Diane Proudfoot

Turing’s analysis of computability has recently been challenged; it is claimed that it is circular to analyse the intuitive concept of numerical computability in terms of the Turing machine. This claim threatens the view, canonical in mathematics and cognitive science, that the concept of a systematic procedure or algorithm is to be explicated by reference to the capacities of Turing machines. We defend Turing’s analysis against the challenge of ‘deviant encodings’.Keywords: Systematic procedure; Turing machine; Church–Turing thesis; Deviant encoding; Acceptable encoding; Turing’s analysis of computability; Turing’s Notational Thesis.

Ignoring the temporal dimension, an object such as a railway tunnel or a human body is a three-dimensional whole composed of three-dimensional parts. The four-dimensionalist holds that a physical object exhibiting identity across time—Descartes, for example—is a four-dimensional whole composed of 'briefer' four-dimensional objects, its temporal parts. Peter van Inwagen (1990) has argued that four-dimensionalism cannot be sustained, or at best can be sustained only by a counterpart theorist. We argue that different schemes of individuation of temporal parts are available, which undermines van Inwagen's argument.