Concrete Digital Computation: What Does it Take for a Physical System to Compute?
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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.
KeywordsConcrete digital computation Computability Cognition Representation Algorithm execution Situated computers Turing machine
- Agassi, J. (unpublished). The Turing Test.Google Scholar
- Bell P., Staines P. J., Mitchell J. (2001) Evaluating, doing and writing research in psychology. Sage publication, LondonGoogle Scholar
- Block N. (2002) Searle’s arguments against cognitive science. In: Preston J., Bishop M. (eds) Views into the Chinese room. Oxford University Press, Oxford, pp 70–79Google Scholar
- Buechner J. (2008) Gödel, Putnam, and functionalism. MIT Press, CambridgeGoogle Scholar
- Copeland B. J. (2003) Computation. In: Floridi L. (eds) The Blackwell guide to the philosophy of computing and information. Wiley-Blackwell, Oxford, pp 3–17Google Scholar
- Cummins R. (1989) Meaning and mental representation. MIT Press, CambridgeGoogle Scholar
- Davis M. (1958) Computability and unsolvability. McGraw-Hill, NYGoogle Scholar
- Dennett C. D. (1998) Brainchildren: Essays on designing minds. MIT Press, CambridgeGoogle Scholar
- Fodor J. A. (1975) The language of thought. Harvard University Press, CambridgeGoogle Scholar
- Gandy R. (1980) Church’s thesis and principles for mechanisms. In: Barwise J., Keisler H. J., Kunen K. (eds) The Kleene symposium. Amsterdam, North-HollandGoogle Scholar
- Hopcroft J. E., Motwani R., Ullman J. D. (2001) Introduction to automata theory, languages and computation. 2nd edn. Addison Wesley, ReadingGoogle Scholar
- Karp R. M. (1972) Reducibility among combinatorial problems. In: Miller R., Thatcher J. (eds) Complexity of computer computations. Plenum, New York, pp 85–104Google Scholar
- Kleene S. C. (2002) Mathematical logic. Dover, New YorkGoogle Scholar
- Marr D. (1982) Vision: A computational investigation into the human representation and processing visual information. Freeman & Company, NYGoogle Scholar
- Nelson R. J. (1982) The logic of mind. Reidel, DordrechtGoogle Scholar
- Parikh R. (1998) Church’s theorem and the decision problem. In: Craig E. (eds) Routledge encyclopedia of philosophy. Routledge, London, pp 349–351Google Scholar
- Penrose R. (1989) The Emperor’s new mind. Oxford University Press, LondonGoogle Scholar
- Putnam H. (1988) Representation and reality. The MIT Press, CambridgeGoogle Scholar
- Pylyshyn Z. W. (1984) Computation and cognition: Toward a foundation for cognitive science. MIT Press, Cambridge, MAGoogle Scholar
- Shagrir O. (1999) What is computer science about?. The Monist 82: 131–149Google Scholar
- Sieg, W. (2008). Church without dogma: Axioms for computability. In S. B. Cooper, B. Löwe, & S. Andrea (Eds.) New computational paradigms (pp. 139–152).Google Scholar
- Smith B. C. (1996) On the origins of objects. MIT Press, Cambridge, MAGoogle Scholar
- Smith B. C. (2002) The foundations of computing. In: Scheutz M. (eds) Computationalism: New directions. MIT Press, Cambridge, pp 23–58Google Scholar
- Smith, B. C. (2008). Rehabilitating representation. Paper presented at the Spring 2008 Colloquia at the Center for Cognitive Science, University at Buffalo, State University of New York.Google Scholar
- Smith, B. C. (2010). Age of significance: Introduction. Retrieved May 3, 2010, from http://www.ageofsignificance.org.
- Smith, B. C. (unpublished). Formal symbol manipulation: Ontological critique. Expected to be published in 2011 at http://www.ageofsignificance.org.
- Thelen E., Smith L. B. (1994) A dynamical systems approach to the development of cognition and action. MIT press, CambridgeGoogle Scholar
- Turing A. M. (1936) On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, Series 42(2): 230–265Google Scholar
- Van Gelder T., Port R. F. (1995) It’s about time: An overview of the dynamical approach to cognition. In: Gelder T., Port R. F. (eds) Mind as motion. MIT Press, Cambridge, pp 23–58Google Scholar