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 , who has himself rejected the doctrine.) The reasons MSF is a carcass are myriad; they are nicely catalogued in Chapter 8 of . 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 , [2d], as we have explained above.