No general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.[4] Contents 1 Early life 2 Professor at Cork 3 Honours and awards 4 Works 4.1 Differential equations 4.2 Analysis 4.3 Symbolic logic 4.3.1 1854 definition of universe of discourse 4.3.2 Treatment of addition in logic 4.4 Probability theory 5 Death 6 Legacy 6.1 19th-century development 6.2 20th-century development 6.3 21st-century celebration 7 Views 8 Family 9 See also 10 Notes 11 References 12 External links Early life[edit] Boole's House and School at 3 Pottergate in Lincoln Boole was born in Lincoln, Lincolnshire, England, the son of John
Boole senior (1779–1848), a shoemaker[5] and Mary Ann Joyce.[6] 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.[7] 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.[2] 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.[8] At age 16,
Boole became the breadwinner for his parents and three younger
siblings, taking up a junior teaching position in
Greyfriars, Lincoln, which housed the Mechanic's Institute Boole participated in the Mechanics Institute, in the Greyfriars,
Lincoln, which was founded in 1833.[2][10] Edward Bromhead, who knew
John Boole through the institution, helped
Plaque from the house in Lincoln From 1838 onwards Boole was making contacts with sympathetic British academic mathematicians and reading more widely. He studied algebra in the form of symbolic methods, as far as these were understood at the time, and began to publish research papers.[1] Professor at Cork[edit] The house at 5 Grenville Place in Cork, in which Boole lived between
1849 and 1855, and where he wrote
Boole's status as mathematician was recognised by his appointment in
1849 as the first professor of mathematics at Queen's College, Cork
(now
Boole's gravestone in Blackrock, Cork, Ireland Detail of stained glass window in
Plaque beneath Boole's window in Lincoln Cathedral Works[edit]
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
m e s x ∈ R ∣ ℜ 1 π ∑ a k x − b k ≥ t = ∑ a k π t displaystyle mathrm mes left xin mathbb R ,mid ,Re frac 1 pi sum frac a_ k x-b_ k geq tright = frac sum a_ k pi t for any real numbers ak > 0, bk, and
t > 0.[29] Generalisations of this identity play an
important role in the theory of the Hilbert transform.[29]
Symbolic logic[edit]
Main article: Boolean algebra
In 1847 Boole published the pamphlet Mathematical Analysis of Logic.
He later regarded it as a flawed exposition of his logical system, and
wanted An Investigation of the Laws of Thought on Which are Founded
the Mathematical Theories of
In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined. The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. Sometimes, in discoursing of men we imply (without expressing the limitation) that it is of men only under certain circumstances and conditions that we speak, as of civilised men, or of men in the vigour of life, or of men under some other condition or relation. Now, whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the universe of discourse. Furthermore, this universe of discourse is in the strictest sense the ultimate subject of the discourse.[34] Treatment of addition in logic[edit]
Boole conceived of "elective symbols" of his kind as an algebraic
structure. But this general concept was not available to him: he did
not have the segregation standard in abstract algebra of postulated
(axiomatic) properties of operations, and deduced properties.[35] 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 it would correspond
only to disjoint union of subsets. Later authors changed the
interpretation, commonly reading it as exclusive or, or in set theory
terms symmetric difference; this step means that addition is always
defined.[32][36]
In fact there is the other possibility, that + should be read as
disjunction.[35] 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 rings 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.[12]
Probability theory[edit]
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.[37]
Death[edit]
In late November 1864, Boole walked, in heavy rain, from his home at
Lichfield Cottage in Ballintemple[38] to the university, a distance of
three miles, and lectured wearing his wet clothes.[39] He soon became
ill, developing pneumonia. As his wife believed that remedies should
resemble their cause, she put her husband to bed and poured buckets of
water over him – the wet having brought on his illness.[39][40][41]
Boole's condition worsened and on 8 December 1864,[42] he died of
fever-induced pleural effusion.
He was buried in the
Bust of Boole at University College Cork
In modern notation, the free
In 1921 the economist
21st-century celebration[edit] "Boole's legacy surrounds us everywhere, in the computers, information storage and retrieval, electronic circuits and controls that support life, learning and communications in the 21st century. His pivotal advances in mathematics, logic and probability provided the essential groundwork for modern mathematics, microelectronic engineering and computer science." —University College Cork.[3] 2015 saw the 200th anniversary of George Boole's birth. To mark the
bicentenary year,
My husband told me that when he was a lad of seventeen a thought struck him suddenly, which became the foundation of all his future discoveries. It was a flash of psychological insight into the conditions under which a mind most readily accumulates knowledge [...] For a few years he supposed himself to be convinced of the truth of "the Bible" as a whole, and even intended to take orders as a clergyman of the English Church. But by the help of a learned Jew in Lincoln he found out the true nature of the discovery which had dawned on him. This was that man's mind works by means of some mechanism which "functions normally towards Monism."[66] In Ch. 13 of Laws of Thought Boole used examples of propositions from
George afterwards learned, to his great joy, that the same conception
of the basis of
Mary Boole claimed that there was profound influence — via her uncle
Think what must have been the effect of the intense Hinduizing of
three such men as Babbage, De Morgan, and
Family[edit] In 1855 he married Mary Everest (niece of George Everest), who later wrote several educational works on her husband's principles. The Booles had five daughters: Mary Ellen(1856–1908)[68] who married the mathematician and author
Jean Hinton (married name Rosner) (1917–2002) peace activist.
Margaret, (1858 – 1935) married Edward Ingram Taylor, an artist. Their elder son
Alicia (1860–1940), who made important contributions to
four-dimensional geometry.
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
See also[edit]
Boolean algebra, a logical calculus of truth values or set membership
Notes[edit] ^ a b c d e O'Connor, John J.; Robertson, Edmund F., "George Boole",
MacTutor History of Mathematics archive, University of St
Andrews .
^ a b c d Hill, p. 149;
References[edit] University College Cork,
External links[edit] Find more aboutGeorge Booleat's sister projects Media from Wikimedia Commons Quotations from Wikiquote Texts from Wikisource Data from Wikidata Roger Parsons' article on Boole
George Boole: A 200-Year View by Stephen Wolfram.
Works by
Authority control WorldCat Identities VIAF: 49282014 LCCN: n83144364 ISNI: 0000 0001 1061 4506 GND: 118661655 SELIBR: 326365 SUDOC: 028119339 BNF: cb122540641 (data) NLA: 35704306 NDL: 00433839 NKC: ola2002153861 BNE: XX1165 |