Bulletin of Symbolic Logic

Computability and Recursion

Robert I. Soare

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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, and its connection to other related areas. After a careful historical and conceptual analysis of computability and recursion we make several recommendations in section §7 about preserving the intensional differences between the concepts of "computability" and "recursion." Specifically we recommend that: the term "recursive" should no longer carry the additional meaning of "computable" or "decidable;" functions defined using Turing machines, register machines, or their variants should be called "computable" rather than "recursive;" we should distinguish the intensional difference between Church's Thesis and Turing's Thesis, and use the latter particularly in dealing with mechanistic questions; the name of the subject should be "Computability Theory" or simply Computability rather than "Recursive Function Theory."

Article information

Source
Bull. Symbolic Logic, Volume 2, Number 3 (1996), 284-321.

Dates
First available in Project Euclid: 20 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1182353451

Mathematical Reviews number (MathSciNet)
MR1416870

Zentralblatt MATH identifier
0861.03031

JSTOR
links.jstor.org

Citation

Soare, Robert I. Computability and Recursion. Bull. Symbolic Logic 2 (1996), no. 3, 284--321. https://projecteuclid.org/euclid.bsl/1182353451


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