Universal Languages of Thought: LoT is a topos
Abstract
The Language of Thought (LoT) hypothesis says that (some) mental abilities have a compositional syntax/semantics akin to language (i.e. a symbol system), in particular, to account for the systematicity and productivity of thought. Yet, this hypothesis raises two questions. (1) Why should thought be that way? (2) How does LoT connect to non-symbolic (spatial) aspects of cognition? Category (Topos) theory is introduced to sketch out answers to both questions, whereby mental representation is a regarded as a functor and mental process as a natural transformation. Individual features of a LoT follow from (categorical) universal constructions that collectively constitute a topos, whence the slogan, "LoT is a topos", and topos theory lies at the nexus of algebra, geometry and logic (cf. language, perception and reasoning). This view suggests that LoT is a kind of “optimal” construction, i.e. the best one can do in the given context.