Compositionality Versus Computability: Topology of Cognitive Computations

In the preceding chapters, we discussed a new topological model of cognition and its employment in deconstructing several cognitive functionalities. However, there are two fundamental ambiguities of cognition per se which have defied resolution in the conventional perspective, viz., compositionality and computability during cognition. In this chapter, we will discuss these two features of compositionality and computability of cognitive computations from the perspective of the proposed model. The proposed model offers a unified conception of cognitive processing, which appears to us as these two different features. According to the proposed model, it is the essential topological nature of cognition that is responsible for this perception of compositionality and computability being different features. This chapter outlines the role of self-reference in creating this cognitive artifact of these features being different when, in reality, they are one and the same.