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So far, we have only considered contexts in which presupposi-tions are assumed to be
true. There are, however, examples of non-factive presuppositions associated with a number of
verbs in English. A non-factive presupposition is one that is assumed not to be true. Verbs
like 'dream', 'imagine', and 'pretend', as shown in [10], are used with the presupposition that
what follows is not true.

[10] a. I dreamed that I was rich. (»I was not rich)
b. We imagined we were in Hawaii. (» We were not
in Hawaii)
c. He pretends to be ill. (» He is not ill)
We have already noted, at the end of the discussion of deixis, a structure that is
interpreted with a non-factive presupposition ('If I had a yacht,... '). Indeed, this type of structure
creates a counter-factual presupposition, meaning that what is presupposed is not only not
true, but is the opposite of what is true, or 'contrary to facts'. Aconditional structure of the type
shown in [11], generally called a counterfactual conditional, presupposes that the informa-tion
in the if-clause is not true at the time of utterance.

[ІІ] If you were my friend, you would have helped me.
(» You are not my friend)
The existence of non-factive presuppositions is part of an inter-esting problem for the
analysis of utterances with complex struc-tures, generally known as 'the projection problem', to
be explored in the next section.
Indicators of potential presuppositions discussed so far are summarized in Table 4. 1.
TABLE 4.1. Protential presuppositions
Type Example Presupposition
existential theX » X exists
factive I regret leaving » I left
non-factive He pretended to be happy » He wasn’t happy
lexical He managed to escape » He tried to escape
structural When did she die? » She died
counterfactual If I weren't ill, » I am ill

Ordered entailments

Generally speaking, entailment is not a pragmatic concept (i.e. having to do with speaker
meaning), but instead is considered a purely logical concept, symbolized by II-. Some
examples of entailment for the sentence in [17] are presented in [І8].

[17] Rover chased three squirrels. (= p)
[І8] a. Something chased three squirrels. (= q)
b. Rover did something to three squirrels. (= r)
c. Rover chased three of something. (= s)
d. Something happened. (= t)

In representing the relationship of entailment between [17] and [І8а.] as p II- q, we have
simply symbolized a logical con-sequence. Let us say that in uttering the sentence in [17], the