Subjective Probability as the Measure of a Non-measurable Set

Publisher Summary This chapter discusses several aspects of axiom systems for subjective and other kinds of probability. It summarizes some verbal philosophy and terminology. Each application of a theory of probability is made by a communication system that has apparently purposive behavior. The chapter also differentiates various kinds of probability, including physical probability, psychological probability, subjective probability, and logical probability. Every measure of a probability can be interpreted as a subjective probability. A single set of axioms should be applicable to all kinds of probability (except psychological probability), namely the axioms of subjective probability. Physical probability automatically obeys axioms, subjective probability depends on axioms, and psychological probability neither obeys axioms nor depends very much on them. The chapter illustrates a black-box flow diagram for the application of formalized scientific theories. The rules of application refer to the method of formalizing the judgments and of deformalizing the mathematical deductions.