This post deals with implications Ex-Cog may have for the philosophical topic of Personal Identity.
Just suppose that there is a kind of close causal coupling (between a cognizing system and its environment) which does issue forth in the constitution of a cognizing system encompassing the coupled environment.
Say cognizing system C1 engages in this sort of coupling with its environment, thereby causing a cognizing system C2 to exist.
C2 has parts, and one of those parts seems to be, simply, C1. The system C1, after all, doesn't cease to exist just because it has coupled with its environment to form C2. Rather, C1 persists, as part of C2.
The physical system C1 persists as part of C2. But suppose that, at least before the coupling, C1 is a person. Call her Carla. There are now two cognizing systems—C1 and C2—which seem to have a prima facie case to be the continuation of Carla. For example, should C2 cease to exist, this would not seem to be a case of Carla's destruction. Rather, Carla continues, in that case, as C1. This is a prima facie case that C1 is the proper continuation of Carla and not C2. Yet, who Carla is seems to have much to do with how Carla cognizes. And once C1 couples with its environment to form C2, it seems as though C2's cognitions have the better claim to be continuations of Carla's own cognitions. For what C2 is trying to cognize its way through is what Carla is trying to cognize her way through. She does this (per the hypothesis stated at the outset of this post) by causing C1 to couple with its environment to form the cognitive system C2.
(The case for C2's being Carla's continuation may seem to assume a Psychologistic account of Personal Identity. I prefer such an account, but I don't want to presume it. In fact, similar arguments for C2's status as Carla-continuer can be built on other accounts of Personal Identity. For the kind of close causal coupling that is supposed to support the formation of an extended mind would seem also to support the formation of an extended cognizing body. Insert difficult discussions about biofunction here, but I think it's clear how, given the Ex-Cog picture, the physical boundary between body and environment is just as indistinct as that between mind and environment. Indeed, the body/environmental blurriness is probably more obvious than the mind/environment blurriness.)
A lot has been skipped over here, but suppose I'm right that both C1 and C2 can lay an equally valid claim to be Carla's continuation. In that case, an interesting situation arises. We have here a case of personal fission—that strange sort of event usually found only in philosophical thought experiments and science fiction stories. Two objects lay equal claim to being the same person as some past personage.
I'm pointing this out because I find it interesting—and kind of exciting—to think that, if the extended mind hypothesis is true, it turns out personal fissions aren't a hypothetical logical possibility that can serve only to jog our rarified philosophical intuitions. Rather, it turns out personal fissions happen regularly, as a matter of course, here on the ground. Our data for working through problems in Personal Identity don't have to be intuitions about what we would or should say given the actualization of various improbable fantasies. Rather, we can work through Personal Identity issues by looking at what people actually do, in the real world, in their day to day persistence as cognitive agents.