Journal of Logic, Language and Information
, Volume 20, Issue 4, pp 513537
First online:
Concrete Digital Computation: What Does it Take for a Physical System to Compute?
 Nir FrescoAffiliated withSchool of History and Philosophy, University of New South Wales Email author
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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 nonequivalent 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.
Keywords
Concrete digital computation Computability Cognition Representation Algorithm execution Situated computers Turing machine Title
 Concrete Digital Computation: What Does it Take for a Physical System to Compute?
 Journal

Journal of Logic, Language and Information
Volume 20, Issue 4 , pp 513537
 Cover Date
 201110
 DOI
 10.1007/s1084901191478
 Print ISSN
 09258531
 Online ISSN
 15729583
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Concrete digital computation
 Computability
 Cognition
 Representation
 Algorithm execution
 Situated computers
 Turing machine
 Authors

 Nir Fresco ^{(1)}
 Author Affiliations

 1. School of History and Philosophy, University of New South Wales, Sydney, Australia