Chomsky construed grammar as a generative system - a set of rules that would generate all and only members of the infinite set of gramatically well-formed sentences of a language. ``Generate'' is used in the sense af a mathematical function precisely generating values depending on given parameters, while the qualification ``infinite'' reflects the creative aspect of human language. Generative grammer is a formalised expression of people's competence, i.e. tacit knowledge of their language.
The Grammar does not refer to production of sentences by a speaker: it is actually neutral between production and reception occuring in humans. What sort of computational system was needed to realise a generative grammar for natural language? Chomsky argued that the following were inadequate:
a. Finite state grammars - Finite number of recursive rules acting on a finite vocabulary. These are described by a finite-state automaton (Markov process) consisting of a finite number of states and probabilistic transitions between the states. Each state has access to a next set of choices. Eg. in a sentence, the first word limits the choices for the second and so on. The device has no memory of the path by which it reached its current state. Such grammars were used in information theoretic models of that time. (See fig. .)
Such a grammar would soon get very complicated, eg. putting the same in words in several different boxes (see Lyons). But complexity is not its most serious problem.
Chomsky argued that a finite-state process is inherently incapable of representing the recursive properties of English constructions: it cannot generate sentences with embedded or dependent clauses while simultaneously excluding strings that contradict these dependencies. eg.
The woman who was talking to the astronauts is the President.
The man who said he would help us is arriving today.
A f-s grammar cannot capture the structural link between ``man'' and ``is arriving'' which are non-adjacent and separated by a simple clause.
Extending this argument, a f-s g (as the name suggests) cannot handle structures which recur indefinitely like embedded clauses.
The boy that the girl that the dog chased kissed had red hair.
The girl that the boy that the mouse that the cat that the dog bit ate frightened kissed had red hair.
Such sentences, though uncommon, ought to be generatable by a grammar. (Embedded structures have a formal simplicity, as seen from a phrase structure analysis; the difficulty of actually producing and processing such sentences was attributed by Chomsky and Miller to limitations of short-term memory.)
Language does not work by slotting a word and indicating what word(s) can follow it. It works at a higher level of abstraction in which certain elements under certain circumstances can be placed within other elements. Here Chomsky was making the same point about language that Karl Lashley had made about serial behaviour.
b. Phrase structure grammars - Structural analysis in terms of clauses, phrases etc., displayed as inverted tree diagram. The diagram is constructed using a finite set of ``phrase structure ... '' or ``re-write rules'' applied to the sentence and its successive strings. (See sec. )
It seems that all sentences in English could be generated by a phrase structure grammar (is there a proof?). Lyons comments that there exist constructions in some other languages which are ``beyond the scope of phrase structure grammar in this sense.'' (Lyons, p. 62)
Problems with phrase structure grammars:
What are you looking for and What are you running for
John is easy to please and John is eager to please
Flying planes can be dangerous?
Chomsky showed that the number of phrase structure rules required for complex sentences is very large, so the system becomes complex and unwieldy. (In comparison, transformational grammar calls for fewer rules, though they may be more complex. But is formal simplicity a persuasive motive? The functional view of language disputes this.) In later publications Chomsky put more weight on the argument that transformational grammar reflects better the ``intuitions'' of native speakers and it is also semantically more ``revealing.''