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Stewart writes :
Berkeley was working on these mathematics texts, whose full title is Arithmetica absque Algebra aut Euclide demonstrata (Arithmetic demonstrated without algebra or Euclid), waiting for the chance to compete for a fellowship. In 1706 a College Fellowship became available and, after taking some extremely demanding competitive examinations, he became a Junior Fellow of Trinity College, Dublin on 9 June 1707. Later in that year, on 19 November, he read his article Of infinites to the Dublin Philosophical Society, but this mathematical and philosophical work was only published after his death. This work, as the previous mathematical ones, clearly shows that Berkeley was much influenced by Locke. As well as carrying out some light tutoring duties, he studied divinity and was ordained deacon in February 1709 and ordained a priest in the following year. During this time he published two important works, An Essay towards a New Theory of Vision in 1709 and A Treatise concerning the Principles of Human Knowledge in 1710. The purpose of the first, as stated by Berkeley, is:
In the second work he examines abstract ideas. He states in the introduction the notions he discusses in depth:
Berkeley sent A Treatise concerning the Principles of Human Knowledge to Samuel Clarke and William Whiston .
He returned to England in August 1714 and towards the end of the year he had a fever which Arbuthnot described with a joke aimed at Berkeley's philosophy:
Berkeley returned to Italy in 1716 with George Ashe, son of the Trinity College provost, and he spent four years there. He gives a vivid description of the eruption of Vesuvius in 1717:
On the journey back to England Berkeley spent some time in Lyon where he wrote the essay De motu (On motion) which he submitted for the Grand Prix of the Academy of Sciences . He was not successful. He reached London early in 1721 and by the start of the 1721-22 academic year he was in Dublin where he was now a Senior Fellow (a position to which he had been appointed in 1717 while in Italy). He took on additional duties such as :
In May 1724 Berkeley resigned his position at Trinity College to become Anglican Dean of Londonderry, but he never resided in the city spending most of the next four years in London. Over these years he planned to establish a College in Bermuda to train the sons of colonists and Native Americans whom he wished to convert to:
Funds of 10000 pounds for Berkeley's project were promised after the House of Commons in London voted:
On 1 August 1728 he married Anne Foster, and soon after they set sail for America. They reached Newport, Rhode Island, and bought a farm. Their first two children Henry and George were born while the family lived near Newport, Rhode Island. There he waited for the 10000 pound grant to be paid which would enable him to build the planned College. However, by the middle of 1731 it became obvious that he would not receive the grant, and he returned to London in October. He wrote a number of articles during his time in America which he published in the two or three years after his return. In January 1734 Berkeley was appointed Bishop of Cloyne and was consecrated in St Paul's Church, Dublin, on 19 May 1734. In this office he devoted himself to the social and economic plight of Ireland, doing his best as an Anglican bishop to help the conditions of all in the predominantly Roman Catholic country. In 1745, at the time of the Jacobite rebellion, Berkeley addressed Roman Catholics in his diocese, and in 1749 he addressed to the Roman Catholic Clergy A Word to the Wise. He received a reply in the Dublin Journal of 18 November 1749 in which the Catholic Clergy expressed:
He was devoted to Cloyne and he always purchased his clothes locally even though this meant that they were not of top quality, but he wanted to support employment. He set up a school to teach spinning to children, and he wanted to make possible the manufacture of linen. He wrote:
Berkeley is best known in the world of mathematics for his attack on the logical foundation of the calculus as developed by Newton . In his tract The analyst: or a discourse addressed to an infidel mathematician, published in 1734, he tried to argue that although the calculus led to true results its foundations were no more secure than those of religion. He declared that the calculus involved a logical fallacy of a shift in the hypothesis. He described derivatives as follows:
Berkeley's criticisms were well founded and important in that they focused the attention of mathematicians on a logical clarification of the calculus. He developed an ingenious theory to explain the correct results obtained, claiming that it was the result of two compensating errors. Ren writes in :
Many of the other references which we give also discuss Berkeley's attack on the calculus; see , , , , , , and . De Moivre , Taylor , Maclaurin , Lagrange , Jacob Bernoulli and Johann Bernoulli all made attempts to bring the rigorous arguments of the Greeks into the calculus. Maclaurin in Treatise on fluxions gave the best response to Berkeley. By the late 1740s Berkeley's health was deteriorating. His youngest son William died in 1751 which added to his decline. Despite this he travelled with his wife to Oxford in July 1752 to see his second son George begin his studies at Christ Church. In fact his intention was to remain at Oxford for the rest of his life, which he anticipated would not be very long. He died of a heart attack on the evening of Sunday 14 January 1753, sitting with his family listening to his wife reading. He died so peacefully that it is said that the event went unnoticed, the family thinking he had fallen asleep. He left instructions that he was not to be buried for at least five days and he was buried at Christ Church, Oxford on 20 January. Source:School of Mathematics and Statistics University of St Andrews, Scotland |