{"id":485,"date":"2010-11-15T09:00:52","date_gmt":"2010-11-14T21:00:52","guid":{"rendered":"https:\/\/blogs.otago.ac.nz\/emxphi\/?p=485"},"modified":"2012-09-25T02:00:58","modified_gmt":"2012-09-24T14:00:58","slug":"newton-on-certainty","status":"publish","type":"post","link":"https:\/\/blogs.otago.ac.nz\/emxphi\/newton-on-certainty\/","title":{"rendered":"Newton on Certainty"},"content":{"rendered":"

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

A few weeks ago<\/a>, I said that in Newton\u2019s early optical papers:<\/p>\n

    Newton claims that his doctrine of colours is a theory, not a hypothesis, for three reasons:
    \n1.\u00a0 It is certainly true, because it is supported by (or deduced<\/em> from) experiment;
    \n2.\u00a0 It concerns the physical properties<\/em> of light, rather than the nature of light; and
    \n3.\u00a0 It has testable<\/em> consequences.<\/ol>\n

    From this set of criteria, we can see that early-Newton\u2019s strong anti-hypothetical stance is closely related to his goal of generating theories that are certainly true.\u00a0 Students from Florida<\/a> have pointed out that Newton’s criterion of certainty seems to set the bar quite high.\u00a0 Indeed it does.\u00a0 So today I will explain early-Newton\u2019s goal of absolute certainty and why he thought it was achievable.<\/p>\n

    For Newton, absolute certainty is closely related to mathematics \u2013 he wants to achieve certainty in the science of colours by making it mathematical.\u00a0 In his first letter to the Royal Society<\/a>, he says:<\/p>\n

      A naturalist would scearce expect to see ye science of those become mathematicall, & yet I dare affirm that there is as much certainty in it as in any other part of Opticks.\u00a0 For what I shall tell concerning them is not an hypothesis but most rigid consequence, not conjectured by barely inferring \u2019tis thus because not otherwise or because it satisfies all Ph\u00e6nomena (the Philosophers universall Topick,) but evinced by ye mediation of experiments concluding directly & without any suspicion of doubt.<\/ol>\n

      In a letter to Hooke, Newton says, ideally the science of colours will be \u201cMathematicall<\/em> & as certain as any part of Optiques\u201d.\u00a0 However, absolute certainty is difficult to achieve because the science of colours<\/p>\n

        depend[s] as well on Physicall Principles as on Mathematicall Demonstrations: And the absolute certainty of a Science cannot exceed the certainty of its Principles.<\/ol>\n

        Thus, Newton thinks that absolute certainty is also closely related to experiment.\u00a0 It is no accident that, in his first paper, Newton attempts to establish the physical principles of colour experimentally by focussing on refrangibility<\/em> rather than colour of light.\u00a0 It would have been difficult to measure precisely changes in colour, but Newton was able precisely to measure degrees of refraction and lengths of refracted images.\u00a0 He hardly even mentions colour until he believes he has established that white light is a mixture of differently refrangible rays.\u00a0 When he is ready to reveal his theory of colour, he does so by first asserting that there is a one-to-one correspondence between refrangibility and colour of light rays.\u00a0 Newton claims that he has established the physical principles of colour with absolute certainty.<\/p>\n

        When he reveals his theory of colour, he does so in a quasi-mathematical style.\u00a0 In a letter to Oldenburg, Newton says:<\/p>\n

          I drew up a series of such Expts on designe to reduce ye Theory of colours to Propositions & prove each Proposition from one or more of those Expts by the assistance of common notions set down in the form of Definitions & Axioms in imitation of the Method by which Mathematicians are wont to prove their doctrines.<\/ol>\n

          This quasi-mathematical \u2018proof\u2019 of his theory of colours is set out in his reply to Huygens<\/a>.<\/p>\n

          To summarise, Newton’s mathematical method and his experimental method are linked by his notion of absolute certainty.\u00a0 Newton claims his theory of colours is certainly true, because (1) his physical principles are established experimentally and are certainty true, and (2) he can use these physical principles as the basis of his mathematical proof.\u00a0 That a lengthy and sometimes heated debate followed Newton’s original paper, shows that his opponents weren’t as convinced by his careful demonstration as he was.<\/p>\n","protected":false},"excerpt":{"rendered":"

          Kirsten Walsh writes… A few weeks ago, I said that in Newton\u2019s early optical papers: Newton claims that his doctrine of colours is a theory, not a hypothesis, for three reasons: 1.\u00a0 It is certainly true, because it is supported […]<\/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":[274,276,275,224],"class_list":["post-485","post","type-post","status-publish","format-standard","hentry","category-ideas","tag-certainty","tag-experiment","tag-mathematics","tag-newton"],"_links":{"self":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/485","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=485"}],"version-history":[{"count":0,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/485\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/media?parent=485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/categories?post=485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/tags?post=485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}