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. 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 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:

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-tple' 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 algebra.

See also

• Science in the Middle Ages
• Scholasticism

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.