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.

It is not widely realised that Turing was probably the first person to consider building computing machines out of simple, neuron-like elements connected together into networks in a largely random manner. Turing called his networks 'unorganised machines'. By the application of what he described as 'appropriate interference, mimicking education' an unorganised machine can be trained to perform any task that a Turing machine can carry out, provided the number of 'neurons' is sufficient. Turing proposed simulating both the behaviour of the network and the training process by means of a computer program. We outline Turing's connectionist project of 1948.

Cognitive science is held, not only by its practitioners, to offer something distinctively new in the philosophy of mind. This novelty is seen as the product of two factors. First, philosophy of mind takes itself to have well and truly jettisoned the ‘old paradigm’, the theory of the mind as embodied soul, easily and completely known through introspection but not amenable to scientific inquiry. This is replaced by the ‘new paradigm’, the theory of mind as neurally-instantiated computational mechanism, relatively opaque to introspection and the proper subject of detailed empirical investigation. Second, in the constitutive disciplines of cognitive science we have for the first time the theoretical, experimental and technological resources to begin this investigation. My concern here is to show that, despite its scientific and philosophical sophistication, the new paradigm is in certain striking ways very similar to the old paradigm and that Wittgenstein's criticisms of the former apply to much of the latter.