David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Informatica 21 (3):425–454 (2010)
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the relativity of mathematical languages used to describe the Turing machines. A deep investigation is performed on the interrelations between mechanical computations and their mathematical descriptions emerging when a human (the researcher) starts to describe a Turing machine (the object of the study) by different mathematical languages (the instruments of investigation). Together with traditional mathematical languages using such concepts as ‘enumerable sets’ and ‘continuum’ a new computational methodology allowing one to measure the number of elements of different infinite sets is used in this paper. It is shown how mathematical languages used to describe the machines limit our possibilities to observe them. In particular, notions of observable deterministic and non-deterministic Turing machines are introduced and conditions ensuring that the latter can be simulated by the former are established.
|Keywords||Theory of automatic computations observability of Turing machines relativity of mathematical languages infinite sets Sapir-Whorf thesis|
|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
No citations found.
Similar books and articles
B. Jack Copeland (2002). Accelerating Turing Machines. Minds and Machines 12 (2):281-300.
Gualtiero Piccinini (2003). Alan Turing and the Mathematical Objection. Minds and Machines 13 (1):23-48.
Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
B. Maclennan (2003). Transcending Turing Computability. Minds and Machines 13 (1):3-22.
Eric Steinhart (2003). Supermachines and Superminds. Minds and Machines 13 (1):155-186.
B. Jack Copeland & Oron Shagrir (2011). Do Accelerating Turing Machines Compute the Uncomputable? Minds and Machines 21 (2):221-239.
D. King (1996). Is the Human Mind a Turing Machine? Synthese 108 (3):379-89.
Joel David Hamkins (2002). Infinite Time Turing Machines. Minds and Machines 12 (4):567-604.
Darren Abramson (2008). Turing's Responses to Two Objections. Minds and Machines 18 (2):147-167.
Leon Horsten (1995). The Church-Turing Thesis and Effective Mundane Procedures. Minds and Machines 5 (1):1-8.
Jack Copeland (1997). The Broad Conception of Computation. American Behavioral Scientist 40 (6):690-716.
Joel David Hamkins & Andy Lewis (2000). Infinite Time Turing Machines. Journal of Symbolic Logic 65 (2):567-604.
Peter Kugel (2002). Computing Machines Can't Be Intelligent (...And Turing Said So). Minds and Machines 12 (4):563-579.
Jack Copeland (1998). Turing's o-Machines, Searle, Penrose, and the Brain. Analysis 58 (2):128-138.
Added to index2010-12-10
Total downloads20 ( #187,884 of 1,907,353 )
Recent downloads (6 months)4 ( #198,541 of 1,907,353 )
How can I increase my downloads?