The versions of Extended Cognition she's addressing are those which posit that we human cognizers are constituted by a fluctuating series of arrays of physical components, normally consisting of our bodies plus sets of tools which we use to embody some of our cognitions. In other words, she's arguing against the idea that we human beings are extended systems which typically include but are not limited to "biological skinbags." (This phrasing is from Andy Clark, one proponent of such a theory.) And importantly, the system a person is constituted by is not the same system over time—at one time it may be one system of physical components, and at another time, it may be some other system. As the tools change, the constitutive system changes. But it's supposed to be that a single person coheres through all of these changes. And what Baker doubts is that it is possible for a single person to cohere in this way.
She asks three questions which she thinks cannot be adequately answered by a proponent of this kind of Extended Cognition thesis: Can such a fluctuating system can be rational, can it be moral, and can it understand what it is doing while it is doing it.
Her answers in each case are negative, and in each case for a similar reason. Take the rationality question. Suppose Otto (a famous case for thinking about Extended Cognition) is an extended system consisting of a biological human whose memory has degenerated, plus a notebook and pen. The notebook and pen function for Otto like a memory. Many EC proponents hold that some of Otto's cognition is taking place over the substrate of the notebook and pen. They're not just aids to thinking—they are doing some of his thinking for him.
Say Otto wants to go to the museum, and upon consulting his notebook, begins to go there by walking down 53rd street. Clearly there is rational action taking place. But Baker asks, is it the extended system that is acting rationally? She argues that it is not—that the rational actor is simply the human skinbag—because in the absence of the notebook, Skinbag Otto would still find ways to come to know the directions to the museum.
But as far as I can tell this reasoning rests on the following unstated premise which I'll term Rational Component:
RC: If X is part of a rational system Y, then Y's rational actions cannot take place without X's integration into Y.(Note that RC implies that my hair is not part of a rational system, since it is not a necessary component of any explanation of my rational actions. This is not a criticism, it is noted here just to make sure the idea is clear.)
Given RC, it follows that since the notebook isn't necessary to enable Otto's rational action, the notebook is not part of the rational system which constitutes Otto.
But RC is questionable. People who have had lobotomies, for example, are still able to walk, to speak, and perform a variety of rational acts. It would seem that the part of the brain removed in the lobotomy did not need to be integrated into them in order to enable such actions. Does this mean, then, that this part of their brain was not part of what these people were as rational systems? That seems dubious! Indeed, to accept this consequence would seem to lead to a notion that prior to the lobotomy, there were two different rational systems inside these bodies—one without the lobotomized brain part, to which certain rational actions belonged, and one with the lobotomized brain part, to which certain other rational actions belonged (namely, the ones that were made impossible by the lobotomy).
I am actually sympathetic with a view that the truth of extended cognition entails the actual existence of some kind of fluctuating hodge-podge of overlapping persons, (I advocated for this very idea in the abovementioned dissertation) but Baker clearly is not. Yet to accept RC would (it seems to me) lead to a very similar picture of rationality, and perhaps even personhood.
Perhaps I am wrong to attribute RC to her argument, though. In this case, I am not sure exactly how to reconstruct her reasoning, and I invite comment in either case!