Algorithms Implemented in Space and Time

A fundamental question regarding computation viewed as a physical phenomenon concerns the criteria under which a physical system can properly be said to implement an abstract formal procedure. I advocate the Simple Mapping Account (SMA) and defend this position against a number of critiques, including semantic and causal accounts. In line with SMA I support the conclusion that realizing or implementing an abstract computational procedure is not an intrinsic property of physical systems, but rather is based on a purely observer-dependent act of ascription. This 'anti-realist' conclusion has traditionally been invoked in an attempt to undermine the Computational Theory of Mind (CTM), which in turn has led supporters of CTM to criticize SMA and propose competing accounts. In contrast, I argue that the version of CTM directly threatened by SMA is one that should not be accepted in any case, and propose an alternative strategy for those who would defend CTM against charges of 'triviality'.