Firstly, for many systems, Φ—as outlined in IIT 3.0—may not be computable as it may never be practical to carry out all possible discrete grainings in space, time and relevant functional elements and maximize over these. Of course, as Barrett himself points out, the fact that something may not be computable does not impact the ontological status of the theory (i.e. classical thermodynamics that deals with ensembles of the order of 1023 particles).
Secondly, even an idealized, abstract feed-forward system that, according to IIT 3.0, has zero Φ, may well have a non-zero Φ if built out of real physical components given reciprocal interactions at the molecular micro-level.
This is a correct observation. The theory as presently formulated  deals with discrete (binary), simulated units implementing transition probability matrices. It remains to be seen whether the actual numerical value for Φ of a physical instantiation of a feed-forward system is numerically non-negligible. This would not, however, invalidate IIT 3.0. Even under these circumstances, it is likely that Φ associated with physically instantiated, strongly connected networks is much larger than Φ of physically instantiated, feed-forward networks (e.g. built with diodes or other one-way rectifiers).
Thirdly, the world is continuous and not discrete. Many physical laws, such as quantum field theory or general relativity, are formulated using continuous fields. Therefore, IIT needs to be reformulated, as Barrett points out in his earlier writing .
Barrett may well be correct that IIT 3.0 needs to be reformulated to account for a continuous world with continuous variables. However, we would also like to point out that whether space–time is ultimately continuous or granular is heavily debated among fundamental physicists and no consensus appears to have been achieved.
We declare we have no competing interests.
We received no funding for this study.
The accompanying comment can be viewed at http://dx.doi.org/10.1098/rstb.2014.0198.
- Accepted November 5, 2015.
- © 2016 The Author(s)