Uncomputability: the problem of induction internalized Export

@article{citeulike:2409658, abstract = {I argue that uncomputable formal problems are intuitively, mathematically, and methodologically analogous to empirical problems in which Hume's problem of induction arises. In particular, I show that a version of Ockham's razor (a preference for simple answers) is advantageous in both domains when infallible inference is infeasible. A familiar response to the empirical problem of induction is to conceive of empirical inquiry as an unending process that converges to the truth without halting or announcing for sure when the truth has been reached. On the strength of the analogies developed, I recommend the adoption of a similar perspective on uncomputable formal problems. One obtains, thereby, a well-defined notion of "hyper-computability" based entirely on classical computational models and on standards of success that have long been regarded as natural in the empirical domain.}, author = {Kelly}, booktitle = {Super-Recursive Algorithms and Hypercomputation}, citeulike-article-id = {2409658}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.tcs.2003.12.013}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6V1G-4BBH5HG-3/2/08c5cb1086ea692c9f81287f8b4ec886}, day = {4}, doi = {10.1016/j.tcs.2003.12.013}, journal = {Theoretical Computer Science}, keywords = {computability, empiricism, induction, ockhams\_razor, philosophy}, month = {June}, number = {1-3}, pages = {227--249}, posted-at = {2008-02-21 23:23:47}, priority = {1}, title = {Uncomputability: the problem of induction internalized}, url = {http://dx.doi.org/10.1016/j.tcs.2003.12.013}, volume = {317}, year = {2004} }

TY - JOUR ID - citeulike:2409658 L3 - citeulike-article-id:2409658 N2 - I argue that uncomputable formal problems are intuitively, mathematically, and methodologically analogous to empirical problems in which Hume's problem of induction arises. In particular, I show that a version of Ockham's razor (a preference for simple answers) is advantageous in both domains when infallible inference is infeasible. A familiar response to the empirical problem of induction is to conceive of empirical inquiry as an unending process that converges to the truth without halting or announcing for sure when the truth has been reached. On the strength of the analogies developed, I recommend the adoption of a similar perspective on uncomputable formal problems. One obtains, thereby, a well-defined notion of "hyper-computability" based entirely on classical computational models and on standards of success that have long been regarded as natural in the empirical domain. IS - 1-3 JF - Theoretical Computer Science EP - 249 TI - Uncomputability: the problem of induction internalized VL - 317 T2 - Super-Recursive Algorithms and Hypercomputation SP - 227 KW - computability KW - empiricism KW - induction KW - ockhams_razor KW - philosophy AU - Kelly PY - 2004/06/04/ UR - http://dx.doi.org/10.1016/j.tcs.2003.12.013 ER -