7.2.7 The Maxim of Quantity

Grice's Maxims.

Quantity

Let's now turn to the maxim of quantity. To be ``as informative as required'', an utterance must (most of the time...) at least be informative at all. We can get a grip on this minimal requirement using inference. The key idea is that an utterance must contain something new to be informative. And to count as something new logically, the content of the utterance must not be implied by the preceding discourse anyway. We know that if it is implied, the implication with the preceding discourse as antecedent and the (not so) new utterance as consequent will be valid.

The Inference Task

So (again given a preceding discourse ) let's suppose we want to to find out whether some utterance is informative. As we said, we check whether

is valid (that means, whether it is a theorem). In our tableaux calculus, we thus have to attempt to construct a closed tableaux for the equivalent:

If we manage to do so, we know that the new utterance is not informative and thus violates the maxim of quantity. Otherwise, we shall take it to be informative.

As an exercise, we ask you to use PLNQ to check whether ``Mary has a husband.'' is informative in the context ``If Mary is married then she has a husband. She is married.'' (treating the pronouns as in our example above).

?- Discussion!

Give examples of violations of the maxims of quality and quantity that would not be detected by our approach!

Let us emphasize again that Grice's point is not that utterances violating any of the conversational maxims are ill-formed in the sense of ungrammatical strings. Rather, a speaker may violate a maxim on purpose, allowing the hearer to infer ``backwards'' to the speaker's intention. Can you think of situations where this happens?

?- Discussion!

Our treatment of the informativity constraint is obviously oversimplified in that it counts to many utterances as violating the maxim of quantity. The problem is that we assume that all consequences of the complete discourse are always equally present to a hearer. How could we solve (or at least alleviate) this problem?