The confluence of ideas in 1936
A half-century survey on The Universal Turing Machine
Recipes, Algorithms, and Programs
Minds and Machines
Minds and Machines
Effective Computation by Humans and Machines
Minds and Machines
Minds and Machines
Minds and Machines
Hypercomputation: philosophical issues
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
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I explore the conceptual foundations of Alan Turing's analysis of computability, which still dominates thinking about computability today. I argue that Turing's account represents a last vestige of a famous but unsuccessful program in pure mathematics, viz., Hilbert's formalist program. It is my contention that the plausibility of Turing's account as an analysis of the computational capacities of physical machines rests upon a number of highly problematic assumptions whose plausibility in turn is grounded in the formalist stance towards mathematics. More specifically, the Turing account conflates concepts that are crucial for understanding the computational capacities of physical machines. These concepts include the idea of an "operation" or "action" that is "formal," "mechanical," "well-defined," and "precisely described," and the idea of a "symbol" that is "formal," "uninterpreted," and "shaped". When these concepts are disentangled, the intuitive appeal of Turing's account is significantly undermined. This opens the way for exploring models of hypercomputability that are fundamentally different from those currently entertained in the literature.