Presupposition
We have seen that a proposition p entails another proposition q if q must be true whenever p is true. In this light, consider the following two propositions:
(70) and (71) are p and q. On our definition of entailment, p certainly entails q: if it’s true that the fortieth pope was German, it must be true that there was a fortieth pope. But notice that q can still be true even if p is negated. Thus, if the fortieth pope was actually Spanish, (71) is still true. Rather than saying that (70) entails (71), we will say that it presupposes (71), and that (71) is a presupposition of (70). A proposition p presupposes another proposition q if both p and the negation of p entail q. (Another way of thinking about presupposition is that a proposition’s presupposition is the precondition of its truth or falsity.)
For ease of reference, let’s call the proposition whose presuppositions we’re interested in the trigger. Thus, (70) is the trigger for (71). Presuppositions differ from entailments in that they are true under negation: a presupposition is true even when its trigger is false. Contrastingly, a trigger whose presupposition is false is neither true nor false. An example would be (72):
This presupposes (incorrectly) that there is a sixth Monday in September; accordingly, (72) is neither true nor false: if asked whether (72) was true or false, the most natural answer would be that the question of truth simply does not arise, since it presupposes a state of affairs that does not exist. (Another possibility would be to answer that (72) is false, on the same grounds.) The existence of presuppositions therefore leads us to posit a third truth-value, neither true nor false, relevant in examples like (72). Presuppositions arise because speakers assume certain propositions as part of the background of what they are saying, rather than specifically asserting them. Specifying a proposition’s presuppositions is thus like specifying the background knowledge a speaker is drawing on, and which the hearer will be expected to share.
As we will see, the existence of presuppositions was originally proposed (by Strawson 1950) in order to deal with cases like (70) above containing a definite description: a noun phrase introduced by the picking out a unique individual (in (70), the fortieth pope; see 6.8 below). More recently, however, the account of presupposition has been extended in order to cover triggers like the following:
Regret and realize are said to presuppose the propositions expressed as their clausal object; here, the presupposition is (75).
Examples (78) and (79) call the very existence of presupposition into question. If presuppositions are defined as propositions which are entailed (must be true) when their trigger is both asserted and negated, (78) and (79) suggest that no such propositions may actually exist: alleged presuppositions sometimes turn out to be true, sometimes false. In short, there may be no consistent category of presupposition which can be given a definition comparable to the definition of entailment proposed in (66). Instead, the question of what propositions are assumed as the background of a given trigger is purely a contextual matter determined by particular utterance situations. The discussion here has done no more than outline the beginnings of this problem: the existence of presuppositions has been a topic of lively and continuing debate in linguistics, and many researchers would by no means accept that (78) and (79) are conclusive evidence that no category of presupposition should be recognized in the study of relations between propositions. See Kempson (1977: Chapter 9) for further discussion.
QUESTION Identify the presuppositions in the following sentences:
a. I recently stopped smoking.
b. Max finally managed to pick the lock.
c. Chirac was not reelected.
d. It was Columbus who discovered America.
e. The president has left the building.
f. She is glad she rejected the offer.
g. Maybe board games will be popular again.
h. Henry didn’t criticize every left-handed DJ.
