Between Mathematics and Experimental Philosophy: Hydrostatics in Scotland About 1700
Many years ago J.B. Conant contrasted Pascal’s and Boyle’s approach to hydrostatics and pneumatics in terms of “two traditions,” one mathematical, the other experimental. Peter Dear has brilliantly recast Conant’s suggestion by linking Pascal’s (so-called
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Between Mathematics and Experimental Philosophy: Hydrostatics in Scotland About 1700 Antoni Malet
Many years ago J.B. Conant contrasted Pascal’s and Boyle’s approach to hydrostatics and pneumatics in terms of “two traditions,” one mathematical, the other experimental.1 Peter Dear has brilliantly recast Conant’s suggestion by linking Pascal’s (so-called) mathematical approach and Boyle’s experimental approach to their contrasting theological views.2 In a more general way, there is a broad consensus that the experimental approach was the distinguishing feature of the teaching of natural philosophy in Britain from the late seventeenth century on. In the early Enlightenment in Britain, Larry Stewart and others have shown, the utilitarian, manipulative, visual, experimentalist side of natural philosophy was favored and stressed to the point that the mathematical content almost disappeared. It was an approach in which hands-on experience and observation not only helped to overcome difficulties in concept-clarification and in mathematical arguments, but appeared as real alternatives to them.3 Although there is much truth in those accounts, we present here evidence that a British mathematical approach to hydrostatics and pneumatics was successfully developed by John Wallis, James Gregorie (or Gregory), Newton, and others. In a sense that we will specify here, their approach is more deeply and more genuinely mathematical than Pascal’s. Finally we also present evidence that such a mathematical understanding of hydrostatics and pneumatics occupied a prominent place in the teaching of natural philosophy in Scottish universities from the late seventeenth century on.
1
Conant, Harvard Case Histories, vol. I, p. 59. Dear, “Miracles, Experiments, and the Ordinary Course of Nature.” 3 Stewart, The Rise of Public Science, passim, but see particularly chap. 4. 2
A. Malet (*) Department d’Humanitats, Universitat Pompeu Fabra, c. Raman Trias Fargas 25, 08005 Barcelona, Spain e-mail: [email protected]
D. Garber and S. Roux (eds.), The Mechanization of Natural Philosophy, Boston Studies in the Philosophy of Science 300, DOI 10.1007/978-94-007-4345-8_7, © Springer Science+Business Media B.V. 2013
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Between Mathematics and Experimental Philosophy
The main and almost only source for seventeenth-century hydrostatics is Simon Stevin’s (1548–1620) De Beghinselen des Waterwichts (The Elements of Hydrostatics). Originally published in Dutch in 1586, it was available in Latin and French from the early years of the seventeenth century.4 Besides new results on the weight or pressure (he does not explicitly distinguish the two notions) that fluids exert upon inclined surfaces, Stevin provides an original mathematical demonstration of the so-called hydrostatic paradox, i.e., that the force acting upon any given surface, S, on which some homogeneous fluid in equilibrium rests, is independent of the volume of fluid resting upon it and depends solely on the measure of the surface and the height (or vertical distance) of
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