7.3 What does this sentence “mean”? Entailments vs. implicatures

Entailments

In this chapter, we are interested in how word meanings combine to arrive at sentence meaning. To analyze the meaning of a word in a language, it’s not useful to just look at that word in isolation. For example, if you wanted to know what the meaning of the verb sigh was, looking at just the word sigh is not insightful. What we want to consider is the interaction of this word with other words in that language: we need to look at how that word is (or isn’t) used in sentences in that language. Because sentences inform us about the meaning of words, we will first think about what we can and cannot conclude from the meaning of sentences.

Consider the sentences in (1) and (2).

If the sentence in (1) is true, then the sentence in (2) is necessarily true, too. We say that the sentence in (1) entails the sentence in (2), or that (2) is an entailment of (1). Using variables p and q as placeholders for sentences, we can define entailment in the following way: p entails q if and only if p being true makes q necessarily true, too.

You can see if something is necessarily true from a sentence by negating the piece of meaning in question with “it is not the case that…” as in (3) and conjoining it with the original sentence with “but…” as in (4). For example, if we want to show that (2) is an entailment of (1), we want to see what happens when we negate (2) and conjoin it with (1).

The ⊥ symbol indicates a contradiction. A contradiction is a sentence that is never true. When you negate an entailment of a sentence, you get a contradiction. So we say that the sentence in (4) is a contradiction. We can also say that the sentence in (3) contradicts the sentence in (1). (4) is a contradiction because if you sigh, it is necessarily the case that you emit a breath; it would be impossible to sigh without doing so. This contradiction informs us what it means for someone to sigh: what’s required of this event.

 Implicatures

Consider other things we might conclude from the sentence in (1), reproduced below as (5). (6) is something we might conclude from hearing (5).

Is (6) an entailment of (5), though? Let’s try the contradiction test.

(8) is not a contradiction, which means that (6) is NOT an entailment of (5). (6) is called an implicature of (5). Once again using the variables p and q as place holders for sentences, p implies q if, based on the context, p has the suggestion that q is true, but q is NOT necessarily true. In other words, an implicature is a possible, but not a guaranteed, conclusion from a sentence. You can show that something is not necessarily true by cancelling it (negating it without a contradiction) as we did in (8). Implicatures are cancellable because they don’t always have to be true. For example, it’s possible in this case that the customer sighed for other reasons: relief, for example. 

Implicatures will be covered in more detail in Chapter 8, but for right now, it is important for us to be aware of what we mean when we say a sentence “means” something: is it an entailment or an implicature?

Presuppositions

Now consider the following sentence.

The sentence in (9) expresses that the restaurant no longer charges extra for guacamole. That’s likely a good thing for customers who are hoping to cut down on lunch costs. However, guacamole enthusiasts may still feel mild annoyance towards what is expressed in this sentence because the sentence also “means” (10).

(10) is an entailment of (9), as shown below:

(10) is a special kind of entailment, called a presupposition. A presupposition is an entailment that a sentence takes for granted. (9) presupposes (10), meaning that (9) assumes that (10) is true already. To illustrate this, imagine this discourse:

In (12), the only thing that Ken is able to contest is whether or not the restaurant stopped charging extra for guac or not. Even when Ken says “that’s not true”, it is still assumed by Ken and Hanna in this conversation that the restaurant has charged extra for guacamole in the past. This is what we mean when we say that the content of the presupposition is taken for granted.

Because a presupposition is what must be true before a sentence is uttered, it cannot be the target of negation or questioning in the main sentence. Consider (13) and (14).

(13) and (14) still presuppose (10): ‘The restaurant used to charge extra for guacamole’. Whether a piece of meaning “survives” negation and questions is a good diagnostic to see if it is a presupposition or not. Contrast (13)/(14) with a regular (non-presupposition) entailment in (15). What happens to the entailment that the customer emitted a breath in (16) and (17)?

The entailment that was there with (15) is no longer there in (16) and (17). If it is not the case that the customer sighed, we cannot necessarily conclude that they emitted a breath. If we are asking if the customer sighed, we also cannot necessarily conclude that they emitted a breath.

In summary, there are two main kinds of sentential meaning relations we discussed in this section: entailments and implicatures. Entailments can further be split into “regular” entailments and presuppositions. 

Check your understanding

Strawson, P. F. (1950). On referring. Mind, 59(235), 320-344.