This book collects research papers on the philosophical foundations of probability, causality, spacetime and quantum theory. The papers are related to talks presented in six subsequent workshops organized by The Budapest-Krakow Research Group on Probability, Causality and Determinism. Coverage consists of three parts. Part I focuses on the notion of probability from a general philosophical and formal epistemological perspective. Part II applies probabilistic considerations to address causal questions in the foundations of quantum mechanics. Part III investigates the question of indeterminism in spacetime theories. It also explores some related questions, such as decidability and observation. The contributing authors are all philosophers of science with a strong background in mathematics or physics. They believe that paying attention to the finer formal details often helps avoiding pitfalls that exacerbate the philosophical problems that are in the center of focus of contemporary research.The papers presented here help make explicit the mathematical-structural assumptions that underlie key philosophical argumentations. This formally rigorous and conceptually precise approach will appeal to researchers and philosophers as well as mathematicians and statisticians.

Part I. Probability and chance-credence norms.- Chapter 1. Can Bayesian agents always be rational? A principled analysis of consistency of an Abstract Principal Principle (Miklós Rédei and Zalán Gyenis).- Chapter 2. Does the Principal Principle imply the Principle of Indifference? (Balázs Gyenis and Leszek Wroński).- Chapter 3. A Mathematical Approach to Lewis’ Principal Principle - An Analysis through Examples (Gergei Bana).- Chapter 4. Three methods for solving the problem of inconsistent marginals in data integration (Christian Wallmann and Jon Williamson).- Part II. Structures for quantum experiments.- Chapter 5. Separate common causes and EPR correlations – an ``almost no-go'' result (Tomasz Placek, Leszek Wroński and Michał Tomasz Godziszewski).- Chapter 6. On quantum nonlocal correlations and probability spaces used to model them (Márton Gömöri and Tomasz Placek).- Chapter 7. Reichenbachian common cause systems of size 3 in general probability theories (Yuichiro Kitajima).- Chapter 8. Two Sources of Non-locality in Quantum Mechanics? (Iñaki San Pedro).- Part III. Indeterminism, Undecidability, and Macrostates.- Chapter 9. On the semantics of spacetime theories (László E. Szabó).- Chapter 10. Indeterminism, Gravitation, and Spacetime Theory (Samuel C. Fletcher).- Chapter 11. Extendible maximal globally hyperbolic spacetimes in classical general relativity: a philosophical survey (Juliusz Doboszewski).- Chapter 12. On the emergence of macrostates (Márton Gömöri, Balázs Gyenis, Gábor Hofer-Szabó).- Chapter 13. Experimental Logics as a Model of Development of Deductive Science and Computational Properties of Undecidable Sentences (Michał Tomasz Godziszewski)