Is the ChurchTuring thesis true?
 Carol E. Cleland
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The ChurchTuring thesis makes a bold claim about the theoretical limits to computation. It is based upon independent analyses of the general notion of an effective procedure proposed by Alan Turing and Alonzo Church in the 1930's. As originally construed, the thesis applied only to the number theoretic functions; it amounted to the claim that there were no number theoretic functions which couldn't be computed by a Turing machine but could be computed by means of some other kind of effective procedure. Since that time, however, other interpretations of the thesis have appeared in the literature. In this paper I identify three domains of application which have been claimed for the thesis: (1) the number theoretic functions; (2) all functions; (3) mental and/or physical phenomena. Subsequently, I provide an analysis of our intuitive concept of a procedure which, unlike Turing's, is based upon ordinary, everyday procedures such as recipes, directions and methods; I call them “mundane procedures.” I argue that mundane procedures can be said to be effective in the same sense in which Turing machine procedures can be said to be effective. I also argue that mundane procedures differ from Turing machine procedures in a fundamental way, viz., the former, but not the latter, generate causal processes. I apply my analysis to all three of the above mentioned interpretations of the ChurchTuring thesis, arguing that the thesis is (i) clearly false under interpretation (3), (ii) false in at least some possible worlds (perhaps even in the actual world) under interpretation (2), and (iii) very much open to question under interpretation (1).
 Title
 Is the ChurchTuring thesis true?
 Journal

Minds and Machines
Volume 3, Issue 3 , pp 283312
 Cover Date
 199308
 DOI
 10.1007/BF00976283
 Print ISSN
 09246495
 Online ISSN
 15728641
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 ChurchTuring thesis
 Turing machine
 effective procedure
 causal process
 analog process
 Authors

 Carol E. Cleland ^{(1)}
 Author Affiliations

 1. Department of Philosophy and Institute of Cognitive Science, University of Colorado, Boulder, CO, USA