{"id":1310,"date":"2011-07-18T12:00:32","date_gmt":"2011-07-18T00:00:32","guid":{"rendered":"https:\/\/blogs.otago.ac.nz\/emxphi\/?p=1310"},"modified":"2012-09-25T02:10:03","modified_gmt":"2012-09-24T14:10:03","slug":"newton%e2%80%99s-4th-rule-for-natural-philosophy","status":"publish","type":"post","link":"https:\/\/blogs.otago.ac.nz\/emxphi\/newton%e2%80%99s-4th-rule-for-natural-philosophy\/","title":{"rendered":"Newton\u2019s 4th Rule for Natural Philosophy"},"content":{"rendered":"

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

In book three of the 3rd<\/sup> edition of Principia<\/em><\/a>, Newton added a fourth rule for the study of natural philosophy:<\/p>\n

    In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.<\/em><\/strong><\/ol>\n
      This rule should be followed so that arguments based on induction be not be nullified by hypotheses.<\/strong><\/ol>\n

      Arguably this is the most important of Newton’s four rules, and it certainly sparked a lot of discussion at our departmental seminar<\/a> last week.\u00a0 Let us see what insights we can glean from it.<\/p>\n

      Rule 4 breaks down neatly into three parts.\u00a0 I shall address each part in turn.<\/p>\n

      1. <\/strong>Propositions (acquired from the phenomena by induction) should be regarded as true or very nearly true.<\/strong><\/p>\n

      While the term \u2018phenomenon\u2019 usually refers to a single occurrence or fact, Newton uses the term to refer to a generalisation from observed physical properties.\u00a0 For example, Phenomenon 1, Book 3:<\/p>\n

        The circumjovial planets [or satellites of Jupiter], by radii drawn to the centre of Jupiter; describe areas proportional to the times, and their periodic times \u2013 the fixed stars being at rest \u2013 are as the 3\/2 powers of their distances from that centre.<\/em><\/ol>\n
          This is established from astronomical observations…<\/ol>\n

          Newton uses the term \u2018proposition\u2019 in a mathematical sense to mean a formal statement of a theorem or an operation to be completed.\u00a0 Thus, he further identifies propositions as either theorems or problems.\u00a0 Propositions are distinguished from axioms in that propositions are not self-evident.\u00a0 Rather, they are deduced from phenomena (with the help of definitions and axioms) and are demonstrated by experiment.\u00a0 For example, Proposition 1, Theorem 1, Book 3:<\/p>\n

            The forces by which the circumjovial planets [or satellites of Jupiter] are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the centre of Jupiter and are inversely as the squares of the distances of their places from that centre.<\/em><\/ol>\n
              The first part of the proposition is evident from phen. 1 and from prop. 2 or prop. 3 of book 1, and the second part from phen. 1 and from corol. 6 to prop. 4 of book 1.<\/ol>\n

              Newton appears to be using \u2018induction\u2019 in a very loose sense to mean any kind of argument that goes beyond what is stated in the premises.\u00a0 As I noted above, his phenomena are generalisations from a limited number of observed cases, so his natural philosophical reasoning is inductive from the bottom up.\u00a0 Newton recognises that this necessary inductive step introduces the same uncertainty that accompanies any inductive generalisation: the possibility that there is a refuting instance that hasn\u2019t been observed yet.<\/p>\n

              Despite this necessary uncertainty, in the absence of refuting instances, Newton tells us to regard these propositions as true or very nearly true.\u00a0 It is important to note that he is not telling us that these propositions are<\/em> true, simply that we should act as though<\/em> they are.\u00a0 Newton is simply saying that if our best theory fits the available data, then we should regard it as true until proven otherwise.<\/p>\n

              2. <\/strong>Hypotheses cannot refute or alter those propositions.<\/strong><\/p>\n

              In a previous post<\/a> I argued that, in his early optical papers, Newton was working with a clear distinction between theory and hypothesis.\u00a0 In Principia <\/em>Newton is working with a similar distinction between propositions and hypotheses.\u00a0 Propositions make claims about observable, measurable physical properties, whereas hypotheses make claims about unobservable, unmeasurable causes or natures of things.\u00a0 Thus, propositions are on epistemically surer footing than hypotheses, because they are grounded on what we can directly experience.\u00a0 When faced with a disagreement between a hypothesis and a proposition, we should modify the hypothesis to fit the proposition, and not vice versa.\u00a0 Newton explains this idea in a letter to Cotes:<\/p>\n

                But to admitt of such Hypotheses in opposition to rational Propositions founded upon Phaenomena by Induction is to destroy all arguments taken from Phaenomena by Induction & all Principles founded upon such arguments.<\/em><\/ol>\n

                3. <\/strong>New phenomena may refute those propositions by contradicting them, or alter those propositions by making them more precise.<\/strong><\/p>\n

                This final point highlights the a posteriori<\/em> justification of Newton\u2019s theories.\u00a0 In Principia<\/em>, two methods of testing can be seen.\u00a0 The first involves straightforward prediction-testing.\u00a0 The second is a more sophisticated method, which involves accounting for discrepancies between ideal and actual motions by a series of steps that increase the complexity of the model.<\/p>\n

                <\/em><\/p>\n

                In short, Rule 4 tells us to prioritise propositions over hypotheses, and experiment over speculation.\u00a0 These are familiar and enduring themes in Newton\u2019s work, which reflect his commitment to experimental philosophy<\/a>.\u00a0 Rule 4 echoes the remarks made by Newton in a letter to Oldenburg almost 54 years earlier, when he wrote:<\/p>\n

                  …I could wish all objections were suspended, taken from Hypotheses or any other Heads then these two; Of showing the insufficiency of experiments to determin these Queries or prove any other parts of my Theory, by assigning the flaws & defects in my Conclusions drawn from them; Or of producing other Experiments wch directly contradict me…<\/em><\/ol>\n","protected":false},"excerpt":{"rendered":"

                  Kirsten Walsh writes… In book three of the 3rd edition of Principia, Newton added a fourth rule for the study of natural philosophy: In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly […]<\/p>\n","protected":false},"author":4582,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[113],"tags":[359,4405,224,4406,4404],"class_list":["post-1310","post","type-post","status-publish","format-standard","hentry","category-ideas","tag-hypothesis","tag-natural-philosophy","tag-newton","tag-principia","tag-rules-of-reasoning"],"_links":{"self":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/1310","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=1310"}],"version-history":[{"count":0,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/1310\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/media?parent=1310"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/categories?post=1310"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/tags?post=1310"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}