Deterministic Chaos and Computational Complexity: the Case of Methodological Complexity Reductions

Some problems rarely discussed in traditional philosophy of science are mentioned: The empirical sciences using mathematico-quantitative theoretical models are frequently confronted with several types of computational problems posing primarily methodological limitations on explanatory and prognostic matters. Such limitations may arise from the appearances of deterministic chaos and (too) high computational complexity in general. In many cases, however, scientists circumvent such limitations by utilizing reductional approximations or complexity reductions for intractable problem formulations, thus constructing new models which are computationally tractable. Such activities are compared with reduction types (more) established in philosophy of science. This revised version was published online in August 2006 with corrections to the Cover Date.