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Cancelling the Maxim of Quantity: Another challenge for a Gricean theory of Scalar Implicatures

Paper · 2014 · Danny Fox

Summary

Fox asks which system produces scalar implicatures (SIs), such as reading "John talked to Mary or Sue" as "not both". One option is general Gricean reasoning built on the Maxim of Quantity (MQ). The other is grammar, through an optional covert exhaustification operator, exh. He argues that conceptual arguments cannot settle this and offers an empirical test instead: contexts where MQ is switched off. Grice's own example is a treasure hunt, where everyone knows the speaker will hold back information. In such games, the inference that the speaker does not know which disjunct is true goes away. The exclusive "not both" reading, however, survives. The grammatical approach predicts this split directly. It treats MQ as producing only ignorance inferences and derives SIs from a parse containing exh. Pragmatic and neo-Gricean accounts derive both kinds of inference from MQ, so they wrongly expect both to vanish together. Fox also examines a pretense-based pragmatic rescue, in which an imagined cooperative speaker stands in for the real one. He finds it workable only with arbitrary extra assumptions, including a hard-wired opinionated speaker.

Key points

  • A disjunction "M or S" yields two distinct inferences. One is the exclusive SI, ¬(M & S). The other is a set of ignorance inferences about each disjunct, written I_x(M) and I_x(S).
  • In the grammatical account, a sentence has two parses, with and without exh. Only the exh parse entails ¬(M & S). Ignorance about the disjuncts comes from MQ under either parse.
  • In a treasure-hunt setting, MQ is cancelled, using examples like "money in box 20 or 25". Ignorance inferences disappear there, but the exclusive inference stays.
  • Asher & Lascarides' adversarial cases, such as a prosecutor questioning a defendant, are different. There a norm to give all relevant information still holds, so ignorance inferences persist.
  • The pretense rescue models an imagined speaker (IS) whose beliefs the actual speaker (AS) shares. Fox raises three objections to it:
    • its key premise lacks justification;
    • it cannot separate ignorance inferences from SIs that have the same content;
    • it needs a stipulated opinionated-speaker assumption.

Interesting ideas

  • I1. The paper's core diagnostic is to test whether two inferences share a source by finding a context that removes one hypothesized source and seeing which inference survives.
  • I2. Fox treats the speaker's ignorance and the "not both" reading as two separate outputs with different triggers, rather than one bundled "or" meaning.
  • I3. In his account, strengthening is an optional operator in the parse, so a sentence carries both a plain and an exhaustified reading.
  • I4. He links whether ignorance inferences apply to a discourse-level flag: does the speaker owe full information here?

For Mova

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

  • I1 (learn): Build negative-control test suites where cooperativity is explicitly suspended, such as games or quizzes, and check that the implicature module drops ignorance inferences while keeping exclusive readings.
  • I2 (frames): In crate prag, store the exh-strengthened reading and the speaker-ignorance inference as separate annotated facts, each carrying its justification, so later stages can retract one without the other.
  • I3 (world): Keep both readings as alternative world states and let context decide which one survives, instead of fixing one reading too early.
  • I4 (answer): When answering questions about fables or games, such as a trickster hiding treasure, read the genre or role flag to avoid wrongly concluding that a character "doesn't know".

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Massachusetts Institute of TechnologyCambridge · United States159 works · 65,157 citations🎓Hebrew University of JerusalemJerusalem · Israel50 works · 9,147 citations

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 9,086 worksArtificial Intelligence · 8,889 worksArts and Humanities · 9,296 worksLanguage and Linguistics · 9,206 works

🧭 Topics 1Research subjects and languages the work is about.Implicature · 72 works

Cite

Cite as Danny Fox. 2014. Cancelling the Maxim of Quantity: Another challenge for a Gricean theory of Scalar Implicatures. Semantics and Pragmatics.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.3765/sp.7.5

@article{fox2014cancelling,
  title = {{Cancelling the Maxim of Quantity: Another challenge for a Gricean theory of Scalar Implicatures}},
  author = {Danny Fox},
  journal = {Semantics and Pragmatics},
  year = {2014},
  doi = {10.3765/sp.7.5},
  url = {https://doi.org/10.3765/sp.7.5}
}

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