published iu 1854, should alone be considered as containing a mature statement of his views. Nevertheless, there is a charm of originality about his earlier logical work which no competent reader can fail to appreciate, and the intro duction gives striking evidence of his profound views and
wide reading.It is not easy to give in a few words a correct notion of Boole s logical system, and only those who are conversant with the principles of symbolical reasoning can exactly apprehend his position. He did not regard logic as a branch of mathematics, as the title of his earlier pamphlet might be taken to imply, but he pointed out such a deep analogy between the symbols of algebra and those which can be made, in his opinion, to represent logical forms and syllogisms, that we can hardly help saying that logic is mathematics restricted to the two quantities, and 1. 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 common adjectives and sub stantives. Thus, if x ? horned, and y ? sheep, then the successive acts of election represented by x and y, if per formed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraical symbols, whence it followed that they could be added, subtracted, multiplied, and even divided, almost exactly in the same manner as numbers. Thus, 1 - x would represent the operation of selecting all things in the 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 form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules.
Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, which formed a general symbolic method of logical infer ence. Given any propositions involving any number of terms, Boole showed how, by the purely symbolic treat ment of the premises, to draw any conclusion logically contained in those premises. The second part of the Laws of Thought contained a corresponding 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 probability of any other event logically connected with the given events. Soon after its publication this method was the subject of a con troversy in the Philosophical Magazine ; but it cannot be said that the exact value of this part of his works has ever been clearly ascertained.
It is often supposed that mathematicians are deficient in judgment and knowledge of other matters. In Boole this was not the case ; for though he published little except the mathematical and logical works already mentioned, his acquaintance with general literature was wide and deep. Dante was his favourite poet, and he preferred the Paradiso to the Inferno. The metaphysics of Aristotle, the ethics of Spinoza, the philosophical works of Cicero, and many less celebrated works of a kindred character, were also frequent subjects of study. His reflections upon scientific, philosophical, and religious questions are to be mainly gathered from four addresses upon The Genius of Sir Isaac 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 personal character of Bo-jle inspired all his 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 royal medal for his memoir of 1844, and the honorary degree of LL.D. from the University of Dublin, it may be said that he neither sought nor received the ordinary rewards to which his discoveries would entitle him.
On the 8th of December 18G4, in the full vigour of his intellectual powers, Boole died of an attack of fever, ending in suffusion on the lungs An excellent sketch of his life and works, by the Ilev. II. Harley, F.R.S., to which the present writer is indebted for many particulars, is to be found in the British Quarterly Revieiv for July 18G6, No. 87.
BOOM, a town of Belgium, in the province of Antwerp, and 12 miles S. of that city, at the junction of the Brussels Canal with the 1 liver Bupel. It is an active industrial town, possessing tanneries, salt-works, starch-factories, breweries, and brick and tile works, and carries on a con siderable trade. Population of the commune, 10,064.
BOOMERANG, a missile instrument of the Australian aborigines, in the use of which they are very dexterous. It consists of a piece of hard wood, with the curve of a parabola, and is about 2 feet long, 2? inches broad, -g- inch thick, and rounded at the extremities. One side is flat, the other is rounded, and it is brought to a bluntish edge. It is discharged with the hand by one end, the convex edge being forward and the flat side upwards. After advancing some distance, and ascending slowly in the air with a quick rotatory motion, it begins to retrograde, and finally falls to the ground behind the thrower. A weapon of similar form, but wanting the return flight, has been found in use among savage tribes both in India and Africa. A very full comparative account of the boomerang is contained in Colonel A. H. Lane Fox s lecture on " Primitive Warfare" (Jour, of the Royal United Service Institution, vol. xii. No. 51).
an ancient family in Lancashire, was born in 1681. He was educated at Westminster school under the celebrated I)r Busby, and his success in the Latin plays, customarily per formed there by the scholars, gave him an inclination for the stage. He was intended for the church ; but at seventeen years of age he ran away from school, and after some vicissitudes obtained employment in a theatrical company in Dublin. His first appearance was hailed with applause ; and he continued to improve daily. After two successful campaigns in Ireland he returned to his native country, having first reconciled himself to his friends. Betterton, to whom he had an introduction, received him with great cordiality, and gave him all the assistance in his power. His success at London was complete, and he established his reputation as only second to his great instructor. He was indebted to a happy coincidence of merit and chance for the celebrity which he at length attained in the character of Cato. The Whigs, in favour of whoso principles Addison s tragedy had been written, thought it their duty tu support it strongly ; while the Tories, at every passage susceptible of a popular turn, were no less vehement in their approbation, and at the close the actor was presented by Lord Bolingbroke with a purse of fifty guineas, "as a slight acknowledgment of his honest opposition to a perpetual dictator, and his dying so bravely in the causa of duty." Booth was twice married, first to a daughter of Sir William Barkham, Bart., and afterwards to Miss Hester Santlow, an actress of great merit. During the twenty years of his management the theatre was in the greatest credit ; and his death, which happened on the 10th of May 1733, contributed not a little to its decline. Booth was a man of excellent character, and greatly
esteemed for his amiability and goodness of heart.