Exchangeability and Algorithmic Randomness - A New Proof of the Principal Principle

Explore the intersection of algorithmic randomness and exchangeability in this academic seminar that presents a novel proof of the Principal Principle in probability theory. Delve into how algorithmic randomness and exchangeable priors can ground chance-credence principles without falling into circular reasoning, building upon previous research on probabilistic constraint laws. Examine the development of a new approach that establishes direct connections between long-run frequencies and short-term credences, providing clarity on the epistemic foundations of chance, typicality, and probabilistic laws. Learn about collaborative research with Jeffrey A. Barrett that addresses fundamental questions in the philosophy of probability and its mathematical foundations. Discover how frequency constraints and exchangeable priors work together to support probabilistic reasoning, offering insights into the theoretical underpinnings of how we understand and apply probability in various contexts. This presentation is part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics, hosted by Chapman University in collaboration with researchers from UC Riverside, CSU San Bernardino, and Pitzer College.