3.2 Properties and diagnostics of presuppositions

A sentence can have both entailed meaning and presupposed meaning. This section covers the distinction between those two types of meaning. Several tests are introduced involving the contrapositive, negation, questioning, conditionals, and denial.

3.2.1 Contraposition

To start, let's consider some properties of entailments. Recall that a proposition p entails q if and only if it is the case that whenever p is true, q is also true. One property of entailments is that something called contraposition holds for entailments. What does this mean? The contrapositive is a statement about the two propositions p and q in an entailment (where p entails q; p being called the 'hypothesis' and q being called the conclusion). It is formed by negating both the hypothesis and the conclusion and interchanging the direction of their relationship. So if p entails q, the contrapositive is the statement that ¬q entails ¬p.

Entailments have the property that contraposition holds. Consider examples (8) and (9):

Confirm for yourself that (8) and (9) stand in an entailment relationship with each other ((8)⇒ (9)): Mary smokes ⇒ Somebody smokes. This can be read as "If Mary smokes, then somebody smokes", which is a true statement. Now we can see what happens when we form the contrapositive (¬(8)⇒ ¬(9)), shown in (10):

The contrapositive expressed in (10) is also true (i.e., the claim that "if nobody smokes, then Mary doesn't smoke" is a true claim).

Presuppositions, however, have the property that contraposition does NOT hold. Consider examples (11) and (12):

The relationship between (11) and (12) is one of presupposition. Specifically, (11) presupposes (12), which means that evaluating the truth of (11) is impossible without (12) already being true. In other words, we can't check whether it's true in a particular world that Bill regrets that he lost if it's not true in that world that he lost. Now we can form the contrapositive by negating (11) and (12) and swapping their order, and we can ask what the resulting relationship is between the two negated propositions:

It's hard to make sense of the expression in (13). Whatever that relationship is (whatever "??" should be), it's not the same as the simple entailment relationship in (10) nor does the expression convey a presupposition. We say that contraposition fails.

3.2.2 Negation

Assessing the status of the contrapositive can be difficult. Another, arguably simpler, test which distinguishes entailments from presuppositions is negation. Entailments are said to be "killed" under negation, whereas presuppositions "survive" negation. If p entails q, ¬p does not entail q. For examples (8) and (9) above about Mary smoking, we can try negation, as in (14).

Although Mary's smoking entails that someone smokes, the negation (that Mary doesn't smoke) no longer entails that someone smokes.

The story is quite different for presupposition under negation. While entailments are killed off, presuppositions survive. For examples (11) and (12) above about Bill regretting having lost, we can try negation, as in (14). The dotted arrow is being used here to link a sentence with its proposition.

Under negation, the presupposition survives: Even if Bill doesn't regret losing, the fact remains that he still lost.

3.2.3 Questioning and conditionals

Entailments and presuppositions also behave differently from each other in contexts that cast doubt on content. Such contexts include questions and conditions. Entailments are killed off by questioning and killed off in conditionals, whereas presuppositions survive. Examples (15-17) show the behaviour of an entailment, an existential presupposition, and a factive presupposition:

In (15), the entailment is killed off by questioning: Ben may have gone to France or not, but the question about whether he went to Paris guarantees us nothing about his presence in France. Likewise, the entailment is killed off by the conditional because the conditional, like a question, raises the possibilty that the event described may not have happened. In (16), the presupposition survives questioning and the conditional: If we ask a question about Ben's dog or make a claim about what would happen if that dog has fleas, we necessarily assume there is a dog that exists. In (17), the presupposition again survives questioning and the conditional: If we ask whether Ben knows that his dog has fleas or consider what would happen conditional on his knowing, we are basing what follows on the fact of the fleas.

3.2.4 Denial

The last diagnostic test requires imagining a dialog context. One speaker makes a claim and the other responds "That's false". The question is what is being falsified. The generalisation is that it's the asserted content (the main point of the utterance and any accompanying entailments) that the speaker can claim is false. It's much more difficult to deny presupposed content, precisely because that content is background to the main assertion. Consider examples (18-20) with a statement from Speaker A and the ensuing denials from Speaker B:

To summarise the diagnostic tests listed here, presuppositions are:

• hard to kill,
• hard to question,
• and hard to deny.

To go on to section 3.3 on "Triggers, accommodation, presupposition failure", click here.