<\/p>\n
Kirsten Walsh writes…<\/strong><\/em><\/p>\n In my last post<\/a>, I considered the experimental support Newton offers for his laws of motion. In the scholium to the laws, Newton argues that his laws of motion are certainly true. However, in support he only cites a handful of experiments and the agreement of other mathematicians. I suggested that the experiments discussed do support his laws, but only in limited cases. This justifies their application in Newton\u2019s mathematical theory, but does not justify Newton\u2019s claims to certainty. In this post, I will speculate that the laws of motion were in fact better established than Newton\u2019s discussion suggests. I introduce the notion \u2018epistemic amplification\u2019 \u2013 suggesting that Newton\u2019s laws gain epistemic status by virtue of their relationship to the propositions they entail. That is, by reasoning mathematically from axioms to theorems, the axioms obtained higher epistemic status, and so the reasoning process effectively amplified<\/em> the epistemic status of the axioms.<\/p>\n I am not arguing that epistemic amplification captures Newton\u2019s thinking<\/em>. In fact, Newton explicitly stated that epistemic gain was not possible. For him, the best one could achieve was avoiding epistemic loss. (I have discussed Newton’s aims of certainty and avoiding epistemic loss here <\/a>and here<\/a>.) I suggest that, objectively speaking, the epistemic status of Newton\u2019s laws increases over the course of the Principia<\/em>.<\/p>\n To begin, recall that Newton has two projects in relation to the laws<\/a>:<\/p>\n Let\u2019s consider the first project. In addition to the support of mathematicians and the experiments that Newton cites, it is plausible that the epistemic status of the laws increases by virtue of their success in the mathematical system: in particular, by entailing Keplerian motion<\/a>. Kepler\u2019s rules and Newton\u2019s laws of motion have independent evidence: as we have seen, Newton\u2019s laws are weakly established by localised experiments and the \u2018agreement of mathematicians\u2019; Kepler\u2019s rules are established by observed planetary motion and were widely accepted by astronomers prior to the Principia<\/em>. Newton\u2019s laws entail Kepler\u2019s rules, which boosts Newton\u2019s justification for his laws. Moreover, Newton\u2019s laws provide additional support for Kepler\u2019s rules, by telling us about the forces required to produce such motions. The likelihood of the two theories is coupled: evidence for one carries over to the other. So Newton\u2019s laws also boost the justification for Kepler\u2019s rules. Thus, Newton achieves epistemic gain<\/em>: the epistemic status of the laws, qua<\/em> mathematical axioms, has increased by virtue of their relationship to Kepler\u2019s rules.<\/p>\n Now let\u2019s consider the second project \u2013 the application of the laws to natural philosophy. Again, the discussion in the scholium justifies their use, but not their certainty. I now suggest that these laws, as physical principles, gain epistemic status through confirmation of Newton\u2019s theory. This occurs in book 3, when Newton explicitly applies his mathematical theory to natural phenomena. As I have previously discussed<\/a>, the phenomena (i.e. the motions of the planets and their moons) are employed as premises in Newton\u2019s argument for universal gravitation<\/a>. However, the phenomena also support the application of the mathematical theory to the physical world: they show that the planets and their moons move in ways that approximate Keplerian motion. As we saw above, the laws of motion entail Kepler\u2019s rules. So, since the phenomena support Kepler\u2019s rules, they also support the laws of motion. So this is a straightforward case of theory-confirmation.<\/p>\n There is also scope for theory-testing in book 1. Each time Newton introduces a new factor (e.g. an extra body, or a resisting medium), the mathematical theory is tested. For instance, the contrasting versions of the harmonic rule in one-body and two-body model systems provides a test: it allows the phenomena to empirically decide between two theories, one involving singly-directed central forces, the other involving mutually-interactive central forces. Similarly, the contrasting two-body and three-body mathematical systems provide a test: they allow the phenomena to select between a theory involving pair-wise interactions and a theory involving universal mutual interaction. Moreover, in the final section of book 2, Newton shows that, unlike his theory, Cartesian vortex theory does not predict Keplerian motion. Thus, the phenomena seem to support his theory, and by extension the laws of motion, and to refute the theory of vortices. Again, the laws seem to gain support by virtue of their relationship to the propositions they entail.<\/p>\n To summarise, Newton claims that his laws are certainly true, but the support he gives is insufficient. Here, I have sketched an account in which Newton\u2019s laws gain epistemic status by virtue of their relationship to the propositions they entail. \u2018Epistemic amplification\u2019 is certainly not something which Newton himself would have had truck with, but the term does seem to capture the support actually acquired<\/em> by Newton\u2019s laws in the Principia<\/em>.\u00a0 What do you think?<\/p>\n <\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Kirsten Walsh writes… In my last post, I considered the experimental support Newton offers for his laws of motion. In the scholium to the laws, Newton argues that his laws of motion are certainly true. However, in support he […]<\/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":[274,16428,226,224,4406],"class_list":["post-3669","post","type-post","status-publish","format-standard","hentry","category-ideas","tag-certainty","tag-confirmation","tag-experimental-philosophy","tag-newton","tag-principia"],"_links":{"self":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/3669","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=3669"}],"version-history":[{"count":0,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/3669\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/media?parent=3669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/categories?post=3669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/tags?post=3669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n