Notre Dame Journal of Formal Logic 48 (2):253-280 (2007)

Authors
Michael Rescorla
University of California, Los Angeles
Abstract
Church's thesis asserts that a number-theoretic function is intuitively computable if and only if it is recursive. A related thesis asserts that Turing's work yields a conceptual analysis of the intuitive notion of numerical computability. I endorse Church's thesis, but I argue against the related thesis. I argue that purported conceptual analyses based upon Turing's work involve a subtle but persistent circularity. Turing machines manipulate syntactic entities. To specify which number-theoretic function a Turing machine computes, we must correlate these syntactic entities with numbers. I argue that, in providing this correlation, we must demand that the correlation itself be computable. Otherwise, the Turing machine will compute uncomputable functions. But if we presuppose the intuitive notion of a computable relation between syntactic entities and numbers, then our analysis of computability is circular.
Keywords Church's thesis  computation  Turing machines
Categories (categorize this paper)
DOI 10.1305/ndjfl/1179323267
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,880
Through your library

References found in this work BETA

Function and Concept.Gottlob Frege - 1997 - In D. H. Mellor & Alex Oliver (eds.), Properties. Oxford University Press. pp. 130-149.
X—Mathematical Intuition.Charles Parsons - 1980 - Proceedings of the Aristotelian Society 80 (1):145-168.
Computability and Recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
Mechanical Procedures and Mathematical Experience.Wilfried Sieg - 1994 - In Alexander George (ed.), Mathematics and Mind. Oxford University Press. pp. 71--117.

View all 8 references / Add more references

Citations of this work BETA

The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Syntax, Semantics, and Computer Programs.William J. Rapaport - 2020 - Philosophy and Technology 33 (2):309-321.
The Representational Foundations of Computation.Michael Rescorla - 2015 - Philosophia Mathematica 23 (3):338-366.
Against Structuralist Theories of Computational Implementation.Michael Rescorla - 2013 - British Journal for the Philosophy of Science 64 (4):681-707.

View all 11 citations / Add more citations

Similar books and articles

SAD Computers and Two Versions of the Church–Turing Thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.
Computability and Recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
The Church-Turing Thesis.B. Jack Copeland - 2008 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
Is the Church-Turing Thesis True?Carol E. Cleland - 1993 - Minds and Machines 3 (3):283-312.

Analytics

Added to PP index
2009-03-18

Total views
179 ( #55,139 of 2,426,358 )

Recent downloads (6 months)
3 ( #245,148 of 2,426,358 )

How can I increase my downloads?

Downloads

My notes