David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 185 (3):429-466 (2012)
The mathematical nature of modern science is an outcome of a contingent historical process, whose most critical stages occurred in the seventeenth century. ‘The mathematization of nature’ (Koyré 1957 , From the closed world to the infinite universe , 5) is commonly hailed as the great achievement of the ‘scientific revolution’, but for the agents affecting this development it was not a clear insight into the structure of the universe or into the proper way of studying it. Rather, it was a deliberate project of great intellectual promise, but fraught with excruciating technical challenges and unsettling epistemological conundrums. These required a radical change in the relations between mathematics, order and physical phenomena and the development of new practices of tracing and analyzing motion. This essay presents a series of discrete moments in this process. For mediaeval and Renaissance philosophers, mathematicians and painters, physical motion was the paradigm of change, hence of disorder, and ipso facto available to mathematical analysis only as idealized abstraction. Kepler and Galileo boldly reverted the traditional presumptions: for them, mathematical harmonies were embedded in creation; motion was the carrier of order; and the objects of mathematics were mathematical curves drawn by nature itself. Mathematics could thus be assigned an explanatory role in natural philosophy, capturing a new metaphysical entity: pure motion. Successive generations of natural philosophers from Descartes to Huygens and Hooke gradually relegated the need to legitimize the application of mathematics to natural phenomena and the blurring of natural and artificial this application relied on. Newton finally erased the distinction between nature’s and artificial mathematics altogether, equating all of geometry with mechanical practice.
|Keywords||Alberti, Leon Batista Curves da Vinci, Leonardo Descartes, René Galilei, Galileo Geometry Geometrical machines Hooke, Robert Huygens, Christiaan Indivisibles Kepler, Johannes Light Mathematical diagrams Mechanics Motion Local Pure Newton, Isaac Optics Order Pendulum Perspectiva Physica Rota Aristotelis Spring Tartaglia, Niccolo Trajectories Traces Vacuum|
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References found in this work BETA
Raz D. Chen-Morris (2001). Optics, Imagination, and the Construction of Scientific Observation in Kepler's New Science. The Monist 84 (4):453-486.
René Descartes (1984). The Philosophical Writings of Descartes. Cambridge University Press.
Ofer Gal & Raz Chen-Morris (2006). The Archaeology of the Inverse Square Law:(2) the Use and Non-Use of Mathematics. History of Science 44:49-67.
Ofer Gal & Raz Chen-Morris (2005). The Archaeology of the Inverse Square Law:(1) Metaphysical Images and Mathematical Practices. History of Science 43:391-414.
Ofer Gal & Raz Chen-Morris (2010). Baroque Optics and the Disappearance of the Observer: From Kepler's Optics to Descartes' Doubt. Journal of the History of Ideas 71 (2):191-217.
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