Here's the next objection: ``It's not clear that the sense in which you claim computation is reversible is relevant. You identify a computation as a sequence of total states of a machine, where the total state specifies the machine state, read/write head location, and tape register contents. You then assert that there is some other program M' which will cause the computer to run through those states in reverse order. But the identity of machine states is not a fact which is separable from the program which is actually running on a machine. Machine state ``1," for example, is not that very state because it has a ``1" pasted to it, but because of the transitions between it and other states which are caused by the program which the machine is running. So in switching from the original program M to M', we no longer have the same machine states available, so the sequence induced by M' isn't the reverse of the original. And one can't reverse a computation by reversing the program in any interesting way. There is, for example, a simple two-state program which will erase a sequence of 1s of any length, but one cannot `reverse' it to get a two-state program which will write out such a sequence."
This objection
saddles Computationalism with machine state functionalism (MSF),
according
to which our mental states are to be identified with the
machine states of
a TM rather than the configurations of such a machine.
Unfortunately, while
it's true that the output of
the algorithm 
of Theorem 1 is never a TM which in any sense
``reverses" the machine states of its input,
machine state functionalism has long ago been buried; no contemporary
computationalist advances this view. (The locus classicus of
MSF is due to Putnam [31], who
has himself rejected the doctrine.) The reasons MSF is a carcass
are myriad; they are nicely catalogued in
Chapter 8 of [41].
One problem with MSF is the apparent unboundedness of human
mental states. It has seemed to many that humans can enter any of
an infinite number of mental states. (One could believe that 1 is
the successor of 0, that 2 is the successor of 1, that 3 is
the successor of 2, 
,
and so on ad infinitum. And of course we would need
to consider
states involving not only beliefs about
arithmetic, but also hopes, fears, dreams, mental images, and
so on.) But every TM has a fixed and finite
set of machine states (while on the other hand
even tiny TMs are capable of entering an
infinite number of configurations.)
Another agreed upon defect plaguing MSF is that
according to it two TMs which compute the same function f but which
differ in their machine states and the arcs connecting them (to
use the critic's scheme) are
classified as giving rise to different cognition. But this
implies that if you share with us (say) a love of
climbing roses of the ``Blaze" color, underlying our attitude must
be one TM with the same exact states -- which hasn't seemed too plausible
to most.
Finally, the present objection is problematic for another reason having nothing to do with the history of Computationalism: Computationalism is the view that cognition (including consciousness) is computation, but computation is not a machine state (or a collection of such states, or a collection of such states linked by arcs). Computation, in the terms our critic prefers, isn't a program; rather, computation is a program in progress. That is, computation is a sequence of configurations [9], [2d], as we have explained above.