We prove the existence of hidden variables, or, what we call generalized common causes, for finite sequences of pairwise correlated random variables that do not have a joint probability distribution. The hidden variables constructed have upper probability distributions that are nonmonotonic. The theorem applies directly to quantum mechanical correlations that do not satisfy the Bell inequalities.

Probability kinematics is studied in detail within the framework of elementary probability theory. The merits and demerits of Jeffrey's and Field's models are discussed. In particular, the principle of maximum relative entropy and other principles are used in an epistemic justification of generalized conditionals. A representation of conditionals in terms of Bayesian conditionals is worked out in the framework of external kinematics.

This is an important collection of essays dealing with the foundations of probability that will be of value to philosophers of science, mathematicians, statisticians, psychologists and educationalists. The collection falls into three parts. Part I comprises five essays on the axiomatic foundations of probability. Part II contains seven articles on probabilistic causality and quantum mechanics, with an emphasis on the existence of hidden variables. The third part consists of a single extended essay applying probabilistic theories of learning to practical questions (...) of education: it incorporates extensive data analysis. Patrick Suppes is one of the world's foremost philosophers in the area of probability, and has made many contributions to both the theoretical and practical side of education. The statistician Mario Zanotti is a long-time collaborator. (shrink)