| Revision as of 04:32, 2 November 2015 edit83.110.193.184 (talk)No edit summary← Previous edit | Revision as of 04:34, 2 November 2015 edit undo115.252.184.213 (talk) ←Blanked the pageTags: blanking Possible vandalismNext edit → | ||
| Line 1: | Line 1: | ||
| {{redirect|Boole}} | |||
| {{Use British English|date=September 2015}} | |||
| {{Use dmy dates|date=May 2013}} | |||
| {{Infobox philosopher | |||
| |region = Western Philosophy | |||
| |era = ] | |||
| |color = #B0C4DE | |||
| |image = George Boole color.jpg | |||
| |caption = George Boole | |||
| |name = George Boole | |||
| |birth_date = {{birth date|df=yes|1814|11|02}} | |||
| |birth_place = ], ], ] | |||
| |death_date = {{death date and age|1864|12|08|1815|11|02|df=y}} | |||
| |death_place = ], ], Ireland | |||
| |nationality = British | |||
| |school_tradition = Mathematical foundations of ] | |||
| |main_interests = Mathematics, ], ] | |||
| |religion = ] | |||
| |influences = ], ], ] | |||
| |influenced = Modern computer scientists, ], ], ], ], ], ], ], ] | |||
| |notable_ideas = ] | |||
| }} | |||
| '''George Boole''' ({{IPAc-en|ˈ|b|uː|l}}; 2 November 1814 – 8 December 1864) was an English ], educator, ] and ]ian. He worked in the fields of ]s and ], and is best known as the author of '']'' which contains ]. Boolean logic is credited with laying the foundations for the information age.<ref name="Commemoration"/> Boole maintained that: | |||
| {{Quote|text= 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.<ref name="Boole Studies in Logic p 273">{{cite book | |||
| | last = Boole | first = George | |||
| | title = Studies in Logic and Probability | |||
| | publisher = Dover Publications | location = Mineola, NY | |||
| | date = 2012 | edition = Reprint | isbn=978-0-486-48826-4 | |||
| | orig-year= Originally published by Watts & Co., London, in 1952 | |||
| | url = https://books.google.com/books?id=pr35F8N9eaoC&lpg=PP1&pg=PA273 <!-- URL for p. 273 --> | |||
| | page = 273 | |||
| | editor-last= Rhees |editor-first= Rush |editor-link= Rush Rhees | |||
| | access-date=27 October 2015}}</ref>}} | |||
| ==Early life== | |||
| Boole was born in ], England. His father, John Boole (1779–1848), was a tradesman in Lincoln<ref>{{Cite EB1911|wstitle=Boole, George}}</ref> and gave him lessons. He had a primary school education, but little further formal and academic teaching. 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.<ref name=Hill149>Hill, p. 149; .</ref> At age 16 Boole became the breadwinner for his parents and three younger siblings, taking up a junior teaching position in ] at Heigham's School.<ref name=Rhees1954>]. (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</ref> He taught briefly in ].<ref name=MacTutor>{{MacTutor Biography|id=Boole}}</ref> | |||
| Boole participated in the local ], the Lincoln Mechanics' Institution, which was founded in 1833.<ref name=Hill149/><ref></ref> ], who knew John Boole through the institution, helped George Boole with mathematics books<ref>{{ODNBweb|id=37224|title=Bromhead, Sir Edward Thomas French|first=A. W. F.|last=Edwards}}</ref> and he was given the calculus text of ] by the Rev. George Stevens Dickson of St Swithin's Lincoln.<ref name=SED>{{Sep entry|boole|George Boole|Stanley Burris}}</ref> Without a teacher, it took him many years to master calculus.<ref name=MacTutor/> | |||
| {|align=right | |||
| |- | |||
| ! style="color:#black; background:#dddddd; font-size:100%; text-align:center;" colspan="2"|Boole's Lincoln House | |||
| |- | |||
| |<gallery> | |||
| File:3 Pottergate - geograph.org.uk - 657140.jpg|Boole's House and School at 3 Pottergate in Lincoln. | |||
| File:BoolePlacque.jpg|Plaque from the house in Lincoln. | |||
| </gallery> | |||
| |} | |||
| At age 19, Boole successfully established his own school in Lincoln. Four years later he took over Hall's Academy in ], outside Lincoln, following the death of Robert Hall. In 1840 he moved back to Lincoln, where he ran a boarding school.<ref name=MacTutor/> | |||
| Boole became a prominent local figure, an admirer of ], the bishop.<ref>Hill, p. 172 note 2; .</ref> He took part in the local campaign for ].<ref name=Hill149/> With ] and others he set up a ] in 1847.<ref>Hill, p. 130 note 1; .</ref> He associated also with the ] ], whose wife was a relation.<ref>Hill, p. 148; .</ref> | |||
| 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 these were understood at the time, and began to publish research papers.<ref name=MacTutor/> | |||
| ==Professor at Cork== | |||
| ] | |||
| Boole's status as mathematician was recognised by his appointment in 1849 as the first professor of mathematics at ] (now ] (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.<ref>Ronald Calinger, ''Vita mathematica: historical research and integration with teaching'' (1996), p. 292; .</ref> He maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution.<ref>Hill, p. 138 note 4; .</ref> | |||
| ==Honours and awards== | |||
| Boole was awarded the ] by the ] in 1855 <ref>{{cite web|url = http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8735503|title= Keith Awards 1827-1890|publisher=Canmbridge Journals Online|accessdate = 29 November 2014}}</ref> and was elected a ] in 1857.<ref name=SED/> He received ] of ] from the ] and ].<ref>], ], ''George Boole: Selected manuscripts on logic and its philosophy'' (1997), p. xiv; .</ref> | |||
| ==Death== | |||
| In 1864, Boole walked two miles in the drenching rain and lectured wearing his wet clothes. He soon became ill, developing a severe cold and high fever. As his wife believed that remedies should resemble their cause, she put her husband to bed and poured buckets of water over him – the wet having brought on his illness.{{citation needed}} Boole's condition worsened and on 8 December 1864, he died of fever-induced ]. | |||
| He was buried in the Church of Ireland cemetery of St Michael's, Church Road, ] (a suburb of ]). There is a commemorative plaque inside the adjoining church.<ref>The plaque reads: ‘To the memory of George Boole, LLD, DCL, FRS, Cork, in whom the highest order of intellect cultivated by unwearied industry produced the fruits of deep humility and childlike trust. He was born in Lincoln on 2 Nov. 1815 and died at Ballintemple on the 8 Dec. 1864. For ever O Lord Thy word is settled in Heaven.’ http://georgeboole.com/boole/life/ucc/death/</ref> | |||
| ] | |||
| ] dedicated to George Boole.]] | |||
| ] | |||
| ==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 '']'' in February 1840 (Volume 2, no. 8, pp. 64–73), and it led to a friendship between Boole and ], the editor of the journal. His works are in about 50 articles and a few separate publications.<ref>A list of Boole's memoirs and papers is in the ''Catalogue of Scientific Memoirs'' published by the ], and in the supplementary volume on differential equations, edited by ]. To the ''Cambridge Mathematical Journal'' and its successor, the '']'', Boole contributed 22 articles in all. In the third and fourth series of the '']'' are found 16 papers. The Royal Society printed six memoirs in the '']'', and a few other memoirs are to be found in the ''Transactions'' of the ] and of the ], in the ''Bulletin de l'Académie de St-Pétersbourg'' for 1862 (under the name G. Boldt, vol. iv. pp. 198–215), and in '']''. Also included is a paper on the mathematical basis of logic, published in the '']'' in 1848.</ref> | |||
| In 1841 Boole published an influential paper in early ].<ref name=SED/> He received a medal from the ] for his memoir of 1844, ''On A General Method of Analysis''. It was a contribution to the theory of ]s, moving from the case of constant coefficients on which he had already published, to variable coefficients.<ref>], ] (editors), ''Mathematics of the 19th Century: function theory according to Chebyshev, ordinary differential equations, calculus of variations, theory of finite differences'' (1998), pp. 130–2; .</ref> The innovation in operational methods is to admit that operations may not ].<ref>], ], ''Episodes in the History of Modern Algebra (1800–1950)'' (2007), p. 66; .</ref> In 1847 Boole published ''The Mathematical Analysis of Logic '', the first of his works on symbolic logic.<ref>George Boole, (London, England: Macmillan, Barclay, & Macmillan, 1847).</ref> | |||
| ===Differential equations=== | |||
| Two systematic treatises on mathematical subjects were completed by Boole during his lifetime. The ''Treatise on Differential Equations''<ref>George Boole, ''A treatsie on differential equations'' (1859), .</ref> appeared in 1859, and was followed, the next year, by a ''Treatise on the ] of Finite Differences'', 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'',<ref>{{cite journal |title=On the Comparison of Transcendents, with Certain Applications to the Theory of Definite Integrals |first=George |last=Boole |journal=Philosophical Transactions of the Royal Society of London |volume=147 |year=1857 |pages=745–803 |jstor=108643 |doi=10.1098/rstl.1857.0037}}</ref> in which he studied the sum of ] of a ]. Among other results, he proved what is now called Boole's identity: | |||
| :<math>\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} </math> | |||
| for any real numbers ''a''<sub>''k''</sub> > 0, ''b''<sub>''k''</sub>, and ''t'' > 0.<ref name=cmr>{{cite book|mr=2129737|last1=Cima|first1=Joseph A.|last2=Matheson|first2=Alec|last3=Ross|first3=William T.|chapter=The Cauchy transform|title=Quadrature domains and their applications|pages=79–111|series=Oper. Theory Adv. Appl.|volume=156|publisher=Birkhäuser|location=Basel|year=2005}}</ref> Generalisations of this identity play an important role in the theory of the ].<ref name=cmr/> | |||
| ===Symbolic logic=== | |||
| {{main|Boolean algebra}} | |||
| In 1847 Boole published the pamphlet ''Mathematical Analysis of Logic''. He later regarded it as a flawed exposition of his logical system, and wanted '']'' 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.<ref>], Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, vol. 24 (2003), pp. 261–288.</ref> Boole's initial involvement in logic was prompted by a current debate on ], between ] who supported the theory of "quantification of the predicate", and Boole's supporter ] who advanced a version of ], as it is now called. Boole's approach was ultimately much further reaching than either sides' in the controversy.<ref name=ODNB>{{ODNBweb|id=2868|title=Boole, George|first=I.|last=Grattan-Guinness}}</ref> It founded what was first known as the "algebra of logic" tradition.<ref name=Marc>Witold Marciszewski (editor), ''Dictionary of Logic as Applied in the Study of Language'' (1981), pp. 194–5.</ref> | |||
| Among his many innovations is his principle of ], which was later, and probably independently, adopted by ] and by logicians who subscribe to standard first-order logic. A 2003 article<ref>Corcoran, John (2003). "Aristotle's Prior Analytics and Boole's Laws of Thought". ''History and Philosophy of Logic'', '''24''': 261–288. Reviewed by Risto Vilkko. ''Bulletin of Symbolic Logic'', '''11'''(2005) 89–91. Also by Marcel Guillaume, ''Mathematical Reviews'' 2033867 (2004m:03006).</ref> provides a systematic comparison and critical evaluation of ] and ]; it also reveals the centrality of ] in Boole's ]. | |||
| ====Boole's 1854 definition of ]==== | |||
| 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.<ref>George Boole. 1854/2003. The Laws of Thought, facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167–169.</ref> | |||
| ====Treatment of addition in logic==== | |||
| Boole conceived of "elective symbols" of his kind as an ]. But this general concept was not available to him: he did not have the segregation standard in ] of postulated (axiomatic) properties of operations, and deduced properties.<ref name=KY>], ], ''Mathematics of the 19th Century: mathematical logic, algebra, number theory, probability theory'' (2001), pp. 15 (note 15)–16; .</ref> His work was a beginning to the ], 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 ]: in the language of ] it would correspond only to ] of subsets. Later authors changed the interpretation, commonly reading it as ], or in set theory terms ]; this step means that addition is always defined.<ref name=Marc/><ref>{{sep entry|algebra-logic-tradition|The Algebra of Logic Tradition|Stanley Burris}}</ref> | |||
| In fact there is the other possibility, that + should be read as ],<ref name=KY/> 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 ]s 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.<ref name=SED/> | |||
| ===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.<ref>{{cite book |last=Boole |first=George |title=An Investigation of the Laws of Thought |publisher=Walton & Maberly |year=1854 |location=London |pages=265–275 |url=http://archive.org/stream/investigationofl00boolrich#page/264/mode/2up}}</ref> | |||
| ==Legacy== | |||
| ] is named after him, as is the crater ] on the Moon. The keyword ''Bool'' represents a ] in many programming languages, though ] and ], among others, both use the full name ''Boolean''.<ref>P. J. Brown, ''Pascal from Basic'', Addison-Wesley, 1982. ISBN 0-201-13789-5, page 72</ref> The library, underground lecture theatre complex and the Boole Centre for Research in Informatics<ref></ref> at ] 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 ]. ] had worked on the ], and ] integrated his work with Boole's during the 1870s.<ref name=GGB>], ], ''George Boole: Selected manuscripts on logic and its philosophy'' (1997), p. xlvi; .</ref> Other significant figures were ], and ]. The conception of a Boolean algebra structure on equivalent statements of a ] is credited to ] (1877), in work surveyed 15 years later by Johnson.<ref name=GGB/> Surveys of these developments were published by ], ], and ]. | |||
| ===20th-century development=== | |||
| ] on basic propositions ''p'' and ''q'' arranged in a ]. The Boolean combinations make up 16 different propositions, and the lines show which are logically related.]] | |||
| In 1921 the economist ] 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.<ref>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."</ref> 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 <ref name=Miller></ref> | |||
| Boole's work and that of later logicians initially appeared to have no engineering uses. ] attended a philosophy class at the ] 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 ], in which he showed how Boolean algebra could optimise the design of systems of electromechanical ]s 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 ]s. ] at Moscow State University (1907–1987) proposed a theory of electric switches based on Boolean logic even earlier than ] in 1935 on the testimony of Soviet logicians and mathematicians ], Gaaze-Rapoport, ], 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 ] design; and Boole, via Shannon and Shestakov, provided the theoretical grounding for the ].<ref>"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."{{cite web |url=http://www.guardian.co.uk/science/2001/mar/08/obituaries.news |publisher=The Guardian |location=United Kingdom |date=8 March 2001 |title=Claude Shannon |first=Andrew |last=Emerson}}</ref>{{Clear}} | |||
| ===21st-century celebration=== | |||
| {{Quote box|width=30%|align=right|quote="Boole's legacy surrounds us everywhere, in the computers, information storage and retrieval, electronic circuits and controls that support life, learning and communications in the 21st century. His pivotal advances in mathematics, logic and probability provided the essential groundwork for modern mathematics, microelectronic engineering and computer science."|source=—University College Cork.<ref name="Commemoration">{{cite news|title=Who is George Boole: the mathematician behind the Google doodle|url=http://www.smh.com.au/technology/technology-news/who-is-george-boole-the-mathematician-behind-the-google-doodle-20151102-gkofyg.html#ixzz3qIcv6ii2|publisher=Sydney Morning Herald|date=2 November 2015}}</ref>}} | |||
| 2015 sees the 200th anniversary of George Boole's birth, in 1815. To mark the bicentenary year, ] will join admirers of Boole around the world to celebrate his life and legacy. | |||
| UCC's project, features 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'' (, 2014). | |||
| The search engine ] marked the 200th anniversary of his birth on 2 November 2015 with an algebraic reimaging of its ].<ref name="Commemoration"/> | |||
| ==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''.<ref>1902 ''Britannica'' article by Jevons; </ref> The first of these was from 1835, when ] gave a bust of Newton to the Mechanics' Institute in Lincoln.<ref>James Gasser, ''A Boole Anthology: recent and classical studies in the logic of George Boole'' (2000), p. 5; .</ref> The second justified and celebrated in 1847 the outcome of the successful campaign for early closing in Lincoln, headed by Alexander Leslie-Melville, of ].<ref>Gasser, p. 10; .</ref> ''The Claims of Science'' was given in 1851 at Queen's College, Cork.<ref>{{cite book|last=Boole |first=George |title=The Claims of Science, especially as founded in its relations to human nature; a lecture |url=https://books.google.com/books?id=BAlcAAAAQAAJ |accessdate=4 March 2012 |year=1851}}</ref> ''The Social Aspect of Intellectual Culture'' was also given in Cork, in 1855 to the Cuvierian Society.<ref>{{cite book |last=Boole |first=George |title=The Social Aspect of Intellectual Culture: an address delivered in the Cork Athenæum, May 29th, 1855 : at the soirée of the Cuvierian Society |url=https://books.google.com/books?id=PFWkZwEACAAJ |accessdate=4 March 2012 |year=1855 |publisher=George Purcell & Co.}}</ref> | |||
| Though his biographer Des MacHale describes Boole as an "agnostic deist",<ref>{{cite book|title=Semiotica, Volume 105|year=1995|publisher=Mouton|page=56|author1=International Association for Semiotic Studies |author2=International Council for Philosophy and Humanistic Studies |author3=International Social Science Council|accessdate=31 March 2013|chapter=A tale of two amateurs|quote=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.}}</ref><ref>{{cite book|title=Semiotica, Volume 105|year=1996|publisher=Mouton|page=17|author1=International Association for Semiotic Studies |author2=International Council for Philosophy and Humanistic Studies |author3=International Social Science Council|accessdate=31 March 2013|quote=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.}}</ref> 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 ] but in the end was said to have chosen ]. Boole came to speak against a what he saw as "prideful" scepticism, and instead, favoured the belief in a "Supreme Intelligent Cause",<ref>Boole, George. Studies in Logic and Probability. 2002. Courier Dover Publications. p. 201-202</ref> He also declared "I firmly believe, for the accomplishment of a purpose of the ] Mind."<ref>Boole, George. Studies in Logic and Probability. 2002. Courier Dover Publications. p. 451</ref><ref>Some-Side of a Scientific Mind (2013). pp. 112-3. The University Magazine, 1878. London: Forgotten Books. (Original work published 1878)</ref> In addition, he stated that he perceived "teeming evidences of surrounding ]" and concluded that "the course of this world is not abandoned to chance and inexorable fate."<ref>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)</ref><ref>Boole, George (1851). The claims of science, especially as founded in its relations to human nature; a lecture, Volume 15. p. 24</ref> | |||
| Two influences on Boole were later claimed by his wife, ]: a universal mysticism tempered by ] thought, and ].<ref name=Ganeri>Jonardon Ganeri (2001), ''Indian Logic: a reader'', Routledge, p. 7, ISBN 0-7007-1306-9; .</ref> Mary Boole stated that an adolescent mystical experience provided for his life's work: | |||
| <blockquote>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 ] 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 ]."<ref name=MaryBoole>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.947–967</ref></blockquote> | |||
| In Ch. 13 of ''Laws of Thought'' Boole used examples of propositions from ] and ]. The work contains some remarks on the relationship of logic to religion, but they are slight and cryptic.<ref>Grattan-Guinness and Bornet, p. 16; .</ref> Boole was apparently disconcerted at the book's reception just as a mathematical toolset: | |||
| <blockquote>George afterwards learned, to his great joy, that the same conception of the basis of Logic was held by ], 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 ] 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.<ref name=MaryBoole/></blockquote> | |||
| Mary Boole claimed that there was profound influence {{mdash}} via her uncle ] {{mdash}} of ]n thought on George Boole, as well as on ] and ]: | |||
| <blockquote>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 1830–65. What share had it in generating the ] and the mathematics by which investigations in physical science are now conducted?<ref name=MaryBoole/></blockquote> | |||
| ==Family== | |||
| In 1855 he married ] (niece of ]), who later wrote several educational works on her husband's principles. | |||
| The Booles had five daughters: | |||
| * Mary Lucy Margret (1856–1908)<ref>''`My Right To Die´, Woman Kills Self'' in ''The Washington Times'' v. 28 May 1908 (); ''Mrs. Mary Hinton A Suicide'' in ''The New York Times'' v. 29 May 1908 ().</ref> who married the mathematician and author ] and had four children: George (1882–1943), Eric (*1884), William (1886–1909)<ref>''Smothers In Orchard'' in ''The Los Angeles Times'' v. 27 February 1909.</ref> and Sebastian (1887–1923) inventor of the ]. Sebastian had three children: | |||
| **Jean Hinton (married name Rosner) (1917–2002) peace activist. | |||
| **] (1919–2004) visited China in the 1930s and 40s and wrote an influential account of the Communist land reform. | |||
| **] (1921–2010) worked for the ] and lived in China from 1948 until her death on 8 June 2010; she was married to ]. | |||
| * Margaret, (1858 – 1935) married ], an artist. | |||
| ** Their elder son ] became a mathematician and a Fellow of the ]. | |||
| ** Their younger son ] was a professor of surgery. | |||
| * ] (1860–1940), who made important contributions to four-dimensional geometry | |||
| * ] (1862–1904), who was first female professor of chemistry in England | |||
| * ] (1864–1960), who married the Polish scientist and revolutionary ] and was the author of the novel '']''. | |||
| ==See also== | |||
| {{Portal|Logic|Mathematics|Biography}} | |||
| * ] | |||
| ==References== | |||
| {{Refbegin}} | |||
| *], ''George Boole 200 Bicentenary Celebration'', . | |||
| *{{Cite EB1911|wstitle=Boole, George}} | |||
| *], ''The Search for Mathematical Roots 1870–1940''. Princeton University Press. 2000. | |||
| *] (1974), ''Victorian Lincoln''; . | |||
| *], '' George Boole: His Life and Work''. . 1985. | |||
| *], '' The Life and Work of George Boole: A Prelude to the Digital Age'' (new edition). . 2014 | |||
| *], '' God Created the Integers''. Running Press, Philadelphia. 2007. | |||
| {{Refend}} | |||
| ==Notes== | |||
| {{Reflist|colwidth=30em}} | |||
| ==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}} | |||
| * | |||
| * {{Gutenberg author |id=Boole,+George | name=George Boole}} | |||
| * {{Internet Archive author |sname=George Boole}} | |||
| * | |||
| * | |||
| * in the database ] | |||
| {{Notable logicians}} | |||
| {{Authority control}} | |||
| {{Persondata <!-- Metadata: see ]. --> | |||
| | NAME = Boole, George | |||
| | ALTERNATIVE NAMES = | |||
| | SHORT DESCRIPTION = British mathematician | |||
| | DATE OF BIRTH = 2 November 1815 | |||
| | PLACE OF BIRTH = ], England | |||
| | DATE OF DEATH = 8 December 1864 | |||
| | PLACE OF DEATH = ], ], Ireland | |||
| }} | |||
| {{DEFAULTSORT:Boole, George}} | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||
| ] | |||