1. Generative grammar as the study of the language faculty^FN2
FN2: What is contrasted here is "generative grammar as the study of language(s)."

What is intended by Chomsky all along, if not practiced quite as such, is that generative grammar is indeed language faculty science, with the understanding that the language faculty manifests itself as I-language, which in turn consists of the Computational System and the mental lexicon.

See Chomsky's (1986) Knowledge of Language (pp. 25-26, for example) for remarks on "E-language" as an "artifact."

In part due to the historical accidents regarding the context in which Chomsky's Syntactic Structures was prepared and published, many practitioners seem to take "E-language" as the object of inquiry for generative grammar. See the first few pages of Chomsky 1975 The Logical Structure of Linguistic Theory, Introduction for the "historical accidents" intended here.

The fist page of chapter 2 of Syntactic Structures states, "The fundamental aim in the linguistic analysis of a language L is to separate the grammatical sequences which are the sentences of L from the ungrammatical sequences which are not sentences of L and to study the structure of the grammatical sequences. The grammar of will thus be a device which generates all the grammatical sequences of L and none of the ungrammatical ones."

Chomsky distinction between I-language and E-language is his attempt to clarify (again) the goal of his research program, in light of what had gone on in the field, in my view.

As I state in Methodology [42415], I believe that, "unless we start accumulating results in language faculty science based on research that rigorously pursues testability, the research program initiated by Chomsky in the mid-1950s will most likely remain to be regarded as a metaphysical speculation, at least by those outside the field" and my current work "is an attempt to articulate how it is possible to pursue language faculty science as an exact science. It provides a conceptual basis for how that is possible in principle and empirical illustration of how that has actually been done."