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# Tag Archives: induction

## Baconian Induction in the Principia

Kirsten Walsh writes…

Recently, I have been looking for clear cases of Baconianism in the Principia. In my last post, I offered Newton’s ‘moon test’ 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’ll consider another possible Baconianism: Steffen Ducheyne’s argument that Newton’s argument for universal gravitation resembles Baconian induction.

Let’s begin with Baconian induction (this account is based on Ducheyne’s 2005 paper). Briefly, Bacon’s 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 or mediate generalisations. Ducheyne refers to this process as ‘inductive gradualism’. 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.

Ducheyne argues that, in the Principia, Newton’s argument for universal gravitation proceeded according to Baconian induction. In the first stage, Newton’s 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—i.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—that gravity is universal—and 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.

Ducheyne notes that Newton didn’t attribute this method of inference to Bacon. Instead, he labelled the two stages ‘analysis’ and ‘synthesis’ respectively, and attributed them to the Ancients. However, Ducheyne argues that we should recognise this approach as Baconian in spirit and inspiration.

This strikes me as a plausible account, and it illuminates some interesting features of Newton’s approach. For one thing, it helps us to make sense of ‘Rule 4’:

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.

Newton’s claim that, in the absence of counter-instances, we should take propositions inferred via induction to be true seems naïve when interpreted in terms of simple enumerative induction. However, given Newton’s ‘inductive gradualism’, Rule 4 looks less epistemically reckless.

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’s theory is sensitive to new evidence. Previously, I have argued that, when we consider how this rule is employed, we find that it’s not the epistemic status of the theory, but its scope, that should be updated. Ducheyne’s Baconian interpretation supports this position—and perhaps offers some precedent for it.

Ducheyne’s suggestion also encourages us to re-interpret other aspects of Newton’s argument for universal gravitation in a Baconian light. Consider, for example, the ‘phenomena’. Previously, I have noted that these are not simple observations but observed regularities, generalised by reference to theory. They provide the explananda for Newton’s theory. In Baconian terms, we might regard the phenomena as the results of a process of experientia literata—they represent the ‘experimental facts’ to be explained. This, I think, ought to be grist for Ducheyne’s mill.

Interpreting Newton’s argument for universal gravity in terms of Baconian induction brings the experimental aspects of the Principia into sharper focus. These aspects have often been overlooked for two broad reasons. The first is that the mathematical aspects of the Principia 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’s being used. Dana Jalobeanu and others have challenged the idea that a completed Baconian natural history is basically a large storehouse of facts. Bacon’s 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’t find such detailed observation reports in the Principia, but we do find some of the features of Baconian natural histories.

So, Ducheyne’s interpretation of Newton’s argument for universal gravitation in terms of Bacon’s gradualist inductive method proves both fruitful and insightful. However, recall that, in my last post, I worried that the resemblance of Newton’s methodology to Bacon’s isn’t enough to establish that Newton was influenced by Bacon’s methodology. If Bacon was just describing a good, general, epistemic method, couldn’t 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’s discussion sufficient to establish influence? What do you think?