David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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)|
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.
Citations of this work BETA
Nir Fresco (2011). Concrete Digital Computation: What Does It Take for a Physical System to Compute? [REVIEW] Journal of Logic, Language and Information 20 (4):513-537.
Aran Nayebi (2014). Practical Intractability: A Critique of the Hypercomputation Movement. [REVIEW] Minds and Machines 24 (3):275-305.
Benjamin Rin (2015). Transfinite Recursion and Computation in the Iterative Conception of Set. Synthese 192 (8):2437-2462.
Similar books and articles
Oron Shagrir (2002). Effective Computation by Humans and Machines. Minds and Machines 12 (2):221-240.
Robert I. Soare (1996). Computability and Recursion. Bulletin of Symbolic Logic 2 (3):284-321.
W. Sieg (2006). Godel on Computability. Philosophia Mathematica 14 (2):189-207.
Wilfried Sieg (1997). Step by Recursive Step: Church's Analysis of Effective Calculability. Bulletin of Symbolic Logic 3 (2):154-180.
Michael Rescorla (2007). Church's Thesis and the Conceptual Analysis of Computability. Notre Dame Journal of Formal Logic 48 (2):253-280.
Jack Copeland (1999). Beyond the Universal Turing Machine. Australasian Journal of Philosophy 77 (1):46-67.
Vincent C. Müller (2011). On the Possibilities of Hypercomputing Supertasks. Minds and Machines 21 (1):83-96.
Yaroslav Sergeyev & Alfredo Garro (2010). Observability of Turing Machines: A Refinement of the Theory of Computation. Informatica 21 (3):425–454.
Saul A. Kripke (2013). The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem. In B. J. Copeland, C. Posy & O. Shagrir (eds.), Computability: Turing, Gödel, Church, and Beyond. MIT Press
Janet Folina (1998). Church's Thesis: Prelude to a Proof. Philosophia Mathematica 6 (3):302-323.
B. Jack Copeland (2002). Accelerating Turing Machines. Minds and Machines 12 (2):281-300.
Leon Horsten (1995). The Church-Turing Thesis and Effective Mundane Procedures. Minds and Machines 5 (1):1-8.
John T. Kearns (1997). Thinking Machines: Some Fundamental Confusions. [REVIEW] Minds and Machines 7 (2):269-87.
Gualtiero Piccinini (2003). Alan Turing and the Mathematical Objection. Minds and Machines 13 (1):23-48.
Eli Dresner (2008). Turing-, Human- and Physical Computability: An Unasked Question. [REVIEW] Minds and Machines 18 (3):349-355.
Added to index2010-09-14
Total downloads22 ( #163,931 of 1,790,307 )
Recent downloads (6 months)3 ( #267,458 of 1,790,307 )
How can I increase my downloads?