presupposition, (1) a relation between sentences or statements, related to but distinct from entailment and assertion; (2) what a speaker takes to be understood in making an assertion. The first notion is semantic, the second pragmatic.
The semantic notion was introduced by Strawson in his attack on Russell’s theory of descriptions, and perhaps anticipated by Frege. Strawson argued that ‘The present king of France is bald’ does not entail ‘There is a present king of France’ as Russell held, but instead presupposes it. Semantic presupposition can be defined thus: a sentence or statement S presupposes a sentence or statement SH provided S entails SH and the negation of S also entails S. SH is a condition of the truth or falsity of S. Thus, since ‘There is a present king of France’ is false, ‘The present king of France is bald’ is argued to be neither true nor false. So construed, presupposition is defined in terms of, but is distinct from, entailment. It is also distinct from assertion, since it is viewed as a precondition of the truth or falsity of what is asserted.
The pragmatic conception does not appeal to truth conditions, but instead contrasts what a speaker presupposes and what that speaker asserts in making an utterance. Thus, someone who utters ‘The present king of France is bald’ presupposes – believes and believes that the audience believes – that there is a present king of France, and asserts that this king is bald. So conceived, presuppositions are beliefs that the speaker takes for granted; if these beliefs are false, the utterance will be inappropriate in some way, but it does not follow that the sentence uttered lacks a truth-value. These two notions of presupposition are logically independent. On the semantic characterization, presupposition is a relation between sentences or statements requiring that there be truth-value gaps. On the pragmatic characterization, it is speakers rather than sentences or statements that have presuppositions; no truth-value gaps are required. Many philosophers and linguists have argued for treating what have been taken to be cases of semantic presupposition, including the one discussed above, as pragmatic phenomena. Some have denied that semantic presuppositions exist. If not, intuitions about presupposition do not support the claims that natural languages have truth-value gaps and that we need a three-valued logic to represent the semantics of natural language adequately. Presupposition is also distinct from implicature. If someone reports that he has just torn his coat and you say, ‘There’s a tailor shop around the corner,’ you conversationally implicate that the shop is open. This is not a semantic presupposition because if it is false that the shop is open, there is no inclination to say that your assertion was neither true nor false. It is not a pragmatic presupposition because it is not something you believe the hearer believes. See also IMPLICATION, IMPLICATURE, MANY -VALUED LOGI. R.B.