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# Huygens and Newton

Kirsten Walsh writes…

In a previous post, I noted that, unlike other members of the Royal Society, Newton saw a role for mathematical reasoning in experimental philosophy. In many ways, it was this mathematical approach that distinguished his methodology from the Baconian experimental philosophy, adopted by Boyle and Hooke.  Given this distinctive mathematical bent, one might be tempted to suggest that Newton’s approach has far more in common with that of mathematicians such as Huygens, than with experimental philosophers such as Boyle and Hooke. (Indeed, Eric Schliesser argues for this position here.) In today’s post, I’ll examine this claim. First I’ll look at Huygens’ and Newton’s mechanics, then I’ll broaden the scope to consider their optical work as well.

Let’s begin by comparing Huygens’ Horologium Oscillatorium (or, the Pendulum Clock) with Newton’s Principia. The Horologium and the Principia are generally regarded as two of the three most important seventeenth-century works on mechanics (the third being Galileo’s Two New Sciences). We know that Newton read, and very much approved of, Huygens’ Horologium well before he began work on his Principia. So it is an obvious source of inspiration and influence for Newton’s work. Moreover, there are important similarities between them. Most obviously, they share fundamental assumptions and content, including axioms regarding motion, analyses of pendulum motion and theories of curves. Furthermore, each work, to some extent, re-derives Galileo’s work on mechanics. But the similarity runs deeper. Firstly, both works display a marked preference for classical-geometrical inference strategies. For one thing, they both exploit the axiomatic structure of geometry as a model of logical rigour. And for another, they employ geometrical diagrams to demonstrate propositions. Secondly, both works draw on experiment (for example, pendulum experiments) to establish the explananda.

Another similarity between the two works is that both authors remain agnostic with regard to the mechanism or cause of gravity. Newton’s (in)famous phrase, Hypotheses non fingo, is a declaration of this. And in part II of the Horologium, Huygens’ second hypothesis begins, “By the action of gravity, whatever its sources…” (my emphasis). On the face of it, this is a feature that unites them. But, despite appearances, it is at this point that they come apart.

After its publication, Huygens criticised the Principia for appearing to support action at a distance. Huygens was committed to the mechanical philosophy and, as far as he was concerned, Newton’s account of gravity couldn’t be given a mechanical explanation. Newton was not swayed. The fact that his account seemed to support an unsavoury metaphysical commitment did not deter him from appreciating its empirical success. In the preface to book 3 of the Principia, Newton wrote that he was wary of its inclusion, since

“…those who have not sufficiently grasped the principles set down here will certainly not perceive the force of the conclusions, nor will they lay aside the preconceptions to which they have become accustomed over many years…” (my emphasis).

Huygens did exactly what Newton was afraid of: he allowed his mechanical preconceptions to prevent him from appreciating “the force of the conclusions”.*  As far as Newton was concerned, “it is enough that gravity really exists and acts according to the laws that we have set forth”. (And in the final paragraph of the Principia we see that Newton hoped to conceive of gravity as a spirit or vapour—he had not given up on the possibility of a local-action explanation. However, he wasn’t willing to sacrifice the rigour of his account in order to provide one.)

And so, one difference between Newton and Huygens lies in their commitment to mechanical philosophy. Where, for Huygens, the ability to give mechanical explanations—appealing to the shape, size, motion and texture of corporeal bodies—is a requirement of natural philosophy, Newton sees this as a needless restriction. Although Huygens’ commitment to the mechanical philosophy aligns him closely with Boyle and other early members of the Royal Society, the mechanical philosophy and the experimental philosophy were distinct. Arguably, Newton’s decoupling of experimental and mechanistic philosophy is one thing that sets him apart from both the early Royal Society and Huygens.

Another difference between Newton and Huygens is revealed when we broaden the scope to consider their optical work as well. Newton, following Isaac Barrow, thought that there was a place for mathematical reasoning in optics and natural philosophy more generally. In mathematics, one can reason deductively from axioms to propositions, without epistemic loss. So too, Newton thought, one can reason in natural philosophy. And so, by starting with experimentally established axioms (or laws), one could reason deductively to propositions, without epistemic loss. In this way, Newton conceived of a ‘science of optics’, grounded in experiment and observation, and inferred via mathematical reasoning. In contrast, Huygens thought that optics required a very different approach than mechanics. Where, in mechanics, it was possible to reason mathematically, without epistemic loss; Huygens thought that the hypothetico-deductive method was more appropriate for optics.

In brief, Newton took his theoretical claims in optics to be certain, as they were (1) mathematically derived from axioms, which were (2) established by careful experiment. Huygens, like the early Royal Society, held that certainty is out of our reach, so the best we can hope to achieve is a high degree of probability. Here we see one way in which Newton diverges from the Baconian experimental philosophy. He distanced himself from the probabilism of the Baconian experimental philosophers—and Huygens.

Here we have seen that there are indeed striking similarities between Huygens’ Horologium and Newton’s Principia. But, if we want to understand their methodological outlooks, we may learn more by considering the differences. The points of disagreement between Huygens and Newton allows us to identify two very different methodological approaches. Huygens was undoubtedly a strong influence on Newton. As were Descartes, Barrow and Hooke—not to mention his early reading of Aristotelian textbooks, his later interest in Pappus, and the many contemporary works of logic and natural philosophy! Despite these influences, or perhaps because of them, the methodology ultimately developed and exemplified by Newton was utterly original. In a nutshell, he saw mathematical deductive inference as compatible with the observations and experiments of Baconian natural history.  In combining these, he forged a new method of experimental philosophy, which eventually superseded Baconian experimental philosophy.

And so, what was Newton’s relationship with the mathematicians? Well, Newton actively engaged with their methodological approaches, and took a lot from them. Just as he did with the experimental philosophers of the early Royal Society.  How distinctive was Newton’s approach?  Mary Domski has argued that the methodology of the Principia should be viewed as a natural extension of the Baconian experimental philosophy – and that this was recognised by Locke.  In my next post, I’ll examine this idea and try to nail down just what was original about Newton’s methodology.

* Incidentally, here I offer a different reading of this passage to the one offered by Eric Schliesser. Where Schliesser argues that Newton was rejecting “a whole package of practices that are (implicitly) captured by the ESD”, I argue that Newton was rejecting the mechanical philosophy. (On the historiography of the mechanical philosophy, including some thoughts on the relationship between the experimental philosophy and the mechanical philosophy, see Peter Anstey’s recent essay review.  He has also posted on the topic here and here.)