Henry M. Sheffer
Henry Maurice Sheffer (1882 – 1964) was an American logician.
Life and career
Sheffer was a Polish Jew born in the western Ukraine, who immigrated to the USA in 1892 with his parents and six siblings. He studied at the Boston Latin School before entering Harvard University, learning logic from Josiah Royce, and completing his undergraduate degree in 1905, his master's in 1907, and his Ph.D. in philosophy in 1908. After holding a postdoctoral position at Harvard, Henry traveled to Europe on a fellowship. Upon returning to the United States, he became an academic nomad, spending one year each at the University of Washington, Cornell, the University of Minnesota, the University of Missouri, and City College of New York. In 1916 he returned to Harvard as a faculty member in the philosophy department. He remained at Harvard until his retirement in 1952. Scanlan (2000) is a study of Sheffer's life and work.
Sheffer proved in 1913 that Boolean algebra could be defined using a single primitive binary operation, "not both . . . and . . .", now abbreviated NAND, or its dual NOR, (in the sense of "neither . . . nor"). Likewise, the propositional calculus could be formulated using a single connective, having the truth table either of the logical NAND, usually symbolized with a vertical line called the Sheffer stroke, or its dual logical NOR (usually symbolized with a vertical arrow or with a dagger symbol). Charles Peirce had also discovered these facts in 1880, but the relevant paper was not published until 1933. Sheffer also proposed axioms formulated solely in terms of his stroke.
