William Ernest Johnson
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William Ernest Johnson, FBA (23 June 1858 – 14 January 1931), usually cited as W. E. Johnson, was a British philosopher,
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 ...
and economic theorist.Zabell, S.L. (2008
"Johnson, William Ernest (1858–1931)"
In: Durlauf S.N., Blume L.E. (eds) ''The New Palgrave Dictionary of Economics.''(2nd ed, 2008.) Palgrave Macmillan, Londo
also online
/ref> He is mainly remembered for his 3 volume ''Logic'' which introduced the concept of
exchangeability In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence ''X''1, ''X''2, ''X''3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change whe ...
.


Life and career

Johnson was born in Cambridge on 23 June 1858 to William Henry Farthing Johnson and his wife, Harriet (''née'' Brimley). He was their fifth child. The family were Baptists and political liberals. He attended the Llandaff House School, Cambridge where his father was the proprietor and headteacher, then the
Perse School (He who does things for others does them for himself) , established = , closed = , type = Public schoolIndependent day school , religion = Nondenominational Christian , president = , head_label = Head , he ...
, Cambridge, and the Liverpool Royal Institution School. At the age of around eight he became seriously ill and developed severe asthma and lifelong ill health. Due to this his education was frequently disrupted. In 1879 he entered
King's College, Cambridge King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the city ...
to read mathematics having won a scholarship and was placed 11th Wrangler in 1882. He stayed on to study for the Moral Sciences Tripos from which he graduated in 1883 with a First Class degree. He was also a
Cambridge Apostle The Cambridge Apostles (also known as ''Conversazione Society'') is an intellectual society at the University of Cambridge founded in 1820 by George Tomlinson, a Cambridge student who became the first Bishop of Gibraltar.W. C. Lubenow, ''The Ca ...
. In 1895 he married Barbara Keymer. After her sudden death in 1904 his sister Fanny moved in with him to care for his two sons. Having failed to win a prize fellowship, he taught mathematics. His first teaching post was as a lecturer in Psychology and Education at the Cambridge Women's Training College ,which he held for several years. He was a University Teacher of Theory of Education 1893-98 and, from 1896 until 1901, University Lecturer in Moral Sciences at the
University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
. In 1902 he was elected a
Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...
of King's College, and appointed to the (newly-created) Sidgwick Lecturership, positions he held until his death. In 1923 he was elected a Fellow of the
British Academy The British Academy is the United Kingdom's national academy for the humanities and the social sciences. It was established in 1902 and received its royal charter in the same year. It is now a fellowship of more than 1,000 leading scholars span ...
. Johnson's students included I. A. Richards,
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 ...
, Frank Ramsey,
Dorothy Wrinch Dorothy Maud Wrinch (12 September 1894 – 11 February 1976; married names Nicholson, Glaser) was a mathematician and biochemical theorist best known for her attempt to deduce protein structure using mathematical principles. She was a champion o ...
,
C. D. Broad Charlie Dunbar Broad (30 December 1887 – 11 March 1971), usually cited as C. D. Broad, was an English people, English epistemology, epistemologist, history of philosophy, historian of philosophy, philosophy of science, philosopher of sc ...
,
R. B. Braithwaite Richard Bevan Braithwaite (15 January 1900 – 21 April 1990) was an English philosopher who specialized in the philosophy of science, ethics, and the philosophy of religion. Life Braithwaite was born in Banbury, Oxfordshire, son of th ...
and
Susan Stebbing Lizzie Susan Stebbing (2 December 1885 – 11 September 1943) was a British philosopher. She belonged to the 1930s generation of analytic philosophy, and was a founder in 1933 of the journal ''Analysis.'' Stebbing was the first woman to hold a p ...
. In 1912 (at
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...
's request) Johnson also attempted to 'coach'
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considere ...
in logic but this was an arrangement that was both brief and unsuccessful. He died in
St Andrew's Hospital St Andrews Hospital is a mental health facility in Northampton, England. It is managed by St Andrew's Healthcare. History Formation The facility was founded by public subscription for "private and pauper lunatics" and opened as the Northampton ...
, Northampton, on 14 January 1931 and is buried at Grantchester, Cambridgeshire.


Work

Johnson, who suffered poor health, published little. That, though "very able", he was "lacking in vigour" and had "published almost nothing" is a matter Bertrand Russell commented upon unsympathetically in a letter to
Ottoline Morrell Lady Ottoline Violet Anne Morrell (16 June 1873 – 21 April 1938) was an English aristocrat and society hostess. Her patronage was influential in artistic and intellectual circles, where she befriended writers including Aldous Huxley, Siegfr ...
of 23 February 1913. Johnson's obituary in ''
The Times ''The Times'' is a British daily national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its current name on 1 January 1788. ''The Times'' and its sister paper ''The Sunday Times'' (fou ...
,'' penned by J. M. Keynes, more kindly reports that "his critical intellect did not readily lend itself to authorship". A memorial in ''
Mind The mind is the set of faculties responsible for all mental phenomena. Often the term is also identified with the phenomena themselves. These faculties include thought, imagination, memory, will, and sensation. They are responsible for various m ...
'' also proffered a charitable partial explanation of his reluctance to publish. Johnson's major publication was a three volume work ''Logic'' (1921,1922, 1924) which was based on his lectures. This may never have been published if it had not been for the efforts of Newnham student Naomi Bentwich (1891–1988). Bentwich persuaded him to publish, typed and co-edited the manuscript and encouraged him to finish the project. The preface to the first volume carries the acknowledgement: "I have to express my great obligations to my former pupil, Miss Naomi Bentwich, without whose encouragement and valuable assistance in the composition and arrangement of the work, it would not have been produced in its present form". A fourth volume on probability was never finished, but parts of it would be published posthumously as articles in ''Mind''. ''Logic'' ensured his election to the British Academy and won him honorary degrees from the universities of Manchester and Aberdeen. Though conceding that ''Logic'' was "dated", even at publication, Sébastien Gandon argues that it would be unfair, given "the richness of his thought", to see Johnson "only as a member of the British logic 'old guard' pushed aside by the ''
Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...
''" of
Alfred North Whitehead Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found applicat ...
and Bertrand Russell. Gandon contends that "many of Johnson's insights are today an integral part of philosophy" and that this is so especially of Johnson's doctrine of determinable and determinate. Johnson's work and influence in this latter regard is discussed in the ''
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Eac ...
'' entry ''on Determinables and Determinates'' by Jessica Wilson. "The Logical Calculus" (1892) reveals the technical capabilities of Johnson's youth, and that he was significantly influenced by the formal logical work of
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 ...
. The article begins as follows:
"As a material machine economises the exertion of force, so a symbolic calculus economises the exertion of intelligence ... the more perfect the calculus, the smaller the intelligence compared to the results."
A. N. Prior's ''Formal Logic'' cites this article several times.
John Passmore John Passmore AC (9 September 1914 – 25 July 2004) was an Australian philosopher. Life John Passmore was born on 9 September 1914 in Manly, Sydney, where he grew up. He was educated at Sydney Boys High School.Sydney High School Old Boys ...
tells us:
"His neologisms, as rarely happens, have won wide acceptance: such phrases as "ostensive definition", such contrasts as those between ... "determinates" and "determinables", "continuants" and "occurrents", are now familiar in philosophical literature." (Passmore, 1957, p.346)
Johnson also wrote three papers on economics. The first two, both published in the ''Cambridge Economic Club'', being 1891's "Exchange and Distribution" and 1894's "On Certain Questions Connected with Demand" (the latter being co-written with C. P. Langer). ‘The Pure Theory of Utility Curves’ (1913) was an important paper, representing "a considerable advance in the development of utility theory". Prior to the latter he would also write fourteen entries for the first edition of R. H. Inglis Palgrave's ''Dictionary of Political Economy'' (1894-1899)''.'' He was also of particular influence on
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 ...
"Johnson, William Ernest."
Complete Dictionary of Scientific Biography The ''Dictionary of Scientific Biography'' is a scholarly reference work that was published from 1970 through 1980 by publisher Charles Scribner's Sons, with main editor the science historian Charles Gillispie, from Princeton University. It consi ...
. via ''
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.'' 21 Jun. 2019
(and had been a colleague of his father
John Neville Keynes John Neville Keynes ( ; 31 August 1852 – 15 November 1949) was a British economist and father of John Maynard Keynes. Biography Born in Salisbury, Wiltshire, Keynes was the child of John Keynes (1805–1878) and his wife Anna Maynard Neville ...
).


Select publications

* '' Treatise on Trigonometry'' (1889).*Free at
Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
(
public domain The public domain (PD) consists of all the creative work A creative work is a manifestation of creative effort including fine artwork (sculpture, paintings, drawing, sketching, performance art), dance, writing (literature), filmmaking, ...
)
* "The Logical Calculus'',"
Mind The mind is the set of faculties responsible for all mental phenomena. Often the term is also identified with the phenomena themselves. These faculties include thought, imagination, memory, will, and sensation. They are responsible for various m ...
,'' Vol 1 (1892): n 3 parts: pp. 3–30, pp. 235–250, pp. 340–357ref name=":9" /> * "Sur la théorie des equations logiques," ''Bibliothèque du Congrès International de Philosophie,'' Volume 3, 1901'', Logique et Histoire des Sciences,'' pp. 185–199. *" The Pure Theory of Utility Curves," ''
The Economic Journal ''The Economic Journal'' is a peer-reviewed academic journal of economics published on behalf of the Royal Economic Society by Oxford University Press. The journal was established in 1891 and publishes papers from all areas of economics.The edito ...
,'' Vol. 23, No. 92 (Dec., 1913) *"Analysis of Thinking," ''Mind'', Vol 27 (1918): n 2 parts: pp. 1–21, pp 133–151ref name=":9" /> * ''Logic, Part I'', (Cambridge, 1921) *'' Logic, Part II'', (Cambridge, 1922) *'' Logic, Part III'', (Cambridge, 1924)*Free at
Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
(
public domain The public domain (PD) consists of all the creative work A creative work is a manifestation of creative effort including fine artwork (sculpture, paintings, drawing, sketching, performance art), dance, writing (literature), filmmaking, ...
), also
hypertext transcription
/ref>
"Probability: The Relations of Proposal to Supposal.,"
''Mind'', vol. 41, no. 161, 1932, pp. 1–16,
"Probability: Axioms,"
''Mind'', vol. 41, no. 163, 1932, pp. 281–96,
"Probability: The Deductive and Inductive Problems,"
''Mind'', vol. 41, no. 164, 1932, pp. 409–23


References


External links


1930 photographic portrait of W. E. Johnson
by
Walter Stoneman Walter Ernest Stoneman (6 April 1876 – 14 May 1958) was an English portrait photographer who took many photographs for the National Portrait Gallery (NPG) in London. Career as a photographer Stoneman was born in Plymouth, Devon, on 6 ...
at the
National Portrait Gallery, London The National Portrait Gallery (NPG) is an art gallery in London housing a collection of portraits of historically important and famous British people. It was arguably the first national public gallery dedicated to portraits in the world when it ...
*1915 Cambridge Moral Science Club
photo
featuring Johnson (with, amongst others,
G.E. Moore George Edward Moore (4 November 1873 – 24 October 1958) was an English philosopher, who with Bertrand Russell, Ludwig Wittgenstein and earlier Gottlob Frege was among the founders of analytic philosophy. He and Russell led the turn from ideal ...
, Bertrand Russell,
Dawes Hicks George Dawes Hicks Fellow of the British Academy, FBA (14 September 1862 – 16 February 1941) was a British philosopher who was the first professor of moral philosophy at University College, London, University College, London from 1904 until 1 ...
, W.R. Sorley, Karin Stephen and
J. M. E. McTaggart John McTaggart Ellis McTaggart (3 September 1866 – 18 January 1925) was an English idealist metaphysician. For most of his life McTaggart was a fellow and lecturer in philosophy at Trinity College, Cambridge. He was an exponent of the phi ...
) * [At
Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
] * David H. Sanford, Sanford, David H. (2011)
''Determinates vs. Determinables''
in the ''
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Eac ...
''.[Archived article now supplanted by Jessica Wilson'
''Determinables and Determinates''
(2017)]
The Story of Llandaff House and its Academy
(a 'local history' article with information about Johnson's school and ancestors). {{DEFAULTSORT:Johnson, William Ernest 1858 births 1931 deaths Fellows of King's College, Cambridge British logicians British philosophers