Church Without Dogma: Axioms for Computability


Authors
Wilfried Sieg
Carnegie Mellon University
Abstract
Church's and Turing's theses dogmatically assert that an informal notion of effective calculability is adequately captured by a particular mathematical concept of computability. I present an analysis of calculability that is embedded in a rich historical and philosophical context, leads to precise concepts, but dispenses with theses. To investigate effective calculability is to analyze symbolic processes that can in principle be carried out by calculators. This is a philosophical lesson we owe to Turing. Drawing on that lesson and recasting work of Gandy, I formulate boundedness and locality conditions for two types of calculators, namely, human computing agents and mechanical computing devices (discrete machines). The distinctive feature of the latter is that they can carry out parallel computations. The analysis leads to axioms for discrete dynamical systems (representing human and machine computations) and allows the reduction of models of these axioms to Turing machines. Cellular automata and a variety of artificial neural nets can be shown to satisfy the axioms for machine computations
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 46,461
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

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.
Synchronous Online Philosophy Courses: An Experiment in Progress.Fritz McDonald - 2018 - APA Newsletter on Philosophy and Computers 18 (1):37-40.

View all 11 citations / Add more citations

Similar books and articles

Computability and Recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
Godel on Computability.W. Sieg - 2006 - Philosophia Mathematica 14 (2):189-207.
Church's Thesis and the Conceptual Analysis of Computability.Michael Rescorla - 2007 - Notre Dame Journal of Formal Logic 48 (2):253-280.
Beyond the Universal Turing Machine.Jack Copeland - 1999 - Australasian Journal of Philosophy 77 (1):46-67.
Church's Thesis: Prelude to a Proof.Janet Folina - 1998 - Philosophia Mathematica 6 (3):302-323.
Accelerating Turing Machines.B. Jack Copeland - 2002 - Minds and Machines 12 (2):281-300.
Alan Turing and the Mathematical Objection.Gualtiero Piccinini - 2003 - Minds and Machines 13 (1):23-48.

Analytics

Added to PP index
2010-09-14

Total views
38 ( #238,535 of 2,286,402 )

Recent downloads (6 months)
3 ( #417,385 of 2,286,402 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature