OK, at this point I'm just going on youtube searches for "pragmatism;" I was not previously familiar with Brandom, though he is apparently well known and studied under Rorty and Princeton and has a beard that looks stunning when backlit.
He has some interesting comments here about the historical point at which pragmatism as we read about it arose and about "analytic pragmatism," i.e. using analytic philosophy tools for treating language in pursuing the pragmatist project. Some of this is a little technical, but you can probably see what he's trying to synthesize in broad strokes. And did you know that Wittgenstein was really an avatar, and not really a blue-skinned alien? Brandom says so!
Here's part II, where he goes into the relation between philosophy of language and cognitive science, which will give you a clue about how weird philosophy of language is, which will be confirmed when we do our Frege and Heidegger episodes (eventually). If you watch far enough to get confused by his talk about modal logic, you have my sympathies.
I was just researching Brandom and this page was the first hit for “robert brandom science”. Cool.