aristotle’s writings about *psychology, in particular of passages in De anima III, which maintained that the intellective part of the soul was composed of two parts: one passive, the other active, sometimes referred to as the potential and the agent intellects. The agent intellect creates knowledge in the potential intellect by imprinting forms. Arguing against Avicenna (*Ibn Sina), who claimed that a separate single agent intellect illuminated each individual’s potential intellect, Averroes contended that all of humanity shared the same potential intellect, to which it was linked to through sensation. Thus, in Averroes’ view, the number of intellects is one and is not identical to the total number of human souls. The negative consequences of this argument for Christian teachings on personal immortality are significant and provoked numerous responses among defenders of ecclesiastical stances. Despite the controversial prominence of this position, it should be noted that the adoption of Averroes’ arguments and the use of his commentaries were not limited to this particular issue. His works were used as a guide to large portions of the Aristotelian corpus, much of which stirred little controversy while it served as a foundation for philosophy in the Middle Ages and Renaissance.

Bibliography

Endress, Gerhard and Jan A. Aertsen, eds. Averroes and the Aristotelian Tradition. Leiden: E.J. Brill, 1999.

Renan, Ernest. Averroès et l’averroïsme. Paris: Maisonneuve & Larose, 2002.

Wolfson, Harry A. The Twice-revealed Averroes. Speculum (1961) 36: 373–392.

CRAIG MARTIN

Latitude of Forms

In medieval natural philosophy and theology, the “latitude of forms” is the dimension of qualities in intensity. In a common example, heat’s intensity is called its latitude. The Latin word latitudo, which appears many times in the Vulgate translation of the Bible, primarily means “breadth,” as when a field is said to have length and breadth or a box is said to have length, breadth, and depth. The word can, however, also mean variability or range of variation. In ancient Greek medicine, health was thought to correspond to a balance or temperament of the bodily humors or fluids, whereas sickness was thought to correspond to an imbalance, meaning that the person or animal was too hot, cold, moist or dry. Deviations from the ideal balance or temperate state were classified into four degrees, with the first degree being moderate or even imperceptible, while the fourth degree would cause death. To be healthy, however, it was not necessary for the humors to be in a state of perfect balance; one could deviate from the ideal within an interval or latitude and still be healthy. Thus health, on this theory, has a latitude or corresponds to a range of conditions. In a related usage, it could be said in medieval economic or ethical theory that the just price for an item has a latitude: traders can agree on higher or lower prices within a certain range without their trade being considered unjust or unfair.

In medieval theology, the latitude of forms typically appeared in commentaries on *Peter Lombard’s Book of Sentences, Book I, distinction 17, in discussions of the Holy Spirit, grace, charity or love. In this context, grace, charity or love were considered to be habits of the human soul (understood as qualities of a substance, as heat may be a quality of a body). Charity or grace, freely given to humans by God, is what enables a human being to love or to do good works. Some humans have more charity or grace than others, so that there is a latitude of charity.

In scholastic natural philosophy and theology, the theory of the latitude of forms, sometimes known as the theory of the intension and remission or forms, was frequently deployed to address problems of many kinds. It is difficult to say whether the primary locus for the development of the theory was in theology or in natural philosophy. In any case, elaborations of theories of the latitude of forms in theology had repercussions on natural philosophy and vice versa. Aristotle had classified motions into three basic kinds: motion in place or locomotion, motion in quantity or augmentation and diminution, and motion in quality or alteration. He argued that motions in all three categories are continuous, insofar as what is gained in each motion is continuous. In medieval Aristotelian terms, the latitude of form gained in alteration is analogous to the distance gained in locomotion. But just as one part of a rotating body may traverse space faster or cover more space in a given time than another part, so one part of a body being heated may become hotter more quickly than another part. As the medium closer to a light source is brighter than a part of the medium farther away, so the part of a body closer to a heat source gains a greater latitude of heat than a part farther away. Hotness in a body could thus be said to have a “longitude” in the sense of an extension in the body (actually three extensions in the three dimensions of the body) and at the same time a latitude in intensity, which could vary from one part of the body to another. On the other hand, charity in a human soul has only intensity or latitude, because the soul is not corporeal and so is not extended in place.

In the later Middle Ages, two theories of the relation of degrees to latitudes of qualities were predominant. In one theory, which might be associated more or less closely with *Thomas Aquinas and which was often held by Dominicans, degrees of quality are indivisible and are related to latitudes as points are related to lines. In the other theory, associated with *Duns Scotus and often held by Franciscans, degrees of quality are not indivisible but are related to latitudes as shorter lines are related to longer lines. When degrees are considered indivisible, alteration may be said to occur by a “succession of forms,” a theory held by Gottfried of Fontaines and Walter Burley, among others. When degrees are considered as smaller continua, alteration may be said to occur by the addition of part to part, a theory expounded by Duns Scotus and widely held by later numerous natural philosophers.

The French natural philosopher and theologian *Nicole Oresme is famous for having proposed geometrical or graphical representations of latitudes of forms, sometimes called “configurations of qualities,” according to which the extension of the form in a body is represented by one line, on which perpendicular lines can be erected representing the intensities of form at each point. Then the area of the figure produced by such a scheme is said to represent the “quantity of quality.” When such a scheme is applied to the case of locomotion, the “extension” of the motion can be taken to be the time elapsed, the “intensity” of the motion at any instant is the velocity, and then the “quantity of the local motion,” or the area of the figure, is the distance traversed. Basing himself on work done earlier at Oxford, Oresme showed graphically that a uniformly accelerated body will traverse the same distance as a body that moves for an equal interval of time with the degree of velocity had at the middle instant of the accelerated motion. Theories of the latitude of forms were a part of the curriculum at late medieval and early modern universities, represented, for instance, by writings on the intension and remission of forms by Blasius of Parma and *Jacopo da Forlì. The theory of the latitude of forms was thus part of the intellectual tradition available to early modern scientists if they chose to use it.

See also Heytesbury, William of; Swineshead, Richard

Bibliography

Clagett, Marshall. The Science of Mechanics in the Middle Ages. Madison: University of Wisconsin Press, 1959.

———. Nicole Oresme and the Medieval Geometry of Qualities and Motions. A Treatise on the Uniformity and Difformity of Intensities Known as Tractatus de configurationibus qualitatum et motuum. Madison: University of Wisconsin Press, 1968.

Kaye, Joel. Economy and Nature in the Fourteenth Century. Money, Market Exchange, and the Emergence of Scientific Thought. New York: Cambridge University Press, 1998.

Maier, Anneliese. Zwei Grundprobleme der Scholastischen Naturphilosophie. Das Problem der Intensiven Grösse. Die Impetustheorie. 3rd. ed. Rome: Edizioni di Storia e Letteratura, 1968.

Murdoch, John, and Edith Sylla. “The Science of Motion.” In Science in the Middle Ages. Edited by David Lindberg. Chicago: University of Chicago Press, 1978.

Sylla, Edith. Medieval Concepts of the Latitude of Forms: The Oxford Calculators. Archives d’histoire doctrinale et littéraire du moyen-âge (1973) 40: 223–283.

EDITH DUDLEY SYLLA

Leather Production

Leather is a material produced from the skin of any vertebrate, whether mammal, bird, fish or reptile, by a series of processes that renders it non-putrescible under warm, moist conditions. A true leather will retain this property despite repeated wetting and drying. Other skin products, such as rawhide, parchment, and alum-tawed pelts, lose this resistance to microbiological attack when wet.

The use of hides and skins is thought to date from before the evolution of Homo sapiens, and the majority of cultures throughout the world have developed more or less complex skin-working techniques. By the pre-dynastic period in Egypt the three major types of tannage had already evolved, as follows:

(a) Treating the skins with fatty materials, such as brains and marrow, often in conjunction with a smoking stage. Fish oils were employed in medieval and later times for producing buff and chamois leathers;

(b) The use of *alum and salt together with various fatty lubricating materials. This technique seems to have been associated particularly with Middle Eastern and Mediterranean cultures;

(c) The vegetable tanning process in which prepared hides and skins are steeped in infusions of specific twigs, leaves, barks, or roots. This appears to have been the most widespread method employed for the production of heavier leathers in Europe in medieval times. Vegetable tanned leathers, however, do not seem to have been manufactured in Northern Europe in the earliest medieval period. Indeed the process seems to have been abandoned in Britain at the end of the Roman period and only reintroduced some centuries later.

The leathermaking crafts were divided into the “heavy” trades of the tanners and curriers and the “light” trades of the fellmongers, whittawyers, glovers, leather dressers, and skinners (fur dressers). The tanners and curriers processed thicker hides using the vegetable tanning process, whereas the light leather processors dealt with sheep, goat, and deer skins as well as those of dogs and other animals. The skinners processed the pelts of a wide range of animals, from cats and rabbits to ermines and squirrels.

The leathermaking processes fall into three groups: the pretanning operations where the skins are cleaned and their structure opened up; the tanning processes where the skin structure is stabilized chemically, and the post-tanning stages which give the desired characteristics to the final product.

In the pretanning operations, the hides were first washed to remove dirt, blood, and dung. They were then treated to loosen the hair, either by leaving them in warm, damp conditions until incipient putrefaction set in or by the action of alkalis such as wood ash or lime. When the hides were judged to be in the correct condition they were spread over a curved beam and the hair was scraped off using a blunt two-handled knife. After further alkali treatment the flesh (the subcutaneous membrane together with fat, muscle and other tissues) was cut off with a sharpened, two-handled knife. It was then cleansed further using enzymes produced either by fermenting barley or from warm suspensions of dog or pigeon dung. It was only after these operations, which could have taken up to three months, that the hides were ready for tanning.

With the vegetable tanning process the hides were first handled into and out of pits containing weak, previously used tanning liquors. The hides were then piled flat in pits with layers of ground vegetable tanning material spread between them. In England extracts of oak bark were employed but the material used depended on what was available locally. When the pit was full, strong, fresh extracts of tanning material were poured onto the hides and they were left for a year or more until the active ingredients had penetrated completely and reacted with the skin structure.

With the alum tawing process the pretanned pelts were thrown into wooden tubs containing a paste made from flour, salt, alum, and water together with lubricating materials such as egg yolk, butter, or olive oil. The paste was worked into the skins by trampling them underfoot. This process was repeated a number of times.

Oil tanning consisted of working marine oils into the pelt in a similar manner and then allowing the oil to oxidize. Cod, herring, seal and porpoise oils were used, and the operation was repeated until the leather was judged to be properly tanned. By the late medieval period fulling stocks similar to those employed in the wool textile industry were widely used to work the oil into the pelts.

Some leathers appear to have been prepared using a combination of alum and oil tannages, and some commentators have suggested that the renowned Cordoban leathers were made using a combination of alum and vegetable tannages.

In the case of heavy vegetable tanned leathers, the post-tanning operations were carried out by a separate group of craftsmen, called curriers. This separation of tanners from curriers appears to have been widespread throughout Europe and was a feature of the quality-control system imposed by the craft guilds. The currier shaved the hides to the required thickness with a specially shaped knife, impregnated them with a mixture of oils and fats, softened them mechanically and, where required, imparted a polished surface finish.

The strict division of tanning and post-tanning operations imposed by the heavy leather guilds was not found among light leather producers. These leathers, whether they were tanned by the oil, alum, vegetable, or combination process, were dyed using a range of natural dyestuffs, dried, softened mechanically and given the desired surface finish. Fur skins were washed, had the subcutaneous membrane cut off and processed in a similar manner to dehaired skins with oil, alum or, occasionally, vegetable tannins. After tanning, the skins were softened and the fur treated to give a rich sheen.

Bibliography

Cameron, E. Sheaths and Scabbards in England A.D. 400–1100. British Archeological Report 301, Oxford, 2000.

Thomson. R. Tanning—Man’s First Manufacturing Process? Transactions of the Newcomen Society (1981) 53: 139.

Thomson, R. “Leather Working Processes” in Esther Cameron, ed. Leather and Fur: Aspects of Early Medieval Trade and Technology. London: Archetype Publications (for the Archeological Leather Group), 1998.

Veale, E. The English Fur Trade in the Late Middle Ages. Oxford: Oxford University Press, 1956.

Waterer, J.W. Leather in Life, Art and Industry. London: Faber & Faber, 1946.

ROY THOMSON AND QUITA MOULD

Logic

Since medieval scientific culture is based mainly on the study of (authoritative) writings on the one hand and on oral disputations on the other, logic is the fundamental science providing the equipment for both coherent interpretation of texts and consistent argumentation in discussions. First, parts of the logical corpus of Aristotle (Organon, “Tool”), viz., On Interpretation and Categories, Porphyry’s Isagoge (“Introduction,” viz., to the Categories), pertinent writings by *Boethius, and entries in early *encyclopedias constituted the basis for the study of logic. In and after the twelfth century, the four parts of the Organon on arguments (Prior and Posterior Analytics, Topics, Sophistical Refutations) together with other sources such as Greek and Arabic commentaries, also became available in Latin. The complete corpus is known as the logica antiquorum (“Logic of the Ancients”), and consists of the logica vetus (“Old Logic”), i.e. the theory of terms and sentences, and the logica nova (“New Logic”), i.e., the theory of arguments. The new wealth of sources soon pushed Latin scholasticism to produce original contributions to Aristotelian logic as supplements (logica modernorum, “Logic of the Moderns”), viz., on the properties of terms, consequences (as a comprehensive theory comprising syllogistics and topics), insolubles, and obligations. Besides these important new translations of sources, the rise of the *universities especially had a significant impact on the history of logic. Every student of the higher faculties of law, medicine, and theology (where also disputations were held) had solid training in logic. The predominance of philosophy and logic at the faculty of arts, however, gave also rise to conflicts with theology, as is shown, for example, by the famous Parisian *Condemnation of 1277 and later discussions.

According to the dominant view of the Middle Ages, logic is the science of the valid argument. Since the validity of an argument depends on the truth-values of the sentences of which it is composed, and the truth-values of the sentences depend on the terms of which they are composed, medieval logic has the following structure: doctrine of terms, of sentences, and of consequences or arguments. The scientific status of logic is discussed within an Aristotelian framework, viz., whether it is a skill (ars) or a science (*scientia), and whether it is a practical or theoretical (speculative) science. The answers to these questions (already discussed in antiquity) depend on the respective definitions of those concepts. In this connection, the distinction between logica utens (“using logic”) and logica docens (“teaching logic”) was introduced as the distinction between the use of arguments (practical) and the reflection on arguments (theoretical). Generally, logic was construed as a practical attitude of the understanding whose immediate end is not pure knowledge, but good acting in the course of arguing and of acquiring knowledge. Insofar as logic is the necessary presupposition of all other sciences, it was called “scientia scientiarum” or “ars artium” or also a “tool” (Greek organon, Latin instrumentum, adminiculum). It was then further discussed, whether the field of logic is language (sermo) or reason (ratio: the Greek logos may mean both), what is reflected in the designations “scientia sermocinalis” vs. “rationalis.” As a science of reason, logic deals (according to *Ibn Sina) with concepts of a second level (intentiones secundae, such as the predicables) which are often construed as mere beings of thought (entia rationis in contrast to entia realia). From a modern point of view, the medieval concept of logic is quite large, insofar as it comprises or touches such disciplines as ontology, semantics, epistemology, philosophy of science, in addition to formal logic.

Terms (Termini)

Since logic is interested in the truth-values of sentences and arguments, terms (i.e., words and ideas or concepts in the sense of uncombined signs of the public and mental language) are the ultimate elements of analysis. Following Aristotle, a distinction between three levels of language is made and accordingly a distinction between written, spoken and mental terms. Such terms are either categorematic, i.e., meaningful in themselves, or syncatgorematic, i.e., functional only without proper meaning. Categorematic terms with their definite meaning (significatio) are either on the level of an object language or on that of a metalanguage (primae vs. secundae intentionis/impositionis). As terms of an object language they must belong to one of the ten Aristotelian categories. The framework of the object language can be described by means of the five terms of the metalanguage of Porphyry’s Isagoge (and Aristotle’s Topics) thus: every category divides into individuals, species and genera, and a species embraces a genus and a specific difference. These internal relations of the categories are necessary and essential and they are the basis for Aristotelian definitions by genus and difference. Relations between categories, however, are contingent. Medieval realism holds that Aristotelian species and genera have existence independently of thought and language and accordingly it holds also that objects (and not only words or concepts) are predicated; finally, it sees the categories as a classification of reality. These very points are rejected by the opposite party of nominalism or conceptualism.

Syncategorematic terms build sentences out of categorematic terms (as the copula, the verb “is” connects subject and predicate), quantify those sentences (signa distributiva, such as “every” or “some”), or negate them, or build more complex sentences out of them (“and,” “or,” “if”).

Properties of Terms (Proprietates Terminorum)

As soon as categorematic terms enter a sentence, they acquire “properties” or functions conditioned by the context. Disregarding any of these functions may cause fallacies, and the theory was first developed also in this connection. The variable list of such properties comprises mainly suppositio, copulatio, appellatio, ampliatio, and restrictio. At first, supposition was regarded as the property of subjects (logically) or substantives (grammatically), and copulation as the property of predicates or adjectives and verbs, but that distinction was soon neglected, so that supposition then was construed as the property of subjects as well as predicates, both of which counted as nouns in a large sense. Thus, supposition became the most important property of terms: it served as a classification of that for which a term in the context of a sentence stands, and in which manner it does so. The first function generated three main species of supposition. A general term in the context of a sentence may stand for: (1) The individuals to which it applies; (2) The universal; (3) Itself or a similar term. Case (1) is known as “personal supposition,” e.g., “A man walks”; case (2) “simple supposition,” e.g., “Man is a species”; case (3) “material supposition,” e.g., “Man is a noun.” First, these examples show that in all three of these cases it is the same (type of) term “man” which supposits in the different ways respectively, and that the cases are not distinguished by different terms. Second, they show that ontology (the debate over universals) plays a role here: nominalists interpreted the signification of a general term as the extensional reference to the individuals to which it applies, realists saw it as the intensional meaning of the corresponding universal (res universalis, forma or natura communis). Accordingly, personal supposition for the nominalists is significative (i.e., corresponding to the original signification) and primary, whereas simple supposition as reference to the universal in the sense of a mental concept is nonsignificative (“man” is not true of the concept of man) and secondary. For the realists, on the contrary, since the intension of a term fixes its extension, simple supposition has semantic primacy. The debate between *William of Ockham and Walter Burley in the fourteenth century is a good example of differences in semantics and ontology.

According to the respective quantity and quality of the sentence, a term in personal supposition refers to its extension differently. The subdivision of personal supposition is carried out with the concepts of descent under and of ascent to a general term. Singular terms supposit discretely, general terms supposit commonly, and that in different ways: In the sentence “Some man walks,” e.g., the descent under the subject term “man” leads to a disjunction of singular sentences, “This man walks,” or “that man walks,” etc., and from each part of the disjunction one can assent to the original general sentence. This mode of common personal supposition is called “determinate.”

In the early period of “modern” logic, the property of appellation meant the reference of a general term to existent individuals. Later on it was used with regard to intensional, temporal and modal contexts. For example, in the sentence “A white thing was black,” the predicate “black” has appellation in the sense that it must have been predicable truly at some past time of the thing referred to by the subject. But the subject term “a white thing” has the property of ampliation in the sense that being black was true of something which is or was white.

Sentences (Propositiones)

Sentences are expressions (orationes) of a special kind, in which a predicate is said (affirmatively or negatively) of a subject, making such expressions true or false. The structure of simple sentences is generally conceived as tripartite (subject + copula + predicate); because of the Aristotelian primacy of the “first” (i.e., individual) substances as the ultimate subjects of predication, the canonical form of an atomic sentence is thus: singular term + copula + general term. The categorematic constituents of a sentence are called its “matter,” the syncategorematic ones are the “form of the sentence.” The matter of sentences is “natural” when the predicate belongs necessarily to the subject, and “contingent” when the predicate may belong to the subject; it is “remote” when it is impossible for the predicate to belong to the subject. Sentences having the structure subject—copula—predicate are called “categorical,” compounds of several sentences are called “hypothetical.” Categorical sentences differ according to quantity (singular vs. general, i.e., indefinite, particular, universal) and quality (affirmative vs. negative). If the copula is not modally determined, the sentence is assertoric (de simplici inesse/inhaerentia), if it is modally determined, the sentence is a modal one (de inhaerentia modificata), e.g., “Socrates is necessarily an animal.” This example is a case of a modal sentence in the “divided” sense and corresponds to the modern notion of a de re modality. There is also a “composite” sense, if the modal operator does not refer to the copula, but to the complete that-clause (“de dicto”), e.g., “It is necessary that Socrates is an animal.” The truth-conditions (causae veritatis) for all these sorts of sentences are stated in the pertinent treatises. A philosophical matter of dispute, especially in the fourteenth century, is the signification of sentences, viz., whether they signify things in the Aristotelian categories or states of affairs in addition to such things.

Consequences (Consequentiae)

Consequences are hypothetical sentences consisting of (at least) two categorical sentences as antecedent and consequent, together with a sign of consequence (nota consequentiae), viz., an “if” in front of the antecedent, or a “therefore” in front of the consequent. The definition of a valid consequence as truth-preserving (if the antecedent is true, the consequent cannot be false) is problematic for the scholastics, because it is related to sentences which are ephemeral lingual or mental beings. For that reason it is sometimes defined in terms of the signification of the antecedent and consequent.

Consequences are either formal or material: formal consequences hold in virtue of their form alone (i.e., in virtue of their syncategorematic constituents in a certain arrangement), whereas in material consequences the validity also depends on the matter (the categorematic terms). Material consequences are further divided into simply valid ones (simpliciter), and conditionally valid ones, viz., only valid right now (ut nunc): “A man walks, therefore an animal walks” is simply valid, because the relation of species to genus is necessary. On the other hand, “Buridan walks, therefore a professor walks” is only valid for the time when Buridan is actually a professor (in other words, the relation of substance to accident is contingent).

The most important kind of formal consequences is the syllogism, as it is laid down by Aristotle in the Prior Analytics. The antecedent there consists of (the conjunction of) two sentences, the major and minor premises, and three terms, major, middle, and minor term. The consequent is the conclusion drawn from these premises, in which the middle term no longer occurs. The arrangement of the three terms in the two premises yields four syllogistic figures (of which the fourth is a matter of dispute). Together with the quantity and quality of the sentences, there are then different modes (of which nineteen are generally held to be valid) for which the scholastics coined the names “Barbara,” “Celarent,” etc., which can be easily remembered. Only syllogisms of the first figure are complete, in the sense of evident, whereas the other figures require proofs that consist in making reductions to the first figure with the help of other inferences, such as conversion. There are several kinds of syllogisms, according to the different kinds of terms (finite vs. infinite, nominative vs. oblique case) and sentences (categorical vs. hypothetical, assertoric vs. modal). Lists of rules were carefully stated for all of these. Important medieval contributions to syllogistics concern expository syllogisms (which have a singular premise) and modal syllogisms.

Insolubles (Insolubilia)

Insolubles were defined as sentences whose solution is difficult, in the sense that it is hard to determine their truth-values. This was especially true of semantic paradoxes of self-reference. The Liar Paradox has been the classical example since antiquity. Self-referential paradoxes were dealt with in many variants, e.g., “This sentence is false”; the problem is whether this sentence is true or false. Among the most prominent medieval solutions of this paradox (besides the Aristotelian theory of fallacies) were the following: the theory of cassatio, which held that such a sentence is meaningless, because nothing is asserted in it, and therefore is neither true nor false. The theory of restrictio simply forbade self-reference altogether, but usually no satisfying criterion for distinguishing between acceptable and vicious self-reference was given. A variant of this is the theory of transcasus, which is based on the intuition that sentences can change their truth-value over the course of time; in principle, it is denied again that the semantic predicate “false” may apply to the very sentence whose part it is. Finally, there is the theory of a twofold signification of sentences: direct signification is due to the predicate, indirect signification is due to the copula by which the sentence is asserted to be true. Therefore, the insoluble in question is false, because it signifies itself to be both true and false. A comprehensive list of fifteen solutions is given by Paul of Venice (d. 1429) in his Logica magna. Many other insolubles and sophisms are discussed by the scholastics with great subtlety, e.g., regarding the concepts of beginning and ceasing, exception and exclusion, part and whole, etc.

Obligations (Obligationes, Ars Obligatoria)

Closely related to consequences and insolubles, both in theory and in teaching, is the theory of obligations. This is the most peculiar medieval contribution to the history of logic. Its purpose was presumably the training of students in consistent argumentation. The name “obligation” is derived from the fact that of two disputants, the “respondens” is obliged to react according to certain rules to a sentence (positum) put forward by the “opponens.” Within the scope of these rules, the opponent tries to drive the respondent into making contradictions, and the latter tries to resist these attempts. In the case of the species of obligation called “position,” a contingently false sentence is usually put forward, e.g., “You are in Rome” when the disputation is held at Paris. The respondent admits the positum which then becomes the “obligatum.” The opponent then puts forth further sentences, to which the respondent can reply in three different ways: “I concede this,” “I deny this,” “I doubt this.” These possibilities of replying depend on the logical relation which the new propositum bears to the original positum, viz., whether it follows from it (pertinens sequens), contradicts it (pertinens repugnans), or is logically independent of it (impertinens). If the logical relation of a new propositum is only to the first positum, the obligational game follows the lines of the so-called “New Response,” if it is to the previous entire game, it follows the “Old Response.” The main rules according to which the respondent has to reply to new proposita are the following: everything that follows has to be conceded; everything that contradicts has to be denied; everything that is logically independent has to be conceded, if it is known to be true, or denied, if it is known to be false, or doubted, if it is neither, i.e., uncertain. Insolubles and sophisms then serve to show that all possibilities of the respondent lead to offenses against the rules, once a vicious positum has been admitted. The solutions which are given in the relevant treatises point out the deficiencies of such an obligational dispute.

See also Abelard, Peter; Albert of Saxony; Aristotelianism; Boethius; Bradwardine, Thomas; Buridan, John; Heytesbury, William of; Kilwardby, Robert; Marsilius of Inghen; Metaphysics; Nature: diverse medieval interpretations; Petrus Hispanus; Pierre d’Ailly; Translation movements

Bibliography

Primary Sources

Buridan, John. Summulae de dialectica. Translated by Gyula Klima. New Haven: Yale University Press, 2001.

Burley, Walter. On the Purity of the Art of Logic. The Shorter and the Longer Treatises. Translated by Paul Vincent Spade. New Haven: Yale University Press, 2000.

Kretzmann, Norman and Eleonore Stump, ed. The Cambridge Translations of Medieval Philosophical Texts. Vol. 1. Logic and the Philosophy of Language. New York: Cambridge University Press, 1988.

Marsilius of Inghen. Treatises on the Properties of Terms. Edited and translated by Egbert P. Bos. Dordrecht: Reidel, 1983.

Paulus Venetus (Paul of Venice). Logica magna. Oxford: Oxford University Press, 1978–1991.

(Petrus Hispanus. Tractatus called afterwards Summule logicales.) Peter of Spain. Language in Dispute. Translated by Francis P. Dinneen. Amsterdam: Benjamins, 1990.

(William of Ockham.) Ockham’s Theory of Terms. Part I of the Summa logicae. Translated by Michael J. Loux. Notre Dame: University of Notre Dame Press, 1974.

(———.) Ockham’s Theory of Propositions. Part II of the Summa logicae. Translated by Alfred J. Freddoso and Henry Schuurman. Notre Dame: University of Notre Dame Press, 1980.

William of Sherwood. Introduction to Logic. Translated by Norman Kretzmann. Minneapolis: Minnesota University Press, 1966.

Secondary Sources

Ashworth, E. J. Language and Logic in the Post-Medieval Period. Dordrecht: Reidel, 1974.

Biard, Joël. Logique et théorie du signe au XIVe siècle. Paris: Vrin, 1989.

Broadie, Alexander. Introduction to Medieval Logic. 2nd Edition. Oxford: Clarendon Press, 1993.

Grass, Rainer. Schlußfolgerungslehre in Erfurter Schulen des 14. Jahrhunderts. Eine Untersuchung der Konsequentientraktate von Thomas Maulfelt und Albert von Sachsen in Gegenüberstellung mit einer zeitgenössischen Position. Philadelphia: Grüner, 2003.

Green-Pedersen, Niels J. The Tradition of the Topics in the Middle Ages. Munich: Philosophia, 1984.

Jacobi, Klaus, ed. Argumentationstheorie. Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns. Leiden: E.J. Brill, 1993.

Kann, Christoph. Die Eigenschaften der Termini. Eine Untersuchung zur Perutilis logica Alberts von Sachsen. Leiden: E.J. Brill, 1994. (Includes a Latin edition of Treatise II of Albert of Saxony’s Logica.)

Keffer, Hajo. De obligationibus. Rekonstruktion einer spätmittelalterlichen Disputationstheorie. Leiden: E.J. Brill, 2001.

Kretzmann, Norman, Anthony Kenny and Jan Pinborg, ed. The Cambridge History of Later Medieval Philosophy. New York: Cambridge University Press, 1982.

Lagerlund, Henrik. Modal Syllogistics in the Middle Ages. Leiden: E.J. Brill, 2000.

Nuchelmans, Gabriel. Theories of the Proposition. Ancient and Medieval Conceptions of the Bearers of Truth and Falsity. Amsterdam: North-Holland, 1973.

Pironet, Fabienne. The Tradition of Medieval Logic and Speculative Grammar. A Bibliography (1977–1994). Turnhout: Brepols, 1997. (A continuation of E. J. Ashworth’s bibliography, Toronto: Pontifical Institute of Mediaeval Studies, 1978.)

Read, Stephen, ed. Sophisms in Medieval Logic and Grammar. Acts of the Ninth European Symposium for Medieval Logic and Semantics, held at St Andrews, June 1990. Dordrecht: Kluwer, 1993.

Rijk, L. M. de. Logica Modernorum. A Contribution to the History of Early Terminist Logic. Two volumes in three parts. Assen: Van Gorcum, 1962 and 1967.

Shank, Michael H. “Unless You Believe, You Shall Not Understand.” Logic, University, and Society in Late Medieval Vienna. Princeton: Princeton University Press, 1988.

Thom, Paul. The Syllogism. Munich: Philosophia, 1981.

———. Medieval Modal Systems. Problems and Concepts. Aldershot: Ashgate, 2003.

Yrjönsuuri, Mikko. Obligationes. 14th Century Logic of Disputational Duties. Helsinki: Societas Philosophica Fennica, 1994.

———, ed. Medieval Formal Logic. Obligations, Insolubles and Consequences. Dordrecht: Kluwer, 2001.

Paul V. Spade. Medieval Logic and Philosophy. May 23, 2004. URL = <http://www.pvspade.com/Logic/>

Gyula Klima. Society for Medieval Logic and Metaphysics. February 19, 2005. URL = <http://www.fordham.edu/gsas/phil/klima/SMLM/>

Edward N. Zalta, ed. The Stanford Encyclopedia of Philosophy. (Spring 2005 Edition). URL = <http://plato.stanford.edu/>

HARALD BERGER

Lombard, Peter

Born in the environs of Novara toward the end of the eleventh century, Peter Lombard’s early life is virtually unknown until his migration north of the Alps to study at the cathedral school of Rheims, about 1134. By 1136, he had moved on to Paris, where he probably was an external student at the school of St. Victor, under the celebrated master, *Hugh. By 1144/1145, he had become a canon of Notre Dame, itself an accomplishment for a foreigner among the closed French, privileged chapter of the cathedral; Peter’s advancement there speaks to his academic accomplishments during the previous decade. As he advanced in the ecclesiastical ranks, he continued to teach in the cathedral school, his lectures the genesis of works in theology and hermeneutics. In 1159, he became bishop of Paris but died scarcely a year later, on July 21 or 22, 1160.

Peter’s works include slightly more than thirty sermons that have survived, a commentary on the Psalms completed before 1138 and commentaries on the Pauline epistles (known collectively as the Collectanea) composed between 1139 and 1141 and revised between 1155 and 1158. Recent scholarship suggests that Peter glossed virtually the entire Bible, a work that he probably bequeathed to the chapter, but which now appears to have been lost. But without question, the most significant of his works was the Sententiae in IV libri distinctae, the result of his course in systematic theology taught at Paris for two decades and published in its final form between 1155 and 1157.

The Lombard’s Sentences are emblematic of a movement beginning in the late eleventh century to develop a systematic theology as a science in its own right. Prior to 1150—and even after the composition of the Sentences—there were many attempts to collect and organize the central tenets of Western Christian doctrine but, as Marcia Colish has shown, they were inferior to Peter’s version in organization, comprehensiveness, coherence, use of source materials, and pedagogical utility. After a brief prologue, in which he professes to limit personal speculation while remaining close to the positions of the Fathers [Sicubi vero parum vox nostra insonuit, non a paternis dicessit limitibus], Peter divides his work into four books, each progressing farther into the historical and doctrinal positions of Christianity. Book I focuses on the existence, trinity, and attributes of God; Book II covers the creation, man, sin, liberty, and grace; Book III is devoted to Christology, redemption, virtues, and commandments; Book IV concludes with the sacraments and eschatology.

While the Sentences did not receive immediate and unanimous acceptance—in his own century, the Lombard’s positions on Christology and the Trinity were attacked, and in the thirteenth century readers such as *Robert Grosseteste and *Roger Bacon worried that the work threatened to displace the Scriptures in the theological curriculum—several early developments helped ensure its eventual canonical position within theological faculties and religious schools across Europe. First, Peter himself seems to have formatted the text for pedagogical use, employing rubrics to indicate patristic citations and parts of the text. Beginning in the twelfth century, the text was glossed according to the medieval technique of accessus ad auctores, indicating that Peter was already esteemed as a significant authority. By about 1222, the Franciscan Alexander of Hales (c. 1180/1190–1245) had begun using it as the text for his theological course at Paris; its subsequent adoption throughout the university and the preeminence of Paris gave the Sentences enormous prestige elsewhere. And finally, Alexander modified the text by devising distinctiones to facilitate precise citations of passages from the Sentences, emulating a technique already adopted by users of Gratian’s Decretum and later adapted to Aristotle’s works. As a result, the Sentences acquired the intellectual cachet invested in these other works, and together they became the significant pedagogical tools of the legal, theological, and arts faculties of nascent universities.

Aside from its role in the theological curriculum, the Sentences also offered opportunities to develop extra-theological, including scientific, issues. Part of the reason for this derives from the educational course followed by students in the late Middle Ages. Whether in arts faculties or schools of religious orders, students lectured on the Sentences following a previous exposure to the philosophical curriculum, chiefly the works of Aristotle. Moreover, the text of the Sentences itself displays Peter’s tendency, like that of many of his contemporaries, to formulate positions using Aristotelian terminology and concepts. Consequently, the Lombard’s discussion of particular topics in the Sentences became a traditional locus for elaboration and expansion of scientific positions.

One such occurs at the very beginning of the work itself. The opening line of Book I, chapter 1, “Omnis doctrina est de rebus vel de signis,” although quoting Augustine’s De doctrina christiana, echoed the incipit to the Posterior Analytics [“Omnis doctrina et omnis disciplina intellectiva fit ex praeexistenti cognitione…”]; readers of both texts drew inspiration from speculative grammar investigations of the relationship between signs and reality. Moreover, twelfth-century prologues to commentaries addressed questions about the author’s intentions, the materia of the work, the branch of knowledge to which it belonged, and its modus tractandi, among other things. This gradually evolved into an “Aristotelian” prologue focused on the four causes: the subject matter, the formal mode of treatment, the authorship, and the final cause or purpose of the work. Throughout the thirteenth century, and extending into the early fourteenth century, commentators on the Sentences devoted considerable space in their prologues to questions regarding the very nature of theology as a potentially scientific discipline along the lines of Aristotle’s emerging views and, by extension, to discussions of the nature of science, the relationships between human and divine science, and theoretical foundations of scientific disciplines.

A second instance occurs near the end of Book I, where Peter Lombard takes up the question of whether God can do better or different than He does. This was one of the most contentious issues of the twelfth century, and already before Peter addressed it, *Peter Abelard had responded negatively, collapsing God’s power and will and arguing that what God wills, He must do necessarily. Although he was not the only one to do so, Peter Lombard vigorously opposed this position, and while he never actually used the terms potentia ordinata and potentia absoluta, much of his discussion hinges on this distinction that bore considerable fruit later when applied to the inviolability of Aristotle’s discussions of nature. As a result, Book I, d. 44 became a frequent site for such questions as “Whether God could make a better world than this world?”

Finally, in taking up sacramental theology in Book IV, Peter examines the status of accidental properties of bread and wine that remain after the sacramental change in the Eucharist. One position that he raises but dismisses is the incomplete change of the elements, so that the accidental properties might inhere in what remains of the bread and wine. The alternative, with which he is clearly not satisfied, is that the substance of bread and wine is totally annihilated and the “accidents remain, subsisting by themselves” [IV, d. 12. c. 1]. Not only did this invite continued discussion of hylomorphic aspects of Eucharistic doctrine, but by the early fourteenth century, issues of motion and the nature of impetus as a causal mechanism came to be applied to sacramental discussions as well.

Fifteenth-century drawing of Peter Lombard. (Corbis)

See also Aristotelianism; Hylomorphism; Scholasticism; Scientia; Vocabulary

Bibliography

Brown, Stephen F. “The Reception and Use of Aristotle’s Works in the Commentaries on Book I of the Sentences by the Friar Preachers in the Early Years of Oxford University.” In Aristotle in Britain during the Middle Ages: Proceedings of the International Conference at Cambridge, 8-11 April 1994 organised by the Société Internationale pour l’Etude de la Philosophie Médiévale. Edited by John Marenbon. Turnhout: Brepols, 1996, pp. 351–369.

Colish, Marcia L. Peter Lombard. 2 volumes. Leiden: E.J. Brill, 1994.

Lombard, Peter. Sententiae in IV libris distinctae. 3rd edn. Edited by I. Brady. Grottaferrata: Collegio S. Bonaventura, 1971–1981.

Medieval Commentaries on the Sentences of Peter Lombard. Current Research. Volume 1. Edited by G. R. Evans. Leiden: E.J. Brill, 2002.

Murdoch, John E. “From Social into Intellectual Factors: An Aspect of the Unitary Character of Late Medieval Learning.” In The Cultural Context of Medieval Learning. Edited by John E. Murdoch and Edith D. Sylla. Dordrecht, Holland; Boston: D. Reidel, 1975, pp. 271–348.

Stegmüller, Friedrich. Repertorium commentariorum in Sententias Petri Lombardi. 2 volumes. Würzburg: Schoningh, 1947; V. Doucet. Supplément. Florence: Coll. S. Bonaventurae, 1954.

Sylla, Edith D. “Autonomous and Handmaiden science: St. Thomas Aquinas and William of Ockham on the Physics of the Eucharist.” In The Cultural Context of Medieval Learning. Edited by John E. Murdoch and Edith D. Sylla. Dordrecht, Holland; Boston: D. Reidel Pub. Co., 1975, pp. 349–391.

STEVEN J. LIVESEY

Bringing Surgery into Medicine

Bibliography

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Secondary Sources

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Secondary Sources

Terms (Termini)

Properties of Terms (Proprietates Terminorum)

Sentences (Propositiones)

Consequences (Consequentiae)

Insolubles (Insolubilia)

Obligations (Obligationes, Ars Obligatoria)

Bibliography

Primary Sources

Secondary Sources

Bibliography

L

Lanfranco of Milan

Lapidaries

“Latin Averroists”

Latitude of Forms

Leather Production

Liuzzi, Mondino De’

Logic

Lombard, Peter