ABSTRACT
Computation explicates mechanism. More recently, the notion of mechanism articulated by philosophers of science has been applied to shed light on computational systems. The notion of computation comes from mathematics. To a first approximation, mathematical computation is the solving of mathematical problems by following an algorithm. Ordinary physical descriptions define trajectories with undenumerably many state transitions, whereas classical computational descriptions such as Turing machine programs define trajectories with denumerably many state transitions. Whether a mechanism in the broad, generic sense computes a Turing-computable function or a Turing-uncomputable function has nothing to do with the original Church–Turing thesis. To construct a mechanistic account of digital computation, the key notion was that of a digit, which is a concrete counterpart of the abstract notion of letter employed by computability theorists. The new mechanists argued forcefully that many special sciences explain by uncovering mechanisms.
