Revisiting the foundations of probability theory

Probabilities are ubiquitous in modern natural sciences. They represent the main conceptual and formal tool used to describe and quantify the likelihood of something to happen, as well as the confidence with which we (do not) know something in a prediction. In particular, since the advent of quantum theory, specifically with the verification of the violation of Bells inequalities, it is possible to make strong arguments in favor of fundamental indeterminism in physics. But are probabilities the straightforwardly appropriate mathematical tools to attribute measures of likelihood to events is of prime importance to model indeterministic theories? The aim of this project is to explore, both at the conceptual and at formal level, the possibility of indeterministic physics where the concept of becoming (thus passage of time) is fundamental, both within quantum theory (where indeterminism is expected) and in classical theories (where there is general consensus about they being fully deterministic). In particular, I will address the capabilities and the limits of using probabilities to describe fundamental indeterminacy in physical theories and develop novel mathematical and conceptual tools to overcome the problems encountered along the way. The proposed project is interdisciplinary in nature. It comprises a more formal mathematical part which will fully deal with the foundations of probability theory and a second more conceptual and interpretational part that aims to provide probabilities and the new tools developed with a clear interpretation. These two parts will allow to develop formal and conceptual tools to describe indeterminism in physics, which remains the main driving force of this project.