- For the theorem of propositional logic based on the same concept, see double negation.
In propositional logic, double negative elimination (also called double negation elimination, double negative introduction, double negation introduction, or simply double negation) are two valid rules of replacement. They are the inferences that if A is true, then not not-A is true and its converse, that, if not not-A is true, then A is true. The rule allows one to introduce or eliminate a negation from a logical proof. The rule is based on the equivalence of, for example, It is false that it is not raining. and It is raining.
The double negation introduction rule is:
- P ¬¬P
and the double negation elimination rule is:
- ¬¬P P
Where "" is a metalogical symbol representing "can be replaced in a proof with."
Read more about Double Negative Elimination: Formal Notation
Famous quotes containing the words double, negative and/or elimination:
“In a symbol there is concealment and yet revelation: here therefore, by silence and by speech acting together, comes a double significance.... In the symbol proper, what we can call a symbol, there is ever, more or less distinctly and directly, some embodiment and revelation of the Infinite; the Infinite is made to blend itself with the Finite, to stand visible, and as it were, attainable there. By symbols, accordingly, is man guided and commanded, made happy, made wretched.”
—Thomas Carlyle (1795–1881)
“Most literature on the culture of adolescence focuses on peer pressure as a negative force. Warnings about the “wrong crowd” read like tornado alerts in parent manuals. . . . It is a relative term that means different things in different places. In Fort Wayne, for example, the wrong crowd meant hanging out with liberal Democrats. In Connecticut, it meant kids who weren’t planning to get a Ph.D. from Yale.”
—Mary Kay Blakely (20th century)
“To reduce the imagination to a state of slavery—even though it would mean the elimination of what is commonly called happiness—is to betray all sense of absolute justice within oneself. Imagination alone offers me some intimation of what can be.”
—André Breton (1896–1966)