George Boole (; 2 November 1815 – 8 December 1864) was a largely
self-taught
Autodidacticism (also autodidactism) or self-education (also self-learning and self-teaching) is education without the guidance of masters (such as teachers and professors) or institutions (such as schools). Generally, autodidacts are individu ...
English
English usually refers to:
* English language
* English people
English may also refer to:
Peoples, culture, and language
* ''English'', an adjective for something of, from, or related to England
** English national ide ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
,
philosopher, and
logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
, most of whose short career was spent as the first professor of mathematics at
Queen's College, Cork
University College Cork – National University of Ireland, Cork (UCC) ( ga, Coláiste na hOllscoile Corcaigh) is a constituent university of the National University of Ireland, and located in Cork.
The university was founded in 1845 as one of ...
in Ireland. He worked in the fields of
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s and
algebraic logic, and is best known as the author of ''
The Laws of Thought
''An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities'' by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathem ...
'' (1854) which contains
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...
. Boolean logic is credited with laying the foundations for the
Information Age
The Information Age (also known as the Computer Age, Digital Age, Silicon Age, or New Media Age) is a historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during ...
.
Early life
Boole was born in 1815 in
Lincoln
Lincoln most commonly refers to:
* Abraham Lincoln (1809–1865), the sixteenth president of the United States
* Lincoln, England, cathedral city and county town of Lincolnshire, England
* Lincoln, Nebraska, the capital of Nebraska, U.S.
* Lincol ...
,
Lincolnshire
Lincolnshire (abbreviated Lincs.) is a Counties of England, county in the East Midlands of England, with a long coastline on the North Sea to the east. It borders Norfolk to the south-east, Cambridgeshire to the south, Rutland to the south-we ...
, England, the son of John Boole senior (1779–1848), a shoemaker and Mary Ann Joyce. He had a primary school education, and received lessons from his father, but due to a serious decline in business, he had little further formal and academic teaching. William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may also have learned at the school of Thomas Bainbridge. He was self-taught in modern languages.
[Hill, p. 149]
Google Books
. In fact, when a local newspaper printed his translation of a Latin poem, a scholar accused him of plagiarism under the pretence that he was not capable of such achievements. At age 16, Boole became the breadwinner for his parents and three younger siblings, taking up a junior teaching position in
Doncaster
Doncaster (, ) is a city in South Yorkshire, England. Named after the River Don, it is the administrative centre of the larger City of Doncaster. It is the second largest settlement in South Yorkshire after Sheffield. Doncaster is situated in ...
at Heigham's School.
[ Rhees, Rush. (1954) "George Boole as Student and Teacher. By Some of His Friends and Pupils", ''Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences''. Vol. 57. Royal Irish Academy] He taught briefly in
Liverpool
Liverpool is a city and metropolitan borough in Merseyside, England. With a population of in 2019, it is the 10th largest English district by population and its metropolitan area is the fifth largest in the United Kingdom, with a populat ...
.
Boole participated in the
Lincoln Mechanics' Institute, in the
Greyfriars, Lincoln, which was founded in 1833.
[ ]Edward Bromhead
Sir Edward Thomas ffrench Bromhead, 2nd Baronet FRS FRSE (26 March 1789 – 14 March 1855) was a British landowner and mathematician, best remembered as patron of the mathematician and physicist George Green and mentor of George Boole.
Life
Born ...
, who knew John Boole through the institution, helped George Boole with mathematics books and he was given the calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
text of Sylvestre François Lacroix by the Rev. George Stevens Dickson of St Swithin's, Lincoln. Without a teacher, it took him many years to master calculus.[
At age 19, Boole successfully established his own school in Lincoln: Free School Lane. Four years later he took over Hall's Academy in Waddington, outside Lincoln, following the death of Robert Hall. In 1840, he moved back to Lincoln, where he ran a boarding school.][ Boole immediately became involved in the Lincoln Topographical Society, serving as a member of the committee, and presenting a paper entitled "On the origin, progress, and tendencies of polytheism", especially amongst the ancient Egyptians and Persians, and in modern India.'
Boole became a prominent local figure, an admirer of John Kaye, the bishop. He took part in the local campaign for early closing.][ With Edmund Larken and others he set up a ]building society
A building society is a financial institution owned by its members as a mutual organization. Building societies offer banking and related financial services, especially savings and mortgage lending. Building societies exist in the United Kingd ...
in 1847. He associated also with the Chartist Thomas Cooper, whose wife was a relation.
From 1838 onwards, Boole was making contacts with sympathetic British academic mathematicians and reading more widely. He studied algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary ...
in the form of symbolic methods, as far as these were understood at the time, and began to publish research papers.[
]
Professorship and Life in Cork
Boole's status as a mathematician was recognised by his appointment in 1849 as the first professor of mathematics at Queen's College, Cork
University College Cork – National University of Ireland, Cork (UCC) ( ga, Coláiste na hOllscoile Corcaigh) is a constituent university of the National University of Ireland, and located in Cork.
The university was founded in 1845 as one of ...
(now University College Cork
University College Cork – National University of Ireland, Cork (UCC) ( ga, Coláiste na hOllscoile Corcaigh) is a constituent university of the National University of Ireland, and located in Cork.
The university was founded in 1845 as one ...
(UCC)) in Ireland. He met his future wife, Mary Everest, there in 1850 while she was visiting her uncle John Ryall who was professor of Greek. They married some years later in 1855. He maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution.[Hill, p. 138 note 4]
Google Books
.
Honours and awards
In 1844, Boole's paper "On a General Method in Analysis" won the first gold prize for mathematics awarded by the Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
. He was awarded the Keith Medal
The Keith Medal was a prize awarded by the Royal Society of Edinburgh, Scotland's national academy, for a scientific paper published in the society's scientific journals, preference being given to a paper containing a discovery, either in mathe ...
by the Royal Society of Edinburgh in 1855 and was elected a Fellow of the Royal Society (FRS) in 1857.[ He received ]honorary degrees
An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or '' ad hon ...
of LL.D.
Legum Doctor (Latin: “teacher of the laws”) (LL.D.) or, in English, Doctor of Laws, is a doctorate-level academic degree in law or an honorary degree, depending on the jurisdiction. The double “L” in the abbreviation refers to the early ...
from the University of Dublin and the University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
.
Works
Boole's first published paper was "Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order", printed in the '' Cambridge Mathematical Journal'' in February 1840 (Volume 2, 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.
In 1841, Boole published an influential paper in early invariant theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit descri ...
.[ He received a medal from the ]Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
for his memoir of 1844, "On a General Method in Analysis". It was a contribution to the theory of linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form
:a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b ...
s, moving from the case of constant coefficients on which he had already published, to variable coefficients. The innovation in operational methods is to admit that operations may not commute
Commute, commutation or commutative may refer to:
* Commuting, the process of travelling between a place of residence and a place of work
Mathematics
* Commutative property, a property of a mathematical operation whose result is insensitive to th ...
. In 1847, Boole published ''The Mathematical Analysis of Logic'', the first of his works on symbolic logic.
Differential equations
Boole completed two systematic treatises on mathematical subjects during his lifetime. The ''Treatise on Differential Equations'' appeared in 1859, and was followed, the next year, by a ''Treatise on the Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
of Finite Differences'', a sequel to the former work.
Analysis
In 1857, Boole published the treatise "On the Comparison of Transcendent, with Certain Applications to the Theory of Definite Integrals", in which he studied the sum of residues of a rational function. Among other results, he proved what is now called Boole's identity:
:
for any real numbers ''a''''k'' > 0, ''b''''k'', and ''t'' > 0. Generalisations of this identity play an important role in the theory of the Hilbert transform
In mathematics and in signal processing, the Hilbert transform is a specific linear operator that takes a function, of a real variable and produces another function of a real variable . This linear operator is given by convolution with the functi ...
.[
]
Symbolic logic
In 1847, Boole published the pamphlet ''Mathematical Analysis of Logic''. He later regarded it as a flawed exposition of his logical system and wanted '' An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities'' to be seen as the mature statement of his views. Contrary to widespread belief, Boole never intended to criticise or disagree with the main principles of Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ph ...
's logic. Rather he intended to systematise it, to provide it with a foundation, and to extend its range of applicability. Boole's initial involvement in logic was prompted by a current debate on quantification, between Sir William Hamilton who supported the theory of "quantification of the predicate", and Boole's supporter Augustus De Morgan who advanced a version of De Morgan duality
In propositional calculus, propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both Validity (logic), valid rule of inference, rules of inference. They are na ...
, as it is now called. Boole's approach was ultimately much further reaching than either sides' in the controversy. It founded what was first known as the "algebra of logic" tradition.[Witold Marciszewski (editor), ''Dictionary of Logic as Applied in the Study of Language'' (1981), pp. 194–5.]
Among his many innovations is his principle of wholistic reference
Wholistic reference is reference to the whole—with respect to the context. In its strongest, unqualified form, the principle of wholistic reference is the proposition that each and every proposition, regardless how limited the referents of its n ...
, which was later, and probably independently, adopted by Gottlob Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic ph ...
and by logicians who subscribe to standard first-order logic. A 2003 article provides a systematic comparison and critical evaluation of Aristotelian logic and Boolean logic; it also reveals the centrality of holistic reference in Boole's philosophy of logic
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application ...
.
1854 definition of the universe of discourse
In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined. The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them, the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. Sometimes, in discoursing of men we imply (without expressing the limitation) that it is of men only under certain circumstances and conditions that we speak, as of civilised men, or of men in the vigour of life, or of men under some other condition or relation. Now, whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the universe of discourse
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.
Overview
The doma ...
. Furthermore, this universe of discourse is in the strictest sense the ultimate subject of the discourse.
Treatment of addition in logic
Boole conceived of "elective symbols" of his kind as an algebraic structure. But this general concept was not available to him: he did not have the segregation standard in abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathe ...
of postulated (axiomatic) properties of operations, and deduced properties.[ Andrei Nikolaevich Kolmogorov, ]Adolf Pavlovich Yushkevich
Adolph-Andrei Pavlovich Yushkevich (russian: Адо́льф-Андре́й Па́влович Юшке́вич; 15 July 1906 – 17 July 1993) was a Soviet historian of mathematics, leading expert in medieval mathematics of the East and the work ...
, ''Mathematics of the 19th century: mathematical logic, algebra, number theory, probability theory'' (2001), pp. 15 (note 15)–16
Google Books
. His work was a beginning to the algebra of sets, again not a concept available to Boole as a familiar model. His pioneering efforts encountered specific difficulties, and the treatment of addition was an obvious difficulty in the early days.
Boole replaced the operation of multiplication by the word "and" and addition by the word "or". But in Boole's original system, + was a partial operation: in the language of set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
it would correspond only to disjoint union
In mathematics, a disjoint union (or discriminated union) of a family of sets (A_i : i\in I) is a set A, often denoted by \bigsqcup_ A_i, with an injection of each A_i into A, such that the images of these injections form a partition of A ( ...
of subsets. Later authors changed the interpretation, commonly reading it as exclusive or
Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false).
It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...
, or in set theory terms symmetric difference
In mathematics, the symmetric difference of two sets, also known as the disjunctive union, is the set of elements which are in either of the sets, but not in their intersection. For example, the symmetric difference of the sets \ and \ is \.
Th ...
; this step means that addition is always defined.[
In fact, there is the other possibility, that + should be read as ]disjunction
In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S ...
.[ 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 In mathematics, a Boolean ring ''R'' is a ring for which ''x''2 = ''x'' for all ''x'' in ''R'', that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2.
Every Boolean ring gives rise to a Boolean al ...
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.[
]
Probability theory
The second part of the ''Laws of Thought'' contained a corresponding attempt to discover a general method in probabilities. Here the goal was algorithmic: from the given probabilities of any system of events, to determine the consequent probability of any other event logically connected with those events.
Death
In late November 1864, Boole walked, in heavy rain, from his home at Lichfield Cottage in Ballintemple to the university, a distance of three miles, and lectured wearing his wet clothes. He soon became ill, developing pneumonia. As his wife believed that remedies should resemble their cause, she wrapped him in wet blankets – the wet having brought on his illness. Boole's condition worsened and on 8 December 1864, he died of fever-induced pleural effusion
A pleural effusion is accumulation of excessive fluid in the pleural space, the potential space that surrounds each lung.
Under normal conditions, pleural fluid is secreted by the parietal pleural capillaries at a rate of 0.6 millilitre per k ...
.
He was buried in the Church of Ireland
The Church of Ireland ( ga, Eaglais na hÉireann, ; sco, label= Ulster-Scots, Kirk o Airlann, ) is a Christian church in Ireland and an autonomous province of the Anglican Communion. It is organised on an all-Ireland basis and is the secon ...
cemetery of St Michael's, Church Road, Blackrock
BlackRock, Inc. is an American multi-national investment company based in New York City. Founded in 1988, initially as a risk management and fixed income institutional asset manager, BlackRock is the world's largest asset manager, with trill ...
(a suburb of Cork). There is a commemorative plaque inside the adjoining church.
Legacy
Boole is the namesake of the branch of algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary ...
known as Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...
, as well as the namesake of the lunar crater
Lunar craters are impact craters on Earth's Moon. The Moon's surface has many craters, all of which were formed by impacts. The International Astronomical Union currently recognizes 9,137 craters, of which 1,675 have been dated.
History
The wor ...
Boole. The keyword ''Bool'' represents a Boolean datatype
In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted ''true'' and ''false'') which is intended to represent the two truth values of logic and Boolean algebra. It is named ...
in many programming languages, though Pascal and Java
Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's mos ...
, among others, both use the full name ''Boolean''. The library, underground lecture theatre complex and the Boole Centre for Research in Informatics at University College Cork
University College Cork – National University of Ireland, Cork (UCC) ( ga, Coláiste na hOllscoile Corcaigh) is a constituent university of the National University of Ireland, and located in Cork.
The university was founded in 1845 as one ...
are named in his honour. A road called ''Boole Heights'' in Bracknell, Berkshire is named after him.
19th-century development
Boole's work was extended and refined by a number of writers, beginning with William Stanley Jevons
William Stanley Jevons (; 1 September 183513 August 1882) was an English economist and logician.
Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in ec ...
, who also authored the article about Boole in the ''Encyclopaedia Britannica''. Augustus De Morgan had worked on the logic of relations, and Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism".
Educated as a chemist and employed as a scientist for t ...
integrated his work with Boole's during the 1870s.[ Ivor Grattan-Guinness, ]Gérard Bornet
Gérard (French: ) is a French masculine given name and surname of Germanic origin, variations of which exist in many Germanic and Romance languages. Like many other early Germanic names, it is dithematic, consisting of two meaningful constitue ...
, ''George Boole: Selected manuscripts on logic and its philosophy'' (1997), p. xlvi
Google Books
. Other significant figures were Platon Sergeevich Poretskii, and William Ernest Johnson
William Ernest Johnson, FBA (23 June 1858 – 14 January 1931), usually cited as W. E. Johnson, was a British philosopher, logician and economic theorist.Zabell, S.L. (2008"Johnson, William Ernest (1858–1931)"In: Durlauf S.N., Blume L.E. ( ...
. The conception of a Boolean algebra structure on equivalent statements of a propositional calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations ...
is credited to Hugh MacColl
Hugh MacColl (before April 1885 spelled as Hugh McColl; 1831–1909) was a Scottish mathematician, logician and novelist.
Life
MacColl was the youngest son of a poor Highland family that was at least partly Gaelic-speaking. Hugh's father died ...
(1877), in work surveyed 15 years later by Johnson.[ Surveys of these developments were published by Ernst Schröder, ]Louis Couturat
Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido.
Life and education
Born in Ris-Orangis, Essonne, France. In 1887 he ...
, and Clarence Irving Lewis
Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logic ...
.
20th-century development
In 1921, the economist John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in ...
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. 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.
Boole's work and that of later logicians initially appeared to have no engineering uses. Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory".
As a 21-year-old master's degree student at the Massachusetts Inst ...
attended a philosophy class at the University of Michigan
, mottoeng = "Arts, Knowledge, Truth"
, former_names = Catholepistemiad, or University of Michigania (1817–1821)
, budget = $10.3 billion (2021)
, endowment = $17 billion (2021)As o ...
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
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
, in which he showed how Boolean algebra could optimise the design of systems of electromechanical relay
A relay
Electromechanical relay schematic showing a control coil, four pairs of normally open and one pair of normally closed contacts
An automotive-style miniature relay with the dust cover taken off
A relay is an electrically operated switch ...
s then used in telephone routing switches. He also proved that circuits with relays could solve Boolean algebra problems. Employing the properties of electrical switches to process logic is the basic concept that underlies all modern electronic digital computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These program ...
s. Victor Shestakov
Victor Ivanovich Shestakov (Russian: ) (1907–1987) was a Russian/Soviet logician and theoretician of electrical engineering. In 1935 he discovered the possible interpretation of Boolean algebra of logic in electro-mechanical relay circuits. He ...
at Moscow State University (1907–1987) proposed a theory of electric switches based on Boolean logic even earlier than Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory".
As a 21-year-old master's degree student at the Massachusetts Inst ...
in 1935 on the testimony of Soviet logicians and mathematicians Sofya Yanovskaya
Sofya Aleksandrovna Yanovskaya (also Janovskaja; russian: Софи́я Алекса́ндровна Яно́вская; 31 January 1896 – 24 October 1966) was a Soviet mathematician and historian, specializing in the history of mathematics, math ...
, Gaaze-Rapoport, Roland Dobrushin, Lupanov, Medvedev and Uspensky, though they presented their academic theses in the same year, 1938. But the first publication of Shestakov's result took place only in 1941 (in Russian). Hence, Boolean algebra became the foundation of practical digital circuit design; and Boole, via Shannon and Shestakov, provided the theoretical grounding for the Information Age
The Information Age (also known as the Computer Age, Digital Age, Silicon Age, or New Media Age) is a historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during ...
.
21st-century celebration
The year 2015 saw the 200th anniversary of Boole's birth. To mark the bicentenary year, University College Cork
University College Cork – National University of Ireland, Cork (UCC) ( ga, Coláiste na hOllscoile Corcaigh) is a constituent university of the National University of Ireland, and located in Cork.
The university was founded in 1845 as one ...
joined admirers of Boole around the world to celebrate his life and legacy.
UCC's George Boole 200 project, featured events, student outreach activities and academic conferences on Boole's legacy in the digital age, including a new edition of Desmond MacHale's 1985 biography '' The Life and Work of George Boole: A Prelude to the Digital Age'', 2014.
The search engine Google
Google LLC () is an American Multinational corporation, multinational technology company focusing on Search Engine, search engine technology, online advertising, cloud computing, software, computer software, quantum computing, e-commerce, ar ...
marked the 200th anniversary of his birth on 2 November 2015 with an algebraic reimaging of its Google Doodle
A Google Doodle is a special, temporary alteration of the logo on Google's homepages intended to commemorate holidays, events, achievements, and notable historical figures. The first Google Doodle honored the 1998 edition of the long-running an ...
.
Views
Boole's views were given in four published addresses: ''The Genius of Sir Isaac Newton''; ''The Right Use of Leisure''; ''The Claims of Science''; and ''The Social Aspect of Intellectual Culture''. The first of these was from 1835 when Charles Anderson-Pelham, 1st Earl of Yarborough
Charles Anderson-Pelham, 1st Earl of Yarborough (8 August 1781 – 5 September 1846), styled Hon. Charles Anderson-Pelham from 1794 to 1823, was one of the founders of the Royal Yacht Squadron and its first Commodore. He lived at Appuldurcombe Ho ...
gave a bust of Newton to the Mechanics' Institute in Lincoln. 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. ''The Claims of Science'' was given in 1851 at Queen's College, Cork. ''The Social Aspect of Intellectual Culture'' was also given in Cork, in 1855 to the Cuvierian Society.
Though his biographer Des MacHale describes Boole as an "agnostic deist", 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
Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in t ...
but in the end was said to have chosen Unitarianism
Unitarianism (from Latin ''unitas'' "unity, oneness", from ''unus'' "one") is a nontrinitarian branch of Christian theology. Most other branches of Christianity and the major Churches accept the doctrine of the Trinity which states that there i ...
. eference?/sup> Boole came to speak against what he saw as "prideful" scepticism, and instead favoured the belief in a "Supreme Intelligent Cause". He also declared "I firmly believe, for the accomplishment of a purpose of the Divine
Divinity or the divine are things that are either related to, devoted to, or proceeding from a deity.[divine< ...](_blank)
Mind." In addition, he stated that he perceived "teeming evidences of surrounding design
A design is a plan or specification for the construction of an object or system or for the implementation of an activity or process or the result of that plan or specification in the form of a prototype, product, or process. The verb ''to design' ...
" and concluded that "the course of this world is not abandoned to chance and inexorable fate."
Two influences on Boole were later claimed by his wife, Mary Everest Boole: a universal mysticism tempered by Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
thought, and Indian logic
The development of Indian logic dates back to the ''anviksiki'' of Medhatithi Gautama (c. 6th century BCE); the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 6th century BCE to 2nd centu ...
.[Jonardon Ganeri (2001), ''Indian Logic: a reader'', Routledge, p. 7, ]
Google Books
. Mary Boole stated that an adolescent mystical experience provided for his life's work:
My husband told me that when he was a lad of seventeen a thought struck him suddenly, which became the foundation of all his future discoveries. It was a flash of psychological insight into the conditions under which a mind most readily accumulates knowledge ..For a few years he supposed himself to be convinced of the truth of "the Bible" as a whole, and even intended to take orders as a clergyman of the English Church. But by the help of a learned Jew
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""T ...
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
Monism attributes oneness or singleness (Greek: μόνος) to a concept e.g., existence. Various kinds of monism can be distinguished:
* Priority monism states that all existing things go back to a source that is distinct from them; e.g., i ...
."[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]
In Ch. 13 of ''Laws of Thought'' Boole used examples of propositions from Baruch Spinoza and Samuel Clarke
Samuel Clarke (11 October 1675 – 17 May 1729) was an English philosopher and Anglican cleric. He is considered the major British figure in philosophy between John Locke and George Berkeley.
Early life and studies
Clarke was born in Norwich, ...
. The work contains some remarks on the relationship of logic to religion, but they are slight and cryptic. Boole was apparently disconcerted at the book's reception just as a mathematical toolset:
George afterwards learned, to his great joy, that the same conception of the basis of Logic was held by Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of ma ...
, the contemporary of Newton. De Morgan, of course, understood the formula in its true sense; he was Boole's collaborator all along. Herbert Spencer, Jowett, and Robert Leslie Ellis understood, I feel sure; and a few others, but nearly all the logicians and mathematicians ignored 53the statement that the book was meant to throw light on the nature of the human mind; and treated the formula entirely as a wonderful new method of reducing to logical order masses of evidence about external fact.
Mary Boole claimed that there was profound influence – via her uncle George Everest
Colonel Sir George Everest CB FRS FRAS FRGS (; 4 July 1790 – 1 December 1866) was a British surveyor and geographer who served as Surveyor General of India from 1830 to 1843.
After receiving a military education in Marlow, Everest joined ...
– of India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
n thought in general and Indian logic
The development of Indian logic dates back to the ''anviksiki'' of Medhatithi Gautama (c. 6th century BCE); the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 6th century BCE to 2nd centu ...
, in particular, on George Boole, as well as on Augustus De Morgan and Charles Babbage:
Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan, and George Boole on the mathematical atmosphere of 1830–65. What share had it in generating the Vector Analysis
Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subjec ...
and the mathematics by which investigations in physical science are now conducted?
Boole maintained that:
Family
In 1855, Boole married Mary Everest (niece of George Everest
Colonel Sir George Everest CB FRS FRAS FRGS (; 4 July 1790 – 1 December 1866) was a British surveyor and geographer who served as Surveyor General of India from 1830 to 1843.
After receiving a military education in Marlow, Everest joined ...
), who later wrote several educational works on her husband's principles.
The Booles had five daughters:
* Mary Ellen (1856–1908) who married the mathematician and author Charles Howard Hinton and had four children: George (1882–1943), Eric (*1884), William (1886–1909) and Sebastian (1887–1923), inventor of the Jungle gym. After the sudden death of her husband, Mary Ellen committed suicide in Washington, D.C.
)
, image_skyline =
, image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, ...
in May 1908. Sebastian had three children:
** Jean Hinton (married name Rosner) (1917–2002), a peace activist.
** William H. Hinton (1919–2004) visited China in the 1930s and 40s and wrote an influential account of the Communist land reform.
** Joan Hinton (1921–2010) worked for the Manhattan Project
The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
and lived in China from 1948 until her death on 8 June 2010; she was married to Sid Engst.
* Margaret (1858–1935), married Edward Ingram Taylor, an artist.
** Their elder son Geoffrey Ingram Taylor
Sir Geoffrey Ingram Taylor OM FRS FRSE (7 March 1886 – 27 June 1975) was a British physicist and mathematician, and a major figure in fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as ...
became a mathematician and a Fellow of the Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
.
** Their younger son Julian Taylor was a professor of surgery.
* Alicia (1860–1940), who made important contributions to four-dimensional geometry.
** Her son Leonard Stott, a medical doctor and tuberculosis pioneer, invented a portable X-ray machine
An X-ray machine is any machine that involves X-rays. It may consist of an X-ray generator and an X-ray detector.
Examples include:
*Machines for medical projectional radiography
*Machines for computed tomography
*Backscatter X-ray machines, used ...
, a pneumothorax
A pneumothorax is an abnormal collection of air in the pleural space between the lung and the chest wall. Symptoms typically include sudden onset of sharp, one-sided chest pain and shortness of breath. In a minority of cases, a one-way valve i ...
apparatus, and system of navigation based on spherical coordinates.[D. MacHale, ''The Life and Work of George Boole: A Prelude to the Digital Age'', Cork University Press, 2014. cited in ]
The Extraordinary Case of the Boole Family
'' by Moira Chas
* Lucy Everest (1862–1904), who was the first female professor of chemistry in England.
* Ethel Lilian (1864–1960), who married the Polish scientist and revolutionary Wilfrid Michael Voynich
Wilfrid Voynich (born Michał Habdank-Wojnicz; Telšiai, Деятели революционного движения в России: Био-библиографический словарь: От предшественников декабри� ...
and was the author of the novel ''The Gadfly
''The Gadfly'' is a novel by Irish-born British writer Ethel Voynich, published in 1897 (United States, June; Great Britain, September of the same year), set in 1840s Italy under the dominance of Austria, a time of tumultuous revolt and upris ...
''.
See also
Concepts
* Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas i ...
, a logical calculus of truth values or set membership
* Boolean algebra (structure), a set with operations resembling logical ones
* Boolean circuit
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible inp ...
, a mathematical model for digital logical circuits.
* Boolean data type
In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted ''true'' and ''false'') which is intended to represent the two truth values of logic and Boolean algebra. It is named ...
is a data type, having two values (usually denoted true and false)
* Boolean expression
In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean c ...
, an expression in a programming language that produces a Boolean value when evaluated
* Boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...
, a function that determines Boolean values or operators
* Boolean model (probability theory), a model in stochastic geometry
* Boolean network, a certain network consisting of a set of Boolean variables whose state is determined by other variables in the network
* Boolean processor, a 1-bit variables computing unit
* Boolean ring In mathematics, a Boolean ring ''R'' is a ring for which ''x''2 = ''x'' for all ''x'' in ''R'', that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2.
Every Boolean ring gives rise to a Boolean al ...
, a ring consisting of idempotent elements
* Boolean satisfiability problem
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfie ...
* Boole's syllogistic is a logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the "empty set".
* Laws of thought
The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based. The formulation and clarification of such rules have a long tradition in the history of philosophy and logic. Generally th ...
* Principle of wholistic reference
Wholistic reference is reference to the whole—with respect to the context. In its strongest, unqualified form, the principle of wholistic reference is the proposition that each and every proposition, regardless how limited the referents of its n ...
Other
* List of Boolean algebra topics
This is a list of topics around Boolean algebra and propositional logic.
Articles with a wide scope and introductions
* Algebra of sets
* Boolean algebra (structure)
* Boolean algebra
* Field of sets
* Logical connective
* Prop ...
* List of pioneers in computer science
This is a list of people who made transformative breakthroughs in the creation, development and imagining of what computers could do.
Pioneers
: ''To arrange the list by date or person (ascending or descending), click that column's small "up-do ...
Notes
References
* Walker, A. (ed) (2019) ''George Boole's Lincoln, 1815–49.'' The Survey of Lincoln, Vol.16.
* University College Cork
University College Cork – National University of Ireland, Cork (UCC) ( ga, Coláiste na hOllscoile Corcaigh) is a constituent university of the National University of Ireland, and located in Cork.
The university was founded in 1845 as one ...
, ''George Boole 200 Bicentenary Celebration''
GeorgeBoole.com
* Ivor Grattan-Guinness, ''The Search for Mathematical Roots 1870–1940''. Princeton University Press. 2000.
* Francis Hill (1974), ''Victorian Lincoln''
Google Books
.
* Des MacHale, '' George Boole: His Life and Work''
Boole Press
1985.
* Des MacHale, '' The Life and Work of George Boole: A Prelude to the Digital Age'' (new edition)
Cork University Press
. 2014
* Stephen Hawking, '' God Created the Integers''. Running Press, Philadelphia. 2007.
External links
Roger Parsons' article on Boole
*
*
by George Boole; a transcription of an article which originally appeared in ''Cambridge and Dublin Mathematical Journal'', Vol. III (1848), pp. 183–98.
George Boole's work as first Professor of Mathematics in University College, Cork, Ireland
George Boole website
Author profile
in the database zbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastruct ...
*
{{DEFAULTSORT:Boole, George
1815 births
1864 deaths
19th-century British mathematicians
19th-century British non-fiction writers
19th-century British philosophers
19th-century British writers
19th-century English mathematicians
19th-century English non-fiction writers
19th-century English philosophers
19th-century English writers
19th-century essayists
19th-century translators
Academics of Queens College Cork
Boolean algebra
British deists
British essayists
British innovators
British male non-fiction writers
British mathematicians
British translators
British Unitarians
Respiratory disease deaths in Ireland
English essayists
English innovators
English logicians
English mathematicians
English non-fiction writers
English translators
English Unitarians
Fellows of the Royal Society
History of algebra
History of logic
History of mathematics
History of philosophy
History of science
Mathematical logicians
People from Lincoln, England
Philosophers of logic
Philosophers of mathematics
Probability theorists
Royal Medal winners
Victorian writers