This paper attempts at an integrated approach to the various semantic properties of English demon- stratives this and that. According to previous scholars, a demonstrative has very diverse functions-spatial and temporal relations with the speaker, discourse deixis, the speaker`s psychological and emotional expressions. This study reviews two representative approaches in order to see whether there are unified principles that can account for all those cases. First, the seman- tic/pragmatic approach tries to find the meanings of the demonstratives this and that from their basic semantic features, proximal/distal from the speaker, and second, the cognitive approach accounts for their meanings in consideration of the possibility of the hearer`s cognitive processing. This paper discusses the merits and limitations of those two approaches, and proposes the following approach as an alternative: the proximal/distal demonstratives this and that are related with the speaker`s and hearer`s projection of focus onto the referent.