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Person: Sheffer, Henry

Henry Sheffer was a mathematical logician who introduced what is now called the NAND operator which lies at the basis of the entire computer industry. He showed that all logical operators can be derived from a single one, NAND.

Mathematical Profile (Excerpt):

• Henry's six surviving siblings were Rose (born about 1889 in Russia), Mary (born about 1890 in Russia), Meyer (born 26 December 1894 in Boston, died 1981), Sadie (born 26 October 1896 in Boston, died 10 June 1987), William (born about 1898 in Boston), and Isadore Mitchell (born 14 October 1901 in Boston).
• Let us remark that Isadore Mitchell Sheffer, who died 20 April 1992, became a mathematician with a Ph.D. from Harvard University in 1927 with George Birkhoff as his advisor; he became a professor of mathematics at Pennsylvania State University.
• The headmaster at this time was Moses Merrill (headmaster from 1871 to 1901) and Sheffer studied the standard course of education offered by the Latin School at that time, namely English, Latin, Greek, French, science, mathematics and classical history.
• For this young Sheffer was presented with a gold medal.
• In the autumn of 1901, Sheffer entered Harvard University.
• Hyman Morrison (1881-1963) was a Jewish student at Harvard University who, like Sheffer, was born in Russia and had emigrated to the United States in 1894.
• Sheffer was awarded a B.A. in 1905 and continued to work towards his Master's Degree.
• Although Sheffer did not agree with Royce's metaphysical views, nevertheless, Royce had been making a deep study of mathematical logic following criticism of his use of logic by Charles S Peirce.
• Sheffer, who approached philosophy in a scientific and mathematical way, was very much in tune with Royce's recent enthusiasm for symbolic logic.
• Sheffer criticises Royce's specific definition from the point of view of the evolving twentieth century conception of axiomatic method and also shows more generally that an unsymmetric order relation cannot be defined in the system of the 1905 paper based on the O-relation.
• We note that the confidence that Sheffer has at this stage in his career, in giving an appendix showing a major error by his thesis advisor who, of course, was also an examiner of the thesis.
• The application contains a nice description of Sheffer: age 27; height 5ft 2 in; forehead high; eyes brown; nose straight; mouth medium; chin square; hair brown; complexion light; face long.
• His first European visit was to be to Bertrand Russell at the University of Cambridge, England, and Royce had written to Russell on 29 June 1910 saying, "we have, in America, no more promising research student of the new logic than Sheffer is." Russell had just published the article Mathematical Logic as Based on the Theory of Types (1908) and Sheffer attended Russell's 'Mathematical Philosophy' lectures in the Michaelmas term.
• After visiting Russell, Sheffer travelled to Göttingen, Germany visiting David Hilbert before going on to Italy where Giuseppe Peano was about to give a course on 'The New Mathematical Logic'.
• Sheffer had just started his one year appointment at the University of Michigan when Josiah Royce died on 14 September 1916.
• Harvard Philosophy Department asked Sheffer to return there as a temporary instructor to help cover their teaching commitments and he took up this position in the winter of 1917.
• We note the uncomfortable fact that, since Sheffer was Jewish, Harvard University insisted his salary should be provided by outside sources.
• By this time Sheffer had already published the ideas for which he is now most famous.
• These three were all published by the American Mathematical Society, the first two are abstracts in the Bulletin of lectures Sheffer gave to the Society, the third is a paper in the Proceedings.
• These contain the now famous "Sheffer stroke".
• is well-known as the discoverer of the eponymous "Sheffer stroke", a binary truth-functional operator with which any truth-functional operator can be defined.
• As the title indicates, Sheffer's stroke operator was not originally developed by him in the context of truth-functional logic, but to use in postulate sets for Boolean Algebra.
• This idea could be applied to the propositional logic of 'Principia Mathematica', and Sheffer does this by giving definitions of the "primitive ideas" of negation and disjunction using his stroke with the interpretation of "p∣qp | qp∣q" as "neither p nor q".
• We note that in fact Sheffer's stroke was discovered by Charles Sanders Peirce in 1880 and is in an unpublished manuscript of this date and another dated 1902.
• This, however, only came to light long after Sheffer's 1913 publication.
• Wittgenstein made extensive use of the Sheffer stroke in his Tractatus, but does not give credit to Sheffer (in fact he gives no sources) but Russell in his Introduction to the Tractatus gives full credit to Sheffer.
• Despite these strong endorsements of Sheffer's work, he remained an instructor at Harvard for ten years.
• One factor was undoubtedly the fact that Sheffer was Jewish.
• It was seen by many as a way of limiting the number of Jewish students and the general anti-Semitic atmosphere must have affected Sheffer.
• When talking with Karl Menger in 1930, Sheffer spoke of his "serious social difficulties at Harvard" and the importance of Russell's support, given the speed with which gossip spreads in universities.
• Sheffer had other problems relating to his health.
• Lewis, who was familiar with the ways of his almost lifelong friend, paid no attention to Sheffer's peculiar noises throughout the meal and kept up a conversation with me alone.
• It was clear to Lewis that Sheffer wanted merely to be with people and not talk to them during these episodes.
• In 1927, after ten years as an instructor, Sheffer was promoted to assistant professor.
• This seems to have been the result of a serious breakdown by Sheffer and the consequent realisation by the philosophy department of how valuable he was as a teacher.
• In the department of philosophy at Harvard, Mr Sheffer has been notably successful in exciting interest among those students with aptitude for this study.
• Now it is clear that the philosophy department supported Sheffer while the university administration was hostile for his promotion to assistant lecturer in 1927 and to associate professor two years later, were both funded by the philosophy department and not from university funds.
• All his life Professor Sheffer has been a kind, quiet, sensitive man, burdened with responsibilities that only an unusually firm will and courageous spirit could sustain.
• Sheffer died at Beth Israel Hospital in Boston at the age of 80 and was buried at the Jewish Congregation Chai Odom cemetery in West Roxbury, Massachusetts.

Born 1 September 1882, Odessa, Russia (now Ukraine). Died 17 March 1964, Boston, Massachusetts, USA.

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References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive