Thus he deduces the existence of time from the existence of motion, which means that time is nothing independent of motion. In contrast to Aristotle, Oresme in his Physics Commentary defines time as the successive duration of things duratio rerum successiva , also duratio successiva rerum or rerum duratio successiva , that is, the duration of the actual existence of things. The Franciscan Gerardus Odonis c. Oresme states that the duration of things without any succession is eternity, which he defines as duratio rerum tota simul.
As with the relation between God and extramundane space, Oresme identifies eternity with God himself Kirschner a, — His theory of motion is highly specific and turns out to be an application of his characteristic condicio -theory of accidents Caroti ; Caroti ; Kirschner , 52—78; Kirschner For Oresme motion is a fluxus , a successive entity of its own that exists in addition to the mobile and the things that are acquired during motion.
This is a clear departure from the nominalistic position. Concerning its ontological status this fluxus is not considered a separate accidental form but only a modus se habendi or a condicio of the mobile. Thus Oresme circumvents the difficulties of a pure nominalistic approach, while simultaneously avoiding the problems that occur if one assigns the fluxus the ontological status of an accidental form, as Buridan did in the case of local motion in his Physics commentary ultima lectura Buridan, Questiones super octo Phisicorum libros Aristotelis , Qu.
Such a uniform concept of motion was one of his major aims. Unfortunately, posterity does not seem to have appreciated his endeavour. In his Livre du ciel et du monde and in other works Questiones super De celo , Questiones de spera Oresme brilliantly argues against any proof of the Aristotelian theory of a stationary Earth and a rotating sphere of the fixed stars.
Similarly, Oresme proves the possibility of a plurality of worlds, but ultimately keeps to the Aristotelian tenet of a single cosmos Clagett , —; Harvey Oresme was a determined opponent of astrology, which he attacked on religious and scientific grounds. In De proportionibus proportionum Oresme first examined raising rational numbers to rational powers before extending his work to include irrational powers.
The results of both operations he termed irrational ratios , although he considered the first type commensurable with rational numbers, and the latter not. In modern terms:. Oresme then asserted that the ratio of any two celestial motions is probably incommensurable Grant , 67— Interestingly, in the first redaction of his Questions on Meteorology Oresme does not yet turn out to be the resolute opponent of astrology as we know him from his later works, but, quite the contrary, adheres to its principles Panzica , 2.
In his De visione stellarum Oresme departs from the standard view of earlier authors in optics such as Ptolemy 2 nd century , Ibn al-Haytham —c. He states — more than years before Robert Hooke — and Newton — that atmospheric refraction occurs along a curve and proposes to approximate the curved path of a ray of light in a medium of uniformly varying density, in this case the atmosphere, by an infinite series of line segments each representing a single refraction Burton , 33— In these works Oresme conceived of the idea of using rectangular coordinates latitudo and longitudo and the resulting geometric figures configurationes to distinguish between uniform and nonuniform distributions of various quantities, such as the change of velocity in relation to time or the distribution of the intensities of a quality in relation to the extension of the subject.
In the discussion of motions the base line longitudo is the time, while the perpendiculars raised on the base line latitudines represent the velocity from instant to instant in the motion. Thus uniform acceleration is represented by a right triangle. Oresme even extended his definition to include three-dimensional figures Clagett , — Most interestingly, Oresme seems to have given a general rule of how to find the sum of all convergent series of the form:.
Murdoch ; Mazet The reverse of this fraction, i. Thus, if we have the series. Busard ed. If a is 2, the sum will be 3. Furthermore Oresme was the first to prove that the harmonic series. Oresme demonstrates by thought experiments that of two actual infinites neither is bigger or smaller than the other.
Thus Oresme shows by the principle of one-to-one correspondence that the collection of odd natural numbers is not smaller than the collection of natural numbers, because it is possible to count the odd natural numbers by the natural numbers Sesiano ; Kirschner , 79—83, 88— Oresme was not the first to use the principle of one-to-one correspondence in discussing the properties of actual infinites.
On the other hand Bradwardine takes it for granted that an infinite subset is smaller than the set of which it is a part. Thus he is of the opinion that under the assumption of an eternal world that has no beginning the multitude of all human souls, which until now have been created, must be greater than the multitude of the male or the female souls alone Bradwardine , E—A.
From this contradiction — an infinite subset cannot be both smaller than and equal to the set of which it is a part — Bradwardine draws the inference that the eternity of the world is impossible Thakkar , — Unlike Bradwardine, Oresme shows that of two actual infinites neither is greater or smaller than the other. Oresme is generally considered the greatest medieval economist. He presented his economic ideas in commentaries on the Ethics , Politics , and Economics , as well as an earlier treatise, De origine, natura, jure et mutationibus monetarum , the first comprehensive work upon money.
Oresme also stated that in a society in which two currencies with the same designation but of different value circulate, the money of lower value drives out the money of higher value. This economic law was also discovered independently of Oresme by Nicolaus Copernicus — , the famous astronomer, who wrote about a reform of the Prussian coinage, and by Thomas Gresham — As Kaye , 2 has argued, the preoccupation with measurement, gradation, and the quantification of qualities, so typical of Oresme and the natural philosophy of his period, was strongly influenced by the contemporary rapid monetization of European society.
Life 2. Teachings 2. Life Nicole Oresme was born around in the diocese of Bayeux in Normandy, possibly in the village of Allemagne now Fleury-sur-Orne on the outskirts of the Norman city of Caen Burton , 6. Prologus et distinctio prima , R. Wood and G. Bonaventure, NY: St. Bonaventure University, Bradwardine, Th. Buridan, J. Frankfurt am Main, Minerva, Crescas, H. Wolfson ed. Trapp OSA and V. Marcolino eds. Oresme, N. Oresme , L. Wolowski ed.
Also in Johnson, Ch. London etc. He observes that sailors and farmers are better at predicting weather than astrologers, and specifically attacks the astrological basis of prediction, noting correctly that the zodiac has moved relative to the fixed stars because of precession of the equinoxes since the zodiac was first described in ancient times.
These first three parts are what Oresme considers the physical influences of the stars and planets including sun and moon on the earth, and while he offers critiques of them, he accepts that effects exist.
The last three parts are what Oresme considers to concern good or bad fortune. They are interrogations, meaning asking the stars when to do things such as business deals; elections, meaning choosing the best time to do things such as getting married or fighting a war; and nativities, meaning the natal astrology with birth charts that forms much of modern astrological practice.
Oresme classifies interrogations and elections as "totally false" arts, but his critique of nativities is more measured. He denies that any path is predetermined by the heavenly bodies, because humans have free will, but he accepts that the heavenly bodies can influence behaviour and habitual mood, via the combination of humours in each person.
Overall, Oresme's skepticism is strongly shaped by his understanding of the scope of astrology. He accepts things a modern skeptic would reject, and rejects some things — such as the knowability of planetary movements, and effects on weather — that are accepted by modern science.
In discussing the propagation of light and sound, Oresme adopted the common medieval doctrine of the multiplication of species, as it had been developed by optical writers such as Alhacen, Robert Grosseteste, Roger Bacon, John Pecham, and Witelo. Oresme maintained that these species were immaterial, but corporeal i. Like most of his scholarly contemporaries, Oresme wrote primarily in Latin, but at the urging of King Charles V, he also wrote in French, providing French versions of his own works and of selected works by Aristotle.
Oresme's most important contributions to mathematics are contained in Tractatus de configurationibus qualitatum et motuum. In a quality, or accidental form, such as heat, he distinguished the intensio the degree of heat at each point and the extensio as the length of the heated rod.
These two terms were often replaced by latitudo and longitudo. For the sake of clarity, Oresme conceived the idea of visualizing these concepts by plane figures, approaching what we would now call rectangular co-ordinates. The intensity of the quality was represented by a length or latitudo proportional to the intensity erected perpendicular to the base at a given point on the base line, which represents the longitudo. Oresme proposed that the geometrical form of such a figure could be regarded as corresponding to a characteristic of the quality itself.
Oresme defined a uniform quality as that which is represented by a line parallel to the longitude, and any other quality as difform. Uniformly varying qualities are represented by a straight line inclined to the axis of the longitude, while he described many cases of nonuniformly varying qualities. Oresme extended this doctrine to figures of three dimensions. He considered this analysis applicable to many different qualities such as hotness, whiteness, and sweetness. Significantly for later developments, Oresme applied this concept to the analysis of local motion where the latitudo or intensity represented the speed, the longitudo represented the time, and the area of the figure represented the distance travelled.
He shows that his method of figuring the latitude of forms is applicable to the movement of a point, on condition that the time is taken as longitude and the speed as latitude; quantity is, then, the space covered in a given time. He then answered his own question, arguing that the irrationality of ratios will not rob the heavens of their beauty and will also not be inconsistent with regular movement.
Oresme also worked on infinite series and argued for an infinite void beyond the Earth. Clagett writes in [ 3 ] :- This brilliant scholar has been credited with None of these claims is, in fact, true, although each is based on discussion by Oresme of some penetration and originality In Livre du ciel et du monde Oresme opposed the theory of a stationary Earth as proposed by Aristotle and in this work he proposed rotation of the Earth some years before Copernicus.
However he rather spoilt this fine piece of thinking by rejecting his own ideas at the end of the work and so, as Clagett writes, cannot be regarded as claiming that the Earth rotated before Copernicus. He wrote Questiones Super Libros Aristotelis de Anima dealing with the nature of light, reflection of light, and the speed of light.
Oresme's work on light is discussed in detail in [ 16 ]. References show. Biography in Encyclopaedia Britannica. M Clagett ed. A treatise on the uniformity and difformity of intensities known as 'Tractatus de configurationibus qualitatum et motuum' Madison, Wis. E Grant ed. O Pederson, Nicole Oresme Copenhagen, L Gribaudo, Was Oresme a precursor of Descartes? Italian , Atti Accad.
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