Computability and Recursion Export

@article{citeulike:2464895, 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."}, author = {Soare, Robert I.}, citeulike-article-id = {2464895}, citeulike-linkout-0 = {http://dx.doi.org/10.2307/420992}, citeulike-linkout-1 = {http://www.jstor.org/stable/420992}, citeulike-linkout-2 = {http://www.people.cs.uchicago.edu/~soare/History/compute.pdf}, doi = {10.2307/420992}, issn = {10798986}, journal = {The Bulletin of Symbolic Logic}, keywords = {church, computability, godel, history, lambda-calculus, recursion, turing}, number = {3}, pages = {284--321}, posted-at = {2009-03-02 12:24:28}, priority = {2}, publisher = {Association for Symbolic Logic}, title = {Computability and Recursion}, url = {http://dx.doi.org/10.2307/420992}, volume = {2}, year = {1996} }

TY - JOUR ID - citeulike:2464895 L3 - citeulike-article-id:2464895 N2 - 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." IS - 3 JF - The Bulletin of Symbolic Logic SN - 10798986 EP - 321 TI - Computability and Recursion PB - Association for Symbolic Logic VL - 2 SP - 284 KW - church KW - computability KW - godel KW - history KW - lambda-calculus KW - recursion KW - turing AU - Soare, Robert PY - 1996/// UR - http://dx.doi.org/10.2307/420992 ER -