{"id":2502,"date":"2012-07-10T12:00:39","date_gmt":"2012-07-10T00:00:39","guid":{"rendered":"https:\/\/blogs.otago.ac.nz\/emxphi\/?p=2502"},"modified":"2012-07-10T10:01:59","modified_gmt":"2012-07-09T22:01:59","slug":"the-experimental-role-of-hypotheses-in-newtons-principia","status":"publish","type":"post","link":"https:\/\/blogs.otago.ac.nz\/emxphi\/the-experimental-role-of-hypotheses-in-newtons-principia\/","title":{"rendered":"The Experimental Role of Hypotheses in Newton’s Principia"},"content":{"rendered":"

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

In the first edition of Principia<\/em> <\/a>(1687), book 3 contained nine hypotheses.\u00a0 But in the second edition (1713), Newton re-structured book 3 so that it contained only two hypotheses.\u00a0 All but one of the old hypotheses were simply re-labelled.\u00a0 Those that specified explanatory constraints were called \u2018Rules of Reasoning\u2019, those that were simply unsupported generalisations were called \u2018Phenomena\u2019, and only the assumptions about nature were called \u2018Hypotheses\u2019.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1st<\/sup> edition<\/strong><\/td>\n2nd<\/sup> edition<\/strong><\/td>\n<\/tr>\n
Hypothesis 1<\/td>\nRule 1<\/td>\n<\/tr>\n
Hypothesis 2<\/td>\nRule 2<\/td>\n<\/tr>\n
Hypothesis 3<\/td>\nReplaced by Rule 3<\/td>\n<\/tr>\n
Hypothesis 4<\/td>\nHypothesis 1<\/td>\n<\/tr>\n
Hypothesis 5<\/td>\nPhenomenon 1<\/td>\n<\/tr>\n
Hypothesis 6<\/td>\nPhenomenon 3<\/td>\n<\/tr>\n
Hypothesis 7<\/td>\nPhenomenon 4<\/td>\n<\/tr>\n
Hypothesis 8<\/td>\nPhenomenon 5<\/td>\n<\/tr>\n
Hypothesis 9<\/td>\nPhenomenon 6<\/td>\n<\/tr>\n
Lemma 3<\/td>\nHypothesis 2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Table: Book 3 changes from 1st<\/sup> to 2nd<\/sup> editions.<\/strong><\/p>\n

These changes seem to indicate that Newton\u2019s attitude to hypotheses changed dramatically between 1687 and 1713 \u2013 probably in response to Leibnizian criticisms and Cotes\u2019 editorial comments.<\/p>\n

On this blog<\/a>, I have given you many reasons to suppose that, as early as 1672, Newton was working with a clear epistemic distinction between theories and hypotheses.\u00a0 More recently<\/a>, I have argued that in fact, Newton was working with a three-way epistemic distinction between theories<\/em>, which are certain and experimentally confirmed, hypotheses<\/em>, which are uncertain and speculative, and queries<\/em>, which are not certain, but provide the proper means to establish the certainty of theories.\u00a0 I call this division Newton\u2019s \u2018epistemic triad\u2019.\u00a0 I argued that hypotheses perform a distinctive and vital supporting role to theories and queries, and that this role is an enduring feature of Newton\u2019s methodology.<\/p>\n

Today I\u2019ll compare the roles of hypotheses and rules of reasoning in book 3, and argue that Newton\u2019s attitude to hypotheses c.1713 was a refinement of his attitude c.1687, but not a dramatic change.<\/p>\n

To begin, consider hypothesis 1 (2nd<\/sup> edition): \u201cThe centre of the system of the world is at rest<\/em>.\u201d<\/p>\n

Upon introducing this hypothesis, Newton explained that:<\/p>\n

    \u201cNo one doubts this, although some argue that the earth, others that the sun, is at rest in the centre of the system.\u00a0 Let us see what follows from this hypothesis.\u201d<\/ol>\n

    This is a simplifying assumption.\u00a0 From this hypothesis, in conjunction with Corollary 4 of the Laws of Motion,<\/p>\n

      \u201cThe common centre of gravity of two or more bodies does not change its state whether of motion or of rest as a result of the actions of the bodies upon one another; and therefore the common centre of gravity of all bodies acting upon one another (excluding external actions and impediments) either is at rest or moves uniformly straight forward\u201d,<\/ol>\n

      Newton derived Proposition 11:\u00a0 \u201cThe common centre of gravity of the earth, the sun, and all the planets is at rest.\u201d<\/em><\/p>\n

      This enabled him to calculate the motions of the planets \u2013 that is, to deduce the observational consequences of his theory.\u00a0 I consider this to be the chief role of hypotheses, and it is experimental.<\/em><\/p>\n

      Now compare this with how Newton uses his rules of reasoning.<\/p>\n

      Rule 1 states:\u00a0 \u201cNo more causes of natural things should be admitted than are both true and sufficient to explain their phenomena.\u201d<\/em><\/p>\n

      And Rule 2 states:\u00a0 \u201cTherefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same.\u201d<\/em><\/p>\n

      In his discussion of Proposition 4, Newton explained:<\/p>\n

        \u201cAnd therefore that force by which the moon is kept in its orbit, in descending from the moon\u2019s orbit to the surface of the earth, comes out equal to the force of gravity here on earth, and so (by rules 1 and 2) is that very force which we generally call gravity.\u201d<\/ol>\n

        These rules didn\u2019t help Newton to deduce the observational consequences of his theory in the same way as his hypothesis 1.\u00a0 They provide an important supporting role for his theory, but it is not an experimental role.<\/p>\n

        To the second edition, Newton also added the General Scholium, in which he (in)famously declared \u00a0\u201chypotheses non fingo<\/em>\u201d.\u00a0 Recently<\/a> I argued that, in this passage, Newton was not railing against hypotheses in general, but rather, against the use of \u2018causal hypotheses\u2019 to illustrate more abstract theories.\u00a0 Given that the first edition did not contain any causal hypotheses, I consider this addition to indicate Newton\u2019s increasing conviction in his method, rather than any dramatic change.<\/p>\n

        So finally, to summarise the developments between the first and second editions of Principia<\/em>:<\/p>\n

        In the first edition:<\/p>\n