Alonzo Church

This article is about the mathematician and logician. For the president of the University of Georgia, see Alonzo Church (college president). For the politician, see A. C. Croom.

Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, and philosopher who made major contributions to mathematical logic and the foundations of theoretical computer science.^[2] He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem ("decision problem"), the Frege–Church ontology, and the Church–Rosser theorem. Alongside his doctoral student Alan Turing, Church is considered one of the founders of computer science.^[3][4]

Alonzo Church
Born	(1903-06-14)June 14, 1903 Washington, D.C., U.S.
Died	August 11, 1995(1995-08-11) (aged 92) Hudson, Ohio, U.S.
Citizenship	United States
Alma mater	Princeton University (BS, PhD)
Known for	Lambda calculus Simply typed lambda calculus Church encoding Church's theorem Church–Kleene ordinal Church–Turing thesis Frege–Church ontology Church–Rosser theorem Intensional logic
Scientific career
Fields	Mathematics, computer science, logic
Institutions	Princeton University (1929–67) UCLA (1967–95)
Thesis	Alternatives to Zermelo's Assumption (1927)
Doctoral advisor	Oswald Veblen
Doctoral students	C. Anthony Anderson, 1977 Peter Andrews, 1964 George Alfred Barnard, 1936 William W. Boone, 1952 Martin Davis, 1950 William Easton, 1964 Alfred Foster, 1930 Leon Henkin, 1947 John George Kemeny, 1949 Stephen Cole Kleene, 1934 Simon B. Kochen, 1959 Maurice L'Abbé, 1951 Isaac Malitz, 1976 Gary R. Mar, 1985 Michael O. Rabin, 1957 Nicholas Rescher, 1951 Hartley Rogers, Jr, 1952 J. Barkley Rosser, 1934 Dana Scott, 1958 Norman Shapiro, 1955 Raymond Smullyan, 1959 Alan Turing, 1938^[1]

Life

Alonzo Church was born on June 14, 1903, in Washington, D.C., where his father, Samuel Robbins Church, was a justice of the peace^[5] and the judge of the Municipal Court for the District of Columbia. He was the grandson of Alonzo Webster Church (1829–1909), United States Senate Librarian from 1881 to 1901, and great-grandson of Alonzo Church, a professor of Mathematics and Astronomy and 6th President of the University of Georgia.^[6] As a young boy, Church was partially blinded by an air gun accident.^[7] The family later moved to Virginia after his father lost his position at the university because of failing eyesight. With help from his uncle, also named Alonzo Church, the son attended the private Ridgefield School for Boys in Ridgefield, Connecticut.^[8] After graduating from Ridgefield in 1920, Church attended Princeton University, where he was an exceptional student. He published his first paper on Lorentz transformations^[9] in 1924 and graduated the same year with a degree in mathematics. He stayed at Princeton for graduate work, earning a Ph.D. in mathematics in three years under Oswald Veblen.

He married Mary Julia Kuczinski in 1925. The couple had three children: Alonzo Jr. (1929), Mary Ann (1933), and Mildred (1938).

After receiving his Ph.D., he taught briefly as an instructor at the University of Chicago.^[10] He received a two-year National Research Fellowship that enabled him to attend Harvard University in 1927–1928, and the University of Göttingen and University of Amsterdam the following year.

He taught philosophy and mathematics at Princeton for nearly four decades, from 1929 to 1967. He held the Flint Professorship of Philosophy and Mathematics at the University of California, Los Angeles, 1967–1990.^[11] He was a Plenary Speaker at the ICM in 1962 in Stockholm.^[12]

He received honorary Doctor of Science degrees from Case Western Reserve University in 1969,^[13] Princeton University in 1985,^[14] and the University at Buffalo, The State University of New York in 1990 in connection with an international symposium in his honor organized by John Corcoran.^[15]

He was elected a Corresponding Fellow of the British Academy (FBA) in 1966,^[16] to the American Academy of the Arts and Sciences in 1967, to the National Academy of Sciences in 1978.^[17]

A deeply religious person, Church was a lifelong member of the Presbyterian church.^[18] He died on August 11, 1995, at the age of 92.^[19] He is buried in Princeton Cemetery.^[20]

Mathematical work

Church is known for the following significant accomplishments:

• His proof that the Entscheidungsproblem, which asks for a decision procedure to determine the truth of arbitrary propositions in a first-order mathematical theory, is undecidable. This is known as Church's theorem.^[21]
• His invention of the lambda calculus.
• His use of the lambda calculus to prove that Peano arithmetic is undecidable.^[11]
• His articulation of what has come to be known as the Church–Turing thesis.
• Being a founding editor of the Journal of Symbolic Logic, editing its reviews section for 43 years from 1936 until 1979.
• His authorship of a prominent textbook in the field of mathematical logic, Introduction to Mathematical Logic.^[22]
• The Church–Rosser theorem

The lambda calculus emerged in his 1936 paper showing the unsolvability of the Entscheidungsproblem. This result preceded Alan Turing's work on the halting problem, which also demonstrated the existence of a problem unsolvable by mechanical means. Upon hearing of Church's work, Turing enrolled at Princeton later that year under Church for a Ph.D.^[23] Church and Turing then showed that the lambda calculus and the Turing machine used in Turing's halting problem were equivalent in capabilities, and subsequently demonstrated a variety of alternative "mechanical processes for computation." This resulted in the Church–Turing thesis.

The efforts for automatically generating a controller implementation from specifications originates from his ideas.^[24]

The lambda calculus influenced the design of Lisp and functional programming languages in general. The Church encoding is named in his honor.

In his honor the Alonzo Church Award for Outstanding Contributions to Logic and Computation was established in 2015 by the Association for Computing Machinery Special Interest Group for Logic and Computation (ACM SIGLOG), the European Association for Theoretical Computer Science (EATCS), the European Association for Computer Science Logic (EACSL), and the Kurt Gödel Society (KGS). The award is for an outstanding contribution to the field published within the past 25 years and must not yet have received recognition via another major award, such as the Turing Award, the Paris Kanellakis Award, or the Gödel Prize.^[25][26]

Philosophical work

Church’s elaboration of a methodology involving the logistic method, his philosophical criticisms of nominalism and his defense of realism, his argumentation leading to conclusions about the theory of meaning, and the detailed construction of the Fregean and Russellian intensional logics, are more than sufficient to place him high up among the most important philosophers of this century.

— C. Anthony Anderson, doctoral student of Church (1977)^[27]

Church is also known for the Frege–Church ontology, which he created based on the philosophical ideas of Gottlob Frege.

Influence

Over the course of his academic career, Church oversaw 31 doctoral students.^[11] Many of them have led distinguished careers in mathematics, computer science, and other academic subjects, including C. Anthony Anderson, Peter B. Andrews, George A. Barnard, David Berlinski, William W. Boone, Martin Davis, Alfred L. Foster, Leon Henkin, John G. Kemeny, Stephen C. Kleene, Simon B. Kochen, Maurice L'Abbé, Isaac Malitz, Gary R. Mar, Michael O. Rabin, Nicholas Rescher, Hartley Rogers, Jr., J. Barkley Rosser, Dana Scott, Raymond Smullyan, and Alan Turing.^[28]

In addition to those he directly supervised, Church also had a large influence on other mathematicians and computer scientists. Haskell Curry, who expanded on Church's ideas with the concept of currying, stated that one of his textbooks, Introduction to Mathematical Logic (first published in 1944), was "written with the meticulous precision which characterizes the author's work generally."^[29]

Bibliography

Books

• Alonzo Church, Introduction to Mathematical Logic (1944) (ISBN 978-0-691-02906-1)^[30]
• Alonzo Church, The Calculi of Lambda-Conversion (1941) (ISBN 978-0-691-08394-0)^[31]
• Alonzo Church, A Bibliography of Symbolic Logic, 1666–1935 (ISBN 978-0-8218-0084-3)
• C. Anthony Anderson and Michael Zelëny, (eds.), Logic, Meaning and Computation: Essays in Memory of Alonzo Church (ISBN 978-1-4020-0141-3)
• Tyler Burge and Herbert Enderton (eds.), The Collected Works of Alonzo Church (2019) (ISBN 978-0-262-02564-5)^[32]

See also

•  Biography portal
•  Philosophy portal

• Church–Turing–Deutsch principle
• Higher-order logic
• List of pioneers in computer science
• Modern Platonism
• Universal set

Notes

1. Bowen, Jonathan P. (2019). "The Impact of Alan Turing: Formal Methods and Beyond". In Bowen, Jonathan P.; Liu, Zhiming; Zhang, Zili (eds.). Engineering Trustworthy Software Systems. SETSS 2018 (PDF). Lecture Notes in Computer Science. Vol. 11430. Cham: Springer. pp. 202–235. doi:10.1007/978-3-030-17601-3_5. ISBN 978-3-030-17600-6. S2CID 121295850.
2. Deutsch, Harry; Marshall, Oliver (2022), "Alonzo Church", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2022 ed.), Metaphysics Research Lab, Stanford University, retrieved 2022-04-14
3. "OBITUARY: Alonzo Church". The Independent. 2011-10-22. Retrieved 2021-05-24.
4. Cooper, S. B. (2012). The selected works of A.M. Turing : his work and impact. J. van Leeuwen. Waltham, MA: Elsevier. ISBN 978-0-12-387012-4. OCLC 840569810.
5. Bundy, Charles S. (1902). "A History of the Office of Justice of the Peace in the District of Columbia". Records of the Columbia Historical Society, Washington, D.C. 5: 259–293. ISSN 0897-9049. JSTOR 40066805.
6. Coulter, E. Merton (1928). College Life in the Old South. University of Georgia Press. ISBN 9-780-8203-3199-7.
7. "Alonzo Church" (PDF). Open Logic. 2022-12-19.
8. The Ridgefield School for Boys, also known as the Ridgefield School, was a private school that existed from 1907 to 1938. See The Ridgefield School.
9. Church, Alonzo (1924). "Uniqueness of the Lorentz Transformation". The American Mathematical Monthly. 31 (8): 376–382. doi:10.1080/00029890.1924.11986368. JSTOR 2298823.
10. "An early history of computing at Princeton". Princeton Alumni Weekly. 2012-04-04. Retrieved 2020-04-19.
11. (PDF). Archived from the original (PDF) on 1 September 2012. Retrieved 2022-04-14.
12. Church, Alonzo (1962). (PDF). Proceedings of the International Congress of Mathematicians. pp. 23–35. Archived from the original (PDF) on 2013-12-28.
13. . case.edu. 2004-02-06. Archived from the original on 2006-09-10.
14. . Princeton University. 2009-12-30. Archived from the original on 2016-02-07.{{cite web}}: CS1 maint: unfit URL (link)
15. . State University of New York at Buffalo Archives. Archived from the original on 2013-10-17.
16. although some sources say he was elected to the British Academy in 1980, he was in fact elected in 1966. See: "Professor Alonzo Church FBA". The British Academy. and (PDF). Archived from the original (PDF) on 2012-09-01. Retrieved 2022-04-14.
17. "Alonzo Church '24 *27". Princeton Alumni Weekly. 2016-01-21. Retrieved 2022-04-14.
18. (PDF). p. 4. Archived from the original (PDF) on 1 September 2012. Retrieved 6 June 2012. A deeply religious person, he was a lifelong member of the Presbyterian church.
19. Nicholas Wade (September 5, 1995). "Alonzo Church, 92, Theorist Of the Limits of Mathematics". The New York Times. p. B6.
20. "Undecidability of First-Order Logic" (PDF).
21. Church, A. (1936). "An unsolvable problem of elementary number theory". American Journal of Mathematics. 58 (2): 345–363. doi:10.2307/2371045. JSTOR 2371045.
22. Church, Alonzo (1996). Introduction to Mathematical Logic. Princeton University Press. ISBN 978-0-691-02906-1.
23. Armstrong *14, April C. "Alonzo Church". Mudd Manuscript Library Blog. Retrieved 2022-04-14.{{cite web}}: CS1 maint: numeric names: authors list (link)
24. Lúcio, Levi; Rahman, Salman; Cheng, Chih-Hong; Mavin, Alistair (2017). "Just Formal Enough? Automated Analysis of EARS Requirements" (PDF). Lecture Notes in Computer Science. Springer International Publishing. pp. 427–434. doi:10.1007/978-3-319-57288-8_31. ISBN 978-3-319-57287-1. ISSN 0302-9743.
25. "Alonzo Church Award". eatcs.org.
26. "Alonzo Church Award for Outstanding Contributions to Logic and Computation 2019 – ACM Special Interest Group on Logic and Computation". siglog.acm.org.
27. (Anderson 1998)
28. "Mathematics Genealogy Project". from the original on 4 August 2010. Retrieved 12 August 2010.
29. "Alonzo Church - Biography". Maths History.
30. Henkin, Leon (1957). "Review: Introduction to Mathematical Logic by Alonzo Church" (PDF). Bull. Amer. Math. Soc. 63 (5): 320–323. doi:10.1090/s0002-9904-1957-10129-3.
31. Frink Jr., Orrin (1944). "Review: The Calculi of Lambda-Conversion by Alonzo Church" (PDF). Bull. Amer. Math. Soc. 50 (3): 169–172. doi:10.1090/s0002-9904-1944-08090-7.
32. Burge, Tyler; Enderton, Herbert, eds. (2019-04-23). The Collected Works of Alonzo Church. Cambridge, MA, USA: MIT Press. ISBN 978-0-262-02564-5.

References

• Enderton, Herbert B., . Introduction to The Collected Works of Alonzo Church, MIT Press, 2019.
• Enderton, Herbert B., In memoriam: Alonzo Church, The Bulletin of Symbolic Logic, vol. 1, no. 4 (Dec. 1995), pp. 486–488.
• Wade, Nicholas, Alonzo Church, 92, Theorist of the Limits of Mathematics (obituary), The New York Times, September 5, 1995, p. B6.
• Hodges, Wilfred, Obituary: Alonzo Church, The Independent (London), September 14, 1995.
• interviewed by William Aspray on 17 May 1984. The Princeton Mathematics Community in the 1930s: An Oral-History Project, transcript number 5.
• Rota, Gian-Carlo, Fine Hall in its golden age: Remembrances of Princeton in the early fifties. In A Century of Mathematics in America, Part II, edited by Peter Duren, AMS History of Mathematics, vol 2, American Mathematical Society, 1989, pp. 223–226. Also available .
• Church, A. (1950). "On Carnap's Analysis of Statements of Assertion and Belief". The Journal of Symbolic Logic. 10 (5): 97–99. doi:10.2307/3326684. JSTOR 3326684.
• Anderson, C. Anthony (1998). "Alonzo Church's contributions to philosophy and Intensional Logic". The Bulletin of Symbolic Logic. 4 (2): 129–171. CiteSeerX 10.1.1.26.7389. doi:10.2307/421020. JSTOR 421020. S2CID 18305417.

External links

• O'Connor, John J.; Robertson, Edmund F., "Alonzo Church", MacTutor History of Mathematics Archive, University of St Andrews
• Princeton University Library, Manuscripts Division, The Alonzo Church Papers, 1924–1995: finding aid.
• A bibliography of Church's reviews for The Journal of Symbolic Logic, with a link to each
• Alonzo Church at Find a Grave
• Alonzo Church, 92, Theorist Of the Limits of Mathematics New York Times obituary
• OBITUARY: Alonzo Church from The Independent
• In memoriam: Alonzo Church (1903–1995) by Irving H. Anellis, Modern Logic Vol. 5, No. 4 (1995).
• In memoriam: Alonzo Church 1903–1995 by H. B. Enderton, The Bulletin of Symbolic Logic Vol. 1, No.5 (1995).