Cancelling the Maxim of QuantityAnother challenge for a Gricean theory of Scalar Implicatures

John talked to Mary or Sue. Hear that sentence and something happens automatically. You almost certainly took "or" to mean "either but not both," and you probably also assumed the speaker doesn't know which one it was. Both of those feelings arrived instantly, uninvited, and they felt like common sense. Danny Fox wants to know where they came from. The answer, it turns out, hinges on a thought experiment involving a television game show and a very particular kind of accusation you can make after the show is over. Those two effects have names. The first is a scalar implicature — specifically, an exclusive inference: from "Mary or Sue," you infer "not both Mary and Sue." The same logic runs with other scalar words; say "some" and listeners infer "not all." The second effect is an ignorance inference: you conclude that the speaker doesn't know which option is true — that she herself is uncertain whether it was Mary or Sue. Both effects are systematic and consistent, but they are not the same thing. The exclusive inference targets the joint possibility — ruling out both being true simultaneously. The ignorance inference targets the speaker's mental state. That distinction becomes the whole ballgame. Two theories have competed to explain where these inferences come from. The Gricean and neo-Gricean account says they come from general reasoning about what a cooperative speaker would have said. The key principle is the Maxim of Quantity, which Fox summarizes as requiring a speaker to convey all the relevant information she has available. Under this pragmatic picture, when someone says "Mary or Sue," you reason: if she knew John talked to both, she would have said so. Since she didn't, she probably doesn't know or she knows it's not both. Both the ignorance inference and the exclusive inference fall out of that single piece of reasoning, sharing a common source. The grammatical theory takes a completely different route. It proposes a covert exhaustification operator — call it exh — that can be silently inserted into sentence structure, functioning like the word "only." A parse of "Mary or Sue" with exh already present in the grammar entails "not both," and that entailment follows from sentence structure alone, not from any reasoning about what a cooperative speaker would have done. On this view, the Maxim of Quantity is responsible for ignorance inferences but not for the exclusive strengthening that exh produces. In normal, everyday conversation, both theories make the same predictions. A disjunction is associated with both an exclusive reading and an ignorance inference, and either theory can explain that. So how do you pull them apart? Fox's answer is to find a context where the Maxim of Quantity is switched off. He finds one that is almost theatrical in its clarity: a television game show. Picture one hundred boxes. Five of them contain one million dollars each. The host knows exactly which five. But everyone watching understands that the host is not going to tell you everything she knows — revealing partial information is the design of the show. The Maxim of Quantity is not just inactive; its suspension is presupposed by every person in the room. Grice himself noticed something important about such contexts. In a treasure hunt scenario, if someone says "The prize is either in the garden or in the attic," you don't infer the speaker is ignorant about which. You know she's withholding information. The ignorance inference disappears because the reasoning that generates it — she would have said more if she knew more — no longer applies. Fox builds directly on this observation, and both theories accept the consequence: in the game-show context, ignorance inferences are gone. This is where the theories diverge sharply. The pragmatic account ties the exclusive inference and the ignorance inference to the same source: the Maxim of Quantity. Deactivate that maxim and both should vanish. Under this account, "There is money in box 20 or 25" and "There is money in box 20 or 25 or both" should be indistinguishable in the game-show context — neither should carry an exclusive inference. The grammatical account predicts something different. Because the exclusive inference comes from a grammatical operator rather than from Quantity reasoning, it doesn't depend on the Maxim of Quantity being active. Ignorance inferences disappear when the maxim is suspended, but the exclusive inference, delivered by exh, can survive. Fox then applies a decisive test. Imagine the host says "There is money in box 20 or 25." The game ends, and both boxes are revealed to contain a million dollars. Can a contestant reasonably say: "What you told us was wrong. You said box 20 or box 25 — but in fact, it was both"? Fox argues yes — that accusation is coherent. The exclusive inference was available, and it was violated. Now run the same scenario with the minimally different sentence: "There is money in box 20 or 25 or both." Both boxes again contain money. The same accusation — "what you said was wrong" — is now anomalous. The complaint doesn't land because the speaker never implied exclusivity in the first place. That contrast is the crux. Two sentences, one context, one difference: the presence or absence of "or both." The exclusive inference is available for the first sentence even in a context where the Maxim of Quantity is deactivated. It is not available for the second. The ignorance inference, by contrast, is gone from both. This is exactly the dissociation the grammatical theory predicts and the pragmatic theory cannot accommodate. Fox runs the same logic with scalar implicatures involving "some." In the game-show context, contestants can coherently accuse the host of being misleading if she says "Some of the red boxes have money" and all of them do — but not if she said "Some or all of the red boxes have money." The exclusive inference survives Maxim of Quantity deactivation for the "some" sentence, but not for the "some or all" sentence. The pattern holds across scalar items. Fox is careful not to ignore the most sophisticated pragmatic response. Some researchers have proposed a pretense-based rescue: when listeners face a speaker who is visibly violating the Maxim of Quantity, they implicitly imagine an idealized speaker who does obey it, derive Gricean inferences about that imaginary speaker, and then transfer conclusions back to the actual one. Fox takes this proposal seriously enough to give it careful scrutiny. He raises three problems with it: how to justify the assumption that the actual speaker shares all of the imaginary speaker's beliefs; how to distinguish the cases where the pretense should and shouldn't apply; and how a neo-Gricean account would derive the "opinionated speaker" assumption needed to generate the exclusive inference in the first place. The grammatical account doesn't require any of these auxiliary moves. It predicts the dissociation directly, from the architecture of the grammar itself. Step back from the technical details and the stakes become clear. This debate is really a debate about what grammar does. The traditional picture — the one Grice articulated in nineteen seventy-five and neo-Griceans have refined since — says that sentence structure gives you the literal meaning, and everything beyond that comes from general reasoning. What you "read between the lines" is a product of rational inference, not language. Fox's finding pushes against that picture. If the exclusive inference from "or" survives the suspension of the very maxim that's supposed to generate it, then it isn't being generated by that maxim. It's being generated by the grammar. That's a striking claim. It means some of what we experience as pragmatic inference — the feeling of reading between the lines — may already be baked into sentence structure before general reasoning ever begins. The "or" in "Mary or Sue" doesn't just mean "at least one." The grammar, Fox argues, has already quietly added "and not both" before any reasoning about speaker cooperation has a chance to run. The next time someone says "She talked to Mary or Sue," and you instantly hear exclusivity, you might be hearing not an inference you drew, but a meaning your grammar already built. This lecture was created by ennepō. Go to https://ennepo.ai to Discover, Create and Follow the latest research in your field. Read when you can. Listen when you want to.