Counterfactuals Can't Count: A Rejoinder To David Chalmers.pdf

1. Introduction
In the first part of this paper, I introduce Discrete State Machines (DSMs) and show how, with input to them defined, their behaviour is described by a simple unbranching sequence of state transitions analogous to that of an inputless FSA. Then I review Putnam's 1988 argument that purports to show how every open physical system implements every inputless FSA. This argument is subsequently applied to a robotic system that is claimed to instantiate genuine phenomenal states as it operates—if the robot system instantiates such states then so must any open system.

2. Discrete state machines
In his 1950 paper, Computing Machinery and Intelligence, Turing defined DSMs as machines that move in sudden jumps or clicks from one quite definite state to another. An example DSM from Turing is that of a wheel machine that clicks round through 120 degrees once a second, but may be stopped by the application of a lever-brake mechanism. The machine's internal (computational) states are labelled by a mapping function f that maps from the physical state of the machine to the computational state of the machine. The input to the DSM is described by an input signal, and the next internal state of the machine is determined solely by its current state and its current input.

3. Putnam's argument
Tucked away in an appendix to Hilary Putnam's 1988 book, 'Representation and Reality', is a short argument that endeavours to prove that any open physical system is a realisation of every abstract inputless Finite State Automaton and hence that Functionalism fails to provide an adequate foundation for the study of the mind. Central to Putnam's original argument is the observation that every open physical system, S, is in different maximal states at every discrete instant and is characterised by a discrete series of non-cyclic modal state transitions. To simplify the following discussion of Putnam's claim, I will replace Putnam's arbitrary open physical system, S, with an Infinite Counting Machine (ICM) generating the non-cyclic counter state sequence in place of the physical system state sequence.

4. Counterfactuals cannot count
This type of argument has previously been criticised on the grounds that Putnam's open system does not correctly implement counterfactuals. However, in a novel extension, I demonstrate that, in the execution of the robot's control program with known input, unless we allow non-executed state transition sequences to directly influence the generation of phenomenal states, the lack of counterfactuals in Putnam's open system cannot rescue functionalism; counterfactuals cannot count.