Cognitive Grammar (CG), in my opinion, is the premiere theory with a cognitive linguistic scientific framework, exhaustive in its linguistic notions built up from general cognitive capacities, elegant in its fundamentals—merely three components: a semantic unit, a phonological unit, together with a symbolic unit—and comprehensive in its scope of linguistic explanation from morpheme, word, phrase, on up to pragmatics and philosophy of language, each level applying the same set of theoretical notions.
Humans are uniquely symbol-based creatures, exploiting this fact with the ability to talk, reflect, rationalize, and project ourselves and others in to the future. A grammatical theory that recognizes, and even makes central, a symbolic hypothesis for language, building an entire infrastructure around it, taking seriously this human uniqueness of communication, with the success that it has had over the past 40+ years in describing so many different languages, is worthy of any serious study and philosophical contemplation.
Some links for the not-so-faint-of-heart:
What is Cognitive Grammar (a helpful book for purchase providing basic details)
An integrated CG paper (a free PDF download of independent research on cognition that integrates with CG)