Scott Aaronson, complexity theory researcher, disputes Tononi's theory of consciousness, that a physical system is conscious if and only if it has a high value of "integrated information". Quote:

So, this is the post that I promised to Max [Tegmark] and all the others, about why I don’t believe IIT.  And yes, it will contain that quantitative calculation [of the integrated information of a system that he claims is not conscious].

...

But let me end on a positive note.  In my opinion, the fact that Integrated Information Theory is wrong—demonstrably wrong, for reasons that go to its core—puts it in something like the top 2% of all mathematical theories of consciousness ever proposed.  Almost all competing theories of consciousness, it seems to me, have been so vague, fluffy, and malleable that they can only aspire to wrongness.

http://www.scottaaronson.com/blog/?p=1799