Three Mathematical Foundations for Syntax

Three different foundational ideas can be identified in recent syntactic theory: structure from substitution classes, structure from dependencies among heads, and structure as the result of optimizing preferences. As formulated in this review, it is easy to see that these three ideas are completely independent. Each has a different mathematical foundation, each suggests a different natural connection to meaning, and each implies something different about how language acquisition could work. Since they are all well supported by the evidence, these three ideas are found in various mixtures in the prominent syntactic traditions. From this perspective, if syntax springs fundamentally from a single basic human ability, it is an ability that exploits a coincidence of a number of very different things.