311511 Logic, decisions, social choice (V) (SoSe 2013)

Formal reasoning has been an integral part of Western philosophical discourse since antiquity. In recent decades, philosophers of the analytic tradition have relied on formal models and methods to address fundamental philosophical questions concerning, e.g., normative requirements for doxastic states, the structure of epistemic justification, or the possibility of collective rationality - frequently in interaction with theoretical economics.

Several of these issues shall be discussed in detail in a subsequent lecture course on social epistemology. The present lecture course will introduce some of the most important mathematical concepts and results for formal epistemology, and will also explain their relevance for ongoing discussions in formal epistemology. Among the mathematical topics treated are: Boolean algebras, ultrafilters, the metamathematics of propositional logic and first-order predicate logic (completeness theorems), probability measures, expected-utility theory, Dutch books. As the climax of the lecture course, we shall start formal philosophical discussions of judgement aggregation, doxastic coherence, and Pascal's Wager, which in part will be continued in the social epistemology course in the following semester.

Bibliography

J.L. Bell and A.B. Slomson. Models and ultraproducts. An introduction. Amsterdam: North-Holland, 1969. REPRINT: Dover Publications, 2006
B. de Finetti. Theory of probability : a critical introductory treatment. Vol. 1. London: Wiley, 1974.
L. Lauwers and L. Van Liedekerke. Ultraproducts and aggregation. Journal of Mathematical Economics, 24(3):217–237, 1995.
F. H., Lecture notes. To be made available over the course of the semester.