George Boole's father, John Boole (1779-1848), was a tradesman of limited means, but of studious character and active mind. Being especially interested in
mathematical science and
logic, the father gave his son his first lessons; but the extraordinary mathematical talents of George Boole did not manifest themselves in early life. At first his favourite subject was classics. Not until the age of 17 did he attack the higher mathematics, and his progress was slowed by a lack of efficient help. When he was about sixteen years of age he became assistant-master in a private school at
Doncaster, Yorkshire in the
United Kingdom, and he maintained himself to the end of his life in one grade or other of the scholastic profession. He was a teacher in Mr William Marrats school in Liverpool in 1833. Few distinguished men, indeed, have had a less eventful life. Almost the only changes which can be called events are his successful establishment of a school at
Lincoln, its removal to
Waddington, his appointment in 1849 as the first professor of mathematics of then Queen's College, Cork (now
University College Cork, where the library and underground lecture complex are named in his honour) in
Ireland, and his marriage in 1855 to Miss Mary Everest (niece of
George Everest), who, as Mrs. Boole, afterwards wrote several useful educational works on her 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 standard works. His earliest published paper was one upon the "Theory of Analytical Transformations," printed in the
Cambridge Mathematical Journal for 1839, and it led to a friendship between Boole and
D.F. Gregory, the editor of the journal, which lasted until the premature death of the latter in 1844. A long list of Boole's memoirs and detached papers, both on logical and mathematical topics, will be found in the
Catalogue of Scientific Memoirs published by the
Royal Society, and in the supplementary volume on
Differential Equations, edited by
Isaac Todhunter. To the
Cambridge Mathematical Journal and its successor, the
Cambridge and Dublin Mathematical Journal, Boole contributed in all twenty-two articles. In the third and fourth series of the
Philosophical 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 Edinburgh and of the Royal Irish Academy, in the
Bulletin de l'Académie de St-Pétersbourg 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 logic, published in the
Mechanic's Magazine for 1848. The works of Boole are thus contained in about fifty scattered articles and a few separate publications.
Only two systematic
treatises on mathematical subjects were completed by Boole during his lifetime. The well-known
Treatise on Differential Equations appeared in 1859, and was followed, the next year, by a
Treatise on the Calculus of Finite Differences, designed to serve as a sequel to the former 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 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 sixteenth and seventeenth chapters of the
Differential Equations we find, for instance, a lucid account of the general symbolic method, the bold and skilful employment of which led to Boole's chief discoveries, and of a general method in 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 objects of calculation. His principal characteristic was perfect confidence in any result obtained by the treatment of symbols in accordance with their primary laws and conditions, and an almost unrivalled skill and power in tracing out these results.
During the last few years of his life Boole was constantly engaged in extending his researches with the object of producing a second edition of his
Differential Equations much more complete than the first edition; and part of his last vacation was spent in the libraries of the Royal Society and the
British Museum. But this new edition was never completed. Even the manuscripts 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 original treatise, and wisely printed them, in 1865, in a supplementary volume.
With the exception of
Augustus de Morgan, Boole was probably the first English mathematician since the time of
John Wallis who had also written upon
logic. His novel views of logical method were due to the same profound confidence in symbolic reasoning to which he had successfully trusted in mathematical investigation. Speculations concerning a
calculus of
reasoning had at different times occupied Boole's thoughts, but it was not till the spring of 1847 that he put his ideas into the pamphlet called
Mathematical Analysis of Logic. Boole afterwards regarded this as a hasty and imperfect exposition of his logical system, and he desired that his much larger work,
An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities (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 is easy to appreciate.
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 (especially his) formal logic is mathematics restricted to the two quantities, 0 and 1. By unity Boole denoted the universe of thinkable objects;
literal symbols, such as x, y, z, v, u, etc., were used with the elective meaning attaching to common adjectives and substantives. Thus, if x=horned and y=sheep, then the successive acts of 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 kind obey the same primary laws of
combination as algebraic 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, formed 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 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.
Though Boole published little except his mathematical and logical works, 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 kindred works, were also frequent subjects of study. His reflections upon scientific, philosophical and religious questions are contained in 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 Boole inspired all his friends with the deepest esteem. He was marked by true modesty, and his life was given to the single-minded pursuit of
truth. Though he received a 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
8 December 1864, in the full vigour of his intellectual powers, he died of an attack of fever, ending in
effusion on the
lungs, caused by giving a lecture in wet clothes from the rain.
The Booles had five daughters:
* Mary, who married the mathematician and author
Charles Howard Hinton and had three children (Howard, William and Joan)
* Margaret, whose son
Geoffrey Ingram Taylor became a mathematician and a Fellow of the
Royal Society
*
Alicia, who made important contributions to four-dimensional geometry
* Lucy, a chemist
*
Ethel Lilian, who married the Polish scientist and revolutionary
Wilfrid Michael Voynich and is the author of the novel
The Gadfly.
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