Abstract Complexity Theory provides avenues for understanding many aspects of language acquisition and use, including the language neuroscientists use to label the brain and to think about its structure and functions. A major concern for neuroscience has been the mapping of structure to function. The tendency has been to seek one-to-one mappings between the two, but advances in research have revealed that the brain is characterized by degeneracy in which two or more architecturally different structures can serve the same function. Thus, the brain can operate with many-to-one mappings. This complexity in neural structure is met with the complexity of synonymy in the lexicon of human language that is used to describe the brain. In this chapter I discuss the relationship between degeneracy and complexity and draw an analogy between neural degeneracy and lexical complexity, specifically as seen in synonymy.