- Hardcover: 496 pages
- Publisher: Birkhauser (March 1982)
- Language: English
- ISBN-10: 0906812089
- ISBN-13: 978-0906812082
- Product Dimensions: 22.9 x 15.2 x 2.5 cm
- Shipping Weight: 626 g
- Amazon Bestsellers Rank: #1,244,394 in Books (See Top 100 in Books)
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The truth about Berkeley's critique of the calculus, May 26 2010
By Viktor Blasjo - Published on Amazon.com
This review is from: Collected Letters of Colin Maclaurin (Hardcover)
A very widespread myth has it that Berkeley's critique of the infinitesimal calculus constituted a profound challenge that forced MacLaurin to write a thorough treatise reexamining its foundations. The facts of the matter, however, are, in MacLaurin's own words, as follows.Berkeley was an incompetent dilettante, whose superficial critique did not shake the foundations of the calculus in the least. Berkeley's critique is "groundless" (p. 427) and the alleged flaws that he "pretends to discover" (p. 427) are all due to him having "not understood" (p. 427) the mathematics in question.
The foundations of the calculus were well understood (and Berkeley's trifling arguments preempted), and in need of no revision whatever. "[Newton's] notion of fluxions has nothing obscure, mysterious, unintelligible or absurd in it." (p. 428) "What this writer [Berkeley] advances against the foundations of the methods of Fluxions serves only to shew that he has not considered or understood what its great Author [Newton] said in their defence when he first published them; for if he had, he would have found the most material of his objections prevented & answered there." (p. 425)
MacLaurin did not write his Treatise of Fluxions in reply to Berkeley's critique. "Upon more consideration I did not think it best to write an Ansuer to Dean Berkeley but to write a treatise of fluxions which might ansuer the purpose and be useful to my scholars." (p. 250). In other words, a reply to Berkeley would not have been "useful to scholars."
Although Berkeley's critique was motivated by religious zealotry, the conflict between mathematics and religion is a figment of his imagination. "I am satisfied that the interests of true Science and true Religion are united, & that they do real prejudice to Mankind who endeavour to represent them as opposite in any measure." (p. 427) "I believe it will be easily granted by all who are acquainted with the History of Learning that there is no other order or Class of Learned Men that has produced fewer writers on the side of Infidelity, or fewer adversarys to natural or revealed Religion than that of the Mathematicians. The greatest Men among them have distinguished themselves as firm in the belief, and ornaments to the practice of Christianity, and particularly these men who invented or promoted the parts which this Author has so warmly attack'd." (p. 426)
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