Against Proposition 1' (and, for that matter, Proposition 1) it might be said, ``This proposition leaves out of the picture something we know to be essential for mentation of the sort we humans enjoy, viz., interchange with the environment. An agent's mentation over some stretch of time doesn't consist solely in computation divorced from the surrounding environment, it consists of computation which reflects a symbiosis with the environment -- because human persons have sensors (for taking in information from the environment) and effectors (for manipulating the environment)."
Though we have argued elsewhere that transaction with the ``outside"
environment is, at least in principle,
entirely superfluous when it comes to consciousness,
we grant here for the sake of argument the claim that sentience
requires such interchange. This concession does imply that Propositions
1 and 1' are indeed unacceptable. But (as we indicated in a slightly
different context: [2f]), it should be easy enough to
remedy the situation. We have only to build in the environmental
interchange to Proposition 1'. In order to do so, let 
hold iff x
is a TM with sensors and effectors; then we have both a corresponding picture
(Figure 3) and a new proposition, viz.,
Figure 3: Bob as Transactional Turing Machine
Proposition 1''.
x is conscious from
to 
, where
this computation -- partly determined by causal interaction with the
environment -- is identical to the consciousness x enjoys through
Now, in order to rebut Objection 3, let's simply expand Max's powers: give him control not only over Bob's ``neuro" billiard balls, but over the homey analogue for the molecular motion involved in the use of sensors and effectors. (We leave the details of the more elaborate analogue to your imagination, but a good start is had by simply assuming that the neuro billiard balls behave the way they do in part because billiard balls from the outside interact with them.) Does this change the picture in any way? No. In fact, Max's handiwork is now all the more irreversible, for reasons already covered; and so reasoning which parallels our argument in the obvious way arises.