ORESME, NICOLE

(b. France, ca. 1320; d. Lisieux, France, 1382)

mathematics, natural philosophy.

Oresme was of Norman origin and perhaps born near Caen. Little is known of his early life and family. In a document originally drawn in 1348, “Henry Oresme” is named along with Nicole in a list of masters of arts of the Norman nation at Paris. Presumably this is a brother of Nicole, for a contemporary manuscript¹ mentions a nephew of Nicole named Henricus iumor. A “Guillaume Oresme” also appears in the records of the College of Navarre at Paris as the holder of a scholarship in grammar in 1352 and in theology in 1353; he is later mentioned as a bachelor of theology and canon of Bayeux in 1376.

Nothing is known of Nicole Oresme’s early academic career. Apparently he took his arts training at the University of Paris in the 1340’s and studied with the celebrated master Jean Buridan, whose influence on Oresme’s writing is evident. This is plausible in that Oresme’s name appears on a list of scholarship holders in theology at the College of Navarre at Paris in 1348. Moreover, in the same year he is listed among certain masters of the Norman nation, as was noted above. After teaching arts and pursuing his theological training, he took his theological mastership in 1355 or 1356; he became grand master of the College of Navarre in 1356.

His friendship with the dauphin of France (the future King Charles V) seems to have begun about this time. In 1359 he signed a document as “secretary of the king,” whereas King John II had been in England since 1356 with the dauphin acting as regent. In 1360 Oresme was sent to Rouen to negotiate a loan for the dauphin.

Oresme was appointed archdeacon of Bayeux in 1361. He attempted to hold this new position together with his grand-mastership, but his petition to do so was denied and he decided to remain in Navarre. Presumably he left Navarre after being appointed canon at Rouen on 23 November 1362. A few months later (10 February 1363) he was appointed canon at Sainte-Chapelle, Paris, obtaining a semiprebend. A year later (18 March 1364) he was appointed dean of the cathedral of Rouen. He held this dignity until his appointment as bishop of Lisieux in 1377, but he does not appear to have taken up residency at Lisieux until 1380. From the occasional mention of him in university documents it is presumed that from 1364 to 1380 Oresme divided his time between Paris and Rouen, probably residing regularly in Rouen until 1369 and in Paris thereafter. From about 1369 he was busy translating certain Aristotelian Latin texts into French and writing commentaries on them. This was done at the behest of King Charles V, and his appointment as bishop was in part a reward for this service. Little is known of his last years at Lisieux.

Scientific Thought. The writings of Oresme show him at once as a subtle Schoolman disputing the fashionable problems of the day, a vigorous opponent of astrology, a dynamic preacher and theologian, an adviser of princes, a scientific popularizer, and a skillful translator of Latin into French.

One of the novelties of thought associated with Oresme is his use of the metaphor of the heavens as a mechanical clock. It has been suggested that this metaphor—which appears to mechanize the heavenly regions in a modern manner—arises from Oresme’s acceptance of the medieval impetus theory, a theory that explained the continuance of projectile motion on the basis of impressed force or impetus. Buridan, Oresme’s apparent master, had suggested the possibility that God could have impressed impetuses in the heavenly bodies, and that these, acting without resistance or contrary inclination, could continue their motion indefinitely, thus dispensing with the Aristotelian intelligences as the continuing movers. A reading of several different works of Oresme, ranging from the 1340’s to 1377, all of which discuss celestial movers, however, shows that Oresme never abandoned the concept of the intelligences as movers, while he specifically rejected impetuses as heavenly movers in his Questiones de celo² In these discussions he stressed the essential differences between the mechanics governing terrestrial motion and that involved in celestial motions. In two passages of his last work, Livre du ciel et du monde d’Aristote³ he suggests (1)the possibility that God implanted in the heavens at the time of their creation special forces and resistances by which the heavens move continually like a mechanical clock, but without violence, the forces and resistances differing from those on earth; and (2)that “it is not impossible that the heavens are moved by a power or corporeal quality in it, without violence and without work, because the resistance in the heavens does not incline them to any other movement nor to rest but only [effects] that they are not moved more quickly.” The latter statement sounds inertial, yet it stresses the difference between celestial resistance and resistance on the earth, even while introducing analogues to natural force and resistance. In other treatments of celestial motions Oresme stated that “voluntary” forces rather than “natural” forces are involved, but that the “voluntary” forces differ from “natural” ones in not being quantifiable in terms of the numerical proportionality theorems applicable to natural forces and resistances.⁴ In addition to his retention of intelligences as movers, a further factor prevents the identification of any of Oresme’s treatments of celestial movers with the proposal of Buridan. For Buridan, impetus was a thing of permanent nature (res natura permanens) which was corruptible by resistance and contrary inclination. But Oresme seems to hold in his Questiones de celo⁵ that impetus is not permanent, but is self-expending by the very fact that it produces motion. If this is truly what Oresme meant, it would be obviously of no advantage to use such impetuses in the explanation of celestial motions, for unless such impetuses were of infinite power (and he would reject this hypothesis for all such powers) they would have to be renewed continually by God. One might just as well keep the intelligences as movers. An even more crucial argument against the idea that Oresme used the impetus theory to explain heavenly motion is that he seems to have associated impetus with accelerated motion, and yet insisted on the uniform motion of the heavens. Returning to the clock metaphor, it should be noted that in the two places in which the metaphor is employed, Oresme did not apply it to the whole, universe but only to celestial motions.

One of these passages in which the clock metaphor is cited leads into one of Oresme’s most intriguing ideas—the probable irrationality of the movements of the celestial motions. The idea itself was not original with Oresme, but the mathematical argument by which he attempted to develop it was certainly novel. This argument occurs in his treatise Proportiones proportionum (“The Ratios of Ratios”). His point of departure in this tract is Thomas Bradwardine’s fundamental exponential relationship, suggested in 1328 to represent the relationships between forces, resistances, and velocities in motions:

Oresme went on to give an extraordinary elaboration of the whole problem of relating ratios exponentially. It is essentially a treatment of fractional exponents conceived as “ratios of ratios.”

In this treatment Oresme made a new and apparently original distinction between irrational ratios of which the fractional exponents are rational, for example, , and those of which the exponents are themselves irrational, apparently of the form In making this distinction Oresme introduced new significations for the terms pars, partes, commensurabilis, and incommensurabilis. Thus pars was used to stand for the exponential part that one ratio is of another. For example, starting with the ratio Oresme would say, in terms of his exponential calculus, that this irrational ratio is “one half part” of the ratio —meaning, of course, that if one took the original ratio twice and composed a ratio therefrom, would result. Or one would say that the ratio can be divided into two “parts” exponentially, each part being (, or more succinctly in modern representation:

Furthermore, Oresme would say that such a ratio as ( is “two third parts” of meaning that if we exponentially divided into

then is two of the three “parts” by which we compose the ratio , again representable in modern symbols as

This new signification of pars and partes also led to a new exponential treatment of commensurability. After this detailed mathematical treatment, Oresme claimed (without any real proof) that as we take a larger and larger number of the possible whole number ratios greater than one and attempt to relate them exponentially two at a time, the number of irrational ratios of ratios (that is, of irrational fractional exponents relating the pairs of whole number ratios) rises in relation to the number of rational ratios of ratios. From such an unproved mathematical conclusion, Oresme then jumps to his central theme, the implications of which reappear in a number of his works: it is probable that the ratio of any two unknown ratios, each of which represents a celestial motion, time, or distance, will be an irrational ratio. This then renders astrology—the predictions of which, he seems to believe, are based on the precise determinations of successively repeating conjunctions, oppositions, and other aspects—fallacious at the very beginning of its operations. A kind of basic numerical indeterminateness exists, which even the best astronomical data cannot overcome. It should also be noted that Oresme composed an independent tract, the Algorism of Ratios, in which he elucidated in an original way the rules for manipulating ratios.

Oresme’s consideration of a very old cosmological problem, the possible existence of a plurality of worlds, was also novel. Like the great majority of his contemporaries, he ultimately rejected such a plurality in favor of a single Aristotelian cosmos, but before doing so he stressed in a cogent paragraph the possibility that God by His omnipotence could so create such a plurality.⁶

All heavy things of this world tend to be conjoined in one mass [masse] such that the center of gravity [centre de pesanteur] of this mass is in the center of this world, and the whole constitutes a single body in number. And consequently they all have one [natural] place according to number. And if a part of the [element] earth of another world was in this world, it would tend towards the center of this world and be conjoined to its mass.… But it does not accordingly follow that the parts of the [element] earth or heavy things of the other world (if it exists) tend to the center of this world, for in their world they would make a mass which would be a single body according to number, and which would have a single place according to number, and which would be ordered according to high and low [in respect to its own center] just as is the mass of heavy things in this world.… I conclude then that God can and would be able by His omnipotence [par toute sa puissance] to make another world other than this one, or several of them whether similar or dissimilar, and Aristotle offers no sufficient proof to the contrary. But as it was said before, in fact [de fait] there never was, nor will there be, any but a single corporeal world.…

This passage is also of interest in that it reveals Oresme’s willingness to consider the possible treatment of all parts of the universe by ideas of center of gravity developed in connection with terrestrial physics.

The passage also illustrates the technique of expression used by Oresme and his Parisian contemporaries, which permitted them to suggest the most unorthodox and radical philosophical ideas while disclaiming any commitment to them.

The picture of Oresme’s view of celestial physics and its relationship to terrestrial phenomena would not be complete without further mention of his well-developed opposition to astrology. In his Questio contra divinatores with Quodlibeta annexa we are told again and again that the diverse and apparently marvelous phenomena of this lower world arise from natural and immediate causes rather than from celestial, incorporeal influences. Ignorance, he claims, causes men to attribute these phenomena to the heavens, to God, or to demons, and recourse to such explanations is the “destruction of philosophy.” He excepted, of course, the obvious influences of the light of the sun on living things or of the motions of celestial bodies on the tides and like phenomena in which the connections appear evident to observers. In the same work he presented a lucid discussion of the existence of demons.“Moreover, if the Faith did not pose their existence,” he wrote, “I would say that from no natural effect can they be proved to exist, for all things [supposedly arising from them] can be saved naturally.”⁷

In examining his views on terrestrial physics, we should note first that Oresme, along with many fourteenth-century Schoolmen, accepted the conclusion that the earth could move in a small motion of translation.⁸ Such a motion would be brought about by the fact that the center of gravity of the earth is constantly being altered by climatic and geologic changes. He held that the center of gravity of the earth strives always for the center of the world; whence arises the translatory motion of the earth. The whole discussion is of interest mainly because of its application of the doctrine of center of gravity to large bodies. Still another question of the motion of the earth fascinated Oresme, that is, its possible rotation, which he discussed in some detail in at least three different works. His treatment in the Du ciel⁹ is well known, but many of its essential arguments for the possibility of the diurnal rotation of the earth already appear in his Questiones de celo¹⁰ and his Questiones de spera.¹¹ These include, for example, the argument on the complete relativity of the detection of motion, the argument that the phenomena of astronomy as given in astronomical tables would be just as well saved by the diurnal rotation of the earth as by the rotation of the heavens, and so on. At the conclusion of the argument, Oresme says in the Questiones de spera (as he did in the later work): “The truth is, that the earth is not so moved but rather the heavens.” He goes on to add, “However I say that the conclusion [concerning the rotation of the heavens] cannot be demonstrated but only argued by persuasion.” This gives a rather probabilistic tone to his acceptance of the common opinion, a tone we often find in Oresme’s treatment of physical theory. The more one examines the works of Oresme, the more certain one becomes that a strongly skeptical temper was coupled with his rationalism and naturalism (of course restrained by rather orthodox religious views) and that Oresme was influenced deeply by the probabilistic and skeptical currents that swept through various phases of philosophy in the fourteenth century. He twice tells us in the Quodlibeta that, except for the true knowledge of faith, “I indeed know nothing except that I know that I know nothing.”¹²

In discussing the motion of individual objects on the surface of the earth, Oresme seems to suggest (against the prevailing opinion) that the speed of the fall of bodies is directly proportional to the time of fall, rather than to the distance of fall, implying as he does that the acceleration of falling bodies is of the type in which equal increments of velocity are acquired in equal periods of time.¹³ He did not, however, apply the Merton rule of the measure of uniform acceleration of velocity by its mean speed, discovered at Oxford in the 1330’s, to the problem of free fall, as did Galileo almost three hundred years later. Oresme knew the Merton theorem, to be sure, and in fact gave the first geometric proof of it in another work, but as applied to uniform acceleration in the abstract rather than directly to the natural acceleration of falling bodies. In his treatment of falling bodies, despite his different interpretation of impetus, he did follow Buridan in explaining the acceleration of falling bodies by continually accumulating impetus. Furthermore, he presented (as Plutarch had done in a more primitive form) an imaginatio—the device of a hypothetical, but often impossible, case to illustrate a theory—of a body that falls through a channel in the earth until it reaches the center. Its impetus then carries it beyond the center until the acquired impetus is destroyed, whence it falls once more to the center, thus oscillating about the center.¹⁴

The mention of Oresme’s geometrical proof of the Merton mean speed theorem brings us to a work of unusual scope and inventiveness, the Tractatus de configurationibus qualitatum et motuum composed in the 1350’s while Oresme was at the College of Navarre. This work applies two-dimensional figures to hypothetical uniform and nonuniform distributions of the intensity of qualities in a subject and to equally hypothetical uniform and nonuniform velocities in time.

There are two keys to our proper understanding of the De configurationibus. To begin with, Oresme used the term configuratio in two distinguishable but related meanings, that is, a primitive meaning and a derived meaning. In its initial, primitive meaning it refers to the fictional and imaginative use of geometrical figures to represent or graph intensities in qualities and velocities in motions. Thus the base line of such figures is the subject when discussing linear qualities or the time when discussing velocities, and the perpendiculars raised on the base line represent the intensities of the quality from point to point in the subject, or they represent the velocity from instant to instant in the motion (Figs. 1-4). The whole figure, consisting of all the perpendiculars, represents the whole distribution of intensities in the quality, that is, the quantity of the quality, or in case of motion the so-called total velocity, dimensionally equivalent to the total space traversed in the given time. A quality of uniform intensity (Fig. 1) is thus represented by a rectangle, which is its configuratio; a quality of uniformly nonuniform intensity starting from zero intensity is represented as to its configuration by a right triangle (Fig. 3), that is, a figure where the slope is constant (GK/EH = CK/GH). Similarly, motions of uniform velocity and uniform acceleration are represented, respectively, by a rectangle and a right triangle. There is a considerable discussion of other possible configurations.

Differences in configuration—taken in its primitive meaning—reflect for Oresme in a useful and suitable fashion internal differences in the subject. Thus we can say by shorthand that the external configuration represents some kind of internal arrangement of intensities, which we can call its essential internal configuration. So we arrive at the second usage of the term configuration, in which the purely spatial or geometrical meaning is abandoned, since one of the variables involved (namely intensity) is not essentially spatial, although, as Oresme tells us, variations in intensity can be represented by variations in the length of straight lines. He suggests at great length how differences in internal configuration may explain many physical and even psychological phenomena, which are not simply explicable on the basis of the primary elements that make up a body. Thus two bodies might have the same amounts of primary elements in them and even in the same intensity, but the configuration of their intensities may well differ, and so produce different effects in natural actions.

The second key to the understanding of the configuration doctrine of Oresme is what we may call the suitability doctrine. It pertains to the nature of configurations in their primitive meaning of external figures and, briefly, holds that any figure or configuration is suitable or fitting for description of a quality, when its altitudes (ordinates, we would say in modern parlance) on any two points of its base or subject line are in the same ratio as the intensities of the quality at those points in the subject. The phrase used by Oresme to describe the key relationship of intensities and altitudes occurs at the beginning of Chapter 7 of the first part, where he tells us that:

Any linear quality can be designated by every plane figure which is imagined as standing perpendicularly on the linear extension of the quality and which is proportional in altitude to the quality in intensity. Moreover a figure erected on a line informed with a quality is said to be “proportional in altitude to the quality in intensity” when any two lines perpendicularly erected on the quality line as a base and rising to the summit of the surface or figure have the same ratio to each other as do the intensities at the points on which they stand.

Thus, if you have a uniform linear quality, it can be suitably represented by every rectangle erected on the given base line designating the extension of the subject (for example, either ADCB or AFEB, or any other rectangle on AB in Fig. 1), because any rectangle on that base line will be “proportional in altitude to the

quality in intensity,” the ratio of any two intensities always being equal to one (that is, MK/IG LK/HG = 1). Similarly, a uniformly difform quality will be represented by every right triangle on the given base line, since two altitudes on any one right triangle will have the same ratio to each other as the corresponding two altitudes over the same points of the base line of any other triangle (that is, in Fig. 2, DB/FE = CB/GE)

The only proviso is, of course, that when we compare figures—say, one uniform quality with another—we must retain some specific figure (say rectangle) as the point of departure for the comparison. Thus, in representing some uniform quality that is twice as intense as the first one, we would have a rectangle whose altitude is everywhere twice as high as that of the rectangle specifying the first uniform quality.

The essential nature of this suitability doctrine was not present in theQuestiones super geometriam Euclidis, and in fact it is specifically stated there that some specific quality must be represented by a specific

figure rather than a specific kind of figure; that is, a quality represented by a semicircle (Fig. 4) is representable only by that single semicircle on the given base line. But in the De configurationibus (pt. 1, ch. 14) Oresme decided in accordance with his fully developed suitability doctrine that such a quality that is representable by a semicircle can be represented by any curved

figure on the same base whose altitudes (ordinates) would have any greater or lesser constant ratio with the corresponding altitudes (ordinates) of the semicircle (for example, in Fig. 4, CD/EF = HD/FG = JD/IF). He was puzzled as to what these higher or lower figures would be. For the figures of higher altitudes, he definitely rejected their identification with segments of circles, and he said he would not treat the figures of lower altitudes. Unfortunately, Oresme had little or no knowledge of conic sections. In fact the conditions he specified for these curves comprise one of the basic ways of defining ellipses: if the ordinates of a circle x²+y²= a² are all shrunk (or stretched) in the same ratio b/a, the resulting curve is an ellipse whose equation is x²/a²+y²/b²=1). Oresme, without realizing it, has given conditions that show that the circle is merely one form of a class of curves that are elliptical. It is quite evident that Oresme arrived at the conclusion of this chapter by systematically applying the basic and sole criterion of suitability of representation, which he has already applied to uniform and uniformly difform qualities; namely, “that the figure be proportional in altitude to the quality in intensity” which is to say that any two altitudes on the base line have the same ratios as the intensities at the corresponding points in the subject. He had not adequately framed this doctrine in the Questiones super geometriam Euclidis, and in fact he denied it there, at least in the case of a quality represented by a semicircle or of a uniform or uniformly difform quality formed from such a difform quality. In this denial he confused the question of sufficiently representing a quality and that of comparing one quality 10 another.

While the idea of internal configuration outlined in the first two parts of the book had little effect on later writers and is scarcely ever referred to, the third part of the treatise—wherein Oresme compared motions by the external figures representing them, and particularly where he showed (Fig. 5) the equality of a right triangle representing uniform acceleration with a rectangle

Triangle ABC=Rectangle AFGB

representing a uniform motion at the velocity of the middle instant of acceleration—was of profound historical importance. The use of this equation of figures can be traced successively to the time of its use by Galileo in the third day of his famous Discorsi (Theorem I). And indeed the other two forms of the acceleration law in Galileo’s work (Theorem II and its first corollary) are anticipated to a remarkable extent in Oresme’s Questiones super geometriam Euclidis¹⁵

The third part of theDe configurationibusis also noteworthy for Oresme’s geometric illustrations of certain converging series, as for example his proof in chap. 8 of the series

He had showed similar interest in such a series in his Questions on the Physics and particularly in his Questiones super geometriam Euclidis. In the latter work he clearly distinguished some convergent from divergent series. He stated that when the infinite series is of the nature that to a given magnitude there are added “proportional parts to infinity” and the ratio a/b determining the proportional parts is less than one, the series has a finite sum. But when a > b, “the total would be infinite,” that is, the series would be divergent. In the same work he gave the procedure for finding the following summation:

In doing so, he seems to imply a general procedure for summation of all series of the form:

His general rule seems to be that the series is equal to y/x when, (1/mⁱ-1/mⁱ⁺¹) being the difference of any two successive terms,

As we survey Oresme’s impressive accomplishments, it is clear that his natural philosophy lay within the broad limits of an Aristotelian framework, yet again and again he suggests subtle emendations or even radical speculations.

NOTES

1. MS Paris, BN lat. 7380, 83v: cf. MS Avranches, Bibl. Munic. 223, 348v.

2. Bk. II, quest. 2.

3. Menut text, 70d-71a; 73d.

4.Questiones de spera, quest. 9; Questiones de celo, bk. II, quest. 2.

5. Bk. II, quest. 13.

6.Du ciel, 38b, 39b-c.

7. MS Paris, BN lat. 15126, 127v.

8.Questiones de spera, quest. 3.

9. 138b-144c; see also Clagett, Science of Mechanics, 600-608.

10. Bk. 11, quest. 13.

11. Quest. 6[8]; see also Clagett, Science of Mechanics, 608, n. 23.

12. BN lat. 15126, 98v, 118v.

13.Questiones de celo, bk. II, quest. 7.

14.Questiones de celo, ibid.; Du ciel 30a-b; Clagett, Science of Mechanics, 570.

15. Clagett, Nicole Oresme and the Medieval Geometry of Qualities, etc., ch. 2, pt. A.

BIBLIOGRAPHY

I. Original Works. Oresme’s scholarly writings reflect a wide range of interests and considerable originality. He was the author of more than thirty different writings, the majority of which are unpublished and remain in manuscript. They can be conveniently grouped into five categories:

1. Collections of, or individual, questiones. These include questions on various works of Aristotle: Meteorologica (perhaps in two versions, with MS St. Gall 839, l-175v being the most complete MS of the vest version); De sensu et sensato (MS Erfurt, Amplon. Q. 299, 128-157v);De anima(MSS Bruges 514, 71-111v; Munich, Staatsbibl. Clm 761, l-40v; a different version with an expositio in Bruges 477, 238v-264r, may also be by Oresme); De generatione et corruptione (MS Florence, Bibl. Naz. Centr., Conv. Soppr. H. ix. 1628, l-77v; a different version in MS Vatican lat. 3097, 103-146; and Vat. lat. 2185, 40v-61v, may be by him); Physica (MS Seville, Bibl. Colomb. 7-6-30, 2-79v); and De celo(MSS Erfurt, Amplon. Q. 299, 1-50; Q. 325, 57-90). These also include questions on the Elementa of Euclid (edit, of H. L. L. Busard [Leiden, 1961]; additional MS Seville, Bibl. Colomb. 7-7-13, 102v-112) and on the Sphere of Sacrobosco (MSS Florence, Bibl. Riccard. 117, I25r-135r; Vat. lat. 2185, 71-77v; Venice Bibl. Naz. Marc. Lat. VIII, 74, 1-8; Seville, Bibl. Colomb. 7-7-13; a different version is attributed to him in Erfurt, Amplon. Q. 299, 113-126). There are other individual questions that are perhaps by him: Utrum omnes impressiones (MS Vat. lat. 4082, 82v-85v; edit, of R. Mathieu, 1959), Utrum aliqua res videatur (MS Erfurt, Amplon. Q. 231, 146-150), Utrum dyameter alicuius quadrati sit commensurabilis coste eiusdem(MS Bern A. 50, 172-176; H. Suter, ed., 1887; see Isis. 50 [1959], 130-133), and Questiones de perfectione specierum (MS Vat. lat. 986, 125—133v). This whole group of writings seems to date from the late 1340’s and early 1350’s, that is, from the period when Oresme was teaching arts.

2. A group of mathematico-physical works. This includes a tract beginning Ad pauca respicientes (E. Grant, ed., 1966), which is sometimes assigned the title De motibus sperarum (MS Brit. Mus. 2542, 59r); a De proportionibus proportionum (E. Grant, ed. [Madison, Wise, 1966]); De commensurabilitate sive incommensurabilitate motuum celi (E. Grant, ed. [Madison, Wise., 1971]); Algorimus proportionum (M. Curtze, ed. [Thorn, 1868], and a partial ed. by E. Grant, thesis [Wisconsin, 1957]); and De configurationibus qualitatum et motuum (M. Clagett, ed. [Madison, Wise, 1968]). These works also probably date from the period of teaching arts, although some may date as late as 1360.

3. A small group of works vehemently opposing astrology and the magical arts. Here we find a Tractatus contra iudiciarios astronomos (H. Pruckner, ed., 1933; G. W. Coopland, ed., 1952); a somewhat similar but longer exposition in French, Le livre de divinacions (G. W. Coopland, ed., 1952); and a complex collection commonly known as Questio contra divinatores with Quodlibeta annexa (MS Paris, BN lat. 15126, 1-158; Florence, Bibl. Laurent. Ashb. 210, 3-70v; the Quodlibeta has been edited by B. Hansen in a Princeton University diss. of 1973). The first two works almost certainly date before 1364; the last is dated 1370 in the manuscripts but in all likelihood is earlier.

4. A collection of theological and nonscientific works. This includes an economic tract De mutationibus monetarum (many early editions; cf. C. Johnson, ed. [London, 1956]; this work was soon translated into French, cf. E. Bridrey’s study), a Commentary on the Sentences of Peter Lombard (now lost but referred to by Oresme); a short theological tract De communicatione ydiomatum (E. Borchert, ed., 1940); Ars sermonicinandi, i.e., on the preaching art (MSS Paris, BN lat. 7371, 279-282; Munich, Clm 18225); a short legal tract, Expositio cuiusdam legis (Paris, BN lat. 14580, 220-222v); a Determinatio facta in resumpta in domo Navarre (MS Paris, BN lat. 16535, 111-114v); a tract predicting bad times for the Church, De malis venturis super Ecelesiam (Paris, BN 14533, 77-83v); a popular and oft-published Sermo coram Urbano V(delivered in 1363; Flaccus lllyricus, ed. [Basel, 1556; Lyons, 1597]), aDecisio an in omni casu (possibly identical with a determinatio in MS Brussels, Bibl. Royale 18977-81, 51v-54v); a Contra mendicacionem (MSS Munich, Clm 14265; Kiel, Univ. Bibl. 127; Vienna, Nat. bibl. 11799); and finally some 115 short sermons for Sundays and Feast Days, Sacre conciones (Paris, BN lat. 16893, 1-128v). The dating of this group is no doubt varied, but presumably all of them except the Commentary on the Sentences postdate his assumption of the grandmastership at Navarre.

5. A group of French texts and translations. This embraces a popular tract on cosmology, Traité de l’espere (L. M. McCarthy, ed., thesis [Toronto, 1943]), which dates from about 1365; a translation and commentary, Le livre de ethiques d’Aristote (A. D. Menut, ed., [New York, 1940]), completed in 1372; a similar translation and commentary of the Politics—Le livre de politique d’Aristote (Vérard, ed. [Paris, 1489; cf. Menut’s ed., in Transactions of the American Philosophical Society, n.s. 60, pt. 6 (1970)]), completed by 1374; the Livre de yconomiqued’Aristote (Verard, ed. [Paris, 1489]; A. D. Menut, ed. [Philadelphia, 1957]), completed about the same time; and finally, Livre du ciel et du monde d’Aristote {A. D. Menut and A. J. Denomy, eds. [Toronto, 1943], new ed., Madison, Wise., 1968), completed in 1377. To these perhaps can be added a translation of Le Quadripartit de Ptholomee (J. F. Gossner, ed., thesis [Syracuse, 1951]), although it is attributed to G. Oresme.

6. Modern editions. These comprise “De configurationibus qualitatum et motuum,” in M. Clagett, ed., Nicole Oresme and the Medieval Geometry of Qualities (Madison, Wisc, 1968); E. Grant, ed., “De proportionibus proportionum and “ “Ad pauca respicientes” (Madison, Wise., 1966); Nicole Oresme and the Kinematics of Circular Motion (Madison, Wisc., 1971); A. D. Menut, ed., Le livre de ethiques d’Atristote (New York, 1940); A. D. Menut and M. J. Denomy, eds., Le livre de ciel et du monde d’Aristote, in Mediaeval Studies, 3-5 (1941-1943), rev. with English trans, by Menut (Madison, Wise., 1968).

II. Secondary Literature. Only a brief bibliography is given here because the extensive literature on Oresme appears in full in the editions of Grant, Clagett, and Menut listed above. These editions include full bibliographical references to the other editions mentioned in the list of Oresme’s works.

Works on Oresme include E. Borchert, “Die Lehre von der Bewegung bei Nicolaus Oresme,” in Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters,31 , no. 3 (1934); M. Clagett, The Science of Mechanics in the Middle Ages (Madison, Wisc, 1959, 1961); M. Curtze, Die mathematischen Schriften des Nicole Oresme (ca. 1320-1382) (Berlin, 1870); P. Duhem, Études sur Léonard de Vinci, 3 vols., (Paris, 1906-1913); Le système du monde, VI-X (Paris, 1954-1959). See also the following works by A. Maier, An der Grenze von Scholastik and Naturwissenschaft, 2nd ed. (Rome, 1952); Die Vorläufer Galileis im 14. Jahrhundert (Rome, 1949); Zwei Grundproblem der scholastischen Naturphilosophie, 2nd ed. (Rome, 1952); and O. Pederson, Nicole Oresme, og hans Naturfilosofiske System. En undersogelse of hans skrift “Le livre du ciel et du monde” (Copenhagen, 1956).

Marshall Clagett

ORESME, NICOLE

(b.Allemagne [later Fleury sur Orne, near Caen, France], c. 1320; d. Lisieux, France, 1382)

mathematics, natural philosophy.

For the original article on Oresme see DSB, vol. 10.

Scholarship since the 1970s has enriched the understanding of Oresme’s contributions to the history of natural philosophy. There is in the early 2000s a more detailed understanding of the nature of the intellectual environment during his studies at the University of Paris. Analyses of his commentaries on Aristotle’s Physics and On the Heavens reveal Oresme’s utilization of the logical and semantical theories of his day. A subsequent critical edition of Oresme’s treatise On Seeing the Stars shows that he made significant contributions to optics and the study of atmospheric refraction that have previously been overlooked by historians of science.

Early Career . New documentary evidence on Nicole Oresme’s earlier academic and ecclesiastical career and a more precise assessment of the University of Paris’s institutional setting has contributed to a different overview of Oresme’s natural philosophy as well as, more generally, of fourteenth-century philosophy. John Buridan’s role in the philosophical training of University of Paris masters such as Nicole Oresme, Albert of Saxony, and Marsilius of Inghen has to be revised, taking into consideration that students only rarely chose their supervising masters; they could attend lectures given by masters as well as disputations outside their Nation, but the notion of “school” must, if one wishes to use it, take into account the peculiar university’s institutional habits and procedures. On the basis of University of Paris rotuli sent to the papal court with the view of obtaining ecclesiastical benefices for the university masters, the date of Oresme’s master’s degree has now been determined to be 1341 or 1342, at least six years earlier than previously thought (1348). According to the new chronology, Oresme studied when the diffusion of William of Ockham’s doctrines, on logic as well as on natural philosophy, was at its apex; moreover, the spread of the ideas of other English authors such as Thomas Bradwardine and William Heytesbury, whose influence on Oresme’s scientific thought is well known, also occurred some years earlier than previously thought. The first years of his academic career in the Faculty of Arts were troubled not only by the diffusion of Ockham’s ideas but also by the condemnations of Nicholas of Autrécourt (1346) and Jean de Mirecourt (1347); the work of both masters was of great importance to Oresme’s scientific thought.

The Possibility of Scientific Knowledge . According to Nicholas of Autrécourt, scientific knowledge can only be obtained through propositions that can be reduced to the principle of contradiction; this condition drastically reduced the possibility of scientific knowledge in natural philosophy, so much so that masters of arts were urged to discuss in their commentaries on Aristotle’s natural works whether a scientific analysis of the problems at issue (usually in the commentaries on the Physics) was even possible. Oresme accurately distinguishes two kinds of evident propositions: (1) the perfectly evident ones, whose contrary implies contradiction, typical of mathematics; and (2) the almost perfectly evident ones, whose contrary is not impossible, which are to be found in natural philosophy (Questions on the Physics, Book I, Question 3). On this basis he shows that skeptical attitudes are excessive with regard to the possibility of human knowledge about physical events.

The distinction between these two kinds of evidence lets Oresme introduce into natural enquiry the so-called imaginary cases (some of them well known by the historian of science, e.g., the plurality of worlds and the Earth’s rotation), which can be proposed because, even though they are not real, they are nonetheless possible. Oresme’s belief in the convenience of using mathematics in natural philosophy relies on this ground. So, even if the methods of analysis of the two disciplines must remain different— that is, natural philosophy cannot proceed in a deductive way like mathematics (Questions on De anima, Book I, Question1)—some mathematical tools such as points, lines, and surfaces (and the rules of geometry) can be found useful in natural philosophy. Oresme favors the application of geometry to explain not only vision (perspectiva), but also physical events, relying explicitly on Robert Grosseteste’s writings (and primarily on De lineis) and having in mind Aristotle’s scientie mediae (Questions on De spera, Question 1).

Views on Substance and Accident . The change in Oresme’s ideas about motion in his commentaries on the Physics (Questions on the Physics, Book III, where motion is considered a modus not different ontologically from the moving body) and On the soul (Questions on De anima, Book II, Question 15, where it is defined as an accidental property of the moving body) was probably caused by the condemnation of Jean de Mirecourt, who introduced in Paris the ontology of modi rerum.

In his only partially edited commentary on the Physics, Oresme deals with physical topics such as motion, space, and time systematically relying on the theory of modi rerum, according to which accidental properties such as those registered in Aristotle’s Praedicamenta are to be considered as modifications of the substance, rather than as real beings inhering to real substances. Oresme presents his solution as a third way of dealing with the ontological problems concerning the relationship between substance and accidents, in addition to the “common opinion” defending the reality of accidental properties (at a lower level of substance, in which they inhere), and to the “nominalistic” theory, according to which accidents are not different from substance (with the exception of qualities, in order to avoid dangerous theological implications). In his Physics commentary Oresme restates his position (already put forth in the previous books) in book 5, where he discusses the intension and remission of qualitative forms, a basic element in the analysis of natural change and a field in which his contribution toward a geometrical study of qualitative changes and motion is particularly original (see the original DSB article). Oresme declares explicitly that his solution is the simplest, and one that can overcome every kind of difficulty (Questions on the Physics, Book V, Question 9).

In introducing his theory of modi rerum Oresme makes use of semantical tools such as the complexe significabile (what can be rendered through a sentence). Only substances can be duly expressed by nouns, while accidents and relations (according to Oresme modi or conditiones rerum) are to be rendered through sentences in the infinitive form: aliquod esse album (that something is white) for the quality “white”; lapidem aliter se habere quam prius(that a stone is in a different position as before) for the motion of a stone. This is not the only passage that permits an ascription to him of a deep acquaintance with logic, possibly exceeding the normal university training, even though he never ventured to write a treatise or a commentary on logical topics.

The Limits of Powers . In his commentary On the Heavens he deals with the problems of the potential limits of natural substances (de maximo et minimo), a topic also discussed by William Heytesbury in his Regulae solvendi sophismata and probably introduced in the debates held at the Faculty of Arts in Paris not earlier than the third decade of the fourteenth century. In this commentary Oresme studies the limits of activity of natural powers on the basis of the fourfold distinction typical of the de maximo et minimo theory (maximum quod sic and minimum quod non for the active powers, representing respectively intrinsic and extrinsic limits; minimum quod sic and maximum quod non for passive powers), and places the limits of active power in an extrinsic limit. The reason for such a choice is to be found in the divisibility of the amount by which the power is greater than resistance (according to the law that in order to have an action the active power must be greater than the resistive one); the limit is to be determined as the least in which the natural power cannot act (minimum quod non). In order to reach this solution Oresme relies on the semantical theory of suppositio(and specifically on suppositio confusa tantum, through which one is not obliged to exhibit a definite limit, in conformity with the infinite divisibility either of the quantity of power or of the space or the temporal duration).

Oresme’s systematic use of the modi rerum theory in his Physics commentary leads to original solutions concerning motion, space, and time, major topics discussed in this book. Viewing motion as a modus of the moving body permits him to avoid shortcomings such as the denial of motion (Ockham’s solution, reducing motion to the moving body) and the problems that result from considering it as an inherent accident as well (John Buridan’s solution); in this case, in fact, it would be very difficult to maintain the basic permanent (totum simul) character of accidental forms, motion being essentially continuous.

Oresme maintains the same semi-reductionist attitude toward the other two major physical topics discussed in Aristotle’s Physics: place and time. These are neither accidental forms nor conceptual devices for describing physical events; they are inner conditions (conditiones seu modi) of bodies, properly rendered through adverbs like “here, there, now, yesterday,” rather than nouns such as “place” and “time,” which would denote them as substances. As for motion, such an ontological commitment gives Oresme the opportunity to elude the problem of the infinite (just because of the insubstantiality of modi rerum), making a mathematical analysis easier. Oresme proposes on this basis a definition of place and time different than Aristotle's: Instead of the “innermost motionless boundary of what contains it” (Aristotle, The Complete Works: Physics, Book IV, 4, 212a20–21, trans. J. Barnes, 1984)), for Oresme place is the “space filled by the body, which would be empty if the body were removed” (Questions on the Physics, Book IV, Question 1); time, rather than the measure of motion (Physics IV, 11, 219b1–2) is successive duration (duratio rerum successiva, Questions on the Physics, Book IV, Question17), a stronger notion that cannot be reduced exclusively to the measure of duration.

Atmospheric Refraction . A 2006 study of Oresme’s treatise De visione stellarum reveals yet another example of his major contributions to natural philosophy. Dan Burton (2006) argues that Oresme was the first to make a theoretical study of atmospheric refraction, a phenomenon of great practical import to astronomers as well as of philosophical significance. After all, if the stars are not where they appear to be, how reliable is knowledge gained through the senses? Oresme proposes that light from the stars travels along a curved path in the atmosphere whose density varies uniformly. Thus refraction need not occur only at the interface of two materials, as had been believed by all his predecessors (Grant, 2007). In his mathematical analysis Oresme uses his knowledge of infinite convergent series. Robert Hooke and Isaac Newton later took up this approach to atmospheric refraction and provided a demonstration of Oresme’s result.

SUPPLEMENTARY BIBLIOGRAPHY

Albert Douglas Menut’s bibliography of Oresme’s works (“A Provisional Bibliography of Oresme’s Writings,” Medieval Studies 28 [1966]: 279–299, and the “Supplementary Note,” Medieval Studies 31 [1969]: 346–347) has been supplanted by the entry “Nicolaus Oresme” in Olga Weijers, Le travail intellectuel à la Faculté des Arts de Paris: Textes et maîtres (ca. 1200–1500), vol. 6. (Turnhout, Belgium: Brepols, 2005). The great part of Oresme’s commentaries on Aristotle’s works has been edited, as follows in the “Works” section.

WORKS BY ORESME

De celo: Claudia Kren, The Questiones super De celo of Nicole Oresme, PhD diss., University of Wisconsin, 1965.

Commentary on John of Holiwood’s De spera: Garrett Droppers, The Questiones De spera of Nicole Oresme. PhD diss., University of Wisconsin, 1966.

Metereologics: Stepen C. McCluskey Jr., Nicole Oresme on Light, Color, and the Rainbow. PhD diss., University of Wisconsin, 1974. Questions on the third book.

Questio contra divinatores horoscopios: Stefano Caroti, “Nicole Oresme, Quaestio contra divinatores horoscopios,” Archives d’Histoire Doctrinale et Littéraire du Moyen Age 43 (1976): 201–310.

De sensu et sensato: Jole Agrimi, Le “Quaestiones de sensu” attribuite a Oresme e Alberto di Sassonia. Florence: La Nuova Italia, 1983.

Quodlibeta: Bert Hansen, Nicole Oresme and the Marvels of Nature: A Study of His “De causis mirabilium.” Toronto: Pontifical Institute of Mediaeval Studies, 1985. Parts 1 and 2.

De anima: Benoît Patar, Nicolai Oresme Expositio et Quaestiones in Aristotelis “De anima.” Edition, étude, critique. Études doctrinales en collaboration avec Claude Gagnon. LouvainLa-Neuve, Louvain, Paris: Éditions de l’Institut Supérieur de Philosophie, Éditions Peeters, 1995.

De generatione et corruptione: Stefano Caroti, ed., Quaestiones super De generatione et corruptione. Munich: Bayerische Akademie der Wissenschaften, 1996.

Physica: Stefan Kirschner, ed., Nicolaus Oresmes Kommentar zur Physik des Aristoteles. Stuttgart: Franz Steiner Verlag, 1997 (books 3–4; questions 6–9 of book 5). The complete edition edited by Stefano Caroti, Jean Celeyrette, Stefan Kirschner, and Edmond Mazet is forthcoming.

De visione stellarum: Dan Burton, Nicole Oresme’s “De visione stellarum” (On Seeing the Stars): A Critical Edition of Oresme’s Treatise on Optics and Atmospheric Refraction, with an Introduction, Commentary, and English Translation. Leiden: Brill, 2006.

OTHER SOURCES

Bosemberg, Zoe “Nicole Oresme et Robert Grosseteste: La conception dynamique de la matière.” In “Quia inter doctores est magna dissensio”: Les débats de philosophie naturelle à Paris au XIVe siècle, edited by Stefano Caroti and Jean Celeyrette. Florence: Leo S. Olschki, 2004.

Busard, Hubertus L. L. “Die Quellen von Nicole Oresme.” Janus58 (1971): 161–193.

Cadden, Joan. “Charles V, Nicole Oresme, and Christine de Pizan: Unities and Uses of Knowledge in Fourteenth-Century France.” In Texts and Contexts in Ancient and Medieval Science: Studies on the Occasion of John E. Murdoch’s Seventieth Birthday, edited by Edith Dudley Sylla and Michael M. McVaugh. Leiden and New York: Brill, 1997.

Caroti, Stefano. “Ordo universalis e impetus nei Quodlibeta di Nicole Oresme.” Archives Internationales d’Histoire des Sciences33 (1983): 213–233.

_____. “Ein Kapitel der mittelalterlichen Diskussion über reactio: Das novum fundamentum Nicole Oresmes und dessen Widerlegung durch Marsilius von Inghen.” In Historia Philosophiae Medii Aevi. Studien zur Geschichte der Philosophie des Mittelalters: Festschrift für Kurt Flach zu seinem 60. Geburtstag, edited by Burkhard Mojsisch and Olaf Pluta, vol. 1. Amsterdam and Philadelphia: Grüner, 1991.

_____. “Oresme on Motion.” Vivarium 31 (1993): 8–36.

_____. “La position de Nicole Oresme sur la nature du mouvement (Questiones super Physicam III, 1–8): Problèmes gnoséologiques, ontologiques et sémantiques.” Archives d’Histoire Doctrinale et Littéraire du Moyen Age 61 (1994): 303–385. _____. “Nicole Oresme et les modi rerum.” Oriens-Occidens 3 (2000): 115–144.

_____. “Time and Modi Rerum in Nicole Oresme’s PhysicsCommentary.” In The Medieval Concept of Time: Studies on the Scholastic Debate and Its Reception in Early Modern Philosophy, edited by Pasquale Porro. Leiden and Boston: Brill, 2001.

Celeyrette, Jean. “Le statut des mathématiques dans la Physique d’Oresme.” Oriens-Occidens 3 (2000): 91–113.

_____. Figura/figuratum par Jean Buridan et Nicole Oresme.” In “Quia inter doctores est magna dissensio”: Les débats de philosophie naturelle à Paris au XIVe siècle, edited by Stefano Caroti and Jean Celeyrette. Florence: Leo S. Olschki, 2004.

_____. , and Edmond Mazet. “La hierarchie des degrés d’être chez Nicole Oresme.” Arabic Sciences and Philosophy 8 (1998): 45–65.

Courtenay, William J. “The Early Career of Nicole Oresme.” Isis91 (2000): 542–548.

Di Liscia, Daniel A. “Sobre la doctrina de las “Configurationes” de Nicolas de Oresme.” Patristica et Mediaevalia 11 (1990): 79–105.

_____. “Aceleracion y caída de los graves en Oresme: Sobre la inaplicabilidad del teorema de la velocidad media.” Patristica et Mediaevalia 13 (1992): 61–84; 14 (1993): 41–56.

Grant, Edward. “Scientific Thought in Fourteenth-Century Paris: Jean Buridan and Nicole Oresme.” In Machaut’s World: Science and Art in the Fourteenth Century, edited by Madeleine Pelner Cosman and Bruce Chandler. New York: New York Academy of Sciences, 1978.

_____. “Nicole Oresme on Certitude in Science and Pseudo-Science.” In Nicolas Oresme: Tradition et innovation chez un intellectuel du XIVe siècle, edited by Pierre Souffrin and Alain P. Ségonds. Paris and Padua: Les Belles Lettres–Programma 1+1 Editori, 1988.

_____. “Nicole Oresme, Aristotle’s ‘On the Heavens,’ and the Court of Charles V.” In Texts and Contexts in Ancient and Medieval Science: Studies on the Occasion of John E. Murdoch’s Seventieth Birthday, edited by Edith Dudley Sylla and Michael R. McVaugh. Leiden and New York: Brill, 1997.

_____. A History of Natural Philosophy: From the Ancient World to the Nineteenth Century. Cambridge, U.K.: Cambridge University Press, 2007.

Hugonnard-Roche, Henri. “Logique et philosophie naturelle au XIVe siècle: La critique d’Aristote par Nicole Oresme.” In Actes du 109^e Congrès national des Sociétés savantes, Dijon 1984. Section Histoire des sciences et des techniques. Paris: Comité des Travaux historiques et scientifiques, 1984.

_____. “Modalités et argumentation chez Nicole Oresme.” In Nicolas Oresme: Tradition et innovation chez un intellectuel du XIVe siècle, edited by Pierre Souffrin and Alain P. Ségonds. Paris and Padua: Les Belles Lettres–Programma 1+1 Editori, 1988.

Kirschner, Stefan. “Oresme on Intension and Remission of Qualities in His Commentary on Aristotle’s ‘Physics.’” Vivarium 38 (2000): 255–274.

_____. “Oresme’s Concepts of Place, Space, and Time in His Commentary on Aristotle’s Physics.” Oriens-Occidens 3 (2000): 145–179.

Marshall, Peter. “Nicole Oresme on the Nature, Reflection, and Speed of Light.” Isis 72 (1981): 357–374.

_____. “Parisian Psychology in the Mid-Fourteenth Century.” Archives d’Histoire Doctrinale et Littéraire du Moyen Age 50 (1983): 101–193.

Lejbowicz, Max. “Argumentation oresmienne et logique divinatoire (quelques remarques sur le De commensurabilitate, III).” In Preuve et raisons à l’Université de Paris: Logique, ontologie et théologie au XIVe siècle, edited by Zénon Kaluza and Paul Vignaux. Paris: Vrin, 1984.

Mazet, Edmond. “Un aspect de l’ontologie d’Oresme: L’équivocité de l’étant et ses rapports avec la théorie des complexe significabilia et avec l’ontologie oresmienne de l’accident.” Oriens-Occident 3 (2000): 67–89.

_____. “Pierre Ceffons et Oresme: Leur relation revisitée.” In “Quia inter doctores est magna dissensio”: Les débats de philosophie naturelle à Paris au XIVe siècle, edited by Stefano Caroti and Jean Celeyrette. Florence: Leo S. Olschki, 2004.

Molland, George A. “Nicole Oresme and Scientific Progress.” In Antiqui und Moderni: Traditionsbewuβtsein und Fortschrittsbewuβtsein im späten Mittelalter, edited by Albert Zimmermann. Berlin: De Gruyter, 1974.

_____. “The Oresmian Style: Semi-Mathematical, Semi-Holistic.” In Nicolas Oresme: Tradition et innovation chez un intellectuel du XIVe siècle, edited by Pierre Souffrin and Alain P. Ségonds. Paris and Padua: Les Belles Lettres–Programma 1+1 Editori, 1988.

Quillet, Jeannine, ed. Autour de Nicole Oresme: Actes du Colloque Oresme organisé à l’Université de Paris XII. Paris: Vrin, 1990.

_____. “Nicole Osreme et la science nouvelle dans le livre du Ciel et du Monde.” In Knowledge and the Sciences in Medieval Philosophy. Proceedings of the Eight International Congress of Medieval Philosophy (SIEPM), edited by Simo Knuuttila, Reijo Työrinoja, and Sten Ebbesen, vol. 2. Helsinki: Societas Philosophica Fennica, 1990.

Rusnock, Paul. “Oresme on Ratios of Lesser Inequality.” Archives Internationales d’Histoire des Sciences 45 (1995): 263–272.

Sarnowsky, Jürgen. “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 Jean Celeyrette. Florence: Leo S. Olschki, 2004.

Souffrin, Pierre. “La quantification du mouvement chez les scolastiques: La vitesse instantanée chez Nicole Oresme.” In Autour de Nicole Oresme: Actes du Colloque Oresme organisé à l’Université de Paris XII, edited by Jeannine Quillet. Paris: Vrin, 1990.

Souffrin, Pierre, and Alain P. Ségonds, eds. Nicolas Oresme: Tradition et innovation chez un intellectuel du XIVe siècle. Paris and Padua: Les Belles Lettres–Programma 1+1 Editori, 1988.

Taschow, Ulrich. “Die Bedeutung der Musik als Modell für Nicole Oresmes Theorie ‘De configurationibus qualitatum et motuum.’” Early Science and Medicine 4 (1999): 37–90.

Thijssen, Hans. “Buridan, Albert of Saxony, and Oresme, and a Fourteenth-Century Collection of Quaestiones on the Physics and on De generatione et corruptione.” Vivarium24 (1986): 70–82.

Von Plato, Jan. “Nicole Oresme and the Ergodicity of Rotations.” Acta Philosophica Fennica32 (1981): 190–197.

Zanin, Fabio. “Passio corruptiva/passio perfectiva: A basic Distinction in Oresme’s Theory of Knowledge.” In “Quia inter doctores est magna dissensio”: Les débats de philosophie naturelle à Paris au XIVe siècle, edited by Stefano Caroti and Jean Celeyrette. Florence: Leo S. Olschki, 2004.

Stefano Caroti

Oresme, Nicole

works by oresme

supplementary bibliography

Nicole Oresme (c. 1325-1382) was a man of broad interests, among which were both moral philosophy and the natural sciences, notably physics and astronomy. Born in a village near Caen, Oresme studied at the University of Paris and took his degree in theology. He was a bursar at thecollege at Navarre from 1348 until 1356, when, having received his master’s degree, he was appointed grand master of his college. In 1361 he received a canonry at Rouen and soon afterward another at the Sainte-Chapelle in Paris. In 1364 he became dean of the cathedral chapter of Rouen, but he was dispensed from taking up residence there at the special request of King Charles v. Oresme’s career reached its zenith in 1378 when he was elevated to the episcopal see of Lisieux, where he died four years later.

Although a scholar rather than a man of action, Oresme enjoyed the confidence of Charles v, king of France, who reigned from 1364-1380, and he was for many years a member of the council. In this capacity Oresme was able to influence policy, especially monetary policy, in accordance with his own ideas. At the behest of his royal master, he translated Aristotle’s Politics, Nicomachean Ethics,and Economics from the Latin into French. (TheEconomics, of course, is not a treatise on economics in the modern sense but a work dealing with household management.) To the text of all these translations Oresme, in medieval fashion, added his own glosses.

At the king’s bidding, Oresme also translated into French De caelo et mundo ( “Concerning Heaven and Earth “), an exposition of Aristotle’s cosmological system. He challenged this system by postulating the theory that the earth rotates in the center of a motionless universe. Although far from anticipating the Copernican system, such a theory at least demonstrates an inclination toward independent inquiry that was hardly common in the fourteenth century. Even more remarkable are Oresme’s views on the atomistic composition of matter.

Oresme is remembered, however, less for his scientific views or his translations from Aristotle than for his Latin treatise on money, Tractatus de origine, natura jure, et mutationibus monetarum(c. 1373b, translated into English as De moneta in 1956). The author himself prepared a French version under the title Traictie de la premiere invention des monnoies. Although the Latin version was republished several times in the course of the sixteenth, seventeenth, and eighteenth centuries, Oresme’s treatise attracted little attention until it was “rediscovered” in 1862 by Wilhelm Roscher, who hailed it as a work of great originality containing the first formulation of sound monetary principles. Such claims are rather extravagant, since Oresme anticipated neither the quantity theory of money nor even Gresham’s law, although he did note that debasement will lead to the disappearance of the better coins and leave the realm void of gold and silver (c. 1373Z?, chapter 20).

The Tractatus, indeed, is more concerned with monetary policy than with monetary theory. Oresme’s approach to economics is purely scholastic, that is, ethical and legal. He was an Aristotelian who, in the introductory and theoretical chapters of his treatise, carried his analysis little further than the Greek philosopher did, and confined himself to some trite remarks on the inconveniences of barter and the functions of money as a standard of value and as a medium of exchange.

Oresme’s originality lies mainly in his elaboration of policies that permit money to perform its functions adequately. Money should be stable, and Oresme, therefore, vigorously opposed debasement of the currency and the use of minting privileges as a source of revenue. Debasing the currency is, in his opinion, cheating and committing a crime worse than usury (c. 1373b, chapter 17). Money, according to Oresme, was instituted for the benefit of the common weal rather than of the prince, who should not alter the standard of the currency except as a last resort and with the people’s consent(consensus populi). An emergency warranting this step would be, for example, the defense of the realm against a foreign foe, or a change in the proportionate value of gold and silver that would necessitate a corresponding adjustment of the coinage. Progressive debasement, Oresme pointed out, benefits only a small minority of money dealers and bankers, whereas it harms the community at large by disturbing trade, undermining the sanctity of contracts, upsetting the existing social order, and bringing ruin to the recipients of rents, pensions, and other fixed incomes. The policy advocated by Oresme was in fact adopted by Charles v, who maintained the same monetary standard from 1365 until the end of his reign.

Oresme did not favor free coinage. He recommended that the cost of minting be borne by the “community/’ that is, not by the prince or the states, but rather by those who deliver bullion to the mint. In any event, seigniorage charges ought not to be high—this would encourage inflation—but just sufficient to cover the actual costs of coinage.

Although Oresme’s treatise represents the summit of scholastic achievement on the subject of money, it is unsatisfactory in many respects and exerted little influence on later writers on the same subject, with the exception of Gabriel Biel (c. 1483),whose treatise is brief, mediocre, and unoriginal. In general, a concern with monetary problems is mercantilistic rather than scholastic. The scholastic doctors of the sixteenth century did make some progress and accepted a crude quantity theory as a matter of course, but they did not delve into the subject with any thoroughness. The basic defect of the scholastic school of economics stems from its normative approach to economic and monetary problems, which warps its analysis in thisfield,as elsewhere.

Raymond de Roover

[For the historical context of Oresme’s work, seeEconomic Thought, article onAncient AND Medieval Thought; and the biography ofAquinas.]

works by oresme

(c. 1371) 1957 Maistre Nicole Oresme: Le livre de yconomique d’Aristote. Edited by Albert D. Menut. American Philosophical Society, Transactions New Series 47: 783-853.

(c. 1373a) 1864 Traictie de la premiere invention des monnoies. Edited and annotated by M. Wolowski. Paris: Guillaumin.

(c. 1373b) 1956 The De moneta of Nicholas Oresme;and English Mint Documents. Edited by Charles Johnson. London and New York: Nelson. → First published as Tractatus de origine, natura jure, et mutationibus monetarum.

supplementary bibliography

Biel, Gabriel(C. 1483) 1930 Treatise on the Power and Utility of Moneys. Edited by Robert B. Burke. Philadelphia: Univ. of Pennsylvania Press. → First published as Tractatus de putestute et utilitate moneturum.

Bridrey, Émile 1906 La theorie de la monnaie au XIV siecle; Nicole Oresme: ttude d’histoire des doctrines et des faits economiques. Paris: Giard & Briere.

Grice-Hutchinson, Marjorie 1952 The School of Salamanca: Readings in Spanish Monetary Theory, 15441605. Oxford: Clarendon.

Oresme, Nicole (ca. 1320-1382)

Bishop of Lisieux, France, in 1378, who published works on theology, politics, economics, mathematics, and physical science. His book Livre de Divinacions expresses orthodox theological thought on various aspects of medieval occultism. The book is titled after the De Divinatione of Cicero and defines the arguments for and against belief in the occult, lists frauds and deceptions in divination, and distinguishes between astrology and astronomy. Oresme accepted alchemy and ascribed occult success to demons.

Oresme was born ca. 1320, probably in Normandy, and entered the College of Navarre in Paris in 1348. As Archdeacon of Bayeux, he accepted the Deanship of Rouen but retained his university office until obliged to relinquish it due to a decision by the Parliament of Paris. In 1378, after his translation of the works of Aristotle into French, he was given the bishopric of Lisieux. He died in 1382.

His Livre de Divinacions was originally written in Latin, subsequently in French. In the absence of an English translation, there was little scholarly discussion of the work until the 1900s. In 1934, Lynn Thorndike devoted three chapters in Volume 3 of History of Magic and Experimental Science to a detailed study of Oresme's work.

Sources:

Coopland, G. W. Nicole Oresme and the Astrologers; A Study of His "Livre de Divinacions." Liverpool, UK: University Press of Liverpool, 1952.

Thorndike, Lynn. History of Magic and Experimental Science. Vol. 3. New York: Columbia University Press, 1923-58.