A presupposition is an assumption related to an utterance. The truth of the utterance is taken for granted in discourse. The presupposition must be assumed by the speaker and hearer for the utterance to be appropriate. The word presupposition is often used in the branch of linguistics known as pragmatics.
The following are examples of presuppositions:
(1) Have you stopped smoking?
(2) Can I borrow your guitar?
(3) Have you seen Jack?
(4) My son no longer plays the guitar.
(5) My wife is sick.
In (1) the presupposition is that the subject has smoked. In (2) the presupposition is that the hearer has a guitar. The third question presupposes that Jack exists. In (4) the presupposition is that the subject's son once played the guitar and in the fifth utterance, the presupposition is that the subject has a wife.
Negation of the utterance does not change the presupposition. We can change (1) to Haven't you stopped smoking? Nevertheless, the presupposition is that the subject has smoked. The question Have you stopped smoking? can be considered a neutral question whereas Haven't you stopped smoking? expresses that the speaker believes the hearer has stopped smoking but is not entirely certain.
However, this is not always the case with entailment. The sentence He was assassinated entails He is dead, but the negative He wasn't assassinated does not necessarily entail He is dead. From the sentence He wasn't assassinated it isn't clear whether or not the subject is dead.
In discourse the truth of the utterance is assumed. This is known as presupposition. Unlike in the case of entailment, negation of the utterance never changes the presupposition.
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