Oxford Calculators

The Oxford Calculators were a group of 14th-century thinkers, almost all associated with Merton College, Oxford,for this reason they were dubbed "The Merton School". These men took a strikingly logico-mathematical approach to philosophical problems. The key "calculators", writing in the second quarter of the 14th century, were Thomas Bradwardine, William Heytesbury, Richard Swineshead and John Dumbleton. These men built on the slightly earlier work of Walter Burley and Gerard of Brussels.

Science

The advances these men made were initially purely mathematical but later became relevant to mechanics. They used Aristotelian logic and physics. They also studied and attempted to quantify every physical and observable characteristic, like heat, force, color, density, and light. Aristotle believed that only length and motion were able to be quantified. But they used his philosophy and proved it untrue by being able to calculate things such as temperature and power. They developed Al-Battani's work on trigonometry and their most famous work was the development of the mean speed theorem, (though it was later credited to Galileo) which is known as "The Law of Falling Bodies". Although they attempted to quantify these observable characteristics, their interests laid more in the philosophical and logical aspects than in natural world. They used numbers to philosophically disagree and prove the reasoning of "why" something worked the way it did and not only "how" something functioned the way that it did.

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.

The mathematical physicist and historian of science Clifford Truesdell, wrote:

The now published sources prove to us, beyond contention, that the main kinematical properties of uniformly accelerated motions, still attributed to Galileo by the physics texts, were discovered and proved by scholars of Merton college.... In principle, the qualities of Greek physics were replaced, at least for motions, by the numerical quantities that have ruled Western science ever since. The work was quickly diffused into France, Italy, and other parts of Europe. Almost immediately, Giovanni di Casale and Nicole Oresme found how to represent the results by geometrical graphs, introducing the connection between geometry and the physical world that became a second characteristic habit of Western thought ...

In Tractatus de proportionibus (1328), Bradwardine extended the theory of proportions of Eudoxus 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 concept of limit, so Bradwardine had to use arguments of his day. Mathematician and mathematical historian Carl Benjamin 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". Yet "Bradwardine and his Oxford colleagues did not quite make the breakthrough to modern science." The most essential missing tool was algebra.

Thomas Bradwardine

He was born in 1290 C.E. in Sussex. He was a student educated at Balliol College, Oxford where he earned various degrees and was an English Cleric, a scholar, a mathematician, and a Physicist. He authored many books including: De Geometria Speculativa (printed in Paris in 1530), De Arithmetica Practica (printed in Paris in 1502), and De proportionibus Velocitatum in motibus in 1328 (printed in Paris in 1495). Aristotle suggested that velocity was proportional to force and inversely proportional to resistance, doubling the force would double the velocity but doubling the resistance would halve the velocity (VαF/R). Bradwardine objected saying that this is not observed because the velocity does not equal zero when the resistance exceeds the force. Instead, he proposed a new theory that, in modern terms, would be written as (Vαlog F/R), which was widely accepted until the late sixteenth century.

Richard Swineshead

He also was an English mathematician, logician, and natural philosopher. He became a member of the Oxford calculators in 1344. His main work was a series of treatises written in 1350. This work earned him the title of "The Calculator". His treatises were named Liber Calculationum, which means "Book of Calculations".

John Dumbleton

He became a member of the calculators in 1338-39 C.E. After becoming a member, he left the calculators for a brief period of time to study theology in Paris in 1345-47. After his study there he returned to his work with the calculators in 1347-48.

See also

• Jean Buridan
• John Cantius
• Gerard of Brussels
• Henry of Langenstein
• Scholasticism
• Science in the Middle Ages
• Domingo de Soto
• Thomas Bradwardine
• Richard Swineshead
• John Dumbleton

References

• Sylla, Edith (1999) "Oxford Calculators", in The Cambridge Dictionary of Philosophy.

Further reading

• Carl B. Boyer (1949), The History of Calculus and Its Conceptual Development, New York: Hafner, reprinted in 1959, New York: Dover.
• John Longeway, (2003), "William Heytesbury", in The Stanford Encyclopedia of Philosophy. Accessed 2012 January 3.
• Uta C. Merzbach and Carl B. Boyer (2011), A History of Mathematics", Third Edition, Hoboken, NJ: Wiley.
• Edith Sylla (1982), "The Oxford Calculators",in Norman Kretzmann, Anthony Kenny, and Jan Pinborg, edd. The Cambridge History of Later Medieval Philosophy: From the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100-1600, New York: Cambridge.