Cooper Harold Langford (25 August 1895, Dublin,

Logan County, Arkansas Logan County (formerly Sarber County) is a county located in the U.S. state of Arkansas. As of the 2010 census, the population was 22,353. Its two county seats are Booneville and Paris. History The Arkansas General Assembly defined the stat ...

– 28 August 1964) was an American

analytic philosopher Analytic philosophy is a branch and tradition of philosophy using analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 20th century in the contemporary era in the United Kingdom, Unit ...

and

mathematical logician Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal sys ...

who co-authored the book ''Symbolic Logic'' (1932) with C. I. Lewis. He is also known for introducing the Langford–Moore paradox.

Biography

After spending his freshman year at the

University of Arkansas The University of Arkansas (U of A, UArk, or UA) is a public land-grant research university in Fayetteville, Arkansas. It is the flagship campus of the University of Arkansas System and the largest university in the state. Founded as Arkansas ...

, Langford transferred in 1915 to

Clark University Clark University is a private research university in Worcester, Massachusetts. Founded in 1887 with a large endowment from its namesake Jonas Gilman Clark, a prominent businessman, Clark was one of the first modern research universities in th ...

, where he received his A.B. degree in 1920. His college education was interrupted by World War I in 1917 when he joined the U.S. army and spent 20 months overseas. After receiving his A.B. degree, Langford enrolled in 1920 as a graduate student at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of high ...

, where he earned his Ph.D. in psychology under

Edwin Boring Edwin Garrigues (Garry) Boring (23 October 1886 – 1 July 1968) was an American experimental psychologist, Professor of Psychology at Clark University and at Harvard University, who later became one of the first historians of psychology. A ''Re ...

in 1924. With the aid of a Sheldon Traveling Fellowship, he studied logic and philosophy at

Cambridge University , 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 ...

during 1924–1925. Upon his return to the U.S., Langford became an instructor at Harvard from 1925 to 1927. After spending two academic years, 1927–1929, as an assistant professor at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seat ...

, he became in the autumn of 1929 an associate professor with tenure in the philosophy department 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 ...

. Langford became a full professor at U. Michigan in 1933, remaining there for the rest of his career. In the academic year 1935–1936, he was a

Guggenheim fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

, dividing his time between Vienna and Cambridge, England. Langford is famous as co-author of the 1932 book ''Symbolic Logic'' and the system of modal logic S5. His doctoral students include

Arthur Burks Arthur Walter Burks (October 13, 1915 – May 14, 2008) was an American mathematician who worked in the 1940s as a senior engineer on the project that contributed to the design of the ENIAC, the first general-purpose electronic digital computer. ...

. In the

philosophy of language In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the ...

, Langford is known for the Langford substitution test. The test distinguishes used from merely mentioned expressions in a given sentence by translating the sentence into a different language (see Langford 1937). If the very same expression reoccurs in the translation, it was mentioned rather than used in the original sentence. If the expression does not reoccur and is replaced by some other (usually synonymous) expression, then it was used in the original sentence. This test is used by a famous argument from

Alonzo Church Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, philosopher, professor and editor who made major contributions to mathematical logic and the foundations of theoretical computer scie ...

concerning

Carnap Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism ...

's treatment of belief attributions and other analyses of beliefs as relations to sentences (see Church 1950). Langford was married twice. His son Cooper H. Langford was a chemist.

Selected works

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Notes

References

External links

Works by C. H. Langford – PhilPapers
{{DEFAULTSORT:Langford, Cooper Harold Clark University alumni 20th-century American philosophers American logicians American philosophy academics Analytic philosophers Harvard University alumni Philosophy teachers University of Michigan faculty 1895 births 1964 deaths