Popular Science Monthly/Volume 17/October 1880/Sketch of George Boole

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Popular Science Monthly Volume 17 October 1880  (1880) 
Sketch of George Boole
PSM V17 D740 George Boole.jpg


"AND pray who is George Boole, that he should be pictured and sketched in 'The Popular Science Monthly'? We thought this department was to be devoted to scientific celebrities, chiefly contemporaneous; but who is this Boole?"

Such will probably be the exclamation of nine of our readers out of ten; but the tenth, or more safely the hundredth, reader will know that George Boole was a man of a very high order of genius, a profound and most original thinker of this century, who will be known in future by his contributions to mathematical and logical science. Yet he can never be widely known, for his work was so recondite that those who can properly appreciate it will always be but very few. We gather the following particulars of his life from the last edition of the "Encyclopædia Britannica":

George Boole was born in Lincoln, on the 2d of November, 1815. His father was a tradesman of limited means, but of studious character and active mind. Being especially interested in mathematical science, the father gave his son early instruction in the rudiments of the science he was so greatly to advance; but it is remarkable that the extraordinary mathematical powers of George Boole did not manifest themselves in early life, as was the case with Zerah Colburn, Babbage, Pascal, Leibnitz, and Saunderson. The classical languages formed at first the favorite subject of his studies. It was not until he had attained his seventeenth year that he attacked the higher mathematics, and his progress was much retarded by the want of efficient help.

When about sixteen years of age he became assistant master in a private school in 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 career. 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 Professor of Mathematics in Queen's College, Cork; and his marriage, in 1855, to Miss Mary Everest.

His works are comprised in about fifty scattered articles and a few separate and individual publications. Only two systematic treatises on mathematical subjects were completed by Boole. These were a "Treatise on Differential Equations," which appeared in 1859, and was followed, next year, by a "Treatise on the Calculus of Finite Differences," designed to serve as a sequel to its predecessor. In the sixteenth and seventeenth chapters of the former work he lays down a lucid exposition of the symbolic method, the bold and skillful employment of which led to his chief discoveries.

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 unrivaled 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 arduous study in the libraries of the Royal Society and the British Museum, for the purpose of acquiring a complete knowledge of the less accessible original memoirs on the subject. It must be always a matter of regret that this new edition was never completed. Even the manuscripts left at his death were so incomplete that Mr. Todhunter, into whose hands they were put, as literary executor, found it impossible to use them in the publication of a second edition of the original treatise, and printed them, as a supplementary volume, in 1865.

Profound and important as were Boole's discoveries in pure mathematics, his writings on logic may be considered as still more original. With the exception of De Morgan, he was probably the first English mathematician since the time of Wallis (1616-1703) who had also written upon logic; and his wholly novel views of logical method were due to the same profound confidence in symbolic reasoning to which he had successfully trusted in mathematical investigation. From the preface to his "Mathematical Analysis of Logic," printed as a separate tract in 1847, we learn that speculations concerning a calculus of reasoning had, at different times, occupied Boole's thoughts, but it was not till the spring of 1847 that a memorable logical controversy led him to put his ideas into a definite form. He afterward regarded this pamphlet as a hasty and imperfect exposition of his logical system, and desired that his much larger work, "An Investigation of the Laws of Thought," etc. (1854), should alone be considered as containing a mature statement of his views.

This is Boole's greatest work, and is an attempt to apply the symbols and operations of mathematics to logic and the laws of thinking. The object of the work, as stated by himself, is "to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a calculus, and upon this foundation to establish the science of logic and construct its method; to make that method itself the basis' of a general method for the application of the mathematical doctrine of probabilities; and, finally, to collect from the various elements of truth, brought to view in the course of these inquiries, some probable intimations concerning the nature and constitution of the human mind."

Of this work Professor Todhunter, in the preface to his "History of the Theory of Probabilities," speaks as "marvelous"; and, in similar language, Professor W. Stanley Jevons speaks of it as "one of the most marvelous and admirable pieces of reasoning ever put together."

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 his mathematical and logical works, his acquaintance with general literature was wide and deep. Dante was his favorite poet, and he preferred the "Paradiso" to the "Inferno." The metaphysics of Aristotle, the ethics of Spinoza, the philosophical works of Cicero, and works of a kindred character, were frequent subjects of his study.

The personal character of Boole 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 ("Philosophical Transactions of the Royal Society," 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 entitled him.

"On the 8th of December, 1864, in the full vigor of his intellectual powers," says W. Stanley Jevons, in his tribute to his friend's life and genius, "George Boole died of an attack of fever, ending in suffusion on the lungs."

The mathematical and logical works of Boole are by far too abstruse to admit of their being used as text-books in schools of even the highest grades; but as works of reference they are invaluable to advanced students and the special cultivators of pure mathematics and the profounder problems of logic.