Computability and recursion

Bulletin of Symbolic Logic 2 (3):284-321 (1996)

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."

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References found in this work

Computing Machinery and Intelligence.Alan M. Turing - 1950 - Mind 59 (October):433-60.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Introduction to Metamathematics.H. Rasiowa - 1954 - Journal of Symbolic Logic 19 (3):215-216.
Grundzüge der theoretischen Logik.D. Hilbert & W. Ackermann - 1928 - Annalen der Philosophie Und Philosophischen Kritik 7:157-157.

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