↩ SocioRhetoric · A New Catalogue of Speech Acts
sociorhetoric · a speech act
framed misfire → orientation mismatch
“Some of the guests have arrived” — and you instantly conclude not all of them have, though the sentence never said so. Where does that extra meaning come from, and why does it evaporate the moment the stronger wording wasn't available?
To assert is to state that something is the case: the plainest, most load-bearing move in the whole catalogue, the one every other act is built on top of. And yet the plainest act delivers more than it says. Hear “some of the guests have arrived” and you walk away believing that not all of them have — a claim the words never made. Logic is no help here: some is perfectly true when all is true, so “some” cannot mean “not all” by entailment. Something else manufactured that extra meaning, and it did so instantly, silently, for free.
That something is an inference about the speaker's choice. A cooperative speaker who could have said the stronger, more informative “all” — and chose the weaker “some” instead — must have had a reason, and the obvious reason is that “all” wasn't true. This is a scalar implicature: the listener reconstructs the sentence and the decision behind it, reading the words the speaker picked against the words the speaker passed over. The meaning lives in the gap between them. Which yields a strange, testable prediction: take away the stronger alternative — make it a word the speaker never had — and the extra meaning should simply die. The instrument below computes exactly this, and lets you kill it.
the honest instrument
Three probability tables, each computed on every input from the equations printed on them. The literal listener L0 takes each word at face value; the pragmatic speaker S1 chooses the word that would most inform a literal listener; the pragmatic listener L1 inverts the speaker to recover the enriched meaning. The headline is L1(all | “some”) — the probability that, on hearing “some”, the world is actually the all world. Watch it sit near zero, then remove “all” from the speaker's vocabulary and watch it climb.
Scalar implicature over ⟨none, some, all⟩
Frank & Goodman (2012) · every distribution live
implicature strength · 1 − L1(all | “some”)
the enriched reading “not all” · posterior mass on the all-world after hearing “some”: —
more than it says
Read the L1 table's “some” row on the default setting. Almost all the posterior mass sits on the some-but-not-all world; the all world holds a sliver — about 0.056. That sliver is the implicature, quantified: hearing “some”, the pragmatic listener assigns only a five-percent chance that everyone arrived. Nobody stated “not all.” The literal content of “some” is fully compatible with “all” — you can confirm it in the L0 row, where the plain word spreads its belief evenly across the some and all worlds, 0.5 and 0.5. The enrichment is entirely the work of the second row of reasoning.
There are three worlds and three words. The literal listener L0 just filters worlds by whether a word is true in them. The speaker S1 then asks, from inside each world, which word would best steer a literal listener toward this world? — and in the all world, “all” wins decisively over “some,” because “all” pins the world exactly while “some” leaves it ambiguous. So a speaker in the all world rarely says “some.” The listener L1 runs that speaker backwards: if I heard “some,” I was probably not being spoken to from the all-world. The famous inference falls straight out of the arithmetic — it is never typed in anywhere.
what to try
Read off the not-all inference. On the default, the big number reads 0.944 — the strength of “some ⇒ not all.” The word “some” never contained it; the model built it from the speaker's decision to pass over “all.” The model produces the inference.
Delete the alternative and watch it die. Untick “all” in the alternatives (or hit no alternative). Now “all” is a word the speaker never had. L1(all | “some”) leaps from 0.056 to 0.500 and the implicature collapses to 0.500 — the meaning existed only because a stronger, unchosen word existed. Remove the road not taken and the inference evaporates.
Crank α and watch it sharpen. Drag rationality from 1 to 8. A barely-rational speaker (α=1) leaves L1(all | “some”) at 0.25; a sharply rational one (α=8) drives it to 0.004. The more you assume the speaker chose deliberately, the more their silence about “all” means. Then skew the prior toward the all-world and watch the implicature weaken — sometimes the world argues back.
meaning from the road not taken
The meaning of what was said is manufactured out of what was not said. “Some” carries “not all” only because “all” was sitting there, available, stronger, and declined. The word does not hold the inference; the contrast set does. That is why the second experiment is a proof — when you strike “all” from the vocabulary, you are not weakening the speaker or muddying the channel, you are removing the specific alternative whose absence was doing all the work. And the inference disappears. It reaches the exact value produced by purely literal reasoning: L1 flattens to 0.5, the point of no implicature.
The same logic explains why implicatures are so easily cancelled in real speech. “Some of the guests have arrived — in fact, all of them” is not a contradiction, because the follow-up simply announces that “all” was never a live alternative the speaker was avoiding. It rewrites the contrast set mid-sentence, and the inference dissolves without anyone feeling lied to. The instrument makes this concrete: cost does the same job more gently. Raise the cost of “all” — imagine it were a long, effortful, marked thing to say — and the speaker's failure to say it becomes forgivable, so the listener reads less into the silence and the implicature softens. Meaning, here, is never in the words alone. It is in the shape of the choice.
model
Three probability rules are printed on the tables. The literal listener. L0(s | u) ∝ ⟦u⟧(s)·P(s): given a word, keep only the worlds where it is literally true, weighted by the prior, and normalise. “Some” is true in the some-world and the all-world, so L0 splits its belief between them — the literal listener draws no implicature at all. The pragmatic speaker. S1(u | s) ∝ exp α(ln L0(s | u) − cost u): standing in a known world, the speaker prefers the word that would make a literal listener most confident of that world — the log-probability is the informativity, cost penalises effort, and α controls how sharply the speaker optimises. At α→0 the speaker picks words at random; at large α the speaker is nearly an argmax over informativity.
The pragmatic listener. L1(s | u) ∝ S1(u | s)·P(s): the listener treats the speaker as data and inverts by Bayes, asking which world best explains the speaker's choice of word. The implicature is a number in this last table — L1(all | “some”), the posterior on the all-world — and the reported strength is 1 − L1(all | “some”). It is a posterior, not an entailment: it can be strong or weak, it moves with α, with cost, with the prior, and it vanishes when the contrast set loses “all.” Every cell in every table normalises to one; every number recomputes the instant you touch a control.
the act ↔ the model
| The talk | The model |
|---|---|
| a state of the world | how much of the set holds — none, some-but-not-all, or all of the guests arrived. |
| an alternative utterance | the stronger thing the speaker could have said (“all”) and audibly did not. |
| the pragmatic speaker S1 | choosing the informative-enough word from a known world — passing over “all” unless it fits. |
| the pragmatic listener L1 | the enriched meaning: inverting the speaker to recover the world behind the word. |
| the implicature | 1 − L1(all | “some”) — the computed strength of “some, therefore not all.” |
| removing the alternative | striking “all” from the vocabulary — and the inference flattening to 0.5, gone. |
how this act misfires
orientation mismatch · scope mismatch
The same words carry different implicatures under different assumed alternative-sets, so two listeners reading at different scopes hear different claims from one utterance. Say “some of the report is wrong” meaning it narrowly, against the alternative “all”; a listener whose live alternative is “nothing is wrong” hears an accusation you never made. Neither of you is arguing in bad faith — you have simply loaded different words into the road-not-taken. This is the catalogue's orientation mismatch in its quietest form: divergent uptake, mistaken for a divergent claim, and then for dishonesty. Tie it to the Scope axis: narrow versus wide readings are, precisely, different contrast sets over the same assertion.
the model is a mechanism, not a constant
The engine derives the implicature by assuming both parties share the same set of alternatives, the same costs, and the same rationality α. That shared common ground is the one thing conversation cannot guarantee. When your “all” is not among my alternatives, or my α reads your word choice as more deliberate than you meant it, the computed inference and the felt inference diverge — and the tool has shown you the mechanism of that divergence, not a universal number to trust. Read the exact percentages as illustrations of a structure, not measurements of a mind. What is robust is the shape: meaning is built from unchosen alternatives, and it lives or dies with the contrast set both speakers imagine they share.
An assertion means the words you chose and the stronger words you didn't.
can you use it?
RECOGNITION — Which utterance carries a scalar implicature? A: “I ate some of the cookies.” B: “I ate the cookies.” C: “I ate some of the cookies — in fact, all of them.”
A. A stronger alternative (“all”) was available and passed over, so “not all” is inferred. B offers no scale; C cancels the inference by announcing that “all” was never being avoided.
THE NEAREST NEIGHBOR — “Some” suggests “not all,” yet “some, in fact all” is no contradiction. What single criterion separates an implicature from an entailment?
Cancellability. An entailment lives in the words and cannot be withdrawn; an implicature lives in the contrast set of unchosen alternatives, so rewriting that set dissolves it without any falsehood.
PRODUCTION — A friend asks how your interview went. Compose a truthful answer that implies it went badly, then check the mechanism.
“It was fine.” The listener reasons: “great” was available, cheap, and unchosen — so probably untrue. Yours works if a stronger word existed and your answer audibly declined it.