Rudolf Carnap: A Critique of Classical and Frequentist Theories in the Foundation of Logical Probability

Abstract

Philosopher Rudolf Carnap sought to establish logical probability and questions of credibility, through which scientific hypotheses could be rationally evaluated. To achieve this, he emphasized redefining the concept of probability itself, believing that the prevailing theories of his time—classical theory and recursive theory—were incapable of providing the required logical foundation Carnap criticizes classical theory and recursive theory, arguing that classical theory is based on the "principle of indistinguishability." Carnap argues that this principle renders the concept of probability a subjective concept based on the observer's "ignorance," rather than an objective relationship. It also leads to logical contradictions. Frequency theory, which defines probability as the rate at which a particular event occurs over a long period of time, is considered by Carnap to be an empirical and statistical concept, not a logical one. He argues that it is useful for describing the frequency of phenomena in the world, but it is not suitable as a basis for inductive logic because it cannot assign a probability value to a specific individual case or to a scientific hypothesis, which is the primary task of corroborative logic. In contrast, Carnap introduces his own concept of "statistical probability," which he defines as "the degree of logical support or confirmation." In this conception, probability is a purely logical relationship between two propositions: one that represents the evidence and another that represents the hypothesis. Statistical probability does not measure anything in the empirical world, but rather the degree of rational support that the evidence provides for the hypothesis. Thus, probability becomes a fundamental analytical tool in constructing scientific and objective inductive logic.