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How does generative grammar explain a speaker’s ability to produce many sentences?

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Ferdinand de Saussure seated in a formal pose, wearing a dark suit with a vest and sporting a thick mustache, circa 1900. — Linguistics Much of the foundation of 20th-century sociolinguistics was created by the Swiss linguist Ferdinand de Saussure (1857–1913).

Generative grammar explains a speaker’s ability to produce an infinite number of sentences from finite means—such as a limited vocabulary and a set of grammatical principles—through the concept of productivity.1

This capacity is primarily achieved through recursive rules. A rule is recursive if it can be applied to its own output an indefinite number of times, allowing for the creation of increasingly complex structures like nested clauses or concatenated phrases. By applying these recursive operations, a speaker can generate a potentially infinite set of grammatical expressions.1

In the framework of generative grammar, these rules are viewed as a formal, explicit system that characterizes the structure of a language. Rather than being a dynamic process of building sentences one by one, the grammar is considered to generate all possible sentences of a language "timelessly" or statically, much like a mathematical formula generates values for different variables. Through operations such as "Merge" (in later theories) or earlier phrase-structure and transformational rules, the system provides the structural descriptions necessary for a speaker to produce and understand an unlimited variety of well-formed sentences.123