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I haven't read the original article yet (I have read some of the original research on the theory on which it is based), but out of several summaries, what the argument seems to boil down to is:
1) It is trivially apparent that "integration" is a characteristic of cognition, not just intelligence but even the most primitive cognition; 2) We can say some interesting things about the nature of the integration that occurs in human cognition, some of which has been demonstrated experimentally; 3) When someone is unconscious -- when cognition is mostly gone -- the amount of integration drops precipitously; 4) Since aspects of the theory have been demonstrated, the theory is entirely and precisely true; 5) Included in this is that since there has been some gross correlation between consciousness and integration (and because, correlation means not just causality but identity -- if two things are correlated they must be identical) then consciousness must be integration, nothing else we must define consciousness as integration -- nothing else: not emotion, theory of mind, psi, aesthetics, spirituality, etc. -- is relevant except as it can be straight-jacketed into an aspect of integration -- has anything to do with what consciousness is; 6) Only very incomplete and imprecise measurements of integration can be made, so a mathematical theory that assumes not just a high level of integration but an infinite capability is not thereby excluded from matching the experimental results (there is a rather good mathematical model of the rate of discovery of bugs in software that assumes any piece of code contains an infinite number of bugs); 7) Since the theory is true and assumes that consciousness requires (or rather is) infinite integration capabilities, humans must have infinite integration capability; 8) No classical system can have infinite integrative capabilities; 9) If you try to describe some quantum systems in classical terms you get infinities (although those infinities disappear when the right formalism is applied and nothing infinite -- e.g., infinite information capabilities -- are ever observable); 10) Given 8 and 9 human consciousness must require quantum systems; 11) Given 8 classical computers cannot be conscious (although, any precise predictions of the theory, must necessarily be based on computer models or models too simple to require a computer model); 12) Let's not even mention quantum computers, they just confuse things.

Overall -- if you take an apparently useful theory about some characteristics of consciousness and push it way outside any reasonable limits on its applicability, and ignore things like an AI using QM based processors, then you can conclude that artificial consciousness is impossible. I really don't have the faintest idea whether artificial consciousness is possible, but this argument is far from a death sentence to the idea. It doesn't even raise any faint difficulty -- it just is used as a justification to essentially assume the conclusion.

AI as a science has been on the ropes for a number of years both ontologically (per Kurt Godel's reasoning regarding the impossibility of constructing a Turing Machine that can know whether a problem is solvable) and phenomenologically per QM theory and the ultimate collapse of the wave function. Machines and their analogs will never be conscious.

Even better than what I was going to write.

Here's a lengthy critique of AI from Skeptic magazine (dated around 2005 or a bit later I think):

Here's a Wired article that brings out the limits of AI in accomplishing anything subtle: "The Mystery of Go, the Ancient Game That Computers Still Can’t Win"

“Go is to Western chess what philosophy is to double-entry accounting.”

i think my head's exploded reading Topher's post. On a less cerebral note -pun intended, it is encouraging that mainstream consciousness researchers are increasingly willing to entertain non-reductionist models of consciousness. Let's hope this is the beginning of a turn against epiphenomalism....

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