What is the scope of a semantic theory consistent with the theoretical assumptions adopted by the generative program? In this paper I will show that the linguistic theory generically known as generative grammar is an extremely coherent Scientific Research Program and within this descriptive framework it’s possible to characterize the main features of an I-semantics. First, will be presented the hardcore of the generative program, its heuristics and Chomsky’s criticism towards formal semantics. Second, I will compare two approaches: the denotational approach by Larson and Segal and the intensional approach by Paul Pietroski. I argue in favor of Pietroski’s approach, because it is more coherent with the core assumptions of the generative program. The main argument is that syntax, in the context of the generative program is explanatory and, in this very context, semantics is not. Therefore, in order to account for the explanatory role of syntax in the generative program it is necessary to review certain foundational assumptions commonly accepted in formal semantics.