Do Rupert, A&A, Misunderstand the Parity Principle?

Menary writes,

These critics think that the main argument for the extended mind is simply the claim that if external processes are sufficiently similar to internal ones, then they are cognitive. Is this really the argument for EM? I believe that the critics have reached this conclusion by misinterpreting the PP.  (Menary, 2010, p. 6).

Clark has previously suggested that Rupert, Adams and Aizawa have been misinterpreting the Parity Principle, but I'm not really sure why he and Menary think this.  What have we written that leads them to think that the PP is the basis for our thinking that one argument for the extended mind is that external processes are sometimes sufficiently similar to internal ones?  Here is why I think that there is such an argument.  It comes from the Inga-Otto example (but also the three modes of Tetris play case.)  Note the following:

For in relevant respects the cases are entirely analogous: the notebook plays for Otto the same role that memory plays for Inga.  The information in the notebook functions just like the information constituting an ordinary non-occurrent belief; it just happens that this information lies beyond the skin (Clark & Chalmers, 1998, p. 13).

Certainly, insofar as beliefs and desires are characterized by their explanatory roles, Otto’s and Inga’s cases seem to be on a par: the essential causal dynamics of the two cases mirror each other precisely (ibid.)

The Parity Principle 3

But, I think that part of what people think might be going on with the Parity Principle, in addition to the idea that in-the-head versus outside-the-head makes no cognitive difference per se, is something to do with recognizing processes as cognitive.

But, Clark and I disagree on what we should recognize as cognitive processes.  Clark thinks that Martians manipulating bitmap images should count, but A&A don't.  So, it looks like what might be worth investigating in the Parity Principle is what should count as a cognitive process.  But, that seems just to be an indirect route to what A&A have loosely described as the mark of the cognitive, about which we have said a lot.

But, Clark has also expressed some scepticism about there being such a thing as the mark of the cognitive.  So, I don't see what payoff there is in more attention to the Parity Principle.  If it's about the MotC, then talk about the MotC.

The Parity Principle 2

Despite the interest that Chalmers, and others, have in the Parity Principle, I'm not really sure what help it is.  Here is what A&A, 2001, had to say about the principle:

In defending what we take to be common sense, we don’t propose to challenge a principle articulated by Clark and Chalmers: “If, as we confront some task, a part of the world functions as a process which, were it done in the head, we would have no hesitation in recognizing as part of the cognitive process, then that part of the world is … part of the cognitive (Clark & Chalmers, 1998, p. 2).  To us, this means that the skull does not constitute a theoretically significant boundary for cognitive science. More specifically, it means that being inside the brain cannot be the mark of the cognitive. This seems to us to be true and obvious. (Adams & Aizawa, 2001, p. 46). 

 So, if the principle is nothing but a "veil of metabolic ignorance" (as Clark sometimes describes it)--so that we should not use an in-the-head versus outside-the-head condition as a basis for telling what is, or is not, cognition--that by itself does not seem to me to speak to whether there is, or is not, extended cognition.

The Parity Principle 1

Chalmers recently suggested in comments here that more attention might be paid to the Parity Principle as a means of arguing for EC.  Mike Wheeler is, I think, doing this in his current book project Extended X.  And Sven Walter also has a paper where he is developing other versions of the principle in an effort to show that there is a kind of pro-EC bias in the current formulation.  Shannon Spaulding also has a paper discussing this.