We should only look for the Computational Mind beyond the scope of the Church-Turing Thesis

We explore the relationship between computational models in Cognitive Science and the Church-Turing Thesis (CTT). We agree that it is a correct interpretation of the CTT to say that all programming languages are able to implement the same set of computable functions and no programming language can compute Turing non-computable functions. However, we argue it is a misinterpretation and it is not correct to say that due to the CTT, \emph{`all programming languages are equivalent'}. We highlight and explore this and other common misinterpretations of the CTT by considering variations to computational processes that demonstrate a TM does not capture all computational properties that are of interest within Cognitive Science. We show that variations that can give rise to greater computational expressivity than that of a TM include: (i) interaction, (ii) concurrency, (iii) continuity (iv) operating in real time, (v) richer forms of input and output, (vi) indeterminancy, and (vii) intentionality and self-reflection. We argue that since these variations in computational processes lead to formalisms being more computationally expressive than TMs, formalisms that support these variations are outside the scope of the CTT. That is, since the CTT only applies to consideration of Turing computablility, when formalisms possess extra computational expressivity than the expressivity of a TM these formalisms cannot be reduced to TMs. Irreducibility in this sense defines the scope of the CTT and shows the CTT is a fundamental yet isolated phenomenon. We show this approach resolves the Chinese Room Argument and has other benefits for Cognitive Science.