Review of ‘The Logic of Mind’


Israel, D. J. Review of `The Logic of Mind’. Computational Linguistics, vol. 11, no. 1, Mar 1985.


In 1936, Alan Turing published “On Computable Numbers, With An Application to the Entscheidungs problem”. In it he introduced the world to Turing machines. These he called simply computing machines, and amongst them he distinguished between “automatic machines” (deterministic Turing machines) and “choice machines” (nondeterministic Turing machines). For reasons that need not detain us, Turing focused on the computable real numbers, not on the nature and extent of the computable functions of natural numbers. In the last two sections of the paper (plus the appendix), Turing presents arguments for what we would now call Turing’s Thesis (relativized to computable numbers), The real question at issue is “What are the possible processes which can be carried out in computing a number?”

Tunng continues:

Computing is normally done by writing certain symbols on paper. We may suppose this paper is divided into squares like a child’s arithmetic book. In elementary arithmetic the two dimensional character of the paper is sometimes used. But such a use is always avoidable, and I think that it will be agreed that the two-dimensional character of paper is no essential of computation. I assume then that the computation is carried out on one dimensional paper, i.e., on a tape divided into squares.

Turing goes on to abstract other essentials of computation from the case of a human being using pencil and paper to compute. Thus, when he speaks (p. 136) of the “behaviour of the computer” being determined by “the symbols he is observing, and his ‘state of mind’ at that moment”, Turing is using the personal pronouns nonmetaphorically. A computer is a person engaged in the act of computing. Indeed, after completing his analysis of the essentials of a computation by a computer, Turing notes (p. 137): “We may now construct a machine to do the work of this computer. To each state of mind of the computer corresponds an ‘m-configuration’ of the machine. The machine scans B squares corresponding to the B squares observed by the computer.” And so on in the same vein. Turing never speaks of a computing machine as a computer; only people are computers.

Keywords: Alan Turing, Turing machines, Logic, Artificial Intelligence, Artificial Intelligence Center, AIC

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