David Carroll, sorry if I am being rude, but 'Philosophy' of the mind sounds like an excuse for not being able to solve the (not at all abstract) problem of understanding how the mind actually works (cognitive science) and it's neural basis (neuroscience).
I find extremely interesting and straightforward the Bayesian Probabilistic Modeling approach for understanding and predicting human behavior, learning, and performing intellectual tasks.
A lot can come from addressing an issue of psychology from the 'computational' point of view, I mean, to consciously simplify the system and work out the mathematics underlying its operation; then making a model that explains the data, running the model in a simulator and test whether the model meets the data.
In order to do all this, one must have developed a strong logical, mathematical point of view; and must be able to (really) solve questions previously addressed only 'philosophically' by using analytical thinking.
Maybe this is the reason why the most important scientists in a lot of different branches of cognitive science and neuroscience are physicists.