On the Significance of the Range Principle, and the Probability Calculus

Abstract

Representation in numbers is by no means an essential mark of probability. A special position is occupied by probabilities which can be represented in numbers. When probabilities are not numeric, no methodology alleviates the lack, though one may still talk about communicating a psychological degree of surety. Acquaintance with the range principle – of probabilities as ratios of ranges – enriches our knowledge, and resolves certain issues in explanation. The range principle is not empirical, in that it is neither proven nor refuted by experience. It does offer a satisfactory explanation of the law of large numbers. The theory of probability has been extended to doctrines of rational methods for preference and choice. Yet there is no general principle by which the value of goods in hand may be compared to the value of a prospect of possessing those goods, as emphasized by a presentation of the St. Petersburg problem.