📄 Gricean views of exhaustification: A note on Westera (2022)

Summary

This commentary examines an argument in Westera (2022) for Attentional Pragmatics. That framework adds attention maxims (A-Quality, A-Relation, A-Quantity) to the familiar information maxims (I-Quality, I-Relation, I-Quantity). Fox (2014) described a game show in which the host gives a disjunctive hint saying that box 20 or box 25 contains cash. The hint does not suggest that either box might hold money, yet listeners still read it as excluding both. Westera explains this pattern by assuming the scenario cancels both I-Quantity and A-Quality. Zumchak and Schwarz show that this creates a problem. In Westera's system, exhaustivity comes from A-Quality and A-Quantity working together, so canceling A-Quality should remove every exhaustivity inference, including exclusivity. The authors offer two repairs:

• Restate A-Quantity: replace its reference to A-Quality with a copy of the default A-Quality condition.
• Weaken cancellation: treat canceling A-Quality as weakening its requirement rather than removing it.

Either repair forces exhaustivity to come from Quantity being satisfied. This departs from Grice's idea that it arises from a clash between maxims. The result may be the first real argument for a restricted Quantity maxim.

Key points

• Fox's scenario has 100 boxes, five of which hold a million dollars each. The host knows which boxes these are and gives only partial hints, so contestants infer no possibility for box 20 or box 25, but they still infer the boxes are not both full.
• Under ordinary conditions, the I-maxims together with a question under discussion containing 20, 25, (20∧25) and (20∨25) yield:
  • the possibility inferences ♢20 and ♢25;
  • the exclusivity inference ¬♢(20∧25).
• Westera's A-Quantity is a conditional that refers to A-Quality. If cancellation turns A-Quality into a tautology, the exclusivity inference disappears along with the possibility inferences.
• A clash-based ("unrestricted") A-Quantity cannot be rescued by either repair:
  • Trivializing A-Quality makes the required inference a contradiction.
  • Weakening A-Quality yields ¬♢(20∨25), which conflicts with the I-Quality inference □(20∨25).
• The authors note that earlier work often assumes a restricted Quantity maxim, but nobody had explicitly argued for it.

Interesting ideas

• I1. Keeping two separate layers of speaker commitment, what is asserted versus which possibilities are made salient, lets possibility and exclusivity inferences be derived and canceled independently.
• I2. "Canceling" a maxim can mean relaxing it (here, from "all" to "at least one") rather than switching it off, and the choice changes which inferences survive.
• I3. A candidate implicature gets rejected when it contradicts an inference already derived from another maxim (e.g. Quality). This works as a built-in consistency check on the whole set of inferences.
• I4. In contexts where the speaker is known to hold back information on purpose, such as a game host or a test-giver, ignorance inferences should not be drawn, but some exclusivity readings may still hold.
• I5. Each maxim is written as an explicit formula over a question under discussion with modal operators, and every inference is derived step by step. This makes a theory's gaps visible and testable.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

• I1 (frames): crate prag could record a disjunction's asserted content apart from its attended alternatives, so each implicature traces back to the layer that produced it.
• I2 (frames): when a context such as a quiz hint or a riddle suspends a maxim, prag could apply a graded relaxation and keep the weaker demand, instead of dropping it entirely.
• I3 (world): the world model could refuse to add any implicature that contradicts beliefs already attributed to the speaker, and log the rejection as part of the explanation.
• I4 (answer): readers of school tests and riddle-like tasks could flag such deliberately partial speakers, so that a hint is not taken as a sign of what the speaker doesn't know.
• I5 (frames): implicature rules in prag could be stored as checkable logical conditions over the current QUD, so failing derivations can be found by running the rules rather than by intuition.