A topological approach to natural languages: Metaphorical mappings between space and time

In this paper, we investigate a metaphorical mapping between a certain kind of locative expressions and temporal expressions in Japanese, and show that topological properties that locative expressions represent are reflected in the usage of temporal ones. Our investigation arose from a dissatisfaction with cognitive linguistics approaches, such as Lakoff s, which use diagrams to explain linguistic data. We claim that diagrams are only tools to help us understand linguistic phenomena intuitively, not essentially, and that a topology-based approach to natural languages is necessary to specify what principles are working behind linguistic phenomena such as correlations between space and time.