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George Boole
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Early life
File:3 Pottergate - geograph.org.uk - 657140.jpg|thumb|Boole's House and School at 3 Pottergate in Lincoln ]]Boole was born in Lincoln, Lincolnshire, England, the son of John Boole senior (1779â€“1848), a shoemakerWEB,weblink John Boole, Lincoln Boole Foundation, 6 November 2015, and Mary Ann Joyce.EB1911, Boole, George, He had a primary school education, and received lessons from his father, but due to a serious decline in business, he had little further formal and academic teaching.BOOK,weblink Math and mathematicians : the history of math discoveries around the world, C., Bruno, Leonard, 2003, 1999, U X L, Baker, Lawrence W., 0787638137, Detroit, Mich., 49, 41497065, William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages.Hill, p. 149; Google Books. In fact, when a local newspaper printed his translation of a Latin poem, a scholar accused him of plagiarism under the pretence that he was not capable of such achievements.BOOK,weblink Math and mathematicians : the history of math discoveries around the world, C., Bruno, Leonard, 2003, 1999, U X L, Baker, Lawrence W., 0787638137, Detroit, Mich., 49â€“50, 41497065, At age 16, Boole became the breadwinner for his parents and three younger siblings, taking up a junior teaching position in Doncaster at Heigham's School.Rhees, Rush. (1954) "George Boole as Student and Teacher. By Some of His Friends and Pupils", Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences. Vol. 57. Royal Irish Academy He taught briefly in Liverpool.{{MacTutor Biography|id=Boole}}(File:Greyfriars, Lincoln - geograph.org.uk - 106215.jpg|thumb|left|Greyfriars, Lincoln, which housed the Mechanic's Institute)Boole participated in the Mechanics Institute, in the Greyfriars, Lincoln, which was founded in 1833.Society for the History of Astronomy, Lincolnshire. Edward Bromhead, who knew John Boole through the institution, helped George Boole with mathematics books{{ODNBweb|id=37224|title=Bromhead, Sir Edward Thomas French|first=A. W. F.|last=Edwards}} and he was given the calculus text of Sylvestre FranÃ§ois Lacroix by the Rev. George Stevens Dickson of St Swithin's, Lincoln.SEP, boole, George Boole, Burris, Stanley, Without a teacher, it took him many years to master calculus.At age 18, Boole successfully established his own school in Lincoln.George Boole: Self-Education & Early Career University College Cork Four years later he took over Hall's Academy in Waddington, outside Lincoln, following the death of Robert Hall. In 1840 he moved back to Lincoln, where he ran a boarding school. Boole immediately became involved in the Lincoln Topographical Society, serving as a member of the committee, and presenting a paper entitled, On the origin, progress and tendencies Polytheism, especially amongst the ancient Egyptians, and Persians, and in modern India.A Selection of Papers relative to the County of Lincoln, read before the Lincolnshire Topographical Society, 1841â€“1842. Printed by W. and B. Brooke, High-Street, Lincoln, 1843. on 30 November 1841.Boole became a prominent local figure, an admirer of John Kaye, the bishop.Hill, p. 172 note 2; Google Books. He took part in the local campaign for early closing. With Edmund Larken and others he set up a building society in 1847.Hill, p. 130 note 1; Google Books. He associated also with the Chartist Thomas Cooper, whose wife was a relation.Hill, p. 148; Google Books.(File:BoolePlacque.jpg|thumb|240px|Plaque from the house in Lincoln)From 1838 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.Professor at Cork
File:Boole House Cork.jpg|thumb|The house at 5 Grenville Place in Cork, in which Boole lived between 1849 and 1855, and where he wrote The Laws of ThoughtThe Laws of ThoughtBoole's status as mathematician was recognised by his appointment in 1849 as the first professor of mathematics at Queen's College, Cork (now University College Cork (UCC)) in Ireland. He met his future wife, Mary Everest, there in 1850 while she was visiting her uncle John Ryall who was Professor of Greek. They married some years later in 1855.Ronald Calinger, Vita mathematica: historical research and integration with teaching (1996), p. 292; Google Books. He maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution.Hill, p. 138 note 4; Google Books.Honours and awards
Boole was awarded the Keith Medal by the Royal Society of Edinburgh in 1855WEB,weblink Keith Awards 1827â€“1890, Cambridge Journals Online, 29 November 2014, and was elected a Fellow of the Royal Society (FRS) in 1857. He received honorary degrees of LL.D. from the University of Dublin and the University of Oxford.Ivor Grattan-Guinness, GÃ©rard Bornet, George Boole: Selected manuscripts on logic and its philosophy (1997), p. xiv; Google Books.File:Grave of George Boole in Ireland.jpg|thumb|Boole's gravestone in Blackrock, Cork, Ireland]]File:BooleWindow(bottom third).jpg|thumb|Detail of stained glass window in Lincoln CathedralLincoln Cathedral(File:BoolePlaque2.jpg|thumb|Plaque beneath Boole's window in Lincoln Cathedral)Works
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 1840 (Volume 2, â„– 8, pp. 64â€“73), and it led to a friendship between Boole and Duncan Farquharson Gregory, the editor of the journal. His works are in about 50 articles and a few separate publications.A list of Boole's memoirs and papers is 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 22 articles in all. In the third and fourth series of the Philosophical Magazine are found 16 papers. The Royal Society printed six 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'AcadÃ©mie de St-PÃ©tersbourg for 1862 (under the name G. Boldt, vol. iv. pp. 198â€“215), and in Crelle's Journal. Also included is a paper on the mathematical basis of logic, published in the Mechanic's Magazine in 1848.In 1841 Boole published an influential paper in early invariant theory. He received a medal from the Royal Society for his memoir of 1844, On A General Method of Analysis. 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.Andrei Nikolaevich Kolmogorov, Adolf Pavlovich Yushkevich (editors), Mathematics of the 19th Century: function theory according to Chebyshev, ordinary differential equations, calculus of variations, theory of finite differences (1998), pp. 130â€“2; Google Books. The innovation in operational methods is to admit that operations may not commute.Jeremy Gray, Karen Hunger Parshall, Episodes in the History of Modern Algebra (1800â€“1950) (2007), p. 66; Google Books. In 1847 Boole published The Mathematical Analysis of Logic, the first of his works on symbolic logic.George Boole, The Mathematical Analysis of Logic, Being an Essay towards a Calculus of Deductive Reasoning (London, England: Macmillan, Barclay, & Macmillan, 1847).Differential equations
Boole completed two systematic treatises on mathematical subjects during his lifetime. The Treatise on Differential EquationsGeorge Boole, A treatise on differential equations (1859), Internet Archive. appeared in 1859, and was followed, the next year, by a Treatise on the Calculus of Finite Differences,George Boole, A treatise on the calculus of finite differences (1860), Internet Archive. a sequel to the former work.Analysis
In 1857, Boole published the treatise On the Comparison of Transcendents, with Certain Applications to the Theory of Definite Integrals,JOURNAL, On the Comparison of Transcendents, with Certain Applications to the Theory of Definite Integrals, George, Boole, Philosophical Transactions of the Royal Society of London, 147, 1857, 745â€“803, 108643, 10.1098/rstl.1857.0037, in which he studied the sum of residues of a rational function. Among other results, he proved what is now called Boole's identity:
mathrm{mes} left{ x in mathbb{R} , mid , Re frac{1}{pi} sum frac{a_k}{x - b_k} geq t right} = frac{sum a_k}{pi t}
for any real numbers a'k > 0, b'k, and t > 0.BOOK, 2129737, Cima, Joseph A., Matheson, Alec, Ross, William T., The Cauchy transform, Quadrature domains and their applications, 79â€“111, Oper. Theory Adv. Appl., 156, BirkhÃ¤user, Basel, 2005, Generalisations of this identity play an important role in the theory of the Hilbert transform.Symbolic logic
In 1847 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.John Corcoran, Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, vol. 24 (2003), pp. 261â€“288. Boole's initial involvement in logic was prompted by a current debate on quantification, between Sir William Hamilton who supported the theory of "quantification of the predicate", and Boole's supporter Augustus De Morgan who advanced a version of De Morgan duality, as it is now called. Boole's approach was ultimately much further reaching than either sides' in the controversy.{{ODNBweb|id=2868|title=Boole, George|first=I.|last=Grattan-Guinness}} It founded what was first known as the "algebra of logic" tradition.Witold Marciszewski (editor), Dictionary of Logic as Applied in the Study of Language (1981), pp. 194â€“5.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 2003 articleCorcoran, John (2003). "Aristotle's Prior Analytics and Boole's Laws of Thought". History and Philosophy of Logic, 24: 261â€“288. Reviewed by Risto Vilkko. Bulletin of Symbolic Logic, 11(2005) 89â€“91. Also by Marcel Guillaume, Mathematical Reviews 2033867 (2004m:03006). 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.1854 definition of universe of discourse
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.George Boole. 1854/2003. The Laws of Thought, facsimile of 1854 edition, with an introduction by John Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167â€“169.Treatment of addition in logic
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.Andrei Nikolaevich Kolmogorov, Adolf Pavlovich Yushkevich, Mathematics of the 19th Century: mathematical logic, algebra, number theory, probability theory (2001), pp. 15 (note 15)â€“16; Google Books. His work was a beginning to the algebra of sets, again not a concept available to Boole as a familiar model. 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". But in Boole's original system, + was a partial operation: in the language of set theory it would correspond only to disjoint union of subsets. 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.SEP, algebra-logic-tradition, The Algebra of Logic Tradition, Burris, Stanley, In fact there is the other possibility, that + should be read as disjunction. This other possibility extends from the disjoint union case, where exclusive or and non-exclusive or both give the same answer. 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 and Jevons struggled over just this issue in 1863, in the form of the correct evaluation of x + x. Jevons argued for the result x, which is correct for + as disjunction. Boole kept the result as something undefined. He argued against the result 0, which is correct for exclusive or, because he saw the equation x + x = 0 as implying x = 0, a false analogy with ordinary algebra.Probability theory
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.BOOK, Boole, George, An Investigation of the Laws of Thought, Walton & Maberly, 1854, London, 265â€“275,weblinkDeath
In late November 1864, Boole walked, in heavy rain, from his home at Lichfield Cottage in BallintempleWEB,weblink Dublin City Quick Search: Buildings of Ireland: National Inventory of Architectural Heritage, to the university, a distance of three miles, and lectured wearing his wet clothes.WEB,weblink Have a look inside the home of UCC maths professor George Boole, Barker, Tommy, 13 June 2015, Irish Examiner, 6 November 2015, He soon became ill, developing pneumonia. As his wife believed that remedies should resemble their cause, she put her husband to bed and poured buckets of water over him â€“ the wet having brought on his illness.BOOK,weblink Math and mathematicians : the history of math discoveries around the world, C., Bruno, Leonard, 2003, 1999, U X L, Baker, Lawrence W., 0787638137, Detroit, Mich., 52, 41497065, Stanford Encyclopedia of Philosophy Boole's condition worsened and on 8 December 1864,ENCYCLOPEDIA, George Boole, EncyclopÃ¦dia Britannica, 30 January 2017, EncyclopÃ¦dia Britannica, inc.,weblink 7 December 2017, he died of fever-induced pleural effusion.He was buried in the Church of Ireland cemetery of St Michael's, Church Road, Blackrock (a suburb of Cork). There is a commemorative plaque inside the adjoining church.WEB,weblink Death-His Life-- George Boole 200,Legacy
File:Bust of George Boole at University College Cork - 133760 (38218465931) (2).jpg|thumb|Bust of Boole at University College CorkUniversity College CorkBoolean algebra is named after him, as is the crater Boole on the Moon. The keyword Bool represents a Boolean datatype in many programming languages, though Pascal and Java, among others, both use the full name Boolean.P. J. Brown, Pascal from Basic, Addison-Wesley, 1982. {{isbn|0-201-13789-5}}, page 72 The library, underground lecture theatre complex and the Boole Centre for Research in InformaticsWEB,weblink Boole Centre for Research in Informatics, at University College Cork are named in his honour. A road called Boole Heights in Bracknell, Berkshire is named after him.19th-century development
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 1870s.Ivor Grattan-Guinness, GÃ©rard Bornet, George Boole: Selected manuscripts on logic and its philosophy (1997), p. xlvi; Google Books. Other significant figures were Platon Sergeevich Poretskii, and William Ernest Johnson. The conception of a Boolean algebra structure on equivalent statements of a propositional calculus is credited to Hugh MacColl (1877), in work surveyed 15 years later by Johnson. Surveys of these developments were published by Ernst SchrÃ¶der, Louis Couturat, and Clarence Irving Lewis.20th-century development
File:Hasse2Free.png|thumb|In modern notation, the free Boolean algebra on basic propositions p and q arranged in a Hasse diagramHasse diagramIn 1921 the economist John Maynard Keynes published a book on probability theory, A Treatise of Probability. Keynes believed that Boole had made a fundamental error in his definition of independence which vitiated much of his analysis.Chapter XVI, p. 167, section 6 of A treatise on probability, volume 4: "The central error in his system of probability arises out of his giving two inconsistent definitions of 'independence' (2) He first wins the reader's acquiescence by giving a perfectly correct definition: "Two events are said to be independent when the probability of either of them is unaffected by our expectation of the occurrence or failure of the other." (3) But a moment later he interprets the term in quite a different sense; for, according to Boole's second definition, we must regard the events as independent unless we are told either that they must concur or that they cannot concur. That is to say, they are independent unless we know for certain that there is, in fact, an invariable connection between them. "The simple events, x, y, z, will be said to be conditioned when they are not free to occur in every possible combination; in other words, when some compound event depending upon them is precluded from occurring. ... Simple unconditioned events are by definition independent." (1) In fact as long as xz is possible, x and z are independent. This is plainly inconsistent with Boole's first definition, with which he makes no attempt to reconcile it. The consequences of his employing the term independence in a double sense are far-reaching. For he uses a method of reduction which is only valid when the arguments to which it is applied are independent in the first sense, and assumes that it is valid if they are independent in second sense. While his theorems are true if all propositions or events involved are independent in the first sense, they are not true, as he supposes them to be, if the events are independent only in the second sense." In his book The Last Challenge Problem, David Miller provides a general method in accord with Boole's system and attempts to solve the problems recognised earlier by Keynes and others. Theodore Hailperin showed much earlier that Boole had used the correct mathematical definition of independence in his worked out problems.WEB,weblink ZETETIC GLEANINGS, 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 1937 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 (1907â€“1987) proposed a theory of electric switches based on Boolean logic even earlier than Claude Shannon in 1935 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, 1938.{{Clarify|date=June 2009}} But the first publication of Shestakov's result took place only in 1941 (in Russian). 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."That dissertation has since been hailed as one of the most significant master's theses of the 20th century. To all intents and purposes, its use of binary code and Boolean algebra paved the way for the digital circuitry that is crucial to the operation of modern computers and telecommunications equipment."WEB,weblink The Guardian, United Kingdom, 8 March 2001, Claude Shannon, Andrew, Emerson, {{Clear}}21st-century celebration
}}2015 saw the 200th anniversary of George Boole's birth. To mark the bicentenary year, University College Cork joined admirers of Boole around the world to celebrate his life and legacy.UCC's George Boole 200WEB,weblink George Boole 200 â€“ George Boole Bicentenary Celebrations, project, featured events, student outreach activities and academic conferences on Boole's legacy in the digital age, including a new edition of Desmond MacHale's 1985 biography The Life and Work of George Boole: A Prelude to the Digital Age,Cork University Press 2014).The search engine Google marked the 200th anniversary of his birth on 2 November 2015 with an algebraic reimaging of its Google Doodle.(File:George Boole House 2017.jpg|thumb|5, Grenville Place in 2017 following restoration by UCC)Litchfield Cottage in Ballintemple, Cork, where Boole lived for the last two years of his life, bears a memorial plaque. His former residence, in Grenville Place, is being restored through a collaboration between UCC and Cork City Council, as the George Boole House of Innovation, after the city council acquired the premises under the Derelict Sites Act.WEB,weblink Boolean logic meets Victorian gothic in leafy Cork suburb,Views
Boole's views were given in four published addresses: The Genius of Sir Isaac Newton; The Right Use of Leisure; The Claims of Science; and The Social Aspect of Intellectual Culture.1902 Britannica article by Jevons; online text. The first of these was from 1835, when Charles Anderson-Pelham, 1st Earl of Yarborough gave a bust of Newton to the Mechanics' Institute in Lincoln.James Gasser, A Boole Anthology: recent and classical studies in the logic of George Boole (2000), p. 5; Google Books. The second justified and celebrated in 1847 the outcome of the successful campaign for early closing in Lincoln, headed by Alexander Leslie-Melville, of Branston Hall.Gasser, p. 10; Google Books. The Claims of Science was given in 1851 at Queen's College, Cork.BOOK, Boole, George, The Claims of Science, especially as founded in its relations to human nature; a lecture,weblink 4 March 2012, 1851, The Social Aspect of Intellectual Culture was also given in Cork, in 1855 to the Cuvierian Society.BOOK, Boole, George, The Social Aspect of Intellectual Culture: an address delivered in the Cork AthenÃ¦um, May 29th, 1855 : at the soirÃ©e of the Cuvierian Society,weblink 4 March 2012, 1855, George Purcell & Co., Though his biographer Des MacHale describes Boole as an "agnostic deist",BOOK, Semiotica, Volume 105, 1995, Mouton, 56, International Association for Semiotic Studies, International Council for Philosophy and Humanistic Studies, International Social Science Council, 31 March 2013, A tale of two amateurs, MacHale's biography calls George Boole 'an agnostic deist'. Both Booles' classification of 'religious philosophies' as monistic, dualistic, and trinitarian left little doubt about their preference for 'the unity religion', whether Judaic or Unitarian., BOOK, Semiotica, Volume 105, 1996, Mouton, 17, International Association for Semiotic Studies, International Council for Philosophy and Humanistic Studies, International Social Science Council, 31 March 2013, MacHale does not repress this or other evidence of the Boole's nineteenth-century beliefs and practices in the paranormal and in religious mysticism. He even concedes that George Boole's many distinguished contributions to logic and mathematics may have been motivated by his distinctive religious beliefs as an "agnostic deist" and by an unusual personal sensitivity to the sufferings of other people., 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. Boole came to speak against a what he saw as "prideful" scepticism, and instead, favoured the belief in a "Supreme Intelligent Cause."Boole, George. Studies in Logic and Probability. 2002. Courier Dover Publications. p. 201-202 He also declared "I firmly believe, for the accomplishment of a purpose of the Divine Mind."Boole, George. Studies in Logic and Probability. 2002. Courier Dover Publications. p. 451Some-Side of a Scientific Mind (2013). pp. 112â€“3. The University Magazine, 1878. London: Forgotten Books. (Original work published 1878) In addition, he stated that he perceived "teeming evidences of surrounding design" and concluded that "the course of this world is not abandoned to chance and inexorable fate."Concluding remarks of his treatise of "Clarke and Spinoza", as found in Boole, George (2007). An Investigation of the Laws of Thought. Cosimo, Inc. Chap . XIII. p. 217-218. (Original work published 1854)Boole, George (1851). The claims of science, especially as founded in its relations to human nature; a lecture, Volume 15. p. 24Two influences on Boole were later claimed by his wife, Mary Everest Boole: a universal mysticism tempered by Jewish thought, and Indian logic.Jonardon Ganeri (2001), Indian Logic: a reader, Routledge, p. 7, {{isbn|0-7007-1306-9}}; Google Books. Mary Boole stated that an adolescent mystical experience provided for his life's work: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 [...] For a few years he supposed himself to be convinced of the truth of "the Bible" as a whole, and even intended to take orders as a clergyman of the English Church. 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."Boole, Mary Everest Indian Thought and Western Science in the Nineteenth Century, Boole, Mary Everest Collected Works eds. E. M. Cobham and E. S. Dummer, London, Daniel 1931 pp.947â€“967In Ch. 13 of Laws of Thought Boole used examples of propositions from Baruch Spinoza and Samuel Clarke. The work contains some remarks on the relationship of logic to religion, but they are slight and cryptic.Grattan-Guinness and Bornet, p. 16; Google Books. Boole was apparently disconcerted at the book's reception just as a mathematical toolset:George afterwards learned, to his great joy, that the same conception of the basis of Logic was held by Leibnitz, 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 [953] 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 â€“ via her uncle George Everest â€“ of Indian thought in general and Indian logic, in particular, on George Boole, as well as on Augustus De Morgan and Charles Babbage: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 1830â€“65. What share had it in generating the Vector Analysis and the mathematics by which investigations in physical science are now conducted?Family
In 1855 he married Mary Everest (niece of George Everest), who later wrote several educational works on her husband's principles.The Booles had five daughters:- Mary Ellen (1856â€“1908)WEB,weblink Family and Genealogy â€“ His Life George Boole 200, Georgeboole.com, 7 March 2016, who married the mathematician and author Charles Howard Hinton and had four children: George (1882â€“1943), Eric (1884), William (1886â€“1909)Smothers In Orchard in The Los Angeles Times v. 27 February 1909. and Sebastian (1887â€“1923), inventor of the Jungle gym. After the sudden death of her husband, Mary Ellen committed suicide in Washington, D.C. in May 1908.`My Right To DieÂ´, Woman Kills Self in The Washington Times v. 28 May 1908 (PDF); Mrs. Mary Hinton A Suicide in The New York Times v. 29 May 1908 (PDF). Sebastian had three children:
- Jean Hinton (married name Rosner) (1917â€“2002), a peace activist.
- William H. Hinton (1919â€“2004) visited China in the 1930s and 40s and wrote an influential account of the Communist land reform.
- Joan Hinton (1921â€“2010) worked for the Manhattan Project and lived in China from 1948 until her death on 8 June 2010; she was married to Sid Engst.
- Margaret (1858â€“1935), married Edward Ingram Taylor, an artist.
- Their elder son Geoffrey Ingram Taylor became a mathematician and a Fellow of the Royal Society.
- Their younger son Julian was a professor of surgery.
- Alicia (1860â€“1940), who made important contributions to four-dimensional geometry.
- Lucy Everest (1862â€“1904), who was the first female professor of chemistry in England.
- Ethel Lilian (1864â€“1960), who married the Polish scientist and revolutionary Wilfrid Michael Voynich and was the author of the novel The Gadfly.
See also
- Boolean algebra, a logical calculus of truth values or set membership
- Boolean algebra (structure), a set with operations resembling logical ones
- Boolean ring, a ring consisting of idempotent elements
- Boolean circuit, a mathematical model for digital logical circuits.
- Boolean data type is a data type, having two values (usually denoted true and false)
- Boolean expression, an expression in a programming language that produces a Boolean value when evaluated
- Boolean function, a function that determines Boolean values or operators
- Boolean model (probability theory), a model in stochastic geometry
- Boolean network, a certain network consisting of a set of Boolean variables whose state is determined by other variables in the network
- Boolean processor, a 1-bit variables computing unit
- Boolean satisfiability problem
- Boole's syllogistic is a logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set."
- List of Boolean algebra topics
- List of pioneers in computer science
Notes
{{Reflist|30em}}References
- University College Cork, George Boole 200 Bicentenary Celebration, GeorgeBoole.com.
- EB1911, Boole, George,
- Ivor Grattan-Guinness, The Search for Mathematical Roots 1870â€“1940. Princeton University Press. 2000.
- Francis Hill (1974), Victorian Lincoln; Google Books.
- Des MacHale, George Boole: His Life and Work. Boole Press. 1985.
- Des MacHale, The Life and Work of George Boole: A Prelude to the Digital Age (new edition). Cork University Press. 2014
- Stephen Hawking, God Created the Integers. Running Press, Philadelphia. 2007.
External links
{{Sister project links| wikt=no | commons=Category:George Boole | b=no | n=no | q=George Boole | s=Author:George Boole | v=no | voy=no | species=no | d=q134661}}- Roger Parsons' article on Boole
- George Boole: A 200-Year View by Stephen Wolfram.
- {{Gutenberg author |id=Boole,+George | name=George Boole}}
- {{Internet Archive author |sname=George Boole}}
- George Boole's work as first Professor of Mathematics in University College, Cork, Ireland
- George Boole website
- Author profile in the database zbMATH
- content above as imported from Wikipedia
- "George Boole" does not exist on GetWiki (yet)
- time: 11:01pm EDT - Thu, May 24 2018
- "George Boole" does not exist on GetWiki (yet)
- time: 11:01pm EDT - Thu, May 24 2018
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