 This example does not include inputs and outputs (which are presumably necessary for computational explanations), so Putnam introduces a small change to allow for automata with inputs and outputs. The idea is similar, except one must take into account an isomorphic mapping between physical states (considered as inputs and outputs) and the inputs and outputs of the relevant automaton. This restriction result in a weaker conclusion: instead of every physical system implementing every finite automaton, any given physical system implements a countably infinite number of finite automata (namely, those that produce the correct input/output pairs). This is because, for any arbitrary input/output pair &lt;i, o&gt;, there are countably infinitely many automata that produce output o when given input i (see Appendix of Putnam 1988 for details).