{"id":960,"date":"2011-03-14T12:00:26","date_gmt":"2011-03-14T00:00:26","guid":{"rendered":"https:\/\/blogs.otago.ac.nz\/emxphi\/?p=960"},"modified":"2012-09-25T02:06:15","modified_gmt":"2012-09-24T14:06:15","slug":"newtons-de-gravitatione","status":"publish","type":"post","link":"https:\/\/blogs.otago.ac.nz\/emxphi\/newtons-de-gravitatione\/","title":{"rendered":"Newton’s Method in ‘De gravitatione’"},"content":{"rendered":"

Kirsten Walsh writes…<\/strong><\/p>\n

Newton\u2019s manuscript De Gravitatione<\/em><\/a> (\u2018De Grav.<\/em>\u2019 for short) was published for the first time in 1962, but no one knows when it was written.\u00a0 Some scholars have argued that Newton wrote De Grav.<\/em> as early as 1664, others, as late as 1685, and there have been arguments for almost every period in between.<\/p>\n

Ostensibly, the topic of De Grav.<\/em> is \u201cthe science of the weight and of the equilibrium of fluids and solids in fluids\u201d.\u00a0 Newton discusses this topic in the form of definitions, axioms, propositions, corollaries, and finally a scholium.\u00a0 However, the scholium ends abruptly and the manuscript is unfinished.\u00a0 One of the most notable features of this manuscript is what Hall & Hall<\/a> describe as a \u201cstructural failure\u201d: what begins as a brief discussion of a definition turns into a lengthy and detailed attack on the Cartesian conception of space and time.\u00a0 This digression is significant.\u00a0 Firstly, it is useful for understanding the development of Newton\u2019s thoughts on many topics.\u00a0 Secondly, it supports the view that, in Principia<\/em><\/a>, Newton\u2019s intended opponent was Cartesian, rather than Leibnizian.<\/p>\n

In this post, I am not going to talk about Newton\u2019s 23-page digression (which may well form the basis of another post).\u00a0 Rather, I am interested in the opening paragraph of this manuscript, in which Newton describes his method.\u00a0 He begins:<\/p>\n

    “It is fitting to treat the science of the weight and of the equilibrium of fluids and solids in fluids by a twofold method.”<\/ol>\n

    The first, he tells us, is a geometrical method.\u00a0 He says he plans to demonstrate his propositions \u201cstrictly and geometrically\u201d by:<\/p>\n

      \n
    1. Abstracting the phenomena from physical considerations;<\/li>\n
    2. Establishing a strong foundation of definitions, axioms and postulates; and<\/li>\n
    3. Formulating lemmas, propositions and corollaries.<\/li>\n<\/ol>\n

      The second is a natural philosophical method.\u00a0 He says he plans to explicate and confirm the certainty of his propositions by the use of experiments.\u00a0 He says that these discussions will be restricted to scholia, to ensure that the two methods are kept separate.<\/p>\n

      This twofold method bears striking resemblance to two other aspects of Newton\u2019s work:<\/p>\n

        \n
      1. It accurately describes the method and structure of Principia<\/em>; and<\/li>\n
      2. It resembles the quasi-mathematical method he uses to \u2018prove\u2019 his theory of colours<\/a>.<\/li>\n<\/ol>\n

        The first point is uncontroversial \u2013 almost boring, given how many times it has been mentioned in the literature. \u00a0But it shows that this method is in use by Newton at least by the mid-1680s.\u00a0 My second point, however, requires some explanation.<\/p>\n

        In an earlier post<\/a> I argued that, at least in the early 1670s, Newton\u2019s goal is absolute certainty.\u00a0 He hopes to achieve certainty in the science of colours by making it \u2018mathematical\u2019.\u00a0 The clearest demonstration of his quasi-mathematical method is found in Newton\u2019s reply to Huygens<\/a>, where he sets out his theory of colours in a series of definitions and propositions, in the style of a geometrical proof.<\/p>\n

        Despite the resemblance, this is not precisely the same method that Newton is advocating in De Grav.<\/em> Experiment appears to play a different role.<\/p>\n

        In his early optical work, propositions are founded on experiment.\u00a0 So experiment should be the first step in any inquiry.\u00a0 For example, in a letter written in 1673, Newton says:<\/p>\n