In linguistics a distinction is made between negation and negation. While the term negation means the logical operation that reverses the truth value of a statement, negation is a linguistic act that is carried out when using a negated sentence. The opposite of a negative, i.e. an affirmative or affirmative statement, is called an affirmation . With regard to negation, a distinction is made between sentence negation and constituent negation. In the case of sentence negation, an entire sentence or fact is negated (e.g. "It's not raining "). In the case of constituent negation, on the other hand, the factual situation described in the sentence is not negated, but only a constituent that is smaller than a sentence (e.g. “Laura didn't find a job far away”).
In formal logic , negation is usually understood to mean sentence negation, i.e. an operation by which the truth value of a statement (a sentence) is turned into its opposite; Here too, the term “negation” (a) can be used to denote the linguistic expression of the negation (for example the negation sign “¬” or the phrase “it is not the case that ...”), (b) its meaning, such as the negative truth value function or (c) the negative statement formed should be meant.
The negation in two-valued logic
In classical logic , in which exactly two truth values - true and false - are considered, the negation can be directly grasped as the inversion of the truth value into its opposite: If one denies a true statement, then a false statement arises; on the other hand, if you deny a false statement, a true statement is made.
Common realizations for the negation of a statement a are , , and . In the Polish notation , the negation is expressed by the preceding capital letter N (e.g. Na ), in the Existential Graphs by Charles S. Peirce a statement is denied by being surrounded by a closed line of lines. In many programming languages the negation is written as or .
The negation can be expressed by other connectives:
- by the conditional : The expression (“If p is true, then any contradiction is true”) is true if and only if p is false and false if and only if p is true;
- by the Sheffer operators NAND and NOR : The expressions p NOR p and p NAND p reverse the truth value of p.
In classical logic, negation has the following properties, among others:
- The double negation of a statement always has the same truth value as the non-negated statement, that is, statements of the form and are always equivalent ( principle of double negation ).
- A statement of the form is always true or valid ( proposition of the excluded third party ).
- A statement of the form is always wrong or invalid ( theorem of contradiction ).
The negation in three-valued logic
There are two types of negation in trivalent logic: weak and strong. The difference is that in the case of strong negation the presuppositions are retained.
Negation, denial and assertion
"So every thought has a contradicting thought ..."
In philosophy , negation means the cancellation of something by something opposite (example: death as the negation of life ). The negation creates a different quality. The negation of the negation creates a new quality that may differ greatly from the initial state. With this type of negation, time plays an important role. It is a representation of every development. At conception death is negated, life arises. The living being develops, is born and then dies again. However, the initial state is not reached again. In the meantime the living being has moved, acted, possibly created offspring (thus passing on its genes) and changed the environment.
Negation in the sense of the philosophical dialectic (Hegel's)
In Hegel's dialectic , negation is an aspect of the critical antithesis. It also represents one of the three aspects of the meaning of the term abolition . Negation is the critical rejection of a positive philosophical system . Following Hegel, Engels postulated the law of the negation of negation .
In this context one has by no means to imagine the antithesis or the opposition as a mere logical negation. Rather, two terms are compared with one another and viewed in their relationship to one another. The negation is the transition from one concept to the other and vice versa. This transition not only starts with the original concept, but is developed from this itself and carried out so completely that the respective original concept, but also the opposite, is argued comprehensively rejected in the reverse.
For specific examples, see the article on the science of logic .
The "miracle of negation"
From an anthropological perspective, negation is sometimes seen as specific to man and his spirituality. The judgment is something “paradoxical” as the connection between two concepts is retained even if the negative sentence can be formulated. “This miracle of a connection, which means that it has been abolished, distinguishes human language from all other forms of communication in the animal kingdom: Nonhuman animals cannot deny or affirm, i.e. they cannot judge. So there is no 'true' or 'false' for them. "
Man as a living being that can say no
In the art , there are various aspects of negation: So an art direction is replaced by another and negates it. New methods take the place of the old ones. L'art pour l'art denied that art was bound to a specific purpose .
While a detailed, realistic representation was the goal in painting for a long time before the invention of photography , painting afterwards shifted to abstract , impressionist , expressionist , cubist and other representations of a reality that was not seen by the camera. Often these art movements also had programs that rejected much of what had been there before.
The Dada denied the entire hitherto applicable art and mocked them. In Richard Huelsenbeck's Dadaist Manifesto it says: “The word Dada symbolizes the most primitive relationship to the surrounding reality, with Dadaism a new reality comes into its own. Life appears as a simultaneous tangle of noises, colors and spiritual rhythms, which is unwaveringly adopted into Dadaist art with all the sensational screams and fevers of its daring everyday psyche and all of its brutal reality. "
Art tries to describe reality , or tries to negate it, like the situationist artist movement of the 60s, which wanted to negate work, capitalism and finally art itself by transferring it to everyday life .
In music , the pause and the silence - the negation of the tone - play a major role. Negation as destruction: Jimi Hendrix musically shredded the American national anthem and lit his guitar. The punk movement negated with their rebellion in all customs and values of middle-class society.
- Complement gate
- Propositional logic
- Particle of negation in French
- Double negative
- Negating art (English article about negation in art)
- Emmy Noether Young Investigator Group “ Psycholinguistics of Negation ”
- Laurence R. Horn & Heinrich Wansing : Negation. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .
- Bross, F. (2020): The why-how alternation and a new test for sentential negation — on negated how-questions . In: Glossa. A Journal of General Linguistics, 5 (1), 63.
- Frege, Gottlob: The negation: a logical investigation. In: Contributions to the philosophy of German idealism I. 3/4 (1919), p. 143. In: Frege, Logical investigations , 3rd edition. (1986) - ISBN 3-525-33518-0 , p. 54 ff.
- Tugendhat / Wolf: Logical-semantic propaedeutics. 1983, p. 214.
- Frege, Gottlob: The negation: a logical investigation. In: Contributions to the philosophy of German idealism I. 3/4 (1919), P. 143. In: Frege: Logical investigations. 3. Edition. 1986, ISBN 3-525-33518-0 , p. 54 (67).
- Reinhardt Brandt: Philosophy: an introduction. Reclam, Stuttgart 2001, p. 53.
- Referent Rehfus: Introduction to the Study of Philosophy , 2nd edition. 1992, ISBN 3-494-02188-0 , p. 117.