Prof. Dr. Thorsten Jungmann (last updated 2026-10-03)
Henry Maurice Sheffer (1882–1964) was an American logician. He was born in Odessa and came to the United States in 1893, two years after his father. He studied at Harvard University, where he completed his undergraduate degree in 1905, his master’s degree in 1907 and his doctorate in philosophy under Josiah Royce in 1908. After a postdoctoral fellowship at Harvard he taught for one year each at several other universities; in 1917 he returned to Harvard, where he became a full professor of philosophy in 1938 and stayed until he retired in 1952.
In 1913 Sheffer proved that Boolean algebra can be defined using a single primitive binary operation, ‘not both … and …’, now abbreviated NAND, or its dual NOR (‘neither … nor’). He also proposed axioms formulated solely in terms of his stroke. Peirce had discovered these facts in 1880–81, but the relevant paper was not published until 1933.
The Sheffer stroke (German: Shefferscher Strich) is named after him. Sheffer himself used the stroke as a sign for NOR; the use for NAND, which corresponds to the NAND gate in digital electronics, became current practice after Jean Nicod used it in that sense in 1917. Like its dual NOR, NAND can be used by itself, without any other logical operator, to constitute a logical formal system; it is functionally complete. This property makes the NAND gate crucial to modern digital electronics, including its use in computer processor design. In the second edition of Whitehead and Russell’s ‘Principia Mathematica’ (1925), Bertrand Russell called the replacement of ‘not’ and ‘or’ by the stroke the most definite improvement in mathematical logic of the previous fourteen years.
Reference and further reading:
https://en.wikipedia.org/wiki/Henry_M._Sheffer
https://en.wikipedia.org/wiki/Sheffer_stroke