The Objects of Probabilities

Probability statements take the form: P(X) = r. For example, the probability that a fair coin lands heads is 1/2: P(heads) = 1/2. Almost all the literature in the philosophy of probability has concerned the nature of P. Meanwhile, the nature of X, the kinds of things to which probabilities are assigned, has been neglected. This project will redress this imbalance. It will answer the question: What are the objects of probabilities? The answer will depend on the type of probability involved, and it will require us to reconsider how probability theory is formulated. This takes us to the foundations of probability and decision theory, and thus of all philosophy, science, and public policy that are based on these theories.