A Learning-Efficiency Explanation of Structure in Language

This paper proposes a learning-efficiency explanation of modular structure in language. An optimal grammar arises as the solution to the problem of learning a language from a minimal number of observations of instances of the use of the language. Agents face symmetry constraints that limit their ability to make a priori distinctions among symbols used in the language and among objects (interpreted as facts, events, speakers intentions) that are to be represented by messages in the language. It is shown that if it is commonly known that the object space is modular and messages are strings, then modularity of the language is sufficient and (essentially) necessary for learning efficiency. Journal of Economic Literature Classification Number: C72.I am grateful to Hsueh-Ling Huynh, Bart Lipman, Ariel Rubinstein and Birger Wernerfelt for stimulating discussions and comments. Many thanks are due to the anonymous referee for suggestions that have helped to improve the focus and presentation of the paper. I have benefitted from comments by seminar participants at Arizona State University, Boston University, the University of California-San Diego, the University of Pittsburgh, the Wissenschaftszentrum Berlin für Sozialforschung (WZB), the Midwest Mathematical Economics Meetings, and the Summer in Tel Aviv (SITA). This research was supported by a Grant from the National Science Foundation.