Embodiment is not the weak claim that you can see small effects of the behaviour of the body in our mental representations of the world. Embodiment is the radical hypothesis that the brain is not the sole resource we have available to us to solve problems. Our bodies, and the meaning-filled perception of the world they allow, do much of the work required to achieve our goals, and this simple fact changes utterly what our theories of 'cognition' will look like.The last part is spot on: Taking embodied cognition seriously requires developing theories of cognition that are quite different from mainstream theories. The first part is, I think, a touch muddled: It confuses the basic requirements for believing in embodiment with a particular solution that Andrew (and I) favor. Some of the confusion has to do with a historic shift in who the opponent of embodiment is.
The basic belief of embodiment
The only basic requirement for an embodied cognitive psychology should be the belief that "cognition" and all other "psychological processes" are entirely embodied. This means that there is never a need to talk about non-material things in the course of describing and explaining mental happenings - Cognating, feeling, thinking, perceiving, etc., are things a body does. This is a very strong claim, and it goes well beyond the now trivial claim that our psychological processes are "effected by" states of the body.
Also worth noting, embodiment is what one must logically be left with if one rejects psycho-physical dualism, and adopts a materialist or a realist stance. Another way of saying this: Embodied cognition is just psychology without magic.
And there we are, the first understanding of the embodiment argument. The opponent is the dualist, and anyone willing to reject dualism and embrace the physical body as the whole of the person is a proponent of embodiment. Thus, people who claim that the brain is where all the action is in psychology are definitely making an "embodied" argument, in so much as they completely reject the idea of a non-corporeal mind / soul.
So what is all the fuss about now?
It has been fashionable for most of the last century for psychologists to declare that they are not dualists, and to embrace brain science as the future of psychology. Alas, few modern psychologists have been willing to see their rejection of dualism through to its logical conclusion. It is mostly lip service, and these psychologists have even managed to muck up the brain scientists. C. S. Peirce told us 150 years ago that you have not had a complete thought until you have considered all the consequences of your idea, and that is ever so obvious in this case.
The most obvious way to demonstrate the problem is to show that modern cognitive science and cognitive neuroscience still uses a framework and a vocabulary that arose back when people believed in the non-physical soul. They claim that we "retrieve memories", "rely on our intelligence", "make choices that guide our action", etc. But embodied cognition, even if brain limited, draws all this into question: Who is it that retrieves memories? Where are they retrieved to? Once it is retrieved, how do we examine it, if not in a Cartesian theatre? What is intelligence that I can rely on it? Where do I keep the intelligence when it is not in use? What is a choice if not the action itself? These are not trivial questions, but they are simple and obvious questions. Someone who believed that the brain was all there was to it, faced with even these simple questions, should realize they are doing something wrong.
Now, I've met at least a few people who know they are doing something wrong, but who persist because it is practical. The standard cognitive language helps them design experiments, get grants, and communicate to the public. Indeed, this is a major stregnth of the cognitive framework, which I have written about elsewhere. I can appreciate the dilemma these colleagues find themselves in, as there is work to be done or one loses their job (or fails to get a job), and many simply know that their strengths lie in the experimental realm and they are just doing what they can do well. These people are not working to fix the problem, but in my experience they are interested in new developments, and they seem willing to adopt a new framework once the kinks have been worked out. However, there is no excuse for the people who don't even realize they are being inconsistent in their stated beliefs. If you reject magic in psychology, you need to be continuously wary, and you need to be willing to give up the ideas you entered the field of psychology with, because lay notions of psychology are pervasively laced with dualism.
Then why are the "embodied" people so pissed off at the "brain" people?
Alright, so now we see at least one part of the modern dilemma regarding embodiment: People think they can escape the perils of dualism while retaining a framework that was created to explore dualistic ideas. Thus, most of the work done in "cognitive neuroscience" rubs us embodied cognition folk the wrong way: Not because the research is bad, and not because we think the brain is irrelevant to psychology, but because perfectly reasonable methods and results sections are almost always stuck between incoherent introductions and conclusions. Every time we see a brain talk that ports in magical soul stuff, it pisses us off. However, that is only one part of the modern battle line.
More important, for many people, is the increasing evidence that the rest of the body is crucial to psychological processes - not just that it influences psychological processes, but that the body is best considered (from a theoretical and research standpoint) as part of the processes. That is, there is evidence that we can solve a lot of mysteries about behavior and cognition by treating the brain, the rest of the body, and the environment, as forming a complex dynamic system.
How on earth could that be more important than the whole dualism thing? Because many psychologists who are now interested in the embodiment conversation entered late in the game. They started their careers in a time when everybody already claimed to have rejected dualism, and as students they were already convinced of this step, likely more firmly than their peers or seniors. That is, for these researchers, drawing the battle line at dualism is not interesting because they tacitly accept that dualism was abandoned long ago. This leads to an interesting situation, well represented by Andrew's quote above: For Andrew and Sabrina, the two problems above - failure to fully reject dualism and failure to include more of the body in embodied theory - are completely intertwined.
And there we are, the second understanding of the embodiment argument. The opponent is the brain-focused psychologist. In this context, anyone willing to admit that the "mind" is constituted by activities of the body beyond the brain is a proponent of embodiment.
Why all this blather and history?
As you know, I'm working on a group-written Ecological Psychology textbook, and you might know that I have hopes of one day producing an Introductory Psychology textbook. One of the major challenges when presenting these concepts is to determine which ideas necessarily go together, and which ideas happened to go together by historical accident. Ideas that are stuck together by historical accident can still be presented together, but it is (I think) best to be explicit about the historic nature of the association.
For example, it is true that those who favor embodied cognition generally dislike brain-focused research in psychology. However, this is a historic accident, and is due to the fact that most brain-focused researchers in psychology still uses a dualistic framework, whether they want to admit it or not. Meanwhile, researchers who come out of some other traditions are simultaneously better at fully rejecting dualism, and at giving more credit to the whole body. Thus it often seems as if the battle line is brain-scientist vs. ecological psychologist / dynamics systems guy, or something like that.
Far from it. I think the battle line is still between the psycho-physical dualist and the materialist monist. The issue of brain-reductionism vs. whole-body embodiment is a different issue, and if we could get rid of the covert dualism, then most of the battle would be over.