The Value, if any, of Decidability
|
Abstract:
Quisani: Hello. It's that time of the year again when we have a discussion, isn't it? Author: Come on in. It is a busy time but I am happy to see you. Q: I am afraid my mood is rather critical today. A: That is all right. Speak your mind. Q: It is about computability and decidability. It seems to me that logicians' computability has little to do with real computability. Some so-called computable functions are not computable in any practical sense. It is ridiculous to call them computable. A: It is well known that some computable functions are not feasibly computable. Q: But in what sense are they computable? You, logicians, have hijacked the notion of computability. Computability should mean practical computability. A: Practical computability is too hard to define. Take a function f, say, from binary strings to binary strings which is not computable by any Turing machine, and define g(x) =
Citations
| 566 | Theory of Recursive Functions and Effective Computability – Rogers - 1988 |
| 147 | An unsolvable problem of elementary number theory – Church - 1936 |
| 33 | Computability and complexity of higher type functions, Logic from Computer Science – Cook - 1991 |
| 23 | The inherent computational complexity of theories of ordered sets: A brief survey – Meyer |
| 3 | Elementary Theories – Taitslin - 1965 |
| 3 | Church's Thesis and Principles for Mechanisms", in: "The Kleene Symposium – Gandy - 1980 |
| 2 | Zero-One Laws", Bulletin of the European Assoc. for Theor – Gurevich - 1992 |
| 1 | Barwise and Paul C. Eklof, "Lefschetz's Principle – Jon - 1969 |
