Henry M. Sheffer

Henry Maurice Sheffer (1882-1964) was an American logician.

Sheffer was a Polish Jew born in the Ukraine, who immigrated to the USA with his parents. He was educated at Harvard University, learning logic from Josiah Royce. Sheffer spent most of his career teaching in Harvard's philosophy department. 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.

Sheffer's discovery won great praise from Bertrand Russell, who used it extensively to simplify his own logic, in the second edition of his "Principia Mathematica". W. V. Quine's "Mathematical Logic" also made much of the Sheffer stroke.

A sheffer connective, subsequently, is any connective in a logical system that functions analogously: one in terms of which all other possible connectives in the language can be expressed. For example, they have been developed for quantificational and modal logics as well.

References

*Scanlan, Michael, 2000, "The Known and Unknown H. M. Sheffer," "The Transactions of the C.S. Peirce Society 36": 193-224.