Minds and Machines 12 (2):259-280 (2002)

Authors
Eric Steinhart
William Paterson University of New Jersey
Abstract
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
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Reprint years 2004
DOI 10.1023/A:1015603317236
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References found in this work BETA

On the Plurality of Worlds.David Lewis - 1986 - Wiley-Blackwell.
On the Plurality of Worlds.William G. Lycan - 1988 - Journal of Philosophy 85 (1):42-47.
On The Plurality of Worlds.Graeme Forbes - 1988 - Philosophical Quarterly 38 (151):222-240.
Theories and Things.W. V. O. Quine (ed.) - 1981 - Harvard University Press.

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Citations of this work BETA

The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
Supermachines and Superminds.Eric Steinhart - 2003 - Minds and Machines 13 (1):155-186.

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