Western Philosophy 19th-century philosophy
George Boole
Name	George Boole
Birth	November 2, 1815 (Lincoln, Lincolnshire, England)
Death	December 8, 1864 (Ballintemple, County Cork, Ireland)
School/tradition	Mathematical foundations of computer science
Main interests	Mathematics, Logic, Philosophy of mathematics
Notable ideas	Boolean algebra
Influenced by	Aristotle, Spinoza, Newton
Influenced	Modern computer scientists, Jevons, De Morgan, Peirce, Johnson, Shannon

George Boole (IPA: [buːl]) (November 2, 1815 – December 8, 1864) was a British mathematician and philosopher. Events 1570 - A Tidal wave in the North Sea devastates the coast from Holland to Jutland, killing more than 1000 Year 1815 ( MDCCCXV) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common year Events 1609 - Biblioteca Ambrosiana opens its reading room the second public library of Europe. Year 1864 ( MDCCCLXIV) was a Leap year starting on Friday (link will display the full calendar of the Gregorian Calendar (or a Leap year The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located A mathematician is a person whose primary area of study and research is the field of Mathematics. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language

As the inventor of Boolean algebra, which is the basis of all modern computer arithmetic, Boole is regarded in hindsight as one of the founders of the field of computer science. Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole in the late 1830s A computer is a Machine that manipulates data according to a list of instructions. Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their

Biography

George Boole's father, John Boole (1779-1848), was a tradesman of limited means, but of "studious character and active mind". ^[1] Being especially interested in mathematical science and logic, the father gave his son his first lessons; but the extraordinary mathematical talents of George Boole did not manifest themselves in early life. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Logic is the study of the principles of valid demonstration and Inference. At first his favourite subject was classics.

It wasn't until his successful establishment of a school at Lincoln, its removal to Waddington, and later his appointment in 1849 as the first professor of mathematics of then Queen's College, Cork (now University College Cork, where the library and underground lecture complex are named in his honour) in Ireland that his mathematical skills were fully realized. Lincoln (ˈlɪŋkən is a Cathedral city and County town of Lincolnshire, England. Waddington is a large rural commuter village in the North Kesteven district of Lincolnshire, England. University College Cork ( UCC) is a constituent university of the National University of Ireland, the university is located in Cork. University College Cork ( UCC) is a constituent university of the National University of Ireland, the university is located in Cork. Ireland (pronounced /ˈaɾlənd/ Éire) is the third largest island in Europe, and the twentieth-largest island in the world In 1855 he married Mary Everest (niece of George Everest), who later, as Mrs. Colonel Sir George Everest ( 4 July, 1790 &ndash 1 December, 1866) was a Welsh surveyor, Geographer and Boole, wrote several useful educational works on her husband's principles.

To the broader public Boole was known only as the author of numerous abstruse papers on mathematical topics, and of three or four distinct publications which have become standard works. His earliest published paper was the "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 D. F. Gregory, the editor of the journal, which lasted until the premature death of the latter in 1844. A long list of Boole's memoirs and detached papers, both on logical and mathematical topics, are found in the Catalogue of Scientific Memoirs published by the Royal Society, and in the supplementary volume on Differential Equations, edited by Isaac Todhunter. The Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660 A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the Isaac Todhunter FRS ( November 23, 1820 &ndash March 1, 1884) was an English Mathematician who is best To the Cambridge Mathematical Journal and its successor, the Cambridge and Dublin Mathematical Journal, Boole contributed twenty-two articles in all. The city of Cambridge (ˈkeɪmbrɪdʒ is a university town and the administrative centre of the county of Cambridgeshire, England Dublin (ˈdʌblɨn/ /ˈdʊblɨn or /ˈdʊbəlɪn/, bˠalʲə aːha klʲiəh or cliə(ɸ is both the largest city and capital of Ireland. In the third and fourth series of the Philosophical Magazine are found sixteen papers. The Royal Society printed six important 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. The Royal Society of Edinburgh is Scotland 's National academy of science and letters The Royal Irish Academy ( RIA) (Acadamh Ríoga na hÉireann is an all-Ireland, independent academic body that promotes study and excellence in the Sciences iv. pp. 198-215), and in Crelle's Journal. Crelle's Journal, or just Crelle, is the common name for a leading German -language Mathematical journal, the Journal für Also included is a paper on the mathematical basis of logic, published in the Mechanic's Magazine in 1848. The works of Boole are thus contained in about fifty scattered articles and a few separate publications.

Only two systematic treatises on mathematical subjects were completed by Boole during his lifetime. A treatise is a formal lengthy systematic Discourse on some subject The well-known Treatise on Differential Equations appeared in 1859, and was followed, the next year, by a Treatise on the Calculus of Finite Differences, designed to serve as a sequel to the former work. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives These treatises are valuable contributions to the important branches of mathematics in question. To a certain extent these works embody the more important discoveries of their author. In the sixteenth and seventeenth chapters of the Differential Equations we find, for instance, an account of the general symbolic method, the bold and skilful employment of which led to Boole's chief discoveries, and of a general method in analysis, originally described in his famous memoir printed in the Philosophical Transactions for 1844. Boole was one of the most eminent of those who perceived that the symbols of operation could be separated from those of quantity and treated as distinct objects of calculation. His principal characteristic was perfect confidence in any result obtained by the treatment of symbols in accordance with their primary laws and conditions, and an almost unrivalled skill and power in tracing out these results.

During the last few years of his life Boole was constantly engaged in extending his researches with the object of producing a second edition of his Differential Equations much more complete than the first edition, and part of his last vacation was spent in the libraries of the Royal Society and the British Museum; but this new edition was never completed. The British Museum is a Museum of human history and culture in London. Even the manuscripts left at his death were so incomplete that Todhunter, into whose hands they were put, found it impossible to use them in the publication of a second edition of the original treatise, and printed them, in 1865, in a supplementary volume.

With the exception of Augustus de Morgan, Boole was probably the first English mathematician since the time of John Wallis who had also written upon logic. Augustus De Morgan ( 27 June, 1806 &ndash 18 March, 1871) was a British Mathematician and Logician. John Wallis ( November 23, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the Logic is the study of the principles of valid demonstration and Inference. His novel views of logical method were due to the same profound confidence in symbolic reasoning to which he had successfully trusted in mathematical investigation. Speculations concerning a calculus of reasoning had at different times occupied Boole's thoughts, but it was not till the spring of 1847 that he put his ideas into the pamphlet called Mathematical Analysis of Logic. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Reasoning is the cognitive process of looking for Reasons for beliefs conclusions actions or feelings Boole afterwards regarded this as a hasty and imperfect exposition of his logical system, and he desired that his much larger work, An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities (1854), should alone be considered as containing a mature statement of his views. The Laws of Thought, more precisely An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, is a very influential Nevertheless, there is a charm of originality about his earlier logical work which is easy to appreciate.

He did not regard logic as a branch of mathematics, as the title of his earlier pamphlet might be taken to imply, but he pointed out such a deep analogy between the symbols of algebra and those which can be made, in his opinion, to represent logical forms and syllogisms, that we can hardly help saying that (especially his) formal logic is mathematics restricted to the two quantities, 0 and 1. Analogy is both the cognitive process of transferring Information from a particular subject (the analogue or source to another particular subject (the target and Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. A syllogism, or logical appeal, (συλλογισμός &mdash "conclusion" "inference" (usually the categorical syllogism) is a kind of By unity Boole denoted the universe of thinkable objects; literal symbols, such as x, y, z, v, u, etc. , were used with the elective meaning attaching to common adjectives and substantives. Thus, if x=horned and y=sheep, then the successive acts of election represented by x and y, if performed on unity, give the whole of the class horned sheep. Boole showed that elective symbols of this kind obey the same primary laws of combination as algebraic symbols, whence it followed that they could be added, subtracted, multiplied and even divided, almost exactly in the same manner as numbers. In combinatorial mathematics, a combination is an un-ordered collection of distinct elements usually of a prescribed size and taken from a given set 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 us all things neither horned nor sheep. By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules. In Logic and Philosophy, proposition refers to either (a the content or Meaning of a meaningful Declarative sentence An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent In Discourse and Logic, a premise is a claim that is a reason (or element of a set of reasons for or objection against some other claim

Still more original and remarkable, however, was that part of his system, fully stated in his Laws of Thought, formed a general symbolic method of logical inference. Inference is the act or process of deriving a Conclusion based solely on what one already knows Given any propositions involving any number of terms, Boole showed how, by the purely symbolic treatment of the premises, to draw any conclusion logically contained in those premises. The second part of the Laws of Thought contained a corresponding attempt to discover a general method in probabilities, which should enable us from the given probabilities of any system of events to determine the consequent probability of any other event logically connected with the given events.

Though Boole published little except his mathematical and logical works, his acquaintance with general literature was wide and deep. Dante was his favourite poet, and he preferred the Paradiso to the Inferno. The metaphysics of Aristotle, the ethics of Spinoza, the philosophical works of Cicero, and many kindred works, were also frequent subjects of study. Metaphysics is the branch of Philosophy investigating principles of reality transcending those of any particular science Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. Ethics is a major branch of Philosophy, encompassing right conduct and good life Baruch or Benedict de Spinoza (ברוך שפינוזה Bento de Espinosa Benedictus de Spinoza ( November 24, 1632 – February 21, Marcus Tullius Cicero ( Classical Latin ˈkikeroː usually ˈsɪsərəʊ in English January 3, 106 BC &ndash December 7, 43 BC was a Roman His reflections upon scientific, philosophical and religious questions are contained in four addresses upon The Genius of Sir Isaac Newton, The Right Use of Leisure, The Claims of Science and The Social Aspect of Intellectual Culture, which he delivered and printed at different times. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements

The personal character of Boole inspired all his friends with the deepest esteem. He was marked by true modesty, and his life was given to the single-minded pursuit of truth. The meaning of the word truth extends from Honesty, Good faith, and Sincerity in general to agreement with Fact or Reality Though he received a medal from the Royal Society for his memoir of 1844, and the honorary degree of LL.D. from the University of Dublin, he neither sought nor received the ordinary rewards to which his discoveries would entitle him. An honorary degree or a degree honoris causa ( Latin: 'for the sake of the honour' is an Academic degree for which a university (or other degree-awarding Doctor of Laws ( Latin: Legum Doctor, LLD) is a Doctorate -level Academic degree in Law. The University of Dublin, corporately designated the Chancellor Doctors and Masters of the University of Dublin (since the 19th century located in Dublin, On 8 December 1864, in the full vigour of his intellectual powers, he died of an attack of fever, ending in effusion on the lungs. Events 1609 - Biblioteca Ambrosiana opens its reading room the second public library of Europe. Year 1864 ( MDCCCLXIV) was a Leap year starting on Friday (link will display the full calendar of the Gregorian Calendar (or a Leap year In chemistry effusion is the process where individual molecules flow through a hole without collisions between molecules lung is the essential Respiration organ in air-breathing Animals including most Tetrapods a few Fish and a few Snails The most primitive

The Booles had five daughters:

• Mary, who married the mathematician and author Charles Howard Hinton and had three children (Howard, William and Joan)
• Margaret, whose son Geoffrey Ingram Taylor became a mathematician and a Fellow of the Royal Society
• Alicia, who made important contributions to four-dimensional geometry
• Lucy, a chemist
• Ethel Lilian, who married the Polish scientist and revolutionary Wilfrid Michael Voynich and is the author of the novel The Gadfly. Charles Howard Hinton (1853 &ndash 1907 was a British mathematician and writer of Science fiction works titled Scientific Romances. Sir Geoffrey Ingram Taylor OM ( 7 March 1886 - 27 June 1975) was a Physicist, Mathematician and expert on Fluid dynamics The Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660 Alicia Boole Stott ( June 8 1860 &ndash December 17 1940) was the third daughter of George Boole, born in Cork, Ireland Ethel Lilian Voynich, Née Boole ( May 11, 1864 – July 27, 1960) was a novelist and musician and a supporter of several Wilfrid Michael Voynich ( 31 October 1865 – 19 March 1930) born Michał Habdank-Wojnicz, was a Polish revolutionary The Gadfly is a Novel by Ethel Lilian Voynich, published in 1897 ( United States, June Great Britain, September of the

Legacy

Boole's work was extended and refined by William Stanley Jevons, Augustus De Morgan, Charles Peirce, and William Ernest Johnson. William Stanley Jevons ( September 1, 1835 - August 13, 1882) English Economist and Logician, was born in Augustus De Morgan ( 27 June, 1806 &ndash 18 March, 1871) was a British Mathematician and Logician. Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher William Ernest Johnson ( June 23, 1858 – January 14, 1931) was a British Logician mainly remembered for his Logic (1921–1924 This work was summarized by Ernst Schröder, Louis Couturat, and Clarence Irving Lewis. For the actor see Ernst Schröder (actor. Ernst Schröder ( 25 November, 1841 Mannheim Germany – Louis Couturat ( January 17, 1868 - August 3, 1914) was a French Logician mathematician, philosopher Clarence Irving Lewis ( April 12, 1883 Stoneham Massachusetts - February 3, 1964 Cambridge Massachusetts) usually

Boole's work (as well as that of his intellectual progeny) was relatively obscure except among logicians, and seemed to have no practical use. Approximately seventy years after Boole's death, Claude Shannon attended a philosophy class at the University of Michigan that introduced him to Boole's studies. Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information The University of Michigan Ann Arbor ( U of M, U-M, UM or simply Michigan) is a top-ranked Coeducational public research Shannon went on to write a master's thesis at the Massachusetts Institute of Technology, in which he showed how Boolean algebra could optimize the design of systems of electromechanical relays then used in telephone routing switches. A relay is an electrical Switch that opens and closes under the control of another Electrical circuit. He also proved that circuits with relays could solve Boolean algebra problems. Employing the properties of electrical switches to do logic is the basic concept that underlies all modern electronic digital computers. A computer is a Machine that manipulates data according to a list of instructions. Hence Boolean algebra became the foundation of practical digital circuit design; and Boole, via Shannon, provided the theoretical grounding for the Digital Age. Digital electronics are Electronics systems that use Digital signals Digital electronics are representations of Boolean algebra also see Information Age is a term that has been used to refer to the present era ^[2]

See also

• Boolean
• Boolean logic
• Digital electronics
• List of Boolean algebra topics
• Gottlob Frege
• Claude Shannon

External links

• O'Connor, John J. Boolean logic is a complete system for Logical operations It was named after George Boole, who first defined an algebraic system of Digital electronics are Electronics systems that use Digital signals Digital electronics are representations of Boolean algebra also see This is a list of topics around Boolean algebra and propositional logic. Friedrich Ludwig Gottlob Frege ( 8 November 1848, Wismar, Grand Duchy of Mecklenburg-Schwerin  &ndash 26 July 1925 Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information & Robertson, Edmund F. , “George Boole”, MacTutor History of Mathematics archive 
• Roger Parsons' article on Boole
• Works by George Boole at Project Gutenberg
• George Boole's work as first Professor of Mathematics in University College, Cork, Ireland
• Boole, G. (1854) An investigation of the laws of thought. Macmillan, London, at the Internet Archive. The MacTutor History of Mathematics archive is an award-winning website maintained by John J Project Gutenberg, abbreviated as PG, is a volunteer effort to Digitize, archive and distribute Cultural works The Internet Archive ( IA) is a Nonprofit organization dedicated to maintaining an on-line Library and archive of Web and

References