Philosophers of science of all stripes draw on the history of science. However, within philosophy of science there are diverging trends between literature in the history and philosophy of science and the work in (what often goes under the name of) ‘general’ philosophy of science. With the caveat that what follows paints a picture with very broad brushstrokes, the trend among those working on integrated history and philosophy of science is towards recognizing particular differences between scientific fields, periods, and practitioners. On the other hand, the driving motivation in general philosophy of science is towards unified frameworks and theories.
These differences in emphasis can make it hard to integrate work with these two broad orientations. Nonetheless, I am particularly interested in work that tries to do so. Harper’s work on Newton’s methodology provides a case study of the kind of work that I have in mind. Most of Harper’s research on this topic is focused on the reasoning that is particular to Newton’s methodology in the Principia. I think of it as belonging in the tradition of integrated history and philosophy of science. However, Harper also draws lessons for broad views on theory acceptance and theoretical progress that are most closely aligned with the interests of general philosophy of science.
I think that interactions between these two approaches are fruitful in both directions. Let me illustrate why by drawing on my own work. In one direction, I have argued that we can gain a better understanding of Newton’s explanatory goals by paying critical attention to the general philosophy of science. In the other, I argue that we can gain better accounts of explanation in general by paying attention to Newton’s methodology in the Principia.
Smith describes Newton’s goal as being that of developing ‘an intermediate level of theory, between mere description of observed regularities in the manner of Galileo’s Two New Sciences, on the one hand, and laying out full mechanisms in the manner of Descartes’ Principia, on the other’. Smith stresses the role of laws of force in allowing us to answer questions about whether or not observed regularities are suitable as evidence. When it comes to explanation, however, this intermediate level of theory raises new difficulties. What could such an intermediate level of explanatory theory be?
If we approach the question from the assumption (found in accounts within general philosophy of science) that to explain physical events, and the regularities among such events, requires causal explanation, then we are pushed to try to make sense of an intermediate-level theory in causal terms. This is difficult to do (though Janiak argues for this option). In particular, it is challenging to reconcile Newton’s disavowal of having provided a causal account of gravitational phenomena with his claim to have an explanatory account that goes beyond mere description of regularities:
Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity […] And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.
If we instead take as our starting point the Scholium to Proposition 69 in Book 1, a natural suggestion is to take Newton as providing a law-based theory (at the level of physics), and law-based explanations:
Mathematics requires an investigation of those quantities of forces and their proportions that follow from any conditions that may be supposed. Then, coming down to physics, these proportions must be compared with the phenomena, so that it may be found out which conditions [or laws] of forces apply to each kind of attracting bodies. And then, finally, it will be possible to argue more securely concerning the physical species, physical causes, and physical proportions of these forces.
Our merry-go-round now circles us back to problems in the general philosophy of science. Here, we face familiar worries about such a proposal. After all, the most prominent general account of how laws explain, the deductive nomological account, runs into several well-known problems with capturing the directionality of explanation and the nature of explanatory irrelevancies. If these problems cannot be addressed, then an interpretation that takes Newton’s theoretical and explanatory focus to be laws makes the position in the Principia ultimately unstable.
In order to see how far we can make stable the position that takes laws as theoretically prior to causes—including the case of explanation—we can again draw on work in both the integrated history and philosophy of science and general philosophy of science. What is it that makes the use of laws in the Principia differ from simple deductions of phenomena of interest from laws? From Harper’s and Smith’s work, we find a compelling account of Newton’s reliance on subjunctive reasoning in the Principia. From Woodward’s influential causal account of explanationcausal account of explanation, we find a similar emphasis on counterfactual considerations. This give us a plausible first step towards providing an account of how laws can do explanatory work that departs from the motivation driving the deductive-nomological account. We can focus on the role of laws in guiding subjunctive reasoning in the Principia. I do not think that this is enough to tackle the difficulties, but it provides the crucial first step.
However, we have not yet done enough to support a ‘laws-first’ interpretation of the methodology in the Principia. To allow that law-based explanations can be epistemically independent from causal underpinnings, we need to account both for
- how laws can do explanatory work, independent of causal underpinnings
- how we can have reason to take some proposition to be a law of nature, independent of knowledge of the causal underpinnings of the proposition.
Round and round we go, and this raises a new question from general philosophy of science: How can we have empirical reasons to take a proposition to be a law—and capable of supporting subjunctive reasoning—rather than merely accidentally true? I am currently working on developing an answer to this question that relies on Harper’s and Smith’s account of the crucial role of subjunctive reasoning and successive approximations in Newton’s methodology. The very rough idea is this: Chains of subjunctive reasoning can be successful (or unsuccessful) at tackling reasoning about a physical system. Moreover, that success is empirically accessible. If we take it to be a defining feature of propositions that are laws that they reliably support subjunctive reasoning, while mere accidents do not, we now have a potential empirically accessible way to distinguish laws from merely true propositions.
Taking a final turn (for now) in our merry-go-round, we return to questions from the history and philosophy of science. How much of the work from general philosophy of science is it legitimate to read into a specific historical text? More specifically, how plausible is it that Newton recognized a distinction between laws and accidents that concerns whether it is legitimate to rely on the principle in question in subjunctive reasoning?
Again, Harper’s work on Newton’s methodology provides a fascinating clue. Newton added a scholium to his argument in Proposition 4, Book 3, for the identification of the force that keeps the planets in orbit with gravity. This scholium relies on taking Kepler’s harmonic rule to extend to non-actual systems:
Curtis Wilson’s search for the first to write of Kepler’s rules as ‘laws’ led him to conclude that it was Leibniz in his ‘Tentamen de motuum coelestium causis’ of 1689 [...] Newton takes advantage of the opportunity afforded by being able to call Kepler’s Harmonic Rule a ‘law’.
At the time of the first publication of the Principia, it was not common to call Kepler’s rules ‘laws’. Only after Leibniz had called them thus was Newton willing to use them in guiding counterfactual reasoning. As Harper notes, this at least suggests that the distinction was a salient one to Newton.
On the one hand, the attention to particular approaches and how they work in a particular context promises to open up new paths for developing unified accounts in the general philosophy of science. On the other hand, new general accounts of explanation, confirmation, laws, and so on promise to offer new interpretative possibilities for the history and philosophy of science. We might go round and round, but it is a fruitful ride!
University of Nottingham
 Newton, 'General Scholium', The Principia: Mathematical Principles of Natural Philosophy, p. 943.
 Newton, 'General Scholium', The Principia: Mathematical Principles of Natural Philosophy, pp. 588-9.