Three Ways of Leaving p Unsettled
How should we distinguish one-sided possibility, explicit two-sided openness, and an explicit report of non-resolution — and what does each predict for the discourse that follows?
A paper in formal semantics and pragmatics. A related master’s thesis, in planning, asks how children’s use of modal expressions relates to their understanding of possibility.
This paper compares three utterances that all leave a question open but need not do the same work in a conversation. Its evidence is linguistic: constructed minimal pairs with explicit context, judgments about which replies and continuations they license, a comparison of existing accounts, and formal derivation. It makes no claim about reaction times, group effect sizes, or what a language model does. Those are empirical questions, and their answers would not decide whether the paper is right.
The three-way distinction
Take the question Where is the key?, and let p be “the key is in the drawer.” Three answers all leave the location unresolved:
- One-sided possibility. “It might be in the drawer.” The relevant information state is compatible with p.
- Bilateral openness. “It might be in the drawer, or it might not.” Both p and not-p are explicitly left open.
- Issue non-resolution. “I don’t know whether it is in the drawer.” The speaker reports being unable to resolve the question.
The distinction matters because the obvious label — “uncertainty” — hides at least three different contributions. Saying might p guarantees only that p is a live possibility; it does not by itself keep not-p open. Saying I don’t know whether p asserts that the speaker does not know the answer, and often additionally conveys an unsettled opinion; neither contribution requires the two answers to be equally likely. So the three cannot be collapsed into a single scale of confidence.
What would tell the accounts apart
The work of the paper is to find observable differences that separate the three. I use a battery of diagnostics rather than any single test, and I weight them honestly:
- Which question each most directly answers. A possibility claim, an explicit two-sided statement, and an ignorance report address different questions under discussion — but this is supporting evidence, not decisive, since a possibility claim can implicate ignorance and an ignorance report can still make p salient.
- A matched grid of replies. Denying that p is true, rejecting the modal update, correcting the claim of ignorance, and simply answering the embedded question are four different moves. Crossing them against the three utterances is sharper than the blunt “just reply No” test, which can point at either the modal or its complement.
- Behaviour under supposition and embedding. “Suppose the key is in the drawer, although Maya doesn’t know whether it is” separates the facts from Maya’s knowledge; “#Suppose the key is in the drawer and it might not be” is contradictory in one information state. This is a known baseline the account must recover, not a new diagnostic.
- Sensitivity to false belief. A negated know whether tends to convey not just an absence of knowledge but the absence of a settled opinion, which is what calibrates the third condition.
- Where a following Why? attaches. After each utterance, an explanation defaults to explaining something different — why p is still possible, why both answers are open, or why the speaker cannot decide. This is the most promising new candidate, and still under check, because Why? can also attach to the whole speech act.
Where existing accounts stop
Each ingredient has been analysed. The attentive contribution of might (Ciardelli and colleagues), question-embedding know, the question under discussion and the space of rejections, and weak assertion and modal update are all established results. The epistemic contradiction under supposition is Yalcin’s, and Dorr and Hawthorne’s. The paper claims to discover none of these.
Its bet is narrower. As far as I have found, no existing account compares all three utterances, on the same balanced contexts, across this full set of diagnostics at once — the matched reply grid, embedding, false-belief sensitivity, and default explanatory attachment together. Whether that comparison turns up a genuinely new constraint, or a clean unification of what is already known, is exactly what is open.
Two routes
The project begins with comparative unification. A stronger interface claim depends on independent judgments:
- Interface analysis. A small set of balanced dialogues that check where default corrections and explanations land, using the embedding and false-belief facts as independent baselines. This upgrades to a stronger claim only if a stable new constraint — or a wrong prediction of the existing combination — actually appears.
- Comparative unification. If it does not, the paper combines existing theories into one account of the three-way distinction and the diagnostics, with no experiment. Its value is then explanatory unification at the scale of a seminar paper or thesis chapter, not a new mechanism.
Status
The project is at the construct stage. The brief that fixes the contrast and the diagnostics is under review by a formal semanticist. Diagnostic materials, a comparative analysis, and draft case-by-case derivations are in place. Independent judgments on the candidate examples are pending, so the proposed empirical differences and any stronger theoretical contribution remain provisional.