Theodore Sider distinguishes two notions of global supervenience: strong global supervenience and weak global supervenience. He then discusses some applications to general metaphysical questions. Most interestingly, Sider employs the weak notion in order to undermine a familiar argument against coincident distinct entities. In what follows, I reexamine the two notions and distinguish them from a third, intermediate, notion (intermediate global supervenience). I argue that (a) weak global supervenience is not an adequate notion of dependence; (b) weak global supervenience does not capture certain assumptions about coincidence relations; (c) these assumptions are better accommodated by the stronger notion of intermediate global supervenience; (d) intermediate global supervenience, however, is also not an adequate notion of dependence; and (e) strong global supervenience is an adequate notion of dependence. It also fits in with anti-individualism about the mental. It does not, however, serve to rebut arguments against coincident entities.

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 visexaudex 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.

The paper criticizes standard functionalist arguments for multiple realization. It focuses on arguments in which psychological states are conceived as computational, which is precisely where the multiple realization doctrine has seemed the strongest. It is argued that a type-type identity thesis between computational states and physical states is no less plausible than a multiple realization thesis. The paper also presents, more tentatively, positive arguments for a picture of local reduction.

This paper challenges two orthodox theses: (a) that computational processes must be algorithmic; and (b) that all computed functions must be Turing-computable. Section 2 advances the claim that the works in computability theory, including Turing's analysis of the effective computable functions, do not substantiate the two theses. It is then shown (Section 3) that we can describe a system that computes a number-theoretic function which is not Turing-computable. The argument against the first thesis proceeds in two stages. It is first shown (Section 4) that whether a process is algorithmic depends on the way we describe the process. It is then argued (Section 5) that systems compute even if their processes are not described as algorithmic. The paper concludes with a suggestion for a semantic approach to computation.