Thomas Bradwardine
Encyclopedia
Thomas Bradwardine was an English
scholar, scientist, courtier and, very briefly, Archbishop of Canterbury
. As a celebrated scholastic philosopher and doctor of theology
, he is often called Doctor Profundus, (medieval epithet, meaning "the Profound Doctor").
in Sussex
or at Chichester
, where his family were settled, members of the smaller gentry or burghers.
He was a precocious student, educated at Balliol College, Oxford
where he was a fellow by 1321; he took the degree of doctor of divinity, and acquired the reputation of a profound scholar, a skilful mathematician
and an able theologian
. He was also a gifted logician with theories on the insolubles
and in particular the liar paradox
.
He subsequently moved to Merton College, Oxford
on a fellowship. He was afterwards raised to the high offices of chancellor of the university and professor of divinity. Bradwardine (like his contemporary William of Occam) was a culminating figure of the great intellectual movement at Oxford that had begun in the 1240s.
Bradwardine was an ordinary secular cleric, which gave him intellectual freedom but deprived him of the security and wherewithal that the Preaching Orders would have afforded; instead he turned to royal patronage. From being chancellor of the diocese of London
as– Dean of St Paul's
, he became chaplain and confessor to Edward III
, whom he attended during his wars in France at the Battle of Crécy
, where he preached at the victory Mass, and at the subsequent siege of Calais. Edward repeatedly entrusted him with diplomatic missions. On his return to England, he was successively appointed prebendary
of Lincoln and archdeacon (1347). In 1349 the canons of the chapter at Canterbury elected him Archbishop following the death of Archbishop John Stratford, but Edward III
withheld his consent, preferring his chancellor John de Ufford
, perhaps loath to lose his trusted confessor. After Ufford died of the Black Death
, 2 May, Bradwardine went to receive confirmation from Clement VI
at Avignon, but on his return he died of the plague at Rochester on 26 August 1349, forty days after his consecration. He was buried at Canterbury.
Chaucer in The Nun's Priest's Tale (line 476) ranks Bradwardine with Augustine
and Boethius
. His great theological work, to modern eyes, is a treatise against the Pelagians, entitled De causa Dei contra Pelagium et de virtute causarum. Bradwardine's major treatise argued that space was an infinite void in which God could have created other worlds, which he would rule as he ruled this one. The "causes of virtue" include the influences of the planets
, not as predestining a human career, but influencing a subject's essential nature. This astrophysical treatise was not published until it was edited by Sir Henry Savile and printed in London, 1618; its circulation in manuscript was very limited. The implications of the infinite void were revolutionary; to have pursued them would have threatened the singular relationship of man and this natural world to God (Cantor 2001); in it he treated theology mathematically. He wrote also De Geometria speculativa (printed at Paris, 1530); De Arithmetica practica (printed at Paris, 1502); De proportionibus velocitatum in motibus (1328) (printed at Paris, 1495; Venice, 1505); De Quadratura Circuli (Paris, 1495); and an Ars Memorative, Sloane manuscripts. No. 3974 in the British Museum
—earning from the Pope the title of the Profound Doctor. Another text, De Continuo is more tenuously credited to him and thought to be written sometime between 1328 and 1325.
. Bradwardine was one of these Oxford Calculators
, studying mechanics with William Heytesbury
, Richard Swineshead
, and John Dumbleton
. The Oxford Calculators distinguished kinematics
from dynamics
, emphasizing kinematics, and investigating instantaneous velocity. They first formulated the mean speed theorem
: a body moving with constant velocity travels the same distance as an accelerated body in the same time if its velocity is half the final speed of the accelerated body. They also demonstrated this theorem — the foundation of "The Law of Falling Bodies" — long before Galileo
, who is generally credited with it.
The mathematical physicist and historian of science Clifford Truesdell
, wrote:
In Tractatus de proportionibus (1328), Thomas Bradwardine extended the theory of proportions of Eudoxus of Cnidus
to anticipate the concept of exponential growth
, later developed by the Bernoulli and Euler
, with compound interest
as a special case. Arguments for the mean speed theorem (above) require the modern mathematical concept of limit
, so Bradwardine had to use arguments of his day. Mathematician and mathematical historian Carl O. Boyer writes, "Bradwardine developed the Boethian theory
of double or triple or, more generally, what we would call 'n-tuple' proportion".
Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry
gleaned from Muslim
sources". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science" (Cantor 2001, p. 122). The most essential missing tool was calculus
.
, a loosely associated group of mnemonic principles and techniques used to organize memory impressions, improve recall, and assist in the combination and 'invention' of ideas. His De Memoria Artificiali (c. 1335) discusses memory training current during his time.
including the liar paradox
were a great influence on the work of Jean Buridan
and therefore, in turn of the more recent philosopher A. N. Prior. His work on the liar paradox has been most recently studied by Paul Spade and Stephen Read (for which see Spade's entry in the Stanford Encyclopedia of Philosophy, which offers a brief exposition).
English people
The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...
scholar, scientist, courtier and, very briefly, Archbishop of Canterbury
Archbishop of Canterbury
The Archbishop of Canterbury is the senior bishop and principal leader of the Church of England, the symbolic head of the worldwide Anglican Communion, and the diocesan bishop of the Diocese of Canterbury. In his role as head of the Anglican Communion, the archbishop leads the third largest group...
. As a celebrated scholastic philosopher and doctor of theology
Doctor of Theology
Doctor of Theology is a terminal academic degree in theology. It is a research degree that is considered by the U.S. National Science Foundation to be the equivalent of a Doctor of Philosophy....
, he is often called Doctor Profundus, (medieval epithet, meaning "the Profound Doctor").
Life
He was born either at HartfieldHartfield
Hartfield is a civil parish in East Sussex, England. Settlements within the parish include the village of Hartfield, Colemans Hatch, Hammerwood and Holtye, all lying on the northern edge of Ashdown Forest.-Geography:...
in Sussex
Sussex
Sussex , from the Old English Sūþsēaxe , is an historic county in South East England corresponding roughly in area to the ancient Kingdom of Sussex. It is bounded on the north by Surrey, east by Kent, south by the English Channel, and west by Hampshire, and is divided for local government into West...
or at Chichester
Chichester
Chichester is a cathedral city in West Sussex, within the historic County of Sussex, South-East England. It has a long history as a settlement; its Roman past and its subsequent importance in Anglo-Saxon times are only its beginnings...
, where his family were settled, members of the smaller gentry or burghers.
He was a precocious student, educated at Balliol College, Oxford
Balliol College, Oxford
Balliol College , founded in 1263, is one of the constituent colleges of the University of Oxford in England but founded by a family with strong Scottish connections....
where he was a fellow by 1321; he took the degree of doctor of divinity, and acquired the reputation of a profound scholar, a skilful mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and an able theologian
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
. He was also a gifted logician with theories on the insolubles
Insolubilia
In the Middle Ages, variations on the liar paradox were studied under the name of insolubilia .Although the liar paradox was well known in antiquity, interest seems to have lapsed until the twelfth century, when it appears to have been reinvented independently of ancient authors...
and in particular the liar paradox
Liar paradox
In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...
.
He subsequently moved to Merton College, Oxford
Merton College, Oxford
Merton College is one of the constituent colleges of the University of Oxford in England. Its foundation can be traced back to the 1260s when Walter de Merton, chancellor to Henry III and later to Edward I, first drew up statutes for an independent academic community and established endowments to...
on a fellowship. He was afterwards raised to the high offices of chancellor of the university and professor of divinity. Bradwardine (like his contemporary William of Occam) was a culminating figure of the great intellectual movement at Oxford that had begun in the 1240s.
Bradwardine was an ordinary secular cleric, which gave him intellectual freedom but deprived him of the security and wherewithal that the Preaching Orders would have afforded; instead he turned to royal patronage. From being chancellor of the diocese of London
Diocese of London
The Anglican Diocese of London forms part of the Province of Canterbury in England.Historically the diocese covered a large area north of the Thames and bordered the dioceses of Norwich and Lincoln to the north and west. The present diocese covers and 17 London boroughs, covering most of Greater...
as– Dean of St Paul's
Dean of St Paul's
The Dean of St Paul's is the head of the Chapter of St Paul's Cathedral in London, England in the Church of England. The most recent Dean, Graeme Knowles, formerly Bishop of Sodor and Man, was installed on 1 October 2007 and resigned on 31 October 2011...
, he became chaplain and confessor to Edward III
Edward III of England
Edward III was King of England from 1327 until his death and is noted for his military success. Restoring royal authority after the disastrous reign of his father, Edward II, Edward III went on to transform the Kingdom of England into one of the most formidable military powers in Europe...
, whom he attended during his wars in France at the Battle of Crécy
Battle of Crécy
The Battle of Crécy took place on 26 August 1346 near Crécy in northern France, and was one of the most important battles of the Hundred Years' War...
, where he preached at the victory Mass, and at the subsequent siege of Calais. Edward repeatedly entrusted him with diplomatic missions. On his return to England, he was successively appointed prebendary
Prebendary
A prebendary is a post connected to an Anglican or Catholic cathedral or collegiate church and is a type of canon. Prebendaries have a role in the administration of the cathedral...
of Lincoln and archdeacon (1347). In 1349 the canons of the chapter at Canterbury elected him Archbishop following the death of Archbishop John Stratford, but Edward III
Edward III of England
Edward III was King of England from 1327 until his death and is noted for his military success. Restoring royal authority after the disastrous reign of his father, Edward II, Edward III went on to transform the Kingdom of England into one of the most formidable military powers in Europe...
withheld his consent, preferring his chancellor John de Ufford
John de Ufford
John de Ufford, sometimes John de Offord or John Offord was chancellor and head of the royal administration to Edward III as well as being appointed to the Archbishopric of Canterbury.-Early life:...
, perhaps loath to lose his trusted confessor. After Ufford died of the Black Death
Black Death
The Black Death was one of the most devastating pandemics in human history, peaking in Europe between 1348 and 1350. Of several competing theories, the dominant explanation for the Black Death is the plague theory, which attributes the outbreak to the bacterium Yersinia pestis. Thought to have...
, 2 May, Bradwardine went to receive confirmation from Clement VI
Pope Clement VI
Pope Clement VI , bornPierre Roger, the fourth of the Avignon Popes, was pope from May 1342 until his death in December of 1352...
at Avignon, but on his return he died of the plague at Rochester on 26 August 1349, forty days after his consecration. He was buried at Canterbury.
Chaucer in The Nun's Priest's Tale (line 476) ranks Bradwardine with Augustine
Augustine of Hippo
Augustine of Hippo , also known as Augustine, St. Augustine, St. Austin, St. Augoustinos, Blessed Augustine, or St. Augustine the Blessed, was Bishop of Hippo Regius . He was a Latin-speaking philosopher and theologian who lived in the Roman Africa Province...
and Boethius
Anicius Manlius Severinus Boethius
Anicius Manlius Severinus Boëthius, commonly called Boethius was a philosopher of the early 6th century. He was born in Rome to an ancient and important family which included emperors Petronius Maximus and Olybrius and many consuls. His father, Flavius Manlius Boethius, was consul in 487 after...
. His great theological work, to modern eyes, is a treatise against the Pelagians, entitled De causa Dei contra Pelagium et de virtute causarum. Bradwardine's major treatise argued that space was an infinite void in which God could have created other worlds, which he would rule as he ruled this one. The "causes of virtue" include the influences of the planets
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
, not as predestining a human career, but influencing a subject's essential nature. This astrophysical treatise was not published until it was edited by Sir Henry Savile and printed in London, 1618; its circulation in manuscript was very limited. The implications of the infinite void were revolutionary; to have pursued them would have threatened the singular relationship of man and this natural world to God (Cantor 2001); in it he treated theology mathematically. He wrote also De Geometria speculativa (printed at Paris, 1530); De Arithmetica practica (printed at Paris, 1502); De proportionibus velocitatum in motibus (1328) (printed at Paris, 1495; Venice, 1505); De Quadratura Circuli (Paris, 1495); and an Ars Memorative, Sloane manuscripts. No. 3974 in the British Museum
British Museum
The British Museum is a museum of human history and culture in London. Its collections, which number more than seven million objects, are amongst the largest and most comprehensive in the world and originate from all continents, illustrating and documenting the story of human culture from its...
—earning from the Pope the title of the Profound Doctor. Another text, De Continuo is more tenuously credited to him and thought to be written sometime between 1328 and 1325.
Science
Merton College sheltered a group of dons devoted to natural science, mainly physics, astronomy and mathematics, rivals of the intellectuals at the University of ParisUniversity of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
. Bradwardine was one of these Oxford Calculators
Oxford Calculators
The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford, who took a strikingly logico-mathematical approach to philosophical problems....
, studying mechanics with William Heytesbury
William Heytesbury
William Heytesbury , philosopher and logician, is best known as one of the Oxford Calculators of Merton College, where he was a fellow by 1330....
, Richard Swineshead
Richard Swineshead
Richard Swineshead was an English mathematician, logician, and natural philosopher. He was perhaps the greatest of the Oxford Calculators of Merton College, where he was a fellow certainly by 1344 and possibly by 1340.His magnum opus was a series of treatises known as the Liber calculationum ,...
, and John Dumbleton
John Dumbleton
John Dumbleton , one of the Oxford Calculators, was a Scholastic logician and natural philosopher at Merton College, Oxford, where he was a fellow by 1338...
. The Oxford Calculators distinguished kinematics
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
from dynamics
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...
, emphasizing kinematics, and investigating instantaneous velocity. They first formulated the mean speed theorem
Mean speed theorem
In the 14th-century, the Oxford Calculators of Merton College and French collaborators such as Nicole Oresme proved the mean speed theorem, also known as the Merton mean speed theorem...
: a body moving with constant velocity travels the same distance as an accelerated body in the same time if its velocity is half the final speed of the accelerated body. They also demonstrated this theorem — the foundation of "The Law of Falling Bodies" — long before Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
, who is generally credited with it.
The mathematical physicist and historian of science Clifford Truesdell
Clifford Truesdell
Clifford Ambrose Truesdell III was an American mathematician, natural philosopher, historian of science, and polemicist.-Life:...
, wrote:
In Tractatus de proportionibus (1328), Thomas Bradwardine extended the theory of proportions of Eudoxus of Cnidus
Eudoxus of Cnidus
Eudoxus of Cnidus was a Greek astronomer, mathematician, scholar and student of Plato. Since all his own works are lost, our knowledge of him is obtained from secondary sources, such as Aratus's poem on astronomy...
to anticipate the concept of exponential growth
Exponential growth
Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
, later developed by the Bernoulli and Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
, with compound interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....
as a special case. Arguments for the mean speed theorem (above) require the modern mathematical concept of limit
Limit (mathematics)
In mathematics, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. The concept of limit allows mathematicians to define a new point from a Cauchy sequence of previously defined points within a complete metric...
, so Bradwardine had to use arguments of his day. Mathematician and mathematical historian Carl O. Boyer writes, "Bradwardine developed the Boethian theory
Note
In music, the term note has two primary meanings:#A sign used in musical notation to represent the relative duration and pitch of a sound;#A pitched sound itself....
of double or triple or, more generally, what we would call 'n-tuple' proportion".
Boyer also writes that "the works of Bradwardine had contained some fundamentals of trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
gleaned from Muslim
Islam
Islam . The most common are and . : Arabic pronunciation varies regionally. The first vowel ranges from ~~. The second vowel ranges from ~~~...
sources". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science" (Cantor 2001, p. 122). The most essential missing tool was calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
.
The Art of Memory
Bradwardine was also a practitioner and exponent of the art of memoryArt of memory
The Art of Memory or Ars Memorativa is a general term used to designate a loosely associated group of mnemonic principles and techniques used to organize memory impressions, improve recall, and assist in the combination and 'invention' of ideas. It is sometimes referred to as mnemotechnics...
, a loosely associated group of mnemonic principles and techniques used to organize memory impressions, improve recall, and assist in the combination and 'invention' of ideas. His De Memoria Artificiali (c. 1335) discusses memory training current during his time.
Influenced
His theories on the insolublesInsolubilia
In the Middle Ages, variations on the liar paradox were studied under the name of insolubilia .Although the liar paradox was well known in antiquity, interest seems to have lapsed until the twelfth century, when it appears to have been reinvented independently of ancient authors...
including the liar paradox
Liar paradox
In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...
were a great influence on the work of Jean Buridan
Jean Buridan
Jean Buridan was a French priest who sowed the seeds of the Copernican revolution in Europe. Although he was one of the most famous and influential philosophers of the late Middle Ages, he is today among the least well known...
and therefore, in turn of the more recent philosopher A. N. Prior. His work on the liar paradox has been most recently studied by Paul Spade and Stephen Read (for which see Spade's entry in the Stanford Encyclopedia of Philosophy, which offers a brief exposition).
Latin Works and English Translations
- Insolubilia (Insolubles), Latin text and English translation by Stephen Read, Leuven, Peeters Editions (Dallas Medieval Texts and TranslationsDallas Medieval Texts and TranslationsDallas Medieval Texts and Translations is a book series sponsored by the and published by , a publishing house based in Louvain, Belgium. Modeled upon the Loeb Classical Library, the Dallas series has the goal "to build a library of medieval Latin texts, with English translations, from the period...
, 10), 2010. - De insolubilibus (On Insolubles), edited by Marie Louise Roure in 'La problématique des propositions insolubles du XIIIe siècle et du début du XIVe, suivie de l'édition des traités de William Shyreswood, Walter Burleigh et Thomas Bradwardine', Archives d'histoire doctrinale et littéraire du moyen Age 37, 1970: 205-326.
- De incipit et desinit (On 'It Begins' and 'It Ceases'), ed. Lauge O. Nielsen, Cahiers de l'Institut du moyen Age grec et latin 42, 1982: 1-83.
- Geometria speculativa (Speculative Geometry), Latin text and English translation with an introduction and a commentary by George Molland, Stuttgart: Steiner Verlag, 1989.
- Arithmetica speculativa (Speculative Arithmetic) Parisiis: G. Marchant, 1495
- De proportionibus velocitatum in motibus (On the Ratios of Velocities in Motions) Latin text and English translation by H. Lamar Crosby, Jr. in: 'Thomas of Bradwardine: His Tractatus de Proportionibus: Its Significance for the Development of Mathematical Physics', Madison, WI: University of Wisconsin Press, 1955.
- De continuo (On the Continuum), edited by John Emery Murdoch in 'Geometry and the Continuum in the Fourteenth Century: A Philosophical Analysis of Thomas Bradwardine's Tractatus de continuo', Ph.D. thesis, University of Wisconsin, 1957.
- De futuris contingentibus (On Future Contingents), edited by Jean-François Genest, Recherches augustiniennes 14, 1979: 249-336.
- De causa Dei contra Pelagium et de virtute causarum ad suos Mertonenses, libri tres (In Defense of God Against the Pelagians and On the Power of Causes, in three books), edited by Henry Savile, London: 1618; reprinted at Frankfurt: Minerva, 1964.
- Commentary on the Sentences of Peter Lombard: some questions found in a manuscript at the Bibliothèque Nationale de Paris are published in: J.-F. Genest and Katherine Tachau, 'La lecture de Thomas Bradwardine sur les Sentences', Archives d'histoire doctrinale et littéraire du Moyen Age 57, 1990: 301-6.
Further readings
- Heiko ObermanHeiko ObermanHeiko Augustinus Oberman was a historian and theologian who specialized in the study of the Reformation.-Life:...
, Archbishop Thomas Bradwardine, a Fourtenth Century Augustinian: A Study of His Theology in Its Historical Perspective, Utrecht: Kemink & Zoon, 1957. - Gordon Leff, Bradwardine and the Pelagians: A Study of His "De Causa Dei" and Its Opponents, Cambridge, England: Cambridge University PressCambridge University PressCambridge University Press is the publishing business of the University of Cambridge. Granted letters patent by Henry VIII in 1534, it is the world's oldest publishing house, and the second largest university press in the world...
, 1957.