Lexical Alternatives as a Source of Pragmatic Presuppositions

Presuppositions are weird. They feel like the ground you're standing on, but step the wrong way and the ground gives. Say, "John stopped smoking," and most of us instantly take for granted that John used to smoke. But say it inside a conditional, or under negation, or with a different verb, and that taken-for-granted bit can wobble. Why does some background feel solid and some feel suspendable? A classic way in is Stalnaker's picture of conversation as a running ledger of shared assumptions, the common ground. A pragmatic presupposition, in that view, is just an assumption you act like we already share. Now, linguists have long split triggers into two camps. Hard triggers—think "again" or "the"—seem to build their presuppositions right into lexical meaning and resist being canceled. Soft triggers—verbs like "know" or "stop"—behave more flexibly. They project their background most of the time, yet, in the right niche, that background can feel negotiable. Kadmon pushed on this divide, arguing the boundary is fuzzy and, for the things we care about—filtering what can be said next and accommodating what wasn't already in the ledger—the origin story might matter less than how the presupposition behaves. You can see why people worry about uniform accounts when you look at a simple verb like "sell." If I say, "John sold his bike to Bill, so you can't use it now," two entailments come along for the ride: the bike moved from John to Bill, and money moved from Bill to John. Our intuitions often treat both as what the speaker is outright asserting. Not one asserted and the other snuck in as presupposed. That transfer and counter-transfer split makes it hard to say there's a single mechanism that always knows where to stash the background. Now, a lot of the modern story about soft triggers starts from a clean, almost commonsense idea: maybe these presuppositions aren't baked into the word. Maybe they arise because the sentence brings a salient set of alternatives into play. That's Rooth's insight about focus—put stress on MARY, and you don't add an existential presupposition that someone won the football pool; you introduce a set of alternatives about who won, and the discourse can treat that set as the current topic. When that set is topical, it's natural to assume that one of the alternatives is true. That assumption—one of the options holds—does the work of a presupposition, but it's pragmatic. Context-driven. Optional. Watch it with "stop." As Sag pointed out, "John stopped smoking at time r" lives alongside an obvious alternative: "John continued smoking at time r." Put those two propositions next to each other, and their disjunction just means "John smoked right before r." That background—he used to smoke—feels like a presupposition. But on this alternative-set view, it isn't inscribed in the meaning of "stop." The verb injects an alternative set C into the discourse. If C is topical, people take it that some member of C is true. The disjunction over that set yields the content that looks like a presupposition, yet the mechanism is conversational. Simons tried to systematize how this conversational machinery gets us the presuppositions of soft triggers. She proposed two principles. First, an interpretation principle: if you raise the question whether q, and q asymmetrically entails p—q guarantees p, but not vice versa—then you're on the hook for believing p. Second, a question-raising link: when you utter a sentence that embeds q, you raise the question whether q. Put them together with a case like "If John knows Mary is having an affair, he'll avoid the dinner." That sentence embeds "John knows …," so, by the second principle, the speaker raises the question whether Mary's having an affair. Since "John knows Mary is having an affair" entails "Mary is having an affair," the first principle would say the speaker believes the affair is happening. Voilà: a route to the familiar factive presupposition surfacing from discourse structure, not lexical stipulation. Except there's a hitch. The same entailing sentence—"John knows Mary is having an affair"—also entails a belief claim about John. So if you let the machine run, you don't just get "Mary is having an affair"; you also get "John believes it." That's too much. In normal use, the presupposition we feel is about the affair, not necessarily about John's beliefs. Simons flagged this overgeneration and leaned into the alternatives route. Let verbs bring along natural counterpoints—stop or continue, win or lose, be right or be wrong, know or be unaware. Compile those into a set C, and let the topicality of C determine whether a presupposition arises. This reframes the effect: soft triggers contribute alternatives, not a semantic presupposition. When those alternatives are what the conversation is about, we default to thinking one is true, and the presupposition follows. This "think locally, act globally" dance shows up beautifully with "know" and with a cousin like "be right." Abusch sharpened it into a dynamic account. Start with "x knows p." Under the alternative-set lens, the salient options are: p and x believes p, or p and x doesn't believe p. Take their disjunction and you're left with p. In other words, when the alternatives tied to "know" are topical, the background that projects is the truth of p. Contrast that with "x is right that p." Its natural options are: p and x believes p, or not-p and x believes p. The disjunction now reduces to x believes p. So the presupposition you feel with "be right" leans toward a belief claim, not a factive one. That distinction, which can seem like a fragile lexical quirk, falls out from how alternatives are packaged. Let's slow that down. We're not claiming the verbs lost their identities. We're saying their identities show up as the shape of the alternative set they add to the discourse model. If that set is topical—if the conversation is pivoting around it—people assume one of those alternatives is true. The resulting assumption, the disjunction of the set, is what you experience as a presupposition. And because the trigger didn't semantically encode the presupposition, this background is soft. It can be suspended if the alternatives aren't topical, or if the structure of the sentence shields them. Focus and it-clefts are a nice stress test. In Rooth's football-pool scenario, just focusing MARY doesn't force you to presuppose that someone won; it only makes alternatives like "Bill won," "Sue won," salient. Whether you treat "someone won" as background depends on whether that set is the current topic of the conversation. Swap in an it-cleft—"It was Mary who won"—and you get a robust, projecting presupposition that someone won. Sag reads that contrast as more evidence that focus, like soft triggers, is an alternative engine. It seeds the set; the discourse decides whether to commit to one member of it. Clefts, by contrast, carry a semantic presupposition straight in their lexical luggage. All of this begs the practical question: how does the context computation actually work when sentences nest inside each other, or show up under negation and conditionals? That's where dynamic semantics earns its keep. Abusch uses a file-change style update rule: think of the global context as your shared ledger. Each embedded clause has a local context, computed by simulating how that clause would update the ledger in its embedding. In plain terms, the system asks: what would have to be true locally for this embedded bit to hook up sensibly with the rest of the sentence? For negation and conditionals, that procedure gives you a local context for the embedded clause that often, in typical uses, entails its content. That observation—stated as a generalization you can almost hear people use every day—goes like this: when a sentence embeds "x knows p," the local context for that embedded phrase usually already supports p. And when it does, the alternatives tied to "know" can deliver the pragmatic presupposition that p holds in the global context too. Take "John knows it's raining." On Abusch's walkthrough, the alternative set looks like "it's raining and John believes it" versus "it's raining and John doesn't." If that set becomes what we're talking about—if it's topical—then we treat one option as true. And the thing that survives, the disjunction, is just "it's raining." Embedding doesn't break this. With conditionals, the local context for the consequent is the global context updated with the antecedent. With negation, the system computes the local preconditions for the negated clause without committing globally. In both cases, the mechanism prefers readings where the local context entails p for soft triggers like "know," which is why the presupposition often still feels like it projects. You can even see how the approach handles quantifiers. In sentences with bound variables, as in "everyone in the house knows it's raining," the alternative set isn't a single static C anymore. It's indexed by the variable—different person, different alternatives—so you don't get a one-size presupposition at the utterance level. The system falls back on topicality and the local–global handoff to determine what, if anything, projects as background. That's a good thing. It mirrors how listeners actually hedge when they can't pool everyone's mental states into a single neat presupposition. Where does that leave the hard-soft distinction? With some clarity. Hard triggers encode their presuppositions semantically, which is why they persist through various embeddings and are less vulnerable to context shifts. Soft triggers don't hard-code the background. They contribute alternative sets. When those sets are topical, people assume one option is true, and the disjunction gives you the presupposition. Because the source is pragmatic, these presuppositions are more pliable. They can be locally accommodated, filtered, or outright canceled if the alternatives aren't in play. Zoom back, and a unifying picture comes into focus. Stalnaker gave us the common ground as the stage. Rooth and Hamblin supplied the cast of alternatives. Simons showed how questions and embeddings make those alternatives salient, and she warned us about overgeneration when we try to wring too much out of entailment. Sag tied focus and clefts to this machinery. Abusch built the dynamic scaffolding that calculates local contexts and lets pragmatic presuppositions rise to the global stage when the discourse invites them. And Kadmon reminded us not to fetishize the line between semantic and pragmatic triggers when our goal is to predict what projects and why. The payoffs are concrete. It explains why "know" and "be right" feel different in their presuppositions without stipulating two unrelated lexical beasts. It explains why "stopped" usually smuggles in a past habit, but can lose that baggage when the alternatives are not topical. It explains why some belief claims sneak in under the guise of presupposition and others don't. And it gives us a compositional recipe: compute the local context from the global one, ask whether the relevant alternative set is topical, and, if so, take the disjunction of that set as the pragmatic presupposition you're licensed to accommodate. If you want a single line to carry into your next conversation, it's this: think locally, act globally. Let the local context do the checking—does this embedded bit make sense here, given what we're temporarily entertaining?—then let the global context decide what gets added to the ledger as background. That stance aligns with Beaver's work on accommodation, and it keeps us honest about where the presupposition came from. There's still work to do. These systems make crisp predictions about what should happen under specific embeddings, or with particular focus patterns and quantifiers. Testing those carefully, and being alert to places where alternatives aren't topical even when the syntax would allow it, is the right next step. But the main arc is steady. Put lexical alternatives at the heart of soft triggers. Let dynamic composition compute the local preconditions. And watch as projection and weakening fall out, not from special-purpose patches, but from the way conversations actually navigate what's up for discussion and what's already on the books.