Heytesbury, William(Before 1313–1372/3)
William Heytesbury, a fellow at Merton College in Oxford from 1330, belonged to the second generation of Mertonian "Calculators." His work depends on Richard Kilvington's Sophismata (1325) and Thomas Bradwardine's Insolubilia and Tractatus de Proportionibus (1328). His technique was to analyze sophismata—ambiguous problematic statements whose truth or falsehood is to be assessed under specified assumptions—and apply supposition theory, a form of semantic-logical analysis, to the explication of their underlying logical grammar. He is particularly noted for his work on motion and the continuum.
Heytesbury's most popular work was the Rules for Solving Sophismata (1335), which contains six treatises: "On Insoluble Sentences (Insolubilia)," dealing with self-referential paradoxes; "On Knowing and Doubting," concerning reference in intensional contexts; "On Relative Terms," considering the reference of relative pronouns; "On Beginning and Ceasing" and "On Maxima and Minima," about continua; and "On the Three Categories," on velocity and acceleration in changes of place, quantity, and quality.
In "On Beginning and Ceasing," Heytesbury considers the sophisma "some part of an object ceases to be seen by Socrates," given that the object is not now, but will, immediately after now, be partly occluded by an object passing in front of it. This statement may assert that there is a given part of the object that will, in every moment after this one, be entirely occluded, and if so, it is false. Or it may assert that at every moment after this present moment, there will be some part of the object entirely occluded at that moment (a different part for each moment), and then it is true.
The Rules became popular, and remained important on the European continent even after the Mertonians began to be ignored in Britain. It was taught at Padua and Paris through the early sixteenth century, influencing the Paduan school, fifteenth-century Italian logicians such as Paul of Venice (d. 1429), and the school of John Major at Paris. With the rest of medieval logic, Heytesbury's work sank into obscurity after that. In addition to Rules Heytesbury wrote two collections of sophismata, in one of which the (obviously false) statement, "you are a donkey," was repeatedly derived from seemingly harmless admissions. He also wrote some shorter works; for instance, "On the Compounded and Divided Senses," which deals with scope ambiguities similar to that involved in the preceding example.
In the sixth chapter of Rules, Heytesbury states the mean-speed theorem for uniformly accelerated motion: A uniformly accelerated body will, over a given period of time, traverse a distance equal to the distance it would traverse if it moved continuously in the same period at its mean velocity (one-half the sum of the initial and final velocities). Elsewhere, he points out, in a particular case, that a uniformly accelerated body will, in the second equal time interval, traverse three times the distance it does in the first. Domingo de Soto observed the applicability of the mean-speed theorem to free fall in 1555.
Bradwardine, Thomas; Kilvington, Richard; Medieval Philosophy; Paul of Venice.
Bibliography
Works by William Heytesbury
Hentisberi de sensu composito et diviso, Regulae solvendi sophismata. Venice: Bonetus Locatellus, 1494.
"William of Heytesbury on the Three Categories." Selections translated by E. A. Moody. In The Science of Mechanics in the Middle Ages, edited by Marshall Claggett. Madison: University of Wisconsin Press, 1959. Reprinted in A Source Book in Medieval Science, edited by Edward Grant. Cambridge, MA: Harvard University Press, 1974.
"William of Heytesbury on the 'Insoluble' Sentences." Translated with notes by Paul Spade. Toronto: Pontifical Institute of Medieval Studies, 1979.
On Maxima and Minima: Chapter 5 of "Rules for Solving Sophismata," with an anonymous fourteenth-century discussion. Translated with introduction and study by John Longeway. Dordrecht: D. Reidel Publishing Company, 1984.
"'The Compounded and Divided Senses,' and 'The Verbs Know and Doubt.'" Translated by Norman Kretzmann and Eleonore Stump. In The Cambridge Translations of Medieval Philosophical Texts. Vol. 1: Logic and Philosophy of Language. Cambridge, U.K.: Cambridge University Press, 1988.
Works About William Heytesbury
Wilson, Curtis. William Heytesbury: Medieval Logic and the Rise of Modern Physics. Madison: University of Wisconsin Press, 1960.
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