The idea that belief comes in degrees is based on the observation that we are more certain of some things than of others. Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as well as his betting, or other, behaviour is concerned.This anthology is the first book to give a balanced overview of these theories. It also explicitly relates these debates to more traditional concerns of the philosophy of language and mind, and epistemic logic, namely how belief simpliciter does or ought to behave. The paradigmatic theory, probabilism (which holds that degrees of belief ought to satisfy the axioms of probability theory) is given most attention, but competing theories, such as Dempster-Shafer theory, possibility theory, and AGM belief revision theory are also considered. Each of these approaches is represented by one of its major proponents.The papers are specifically written to target advanced undergraduate students with a background in formal methods and beginning graduate students, but they will also serve as first point of reference for academics new to the area.

Christoph Schmidt-Petri has been awarded a PhD in Philosophy from the London School of Economics in 2005, where he also held a pre-doctoral Jacobsen Fellowship. He has been a member of the Philosophy, Probability and Modeling Group at the University of Konstanz, the Faculty of Economics at Witten/Herdecke University, and the Departments of Philosophy at the Universities of Glasgow, Saarbr++cken and Leipzig. From 2002 till 2008, he has been Managing Editor of Economics and Philosophy. He has published articles in journals such as The Philosophical Quarterly, Philosophy of Science, Analyse & Kritik, and is the editor of several other books in political philosophy and the philosophy of the social sciences.Franz Huber received his PhD from the University of Erfurt in 2003. From 2002 to 2005 he was postdoctoral researcher in the Philosophy, Probability, and Modeling group at the University of Konstanz. From 2005 to 2007 he was Ahmanson postdoctoral instructor at the California Institute of Technology and then visiting researcher at the Department of Logic and Philosophy of Science at UC Irvine. Since 2008 he is director of the Formal Epistemology Research Group at the University of Konstanz. Huber has published in journals such as Artificial Intelligence, The British Journal for the Philosophy of Science, The Journal of Philosophical Logic, Philosophical Studies, Philosophy of Science, Studia Logica and Synthese.