The paper presents an extended argument for the claim that mental content impacts the computational individuation of a cognitive system (section 2). The argument starts with the observation that a cognitive system may simultaneously implement a variety of different syntactic structures, but that the computational identity of a cognitive system is given by only one of these implemented syntactic structures. It is then asked what are the features that determine which of implemented syntactic structures is the computational structure of the system, and it is contended that these features are certain aspects of mental content. The argument helps (section 3) to reassess the thesis known as computational externalism, namely, the thesis that computational theories of cognition make essential reference to features in the individual's environment. It is suggested that the familiar arguments for computational externalism—which rest on thought experiments and on exegesis of Marr's theories of vision—are unconvincing, but that they can be improved. A reconstruction of the visex/audex thought experiment is offered in section 3.1. An outline of a novel interpretation of Marr's theories of vision is presented in section 3.2. The corrected arguments support the claim that computational theories of cognition are intentional. Computational externalism is still pending, however, upon the thesis that psychological content is extrinsic.