In recent years numerous attempts have been made by analytic philosophers to naturalize various different domains of philosophical inquiry. All of these attempts have had the common goal of rendering these areas of philosophy amenable to empirical methods, with the intention of securing for them the supposedly objective status and broad intellectual appeal currently associated with such approaches. This volume brings together internationally recognised analytic philosophers, including Alvin Plantinga, Peter van Inwagen and Robert Audi, to question the project of naturalism. The articles investigate what it means to naturalize a domain of philosophical inquiry and look at how this applies to the various sub-disciplines of philosophy including epistemology, metaphysics and the philosophy of the mind. The issue of whether naturalism is desirable is raised and the contributors take seriously the possibility that excellent analytic philosophy can be undertaken without naturalization. Controversial and thought-provoking, Analytic Philosophy Without Naturalism examines interesting and contentious methodological issues in analytic philosophy and explores the connections between philosophy and science.

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Goedel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Goedel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.

In recent years, numerical and experimental investigations on the draft tube performance have confirmed the importance of the inlet swirling flow created by the runner vanes. The results indicate that it is still a challenge to get the optimal flow distribution at the draft tube inlet which gives the best machine performance over a range of operation points. Consequently, there is a need to adjust the runner-draft tube coupling to minimize the losses arising from the inlet flow distribution. This work focuses on establishing an automatic optimization method to improve the swirling flow characteristics at the draft tube inlet. The coupling of iSIGHT(r), FLUENT(r) and MATLAB(r) commercial softwares has been performed to determine the best inlet flow shape which leads to increase overall machine performance. It is expected that a properly modeled inlet velocity profile can suppress or mitigate the undesirable draft tube flow characteristics such as secondary flow, irregular evolution and excessive velocity through this important component of the turbine. This book is a must for graduate students, researchers and implementers whose work involves the design of hydraulic tur