Algebraic Methods in Computational Complexity

From 11.10. to 16.10.2009, the Dagstuhl Seminar 09421 “Algebraic Methods in Computational Complexity “ was held in Schloss Dagstuhl-Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

A metaphysically neutral theory of singular scientific explanation

Modern philosophical debate on explanation began with Hempel and Oppenheim's 1948 article: Studies in the Logic of Explanation . Hempel and Oppenheim's view: their Deductive-Nomological model of explanation for deterministic phenomena, and the Inductive-Statistical model of explanation for indeterministic phenomena, were for many years the received view on the subject. That view has since fallen out of favour, however, and in its wake, many alternative models have been proposed. Of these, Peter Railton's Deductive-Nomological-Probabilistic model represents an exceptionally promising proposal. In this thesis, I argue that while we should accept the essentials of Railton's account, we should not endorse it in its totality. Railton's account of explanation forces us to ascribe to a hard form of reductionism. It also forces us to accept a propensity interpretation of probability and a causal interpretation of irreducibly indeterministic phenomena. In this thesis I argue that one should not have to engage in these metaphysical debates--that an account of explanation should be neutral with respect to these issues