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  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.

 BOONE, JAMES SHERGOLD (1799–1859), miscellaneous writer, was born on 30 June 1799. In 1812 he was sent to Charterhouse, where he distinguished himself winning composition prizes in 1814 and 1816 (see Charterhouse, 1816). In 1816 he became a student of Christ Church, Oxford. In 1817 he obtained a Craven scholarship, won the chancellor's prize for Latin verse on ‘The Foundation of the Persian Empire,’ and the Newdigate for English verse (The Christ Church Newdigate Prize Poems, 1810-21 (1823), pp. 23-26). Whilst an undergraduate he wrote ‘The Oxford Spy in Verse,’ the first four ‘dialogues’ of which appeared in 1818, the fifth and last in 1819. This anonymous satire on Oxford University life created a great sensation at the time of its publication. In 1820 he received the chancellor's prize for the Latin essay, and contenting himself with an ordinary degree took his B.A. 24 May 1820. Soon after he left Oxford he was offered a seat in the House of Commons by an owner of a pocket borough who was struck with his great abilities. Boone declined this offer, and occupied his time in lecturing in London on the union and mutual relation of art and science. In June 1822 the first number of ‘The Council of Ten’ was published. Of this monthly periodical he was the editor and almost the sole contributor. Its life, however, was a short one, and it expired with its twelfth number. Boone took his degree of M.A. 4 March 1823, and about this time published ‘Men and Things in 1823: a Poem in three Epistles with Notes,’ in which he showed his great admiration for Canning. For some years he was a master at the Charterhouse; but having taken orders he accepted in June 1832 the appointment of incumbent of St. John's Church, Paddington. Here he remained until his death on 26 March 1859. A brass was erected to his memory in the