ALBERT OF SAXONY

(b. Helmstedt, Lower Saxony, c. 1320; d. Halberstadt, Saxony, 8 July 1390)

physics, logic, mathematics. For the original article on Albert of Saxony see DSB, vol. 1.

Recent research has revealed more information about Albert’s life and writings. For example, although his contributions to natural philosophy reflected his reading of John Buridan and Nicole Oresme, they also contained many original elements.

Biographical Information. Albert of Saxony’s name appears for the first time in the records in 1351, when he obtained the degree of master of arts at the University of Paris under master Albert of Bohemia. This date implies that he must have been in Paris at the end of 1350. He was probably born in 1320 (not in 1316, as has been traditionally assumed). It is very unlikely that Albert studied at the University of Prague before moving to Paris. The university in Prague was only founded in 1349, and the curricular requirements at Prague and at Paris exclude such a transition. Although there are no records, it is more likely that Albert would have received his early training at schools in his diocese, at Halberstadt or Magdeburg, and then moved to the studium generale of Erfurt. Only one work, if it is authentic, dates from the pre-Paris period, the Philosophia pauperum, which has references to Erfurt.

Once in Paris, Albert became involved in administrative duties for the English-German nation to which he belonged, and for the entire arts faculty. He was proctor, examiner, receptor, and in 1353 rector. In 1352 and 1355, he was one of the members of the committee who prepared the list of applications for papal benefices for university masters (rotulus).

In addition to these administrative duties, Albert was chiefly concerned with teaching and writing. The university

records show the names of approximately forty students who obtained their master’s degree under Albert. His more than twenty writings, which cover logic and natural philosophy, but also ethics, are usually in the literary format of commentaries on Aristotle, and all originated at Paris. In addition, he started his study in theology as early as 1353 but he never finished, and there are no writings in this discipline.

Probably in 1361 Albert left Paris. The period 1362– 1364 in Albert’s career is blank, but the two letters that bind this period indicate that he was busy at Avignon for Pope Urban V and in Vienna at the court of Duke Rudolph IV. He was involved in the founding of the University of Vienna in 1365, and became its first rector. Because of the death of Duke Rudolph IV, and the ensuing rivalry between his two brothers, the university did not flourish and had only a faculty of arts. The university was reestablished in 1383–1384. Albert of Saxony left Vienna within a year, to become bishop of Halberstadt in 1366. He remained bishop until his death on 8 July 1390.

Writings on Natural Philosophy. Although several works by Albert of Saxony have been edited since the original DSB article, it is not possible yet to place his thought within its fourteenth-century context. It seems clear, however, that the assessment in the original DSB article that Albert of Saxony depended heavily on the works by Buridan, and lacked originality, needs to be revised. In the past, Albert of Saxony, together with Oresme and a few other Parsian thinkers, has been perceived as a proponent of the Buridan school, with all the connotations that this label may have, such as that of student-teacher relationships, and a unified homogeneous school of thought. Closer examination of the doctrines and dating of texts has replaced this picture of the Buridan school with that of a small intellectual network of nearly contemporary masters of arts, who were familiar with each others’ work and at times responded to one another.

Albert of Saxony’s most important work in logic is his Perutilis logica (Very useful logic), written around 1356. It is a handbook in logic, organized into six treatises. It covers all the basics of medieval logic, such as propositions, properties of terms, consequences, fallacies, insolubles, and obligations. Although the influence of William of Ockham is discernible, it is an independent treatise with its own original twists. Albert distances himself in many respects from Buridan’s logic. Another logical work from about the same period is the Quaestiones circa logicam(Questions on Logic). This is a set of disputed questions about the signification of terms, reference, and truth. The Sophismata, a set of propositions whose interpretation raises semantic problems because of the presence of certain logical terms, shows the influence of William of Heytesbury. Albert’s solutions to the semantic difficulties rely on Heytesbury’s theory of sensus divisus and compositus, that is, the position and scope of modal operators in propositions.

One of Albert’s most important works in natural philosophy is his Quaestiones super libros Physicorum, a question-commentary on Aristotle’s Physics. It raises many of the problems that are also raised in Buridan’s question-commentary. The relation between the two works, however, is more complex than was initially thought. It is clear in the early 2000s that Albert of Saxony had access to a previous version of Buridan’s question-commentary on the Physics, the so-called tertia lectura. In his final version of the question-commentary on the Physics, Buridan responded to Albert of Saxony. In other words, Albert’s Quaestiones on the Physics are chronologically located between Buridan’s tertia lectura and his ultima lectura. Albert of Saxony’s Quaestiones super libros Physicorum are usually dated shortly after 1351. This date is suggested by one of its copies, whose introductory remarks tie the text to Albert’s opening lecture (principium) on Aristotle’s Physics, which was held in 1351. This does not imply, however, that the entire commentary was finished by that time. The most plausible conclusion is that the work must have been finished sometime between 1352 and 1357, before Buridan’s ultimate question-commentary.

Buridan and Albert of Saxony held opposing views about the ontological status of spatial extension. In general, medieval thinkers believed that spatial extension belonged in the category of quantity, and that some substances, such as bodies, have extension as their most important feature. However, not only the substance of body, but also many of its qualities were considered to be extended. The dimensions of Socrates’s whiteness, for instance, were believed to coincide with Socrates himself, that is, with substance. But is it really accurate to equate quantity with substance and quality, respectively, or should quantity be considered a separate entity? Buridan held the latter view. One of the many arguments in support of this position hinges on the phenomenon of condensation and rarefaction. Experience teaches that the extension or quantity of a given substance can vary, whereas the amount; of substance and its quality remain constant: no new parts of substance are added, nor any destroyed (in contrast to the phenomena of growth and diminution). Albert of Saxony defended the position that extension or quantity coincides with substance. He attributes condensation and rarefaction to the local motion of the parts, which supposedly have some kind of elasticity.

On the question of the ontological status of motion, Albert follows the view of Ockham that motion is not something different from the moving body. However, on the basis of an argument involving God’s supernatural interference, he concludes that motion is an inherent flux in a moving body. In other words, motion is a distinct property of a body, a position Buridan also defended.

In his discussion of projectile motion, Albert qualifies Buridan’s view as the truest view (quam pro nunc reputo veriorem). It attributes the projectile’s motion to a certain motive force, a virtus motiva or virtus impressa, an impressed power. Albert does not use the term impetus. Buridan introduced this new term only in his last version of his question-commentary on the Physics, which Albert did not know. Albert interprets Aristotle’s views with respect to motion and velocity, in Physics book 7, in accordance with Bradwardine’s rules. In an effort to solve the apparent contradictions between Bradwardine’s approach and Aristotle’s text, Albert states that Aristotle’s text has probably been mistranslated.

Albert’s discussion of the void shows striking similarities to that by Oresme. He must have known Oresme’s Physics. Albert’s well-organized question-commentary on Aristotle’s De caelo provides further evidence of his thoughtful and independent approach to contemporary issues in natural philosophy. Albert includes many questions that had been raised by both Oresme and Buridan, but approximately one-third of Albert’s fifty-six questions do not appear in the De caelo questions of Oresme and Buridan. Also noteworthy is that, unlike almost all other scholastic natural philosophers, Albert grouped related questions together under three major themes. This broke with the traditional way of organizing questions by simply following Aristotle’s text.

What emerges from these varied examples is that Albert of Saxony was not a plagiarizer, but rather that he was well versed in the works of some of his contemporaries and used them in his own philosophical endeavors.

SUPPLEMENTARY BIBLIOGRAPHY

A survey of all of Albert of Saxony’s works and the known manuscript sources is provided in Jürgen Sarnowsky, Die aristotelisch-scholastische Theorie der Bewegung (see below). See further Olga Weijers, Le travail intellectuel à la faculté des arts de Paris: Textes et maîtres (ca. 1200–1250), vol. 1 (Turnhout, Belgium: Brepols, 1994); also the extremely useful bibliographical guide by Harald Berger, “Albert von Sachsen (1316?–1390): Bibliographie der Sekundärliteratur” and its supplements (see below).

WORKS BY ALBERT OF SAXONY

Muñoz García, Angel. Perutilis logica, o, Lógica muy útil (o utilísima). México: Universidad Nacional Autónoma de México, 1988. Provides a transcription (and a Spanish translation) of the incunabular edition (Venice 1522) of Albert’s logical handbook.

Kann, Christoph. Die Eigenschaften der Termini: Eine Untersuchung zur “Perutilis Logica” des Alberts von Sachsen. New York: Brill, 1994. Includes an edition of treatise two of the Perutilis logica.

Patar, Benoît. Expositio et Quaestiones in Aristotelis libros Physicoram ad Albertum de Saxonia attributae. 3 vols. Louvain: Editions Peeters, 1999. The authenticity of this question-commentary by Albert of Saxony has never been doubted, except by this editor. He believes that the text is the first version of the commentary by John Buridan, but his thesis is not supported by textual or paleographical evidence.

Fitzgerald, Michael J. Albert of Saxony’s Twenty-Five Disputed Questions on Logic. Leiden: Brill, 2002. Provides a critical edition of a set of logical disputations, the so-called Quaestiones circa logicam.

OTHER SOURCES

Berger, Harald. “Albert von Sachsen (1316?–1390):

Bibliographie der Sekundärliteratur.” Bulletin de Philosophie Mediévale 36 (1994): 148–185.

———. “Fortsetzung und Ergänzungen zur Bibliographie der Sekundärliteratur.” Bulletin de Philosophie Mediévale 37 (1995): 175–186.

———. “Albert von Sachsen (+1390): 2. Fortsetzung und Ergänzungen zur Bibliographie der Sekundärliteratur.” Bulletin de Philosophie Mediévale 38 (1996): 143–152

.———. “Albert von Sachsen (+1390): 3. Fortsetzung und Ergänzungen zur Bibliographie der Sekundärliteratur.” Bulletin de Philosophie Mediévale 40 (1998): 103–116.

———. “Albert von Sachsen (+1390): 4. Fortsetzung und Ergänzungen zur Bibliographie der Sekundärliteratur” Acta Mediaevalia 17 (2004): 253–279.

Biard, Joël. “Les sophismes du savoir: Albert de Saxe entre Jean Buridan et Guillaume Heytesbury.” Vivarium 27 (1989): 36–50

.———, ed. Itinéraires d’Albert de Saxe, Paris-Vienne au XIVe siècle: Actes du colloque organisé le 19–22 juin 1990 dans le cadre des activités de l’URA 1085 du CNRS à l’occasion du 600e anniversaire de la mort d’Albert de Saxe. Paris: Vrin, 1991.

Grant, Edward. “The Unusual Structure and Organization of Albert of Saxony’s Questions on De caelo.” In Itinéraires d’Albert de Saxe, Paris-Vienne au XIVe siècle, edited by Joël Biard. Paris: Vrin, 1991.

Sarnowsky, Jürgen. Die aristotelisch-scholastische Theorie der Bewegung: Studien zum Kommentar Alberts von Sachsen zur Physik des Aristoteles. Münster: Aschendorff, 1989. The most fundamental monograph on Albert of Saxony’s physics to date.

———. “Place and Space in Albert of Saxony’s Commentaries on the Physics.”Arabic Sciences and Philosophy 9 (1999): 25–45.

———. “Nicole Oresme and Albert of Saxony’s Commentary on the Physics: The Problems of Vacuum and Motion in a Void.” In Quia inter doctores est magna dissensio: Les débats de philosophie naturelle à Paris au XIVe siècle, edited by Stefano Caroti and J. Celeyerette. Florence, Italy: Olschki, 2004.

Thijssen, J. M. M. H. “The Buridan School Reassessed: John Buridan and Albert of Saxony.” Vivarium 42, no. 1 (2004): 18–42.

Johannes M. M. H. Thijssen

Albert of Saxony

(b. Helmstedt, Lower Saxony, ca. 1316; d. Halberstadt, Saxony, 8 July 1390)

physics, logic, mathematics.

The family name of Albert of Saxony was de Ricmestrop his father, Bernard de Ricmestorp was a well-to-do burgher of Helmstedt. A brother, John, was a master of arts at the University of Paris in 1362, while Albert of himself was still there. Of Albert’s youth and early schooling nothing is known, although there is some evidence to Paris, where he obtained the degree of master of arts in 1351.

He quickly achieved renown as a teacher on the faculty of arts at Paris and was made rector of the university in 1353. During most of the period of Albert’s study and teaching at Paris, the most influential figure on the faculty of arts was Jean Buridan, and Albert’s own lectures on natural philosophy, represented by his books of questions on Aristole’s Physics and De caelo et mundo, were modeled closely on those of Buridan. Nicole Oresme, another pupil of Buridan, also taught at Paris at this time, and there is evidence that he influenced Albert in the direction of mathematical studies. Albert apparently studied theology also but never received a theological degree.

It is believed that he left Paris by the end of 1362, going to Avignon and spending the next two years carrying out various commissions for Pope Urban V. The pope obtained for him a benefice at Mainz, later made him parochial priest at Laa, and shortly afterward canon of Hildesheim. Albert played a major role in obtaining the authorization of the pope for the establishment of a university at Vienna and in drawing up its statutes. When the university was established in June 1365, Albert was its first rector. But he held this position for only a year; at the end of 1366 he was appointed bishop of Halberstadt and his academic career came to an end. His twenty-four years as bishop were marred by political and financial difficulties and at one point he was even accused of heresy by some inimical clergy of his own region who intimated that he was “more learned in human science than in divine wisdom,” and that the had openly taught an astrological determinism with denial of human freedom of choice. Surviving these vicis situdes he held the bishopric until he died at the age of seventy-six. He was buried in the cathedral of Halberstadt.

Albert’s writings, which were probably composed during the years when he was teaching at Paris, consist mostly of books question on Aristole’s treatises and of some treatises of his own on logic and mathematical subjects. Extant in early printed editions are questions on Aristotle’s Physics, De caelo et mundo. De generatione et corruptione, Posterior Analytics, and on the “old logic” (Prophyry’s Predicables and Aristotle’s Categories and De interpretatione): a complete textbook of logic published in 1522, under the title Logica Albertutii; an extensive collection of logical puzzles, entitled Sophismata; and a treatise on the mathematical analysis of motion, entitled Tractatus proportionum. In unpublished manuscripts there are sets of questions on Aristotle’s Meteora, Ethics, De sensu et sensato, and Oeconomica; a book of questions on John of Sacrobosco’s De sphaera; and two short treatises on the mathematical problems of “squaring the circle” and of determining the ratio of the diameter of a square to its side. Suter’s ascription of the second of these mathematical treatises to Albert has been questioned by Zoubov (see Bibliography), who attributes it to Oresme. It does in fact echo passages found in one of Oresme’s known works, but since Albert often paraphrased the content of works whose ideas he borrowed, this does not prove that the work was not written by Albert. There is much uncertainty concerning the attribution of a number of these manuscript works to Albert. It has been shown that his Questions on the Ethics, although written by Albert as his own work, is an almost literal plagiarism of the corresponding work of Walter Burley.

Albert’s significance in the history of science is primarily that of a transmitter and an intelligent compiler of scientific ideas directly drawn from the works of Buridan, Thomas Bradwardine, William of Ockham, Burley, Oresme, and other writers in the medieval scientific tradition. His works in physics are heavily dependent on the corresponding works of Buridan, to the extent that all but a few of the questions devoted to the Physics and the De caelo et mundo correspond directly to those of Buridan’s works of similar title, both in form and in content. Most of the questions that Albert adds, and which are not found in Buridan’s works, draw their materials from the Oxford tradition of Bradwardine and his Mertonian pupils, or, in a few cases, from the early thirteenth-century works on statics and hydrostatics associated with Jordanus de Nemore. Albert’s Tractatus Proportionum is modeled directly on Bradwardine’s treatise De proportionibus velocitatum in motibus, although it adds some refinements in terminology and in the analysis of curvilinear motions that reflected the later Mertonian developments and probably also the influence of Oresme.

Despite his lack of originality Albert contributed many intelligent discussions of aspects of the problems dealt with, and he had the particular merit of seeing the importance of bringing together the mathematical treatments of motion in its kinematic aspect, stemming from the Oxford tradition of Bradwardine, with the dynamical theories that Buridan had developed without sufficient concern for their mathematical formulation. As a transmitter of Buridan’s work, Albert played an important part in making known the explanations of projectile motion and of gravitational acceleration provided by Buridan’s theory of impetus, although he tended to blur the distinction between Buridan’s quasi-inertial concept of impetus and the older doctrine of the self-expending “impressed virtue.” Unlike Buridan, he introduced an error into the analysis of projectile motion, by supposing that there is a short period of rest between the ascent of a projectile hurled directly upward and its descent. Yet this led him to initiate a fruitful discussion by raising the question of the trajectory that would be followed by a projectile shot horizontally from a cannon. He supposed that it would follow a straight horizontal path until its impetus ceased to exceed the force of its gravity, but that it would then follow a curved path for a short period in which its lateral impetus would be compounded with a downward impetus caused by its gravity, after which it would fall straight down. Leonardo da Vinci took up the problem, but it remained for Nicoló Tartaglia to show that the entire trajectory would be a curve determined by a composition of the two forces.

Albert’s textbook of logic is one of the best organized of the late medieval works in the field. In its first three sections it presents the analysis of the signification and supposition of terms, and the internal analysis and classification of propositional forms, provided by the work of Ockham and Buridan. The fourth section, on “consequence,’ shows influence by Burley and Buridan, developing the theory of inference on the foundation of the logic of unanalyzed propositions, exhibiting the syllogism as a special type of consequence, and ending with a very full treatment of modal syllogisms and a shorter formulation of the rules of topical argumentation. The last two sections deal with logical fallacies, with the “insoluble” (or paradox of self-reference), and with the rules of disputation known as Obligationes. There is little that is not directly traceable to the sources Albert used, but these materials are skillfully integrated, reduced to a uniform terminology, and presented with systematic elegance.

Despite its excellence as a textbook, this work did not achieve the popularity or influence attained by Albert’s Tractatus proportionum and by his questions on the physical treatises of Aristotle. These, printed in many editions at Venice, Padua, and Pavia, became the principal means by which the contributions of the northern Scholastics of the fourteenth century to the science of mechanics were made known to the physicists and mathematicians of Italy, from Leonardo da Vinci to Galileo himself.

BIBLIOGRAPHY

I. Original Works. Expositio aurea et admodum utilis super artem veterem … cum quaestionibus Alberti parvi de Saxonia (Bologna, 1496); Quaestiones subtilissimae Alberti de Saxonia super libros Posteriorum (Venice, 1497); Logica Albertutii (Venice, 1522); Sophismata Alberti de Saxonia (Paris, 1490, 1495); Tractatus obligationum (Lyons, 1498; with Albert’s Insoluhilia, Paris, 1490, 1495); Subtilissimae quaestiones super octo libros Physicorum (Venice, 1504, 1516); Quaestiones in libros de caelo et mundo (Pavia, 1481; Venice, 1492, 1497, 1520); Quaestiones in libros de generatione et corruptione (Venice, 1504, 1505, 1518); Quaestiones et decisiones physicales insignium virorum..., Georgius Lockert, ed. (Paris, 1516, 15178), contains Albert’s questions on the Physics and the De caelo et mundo; Tractatus proportionum (Bologna, 1502, 1506; Padua, 1482, 1484, 1487; Venice, 1477, 1494, 1496; Paris, s.a.).

II. Secondary Literature. Philotheus Boehner, Medieval Logic (Chicago, 1952); B. Boncompagni, “Intorno al Tractatus proportionum di Alberto de Sassonia,” in Bolletino di bibliografia e di storia dele scienze matematiche e fisiche, 4 (1871), 498 ff.; Maximilian Cantor, Vorlesungen über die Geschichte der Mathematik, II 2nd. ed. (1900), 137–154; Marshall Clagett, The Science of Mechanics in the Middle Ages (Madison, Wis., 1959); Pierre Duhem, Études sur Lèonard de Vinci, Vols. I-III (Paris, 1906–1913); A. Dyroff, “Ueber Albertus von Sachsen,” in Baeumker-Festgabe (Münster, 1913), pp. 330–342; G. Heidingsfelder, “Albert von Sachsen: Sein Lebensgang und sein Kommentar zur Nikomachischen Ethik des Aristoteles,” in Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters, 22, 2nd ed. (Ménster, 1926); M. Jullien, “Un scolastique de la décadence; Albert de Saxe,” in Revue Augustinienne, 16 (1910), 26–40; Anneliese Maier, Zwei Grundprohleme der scholastischen naturphilosophie (Rome, 1951), pp. 259–274; C. Prantl, Geschichte der Logik im Abendlande, 4 (Leipzig, 1870), 60–88; H. Suter, “Der Tractatus ’De quadratura circuli’ des Albertus de Saxonia,” in Zeitschrift für Mathematik und Physik, 29 (1884), 81–102 (reedited and translated in M. Clagett, Archimedes in the middle Ages [Madison, Wis., 1964] pp.398–432); H. Suter, “Die Quaestio ’De proportione dyametri quadrati ad costam eiusdem’ des Albertus de Saxonoia,” in Zeitschrift für Mathematick und Physik32 (1887), 41–56; V.P. Zoubov, “Quelques Observations sur l’Auteur du Traité Anonyme ’Utrum dyameter alicuius quadrati sit commensurabilis costae ejusdem,’” in Isis, 50 (1959), 130–134.

Ernest A. Moody

ALBERT OF SAXONY

Nominalist philosopher of Paris and bishop; b. Rick-mersdorf, lower Saxony, 1316; d. 1390. He was an outstanding master in arts at the University of Paris from 1351 to 1362 and rector of the University in 1357 and 1362. In his Quaestiones super libros Physicorum (Venice 1504), Quaestiones in libros de caelo et mundo (Venice 1520), and Quaestiones in libros de generatione (Venice 1504) he was much influenced by the teaching of john buridan and nicholas oresme, notable on the theory of impetus and on the configuration of forms that can be increased and decreased. In his Logica (Venice 1522), Quaestiones super libros Posteriorum (Venice 1497), and Sophismata (Paris 1489) he was greatly influenced by the nominalism of william of ockham. His Tractatus obligationum and Insolubilia (Paris 1490) clearly show the influence of Oxford logicians. He promulgated and developed the new physics initiated by thomas bradwardine and John Buridan. He wrote a number of short treatises on proportionality and the square of the circle that became popular textbooks in universities. In his unedited commentary on the Nicomachean Ethics of Aristotle he followed closely the commentary of walter burley. In 1365 he was named the first rector of the new University of Vienna. In 1366 he was nominated and consecrated bishop of Halberstadt; he served in this office until his death. His writings in natural philosophy were widely read until the 17th century.

Bibliography: b. nardi, Enciclopedia filosofica 1:128. a. maier, Die Vorläufer Galileis im 14. Jahrhundert (Rome 1949); An der Grenze von Scholastik und Naturwissenschaft (2d ed. Rome 1952). m. clagett, The Science of Mechanics in the Middle Ages (Madison, Wis. 1959). É. h. gilson, History of Christian Philosophy in the Middle Ages 516–20. p. hossfeld, Lexikon für Theologie und Kirche 1:281.

[j. a. weisheipl]