Computation in cognitive science: it is not all about Turing-equivalent computation

One account of the history of computation might begin in the 1930's with some of the work of Alonzo Church, Alan Turing, and Emil Post. One might say that this is where something like the core concept of computation was first formally articulated. Here were the first attempts to formalize an informal notion of an algorithm or effective procedure by which a mathematician might decide one or another logico-mathematical question. As each of these formalisms was shown to compute the same set of functions—the partial recursive functions—each of them might be described as a form of Turing-equivalent computation. This work set the cornerstone for what we might call computation theory. This history might then proceed to give pride of place to this form of computation in subsequent developments in cognitive science and in related disciplines and subdisciplines. Such a history might note that, in the 1940's, the results of this work would have been transferred into the emerging field of computer science with the design and construction of the first electronic digital computers. Here one would mention Turing again, as well as perhaps Norbert Wiener, Julian Bigelow, John von Neumann, and many others. At about the same time, this theory of computation would have been inserted into the theory of neural networks by way of Warren McCulloch and Walter Pitts's seminal work, “A Logical Calculus of the Ideas Immanent in Nervous Activity.” Somewhat later, during the 1960's, Hilary Putnam introduced Turing machine tables into the philosophy of mind as a tool for illuminating various features of the mind-body problem, eventually transforming the intellectual landscape in..
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DOI 10.1016/j.shpsa.2010.07.013
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B. Jack Copeland (2002). Hypercomputation. Minds and Machines 12 (4):461-502.
Alan Turing (1936). On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 42 (1):230-265.

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