3/28/2023 0 Comments The infinitesimals![]() ![]() The new optical science sought experimental confirmation for its basic notions and results and thus provided a direct methodological antecedent to Newton's Principia. I argue that Gregorie, Barrow, and Newton produced a methodological revolution in geometrical optics. A major center of interest is the origins of the notion of geometrical optical image, which are shown to have been influenced by the philosophical empiricism. The second chapter studies Gregorie's contributions to optics, including a description of a hitherto unpublished manuscript. It is argued that John Collins, representing the world of practical mathematicians, was a source of motivations for some of Gregorie's mathematical discoveries, and that Gregorie's attempts to publicize his contributions failed because of institutional practices characteristic of the early Royal Society. ![]() Gregorie's correspondence with Newton is studied. Evidence on Gregorie's life within 17th-century Scottish universities, his involvement in setting up the St Andrews observatory, his activities in the early 1670's as leader of a Scottish network of mathematical virtuosi, and his juvenile astrological concerns is here produced for the first time. The first chapter contains a narrative of Gregorie's life and works. "As a general conclusion this dissertation suggests that the mathematical and optical contributions of James Gregorie, Isaac Barrow and Isaac Newton are more closely related to one another than it is usually acknowledged. I conclude by dealing with some of the common misunderstandings which occur when Deleuze is read as endorsing a modern mathematical interpretation of the calculus. By highlighting the sub-representational character of the differential in his system I show how the differential is a key moment in Deleuze’s formulation of a transcendental empiricism. For Deleuze, instead, I show that the differential must be understood as escaping from both finite and infinite representation. I analyse Hegel’s justification for this introduction of dialectical reason by looking at his responses to Berkeley’s criticisms of the calculus. For Hegel, this involves attempting to show that the foundations of the calculus cannot be thought by the finite understanding, and necessitate a move to the standpoint of infinite reason. I show how both Deleuze and Hegel see the calculus as providing a way of thinking outside of finite representation. The aim of this paper is to explore the uses made of the calculus by Gilles Deleuze and G.W.F. ![]()
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