What was the goal of Rudolf Carnap’s Logical Foundations of Probability?

In his 1950 work Logical Foundations of Probability, the German-American philosopher Rudolf Carnap aimed to construct a formal system of inductive logic that would serve as a quantitative counterpart to deductive logic.12

His primary goal was to define a precise, purely logical concept of "degree-of-confirmation"—a measure representing the degree of rational credibility or probability that a given body of evidence confers upon a proposed hypothesis. By utilizing artificially constructed languages with precisely specified syntactic and semantic rules, Carnap sought to identify a function that could assign a numerical value to the support provided by evidence for a hypothesis.12

Ultimately, Carnap argued that this degree-of-confirmation function must satisfy the axioms of the probability calculus, treating inductive inferences as probabilistic inferences. While he acknowledged that his project faced limitations—such as the inability to uniquely determine the optimal inductive method—his work remains a foundational effort to provide a rigorous, empirical basis for inductive reasoning.321