The paper Numerical Methods, Complexity, and Epistemic Hierarchies, written jointly with Sorin Bangu, re-examines the epistemological dimensions of concept of computational complexity.
Numerical Methods, Complexity, and Epistemic Hierarchies
Nicolas Fillion and Sorin Bangu
Philosophy of Science
Abstract: Modern mathematical sciences are hard to imagine without appeal to efficient computational algorithms. We address several conceptual problems arising from this interaction by outlining rival but complementary perspectives on mathematical tractability. More specifically, we articulate three alternative characterizations of the complexity hierarchy of mathematical problems that are themselves based on different understandings of computational constraints. These distinctions resolve the tension between epistemic contexts in which exact solutions can be found and the ones in which they cannot; however, contrary to a persistent myth, we conclude that having an exact solution is not generally more epistemologically beneficial than lacking one.
Cite as (APA format):
Fillion, N. & Bangu, S. (2015). Numerical Methods, Complexity, and Epistemic Hierarchies, Philosophy of Science, 82, 941-955.