This book has grown out of a conference on "Degrees of Belief" that was held at the University of Konstanz in July 2004, organised by Luc Bovens, Wolfgang Spohn, and the editors. The event was supported by the German Research Fo- dation (DFG), the Philosophy, Probability, and Modeling (PPM) Group, and the CenterforJuniorResearchFellows(since2008: Zukunftskolleg)attheUniversityof Konstanz. The PPM Group itself - of which the editors were members at the time - was sponsored by a So a Kovalevskaja Award by the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research, and the Program for the Investment in the Future (ZIP) of the German Government to Luc Bovens, who co-directed the PPM Group with Stephan Hartmann. The publication of this book received further support from the Emmy Noether Junior Research Group Formal Epistemology at the Zukunftskolleg and the Department of Philosophy at the U- versity of Konstanz, directed by Franz Huber, and funded by the DFG. We thank everyone involved for their support. Dedicated to the memory of Philippe Smets and Henry Kyburg. Konstanz, Germany Franz Huber Christoph Schmidt-Petri v Contents Belief and Degrees of Belief. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Franz Huber Part I Plain Belief and Degrees of Belief Beliefs, Degrees of Belief, and the Lockean Thesis. . . . . . . . . . . . . . . . . . . . . . 37 Richard Foley The Lockean Thesis and the Logic of Belief. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 James Hawthorne Partial Belief and Flat-Out Belief. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Keith Frankish Part II What Laws Should Degrees of Belief Obey? Epistemic Probability and Coherent Degrees of Belief . . . . . . . . . . . . . . . . . .

This book has grown out of a conference on "Degrees of Belief" that was held at the University of Konstanz in July 2004, organised by Luc Bovens, Wolfgang Spohn, and the editors. The event was supported by the German Research Fo- dation (DFG), the Philosophy, Probability, and Modeling (PPM) Group, and the CenterforJuniorResearchFellows(since2008: Zukunftskolleg)attheUniversityof Konstanz. The PPM Group itself - of which the editors were members at the time - was sponsored by a So a Kovalevskaja Award by the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research, and the Program for the Investment in the Future (ZIP) of the German Government to Luc Bovens, who co-directed the PPM Group with Stephan Hartmann. The publication of this book received further support from the Emmy Noether Junior Research Group Formal Epistemology at the Zukunftskolleg and the Department of Philosophy at the U- versity of Konstanz, directed by Franz Huber, and funded by the DFG. We thank everyone involved for their support. Dedicated to the memory of Philippe Smets and Henry Kyburg. Konstanz, Germany Franz Huber Christoph Schmidt-Petri v Contents Belief and Degrees of Belief. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Franz Huber Part I Plain Belief and Degrees of Belief Beliefs, Degrees of Belief, and the Lockean Thesis. . . . . . . . . . . . . . . . . . . . . . 37 Richard Foley The Lockean Thesis and the Logic of Belief. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 James Hawthorne Partial Belief and Flat-Out Belief. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Keith Frankish Part II What Laws Should Degrees of Belief Obey? Epistemic Probability and Coherent Degrees of Belief . . . . . . . . . . . . . . . . . .

This is the first of two volumes on belief and counterfactuals. It provides an introduction to ranking theory, which is a powerful formal theory with a broad range of applications in different areas of analytic philosophy. Drawing on formal logic, ranking theory can account for degrees of belief, which can change with the introduction of new information. In Belief and Counterfactuals, Franz Huber applies ranking theory and belief revision to metaphysics and epistemology. Though based on his technical writings, the volume is intended to be as accessible as possible, in order to fully present the utility of ranking theory to a wide range of philosophical issues. The volume contains several novel arguments, accounts, and applications-including the consistency argument for ranking theory, the conditional theory of conditional belief, as well as solutions to the problems of conceptual belief change, logical learning, and learning conditionals. Huber also presents a defense of the instrumentalist understanding of normativity, or rationality, and an argument for the thesis that there are only hypothetical imperatives and no categorical imperatives. His distinctive use of means-end philosophy as a unifying methodological approach establishes a treatment of philosophy as a normative discipline, and of philosophical problems as entangled with one another. This position also explains the importance of logic to philosophy, without devolving into a separate technical theory.

A Logical Introduction to Probability and Induction is a textbook on the mathematics of the probability calculus and its applications in philosophy. On the mathematical side, the textbook introduces these parts of logic and set theory that are needed for a precise formulation of the probability calculus. On the philosophical side, the main focus is on the problem of induction and its reception in epistemology and the philosophy of science. Particular emphasis is placed on the means-end approach to the justification of inductive inference rules. In addition, the book discusses the major interpretations of probability. These are philosophical accounts of the nature of probability that interpret the mathematical structure of the probability calculus. Besides the classical and logical interpretation, they include the interpretation of probability as chance, degree of belief, and relative frequency. The Bayesian interpretation of probability as degree of belief locates probability in a subject's mind. It raises the question why her degrees of belief ought to obey the probability calculus. In contrast to this, chance and relative frequency belong to the external world. While chance is postulated by theory, relative frequencies can be observed empirically. A Logical Introduction to Probability and Induction aims to equip students with the ability to successfully carry out arguments. It begins with elementary deductive logic and uses it as basis for the material on probability and induction. Throughout the textbook results are carefully proved using the inference rules introduced at the beginning, and students are asked to solve problems in the form of 50 exercises. An instructor's manual contains the solutions to these exercises as well as suggested exam questions. The book does not presuppose any background in mathematics, although sections 10.3-10.9 on statistics are technically sophisticated and optional. The textbook is suitable for lower level undergraduate courses in philosophy and logic.

A Logical Introduction to Probability and Induction is a textbook on the mathematics of the probability calculus and its applications in philosophy. On the mathematical side, the textbook introduces these parts of logic and set theory that are needed for a precise formulation of the probability calculus. On the philosophical side, the main focus is on the problem of induction and its reception in epistemology and the philosophy of science. Particular emphasis is placed on the means-end approach to the justification of inductive inference rules. In addition, the book discusses the major interpretations of probability. These are philosophical accounts of the nature of probability that interpret the mathematical structure of the probability calculus. Besides the classical and logical interpretation, they include the interpretation of probability as chance, degree of belief, and relative frequency. The Bayesian interpretation of probability as degree of belief locates probability in a subject's mind. It raises the question why her degrees of belief ought to obey the probability calculus. In contrast to this, chance and relative frequency belong to the external world. While chance is postulated by theory, relative frequencies can be observed empirically. A Logical Introduction to Probability and Induction aims to equip students with the ability to successfully carry out arguments. It begins with elementary deductive logic and uses it as basis for the material on probability and induction. Throughout the textbook results are carefully proved using the inference rules introduced at the beginning, and students are asked to solve problems in the form of 50 exercises. An instructor's manual contains the solutions to these exercises as well as suggested exam questions. The book does not presuppose any background in mathematics, although sections 10.3-10.9 on statistics are technically sophisticated and optional. The textbook is suitable for lower level undergraduate courses in philosophy and logic.