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Isaac Newton's Natural Philosophy (Dibner Institute Studies in the History of Science and Technology) Paperback – January 30, 2004
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""The authors are well-known Newton experts, and their contributions add many nuances to our image of Newton ..."
About the Author
Jed Z. Buchwald is Director of the Dibner Institute for the History of Science and Technology and Bern Dibner Professor of the History of Science at the Massachusetts Institute of Technology.
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One reads with envy about the gravity attached to matters of scientific research policy at the time: "there has been much canvassing and intrigue made use of, as if the fate of the Kingdome depended on it" (p. 77). "On the eve of Newton's election as president, matters had deteriorated to such an extent that various fellows could be restrained only with difficulty from a public exchange of blows (or, in one case, the drawing of swords)" (p. 93).
So what was this conflict on which "the fate of the Kingdome" depended? The "philomats" identifying with Newton attacked the naturalists thus: "That Great Man [Newton] was sensible, that something more than knowing the Name, the Shape and obvious Qualities of an Insect, a Pebble, a Plant, or a Shell, was requisite to form a Philosopher, even of the lowest rank, much more to qualifie one to sit at the Head of so great and learned a Body." (p. 77)
The naturalists, for their part, identified with Bacon, who had complained about "the daintiness and pride of mathematicians, who will needs have this science almost domineer over Physic. For it has come to pass, I know not how, that Mathematics and Logic, which ought to be but the handmaids of Physic, nevertheless presume on the strength of the certainty which they possess to exercise dominion over it." (p. 80)
Similar points were raised many times, as here in 1700 by a minor figure: "Mathematical Arguments, of which the World is become most immoderately fond, looking upon every thing as trivial, that bears no relation to the Compasse, and establishing the most distant parts of Humane Knowledge; all Speculations, whether Physical, Logical, Ethical, Political, or any other upon the particular results of number and Magnitude. ... In any other commonwealth but that of Learning such attempts towards an absolute monarchy would quickly meet with opposition. It may be a kind of treason, perhaps, to intimate thus much; but who can any longer forbear, when he sees the most noble, and most usefull portions of Philosophy lie fallow and deserted for opportunities of learning how to prove the Whole bigger than the Part, etc." (p. 90)
As an illustration of the importance of this conflict, Feingold suggests that Newton withdrew from engagement with the society following the optics dispute of the 1670s "not, as some historians assume, on account of his distaste for controversies, but because he came to consider the Royal Society a forum inhospitable to his beliefs" (p. 84). Indeed, Newton's communications with the society contained pointed methodological proclamations that were omitted from their printed Transactions (p. 83).
So as not to focus exclusively on this chapter of the book I may comment briefly on Blay's chapter as well. Blay alleges that there were certain "conceptual difficulties involved in Newton's construction of the concept of force in the sense of a continuous action" (p. 228), which were to be resolved (or perhaps dissolved) only by Varignon.
Blay shows that Newton's second law as stated is not F=ma or F=(mv)' but rather F=Delta(mv). That is to say, Newton's "Newton's law" is based on an impulse notion of force and does not involve the variable of time in any way. Indeed, Blay is able to quote several later passages of the Principia which clearly uses this rather dubious conception of force.
I submit, however, that the matter is largely cosmetic. Blay fails to recognise that the quoted passages supporting his point are all from statements of laws and theorems, while it is in the proofs that one finds the de facto meaning of mathematical concepts. And indeed the proofs invariably begin "let the time be divided into equal intervals ..." (p. 227 and again p. 230) and then duly proceed precisely as if the law was F=ma after all, with the time variable properly acknowledged and the matter of the continuous force acting by impulses amounting to nothing more than the usual estimation of curves by infinitesimal line segments everywhere in the calculus. Thus I conclude that the alleged conceptual difficulties are merely artifacts of Newton's use of antiquated language in the statements of theorems rather than actual obstacles of thought.