Comparative Probability as a Foundation for Logic

Charles Morgan
University of Victoria

As a model of belief, numerically based probability theories are often criticized for their over-specificity. As a partial response to such criticisms, Carnap proposed a comparative probability theory. We discuss several deficiencies with Carnap's theory. We then develop a comparative probability theory which is not based on a provability relation but is suitable as a formal semantic theory for (almost) any extension of classical logic, quantified or propositional.

While Carnap attempted to use deductive logic as a foundation for probability, we propose probability as a foundation for deductive logic. We discuss the relation of our theory to Carnap's and suggest areas for further research.