{"id":3930,"date":"2015-11-02T12:00:15","date_gmt":"2015-11-02T00:00:15","guid":{"rendered":"https:\/\/blogs.otago.ac.nz\/emxphi\/?p=3930"},"modified":"2015-11-05T05:29:30","modified_gmt":"2015-11-04T17:29:30","slug":"baconian-induction-in-newtons-principia","status":"publish","type":"post","link":"https:\/\/blogs.otago.ac.nz\/emxphi\/baconian-induction-in-newtons-principia\/","title":{"rendered":"Baconian Induction in the Principia"},"content":{"rendered":"

Kirsten Walsh writes\u2026<\/em><\/strong><\/p>\n

Recently, I have been looking for clear cases of Baconianism in the Principia<\/em>. In my last post<\/a>, I offered Newton\u2019s \u2018moon test\u2019 as an example of a Baconian crucial instance, ending with a concern about establishing influence between Bacon and Newton. Newton used his calculations of the accelerations of falling bodies to provide a crucial instance which allowed him to choose between two competing explanations. However, one might argue that this was simply a good approach to empirical support, and not uniquely Baconian. In this post, I\u2019ll consider another possible Baconianism: Steffen Ducheyne\u2019s argument that Newton\u2019s argument for universal gravitation resembles Baconian induction.<\/p>\n

Let\u2019s begin with Baconian induction (this account is based on Ducheyne\u2019s 2005 paper<\/a>). Briefly, Bacon\u2019s method of ampliative inference involved two broad stages. The first was a process of piecemeal generalisation. That is, in contrast to simple enumerative induction, shifting from the particular to the general in a single step, Bacon recommended moving from particulars to general conclusions via partial<\/em> or mediate<\/em> generalisations. Ducheyne refers to this process as \u2018inductive gradualism\u2019. The second stage was a process of testing and adjustment. That is, having reached a general conclusion, Bacon recommended deducing and testing its consequences, adjusting it accordingly.<\/p>\n

Ducheyne argues that, in the Principia<\/em>, Newton\u2019s argument for universal gravitation proceeded according to Baconian induction. In the first stage, Newton\u2019s argument proceeded step-by-step from the motion of the moon with respect to the Earth, the motions of the moons of Jupiter and Saturn with respect to Jupiter and Saturn, and the motions of the planets with respect to the Sun, to the forces producing those motions. He inferred that the planets and moons maintain their motions by an inverse square centripetal force, and concluded that this force is gravity\u2014i.e. the force that causes an apple to fall to the ground. And, in a series of further steps (still part of the first stage), Newton established that, as the Sun exerts a gravitational pull on each of the planets, so the planets exert a gravitational pull on the Sun. Similarly, the moons exert a gravitational pull on their planets. And finally, the planets and moons exert a gravitational pull on each other. He concluded that every body attracts every other body with a force that is proportional to its mass and diminishes with the square of the distance between them: universal gravitation. Moving to the second stage, Newton took his most general conclusion\u2014that gravity is universal\u2014and examined its consequences. He demonstrated that the irregular motion of the Moon, the tides and the motion of comets can be deduced from his theory of universal gravitation.<\/p>\n

Ducheyne notes that Newton didn\u2019t attribute this method of inference to Bacon. Instead, he labelled the two stages \u2018analysis\u2019 and \u2018synthesis\u2019 respectively, and attributed them to the Ancients. However, Ducheyne argues that we should recognise this approach as Baconian in spirit and inspiration.<\/p>\n

This strikes me as a plausible account, and it illuminates some interesting features of Newton\u2019s approach. For one thing, it helps us to make sense of \u2018Rule 4\u2019:<\/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.<\/p><\/blockquote>\n

Newton\u2019s claim that, in the absence of counter-instances, we should take propositions inferred via induction to be true seems na\u00efve when interpreted in terms of simple enumerative induction. However, given Newton\u2019s \u2018inductive gradualism\u2019, Rule 4 looks less epistemically reckless.<\/p>\n

Moreover, commentators have often been tempted to interpret this rule as an expression of the hypothetico-deductive method, in which the epistemic status of Newton\u2019s theory is sensitive to new evidence. Previously<\/a>, I have argued that, when we consider how this rule is employed, we find that it\u2019s not the epistemic status of the theory, but its scope, that should be updated. Ducheyne\u2019s Baconian interpretation supports this position\u2014and perhaps offers some precedent for it.<\/p>\n

Ducheyne\u2019s suggestion also encourages us to re-interpret other aspects of Newton\u2019s argument for universal gravitation in a Baconian light. Consider, for example, the \u2018phenomena\u2019. Previously<\/a>, I have noted that these are not simple observations but observed regularities, generalised by reference to theory. They provide the explananda<\/em> for Newton\u2019s theory. In Baconian terms, we might regard the phenomena as the results of a process of experientia literata<\/em><\/a>\u2014they represent the \u2018experimental facts\u2019 to be explained. This, I think, ought to be grist for Ducheyne\u2019s mill.<\/p>\n

Interpreting Newton\u2019s argument for universal gravity in terms of Baconian induction brings the experimental aspects of the Principia<\/em> into sharper focus. These aspects have often been overlooked for two broad reasons. The first is that the mathematical aspects of the Principia<\/em> have distracted people from the empirical focus of book 3. I plan to examine this point in more detail in my next post. The second is that the Baconian method of natural history has largely been reduced to a caricature, which has made it difficult to recognise it when it\u2019s being used. Dana Jalobeanu<\/a> and others have challenged the idea that a completed Baconian natural history is basically a large storehouse of facts. Bacon\u2019s Latin natural histories are complex reports containing, not only observations, but also descriptions of experiments, advice and observations on the method of experimentation, provisional explanations, questions, and epistemological discussions. We don\u2019t find such detailed observation reports in the Principia<\/em>, but we do find some of the features of Baconian natural histories.<\/p>\n

So, Ducheyne\u2019s interpretation of Newton\u2019s argument for universal gravitation in terms of Bacon\u2019s gradualist inductive method proves both fruitful and insightful. However, recall that, in my last post, I worried that the resemblance<\/em> of Newton\u2019s methodology to Bacon\u2019s isn\u2019t enough to establish that Newton was influenced by <\/em>Bacon\u2019s methodology. If Bacon was just describing a good, general, epistemic method, couldn\u2019t Newton have simply come up with it himself? He was, after all, an exceptional scientist who gave careful thought to his own methodology. Is Ducheyne\u2019s discussion sufficient to establish influence? What do you think?<\/p>\n","protected":false},"excerpt":{"rendered":"

Kirsten Walsh writes\u2026 Recently, I have been looking for clear cases of Baconianism in the Principia. In my last post, I offered Newton\u2019s \u2018moon test\u2019 as an example of a Baconian crucial instance, ending with a concern about establishing influence […]<\/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":[289,12272,349,224,4406],"class_list":["post-3930","post","type-post","status-publish","format-standard","hentry","category-ideas","tag-baconian","tag-induction","tag-natural-history","tag-newton","tag-principia"],"_links":{"self":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/3930","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=3930"}],"version-history":[{"count":0,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/3930\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/media?parent=3930"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/categories?post=3930"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/tags?post=3930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}