Abstract

In this article, we propose an initial formal model of computationalism based on mathematical relations between cognition and computation. More specifically, based on a set of cognitive constituents as a domain, and a set of computational implementations as a range, we define two relations of transformation over these sets. Moreover, we define the principles of implementability, describability, and phenomena correspondence, and we conjecture that full computationalism does not hold since these principles are not fulfilled. Particularly, many cognitively-tied phenomena fail to respect the describability principle which is necessary for representing a cognitive state by a computational state.