The theory of language structures first proposed in Chomsky's Syntactic Structures (1957). Just as physics studies the forms of physically possible processes, so linguistics should study the form of possible human languages. This would define the limits of language by delimiting the kinds of processes that can occur in language from those that cannot. The result would be a universal grammar, from which individual languages would derive as, in effect, different ways of doing the same thing. Variations such as vocabulary and principles governing word order would be revealed as different applications of the same underlying rules. Tacit knowledge of this universal grammar is pre-programmed, an innate biological endowment of normal human infants. The argument with which Chomsky supported the claim for such an endowment is known as the argument from the ‘poverty of stimulus’: it is argued that language-learning proceeds so fast in response to such a relatively slender body of ‘data’ that the infant must be credited with an innate propensity to follow the grammar of everybody else. The extent to which this argument treats the infant as a theorist or ‘little linguist’ has been much debated (see also language of thought hypothesis). In Chomsky's original model, language consists of phrase structure rules and transformations. Phrase structure rules represent the grammatically basic constituent parts of the sentence (e.g. a sentence might be a noun phrase + a verb phrase). Transformation rules change relations (as in the active/passive transformation) and determine how complex sentences may be formed from more simple ones. This latter function became taken over by the phrase structure rules in the later work (Aspects of the Theory of Syntax, 1965) that introduced what became known as the standard theory. In this, phrase structure rules perform the task of defining the deep structure of a sentence, from which its surface structure is thought of as derived by means of possible repeated transformations. Deep structure bears some affinity to the idea of the logical structure of a sentence, thought of as the representation of the sentence that reveals its inferential properties. The notion did not survive in generative semantics, one of the successors to Chomsky's standard theory, in which transformation rules map semantic representations onto surface structures. The introduction of semantics is often thought to be a necessary amendment to the purely syntactic and grammatical approach of Chomsky's early theory.
After the standard theory came the extended standard theory, and eventually government-binding theory, both of which maintain an abstract and mathematical approach to the discovery of linguistic principles of the highest generality. Philosophically most interest has centred on the claim that complex grammatical principles might be innate, and on the relationship between syntax and semantics that is presupposed in the idea of a generative grammar. In general, philosophical formalists have been more interested in the possibility of unravelling concealed semantic structure, rather than in the more purely grammatical problems of linguistics.