I suspect that you mean that there is no meaningful distinction between perception and cognition, since perception (I would say) is a form of cognition.
Yes ... and no (go away, Zizek!). The question isn't how to "correctly" partition the brain's different functions into disjoint, or overlapping, subsets / categories, nor how to label them. Each map you construct should be suited for the given purpose, and in this case talking about "perception" separately from "cognition" is -- far from 'paying rent' -- making a subtle mistake. That of a well meaning but slightly disingenuous parent buying into his own explanation.
Bear with me: The reason that the rubber hand illusion and related material may be a good preaching tool is because it neatly sidesteps the many tribal affiliations / social signals associated with correcting someone, it groups itself with "optical illusions" rather than "this is where you reason wrongly".
It's a situation a bit like (da-da-dumm!) sailing between Scylla and Charybdis: If you told people you really try to cure them of some of their many cognitive biases, the ones prone to being offended (cough everyone) would be so, and the distinct advantage of the smoke-and-mirrors (well, mirrors at least) 'perception experiment' would be lost. On the other hand, the PERCEPTION ONLY, NO COGNITION INVOLVED disclaimer could correctly be seen as disingenious, since we don't actually care about the perception aspect, not for our purposes, anyways. However, that's an acceptable price to pay (I'd imagine the ensuant conversation along the lines of "Remember back then, you really wanted to use the rubber [hand] to improve my cognition, didn't you?" - "Well, admittedly so ... sorry, but it was a good hook [with fingers, nonwithstanding], eh? Can we rejoin the love-pile, now?").
The reason I was iffy on us upholding that distinction was that we're not undergoing the experiment, and we should be clear on what we're doing (a function of cognition, rather than one revolving around perception), and which pedagogical trick we're exploiting for doing so. After all, we still need to be able to look at ourselves in the mirror. Or, you know, at some rubber facsimile of us.
A related concept is the aforementioned Wittgenstein's Ladder. It wasn't an important remark, but you did ask ...
Would you be willing to point out the things that you think are obscuring my conclusion?
Just referring to the paragraphs following your concluding remarks (albeit in "()" (brackets, that is)). While endnotes are unobtrusive, in this format a host of only tangentially related asides detracts from your central message; the coda should provide closure, not be an unrelated personal message to Eliezer.
I had to read this many times for it to really sink in, so I'm going to try performing an ideological Turing test just to make sure that I'm on the same page as you (I assume that term applies to what I'm about to do even though the examples in that post had to do with political and theological arguments):
Our purpose, both in performing the experiment and educating people about cognitive biases, is to demonstrate that people can misinterpret reality. To make a distinction between the purposes of the two forms of demonstration -- besides being a useless exe...
It seems that the CFAR workshops so far have been dedicated to people who have preconceptions pretty close in ideaspace to the sorts of ideas proposed on LW and by the institutions related to it. This is not a criticism; it's easier to start out this way: as has been said, in a different context and perhaps not in so many words, we should focus on precision before tractability. We're not going to learn a thing about the effectiveness of rationality training from people who won't even listen to what we have to say. Nevertheless, there will come a day when these efforts must be expanded to people who don't already view us as high in social status, so we still have to solve the problem of people being more concerned with both our and their social status than with listening to what we have to say. I propose that the solution is to divorce the consideration of social status from the argument.
There is a lot of talk of cognitive biases on LW, and for good reason, but ultimately what we are trying to teach people is that they are prone to misinterpreting reality, and cognitive biases are only one component of this. One of the problems with trying to teach people about biases is that people feel personally responsible for being biased; many people have a conception of thinking as an 'active' process, so they feel as though it reflects upon their character. On the other hand, many people conceive of perception as a 'passive' process; no one feels personally responsible for what they perceive. So, I propose that we circumvent this fear of character assassination by demonstrating how people can misinterpret reality through perception. Enter: the rubber hand illusion.
In case you're unfamiliar with this illusion, to demonstrate the rubber hand illusion, a subject sits at a table, a rubber hand is placed in front of them, oriented relative to their body as a natural hand would be, and a partition is placed between the rubber hand and their 'real' hand such that they are unable to see the 'real' hand. Then, the experimenter simultaneously 'stimulates' both hands at random intervals (usually by stroking each hand with a paintbrush). Then, the experimenter overextends the tips of a finger on each hand, the rubber hand about 90 degrees, and the 'real' hand about 20 degrees (it's not really overextension, and it wouldn't cause pain outside of the experiment's conditions). Measurements of skin conductance response indicate that subjects anticipate pain when this is done, and a very small selection of subjects even report actually experiencing pain. Also, (just for kicks) when subjects are questioned about the degree to which they believe their 'real' finger was bent, they overestimate, by an average of about 20 degrees.
As Dr. Vilayanur Ramachandran has demonstrated, the rubber hand illusion isn't the most general example of this sort of illusion: the human mind can even anticipate pain from injury to the surface of a table. In fact, there is evidence that the human mind's evaluation of what is and is not part of its body isn't even dependent upon distance: Dr. Ramachandran has also demonstrated this with rubber hands attached to unnaturally long rubber arms.
I think that there are also three beneficial side effects to this exercise. (1) We are trying to convince people that Bayesian inference is a useful way to form beliefs, and this illusion demonstrates that every human mind already unconsciously uses Bayesian inference all of the time (namely, to infer what is and isn't its body). To further demonstrate the part about Bayesian inference, I would suggest that subjects also subsequently be shown how the illusion does not occur when the rubber hand is perpendicular to the 'real' hand or when the 'stimulations' aren't simultaneous. (2) After the fact, the demonstration grants social status to the demonstrator in the eyes of the subject: "This person showed me something that I consider extremely significant and that I didn't know about, therefore, they must be important." (3) Inconsistencies in perception instill feelings of self-doubt and incredulity, which makes it easier to change one's mind.
Addendum: This post has been substantially edited, both for brevity and on the basis of mistakes mentioned in the comments, such that some of the comments now appear nonsensical. Here is a draft that I found on my desktop which as far as I can tell is identical to the original post: http://pastebin.com/BL81VQVp