David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Minds and Machines 12 (2):259-280 (2002)
I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds.
|Keywords||convergence fixed-point infinite algorithm infinite machine infinite mind limit possible world situation super-Turing computer|
|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
B. Jack Copeland & Oron Shagrir (2011). Do Accelerating Turing Machines Compute the Uncomputable? Minds and Machines 21 (2):221-239.
Similar books and articles
P. D. Welch (2000). Eventually Infinite Time Turing Machine Degrees: Infinite Time Decidable Reals. Journal of Symbolic Logic 65 (3):1193-1203.
B. Jack Copeland (2002). Accelerating Turing Machines. Minds and Machines 12 (2):281-300.
Joel David Hamkins (2002). Infinite Time Turing Machines. Minds and Machines 12 (4):567-604.
Joel David Hamkins & Andy Lewis (2000). Infinite Time Turing Machines. Journal of Symbolic Logic 65 (2):567-604.
D. King (1996). Is the Human Mind a Turing Machine? Synthese 108 (3):379-89.
B. Jack Copeland & Oron Shagrir (2007). Physical Computation: How General Are Gandy's Principles for Mechanisms? [REVIEW] Minds and Machines 17 (2):217-231.
Peter Kugel (2002). Computing Machines Can't Be Intelligent (...And Turing Said So). Minds and Machines 12 (4):563-579.
Eric Steinhart (2003). Supermachines and Superminds. Minds and Machines 13 (1):155-186.
Added to index2009-01-28
Total downloads23 ( #126,204 of 1,724,741 )
Recent downloads (6 months)4 ( #167,193 of 1,724,741 )
How can I increase my downloads?