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Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief.

Contemporary epistemologists are roughly divided into those relying largely on common-sense considerations and focusing on examples and counterexamples for advancing or rejecting various epistemological theses, and those applying a variety of tools and methods from logic, computability theory or probability theory to the theory of knowledge. The two sorts, and the traditions to which they hitherto are taken to belong, have unfortunately proceeded largely in isolation from one another. But on closer examination the approaches have much in common, may be bridged for their mutual benefit and the advancement of epistemology in general. Here are 7 ways of doing it as the invited papers in this special issue of Philosophical Studies demonstrate the fruitful interaction between informal considerations and various formal apparata in order to support, sharpen, undermine, realize, or contribute in some other pertinent way to fundamental epistemological themes.

This book provides a valuable look at the work of up and coming epistemologists. The topics covered range from the central issues of mainstream epistemology to the more formal issues in epistemic logic and confirmation theory. This book should be read by anyone interested in seeing where epistemology is currently focused and where it is heading. - Stewart Cohen , Arizona State University..

Formal epistemology is the study of crucial concepts in general or mainstream epistemology including knowledge, belief (-change), certainty, rationality, reasoning, decision, justi…cation, learning, agent interaction and information processing using a spread of di¤erent formal tools. The formal tools may be drawn from logic, probability theory, game theory, decision theory, formal learning theory, distributed computing and is thus not simply a purely philosophical province. Its practitioners include philosophers, computer scientists, social scientists, cognitive psychologists, theoretical economists, mathematicians, and theoretical linguists. Formal epistemology is a thoroughly interdisciplinary …eld with many agendas, actors and issues. What follows is a breezy overview of formal epistemology as organized around notions of agency and interaction.

The goal with these questions is to gain a sense of what contemporary epistemology is up to and its broader intellectual environment , with particular emphasis on the meeting point between mainstream and formal epistemology.

As Vincent Hendricks remarks early on in this book, the formal and mainstream traditions of epistemic theorising have mostly evolved independently of each other. This initial impression is confirmed by a comparison of the main problems and methods practitioners in each tradition are concerned with. Mainstream epistemol- ogy engages in a dialectical game of proposing and challenging definitions of knowledge. Formal epistemologists proceed differently, as they design a wide variety of axiomatic and model-theoretic methods whose consequences they investigate independently of the need of giving counterexample-free definitions of knowledge. Or at least, this is a common way to explain where both disciplines stand in the larger landscape of epistemic theorising, and why interactions between them remain scarce. The main ambition of this book is to show that the distinction between formal and mainstream approaches should not preclude a fruitful interaction, and that it only takes the right outlook on their respective practices to disclose plenty of room for interaction.