# Computability and Recursion

@article{Soare1996ComputabilityAR, title={Computability and Recursion}, author={Robert Irving Soare}, journal={Bulletin of Symbolic Logic}, year={1996}, volume={2}, pages={284 - 321} }

Abstract We consider the informal concept of “computability” or “effective calculability” and two of the formalisms commonly used to define it, “(Turing) computability” and “(general) recursiveness”. We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory…

## 231 Citations

Implicit and Explicit Examples of the Phenomenon of Deviant Encodings

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The idea that Carnapian explications provide a much more adequate framework for understanding the concept of computation, than the classical philosophical analysis is developed.

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- 2006

In section 9 of his paper, “On Computable Numbers,” Alan Turing outlined an argument for his version of what is now known as the Church–Turing thesis: “the [Turing machine] ‘computable’ numbers…

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Contents Incomputability, Turing Functionals, and Open Computing

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- 2008

One of the most important concepts in all of computability, Turing’s notion 1939 §4 of an oracle machine (o-machine) defines the computability of one set B relative to another set A which during the computation can be interrogated as a oracle (database).

Mathematical and Technological Computability

- Computer Science
- 2018

This chapter begins with a brief history of computations and the technical means used to support them, and a discussion of the Turing machine, including a detailed explanation of why it can be said to cover all systems of rule-bound symbol manipulation.

The Representational Foundations of Computation

- Computer Science
- 2015

Computability theory studies notations for various non-linguistic domains and illuminates how different ways of representing a domain support different finite mechanical procedures over that domain.

Are Gandy Machines Really Local

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A precise definition of the realization of a Turing-computable algorithm into a physical situation is given and Gandy machines, intended in a physical sense, are analysed as a case study and an inaccuracy in Gandy’s analysis with respect to the locality notion is shown, showing the epistemological relevance of this realization concept.

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- PhilosophyTuring's Legacy
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The sections from §2—§9 challenge the conventional wisdom and traditional ideas found in many books and papers on computability theory and are based on a half century of study of the subject beginning with Church at Princeton in the 1960s and on a careful rethinking of these traditional ideas.

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