Cellular automata machines: a new environment for modeling
Cellular automata machines: a new environment for modeling
Mind children: the future of robot and human intelligence
Mind children: the future of robot and human intelligence
Computability and logic: 3rd ed.
Computability and logic: 3rd ed.
Cognitive science: an introduction
Cognitive science: an introduction
The simple dynamics of super Turing theories
Theoretical Computer Science - Special issue on universal machines and computations
Computation, dynamics, and cognition
Computation, dynamics, and cognition
Complexity and real computation
Complexity and real computation
Complexity - Special issue on uncoventional models of computation
Representation and Reality
Elementary Differential Equations With Mathematica
Elementary Differential Equations With Mathematica
The Recursive Universe; Cosmic Complexity and the Limits of Scientific Knowledge
The Recursive Universe; Cosmic Complexity and the Limits of Scientific Knowledge
Minds and Machines
Two Dogmas of Computationalism
Minds and Machines
When Physical Systems Realize Functions...
Minds and Machines
Minds and Machines
Theoretical Computer Science - Super-recursive algorithms and hypercomputation
Accelerating machines: a review
International Journal of Parallel, Emergent and Distributed Systems
Do Accelerating Turing Machines Compute the Uncomputable?
Minds and Machines
Supertasks do not increase computational power
Natural Computing: an international journal
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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.