Moses Ilyich Schönfinkel (Russian: Моисей Эльевич Шейнфинкель, romanized: Moisei El'evich Sheinfinkel; 29 September 1888 – 1942 (1943)) was a logician and mathematician, known for the invention of combinatory logic.
Life Moses Schönfinkel was born on (1888-09-29)29 September 1888 in Ekaterinoslav, Russian Empire (now Dnipro, Ukraine) to a Jewish family. His father was Ilya Girshevich Schönfinkel, a merchant of first guild, who was in the grocery trade; his mother, Maria “Masha” Gertsovna Schönfinkel (née Lurie), came from the prominent Lurie family. Moses had siblings named Deborah, Natan, Israel and Grigoriy. Schönfinkel attended Novorossiysk University of Odessa, studying mathematics under Samuil Osipovich Shatunovskii (1859–1929), who worked in geometry and the foundations of mathematics. From 1914 to 1924, Schönfinkel was a member of David Hilbert's group at the University of Göttingen in Germany. On 7 December 1920 he delivered a talk entitled Elemente der Logik ("Elements of Logic") to the group where he outlined the concept of combinatory logic. Heinrich Behmann, a member of Hilbert's group, later revised the text and published it in 1924. In 1928, Schönfinkel had one other paper published, on special cases of the decision problem (Entscheidungsproblem), which was prepared by Paul Bernays. After he left Göttingen, Schönfinkel returned to Moscow. By 1927 he was reported to be mentally ill and in a sanatorium. His later life was spent in poverty, and he died in Moscow some time in 1942 (aged 53–54) . His papers were burned by his neighbors for heating.
Work Schönfinkel developed a formal system that avoided the use of bound variables. His system was essentially equivalent to a combinatory logic based upon the combinators B, C, I, K, S and a combinator for a universally quantified nand function which he called U. Schönfinkel stated that the system could be reduced to just K, S, and U (a colleague stated that U could be factored to the end of any expression and thus not always explicitly written) and outlined a proof that a version of this system had the same power as predicate logic. His paper also showed that functions of two or more arguments could be replaced by functions taking a single argument. This replacement mechanism simplifies work in both combinatory logic and lambda calculus and would later be called currying, after Haskell Curry. While Curry attributed the concept to Schönfinkel, it had already been used by Frege (an example of Stigler's law). The complete known published output of Schönfinkel consists of just two papers: his 1924 On the Building Blocks of Mathematical Logic, and another, 31-page paper written in 1927 and published 1928, coauthored with Paul Bernays, entitled Zum Entscheidungsproblem der mathematischen Logik (On the Decision Problem of Mathematical Logic).
Publications Schönfinkel, Moses (1924). "Über die Bausteine der mathematischen Logik" (PDF). Mathematische Annalen (in German). 92 (3–4): 305–316. doi:10.1007/bf01448013. S2CID 118507515. English translation: Schönfinkel (1967) Schönfinkel, Moses (1967) [1924]. Van Heijenoort, Jean (ed.). Über die Bausteine der mathematischen Logik [On the building blocks of mathematical logic]. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Translated by Bauer-Mengelberg, Stefan. Cambridge, MA, USA: Harvard University Press. pp. 355–366. ISBN 978-0674324497. OCLC 503886453. Bernays, Paul; Schönfinkel, Moses (1928). "Zum Entscheidungsproblem der mathematischen Logik" (PDF). Mathematische Annalen (in German). 99: 342–372. doi:10.1007/bf01459101. S2CID 122312654.
See also Combinatory logic Bernays–Schönfinkel class Currying
References
Further reading Cardone, Felice; Hindley, J. Roger (2006), "History of Lambda-calculus and Combinatory Logic", in Gabbay, Dov M.; Woods, John (eds.), Handbook of the History of Logic, vol. 5, Elsevier Curry, Haskell (November 1927), Notes on Schönfinkel, 271128A (T271128A), Curry archives.{{citation}}: CS1 maint: deprecated archival service (link) Kline, G.L.; Anovskaa, S. A. (1951). "Review of Foundations of mathematics and mathematical logic by S. A. Yanovskaya". Journal of Symbolic Logic. 16 (1): 46–48. doi:10.2307/2268665. JSTOR 2268665. S2CID 119004002. Reynolds, John C. (1998). "Definitional Interpreters for Higher-Order Programming Languages". Higher-Order and Symbolic Computation. 11 (4): 374. doi:10.1023/A:1010027404223. S2CID 43352033. Slonneger, Kenneth; Kurtz, Barry L. (1995), Formal Syntax and Semantics of Programming Languages Strachey, Christopher (2000). "Fundamental Concepts in Programming Languages". Higher-Order and Symbolic Computation. 13: 11–49. doi:10.1023/A:1010000313106. S2CID 14124601. (Reprinted lecture notes from 1967.) Wolfram, Stephen (2021a). "Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel". Combinators: A Centennial View. Wolfram Research. pp. 213–277 (Addendum 281–294). ISBN 978-1-57955-043-1. A celebration of the development of combinators, a hundred years after they were introduced by Schönfinkel (1924) (eBook: ISBN 978-1-57955-044-8)
External links Media related to Moses Schönfinkel at Wikimedia Commons Wolfram, Stephen. Combinators: 100-Year Celebration. Wolfram Physics Project on YouTube. Retrieved 26 September 2023. Wolfram, Stephen (7 December 2020). "Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel". arXiv:2108.08707. Retrieved 26 September 2023. Biographical information Wolfram, Stephen (29 March 2021). "A Little Closer to Finding What Became of Moses Schönfinkel, Inventor of Combinators". Retrieved 26 September 2023. Continuation
