David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Church's and Turing's theses dogmatically assert that an informal notion of effective calculability is adequately captured by a particular mathematical concept of computability. I present an analysis of calculability that is embedded in a rich historical and philosophical context, leads to precise concepts, but dispenses with theses. To investigate effective calculability is to analyze symbolic processes that can in principle be carried out by calculators. This is a philosophical lesson we owe to Turing. Drawing on that lesson and recasting work of Gandy, I formulate boundedness and locality conditions for two types of calculators, namely, human computing agents and mechanical computing devices (discrete machines). The distinctive feature of the latter is that they can carry out parallel computations. The analysis leads to axioms for discrete dynamical systems (representing human and machine computations) and allows the reduction of models of these axioms to Turing machines. Cellular automata and a variety of artificial neural nets can be shown to satisfy the axioms for machine computations
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Nir Fresco (2011). Concrete Digital Computation: What Does It Take for a Physical System to Compute? [REVIEW] Journal of Logic, Language and Information 20 (4):513-537.
Aran Nayebi (2014). Practical Intractability: A Critique of the Hypercomputation Movement. [REVIEW] Minds and Machines 24 (3):275-305.
Benjamin Rin (2015). Transfinite Recursion and Computation in the Iterative Conception of Set. Synthese 192 (8):2437-2462.
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