In this paper, representational structures of arithmetical thinking, encoded in human minds, are described. On the basis of empirical research, it is possible to distinguish four types of mental number lines: the shortest mental number line, summation mental number lines, point-place mental number lines and mental lines of exact numbers. These structures may be treated as generative mechanisms of forming arithmetical representations underlying our numerical acts of reference towards cardinalities, ordinals and magnitudes. In the paper, the theoretical framework for a (...) formal model of mental arithmetical representations is constructed. Many competitive conceptions of the mental system responsible for our arithmetical thinking may be unified within the presented framework. The paradigm underlying our research may be interpreted philosophically as a neo-Kantian approach to modeling the mind’s representational structures. (shrink)

The theoretical and methodological underpinnings of the cognitive paradigm have traditionally been discussed against the background of generative grammar, its immediate predecessor. A significantly less researched yet no less interesting relationship is the one between the cognitive and structuralist paradigm. This article focuses on the in part converging, in part diverging semiotic assumptions underlying European structural linguistics and Cognitive Grammar. A comparison of important concepts of both theories shows that, although Cognitive Grammar arrives at a more realistic understanding of how (...) language works in discourse, the theory fails to offer a coherent theory of the linguistic sign. (shrink)