Subsection Phrase-structure rules and compositionality
We know how to construct the expression
red ball formally: we apply the rules in (a):
- (1a)
[
\(_{\text{AP}}\) (ADV) ADJ (PP)]
- (1b)
[
\(_{\text{NP}}\) (DET) (AP) N]
Red is an adjective, and according to the rule in (1a), an AP can consist of just an adjective, so it is also an adjective phrase;
ball is a noun, and according to the rule in (1b), an noun directly preceded by an adjective phrase forms a noun phrase. Applying the rules gives us the structure in (2):
- (2)
[
\(_{\text{NP}}\) [
\(_{\text{AP}}\) [
\(_{\text{ADJ}}\) red ] [
\(_{\text{N}}\) ball]
We also know that
red ball has the meaning “the set of entities that are red and that are balls”, i.e., it is the combination of the predicates in (3a) and (3b), as shown in (3c):
This relationship between form and meaning can be captured adding instructions for semantic composition to the phrase-structure rule itself — something like (4a), represented more formally in (4b)::
Remark 8.9.1. Terminology.
We use PRED
\(_{\text{ADJ}}\)(x) to represent the predicate associated with the adjective and PRED
\(_{\text{N}}\) to represent the meaning of the noun (which, as you recall, can be thought of as a predicate, too). This is not a standardly used notation — one notation that you will often see in formal semantics is the following: ⟦ADJ⟧, ⟦N⟧, ⟦red⟧, ⟦ball⟧, etc, where the white square brackets mean “the meaning of” whatever is enclosed in them. We do not use this notation here because we feel you have enough brackets to distinguish already (and, we are not formal semanticists).
If we apply the rule in (4b) to the words
red and
ball, we specify that the AP is the adjective
red and the PRED
\(_{\text{AP}}\) is RED(x) and that the N is the noun
ball and the PRED
\(_{\text{N}}\) is BALL(x), giving us the correct form and meaning of the phrase:
- (5)
[
\(_{\text{NP}}\) [
\(_{\text{AP}}\) (DET) [
\(_{\text{ADJ}}\) red ] [
\(_{\text{N}}\) ball] / RED(x) ∧ BALL(x)
By attaching such instructions (or semantic representations) to all phrase structure rules, we can model the compositional meaning of any complex expression. Of course, this is very difficult in actual practice, as languages are very complex systems, and there is a lot of disagreement in linguistics as to how best to do it, but the basic idea is straightforward and widely agreed upon.
Subsection Phrase-structure rules and idiomaticity
If we claim that the account sketched out above can account for the compositional meanings of complex expressions, we also have to think about how it could deal with idomaticity — for example, with the phrase
red herring, whose meaning has nothing to do with the colour red or with herrings, but instead is “information presented as a distraction”.
One idea would be to claim that it it not a syntactic phrase at all, but a single word — a compound, like
redneck or even one that just happens to look as though it contains the elements
red and
herring, like
redaction could be misconstrued as consisting of the elements
red and
action. There would be nothing to explain, we could treat it like any other word.
The problem with this approach is that while the meaning of the phrase
red herring is not composed of the meaning of its parts, those parts still behave as though they are individual words. The adjective
red can be inflected, for example:
- (6a)
Carbon offsets are an even
redder herring than Zoe had thought.
- (6b)
Carbon offsets are not simply a red herring, they are the
reddest herring in the entire climate change debate.
In other words, we have to assume that the form of an idiom is constructed in the same way as that of a corresponding compositional phrase, while its meaning is not. We can represent this in the same format, as compositional cases, replacing the compositional meaning with the idiomatic meaning, as informally paraphrased in (7a) and represented more formally in (7b):
Instead of a specifying a very general rule for the interpretation of noun phrases (see 4b), (7b) represents a very specific rule that applies only to the combination
red herring. Instead of calling it a “rule”, we could also think of it as stating an exception to this very general rule.
Representing idioms in this way models their non-compositional meaning, while capturing three important facts about them. First, as already mentioned, it captures the fact that idioms behave syntactically like phrases (for example, their individual parts can, to some extent, be inflected). Second, it captures the fact that idioms can also be interpreted literally —
This is red herring can mean ‘this is a herring and it is red’ (if we interpret it according to the rule in 4b),
or it can mean ‘this is information that is presented in order to distract someone’ (if we interpret it according to the rule (or exception) in 7b). Third, it captures the fact that even if we do interpret an expression idiomatically, we can recognize its literal meaning simultaneously.
