FORMAL EPISTEMOLOGY: Representing the fixation of belief and its undoing

Formal epistemology is a discipline with various branches and sub-branches dealing with precise representations of attitudes and their flux. The formal tools utilized for this purpose go from standard probability theory to non-standard (or infinitesimal) probability, to decision theoretical tools to logical tools. These lectures are divided in two parts. The first part deals with static representations of knowledge and belief via epistemic and doxastic operators. This is perhaps the oldest sub-branch of formal epistemology, as well as one of the parts of the discipline that has witnessed a strong renaissance in recent years, mainly due to related work in computer science and mathematical economics. Even in this first part we will see that apparently subtle philosophical distinctions between knowledge as a standard for serious possibility and a more external conception of knowledge where agents are seen as potential sources of knowledge, leads to very different formal models. We will explore both while considering mainly propositional languages. Pointers to richer models are nevertheless provided and, time-permitting, we will devote some sessions to consider models of knowledge and belief of more expressive power where quantification plays an essential role. Under the logical point of view the first part provides a self-contained introduction to the study of salient examples of epistemic logics and various semantics for them. We will start with Jaakko Hintikka’s models of epistemic and doxastic operators, and then we will show that some of the primitives of these semantics can be clarified in the context of a semantic approach of greater scope and power, deriving from early work by Dana Scott and Richard Montague. The epistemic operators interpreted via these semantic frameworks deal with formal models of