A contradiction (from latin contra , "against" and Latin dictio , "the shots, speeches," "reply, contradiction") located in the logic when two terms , sentences or statements in contradiction stand and each other, a mutual negation represent. Opposite - and adversarial - is the contrary opposition .

## General

Adversarial or contrary are both opposites in themselves. While contradiction concerns two mutually exclusive and mutually negating terms, judgments, or statements, contradicting terms in a series of coordinated terms are most distant and differ as widely as possible. Contrary terms, judgments or statements do not only have to consist of two opposites, more are also possible.

A contradiction, also known as a contradiction , is a statement that claims that two contradicting statements apply at the same time. In other words, it is the conjunction of two contradicting statements, for example the statement “The earth is round and the earth is not round” or the expression . In classical logic , a contradiction is always wrong and thus a falsum ( Latin falsum , "the wrong thing"). In a broader sense, all statements that are always wrong for purely formal-logical reasons are called contradiction, even if they do not have the form of a conjunction. The common symbol for a contradiction is . ${\ displaystyle P \ land \ neg P}$ ${\ displaystyle \ bot}$

A distinction must be made between the contradictory relationship and the contradicting relationship that exists between two statements when both cannot be true at the same time, but can also be false.

The oxymoron figure of speech is thematically related to contradiction . The opposite of contradiction is tautology . The figure of speech of pleonasm forms a contrast to the oxymoron .

## Examples

In contradiction, either “ yes ” or “ no ”, “ guilty ” or “ not guilty ”, “ truth ” or “ untruth ”, there is no third option. That is why the opposite of the contradiction itself is a contradiction because there is no third possibility.

For example, you can

• on the one hand, conclude that if the statement "The world is not round" is true, the statement "The world is round" must be false;
• on the other hand, if the statement "The world is not round" is false, the statement "The world is round" must be true.

While these two statements are adversarial because of their form (one is the negative of the other), many pairs of statements are adversarial because of their content. Content-wise contradicting, for example, the statements “The child is healthy” and “The child is sick”, because whoever is not healthy is sick and who is not sick is healthy. Whether two statements are contradictory to one another depends mainly on the meaning of the content ( intention ) of the predicators involved , here on the predicators “healthy” and “sick”.

• A propositional conjunction of the form "A and not A" (for example " The earth is a disk , and it is not the case that the earth is a disk") is a contradiction, since it always has the truth value "false", regardless of whether the truth value of "A" is true or false.
• In the logical square , on the one hand, the quantor logic statements “All S are P” and “Some S are not P”, and on the other hand the statements “No S is P” and “Some S are P” are contradicting each other. The statements “All x are P” and “No x is P” are contrary to each other (both cannot be true at the same time, but can be false at the same time).
• The statement “I always lie” is sometimes taken to be implicitly adversarial. Because if the statement were true, then it would have to be false at the same time (since the speaker then always lies); but if it were wrong, the speaker would lie and therefore tell the truth. But even if the speaker lies with the statement, it does not follow that he always lies. If, on the other hand, he occasionally tells the truth, he is lying when he claims to always lie - but nothing contradicting follows from this. (See also Epimenides's Paradox .)
• In fact, there is a similar and really problematic statement, namely the statement “This statement is false” (hereinafter abbreviated as “A”). Suppose A were true; then what A says would apply, namely that A is false. And suppose A was wrong; then what A says would not be true, so then it would not be true that A is wrong. Both assumptions (that A is true and that A is false) really lead to a contradiction here. This statement is one of the so-called semantic paradoxes that, according to Alfred Tarski , come about because natural languages ​​- in contrast to formal object languages - contain their own truth predicate (see also Liar's Paradox ).
• In order to state that a statement is contradictory, Ludwig Wittgenstein uses the phrase in Tractatus Logico-Philosophicus that the truth conditions of the sentence are contradictory: "If the sentence is false for all truth possibilities, the truth conditions are contradictory".

In Austria , the interrogation of adversaries has been known since 1993 within the framework of criminal proceedings . An adversarial questioning of the accused or a witness is permissible according to § 165 StPO if there is a risk that the questioning in a main hearing will not be possible for factual or legal reasons. The witnesses are interviewed separately so that the accused and the witnesses do not meet directly. The adversarial interrogation is also called "gentle interrogation" because the injured party or witness is spared a confrontation with the accused.