The otter in the straw hat swallowed the stapler. Nobody has ever said that sentence, and you understood it in a second — you can even see it. You did not memorise it. You worked it out as you read.
The procedure sounds humble: know each word, then put the meanings together the way the words are put together. That humble idea has a name, the principle of compositionality — the meaning of a sentence is fixed by the meanings of its parts plus the way they are combined. The reason regrouping changes meaning, as in the issue on sentence skeletons, is that the second half of that formula is doing work.
And yet a fake gun is not a kind of gun. A red apple is red and is an apple; both conditions hold. A fake gun cancels the second one outright. Same shape — adjective plus noun — and two completely different results.
This issue follows that crack: how meaning gets computed, what the result of the computation even is, and why one class of words has no determinate answer at all.
First, let us turn that into an experiment somebody can actually run.
Lake, Linzen and Baroni in 2019 asked people to learn a small invented language: a few nonsense words standing for coloured dots — one word means a single red dot, say. A few other nonsense words do not stand for anything; they are operations, like repeat the previous thing three times, or swap the order of the two sides. Each word came with only a handful of examples, and then people were tested on combinations they had never seen. Most did it quickly and accurately, and applied the newly learned operations to words they had never been paired with. People really are computing, and a few examples are enough.
The procedure has exceptions, the famous ones being idioms. Kick the bucket means to die and has nothing to do with buckets; passivise it or add a modifier and the figurative reading evaporates. But not every idiom is one solid lump. Gibbs and Nayak in 1989 compared a batch of them and found that the more an idiom's figurative meaning can be parcelled out to its individual words, the more syntactically flexible it is. In pop the question, the question roughly corresponds to the proposal, so the question was finally popped is still understood; kick the bucket cannot be parcelled out, and so it cannot be moved either. Mandarin 拍马屁 (pāi mǎ pì) — literally "pat the horse's rump", meaning to flatter someone — belongs to the flexible type, and the variant 马屁拍到马腿上 (mǎ pì pāi dào mǎ tuǐ shàng) — "the flattery landed on the horse's leg", said of flattery that backfires — works precisely because the rump part still carries a role inside. So idioms are not one big counterexample to compositionality; they are a scale running from fully assembled to not assembled at all.
The real trouble lies with the pairings that look most well behaved.
A red apple is the overlap of two conditions. A skilful surgeon is not — he need not be good at tennis. Skilful is measured only against operating, so the adjective has to climb inside the noun first and use the noun's own scale as its yardstick. A fake gun is more extreme still: it is not in the gun pile at all, because the adjective cancelled the noun's condition outright.
So combining is not one operation but a family of them. A word carries not only a meaning but its own way of attaching. When a word enters a sentence, its attachment method comes along with it.
We have been saying meaning gets computed, but what is the thing that comes out? There is a wonderfully plain test: if you claim to have understood a sentence, then tell me what the world would have to be like for it to hold. If you can, you understood it; if you cannot, you merely recognised the words. This is what semantics calls truth conditions.
It turns understanding into something you can check on the spot. Developmental psychology has leaned on this for decades in the truth-value judgement task: act out a small scene in front of a child, then ask whether some sentence about it is right. Four-year-olds can do it, and the line between what they accept and what they reject draws out the meaning the sentence has for them.
The method reveals something introspection misses. Every student read a book describes two quite different scenes: three students each reading a different book, or three students reading one and the same book. Both make the sentence true. A sentence does not correspond to a picture; it corresponds to a set of pictures.
That boundary shifts from language to language. Scontras and colleagues compared English and Mandarin with truth-value judgement tasks. English speakers accept the inverse reading of sentences where the indefinite comes first and the universal second — letting the later word take wide scope over the earlier one. In the crucial Mandarin materials, not a single participant accepted it: 一个学生读了每本书 (yī gè xuéshēng dú le měi běn shū), "a student read every book", can only mean that one and the same student got through all the books. Strength of evidence: several experiments point the same way, but later work found inverse readings available in Mandarin inside relative clauses and adverbial clauses, so a blanket ban is too strong — it now looks structure-by-structure.
There is one more layer: truth conditions are not all of meaning. The morning star and the evening star are the same planet, Venus. Yet the morning star is the morning star is empty, while the morning star is the evening star was an astronomical discovery. The two sentences point at exactly the same objects and are worth wildly different amounts. That is why Frege split reference (which thing you point at) from sense (the route by which you point at it). Meaning contains both the destination and the road.
Two metres is tall. Someone a millimetre shorter than a tall person is still tall. A millimetre less again, still tall. Run it all the way down to a metre and a half and the reasoning says he is tall too, which is plainly absurd. Somebody laid out this chain more than two thousand years ago; it is called the sorites paradox. It is not word-play: every step is right and the conclusion is wrong, which means the word tall is not built the way we assume.
Alxatib and Pelletier brought it into the lab in 2011. They showed people a police line-up of five suspects of different heights and asked them to mark a set of sentences true, false, or can't tell. For the man whose height fell right in the middle, most participants would not call he is tall true, and would not call he is not tall true either — yet a substantial number accepted he is tall and not tall, which sounds like a flat contradiction. Their reading is that the sentence was taken to say he is a borderline case. Strength of evidence: a single clean experiment, but one that has been redone and modelled many times since, with a stable direction.
Why does this happen? Because tall carries no threshold of its own; the threshold is borrowed on the spot. A tall third-grader is far shorter than a short professional centre, and neither description is wrong — tall is always relative to a comparison class. So hesitation over borderline cases is not imprecise measurement. There is simply no fact there to measure.
Languages differ in the machinery they use for this. Washo — an Indigenous language of the area straddling the California–Nevada border — has no counterpart to the English comparative -er or more; comparison is expressed by juxtaposing two clauses, roughly this one is big, that one is small. Bochnak argued in 2015 that gradable words in the language therefore do not introduce a degree at all, and Beck and colleagues reached a similar conclusion for Motu, spoken in Papua New Guinea. Strength of evidence: careful fieldwork plus a cross-linguistic parameter hypothesis, with other languages that fit neither side of the split. The thing not to conclude is that its speakers do not compare — they compare perfectly well, with different equipment: no dedicated part in the syntax, and the job done by putting two clauses side by side.
Looking back, vagueness is no counterexample to compositionality. Tall combines by the rules like everything else; the piece it contributes simply has a blank in it, waiting for context to fill in. The three adjective types earlier were about how things attach. This is about a piece that arrives unfinished.
One answer is that the rule is intact and each word simply carries its own way of attaching, and fake attaches by cancelling. But then any counterexample can be met by declaring that this word has a special attachment method — so what could ever falsify the principle? What discovery would make you say this one really was not composed?
Commands, questions and good wishes do not describe the world and cannot be true or false, yet you obviously understand them. Is knowing when it would be true just the recipe for one kind of sentence, with another kind needing knowing what would count as satisfying it? If there are two systems, how do they coexist in one head?
If it is, why do so many people accept it and feel they have expressed themselves precisely? If it is not, has not tall already shifted its meaning from what it means standing alone? Is there an experiment that could pull those two explanations apart?
Not that its speakers do not compare — two juxtaposed clauses say the comparison perfectly well. But something does change: if comparison requires two full clauses, how do you express a fine gradation like just slightly taller than him? Which constructions would you have to look at to tell whether the difference lies in the language's equipment or only in habits of phrasing?