I think we can exaggerate the impact of this sort of cognitive science on philosophy. It's very important IF we start from the assumption, as most philosophy has since the 17th century, that we won't figure anything out until we can figure out how the mind thinks and what sorts of things it can think about. That is certainly one way to do philosophy, and still an important branch of philosophy today, but by no means is it any longer considered to be First Philosophy. For example, it's hard to see how much of Lakoff's work will be relevant to contemporary metaphysics. Understanding the mind's classificatory mechanisms does little to help us understand the nature of necessity and possibility, of time and space. To some degree, absolutely, it's not irrelevant. For example, some of Lakoff's work on how spatial information is encoded in metaphor is important for understanding how we conceive of space, and whether a certain conception is an illusion of thought or revelatory of the nature of space. But no very interesting or central question in the metaphysics of space has been or likely will be solved that way, but that is as much real philosophy as the sort discussed in this post.
I think we can exaggerate the impact of this sort of cognitive science on philosophy. It's very important IF we start from the assumption, as most philosophy has since the 17th century, that we won't figure anything out until we can figure out how the mind thinks and what sorts of things it can think about. That is certainly one way to do philosophy, and still an important branch of philosophy today, but by no means is it any longer considered to be First Philosophy. For example, it's hard to see how much of Lakoff's work will be relevant to contemporary metaphysics. Understanding the mind's classificatory mechanisms does little to help us understand the nature of necessity and possibility, of time and space. To some degree, absolutely, it's not irrelevant. For example, some of Lakoff's work on how spatial information is encoded in metaphor is important for understanding how we conceive of space, and whether a certain conception is an illusion of thought or revelatory of the nature of space. But no very interesting or central question in the metaphysics of space has been or likely will be solved that way, but that is as much real philosophy as the sort discussed in this post.