Western Philosophy 19th-century philosophy
George Boole
Name In the 18th century the philosophies of The Enlightenment would begin to have dramatic effect, and the landmark works of philosophers such as Immanuel Kant and Jean-Jacques Rousseau would have an electrifying effect on a new generation of thinkers. ... Image File history File links No higher resolution available. ...	George Boole
Birth	November 2, 1815 ( Lincoln, Lincolnshire, England ) is the 306th day of the year (307th in leap years) in the Gregorian calendar. ... April 5-12: Mount Tambora explodes, changing climate. ... Lincoln (pronounced //) is a cathedral city and county town of Lincolnshire, England. ... For other uses, see England (disambiguation). ...
Death	December 8, 1864 ( Ballintemple, County Cork, Ireland ) is the 342nd day of the year (343rd in leap years) in the Gregorian calendar. ... 1864 (MDCCCLXIV) was a leap year starting on Friday (see link for calendar) of the Gregorian calendar or a leap year starting on Sunday of the 12-day-slower Julian calendar. ... Ballintemple (from the Irish Gaelic ’Baile an Teampaill’, the town of the church) is a suburb of Cork City, Ireland. ... Statistics Province: Munster County Town: Cork Code: C (CK proposed) Area: 7,457 km² Population (2006) 480,909 (including City of Cork); 361,766 (without Cork City) Website: www. ...
School/tradition	Mathematical foundations of computer science Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...
Main interests	Mathematics, Logic, Philosophy of mathematics For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... // Philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. ...
Notable ideas	Boolean algebra Boolean algebra is the finitary algebra of two values. ...
Influences	Aristotle, Spinoza, Newton For other uses, see Aristotle (disambiguation). ... Baruch de Spinoza (‎, Portuguese: , Basque: , Latin: ) (November 24, 1632 – February 21, 1677) was a Dutch philosopher of Portuguese Jewish origin. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ...
Influenced	Modern computer scientists, Jevons, De Morgan, Peirce, Johnson, Shannon [William Stanley Jevons] William Stanley Jevons (September 1, 1835 - August 13, 1882), English economist and logician, was born in Liverpool. ... The tone or style of this article or section may not be appropriate for Wikipedia. ... Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... William Ernest Johnson (June 23, 1858 – January 14, 1931) was a British logician known for his three volume work Logic (1921-1924). ... Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001), an American electrical engineer and mathematician, has been called the father of information theory,[1] and was the founder of practical digital circuit design theory. ...

George Boole (IPA: [buːl]) (November 2, 1815 – December 8, 1864) was a British mathematician and philosopher. George Stephen Boolos (September 4, 1940, New York City - May 27, 1996) was a philosopher and a mathematical logician. ... Boole is a lunar crater that lies along the northwestern limb of the Moon, to the northwest of Gerard crater. ... is the 306th day of the year (307th in leap years) in the Gregorian calendar. ... April 5-12: Mount Tambora explodes, changing climate. ... is the 342nd day of the year (343rd in leap years) in the Gregorian calendar. ... 1864 (MDCCCLXIV) was a leap year starting on Friday (see link for calendar) of the Gregorian calendar or a leap year starting on Sunday of the 12-day-slower Julian calendar. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ...

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, although computers did not exist in his day. (See "Legacy" below.) Boolean algebra is the finitary algebra of two values. ... This article is about the machine. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...

Biography

George Boole's father, John Boole (1779-1848), was a tradesman of limited means, but of studious character and active mind. 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. At first his favourite subject was classics. Not until the age of 17 did he attack the higher mathematics, and his progress was slowed by a lack of efficient help. When he was about sixteen years of age he became assistant-master in a private school at Doncaster, Yorkshire in the United Kingdom, and he maintained himself to the end of his life in one grade or other of the scholastic profession. He was a teacher in Mr William Marrats school in Liverpool in 1833. Few distinguished men, indeed, have had a less eventful life. Almost the only changes which can be called events are his successful establishment of a school at Lincoln, its removal to Waddington, 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, and his marriage in 1855 to Miss Mary Everest (niece of George Everest), who, as Mrs. Boole, afterwards wrote several useful educational works on her husband's principles. Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of figures and numbers. Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... For other places with the same name, see Doncaster (disambiguation). ... Look up Yorkshire in Wiktionary, the free dictionary. ... Lincoln (pronounced Lin-kun) is a cathedral city and county town of Lincolnshire, England, a bridging point over the River Witham that flows to Boston. ... Waddington village (left), and RAF base Waddington (population of 6086 at Census 2001) is a large rural commuter village in the North Kesteven district of Lincolnshire, England. ... University College Cork - National University of Ireland, Cork - or more commonly University College Cork (UCC) - is a constituent university of the National University of Ireland and is located in Cork. ... Photograph of Everest Colonel Sir George Everest (4 July 1790 – 1 December 1866) was a Welsh surveyor, geographer and Surveyor-General of India from 1830 to 1843. ...

To the 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 one upon the "Theory of Analytical Transformations," printed in the Cambridge Mathematical Journal for 1839, 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, will be found 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 in all twenty-two articles. In the third and fourth series of the Philosophical Magazine will be 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. iv. pp. 198-215), and in Crelle's Journal. To these lists should be added a paper on the mathematical basis of logic, published in the Mechanic's Magazine for 1848. The works of Boole are thus contained in about fifty scattered articles and a few separate publications. For other uses, see Royal Society (disambiguation). ... In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... Isaac Todhunter (November 23, 1820 – March 1, 1884), was an English mathematician. ... This article is about the city in England. ... For other uses, see Dublin (disambiguation). ... The Royal Society of Edinburghs Building on the corner of George St. ... The Royal Irish Academy (RIA) is one of Irelands premier learned societies and cultural institutions. ... Crelles Journal, or just Crelle, is the common name for the Journal für die reine und angewandte Mathematik founded by August Leopold Crelle. ...

Only two systematic treatises on mathematical subjects were completed by Boole during his lifetime. 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. These treatises are valuable contributions to the important branches of mathematics in question, and Boole, in composing them, seems to have combined elementary exposition with the profound investigation of the philosophy of the subject in a manner hardly admitting of improvement. 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, a lucid 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. Look up Treatise in Wiktionary, the free dictionary. ... For other uses, see Calculus (disambiguation). ...

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. 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 wisely printed them, in 1865, in a supplementary volume. The British Museum in London, England is a museum of human history and culture. ...

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. 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. 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. Nevertheless, there is a charm of originality about his earlier logical work which is easy to appreciate. The tone or style of this article or section may not be appropriate for Wikipedia. ... John Wallis John Wallis (November 22, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the development of modern calculus. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... For other uses, see Calculus (disambiguation). ... Reasoning is the mental (cognitive) process of looking for reasons to support beliefs, conclusions, actions or feelings. ... 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 19th century book on logic by George Boole, the second of his two monographs on algebraic logic. ...

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. 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. 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. Analogy is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ... This article is about the branch of mathematics. ... A syllogism (Greek: — conclusion, inference), usually the categorical syllogism, is a kind of logical argument in which one proposition (the conclusion) is inferred from two others (the premises) of a certain form. ... Look up literal, literally in Wiktionary, the free dictionary. ... For other uses, see Combination (disambiguation). ... This article is about the word proposition as it is used in logic, philosophy, and linguistics. ... An equation is a mathematical statement, in symbols, that two things are the same (or equivalent). ... In mathematics and logic, premises are the formulas on which a step of a logical argument depends to obtain a consequence of those premises. ...

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. 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. Inference is the act or process of deriving a conclusion based solely on what one already knows. ...

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. 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. DANTE is also a digital audio network. ... Plato (Left) and Aristotle (right), by Raphael (Stanza della Segnatura, Rome) Metaphysics is the branch of philosophy concerned with explaining the ultimate nature of reality, being, and the world. ... For other uses, see Aristotle (disambiguation). ... For other uses, see Ethics (disambiguation). ... Baruch de Spinoza (‎, Portuguese: , Basque: , Latin: ) (November 24, 1632 – February 21, 1677) was a Dutch philosopher of Portuguese Jewish origin. ... For other uses, see Cicero (disambiguation). ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ...

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. 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. 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, caused by giving a lecture in wet clothes from the rain. Time Saving Truth from Falsehood and Envy, François Lemoyne, 1737 For other uses, see Truth (disambiguation). ... An honorary degree (Latin: honoris causa ad gradum, not to be confused with an honors degree) is an academic degree awarded to an individual as a decoration, rather than as the result of matriculating and studying for several years. ... Legum Doctor (English: Doctor of Laws; abbreviated to LL.D.) In the UK the LL.D. is a higher doctorate awarded on the basis of exceptionally insightful and distinctive publications, containing significant and original contributions to the science or study of law. ... The University of Dublin, corporately designated the Chancellor, Doctors and Masters of the University of Dublin located in Dublin, Ireland, was founded in 1592 by Queen Elizabeth I, making it Irelands oldest university. ... is the 342nd day of the year (343rd in leap years) in the Gregorian calendar. ... 1864 (MDCCCLXIV) was a leap year starting on Friday (see link for calendar) of the Gregorian calendar or a leap year starting on Sunday of the 12-day-slower Julian calendar. ... Effusion can refer to: In literature, effusion is the process of opening the flood gates to ones emotions, so to speak. ... Human respiratory system The lungs flank the heart and great vessels in the chest cavity. ...

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 (1853-1907) was a British mathematician and writer of science fiction works that he called scientific romances. ... Sir Geoffrey Ingram Taylor (7 March 1886 - 27 June 1975) was a physicist, mathematician and expert on fluid dynamics and wave theory. ... For other uses, see Royal Society (disambiguation). ... Alicia Boole Stott (June 8, 1860 - December 17, 1940) was the third daughter of George Boole. ... Ethel Lilian Voynich, née Boole (May 11, 1864, County Cork, Ireland - July 27, 1960, New York City) was a novelist and musician, and a supporter of several revolutionary causes. ... Wilfrid Michael Voynich, or Wilfryd Michał Habdank-Wojnicz (31 October 1865 – 19 March 1930), was a Polish-born American bibliophile. ... The Gadfly is a novel by Ethel Lilian Voynich (1864-1960). ...

Legacy

Boole's work was extended and refined by William Stanley Jevons, Augustus De Morgan, Charles Peirce, and William Ernest Johnson. This work was summarized by Ernst Schröder, Louis Couturat, and Clarence Irving Lewis. [William Stanley Jevons] William Stanley Jevons (September 1, 1835 - August 13, 1882), English economist and logician, was born in Liverpool. ... The tone or style of this article or section may not be appropriate for Wikipedia. ... Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... William Ernest Johnson (June 23, 1858 – January 14, 1931) was a British logician known for his three volume work Logic (1921-1924). ... Ernst Schröder Ernst Schröder (25 November 1841 Mannheim, Germany - 16 June 1902 Karlsruhe Germany) was a German mathematician mainly known for his work on algebraic logic. ... Louis Couturat (January 17, 1868 - August 3, 1914) was a French logician, mathematician, philosopher, and linguist. ... Clarence Irving Lewis (April 12, 1883 Stoneham, Massachusetts - February 3, 1964 Cambridge, Massachusetts) was an American academic philosopher. ...

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 discovered Boolean algebra while taking a philosophy class at the University of Michigan. 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. 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. Hence Boolean algebra became the foundation of practical digital circuit design; and Boole, via Shannon, provided the theoretical grounding for the Digital Age. Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001), an American electrical engineer and mathematician, has been called the father of information theory,[1] and was the founder of practical digital circuit design theory. ... The University of Michigan, Ann Arbor (U of M, UM or simply Michigan) is a coeducational public research university in the state of Michigan, and one of the foremost universities in the United States. ... “MIT” redirects here. ... Relay as used in cars A relay is an electromechanical switch that uses an electromagnet to open or close one or many sets of contacts. ... ... Digital circuits are electric circuits based on a number of discrete voltage levels. ... It has been suggested that this article or section be merged into Information Age. ...

See also

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

For use in mathematics, see Boolean algebra (structure). ... Boolean logic is a complete system for logical operations. ... A digital circuit that acts as a binary clock, hand-wired on a series of breadboards Digital electronics are electronics systems that use digital signals. ... Algebra of sets George Boole Boolean algebra Boolean function Boolean logic Boolean homomorphism Boolean Implicant Boolean prime ideal theorem Boolean-valued model Boolean satisfiability problem Booles syllogistic canonical form (Boolean algebra) compactness theorem Complete Boolean algebra connective -- see logical operator de Morgans laws Augustus De Morgan duality (order... Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, IPA: ) was a German mathematician who became a logician and philosopher. ...

External links

• O'Connor, John J; Edmund F. Robertson "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

The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... Project Gutenberg, abbreviated as PG, is a volunteer effort to digitize, archive and distribute cultural works. ...

References

• This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.
• Ivor Grattan-Guinness, The Search for Mathematical Roots 1870-1940. Princeton University Press. 2000.

Logic Portal