# George Boole His Life And Work Pdf

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*He worked in the fields of differential equations and algebraic logic , and is best known as the author of The Laws of Thought which contains Boolean algebra. Boolean logic is credited with laying the foundations for the information age. No general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.*

He also worked on differential equations, the calculus of finite differences and general methods in probability. View four larger pictures. John made shoes but he was interested in science and in particular the application of mathematics to scientific instruments. Mary Ann was a lady's maid and she married John on 14 September They moved to Lincoln where John opened a cobbler's shop at 34 Silver Street.

## The Life and Work of George Boole: A Prelude to the Digital Age

He worked in the fields of differential equations and algebraic logic , and is best known as the author of The Laws of Thought which contains Boolean algebra.

Boolean logic is credited with laying the foundations for the information age. No general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.

He was self-taught in modern languages. Boole participated in the Lincoln Mechanics' Institute , in the Greyfriars, Lincoln , which was founded in In , he moved back to Lincoln, where he ran a boarding school.

Boole became a prominent local figure, an admirer of John Kaye , the bishop. From onwards, Boole was making contacts with sympathetic British academic mathematicians and reading more widely. He studied algebra in the form of symbolic methods, as far as these were understood at the time, and began to publish research papers. He met his future wife, Mary Everest , there in while she was visiting her uncle John Ryall who was professor of Greek.

They married some years later in Larken in a campaign to reduce prostitution. Boole's first published paper was "Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order", printed in the Cambridge Mathematical Journal in February Volume 2, No. His works are in about 50 articles and a few separate publications. In , Boole published an influential paper in early invariant theory. It was a contribution to the theory of linear differential equations , moving from the case of constant coefficients on which he had already published, to variable coefficients.

Boole completed two systematic treatises on mathematical subjects during his lifetime. The Treatise on Differential Equations [29] appeared in , and was followed, the next year, by a Treatise on the Calculus of Finite Differences , [30] a sequel to the former work.

In , Boole published the treatise "On the Comparison of Transcendent, with Certain Applications to the Theory of Definite Integrals", [31] in which he studied the sum of residues of a rational function. Among other results, he proved what is now called Boole's identity:. In , Boole published the pamphlet Mathematical Analysis of Logic. He later regarded it as a flawed exposition of his logical system and wanted An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities to be seen as the mature statement of his views.

Contrary to widespread belief, Boole never intended to criticise or disagree with the main principles of Aristotle 's logic. Rather he intended to systematise it, to provide it with a foundation, and to extend its range of applicability. Boole's approach was ultimately much further reaching than either sides' in the controversy.

Among his many innovations is his principle of wholistic reference , which was later, and probably independently, adopted by Gottlob Frege and by logicians who subscribe to standard first-order logic.

A article [36] provides a systematic comparison and critical evaluation of Aristotelian logic and Boolean logic ; it also reveals the centrality of wholistic reference in Boole's philosophy of logic.

In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined.

The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them, the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. Sometimes, in discoursing of men we imply without expressing the limitation that it is of men only under certain circumstances and conditions that we speak, as of civilised men, or of men in the vigour of life, or of men under some other condition or relation.

Now, whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the universe of discourse. Furthermore, this universe of discourse is in the strictest sense the ultimate subject of the discourse.

Boole conceived of "elective symbols" of his kind as an algebraic structure. But this general concept was not available to him: he did not have the segregation standard in abstract algebra of postulated axiomatic properties of operations, and deduced properties. His pioneering efforts encountered specific difficulties, and the treatment of addition was an obvious difficulty in the early days. Boole replaced the operation of multiplication by the word "and" and addition by the word "or".

Later authors changed the interpretation, commonly reading it as exclusive or , or in set theory terms symmetric difference ; this step means that addition is always defined. Handling this ambiguity was an early problem of the theory, reflecting the modern use of both Boolean rings and Boolean algebras which are simply different aspects of one type of structure. Boole kept the result as something undefined. The second part of the Laws of Thought contained a corresponding attempt to discover a general method in probabilities.

Here the goal was algorithmic: from the given probabilities of any system of events, to determine the consequent probability of any other event logically connected with those events. In late November , Boole walked, in heavy rain, from his home at Lichfield Cottage in Ballintemple [41] to the university, a distance of three miles, and lectured wearing his wet clothes. As his wife believed that remedies should resemble their cause, she wrapped him in wet blankets — the wet having brought on his illness.

There is a commemorative plaque inside the adjoining church. Boole is the namesake of the branch of algebra known as Boolean algebra , as well as the namesake of the lunar crater Boole.

The keyword Bool represents a Boolean datatype in many programming languages, though Pascal and Java , among others, both use the full name Boolean. A road called Boole Heights in Bracknell, Berkshire is named after him. Boole's work was extended and refined by a number of writers, beginning with William Stanley Jevons. Augustus De Morgan had worked on the logic of relations , and Charles Sanders Peirce integrated his work with Boole's during the s.

The conception of a Boolean algebra structure on equivalent statements of a propositional calculus is credited to Hugh MacColl , in work surveyed 15 years later by Johnson.

Keynes believed that Boole had made a fundamental error in his definition of independence which vitiated much of his analysis. Theodore Hailperin showed much earlier that Boole had used the correct mathematical definition of independence in his worked out problems. Boole's work and that of later logicians initially appeared to have no engineering uses. Claude Shannon attended a philosophy class at the University of Michigan which introduced him to Boole's studies.

Shannon recognised that Boole's work could form the basis of mechanisms and processes in the real world and that it was therefore highly relevant. In Shannon went on to write a master's thesis, at the Massachusetts Institute of Technology , in which he showed how Boolean algebra could optimise the design of systems of electromechanical relays then used in telephone routing switches.

He also proved that circuits with relays could solve Boolean algebra problems. Employing the properties of electrical switches to process logic is the basic concept that underlies all modern electronic digital computers. Victor Shestakov at Moscow State University — proposed a theory of electric switches based on Boolean logic even earlier than Claude Shannon in on the testimony of Soviet logicians and mathematicians Sofya Yanovskaya , Gaaze-Rapoport, Roland Dobrushin , Lupanov, Medvedev and Uspensky, though they presented their academic theses in the same year, Hence, Boolean algebra became the foundation of practical digital circuit design; and Boole, via Shannon and Shestakov, provided the theoretical grounding for the Information Age.

The year saw the th anniversary of Boole's birth. To mark the bicentenary year, University College Cork joined admirers of Boole around the world to celebrate his life and legacy.

The search engine Google marked the th anniversary of his birth on 2 November with an algebraic reimaging of its Google Doodle. Litchfield Cottage in Ballintemple, Cork, where Boole lived for the last two years of his life, bears a memorial plaque. Though his biographer Des MacHale describes Boole as an "agnostic deist", [61] [62] Boole read a wide variety of Christian theology.

Combining his interests in mathematics and theology, he compared the Christian trinity of Father, Son, and Holy Ghost with the three dimensions of space, and was attracted to the Hebrew conception of God as an absolute unity.

Boole considered converting to Judaism but in the end was said to have chosen Unitarianism. Two influences on Boole were later claimed by his wife, Mary Everest Boole : a universal mysticism tempered by Jewish thought, and Indian logic.

My husband told me that when he was a lad of seventeen a thought struck him suddenly, which became the foundation of all his future discoveries. It was a flash of psychological insight into the conditions under which a mind most readily accumulates knowledge [ But by the help of a learned Jew in Lincoln he found out the true nature of the discovery which had dawned on him. This was that man's mind works by means of some mechanism which "functions normally towards Monism.

In Ch. The work contains some remarks on the relationship of logic to religion, but they are slight and cryptic. George afterwards learned, to his great joy, that the same conception of the basis of Logic was held by Leibniz , the contemporary of Newton. De Morgan, of course, understood the formula in its true sense; he was Boole's collaborator all along. Herbert Spencer, Jowett, and Robert Leslie Ellis understood, I feel sure; and a few others, but nearly all the logicians and mathematicians ignored [] the statement that the book was meant to throw light on the nature of the human mind; and treated the formula entirely as a wonderful new method of reducing to logical order masses of evidence about external fact.

Mary Boole claimed that there was profound influence — via her uncle George Everest — of Indian thought in general and Indian logic , in particular, on George Boole, as well as on Augustus De Morgan and Charles Babbage : [71]. Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan, and George Boole on the mathematical atmosphere of — What share had it in generating the Vector Analysis and the mathematics by which investigations in physical science are now conducted?

In , Boole married Mary Everest niece of George Everest , who later wrote several educational works on her husband's principles. From Wikipedia, the free encyclopedia. English mathematician, philosopher and logician. For other uses, see Boole disambiguation. Not to be confused with George Boolos. Lincoln , Lincolnshire , England. Ballintemple , Cork , Ireland. Aristotle , Spinoza , Leibniz , Newton. Main article: Boolean algebra. His pivotal advances in mathematics, logic and probability provided the essential groundwork for modern mathematics, microelectronic engineering and computer science.

Philosophy portal Mathematics portal Biography portal. Sydney Morning Herald. Rhees, Rush ed. Mineola, New York: Dover Publications. Retrieved 27 October Lincoln Boole Foundation. Archived from the original on 8 March Retrieved 6 November

## George Boole

Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use—from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer , Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras—mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon—advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond. Nahin leavens the math and engineering with humor and an infectious intellectual curiosity, and the parallels between Boole and Shannon are convincingly drawn. Although the book is technical, it is always easily understandable for anyone for those who need it, some basic rules for electrical circuits are collected in a short appendix. It is not only understandable but also pleasantly bantering and at occasions even facetious.

## George Boole

George Boole — was an English mathematician and a founder of the algebraic tradition in logic. He revolutionized logic by applying methods from the then-emerging field of symbolic algebra to logic. George Boole was born November 2, in Lincoln, Lincolnshire, England, into a family of modest means, with a father who was evidently more of a good companion than a good breadwinner. This love of learning was clearly inherited by Boole. Without the benefit of an elite schooling, but with a supportive family and access to excellent books, in particular from Sir Edward Bromhead, FRS, who lived only a few miles from Lincoln, Boole was able to essentially teach himself foreign languages and advanced mathematics.

Welcome back. Read 9 reviews from the world's largest community for readers. This book is a powerful and enlightening text that can help anyone understand the concepts that drive data science. Be the first to ask a question about The Laws of Thought. A dark secret spans several

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*Boole's father was a simple tradesman skilled in the construction of optical instruments, but extremely interested in mathematics and sciences, an interest which he passed on to his son.*

#### Desmond Machale - George Boole : His Life and Work download ebook DJV, MOBI, FB2

Увидев тело Хейла, Стратмор вздрогнул от ужаса. - О Боже! - воскликнул. - Что случилось. ГЛАВА 93 Причастие. Халохот сразу же увидел Беккера: нельзя было не заметить пиджак защитного цвета да еще с кровавым пятном на боку. Светлый силуэт двигался по центральному проходу среди моря черных одежд.

Сьюзан не было дома. Он не мог понять, куда она подевалась. Всякий раз включался автоответчик, но Дэвид молчал. Он не хотел доверять машине предназначавшиеся ей слова. Выйдя на улицу, Беккер увидел у входа в парк телефонную будку.

Тот, что был в парке. Я рассказал о нем полицейскому. Я отказался взять кольцо, а эта фашистская свинья его схватила. Беккер убрал блокнот и ручку. Игра в шарады закончилась.

Джабба посмотрел на экран и в отчаянии всплеснул руками. Новый порядок букв показался не более вразумительным, чем оригинал. P F Е Е S Е S N R Е Т М Р F Н А I R W E О О 1 G М Е Е N N R М А Е N Е Т S Н А S D С N S I 1 А А I Е Е R В R N К S В L Е L О D 1 - Ясно как в полночь в подвале, - простонал Джабба. - Мисс Флетчер, - потребовал Фонтейн, - объяснитесь.

Знаю, Чед. Мне не нужно напоминать. Через тридцать секунд она уже сидела за его столом и изучала отчет шифровалки. - Видишь? - спросил Бринкерхофф, наклоняясь над ней и показывая цифру.

Острая боль обожгла грудь Беккера и ударила в мозг. Пальцы у него онемели. Он упал. И в следующее мгновение не осталось ничего, кроме черной бездны. ГЛАВА 102 Стратмор спустился на нижний этаж ТРАНСТЕКСТА и ступил с лесов в дюймовый слой воды на полу.

Сьюзан с трудом воспринимала происходящее. - Что же тогда случилось? - спросил Фонтейн. - Я думал, это вирус.

*Джабба покачал головой: - Лично я сомневаюсь, что Танкадо собирался зайти так. Я думаю, он собирался оставаться поблизости и вовремя все это остановить.*

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