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Ampheck, from Greek ἀμφήκης 'double-edged', is a term coined by Charles Sanders Peirce for either one of the pair of logically dual operators, variously referred to as Peirce arrows, Sheffer strokes, or NAND and NNOR. Either of these logical operators is a sole sufficient operator for deriving or generating all of the other operators in what is variously called the subject matter of boolean functions, propositional calculus, sentential calculus, or zeroth order logic. Charles Sanders Peirce Charles Sanders Peirce (September 10, 1839 – April 19, 1914) was an American logician, philosopher, scientist, and mathematician. ...
NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ...
NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ...
NOR Logic Gate Logical nor (not or), joint denial, or Webb-operation is a boolean logic operator which produces a result that is the inverse of logical or. ...
In mathematics, a Boolean function is usually a function F(b1, b2, ... , bn) of a number n of Boolean variables bi from the two-element Boolean algebra {0,1}, and such that F also takes values in {0, 1}. A function on a general domain of a function taking values...
In mathematical logic the propositional calculus or sentential calculus is a formal deduction system whose atomic formulas are propositional variables. ...
- For example,
 signifies that x is f and y is f. Then  , or  , will signify that z is f, but that the statement that x and y are both f is itself f, that is, is false. Hence, the value of  is the same as that of  ; and the value of  is f, because it is necessarily false; while the value of  is only f in case is v; and  is necessarily true, so that its value is v. - With these two signs, the vinculum (with its equivalents, parentheses, brackets, braces, etc.) and the sign
 , which I will call the ampheck (from ἀμφηκής, cutting both ways), all assertions as to the values of quantities can be expressed. (C.S. Peirce, CP 4.264). In the above passage, Peirce introduces the term ampheck for the 2-place logical connective or the binary logical operator that is currently called the joint denial in logic, the NNOR operator in computer science, or indicated by means of phrases like 'neither-nor' or 'both not' in ordinary language. For this operation he employs a symbol that the typographer most likely set by inverting the zodiac symbol for Aries, but set above by commandeering the symbol for the bottom element of a lattice or partially ordered set. A vinculum is a horizontal line placed over a mathematical expression, used to indicate that it is to be considered a group. ...
Zodiac signs, 16th century , medieval woodcuts The zodiac (from Greek zoon, animal) is an imaginary belt in the heavens extending approximately 8 degrees on either side of the Suns apparent path (the ecliptic), that includes the apparent paths of the Moon and the planets Mercury, Venus, Mars, Jupiter, Saturn. ...
Aries ( , Latin for Ram) is one of the constellations of the zodiac. ...
In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set is an element of S which is greater than or equal to any other element of S. The term least element is defined dually. ...
The term lattice derives from the shape of the Hasse diagrams that result from depicting these orders. ...
In mathematics, especially order theory, a partially ordered set (or poset for short) is a set equipped with a partial order relation. ...
In the same paper, Peirce introduces a symbol for the logically dual operator, rendered by the editors of CP by means of a bar or serif at the top of the inverted Aries symbol, in this way denoting the connective or operator that is currently called the alternative denial in logic, the NAND operator in computer science, or invoked by means of phrases like 'not-and' or 'not both' in ordinary language. It is not clear whether it was Peirce himself or later writers who initiated the practice, but on account of their dual relationship it became common to refer to these two operators in the plural, as the amphecks. NAND Logic Gate The alternative denial, |, also called Sheffer stroke and in Boolean algebra and digital circuitry known as the NAND (Not AND) operation, is a logical operator which is the negation of the conjunction operator. ...
References
- Clark, Glenn, "New Light on Peirce's Iconic Notation for the Sixteen Binary Connectives", pp. 304-333 in Houser, Roberts, Van Evra (eds.), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, Bloomington, IN, 1997.
- McCulloch, W.S., "What Is a Number, that a Man May Know It, and a Man, that He May Know a Number?" (Ninth Alfred Korzybski Memorial Lecture), General Semantics Bulletin, Nos. 26 & 27, 7-18, Institute of General Semantics, Lakeville, CT, 1961. Reprinted as pp. 1-18 in Embodiments of Mind.
- Peirce, C.S., "The Simplest Mathematics" (1902). First published as CP 4.227-323 in Collected Papers.
- Zellweger, Shea, "Untapped Potential in Peirce's Iconic Notation for the Sixteen Binary Connectives", pp. 334-386 in Houser, Roberts, Van Evra (eds.), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, Bloomington, IN, 1997.
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Alfred Korzybski Alfred Korzybski was born on July 3, 1879 in Warsaw, Poland, and died on March 1, 1950) in Lakeville, Connecticut, USA. He came from an aristocratic family which had worked as mathematicians, scientists, and engineers for generations, and he chose to train as an engineer. ...
Charles Sanders Peirce Charles Sanders Santiago Peirce (pronounced purse), (September 10, 1839, Cambridge, Massachusetts – April 19, 1914, Milford, Pennsylvania) was an American polymath. ...
Bibliography
Primary literarure - Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1-6, Charles Hartshorne and Paul Weiss (eds.), vols. 7-8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931-1935, 1958.
Charles Sanders Peirce Charles Sanders Santiago Peirce (pronounced purse), (September 10, 1839, Cambridge, Massachusetts – April 19, 1914, Milford, Pennsylvania) was an American polymath. ...
Charles Hartshorne (June 5, 1897 – October 9, 2000) was a prominent philosopher who concentrated primarily on the philosophy of religion and metaphysics. ...
Paul Weiss is a leading nanoscientist at the Pennsylvania State University. ...
Secondary literature - Houser, N., Roberts, Don D., and Van Evra, James (eds.), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, Bloomington, IN, 1997.
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See also The phrase Laws of Form refers to either of two things: The book, hereinafter abbreviated LoF: G. Spencer-Brown, 1979. ...
A logical graph is a special type of graph-theoretic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic. ...
NOR Logic Gate Logical nor (not or), joint denial, or Webb-operation is a boolean logic operator which produces a result that is the inverse of logical or. ...
NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ...
NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ...
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