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J.B. Shank

I’d start by suggesting that there is another contemporary scholarly reading of this review that does not treat it as the response of a Cartesian mechanist, namely Alan Gabbey’s “Newton’s Mathematical Principles of Natural Philosophy: A Treatise on ‘mechanics’?” in the A. Shapiro and P. Harman eds., The Investigation of Difficult Things Essays on Newton and the History of the Exact Sciences in Honour of D. T. Whiteside. I followed the lead of this article in my own research, that will be out in its full development soon as Before Voltaire: The French Origins of “Newtonian” Mechanics, 1680-1715 (University of Chicago Press) and in the OUP Handbook article that you cite. In particular, two themes are key in separating this reviewer from the general description of a seventeenth-century Cartesian mechanist: 1.) he (we can be almost certain that the reviewers was a man) is reading this book as a work of mathematics, not as a new kind of mathematical natural philosophy; and 2.) treating it as a book of brilliant mathematical with an odd natural philosophical argument attached to it, he is also seeking to praise the first while dismissing the second.

Re: 1, Gabbey’s suggestion, which I agree with, is that we recognize how novel it was in 1687 to claim that natural philosophy could be built from mathematical principles. Yes, Galileo and Huygens especially had pointed in that direction, and Kepler’s laws were mathematical foundations for a new kind of account of the heavens, but no one before Newton proposed to make geometry the basis for causal natural philosophical claims as opposed to simple mechanical description and explanation. The French reviewer is recognizing this novelty, but also showing a way to resolve it that became very powerful in France in the first decades after the Principia appeared.Namely, one should read, he argues, the first two books as important contributions to the mathematical discipline of mechanics while ignoring the third empirical and experimental book as an unfounded and merely hypothetical natural philosophy that was untenable epistemologically because of the absence of any firm causal demonstrations. The ket is that this did not result in a dismissal of the Principia altogether because of its failures from the perspective of causal natural philosophy. It rather led to a robust reception of books I and II, and to new developments in mechanics in their wake, while avoiding altogether the bigger natural philosophical arguments of the treatise as a whole. Those arguments were delayed, and became the central pre-occupation of the reception only after 1700, and really only with the publication of the second edition in 1713, with its polemical preface by Cotes setting the book up as a natural philosophical intervention, and with Newton’s “General Scholium” adding his own voice to the the emerging debate about his natural philosophical understandings. All of this was also catalyzed by the appearance after 1705 of the Opticks, with its empirical/experimental arguments about gravity, and the added “Queries” which began to appear.

But going back to 1688, when the Journal des savants review appeared, none of this was yet on the horizon, and what the reviewer reveals is how Newton’s Principia could be read as an important and innovative work in mechanics even if he was not taken seriously yet as a natural philosopher. Back to the review, what this bifurcated reception reveals is the origins, mostly in France I believe, of what I.B. Cohen back in the 1970s liked to call the “Newtonian Way” of mathematical physics. For Cohen, this “Newtonian Way” was the ability to separate mathematics from physics (or, in 17th C terms, mathematical mechanics from natural philosophy), practicing the first with gusto, and not worrying about the second. This was not at all how Newton actually worked, but it is how Pierre Varignon began to operate after 1690, creating what he called his “nouvelle theorie de motion” through a use of calculus-based mathematics to create systematic accounts of terrestrial and celestial mechanics that he bragged were applicable to any causal system of natural philosophy you could provide. In short, as he bragged, he was developing a universal mathematical physics so general that it could be used with whatever physical laws you would find. He also had no reason to worry about which physical laws were in fact operative in the world, since his project was to develop a universal mathematics, not to match it, as Newton had done, to concrete empirical and experimental results. What resulted was Varignon developing what Cohen came to call the essence of the “Newtonian Way” by following Newton in some ways, but also by turning the Principia into something that it really was not. No matter how you parse this, what is not present here is a rejection of Newton according to the Cartesiasn mechanistic principles of natural philosophy, as you rightly state.

A few other thoughts: I find that by and large in France, most Cartesians are like Huygens as you describe him, and are also empirical and experimental Cartesians of the sort written about by Roger Ariew and Mihnea Dobre. Speaking in purely physical and natural terms, they were believers in hypothetical approaches to natural philosophy, and yet for them using a match between theoretical mathematical analysis and quantitative empirical results to ground the causal truth of gravity was simply an illegitimate epistemological operation. Either Newton needed to demonstrate the causal mechanism that produced these quantitative mathematical results, or he had to accept that his was simply a mathematical argument (or mechanical, since to work geometrically meant working with synthetic certainty). This is what I take the reviewer in the JS to be saying in 300 very well chosen words. As a result of the Principia, the relationship between words like analysis and synthesis, geometric and mechanical, and mechanical causal and empire-descriptive were going to be fundamentally transformed, and the meaning of Cartesianism will be changed as well. Another perspective is that found among the authors of the Port Royal Logic and their sympathizers, who were developing a kind of mathematically certain understanding of epistemology. Here Newton’s whole enterprise was suspect because he was trying to discern underlying laws analytically and then to prove them through empirical-experimental demonstration. These people called themselves Cartesians, but they were of a very different sort, I think, than Huygens, Rouault, Regis, Fontanelle, and pretty much everyone in the Académie Royale des Sciences. Lastly, I like the reference to du Chatelet, who is indeed an important figure in taking stock of what happened in France between 1690-1730. “Newtonian rationalism” is a very good term for it, and its applicable to someone like d’Alembert and Lagrange as well, but not to Clairaut and Lapace. This the divisions that were present in 1690 do not disappear even if they change over time. And think about how different developments in Britain were in the same period. In this way, "Newtonian mechanics” understood as 18th-century rational mechanics was really a French invention, provoked by but in no way originated in the Principia. Or so my book argues.

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