William of Ockham (C.1287-1347)

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HPS 322 Michael J. White History of Science Fall semester, 2013 The 14th century A.D.: A. (1) William of Ockham (c.1287-1347). (2) The ‘Oxford Calculators’ or ‘Mertonians’ (after Merton College, Oxford) of the 14th century: Thomas Bradwardine, William Heytesbury, Richard Swineshead, John Dumbleton. The graphic/geometrical representation of the ‘intension and remission of forms’ (of which ‘speed’ is only one). ‘Uniform’, ‘uniformly difform’, and ‘difformly difform’ continuous change (i.e., continuous qualitative ‘intension’ or increase and ‘remission’ or decrease–which includes intension/remission of speed). Statement and proof of a ‘mean-value theorem’: a body moving with at a constant speed v/2 travels the same distance s in a time t as does a body uniformly accelerated body from rest to speed v in the same time t. Representation of quantity of motion (distance traversed) as area of plane figure. B. Those associated with the University of Paris: Jean Buridan (ca. 1300-1361)–further development of impetus theory. Nicole Oresme (ca. 1323-1382). C. Oresme on commensurability/incommensurability of the orbital periods of the celestial bodies. Recollect that: magnitudes A and B are commensurable iff (if and only if) there exists some positive magnitude M that is a common ‘aliquot part’ of both A and B (i.e., there exist positive integers n and m such that A = M × n and B = M × m). Consider any spatial configuration S of alignment of celestial bodies (e.g., planets) P1 and P21 and assume that the periods of P and P2 (T1 and T2, respectively) are incommensurable. Will P12 and P ever again assume exactly that alignment S? Answer: no. Proof by reductio: Assume they do. Then that realignment will occur in some definite time T3. But, then T31 will take some natural number n of orbital periods of P and some natural number m of orbital periods of P23; that is, T = T1 × n and T3 = T2 × m ). But then (by some 67 algebra), it follows that T/12T = m/n. So T1 and T2 are commensurable. (See .pdf file giving account of conclusion of De commensurabilitate vel incommensurabilitate motuum caeli.) D. Oresme on the apparent diurnal motion of the heavens: Is this due to the (rotational) motion of the celestial sphere (sphere of fixed stars)? Or is it due to the (rotational) motion of the earth? (See other Oresme .pdf file–selections from his Le livre du ciel et du monde.) E. The consequences of Oresme’s theological voluntarism..

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