Thomas Bradwardine

Quick Info

about 1295
Chichester, England
26 August 1349
Lambeth, London, England

Thomas Bradwardine was an English mathematician and theologian who examined Aristotle's theories of dynamics.


Thomas Bradwardine's date of birth is not known with any certainty. In [1] the date is given as between 1290 and 1300, in [2] the date is given as about 1290 while, for example, in [15] it is given as about 1300. These are merely guesses based on the first definite date we know for Bradwardine and that is August 1321 when he became a Fellow of Merton College, Oxford. August 1321 is the date on which Bradwardine was awarded his B.A. We have merely taken an average of the various birth dates suggested!

We have given Bradwardine's birthplace as Chichester, but again this is based on little evidence. We know from Bradwardine's writings that his father, at the time of writing, was living in Chichester but since this must have been written more than twenty years after Bradwardine was born, it is somewhat fanciful to assume his father had not moved.

Although it is not certain, there is strong evidence to suggest that Bradwardine remained at Merton College until 1335. He held various university posts during this time including proctor and he received a number of degrees such as M.A. in 1323 and B.Th. some time before 1333. It is during this period at Oxford that almost all of his works on logic, mathematics, and philosophy were written.

In 1333 Bradwardine was appointed canon of Lincoln then, in 1335, he joined the group of men surrounding Richard de Bury who was Bishop of Durham. He moved to London two years later when he was made chancellor of St Paul's Cathedral on 19 September 1337. Soon after this he became chaplain to King Edward III.

King Edward III claimed the title of king of France in January 1340. His claim was not totally without justification since through his mother he was more closely related to the last ruler of the Capetian dynasty than was the French King Philip VI. Edward won a naval victory off the Flemish city of Sluis in June 1340 but lack of resources to press forward forced him to make a truce. In July 1346 Edward landed in Normandy accompanied by his eldest son Prince Edward (known as the Black Prince). Bradwardine was certainly part of Edward's invasion force.

The English invading force won a decisive victory over the French at Crécy on 26 August 1346. They then laid siege to Calais in September 1346 and it surrendered in August 1347. David II of Scotland was an ally of the French and realising that Edward was occupied in the siege of Calais, invaded the north of England in October 1346. Edward had expected this and left a strong force on the north of England to deal with the Scots. David II was defeated at the Battle of Neville's Cross (near Durham). At a victory celebration in France to celebrate the victories at both Crécy and Neville's Cross, Bradwardine gave as address the Sermo epinicius in the presence of Edward III, the text of which has survived.

Edward returned to England in October 1347. Bradwardine was elected Archbishop of Canterbury on 31 August 1348, but rather strangely Edward annulled the appointment. On 4 June 1349 Bradwardine was elected Archbishop of Canterbury for the second time, without it appears any objections from Edward. He was consecrated at Avignon on 10 July 1349 but died of the plague soon after he returned to London to take up his duties. The Black Death had spread to England and France in 1348 and perhaps a third of the population of London died as a result at around the same time as Bradwardine.

Bradwardine was a noted mathematician as well as theologian and was known as 'the profound doctor'. He studied bodies in uniform motion and ratios of speed in the treatise De proportionibus velocitatum in motibus (1328). This work takes a rather strange line between supporting and criticising Aristotle's physics. Perhaps it is not really so strange because Aristotle views were so fundamental to learning at that time that perhaps all that one could expect of Bradwardine was the reinterpretation of Aristotle's views on bodies in motion and forces acting on them. It is likely that his intention was not to criticise Aristotle but rather to justify mathematically a reinterpretation of Aristotle's statements.

Aristotle claimed that motion was only possible when the force acting on a body exceeded the resistance. Although he did not express it in these terms, it had also been deduced from Aristotle's Physics that the velocity of a body was proportional to the force acting on it divided by the resistance. Bradwardine used a mathematical argument to show that these two were inconsistent. He did this by assuming an initial force and resistance, then supposed that the resistance doubled, doubled again etc keeping the force constant. At some point, argues Bradwardine, the resistance will exceed the force so the body cannot move. But the velocity, given by the second rule, could not be zero.

Bradwardine then claims that an arithmetic increase in velocity corresponds with a geometric increase in the original ratio of force to resistance. This cleverly removes the contradiction, but of course is incorrect. His view, however, was very influential and it was accepted as a law of mechanics for over a hundred years. For example Oresme followed Bradwardine's ideas of mechanics. Takahashi in [16] gives an interesting new interpretation of Bradwardine notion of ratios.

Another interesting, but fallacious, argument was produced by Bradwardine when he tried to disprove atomism using geometry. However, he questioned the logic of his own arguments as he felt perhaps the existence of geometry already assumes that atomism is false.

Bradwardine was the first mathematician to study "star polygons". They were later investigated more thoroughly by Kepler. Other works by Bradwardine include the following.

On insolubles which discusses logical problems such as "I am telling a lie".

On "it begins" and "It ceases" which argues that a temporal interval has a first instant but no last instant. The end of the interval is marked by the first instant of its non-existence.

Speculative geometry contains elementary geometry which is not all based on Euclid. For example the "star polygons" referred to above appear here as does a discussion of the problem of the filling of space by touching polyhedra. This work, in four sections, is discussed in detail in [12].

Speculative arithmetic is based on a text by Boethius. There is argument between historians about which arithmetic text is the one due to Bradwardine. This is discussed, and a theory proposed, in [8].

On the continuum discusses the atomic theory. It follows Aristotle's views fairly closely. In it Bradwardine states:-
No continuum is made up of atoms, since every continuum is composed of an infinite number of continua of the same species.
This work is discussed in [14] where the author notes that this work by Bradwardine is a good early example of the application of mathematics to natural philosophy.

On future contingents and In defence of God against the Pelagians and on the power of causes are Bradwardine's two major theological works. They attempt to argue against free will and in favour of Divine Will.

References (show)

  1. J E Murdoch, Biography in Dictionary of Scientific Biography (New York 1970-1990).
    See THIS LINK.
  2. Biography in Encyclopaedia Britannica.
  3. H L Crosby, Thomas of Bradwardine. His Tractus de Proportionibus. Its significance for the development of Mathematical Physics (Madison, Wis., 1955).
  4. E W Dolnikowski, Thomas Bradwardine : a view of time and a vision of eternity in fourteenth- century thought (Leiden, 1995).
  5. J-F Genest, Prédétermination et Liberté Crée à Oxford au XIV Siècle : Buckingham conta Bradwardine (Paris, 1992).
  6. P V Spade, Insolubilia and Bradwardine's theory of signification, Lies, language and logic in the late Middle Ages (London, 1988).
  7. I Boh, Bradwardine's (?) critique of Ockham's modal logic, in Historia philosophiae medii aevi Band I, II (Amsterdam, 1991), 55-70.
  8. H L L Busard, Zwei mittelalterliche Texte zur theoretischen Mathematik: die 'Arithmetica speculativa' von Thomas Bradwardine und die 'Theorica numerorum' von Wigandus Durnheimer, Arch. Hist. Exact Sci. 53 (2) (1998), 97-124.
  9. S Drake, Bradwardine's function, mediate denomination, and multiple continua, Physis - Riv. Internaz. Storia Sci. 12 (1) (1970), 51-68.
  10. S Drake, Medieval ratio theory vs compound medicines in the origins of Bradwardine's rule, Isis 64 (221) (1973), 67-77.
  11. J E Hofmann, Zum Gedenken an Thomas Bradwardine, Centaurus 1 (1951), 293-308.
  12. A G Molland, An examination of Bradwardine's 'Geometry', Arch. History Exact Sci. 19 (2) (1978), 113-175.
  13. A G Molland, Addressing ancient authority : Thomas Bradwardine and Prisca Sapientia, Annals of Science 53 (1996), 213-233.
  14. J E Murdoch, Thomas Bradwardine : mathematics and continuity in the fourteenth century, in Mathematics and its applications to science and natural philosophy in the Middle Ages (Cambridge-New York, 1987), 103-137.
  15. E D Sylla, International Encyclopedia of the Social Sciences 1 (New York, 1968), 863-867.
  16. K Takahashi, The mathematical foundations of Bradwardine's rule, Historia Sci. 26 (1984), 19-38.
  17. V P Zubov, Le traité 'De continuo' de Bradwardine (Russian), Istor.-Mat. Issled. 13 (1960), 385-440.

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Written by J J O'Connor and E F Robertson
Last Update July 2000