The concept of similarity evokes different meanings for different people. However similarity is conceived, it certainly plays an important role in the modelling of pattern perception. The contrasting approaches toward psychological similarity taken by the measurement theorists, the psychometricians of multidimensional scaling, and the process model oriented cognitive psychologists should be reconciled if a full account of the role of similarity in perception is to be adequately developed. This chapter attempts to initiate a preliminary synthesis of these approaches while introducing some important philosophical quesdons concerning the application of multidimensional scaling (MDS) models of similarity. These questions arise from a deeper analytical investigation of the foundations of modelling perception. Along the way, the reader is introduced to mathematical concepts from topology and geometry that underlie the use of MDS. It is hoped that the discussion will provide some tutorial benefits as well as open the door to a more unified treatment of similarity and its role in psychological representation.