Computation and cognition: toward a foundation for cognitive science
Computation and cognition: toward a foundation for cognitive science
Computer science as empirical inquiry: symbols and search
Communications of the ACM
Brainchildren: Essays on Designing Minds
Brainchildren: Essays on Designing Minds
Representation and Reality
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
Reflections on Gödel's and Gandy's Reflections on Turing's Thesis
Minds and Machines
The Scope of Turing's Analysis of Effective Procedures
Minds and Machines
Vision: A Computational Investigation into the Human Representation and Processing of Visual Information
Physical Computation: How General are Gandy's Principles for Mechanisms?
Minds and Machines
An Analysis of the Criteria for Evaluating Adequate Theories of Computation
Minds and Machines
Explaining Computation Without Semantics: Keeping it Simple
Minds and Machines
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This paper deals with the question: what are the key requirements for a physical system to perform digital computation? Time and again cognitive scientists are quick to employ the notion of computation simpliciter when asserting basically that cognitive activities are computational. They employ this notion as if there was or is a consensus on just what it takes for a physical system to perform computation, and in particular digital computation. Some cognitive scientists in referring to digital computation simply adhere to Turing's notion of computability. Classical computability theory studies what functions on the natural numbers are computable and what mathematical problems are undecidable. Whilst a mathematical formalism of computability may perform a methodological function of evaluating computational theories of certain cognitive capacities, concrete computation in physical systems seems to be required for explaining cognition as an embodied phenomenon. There are many non-equivalent accounts of digital computation in physical systems. I examine only a handful of those in this paper: (1) Turing's account; (2) The triviality "account"; (3) Reconstructing Smith's account of participatory computation; (4) The Algorithm Execution account. My goal in this paper is twofold. First, it is to identify and clarify some of the underlying key requirements mandated by these accounts. I argue that these differing requirements justify a demand that one commits to a particular account when employing the notion of computation in regard to physical systems. Second, it is to argue that despite the informative role that mathematical formalisms of computability may play in cognitive science, they do not specify the relationship between abstract and concrete computation.