Having dismissed the finite-state model, chapter 4 of Syntactic Structures introduces phrase structure grammar — a formalization of the “constituent analysis” then standard in structural linguistics, as a system of rewrite rules. A rule like “Sentence → NP + VP” replaces one symbol with a string of others, applied in sequence from an initial symbol. Chomsky calls this set of rules a [Σ, F] grammar (Σ the initial symbols, F the rules).
This is clearly stronger than the finite-state model. But chapter 5 shows, with three examples, that it is still not strong enough.
1. Conjunction: Where Can “And” Go?
Start with the rule for conjoining. Compare:
- “the liner sailed down the river”
- “the tugboat chugged up the river”
Try to conjoin the shared piece — both end in “the river” — and it fails: “the liner sailed down the and tugboat chugged up the river” is not English.
By contrast, this pair conjoins cleanly:
- “the scene of the movie was in Chicago” + “the scene of the play was in Chicago” → “the scene of the movie and of the play was in Chicago”
What’s the difference? In the second pair, “of the movie” and “of the play” are the same kind of constituent, sitting in freely interchangeable positions. In the first pair, they are not. So the rule “conjoin only constituents of the same kind” gets the facts right.
But this rule runs into a serious problem.
we cannot incorporate the rule (26) or anything like it in a grammar [Σ, F] of phrase structure, because of certain fundamental limitations on such grammars.
Why not? A rewrite rule X→Y only looks at a string’s present shape. But deciding “is this the same kind of constituent” requires knowing what derivational path — which node of the phrase marker — produced that shape: its history. A [Σ, F] grammar has no mechanism at all for looking back.
2. Pieces That Come Apart: The Auxiliary Phrase
The second problem is how auxiliary verbs are built. English has forms like “has been reading” — assembled from two discontinuous pieces, have…en and be…ing.
Chomsky handles this by analyzing the auxiliary as Aux → C (M) (have+en) (be+ing), then applying a supplementary rule that swaps an affix (Af) with the root to its right, rewriting Af+v as v+Af — this is exactly what produces the word order of “was reading.” But this two-step procedure already steps outside a single rewrite rule: applying it requires anticipating the result of another rule. That, too, cannot be written as one rewrite step.
3. The Passive: An Operation of Swapping
The third and heaviest example is the relation between active and passive sentences.
The passive of “everyone in the lab considers John incompetent” is “John is considered incompetent by everyone in the lab.” Chomsky argues this conversion requires an actual swap of subject and object.
One might think it enough to rewrite “NP₁ - Aux - V - NP₂” as “NP₁ - Aux+be+en - V - by+NP₂” without any swap. But this breaks down for pairs like “John admires sincerity”: “sincerity is admired by John” is natural, while “sincerity admires John” is not — meaning the subject and object of the active sentence stand in an asymmetric relation, and the passive must reproduce that relation in reverse. It is not a matter of adding material; the essential operation is an exchange of position.
And this swap cannot be written by a rule that only looks at a string’s contents. Building the passive requires reading off, from the history of the phrase structure, which part was the subject and which was the object.
What the Three Examples Point To
Conjunction, the discontinuous auxiliary, and the passive attack the limits of simple rewrite rules from three different angles. What they share is this: the string’s present shape is not enough — you need to consult how it was built. To get past this wall, Chomsky introduces the transformation, a stronger kind of rule that rewrites a whole sentence into another whole sentence. The concrete machinery — negation, questions, and the insertion of “do” — is the subject of the next article.