As discussed above, intensional contexts are contexts where the denotation of an expression (e.g., the truth value of a sentence) cannot be determined from the denotations of its constituent parts. In addition to those we have already mentioned, namely propositional attitude verbs and non-intersective adjectives, a number of other linguistic features are known to create such contexts as well. These include tense, modality, and counterfactuals. We will discuss these topics in more detail in later chapters; here we focus only on issues of compositionality.
To begin with, let us contrast the intensional behavior of modality (markers of possibility and necessity) with the behavior of a non-intensional operator, negation. Modals are similar to negation in certain ways: both combine with a single proposition to create a new proposition. The crucial difference is this: in order to determine the truth value of a negated proposition, we only need to know the truth value of the original proposition. For example, both of the sentences in (21), if spoken in 2006, would have been false. For that reason, we can be sure that both of the negated sentences in (22), if spoken in 2006, would have been true.
(21) (spoken in 2006)
a. Barack Obama is the first black President of the United States. [F]
b. Nelson Mandela is the first black President of the United States. [F]
(22) (spoken in 2006)
a. Barack Obama is not the first black President of the United States. [T]
b. Nelson Mandela is not the first black President of the United States. [T]
But with modal operators like might, could, must, etc., it is not enough to know the truth value of the original proposition; we need to evaluate its meaning, in combination with that of the modal operator. Even though both of the sentences in (21) had the same truth value in 2006, the addition of the modal in (23) creates sentences which would have had different truth values at that time.
(23) (spoken in 2006)
a. Barack Obama could be the first black President of the United States. [T]
b. Nelson Mandela could be the first black President of the United States. [F]
Tense is another operator which combines with a single proposition to create a new proposition. As with modality, knowing the truth value of the original proposition does not allow us to determine the truth value of the tensed proposition. Both of the present tense sentences in (24a–b), spoken in 2014, are false; but the corresponding past tense sentences in (24c–d) have different truth values.
(24) (spoken in 2014)
a. Hillary Clinton is the Secretary of State. [F]
b. Lady Gaga is the Secretary of State. [F]
c. Hillary Clinton was/has been the Secretary of State. [T]
d. Lady Gaga was/has been the Secretary of State. [F]
Similarly, knowing that the present tense sentence in (25a) is true does not allow us to determine the truth value of the corresponding future tense sentence (25b).
(25) a. Henry is Anne’s husband. [assume T]
b. In five years, Henry will (still) be Anne’s husband. [?]
As we have seen, one of the standard diagnostics for intensional contexts is the failure of substitutivity: in intensional contexts, substituting one expression with another that has the same denotation may affect the truth value of the sentence as a whole. The examples in (26) illustrate again the failure of substitutivity in the complement clause of a propositional attitude verb. They refer to an Englishman named James Brooke who, through a combination of military success and diplomacy, made himself the king (or Rajah) of Sarawak, comprising most of northwestern Borneo. During the years 1842 to 1868, the phrases James Brooke and the White Rajah of Borneo referred to the same individual. Suppose that sentence (26a) was spoken in 1850, perhaps by one of Brooke’s old mates from the Bengal Army. Even if (26a) was true at the time of speaking, sentence (26b) spoken at that same time by the same speaker would certainly have been false.
(26) (spoken in 1850)
a. I do not believe that James Brooke is the White Rajah of Borneo.
b. I do not believe that James Brooke is James Brooke.
The examples in (27) illustrate the failure of substitutivity in a counterfactual statement. Sentence (27a) is something that a rational person might believe; at least it is a claim which could be debated. Sentence (27b) is derived from (27a) by substituting one NP (the first black President of the United States) with another (Barack Obama) that has the same denotation. Clearly sentence (27b) is not something that a rational person could believe.
(27) a. Martin Luther King might have become the first black President of the United States.
b. Martin Luther King might have become Barack Obama.
The examples in (28) also illustrate the failure of substitutivity in a counterfactual; but instead of replacing one NP with another, this time we replace one clause with another. The two consequent clauses are based on propositions which have the same truth value in our world: both would be false if expressed as independent assertions. But replacing one clause with the other changes the truth value of the sentence as a whole: (28a) is clearly true, while (28b) is almost certainly false.
(28) a. If Beethoven had died in childhood, we would never have heard his magnificent symphonies.
b. If Beethoven had died in childhood, Columbus would never have discovered America.
Another class of verbs which create intensional contexts are the so-called intensional verbs. Prototypical examples of this type are the verbs of searching and desiring. These verbs license de dicto vs. de re ambiguities in their direct objects, as illustrated in (29). Sentence (29a) could mean that the speaker is looking for a specific dog (de re), perhaps because it got lost or ran away; or it could mean that the speaker wants to acquire a dog that fits that description but does not have a specific dog in mind (de dicto). Sentence (29b) could mean that John happens to be interested in the same type of work as the addressee (de re); or that John wants to be doing whatever the addressee is doing (de dicto).
(29) a. I’m looking for a black cocker spaniel.
b. John wants the same job as you.
The direct objects of such verbs are referentially opaque, meaning that substitution of a coreferential NP can affect the truth value of a sentence. Suppose that Lois Lane is looking for Superman, and that she does not know that Clark Kent is really Superman. Under these circumstances, sentence (30a) would be true, but (30b) would (arguably) be false.5
(30) a. Lois Lane is looking for Superman.
b. Lois Lane is looking for Clark Kent.
Furthermore, if the direct objects of intensional verbs fail to refer in a particular situation, it may still be possible to assign a truth value to the sentence. Both sentences in (31) could be true even though in each case the denotation set of the direct object is empty. All of these properties are characteristic of intensional contexts.
(31) a. Arthur is looking for the fountain of youth.
b. John wants a unicorn for Christmas.
5 This example comes from Forbes (2013). Forbes points out that not all semanticists share this judgement about (30b).