Logically possible machines

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

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Eric Steinhart
William Paterson University of New Jersey

Citations of this work

The Tractable Cognition Thesis.Iris Van Rooij - 2008 - Cognitive Science 32 (6):939-984.
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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References found in this work

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Ontological relativity.W. V. O. Quine - 1968 - Journal of Philosophy 65 (7):185-212.
Theories and things.W. V. Quine (ed.) - 1981 - Cambridge, Mass.: Harvard University Press.

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