Sir Isaac Newton's Rivals

  • #1

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Other than Robert Hooke, Gottfried Wilhelm Leibniz and John Flamsteed, did the great astronomer, mathematician, physicist, philosopher and theologician, Isaac Newton have any rivals. He is "eminent" for having a great number of opponents, presumably due to his all-round polymathic intellectual capacities.
 

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  • #2
Stephen Tashi
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An opponent: William Chaloner
 
  • #3
William Chaloner is indeed quite an intriguing case.
 
  • #4
epenguin
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A critic, though after his time, of both his dynamics and calculus, or at least the common understanding of them, Bishop Berkeley.
 
  • #5
WWGD
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And I understand he was not the most gracious person and not easy to deal with often. That may have worsened problems originating from existing differences in personality.
 
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A critic, though after his time, of both his dynamics and calculus, or at least the common understanding of them, Bishop Berkeley.
Maybe it was all in Berkeley's mind? :).
 
  • #7
Berkeley, an Irish philosopher, argued against Newton's doctrine which was based upon absolute space, time and motion. This Irish philosopher additionally ridiculed those who believed Newton was a genius and derided his religious faith. Berkeley's criticism stemmed from his belief that calculus was no more logically rigorous than religion. Certainly a very intriguing case, just as all the others have been.
 
  • #8
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Berkeley, an Irish philosopher, argued against Newton's doctrine which was based upon absolute space, time and motion. This Irish philosopher additionally ridiculed those who believed Newton was a genius and derided his religious faith. Berkeley's criticism stemmed from his belief that calculus was no more logically rigorous than religion. Certainly a very intriguing case, just as all the others have been.
Still, ultimately Mathematics and Berkeley's claims that limits were "Ghosts of departed quantities" was put to rest by Cauchy's clearer, more formal/rigorous definitions. Similar for Abraham Robinson's layout of infinitesimals. Unlike with most of religion, if I may --I did not set out to start a fire here.
 
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epenguin
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Berkeley, an Irish philosopher, argued against Newton's doctrine which was based upon absolute space, time and motion. This Irish philosopher additionally ridiculed those who believed Newton was a genius and derided his religious faith. Berkeley's criticism stemmed from his belief that calculus was no more logically rigorous than religion. Certainly a very intriguing case, just as all the others have been.
Still, ultimately Mathematics and Berkeley's claims that limits were "Ghosts of departed quantities" was put to rest by Cauchy's clearer, more formal/rigorous definitions. Similar for Abraham Robinson's layout of infinitesimals. Unlike with most of religion, if I may --I did not set out to start a fire here.

My Bible math textbook by Massey and Kestleman, which I think most people would call 'down-to-earth' allows itself in its almost 1000 pages this amount of philosophy:

When Newton and Leibniz developed the calculus in the 17th century they did so without the rigourous theory of limits which we use today and which is due to the 19th century mathematician Cauchy. Lacking the language and subtle vocabulary of a sound theory of limits, much of the early theory of calculus had a nebulous character which contrasted strongly with the absolute precision claimed for its results. It is hardly possible to doubt that Newton and Leibniz had a direct and intuitive understanding of limits, and that their confidence in the methods of the calculus did not rest, as it may have done for others, on the indisputable results which of these methods produced. The literal reading of their arguments and of their apparently careless use of vanishingly small quantities could reasonably lead a critical mind to the conclusion that only a series of compensating errors, one absurdity cancelling another, could produce science, or even fact, out of such obscurity. It is instructive, even today, to study the penetrating objections to the calculus advanced by the philosopher Berkeley in his essays The Analyst and A Defence of Freethinking in Mathematics (1784). His distinction between the validity of a rule and a proof, and his criticism of symbols which start by economising thought an end by inhibiting it, have lost none of their significance. If scientists today continue to practice the errors condemned by Berkeley it is because on most occasions they are content with the rules not proofs. They believe that mathematicians have proved the consistency of the rules, and they suspect the complete accuracy of formulation can be achieved only by cumbersome symbols which obstruct the flow of direct ideas. The theory of differentials, which we now propose to discuss, attempts to state propositions of the calculus in a language which is capable of sustaining completely rigourous arguments without obscuring the essentially simple and direct ideas which underlie them.

Hmm. I did find in the biog. of Newton (Never at Rest, RS Westfall) find this passage which seems to me close to present day doctrine
Quantities, and the the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach nearer to each other then by any given difference, become ultimately equal.

And then, did not Newton recast his theory in entirely classical geometrical form, believing only this constituted proper and rigorous proof?

And although you and my textbook authors commend this Cauchy approach, is it not true that there are still others still unconvinced and who seek other approaches?

Would this by any chance, have any relation with the fact that about the most frequent difficulties about which we are asked in the homework section concerned exactly these limit questions? Maybe we do not have the most final and perfect formulation?
 
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  • #10
StatGuy2000
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Other than Robert Hooke, Gottfried Wilhelm Leibniz and John Flamsteed, did the great astronomer, mathematician, physicist, philosopher and theologician, Isaac Newton have any rivals. He is "eminent" for having a great number of opponents, presumably due to his all-round polymathic intellectual capacities.
My understanding was that opposition to Isaac Newton was based as much on his difficult personality as his all-round polymathic intellectual capacities and his various accomplishments, of which a considerable were quite controversial at the time (I'm specifically thinking of his formulation of the calculus as an example).
 
  • #11
WWGD
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My understanding that opposition to Isaac Newton was based as much on his difficult personality as his all-round polymathic intellectual capacities and his various accomplishments, of which a considerable were quite controversial at the time (I'm specifically thinking of his formulation of the calculus as an example).
And his ideas were , understandably, not fully fleshed out. 'Fluxions' and his treatment of infinitesimals were hard to understand.
 

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