Outline of one of the main arguments of Rupert (2004)
Premise 1. The hypothesis of embedded cognition (HEMC) is a competitor to the hypothesis of extended cognition (HEC) as a general philosophy of cognitive science, or at least as a treatment of the cases that often motivate HEC (Rupert, "Challenges to the Hypothesis of Extended Cognition," Journal of Philosophy, 2004, pp. 395-97).
Premise 2. Conservatism favors HEMC (ibid., pp. 395, 405-06).
Intermediate conclusion 1. Thus, other things being equal, HEMC should be preferred to HEC (ibid, p. 395).
Intermediate conclusion 2. Thus, we should accept Clark and Chalmers's endorsement of HEC only if Clark and Chalmers provide a substantial argument in support of HEC (i.e., only if they can show that other things are not equal).
Premise 3. Clark and Chalmers offer two identifiable arguments in support of HEC, one intuitive and commonsensical (the Otto's-notebook argument and the intuitive criteria derived from it), the other an argument in philosophy of cognitive science (the natural- or causal-explanatory-kinds argument) (ibid., pp. 401-07).
Premise 4. The intuitive argument falls to a dilemma: either one accepts Clark and Chalmers's conscious-endorsement criterion, effectively collapsing HEC into HEMC, or one rejects the conscious-endorsement criterion leaving in place only the remaining three criteria; but these are subject to obvious counterexamples—see cases involving cognitive bloat (ibid., pp. 402-05).
Premise 5. The natural-kinds argument falls to a different dilemma: either we individuate the relevant causal-explanatory kinds in a fine-grained way, in which case Clark and Chalmers's argument falls to the worries about fine-grained differences, or we treat the relevant causal-explanatory kinds as coarse-grained—which I called "generic"—kinds, which leads to bloat and also robs such kinds of any causal-explanatory power not accommodated by HEMC (ibid., sections V-VIII; for the two options – fine-grained v. coarse-grained kinds – explicitly presented side-by-side, see pp. 407, 418-19, 424).
Conclusion. Therefore, we have no good reason to accept HEC, given the current state of the evidence (ibid., pp. 428).
Note that this argument (a) does not presuppose that we've identified the essence of any particular kind of mental state (we may have, but the argument need not be so commital), (b) has nothing directly to do with what has come to be known as the Parity Principle (issues to do with parity are simply ignored, in favor of what I took to be the more pressing issue – the sorts of characteristics that appear to do causal-explanatory work in cognitive science), and (3) does not constitute a differences argument against HEC (differences are emphasized in connection with one half of a dilemma that criticizes one premise of one argument for HEC).