Grammar, Geometry, and Brain

J. E. Fenstad has a provocative little book called Grammar, Geometry, and Brain (CSLI 2010). It is speculative and is sort of like an annotated bibliography, but as such it is very valuable as a discussion of work in cognitive science and brain modeling at the interface with linguistics. Fenstad is a mathematical logician and occasional linguist. The book is filled with his own preferences and experience, but it is very forward thinking, perhaps venturing into the crackpot, but that's OK with me. It is inspiring.

Fenstad states "you can never be more than the mathematics you know," something I heartily agree with. Like him I will continue to seek out new mathematics to apply in linguistics. I'm tired of formal language theory and logic, these tools cannot be everything for linguistic theory. Fenstad's suggestion is that Geometry can provide a direct link between linguistic theory and cognitive modeling. He points to the Conceptual Spaces framework of Gärdenfors (MIT Press 2000) for a geometrical theory of semantics which he suggests could be connected to syntax using attribute-value grammar. He also discusses several works in cognitive neuroscience, suggesting how geometry could play a role in a bridging model connecting neuronal assemblies to conceptual spaces. It's an interesting book that pointed me to a lot of other readings.