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BOOLE, GEORGE (1815-1864)
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See also:BOOLE, See also:GEORGE (1815-1864) , See also:English logician and mathematician, was See also:born in See also:Lincoln on the 2nd of See also:November 1815. His See also:father was a tradesman of limited means, but of studious See also:character and active mind. Being especially interested in mathematical See also:science, the father gave his son his first lessons; but the extraordinary mathematical See also:powers of George Boole did not See also:manifest themselves in See also:early See also:life. At first his favourite subject was See also:classics. Not until the See also:age of seventeen did he attack the higher See also:mathematics, and his progress was much retarded by the want of efficient help. When about sixteen years of age he became assistant-See also:master in a private school at See also:Doncaster, and he maintained himself to the end of his life in one grade or other of the scholastic profession. Few distinguished men, indeed, have had a less eventful life. Almost the only changes which can be called events are his successful See also:establishment of a school at Lincoln, its removal to See also:Waddington, his See also:appointment in 1849 as See also:professor of mathematics in the See also:Queen's See also:College at See also:Cork, and his See also:marriage in 1855 to See also:Miss See also:Mary See also:Everest, who, as Mrs Boole, afterwards wrote several useful educational See also:works on her See also:husband's principles. To the public Boole was known only as the author of numerous abstruse papers on mathematical topics, and of three or four distinct publications which have become See also:standard works. His earliest published See also:paper was one upon the "Theory of See also:Analytical Transformations," printed in the See also:Cambridge Mathematical See also:Journal for 1839, and it led to a friendship between Boole and D. F. See also:Gregory, the editor of the journal, which lasted until the premature See also:death of the latter in 1844. A See also:long See also:list of Boole's See also:memoirs and detached papers, both on logical and mathematical topics, will be found in the See also:Catalogue of Scientific Memoirs published by the Royal Society, and in the supplementary See also:volume on See also:Differential Equations, edited by See also:Isaac See also:Todhunter. To the Cambridge Mathematical Journal and its successor, the Cambridge and See also:Dublin Mathematical Journal, Boole contributed in all twenty-two articles. In the third and See also:fourth See also:series of the Philosophical See also:Magazine will be found sixteen papers. The Royal Society printed six important memoirs in the Philosophical Transactions, and a few other memoirs are to be found in the Transactions of the Royal Society of See also:Edinburgh and of the Royal Irish See also:Academy, in the Bulletin de l'Academie de St-Petersbourg for 1862 (under the name G. Boldt, vol. iv. pp. 198-215), and in Crelle's Journal. To these lists should be added a paper on the mathematical basis of See also:logic, published in the Mechanic's Magazine for 1848. The works of Boole are thus contained in about fifty scattered articles and a few See also:separate publications. Only two systematic See also:treatises on mathematical subjects were completed by Boole during his lifetime. The well-known235 See also:Treatise on Differential Equations appeared in 1859, and was followed, the next See also:year, by a Treatise on the Calculus of Finite See also:Differences, designed to serve as a sequel to the former See also:work. These treatises are valuable contributions to the important branches of mathematics in question, and Boole, in composing them, seems to have combined elementary exposition with 'the profound investigation of the See also:philosophy of the subject in a manner hardly admitting of improvement. To a certain extent these works embody the more important discoveries of their author. In the 16th and 17th chapters of the Differential Equations we find, for instance, a lucid See also:account of the See also:general symbolic method, the bold and skilful employment of which led to Boole's See also:chief discoveries, and of a general method in See also:analysis, originally described in his famous memoir printed in the Philosophical Transactions for 1844. Boole was one of the most eminent of those who perceived that the symbols of operation could be separated from those of quantity and treated as distinct See also:objects of calculation. His See also:principal characteristic was perfect confidencein any result obtained by the treatment of symbols in accordance with their See also:primary See also:laws and conditions, and an almost unrivalled skill and See also:power in tracing out these results.
During the last few years of his life Boole was constantly engaged in extending his researches with the See also:object of producing a second edition of his Differential Equations much more See also:complete than the first edition; and See also:part of his last vacation was spent in the See also:libraries of the Royal Society and the See also:British Museum. But this new edition was never completed. Even the See also:manuscripts See also:left at his death were so incomplete that Todhunter, into whose.hands they were put, found it impossible to use them in the publication of a second edition of the See also:original treatise, and wisely printed them, in 1865, in a supplementary volume.
With the exception of See also:Augustus de See also:Morgan, Boole was probably the first English mathematician since the See also:time of See also: By unity Boole denoted the universe of thinkable objects; literal symbols, such as x, y, z, v, u, &c., were used with the elective meaning attaching to See also:common adjectives and substantives. Thus, if x=horned and y=See also:sheep, then the successive acts of See also:election represented by x and y, if performed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this See also:kind obey the same primary laws of See also:combination as algebraical symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as See also:numbers. Thus, 1—x would represent the operation of selecting all things in the See also:world except horned things, that is, all not horned things, and (1—x) (1—y) would give us all things neither horned nor sheep. By the use of such symbols propositions could be reduced to the See also:form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the See also:middle See also:term according to See also:ordinary algebraic rules. Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, which formed e a general symbolic method of logical inference. Given any propositions involving any number of terms, Boole showed how, by the purely symbolic treatment of the premises, to draw any conclusion logically contained in those premises. The second pact of the Laws of Thought contained a corresponding See also:attempt to discover a general method in probabilities, which should enable us from the given probabilities of any system of events to determine the consequent See also:probability of any other event logically connected with the given events. Though Boole published little except his mathematical and logical works, his acquaintance with general literature -was wide and deep. See also:Dante was his favourite poet, and he preferred the Paradiso to the Inferno. The See also:metaphysics of See also:Aristotle, the See also:ethics of See also:Spinoza, the philosophical works of See also:Cicero, and many kindred works, were also frequent subjects of study. His reflections upon scientific, philosophical and religious questions are contained in four addresses upon The See also:Genius of See also:Sir Isaac See also:Newton, The Right Use of Leisure, The Claims of Science and The Social Aspect of Intellectual Culture, which he delivered and printed at different times. The See also:personal character of Boole inspired all his See also:friends with the deepest esteem. He was marked by the modesty of true genius, and his life was given to the single-minded pursuit of truth. Though he received a See also:medal from the Royal Society for his memoir of 1844, and the honorary degree of LL.D. from the university of Dublin, he neither sought nor received the ordinary rewards to which his discoveries would entitle him. On the 8th of See also:December 1864, in the full vigour of his intellectual powers, he died of an attack of See also:fever, ending in suffusion on the lungs. An excellent See also:sketch of his life and works, by the Rev. R. Harley, F.R.S., is to be found in the British Quarterly See also:Review for See also:July 1866, No. 87. (W. S. Additional information and CommentsThere are no comments yet for this article.
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