The `Analyst' Controversy: Index of Papers
A number of pamphlets and other writings relevant to the Analyst
controversy are available here, and are listed below under the
following headings:
The following texts by Isaac Newton, from the
Principia and elsewhere, are particularly
relevant to the Analyst controversy:
In 1734, George Berkeley, Bishop of Cloyne, in Ireland,
published The Analyst; or a Discourse Addressed to an
Infidel Mathematician. Wherein it is examined whether the Object,
Principles and Inferences of the modern Analysis are more
distinctly conceived, or more evidently deduced, than
Religious Mysteries and Points of Faith.
As is apparent from the title, Berkeley was motivated by more
than simply a concern for the soundness of the mathematical
methods then in vogue. Nevertheless he developed his argument by
criticising certain passages to be found in the
Philosophiae Naturalis Principia Mathematica and
the Introductio ad Quadraturum Curvarum of
Isaac Newton, and in the Analyse des infiniment petits pour
l'intelligence des lignes courbes of the Marquis de
l'Hôpital. Berkeley subsequently published a number of
other works arising out of the controversy generated by the
Analyst, replying to responses by `Philalethes Cantabrigiensis'
[James Jurin] and Jacob Walton.
The following texts are available here:
Berkeley's parting shot took the form of a
footnote in Siris
The first to respond to Berkeley's Analyst was
James Jurin, who wrote under the pseudonym of `Philalethes
Cantabrigiensis'. Jurin had for a time been Secretary of
the Royal Society, and was a noted physician in London.
The following responses to Berkeley are available here:
The differing approaches taken by James Jurin and Benjamin Robins in
their respective defences of the methods of Isaac Newton subsequently
gave rise to a
controversy between Robins and Jurin,
conducted in the pages of The Present State of the Republick of
Letters.
Another who responded to Berkeley's Analyst was the
Dublin-based mathematician Jacob Walton. Very little is known
about Walton; some information about him is however to be found
in the following article:
Wallis, Ruth, `Who was J. Walton, adversary of Bishop Berkeley?',
Annals of science 51 (1994), 539-540.
The following responses to Berkeley are available here:
Benjamin Robins wrote what is perhaps the most thorough and
well-written response to Berkeley, with the exception of
Colin Maclaurin's two-volume Treatise of Fluxions.
Works of Robins are available here include the following:
Benjamin Robins and James Jurin differed considerably in
their interpretation of certain passages in the works of Sir
Isaac Newton. These differences were discussed in the pages of
The Present State of the Republick of Letters in the
years 1735 and 1736. (The dispute was continued between James
Jurin and Henry Pemberton, in December 1836 and in 1837.)
The following contributions to this controversy are available
here:
- Benjamin Robins,
Account of `A discourse concerning the nature and
certainty of Sir Isaac Newton's methods of fluxions, and of prime
and ultimate ratios'.
(The present state of the Republick of Letters, October 1735,
pp. 245-270.)
- James Jurin,
Considerations upon some passages contained in two letters
to the Author of the Analyst, written in defence of Sir Isaac
Newton, and the British Mathematicians.
(The present state of the Republick of Letters, November 1735,
pp. 369-396.)
- Benjamin Robins,
A review of some of the principal objections that have been
made to the doctrines of fluxions and ultimate proportions; with
some remarks on the different methods that have been taken to
obviate them.
(The present state of the Republick of Letters, December 1735,
pp. 436-447.)
- James Jurin,
Considerations occasioned by a paper in the last Republick
of Letters, concerning some late objections against the doctrine
of fluxions, and the different methods that have been taken to
obviate them.
(The present state of the Republick of Letters, January 1736,
pp. 72-91.)
- Benjamin Robins,
A dissertation shewing, that the account of the doctrines
of fluxions, and of prime and ultimate ratios, delivered in a
treates entitled, A discourse concerning the nature and certainty
of Sir Isaac Newton's methods of fluxions, and of prime and
ultimate ratios, is agreeable to the real sense and meaning of
their great inventor.
(The present state of the Republick of Letters, April 1736,
pp. 290-335.)
- James Jurin,
Considerations upon some passages of a Dissertation
concerning the doctrine of fluxions, published by Mr. Robins in
the Republick of Letters for April last.
(The present state of the Republick of Letters, July 1736,
pp. 45-82.)
- Benjamin Robins,
Remarks on the considerations relating to fluxions, &c.
that were published by Philalethes Cantabrigiensis in the
Republick of Letters for the last month.
(The present state of the Republick of Letters, August 1736,
pp. 87-110.)
- James Jurin,
The remainder of the paper begun in our last, entituled,
Considerations upon some passages of a Dissertation concerning
the doctrine of fluxions, published by Mr. Robins in the
Republick of Letters for April last.
(The present state of the Republick of Letters, August 1736,
pp. 111-179)
- Benjamin Robins,
Remarks on the remainder of the considerations relating to
fluxions, &c. that was published by Philalethes
Cantabrigiensis in the Republick of Letters for the last Month.
To which is added by Dr. Pemberton a postscript occasioned by a
passage in the said considerations.
(The present state of the Republick of Letters, September 1736,
Appendix, pp. 2-40.)
- James Jurin,
Observations upon some remarks relating to the method of
fluxions, published in the Republick of Letters for August last,
and in the appendix to that for September.
(The present state of the Republick of Letters, November 1736,
pp. 2-79)
- Benjamin Robins,
Advertisement.
(The present state of the Republick of Letters, December 1736,
Appendix, pp. 491-492.)