Moses Schönfinkel

Moses Ilyich Schönfinkel (Template:Langx; 29 September 1888 – Template:Death date text) 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)Template:Sfn 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.Template:Sfn 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.Template:Sfn 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.Template:Sfn In 1928, Schönfinkel had one other paper published, on special cases of the decision problem (Entscheidungsproblem), which was prepared by Paul Bernays.Template:Sfn

After he left Göttingen, Schönfinkel returned to Moscow. By 1927 he was reported to be mentally ill and in a sanatorium.Template:SfnTemplate:Sfn 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.Template:Sfn

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.Template:Sfn

His paper also showed that functions of two or more arguments could be replaced by functions taking a single argument.Template:SfnTemplate:SfnTemplate:Sfn 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 FregeTemplate:Refn (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).

See also

• Combinatory logic
• Bernays–Schönfinkel class
• Currying

Further reading

• (Reprinted lecture notes from 1967.)
• (eBook: Template:ISBN)

External links

• Template:Sister-inline