Much has been said about the plausibility of [extended cognition]. One obvious problem is conceptual: despite functional equivalence, external processes do not seem to meet traditional criteria of the cognitive. Adams and Aizawa (2001), for instance, argue that real cognitive processes involve non-derived content (which e-cog processes don’t), and that the causal mechanisms underlying external and internal processes are too different to form a cognitive kind. (Vaesen, 2010, p. 6).This is not exactly how I would put it. The objection is that, by the standards implicit in contemporary cognitive psychology, Inga and Otto are not functionally equivalent. And, this seems to me to have been fairly widely accepted, since the principal EC rejoinder is to claim that there is some sort of "coarse" functional equivalence. "Coarse", of course, needs some explication (that I don't think it's been given in the literature). To try to sharpen the point a bit, notice that Inga and Otto are not even what Pylyshyn would call "weakly equivalent." Inga forgets things that Otto does not. Evidently, "liberal functionalism" is going to have to be so liberal as to not even require input-output equivalence.
So, barring some explication of "function equivalence" I want to resist any concessions on that score.
Vaesen, K. (2010) "Knowledge without credit, exhibit 4: extended cognition" Synthese online. DOI 10.1007/s11229-010-9744-0