Boole, George (DNB00)

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BOOLE, GEORGE (1815–1864), mathematician and logician, was born on 2 Nov. 1815, His father was a small tradesman in Lincoln, and besides his own direct help-which must have been of some value, for he was an ingenious man with a decided turn for mechanics and elementary mathematics -was only able to give his son such instruction as it national school in Lincoln, and subsequently a small commercial school, afforded. From the age of sixteen Boole was himself employed in teaching, first at a school in Lincoln and then at one in the neighbouring village of Waddington. He was only in his twentieth year when he opened a school on his own account. During these earlier years every moment of spare time was devoted to his private study, and he thus acquired an extensive knowledge not only of Greek and Latin, but also of the modern languages, such as French, German, and Italian. His devotion to mathematics was of somewhat later growth than is usual in cases of such remarkable subsequent eminence.

In the year 1849 he was appointed to the mathematical chair in the newly formed Queen's College at Cork, where the rest of his life was spent in the active prosecution of his professorial duties. He afterwards held the office of public examiner for degrees in the Queen's University, with great success. The principal recognitions of his eminence by other puhlic bodies during the next few years were the bestowal of a Royal Society medal in 1844, of the Keith medal by the Royal Society of Edinburgh in 1857, and the degrees of LL.D. and D.C.L. by the universities of Dublin and Oxford respectively. In 1855 he married Miss Everest, daughter of the Rev. T. R. Everest, a niece of the distinguished Indian surveyor, Colonel Everest, with whom he lived in perfect domestic happiness, and by whom he had a family of five daughters.

His constitution, which had never been very strong, was probably somewhat weakened by his strenuous studies. His death was rather sudden, the result of a feverish cold and congestion of the lungs following on exposure to the rain when going to the college. He died on 8 Dec. 1864. By the unanimous testimony of those who knew him he was a man of much sweetness and reverence of temper, of wide culture and sympathy, and of remarkable modesty.

His principal productions were in the province of pure mathematics. Besides two text-books, of very high merit and including much original research, on ‘Differential Equations’ and on ‘Finite Differences,' he published a number of papers in various mathematical and other journals. Of these the most remarkable are his ‘Researches on the Theory of Analytical Transformations,’ contributed to the ‘Cambridge Mathematical Journal’ in 184l, the ‘General Method in Analysis’ (1844), ‘The Comparison of Transcendents’ (1857); also several papers on ‘Differential Equations’ (1862, 1864). these being published in the ‘Philosophical Transactions of the Royal Society.' He also contributed several papers on ‘Probability’ to the ‘Philosophical Magazine’ and to the ‘Philosophical Transactions.’

It is, however, to his ‘Laws of Thought’ (1854), the leading principles of which had been published in the form of a pamphlet in 1847, under the title of ‘The Mathematical Analysis of Logic,’ that his most durable fame will attach. It is a work of astonishing originality and power, and one which has only recently come to be properly appreciated and to exercise its full influence on the course of logical speculation. Here Boole built almost entirely on his own foundations, for no previous attempts in this direction seem to have been known to him, nor indeed were there any in existence, with the exception of some remarkable but forgotten speculations of Lambert, and a few pregnant hints by Leibnitz and others. Boole’s work is not so much an attempt (as used to be commonly said) to ‘reduce logic to mathematics,’ as the employment of symbolic language and notation in a wide generalisation of purely logical processes. His fundamental process is really that of continued dichotomy, or subdivision, in respect of all the class terms which enter into the system of propositions in question. This process in itself is essentially the same as that which Jevons has so largely employed in his various logical treatises, but in Boole's system it is exhibited in a highly abstract and mathematical form, and called, Development. This process in its à priori form furnishes us with a complete set of possibilities, which, however, the conditions involved in the statement of the assigned propositions necessary reduce to a more limited number of actualities: Boole’s system being essentially one for displaying the solution of the prob em in the form of a complete enumeration of these actualities, As subsidiary to this, he has given a definite solution of the problem of logical elimination, viz. the statement of the relation of any one term to such a selection of the remaining terms as we may happen to seek. By these devices problems of a degree of complexity such as no previous logician had ever thought of approaching admit of solution. Theoretically indeed he has given a complete answer to the most general logical demand:-Given any number of propositions, involving any number of terms, find a full logical definition of any function of any of these terms, in respect of any selection of the remaining terms. These remarks apply to the first part of the ‘laws of Thought;’ the second part deals with the application of these logical principles to the theory of probability.

Later speculators have made a few modifications, some of these being of real importance, in Boole’s main theorems; but their principal work has been to introduce a number of practical simplifications into his methods, for his actual procedure was too cumbrous to be employed in any but comparatively simple examples. Amongst these writers may be mentioned: in England, Jevons, who was certainly the first to popularise the new conceptions of symbolic logic, and W. Maccoll; in America, C. H. Pierce, E. H. Mitchell, and Miss Ladd; and in Germany, H. Grassmann and Professor Schröder.

[Personal information from Mrs. Boole; obituary notice in Proc. of Royal Society]

J. V.