être en contradiction - translation to English
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être en contradiction - translation to English

FORM OF INDIRECT PROOF THAT ESTABLISHES THE TRUTH OR VALIDITY OF A PROPOSITION
Indirect proof; Prove by contradiction; Proof by Contradiction; Proofs by contradiction; Refutation by contradiction

être en contradiction      
conflict, collide

Definition

contradict
(contradicts, contradicting, contradicted)
1.
If you contradict someone, you say that what they have just said is wrong, or suggest that it is wrong by saying something different.
She dared not contradict him...
His comments appeared to contradict remarks made earlier in the day by the chairman...
He often talks in circles, frequently contradicting himself and often ends up saying nothing.
VERB: V n, V n, V pron-refl
2.
If one statement or piece of evidence contradicts another, the first one makes the second one appear to be wrong.
The result seems to contradict a major U.S. study reported last November.
VERB: V n

Wikipedia

Proof by contradiction

In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid.

More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, and reductio ad impossibile.

A mathematical proof employing proof by contradiction usually proceeds as follows:

  1. The proposition to be proved is P.
  2. We assume P to be false, i.e., we assume ¬P.
  3. It is then shown that ¬P implies falsehood. This is typically accomplished by deriving two mutually contradictory assertions, Q and ¬Q, and appealing to the law of noncontradiction.
  4. Since assuming P to be false leads to a contradiction, it is concluded that P is in fact true.

An important special case is the existence proof by contradiction: in order to demonstrate that an object with a given property exists, we derive a contradiction from the assumption that all objects satisfy the negation of the property.

Examples of use of être en contradiction
1. Je ne voulais pas être en contradiction avec moi–même en l‘acceptant.» Du coup, Devedjian promet d‘occuper «le ministère de la parole». «Je retrouve ma liberté d‘expression et, croyez–moi, cela m‘est cher tant il y a des choses à dire.
2. Elle aura besoin qu‘on s‘engage par le ministère de la parole pour apporter la conviction parce que les résultats électoraux ne peuvent satisfaire personne". Interrogé sur les raisons pour lesquelles il n‘avait pas accepté le poste de ministre délégué à l‘Aménagement du territoire, il a répondu÷ "J‘ai toujours pensé que c‘était un ministère inutile et je ne voulais pas être en contradiction avec moi–même.