Born in the same year as the great composers Johann Sebastian Bach, Georg Frideric Handel, and Domenico Scarlatti, Berkeley was one of the seminal figures in Western philosophy, his doctrines exerting a particularly significant influence on analytic philosophy. As a mathematician, George Berkeley is known for his thought-provoking critique of the mathematical theories of his time, particularly infinitesimalcalculus.
Of English descent, Berkeley was born near Kilkenny, Ireland, and always considered himself an Irishman. Educated at Trinity College, Dublin, he studied mathematical logic, and philosophy. Berkeley graduated in 1704, publishing a short Latin work on mathematics in 1707. In 1710, the year he published his famous work A Treatise Concerning the Principles of Human Knowledge, he was ordained priest of the Church of England. After holding several academic appointments, he was named dean of Derry in 1724. Owing to his keen interest in education, Berkeley soon left for London, hoping to receive government funding for a college in Bermuda, where he intended to provide education for English and local youths. In 1728 he married Anne Forster, the well-educated daughter of a chief justice. Soon after the wedding, Berkeley and his new wife set sail, getting as far as Newport, Rhode Island, which he then decided was a better location for his school. However, the project was abandoned when promised funding failed to materialize, and the Berkeleys returned to London in 1731.
Berkeley was appointed bishop of Cloyne in 1734, and his home there became a social and cultural center, as well as a dispensary in times of epidemics. The Berkeleys eventually had six children, four sons (one became canon of Canterbury) and two daughters. They retired to Oxford in 1752, and after Berkeley's death in 1753, Anne Berkeley continued to defend her husband's philosophy. An indefatigable writer, polemicist, and researcher, Berkeley was also a clergyman, who took his pastoral duties very seriously, ministering to the needs of people far removed from the world of 18th-century philosophy and science.
Berkeley denied the existence of matter. The essence of his philosophy is expressed by the statement esse est percipi (to exist is to be perceived), which means that an object can be said to exist only insofar as it is perceived by a spirit--finite (a human being) or infinite (God). Certainly, Berkeley, being a very practical person, did not claim that the world of physical objects should be treated as an illusion, as some of his detractors naively assumed. In essence, Berkeley asserted that the postulate suggesting that matter existed independently of a percipient observer was based on illogical and unclear thinking. However, Berkeley does not deny the validity of general terms. As Copleston has written in his discussion of Berkeley's philosophy, "A proper name such as William, signifies a particular thing, while a general word signifies indifferently a plurality of things of a certain kind. Its universality is a matter of use or function. If we once understand this, we shall be saved from hunting for mysterious entities corresponding to general words. We can utter the term 'material substance', but it does not denote any abstract general idea; and if we suppose that because we can frame the term it must signify an entity apart from the objects of perception, we are misled by words. . . . 'Matter' is not a name in the way in which William is a name, though some philosophers seem to have thought mistakenly that it is."
Berkeley accepted mathematics as a practical science and pursuit, but adamantly rejected, in accordance with his criticism of meaningless concepts, the idea of number. As J. O. Urmson explains, to Berkeley, the term ten may denote the fact that there are ten individual entities in a group, but nothing more than that, and certainly not an abstract idea of ten, independent of any practical context. It is also important to note that Berkeley supplemented his purely philosophical critique of infinitesimal calculus with solid mathematical arguments. What Berkeley strenuously objected to was the practice, accepted by his contemporaries, of assuming that the quantity dx, being infinitesimally small, could simply be eliminated in mathematical derivations. Thus, though Berkeley's criticism may be irrelevant to modern applications of infinitesimals, he was nevertheless right in questioning the practice of treating an infinitesimal quantity as zero.
In the history of mathematics, Berkeley is best known for attacking the logical foundations of Isaac Newton's calculus."Newton's theory," according to Tobias Dantzig, "dealt with continuous magnitudes and yet postulated the infinite divisibility of space and time; it spoke of a flow and yet dealt with this flow as if it were a succession of minute jumps." This theory of fluxions (Newton's term denoting the rate of change of a variable, such as length, speed, area, etc.) was open to criticism because it attempted to reconcile a smooth flow with a series of leaps. In The Analyst Berkeley asked: "And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, or quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities"" Although Berkeley felt that Newton's calculus yielded true results (even developing a clever explanation for these correct results), he nonetheless felt compelled to point out the logical fallacy on which he believed the calculus was based. In this way, he inspired other mathematicians to focus their attention on a logical clarification of calculus.
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