Isaac Levi

(1930 - 2018)

In Chapter I of his celebrated Foundations of Probability, A. N. Kolmogorov proposed an axiomatic treatment of the mathematical theory of probability—the approach that assimilated probability theory into measure theory. Kolmogorov followed his statement of the axioms with an account of how “we apply the theory of probability to the actual world of experiments.”

This chapter contains sections titled: Deductive Rules and Fulfilling Commitments Rules as Programs for Routine Expansion Rules in Deliberate or Inferential Expansion What Recommends Scientific Method over Other Methods of Fixing Belief? Deliberation and Inconsistency.

In the introduction to Probabilistic Metaphysics, Patrick Suppes declares his intention to refute each of five central tenets of “neotraditional metaphysics”. These tenets run as follows:The future is determined by the past.Every event has a sufficient determinant cause.Knowledge must be grounded in certainty.Scientific knowledge can in principle be made complete.Scientific knowledge and method can in principle be unified.

This is a brief review of issues over which Henry Kyburg and I differed concerning the requirement that full beliefs should be closed under deductive consequence.