Self-Referential Probability


This thesis focuses on expressively rich languages that can formalise talk about probability and which have sentences that say something about the probability of themselves. For example:

(π): “The probability of the sentence labelled π is not greater than 1/2.”

Such sentences lead to philosophical and technical challenges. For example seemingly harmless principles, such as an introspection principle, lead to inconsistencies with the axioms of probability in this framework. Throughout the thesis, our motivating concept of probability is as measuring an agent’s degrees of belief.

This thesis investigates the following two questions relevant to such frameworks:

PhD thesis - LMU München