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Philosophers at War: The Quarrel between Newton and Leibniz, by Alfred Rupert Hall
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Probably the most celebrated controversy in all of the history of science was that between Newton and Leibniz over the invention of the calculus. The argument ranged far beyond a mere priority dispute and took on the character of a war between two different philosophies of nature. Newton was the first to devise the methods of the calculus, but Leibniz (who independently discovered virtually identical methods) was the first to publish, in 1684. Mutual toleration passed into suspicion and, at last, denunciation of each by the other as a fraud and a plagiarist. The affair became a scandal, as British mathematicians asserted Newton's claims before the public while their Continental colleagues hotly defended Leibniz's priority. Professor Hall analyzes the situation out of which the dispute arose, the circumstances that caused it to become embittered, the dispositions of the chief actors, and the shifts in their opinions of each other.
- Sales Rank: #4204742 in Books
- Published on: 1980-05-30
- Ingredients: Example Ingredients
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x 1.10" w x 5.98" l, 1.51 pounds
- Binding: Hardcover
- 352 pages
Most helpful customer reviews
7 of 8 people found the following review helpful.
Uninspired
By Viktor Blasjo
This is an uninspired and moderately useful history of the calculus priority dispute. The standard account of the dispute, which occupies a few pages in any history of mathematics book, is essentially accurate. Hall's account adds nothing in particular and has no particular goal or thesis.
Many problems arise from Hall's superficial understanding of the mathematics involved. He usually relies very heavily on Whiteside, but when he has to stand on his own legs the results are not good. Sometimes he simply refuses to comment at all. For example, Leibniz apparently claimed that "it was evident from the Principia that Newton had not known the differential calculus in 1687, because he had avoided its use in circumstances that demanded it" (p. 204). Hall leaves this with no comment and no further information. What circumstances? Is there any merit in this argument? Did anyone find it convincing? Hall usually answers questions such as these when he can do so by simply transcribing Whiteside, but not otherwise, apparently. Such opportunism prevents this book from being a definite history of the calculus dispute. It is no better when he actually tries to comment on the mathematics. For example, he singles out Newton's proof of (x^n)'=nx^n-1 in Lemma II of Book II of the Principia as "highly unsound" and "self-nullifying" (p. 32). But this proof is no more "self-nullifying" than any other proof in the Principia or any other infinitesimal argument published that century. It is in fact the modern proof used today in every calculus textbook, differing only is superficial gloss. Another example is Hall's mischaracterisation of the relation between infinite series and the calculus (p. 188).
Hall's judgement is sometimes hasty and uncritical even beyond the mathematical. For example, he has made up his mind in advance that the dispute was bitter and destructive, and imposes this gloominess even where the evidence does not support it. Newton's contribution to the dispute was a useful and thorough and essentially correct piece of historical scholarship, but Hall sees only destructiveness and calls it a "tragedy" (p. 23) that Newton entered the dispute in this way. Similarly, the dispute drove the Bernoullis to look for errors in the Principia, and indeed they found one or two slips which Newton corrected in subsequent editions. Again Hall bemoans this as "destructive" (p. 194). To seriously assess the destructiveness of the dispute one would want to know, for example, to what extent the split between the British and the Continent was due to the dispute. But Hall is of little help; the dispute was simply destructive by decree.
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