{"id":3143,"date":"2013-04-15T16:00:46","date_gmt":"2013-04-15T04:00:46","guid":{"rendered":"https:\/\/blogs.otago.ac.nz\/emxphi\/?p=3143"},"modified":"2013-04-23T09:26:24","modified_gmt":"2013-04-22T21:26:24","slug":"newton-on-experiment-and-mathematics","status":"publish","type":"post","link":"https:\/\/blogs.otago.ac.nz\/emxphi\/newton-on-experiment-and-mathematics\/","title":{"rendered":"Newton on Experiment and Mathematics"},"content":{"rendered":"

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

In my last post<\/a>, I discussed our 20 revised theses<\/a> and why I altered thesis 5.\u00a0 In this post, I\u2019ll discuss why I replaced thesis 8.<\/p>\n

In 2011<\/a>, I claimed that:<\/p>\n

    8.\u00a0 The development of Newton\u2019s method from 1672 to 1687 appears to display a shift in emphasis from experiment to mathematics.<\/ol>\n

    But at the start of this year, I replaced this thesis with a new thesis 8:<\/p>\n

      8.\u00a0 In his early work, Newton\u2019s use of the terms \u2018hypothesis\u2019 and \u2018query\u2019 are Baconian.\u00a0 However, as Newton\u2019s distinctive methodology develops, these terms take on different meanings.<\/ol>\n

      Since my new thesis is a replacement of the original thesis, rather than a modification, two explanations are required. \u00a0So in today\u2019s post, I\u2019ll tell you why I decided to remove my original thesis 8, and in my next post, I\u2019ll tell you about my new thesis 8.<\/p>\n

      I originally included thesis 8 because there are some obvious differences in the styles of Newton\u2019s early work on optics and his Principia<\/em>.\u00a0 In Newton\u2019s first paper on optics<\/a> (1672), there is a strong emphasis on experiment.\u00a0 Experiment drives his research and guides his rejection of various possible explanations of the phenomena under consideration.\u00a0 Ultimately, he presents an Experimentum Crucis<\/em><\/a> as proof for the certainty of his proposition that white light is heterogeneous.\u00a0 In contrast, the Principia<\/em><\/a> (1687) displays a strong emphasis on mathematics.\u00a0 The full title of the work, the Author\u2019s Preface to the Reader, and the fact that Book I opens with 11 lemmas outlining the mathematical framework of the work are just a few features that make it clear that Principia<\/em> is primarily a mathematical treatise.<\/p>\n

      I now think that my original thesis 8 is misleading.<\/p>\n

      Firstly, as I have emphasised on this blog, Newton\u2019s early work had a mathematical style that made it unique among his contemporaries.\u00a0 While they recognised him as an experimental philosopher<\/a>, his claims of obtaining certainty via geometrical proofs<\/a> set him apart from the Baconian-experimental philosophers.\u00a0 Moreover, his methodological statements show evidence of a tension between experiment and mathematical certainty.\u00a0 For example, he says that the science of colours,<\/p>\n

        \u201cdepend[s] as well on Physicall Principles as on Mathematicall Demonstrations: And the absolute certainty of a Science cannot exceed the certainty of its Principles.\u00a0 Now the evidence by wch I asserted the Propositions of colours is in the next words expressed to be from Experiments & so but Physicall: Whence the Propositions themselves can be esteemed no more then Physicall Principles of a Science.\u201d<\/ol>\n

        Secondly, Newton continued to identify as an experimental philosopher until the end of his life.\u00a0 For example, in the General Scholium<\/a> at the end of Principia<\/em>, he says:<\/p>\n

          \u201cand hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy.\u201d<\/ol>\n

          This resembles Newton\u2019s earlier emphasis on grounding propositions on empirical evidence, rather than on speculative conjectures.<\/p>\n

          Thirdly, in Principia<\/em>, Newton appears to be negotiating a similar tension between experiment and mathematical certainty that we saw in his early work.\u00a0 For example, in the Scholium to the Laws of Motion he asserts the certainty of his Laws, while at the same time, acknowledging their experimental basis:<\/p>\n

            \u201cThe principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds.\u201d<\/ol>\n

            And:<\/p>\n

              \u201cBy these examples [i.e. the experiments mentioned above] I wished only to show the wide range and the certainty of the third law of motion.\u201d<\/ol>\n

              From these three points, we can see that the methodological differences between Newton\u2019s early papers and Principia<\/em> aren\u2019t as great as they first appear.\u00a0 But I did not remove my original thesis 8 because I think that the methodology of the 1672 paper is precisely the same<\/em> as the methodology displayed in Principia<\/em>.\u00a0 Rather, I don\u2019t think my original thesis 8 captures what is important about these differences.<\/p>\n

              As I have explained here<\/a>, my project is to distinguish between those features of Newton\u2019s methodology that changed, and those that stayed the same.\u00a0 Some aspects of Newton\u2019s methodology developed over time.\u00a0 For example, he came to value geometrical synthesis over algebraic analysis<\/a>.\u00a0 Other aspects of his methodology varied according to context.\u00a0 For example, in Opticks<\/em>, he employs \u2018experiments\u2019 and \u2018observations\u2019, but in Principia<\/em>, he employs \u2018phenomena\u2019.\u00a0 But this triumvirate of methodological ideas \u2013 experiment, mathematics and certainty \u2013 should be considered an enduring feature of Newton\u2019s methodology.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Kirsten Walsh writes… In my last post, I discussed our 20 revised theses and why I altered thesis 5.\u00a0 In this post, I\u2019ll discuss why I replaced thesis 8. In 2011, I claimed that: 8.\u00a0 The development of Newton\u2019s method […]<\/p>\n","protected":false},"author":4582,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[113],"tags":[226,275,224],"class_list":["post-3143","post","type-post","status-publish","format-standard","hentry","category-ideas","tag-experimental-philosophy","tag-mathematics","tag-newton"],"_links":{"self":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/3143","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/users\/4582"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/comments?post=3143"}],"version-history":[{"count":0,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/3143\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/media?parent=3143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/categories?post=3143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/tags?post=3143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}