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| | Hi usually there. My name is Kiesha Florian. Ohio is where my house is but I need to move for my kinds. He is currently an application developer but soon his wife and him commence their own home based business. One of the things I love most might be to bungee jump and now I have time to take on new . Check out my website here: http://googledealer.com/index.php?do=/profile-81225/info/info/<br><br>My blog :: [http://googledealer.com/index.php?do=/profile-81225/info/info/ Enlarge Penis Size] |
| {{redirect|Boole}}
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| {{EngvarB|date=May 2013}}
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| {{Use dmy dates|date=May 2013}}
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| {{Infobox philosopher
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| |region = Western Philosophy
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| |era = [[19th-century philosophy]]
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| |color = #B0C4DE
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| |image = George Boole color.jpg
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| |caption = George Boole
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| |name = George Boole
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| |birth_date = 2 November 1815
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| |birth_place = [[Lincoln, Lincolnshire]], England
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| |death_date = {{death date and age|1864|12|08|1815|11|02|df=y}}
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| |death_place = [[Ballintemple]], [[County Cork]], Ireland
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| |nationality = English
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| |school_tradition = Mathematical foundations of [[computer science]]
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| |main_interests = Mathematics, [[Logic]], [[Philosophy of mathematics]]
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| |religion = [[Unitarianism|Unitarian]]
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| |influences = [[Aristotle]], [[Baruch Spinoza|Spinoza]], [[Isaac Newton|Newton]]
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| |influenced = Modern computer scientists, [[William Stanley Jevons|Jevons]], [[Augustus De Morgan|De Morgan]], [[John Maynard Keynes|Keynes]], [[Bertrand Russell|Russell]], [[Charles Sanders Peirce|Peirce]], [[William Ernest Johnson|Johnson]], [[Claude Shannon|Shannon]], [[Victor Shestakov|Shestakov]]
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| |notable_ideas = [[Boolean algebra]]
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| }}
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| '''George Boole''' ({{IPAc-en|ˈ|b|uː|l}}; 2 November 1815 – 8 December 1864) was an English mathematician, philosopher and [[logician]]. He worked in the fields of [[differential equation]]s and [[algebraic logic]], and is now best known as the author of ''[[The Laws of Thought]]''. As the inventor of the prototype of what is now called [[Boolean logic]], which became the basis of the modern [[digital computer]], Boole is regarded in hindsight as a founder of the field of [[computer science]]. Boole said,
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| <blockquote>... no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise ... those universal laws of thought which are the basis of all reasoning ...<ref>{{cite web|url=http://www.kerryr.net/pioneers/boole.htm |title=George Boole (1815–1864) |publisher=Kerryr.net |date= |accessdate=2013-04-22}}</ref></blockquote>
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| ==Early life==
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| Boole was born in [[Lincoln, Lincolnshire]]. His father, John Boole (1779–1848), was a tradesman in Lincoln,<ref>{{Cite EB1911|wstitle=Boole, George}}</ref> and gave him lessons. He had an elementary 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; [http://books.google.co.uk/books?id=-A89AAAAIAAJ&pg=PA149 Google Books].</ref> 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.<ref name=Rhees1954>[[Rush Rhees|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</ref> He taught briefly in [[Liverpool]].<ref name=MacTutor>{{MacTutor Biography|id=Boole}}</ref>
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| Boole participated in the local [[Mechanics Institute]], the Lincoln Mechanics' Institution, which was founded in 1833.<ref name=Hill149/><ref>[http://www.freewebs.com/sochistastro/lincolnshire.htm Society for the History of Astronomy, ''Lincolnshire''.]</ref> [[Edward Bromhead]], 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 [[Sylvestre François Lacroix]] by Rev. George Stevens Dickson, of St Swithin 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/>
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| {|align=right
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| ! style="color:#black; background:#dddddd; font-size:100%; text-align:center;" colspan="2"|Boole's Lincoln House
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| |<gallery>
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| File:3 Pottergate - geograph.org.uk - 657140.jpg|Boole's House and School at 3 Pottergate in Lincoln.
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| File:BoolePlacque.jpg|Plaque from the house in Lincoln.
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| </gallery>
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| |}
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| At age 19 Boole successfully established his own school at Lincoln. Four years later he took over Hall's Academy, at [[Waddington, Lincolnshire|Waddington]], outside Lincoln, following the death of Robert Hall. In 1840 he moved back to Lincoln, where he ran a boarding school.<ref name=MacTutor/>
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| Boole became a prominent local figure, an admirer of [[John Kaye (bishop)|John Kaye]], the bishop.<ref>Hill, p. 172 note 2; [http://books.google.co.uk/books?id=-A89AAAAIAAJ&pg=PA172 Google Books].</ref> He took part in the local campaign for [[early closing]].<ref name=Hill149/> With [[E. R. Larken]] and others he set up a [[building society]] in 1847.<ref>Hill, p. 130 note 1; [http://books.google.co.uk/books?id=-A89AAAAIAAJ&pg=PA130 Google Books].</ref> He associated also with the [[Chartism|Chartist]] [[Thomas Cooper (poet)|Thomas Cooper]], whose wife was a relation.<ref>Hill, p. 148; [http://books.google.co.uk/books?id=-A89AAAAIAAJ&pg=PA148 Google Books].</ref>
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| 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/>
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| ==Professor at Cork==
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| [[File:Boole House Cork.jpg|thumb|The house in Cork in which Boole lived between 1849 and 1855.]]
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| Boole's status as mathematician was recognised by his appointment in 1849 as the first professor of mathematics at [[Queen's College, Cork]] 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; [http://books.google.co.uk/books?id=D21wKHoYGg0C&pg=PA292 Google Books].</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; [http://books.google.co.uk/books?id=-A89AAAAIAAJ&pg=PA138 Google Books].</ref>
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| Boole was elected [[Fellow of the Royal Society]] in 1857;<ref name=SED/> and received [[honorary degrees]] of [[LL.D.]] from the [[University of Dublin]] and [[Oxford University]].<ref>[[Ivor Grattan-Guinness]], [[Gérard Bornet]], ''George Boole: Selected manuscripts on logic and its philosophy'' (1997), p. xiv; [http://books.google.com/books?id=pzg7UFsIVJIC&pg=PR14 Google Books].</ref>
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| ==Death==
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| On 8 December 1864, Boole died of an attack of fever, ending in [[pleural effusion]]. He was buried in the Church of Ireland cemetery of St Michael's, Church Road, [[Blackrock, Cork|Blackrock]] (a suburb of [[Cork City]]). There is a commemorative plaque inside the adjoining church.{{citation needed|date=June 2013}}
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| [[File:2010-05-26 at 18-05-02.jpg|thumb|Boole's gravestone, Cork, Ireland.]]
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| [[File:BooleWindow(bottom third).jpg|thumb|Detail of stained glass window in [[Lincoln Cathedral]] dedicated to George Boole.]]
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| [[File:BoolePlaque2.jpg|thumb|Plaque beneath Boole's window in Lincoln Cathedral.]]
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| ==Works==
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| 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, no. 8, pp. 64–73), 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.<ref>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'Académie de St-Pétersbourg'' for 1862 (under the name G. Boldt, vol. iv. pp. 198–215), and in ''[[Crelle's Journal]]''. Also included is a paper on the mathematical basis of logic, published in the ''[[Mechanic's Magazine]]'' in 1848.</ref>
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| In 1841 Boole published an influential paper in early [[invariant theory]].<ref name=SED/> 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 equation]]s, moving from the case of constant coefficients on which he had already published, to variable coefficients.<ref>[[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. 130–2; [http://books.google.co.uk/books?id=Mw6JMdZQO-wC&pg=PA130 Google Books].</ref> The innovation in operational methods is to admit that operations may not [[commutative law|commute]].<ref>[[Jeremy Gray]], [[Karen Hunger Parshall]], ''Episodes in the History of Modern Algebra (1800–1950)'' (2007), p. 66; [http://books.google.co.uk/books?id=zMSl6QLlJZsC&pg=PA66 Google Books].</ref> In 1847 Boole published ''The Mathematical Analysis of Logic '', the first of his works on symbolic logic.<ref>George Boole, [http://books.google.com/books?id=zv4YAQAAIAAJ&pg=PP9#v=onepage&q&f=false ''The Mathematical Analysis of Logic, Being an Essay towards a Calculus of Deductive Reasoning''] (London, England: Macmillan, Barclay, & Macmillan, 1847).</ref>
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| ===Differential equations===
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| Two systematic treatises on mathematical subjects were completed by Boole during his lifetime. The ''Treatise on Differential Equations'' appeared in 1859, and was followed, the next year, by a ''Treatise on the [[Calculus]] of Finite Differences'', a sequel to the former work. In the sixteenth and seventeenth chapters of the ''Differential Equations'' is an account of the general symbolic method, and of a general method in analysis, originally described in his memoir printed in the ''Philosophical Transactions'' for 1844.{{citation needed|date=June 2013}}
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| During the last few years of his life Boole worked on a second edition of his ''Differential Equations'', and part of his last vacation was spent in the libraries of the Royal Society and the [[British Museum]]; but it was left incomplete. [[Isaac Todhunter]] printed the manuscripts in 1865, in a supplementary volume.{{citation needed|date=June 2013}}
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| ===Analysis===
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| 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}}</ref> in which he studied the sum of [[residue (complex analysis)|residues]] of a [[rational function]]. Among other results, he proved what is now called Boole's identity:
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| :<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>
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| 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 [[Hilbert transform]].<ref name=cmr/>
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| ===Symbolic logic===
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| {{main|Boolean algebra}}
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| In 1847 Boole published the pamphlet ''Mathematical Analysis of Logic''. He later regarded it as a flawed exposition of his logical system, and wanted ''[[The Laws of Thought|An Investigation of the Laws of Thought (1854), 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 criticize or disagree with the main principles of Aristotle’s logic. Rather he intended to systematize it, to provide it with a foundation, and to extend its range of applicability.<ref>[[John Corcoran (logician)|JOHN CORCORAN]], 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 [[quantification#Logic|quantification]], between [[Sir William Hamilton, 9th Baronet|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.<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>
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| Boole did not regard logic as a branch of mathematics, but he provided a general symbolic method of [[logical inference]]. Boole proposed that logical propositions should be expressed by means of algebraic equations. Algebraic manipulation of the symbols in the equations would provide a fail-safe method of logical deduction: i.e. logic is reduced to a type of algebra.{{citation needed|date=June 2013}}
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| By 1 (unity) Boole denoted the "universe of thinkable objects"; [[literal (computer programming)|literal]] symbols, such as ''x'', ''y'', ''z'', ''v'', ''u'', etc., were used with the "elective" meaning attaching to adjectives and nouns of [[natural language]]. Thus, if ''x'' = horned and ''y'' = sheep, then the successive acts of election (i.e. choice) represented by ''x'' and ''y'', if performed on unity, give the class "horned sheep". Thus, (1 – ''x'') would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and (1 – ''x'') (1 – ''y'') would give all things neither horned nor sheep.{{citation needed|date=June 2013}}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 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 [[Aristotelian logic]] and [[Boolean logic]]; it also reveals the centrality of [[wholistic reference]] in Boole's [[philosophy of logic]].
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| ====Boole’s 1854 Definition of [[Universe of Discourse]]====
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| 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 civilized 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
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| properly be termed the universe of discourse.
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| 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>
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| ====Treatment of addition in logic====
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| 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.<ref name=KY>[[Andrei Nikolaevich Kolmogorov]], [[Adolf Pavlovich Yushkevich]], ''Mathematics of the 19th Century: mathematical logic, algebra, number theory, probability theory'' (2001), pp. 15 (note 15)–16; [http://books.google.co.uk/books?id=X3u5hJCkobYC&pg=PA15 Google Books].</ref> 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.
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| 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.<ref name=Marc/><ref>{{sep entry|algebra-logic-tradition|The Algebra of Logic Tradition|Stanley Burris}}</ref>
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| In fact there is the other possibility, that + should be read as [[disjunction]],<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 [[Boolean ring]]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/>
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| ===Probability theory===
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| 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 the 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>
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| ==Legacy==
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| [[Boolean algebra]] is named after him, as is the crater [[Boole (crater)|Boole]] on the Moon. The keyword ''Bool'' represents a [[Boolean datatype]] in many programming languages, though [[Pascal (programming language)|Pascal]] and [[Java (programming language)|Java]], 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>[http://www.bcri.ucc.ie Boole Centre for Research in Informatics]</ref> at [[University College Cork]] are named in his honour.
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| ===19th-century development===
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| 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.<ref name=GGB>[[Ivor Grattan-Guinness]], [[Gérard Bornet]], ''George Boole: Selected manuscripts on logic and its philosophy'' (1997), p. xlvi; [http://books.google.co.uk/books?id=pzg7UFsIVJIC&pg=PR46 Google Books].</ref> 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.<ref name=GGB/> Surveys of these developments were published by [[Ernst Schröder]], [[Louis Couturat]], and [[Clarence Irving Lewis]].
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| ===20th-century development===
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| In 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.<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>[http://zeteticgleanings.com/boole.html http://zeteticgleanings.com/boole.html]</ref>
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| [[File:Hasse2Free.png|thumb|In modern notation, the [[free Boolean algebra]] on basic propositions ''p'' and ''q'' arranged in a [[Hasse diagram]]. The Boolean combinations make up 16 different propositions, and the lines show which are logically related.]]
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| 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 computer]]s. [[Victor Shestakov]] at Moscow State University (1907–1987) 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 [[Yanovskaya]], Gaaze-Rapoport, [[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 [[Digital Age]].<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>{{-}}
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| ==Views==
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| 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; [http://www.1902encyclopedia.com/B/BOO/george-boole.html online text.]</ref> The first of these was from 1835, when [[Charles Anderson-Pelham, 2nd Baron Yarborough]] 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; [http://books.google.co.uk/books?id=A2Q5Yghl000C&pg=PA5 Google Books].</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 [[Branston Hall]].<ref>Gasser, p. 10; [http://books.google.co.uk/books?id=A2Q5Yghl000C&pg=PA10 Google Books].</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=http://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=http://books.google.com/books?id=PFWkZwEACAAJ |accessdate=4 March 2012 |year=1855 |publisher=George Purcell & Co.}}</ref>
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| 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]]. However, his biographer, Des MacHale, describes him 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>
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| Two influences on Boole were later claimed by his wife, [[Mary Everest Boole]]: a universal mysticism tempered by [[Jewish]] thought, and [[Indian logic]].<ref name=Ganeri>Jonardon Ganeri (2001), ''Indian Logic: a reader'', Routledge, p. 7, ISBN 0-7007-1306-9; [http://books.google.co.uk/books?id=t_nOiqFmxOIC&pg=PA7 Google Books].</ref> Mary Boole stated that an adolescent mystical experience provided for his life's work:
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| <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 [[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]]."<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>
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| In Ch. 13 of ''Laws of Thought'' Boole used examples of propositions from [[Benedict Spinoza]] and [[Samuel Clarke]]. 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; [http://books.google.co.uk/books?id=pzg7UFsIVJIC&pg=PR16 Google Books].</ref> Boole was apparently disconcerted at the book's reception just as a mathematical toolset:
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| <blockquote>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 [[Leslie Ellis]] understood, I feel sure; and a few others, but nearly all the logicians and [[mathematician]]s 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.<ref name=MaryBoole/></blockquote>
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| Mary Boole claimed that there was profound influence — via her uncle [[George Everest]] — of [[India]]n thought on George Boole, as well as on [[Augustus De Morgan]] and [[Charles Babbage]]:
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| <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 [[Vector Analysis]] and the mathematics by which investigations in physical science are now conducted?<ref name=MaryBoole/></blockquote>
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| ==Family==
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| In 1855 he married [[Mary Everest Boole|Mary Everest]] (niece of [[George Everest]]), who later wrote several educational works on her husband's principles.
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| The Booles had five daughters:
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| * Mary Lucy Margret (1856–1908)<ref>''`My Right To Die´, Woman Kills Self'' in ''The Washington Times'' v. 28 May 1908 ([http://chroniclingamerica.loc.gov/lccn/sn84026749/1908-05-28/ed-1/seq-1.pdf PDF]); ''Mrs. Mary Hinton A Suicide'' in ''The New York Times'' v. 29 May 1908 ([http://query.nytimes.com/mem/archive-free/pdf?res=9E02E5DB1631E233A2575AC2A9639C946997D6CF PDF]).</ref> who married the mathematician and author [[Charles Howard Hinton]] 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 [[Jungle gym]]. Sebastian had three children:
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| **[[William H. Hinton]] (1919–2004) visited China in the 1930s and 40s and wrote an influential account of the Communist land reform.
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| **[[Joan Hinton]] (1921–2010) worked for the [[Manhattan Project]] and lived in China from 1948 until her death on 8 June 2010; she was married to [[Sid Engst]].
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| **Jean Hinton (married name Rosner) (1917–2002) peace activist.
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| * Margaret, (1858 – ?) married [[Edward Ingram Taylor]], an artist.
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| ** Their elder son [[Geoffrey Ingram Taylor]] became a mathematician and a Fellow of the [[Royal Society]].
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| ** Their younger son [[Julian Taylor (surgeon)|Julian]] was a professor of surgery.
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| * [[Alicia Boole Stott|Alicia]] (1860–1940), who made important contributions to four-dimensional geometry
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| * [[Lucy Everest Boole|Lucy Everest]] (1862–1905), who was first female professor of chemistry in England
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| * [[Ethel Lilian Voynich|Ethel Lilian]] (1864–1960), who married the Polish scientist and revolutionary [[Wilfrid Michael Voynich]] and was the author of the novel ''[[The Gadfly]]''.
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| ==References==
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| {{Refbegin}}
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| *{{Cite EB1911|wstitle=Boole, George}}
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| *[[Ivor Grattan-Guinness]], ''The Search for Mathematical Roots 1870–1940''. Princeton University Press. 2000.
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| *[[Francis Hill]] (1974), ''Victorian Lincoln''; [http://books.google.co.uk/books?id=-A89AAAAIAAJ&pg=PA149 Google Books].
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| *[[Des MacHale]], '' George Boole: His Life and Work''. [http://boolepress.com/ Boole Press]. 1985.
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| *[[Stephen Hawking]], '' God Created the Integers''. Running Press, Philadelphia. 2007.
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| {{Refend}}
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| ==Notes==
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| {{reflist|colwidth=30em}}
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| ==External links==
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| {{Portal|Biography|Logic}}
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| {{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}}
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| *[http://www.rogerparsons.info/george/boole.html Roger Parsons' article on Boole]
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| *{{gutenberg author|id=George_Boole|name=George Boole}}
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| *[http://www.ucc.ie/academic/undersci/pages/sci_georgeboole.htm George Boole's work as first Professor of Mathematics in University College, Cork, Ireland]
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| {{Logic}}
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| {{Authority control|VIAF=49282014|PND=118661655|LCCN=n/83/144364}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Boole, George
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = British mathematician
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| | DATE OF BIRTH = 2 November 1815
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| | PLACE OF BIRTH = [[Lincoln, Lincolnshire]], England
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| | DATE OF DEATH = 8 December 1864
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| | PLACE OF DEATH = [[Ballintemple]], [[County Cork]], Ireland
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| }}
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| {{DEFAULTSORT:Boole, George}}
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| [[Category:1815 births]]
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| [[Category:1864 deaths]]
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| [[Category:People from Lincoln, England]]
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| [[Category:Deists]]
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| [[Category:English agnostics]]
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| [[Category:English logicians]]
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| [[Category:English philosophers]]
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| [[Category:English Unitarians]]
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| [[Category:Victorian writers]]
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| [[Category:19th-century English writers]]
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| [[Category:19th-century English mathematicians]]
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| [[Category:19th-century philosophers]]
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| [[Category:Mathematical logicians]]
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| [[Category:Fellows of the Royal Society]]
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| [[Category:Academics of Queens College Cork]]
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| [[Category:Royal Medal winners]]
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