Posts Tagged ‘rule 4’
Monday, December 17th, 2012 | Comments Off
Kirsten Walsh writes…
In 1718, Newton published the second edition of Opticks. Query 23 was renamed Query 31, and in this query Newton expanded on his method of analysis. He wrote:
- “If no Exception occur from Phænomena, the Conclusion may be pronounced generally. But if at any time afterwards any Exception shall occur from Experiments, it may then begin to be pronounced with such Exceptions as occur.”
At first glance, this passage suggests that Newton adopted the hypothetico-deductive method, in that the epistemic status of a theory is sensitive to new evidence. However, if we consider how Newton put this methodology into practice, in Principia book III, we will get a different reading of this passage.
In the 3rd edition of Principia, Newton introduced a 4th rule of philosophising:
- “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.”
The similarities between this rule and the earlier passage from Query 31 are striking: that new evidence can make a proposition “either more exact or liable to exceptions” is similar to pronouncing the conclusion either “more generally” or “with such Exceptions as occur”. So looking at how this rule was employed should tell us a lot about how to interpret the earlier passage.
In Principia, Newton only explicitly employed rule 4 once: in proposition 5 book III. In this proposition, Newton made his argument for universal gravitation by generalising step-by-step from the motions of the planets around the sun, and the satellites of Saturn and Jupiter around their respective centres, to the forces producing those motions. Newton introduced three corollaries, the third of which states that “all planets gravitate towards one another”.
In the scholium following this corollary, Newton said:
- “Hitherto we have called ‘centripetal’ that force by which celestial bodies are kept in their orbits. It is now established that this force is gravity, and therefore we shall call it gravity from now on. For the cause of the centripetal force by which the moon is kept in its orbit ought to be extended to all the planets, by rules 1, 2, and 4.”
Rules 1 and 2 tell us not to postulate more causes than necessary, and that we should assume that effects of the same kind have causes of the same kind. In this context, rule 4 tells us that, if exceptions to universal gravitation occur, then instead of reducing our credence in the theory, we should reduce the scope of the theory: it is still true, but true of less instances. De-generalising a theory doesn’t reduce its certainty; rather, it reduces the scope of the theory while maintaining its certainty. So according to rule 4:
- In the absence of exceptions, we should take gravity to be universal.
- If exceptions to universal gravitation are found, we should infer that the domain of gravity is limited (i.e. not universal).
- We should not allow our assumptions about matter theory (e.g. the improbability of action at a distance) to have any influence on our epistemic attitude towards universal gravitation.
Instead of reading rule 4 and the passage from Query 31 as accounts of hypothetico-deductivism, we should read them as accounts of what I Bernard Cohen called the ‘Newtonian Style’: a way of modelling the world in a series of increasingly complex and increasingly accurate idealisations (i.e. approximations that would hold exactly in certain specifiable circumstances).
On this blog, I have often discussed Newton’s aim of certainty and his corresponding claims to have achieved this aim. Newton’s youthful aim of certainty places him in a position that is quite isolated from his contemporaries. Most of the experimental philosophers of the Royal Society thought it epistemically irresponsible to make such bold claims. Instead, they had more modest aims: obtaining highly probable theories. Rule 4, and the passage from Query 31, suggest that Newton eventually adopted a version of the hypothetico-deductivism preferred by his contemporaries. I have argued, however, that this is a misleading way of reading these passages. Newton uses rule 4, not to update the epistemic warrant of the theory, but its scope.