The Newton/Leibniz Conflict in Context

Editor's Remarks

The first draft dealt to a large extent with the peculiar views of the Clarks [Cl], might provide an interesting subject for further sociological analysis, and the less peculiar views of Meli, which were a bit off-center from our eventual point of view, with an excessive emphasis on Leibniz' essay on a mechanical explanation for the law of gravity and its consequences, referred to by its Latin abbreviation, the Tentamen. This turned out not to be a good route into the subject for us, though it's not clear that it had to be entirely discarded either.

After Professor Kosinski pointed out to us the excellent work by A. Rupert Hall on the Newton/Leibniz conflict, things fell neatly into place. Your point of departure was your question as to whether something in Newton's personality made him unusually prone to professional conflict, a question which was certainly raised by the Clarks in the process of begging it. A. Rupert Hall himself points out that the mores of academic life have changed over time, and that the normal career of an academician of Newton's day involved substantial doses of aggressive behavior, including varieties frowned on today.

I'm not sure Christianson is helpful here. While he is a specialist in the area, and writes extensively on it, he seems to have chosen a more popular and facile vein.

Your previous draft, following Meli, made something of the rivalry between Newton and Leibniz as physicists. Hall explains rather clearly how this became entangled with the priority dispute over the calculus, and how it may have provided a spark to actually ignite the affair.

The quotation from Arnold regarding "universal methods" seems to me to prove the opposite of what you are aiming at; Arnold is given to sarcasm. He does not much approve of Leibniz' algebraic or logical predisposition, and disapproves of his naive optimism, though I suspect he might possibly approve highly of that same quality in the case of Kepler. Arnold is a provocateur by inclination and habit.

"The Newton/Leibniz debate has already been covered in great detail ... ." One would think so. In any case, it has been alluded to frequently, and casually debated, but perhaps in less detail than one might reasonably expect, until Hall's work.

This draft is based mainly on the accounts of Hall and Hofmann and remains as a result on ground which is both firm and interesting. I question the assertion that Hall's judgement of the priority dispute may be regarded as definitive; I see no reason to cast aside Hofmann's opinions. In a purely chronological sense Hall has had the "last word", and the topic seems to have been dealt with both systematically conscientiously. Hall openly relies on the opinions of others as far as the mathemat ical issues are concerned, and argues that the historians may take these as settled. To me this seems excessive.

It is interesting that Keill and Jean Bernoulli were born in 1671 and 1667 respectively, in other words about the time that the work about whose development they were wrangling was actually done. It seems to me that the attribution to Newton of an "algorithm" by Hall is curious; Newton appears to have been more or less openly opposed to the idea that it was useful to present these ideas as algorithms, and his main general purpose tool for the purposes of calculation was the infinite series, which does not lend itself particularly naturally to algorithmic manipulation (being infinite), and it seems he frequently resorted to geometry in any case, rather than to calculation.

As far as the issue of reverse plagiarism is concerned, Newton seems to have rather too much of a head start for this to be taken very seriously, but on the other hand he does seem to have reworded his earlier results to bring out the similarities with Leibniz' work. I don't think one would call that plagiarism, but it is certainly underhanded.

Regarding the "arithmetical quadrature" of the circle, the example of Leibniz' correspondence illustrates the situation even more fully than intended. In fact the claim that Oldenburg relayed to Leibniz about the "impossibility" of this sum seems to be based on a misunderstanding; not only was Leibniz perfectly correct, but the British knew that, and had reached the same result earlier. It's possible that Leibniz was arguing that his infinite series might be "summed" to a finite one, and that Gregory argued against this; but it's also possible that Oldenburg was simply confused about the issues and their status, and provided information that Leibniz could make nothing useful of.

Both Aldous Huxley and V. Arnold have told us that Newton was, in human terms, a monster: is the latter repeating the former? (are they both repeating Voltaire?) Perhaps this is yet another legend, a complement to the early hagiographies. It's a pity the signal-to-noise ratio in the literature is so low, but after going through two drafts of your paper, and the excellent references, I begin to see what the issues are.

In particular it seems to me the conflict between the creative and intuitive mathematician Newton with a strong interest in applications, and the builder of formal systems Leibniz, with a point of view now variously classified as falling in the domains of algebra, logic, or even computer science, remains very much alivetoday.

I find the mathematical issues involved fairly knotty, and I find myself disagreeing fairly regularly with certain aspects of specific assessments of both Hall and Hofmann, though not in ways that seem very central to their arguments. In any case they b oth seem to work from the facts toward their conclusions, rather than the other way around.

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