Alright, I'm going to try to piece things together and start by backing up. 
The determination of whether matter, described by QM, has a spectrum gap 
has recently been shown to be undecidable per the third link in first post. 
This implies some aspect of physics is not computable, and therefore the 
Strong Church Turing thesis and digital physics are invalidated. It also 
implies that the reductionist hypothesis is invalid because there will be 
explanatory gaps from the microscopic to the macroscopic, and that 
emergence (sum is greater than parts) should be elevated to a first-class 
component of nature. The phi measure in IIT "will be high when there is a 
lot of information generated among the parts of a system as opposed to 
within them" and therefore can be by definition considered a measure of 
emergence. Tononi/Koch claim it's a measure of consciousness, though Koch 
is ironically a self-proclaimed "romantic reductionist." As reductionism is 
invalidated, the sum-greater-than-parts measure phi by Tononi/Koch 
corresponds to one hypercomputable aspect of nature; we say that to be 
hypercomputable or irreducable (i.e., to an algorithm) is to be emergent 
(sum-greater-than-parts). However, the interpretation of phi (a measure of 
emergence) as consciousness is based on intuition. It has not been 
verified. If this association of phi with consciousness could be verified, 
then we could safely assume HHI hypothesis to be true, i.e. that 
consciousness is a hypercomputable aspect of nature.

The argument by Maguire et al. starting with IIT (and also corroborating 
HHI hypothesis) seems to agree with the recent indirect proof that 
reductionism is invalid. However, it doesn't invalidate IIT as claimed 
because IIT implies hypercomputability; the phi measure is a measure of 
emergence. If consciousness is demonstrated to correlate with phi and thus 
proved to be hypercomputable, Goertzel says we can still produce humanlike 
AI with Turing machines by modeling imitation, intuition and chance. 
Furthermore, If HHI is true, then any reductionist attempts to describe 
consciousness like the OrchOR theory by Penrose/Hameroff are doomed to fail 
because a hypercomputable (emergent) process, by definition, cannot be 
described in any formal language (as Goertzel points out in his paper).

Aaronson's zombie argument is just claiming that no scientific theory could 
explain the first-person experience and solve the Hard Problem of 
consciousness. He just observes it would be ridiculous if 'someone claims 
that integrated information “explains” why consciousness exists.' Notice 
that if consciousness is hypercomputable (correlates with phi), then that 
is exactly what Goertzel concludes in his paper. Aaronson even admits 'we 
can easily interpret IIT as trying to do something more “modest” than solve 
the Hard Problem, although still staggeringly audacious. Namely, we can say 
that IIT “merely” aims to tell us which physical systems are associated 
with consciousness and which aren’t, purely in terms of the systems’ 
physical organization. The test of such a theory is whether it can produce 
results agreeing with “commonsense intuition”: for example, whether it can 
affirm, from first principles, that (most) humans are conscious; that dogs 
and horses are also conscious but less so; that rocks, livers, bacteria 
colonies, and existing digital computers are not conscious (or are hardly 
conscious); and that a room full of people has no “mega-consciousness” over 
and above the consciousnesses of the individuals.'

On Thursday, December 10, 2015 at 9:37:03 PM UTC-5, Brent wrote:
>
> But see
>
> http://www.scottaaronson.com/blog/?p=1799
>
> Brent
>
> On 12/10/2015 5:54 PM, Dan wrote:
>
> I should mention this paper, which gives credence to HHI by beginning with 
> Tononi's Integrated Information Theory of consciousness and, by assuming 
> consciousness is a lossless integrative process, concluding that it would 
> not be computable. 
>
>    - http://arxiv.org/abs/1405.0126
>    
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