Ten Puzzles and Paradoxes about Knowledge and Belief

Reasoning about the knowledge and beliefs of a single agent or group of agents
is an interdisciplinary concern spanning computer science, mathematics, game
theory and philosophy. Inspired, in part, by issues in these different
"application" areas, many different notions of knowledge and belief have been
identified and analyzed in the formal epistemology literature. The main
challenge is not to argue that one particular account of belief or knowledge
is primary , but, rather, to explore the logical space of definitions and
identify interesting relationships between the different notions. A second
challenge (especially for students) is to keep track of the many different
formal frameworks used in this broad literature (typical examples include
modal logics of knowledge and belief or the theory of subjective probability,
but there are many variants). This foundational course will introduce students
to key methodological, conceptual and technical issues that arise when
designing a formalism to make precise intuitions about the knowledge and
beliefs of a group of agents.
The course will serve as a introduction to epistemic logic and Bayesian
epistemology; however, we will not follow the standard textbook presentation
of this material. For example, as found in Reasoning about Knowledge by
Fagin, Halpern, Moses and Vardi, Dynamic Epistemic Logic by van Ditmarsch,
van der Hoek and Kooi or Modal Logic for Open Minds by van Benthem. Rather
than focusing on the technical details of a specific formalism, we will focus
on the key foundational questions (of course, introducing formal details as
needed). There are good reasons for taking an "issue-oriented" approach to
introducing formal models of knowledge and belief (especially at a summer
school such as ESSLLI). Many of the recent developments concerning formal
models of knowledge and belief have been driven by analyzing concrete
examples. These range from toy examples, such as the infamous muddy children
puzzle to philosophical quandaries, such as the knowability paradox or the
surprise examination paradox, to everyday examples of social interaction.
Different formal frameworks are then judged, in part, on how well they conform
to the analyst's intuitions about the relevant set of examples. Thus, in order
to appreciate the usefulness and limits of the different formal frameworks, it
is important to understand the issues that motivate the key technical
developments.