The languages of the world vary greatly, but within systematic limits that linguists have been uncovering for decades. Our research has been developing a unified explanation of semantic universals: properties of meaning shared by all natural languages. In this second talk, we will present ongoing work extending the argument from the first talk in two different directions. First: is learnability the fundamental explanation, or could the universals be explained by a general notion of complexity, which also explains the learnability facts? We will discuss in somewhat general terms the relation between learnability and complexity, before presenting preliminary results on applying (approximate) Kolmogorov complexity to quantifiers which suggest that learnability may be a better explanation. Second: how does learnability exert pressure on language structure over time? To answer this question, we present a study in which we apply the framework of iterated learning to quantifier meanings, with neural network agents and learning. Our initial results are promising: monotone quantifiers robustly evolve in this setting.