What role did symbolic logic play in Rudolf Carnap’s philosophy?

In the philosophy of Rudolf Carnap, symbolic logic served as a fundamental tool for achieving the precision and rigor of the exact sciences, which he believed was essential for developing a "scientific world view."1

Carnap’s use of symbolic logic played several critical roles:

• Logical Analysis of Language: He argued that philosophical perplexities often arise from the misuse of language. To resolve these, he advocated for the "logical analysis of language," utilizing artificially constructed languages with precisely specified syntactic and semantic rules rather than relying on the ambiguities of ordinary language.2
• Empiricist Reducibility: Carnap employed symbolic logic to provide a precise interpretation of empiricism. He sought to demonstrate that empirical statements are "reducible" to statements about immediate experience, a project he developed with great rigor in his early work, The Logical Structure of the World.1
• Formalizing Inductive Logic: Later in his career, Carnap focused on constructing a formal system of inductive logic. He used probabilistic logic to represent the degree of rational credibility that evidence confers upon a hypothesis, most notably in his Logical Foundations of Probability.2

By applying these logical techniques, Carnap aimed to clarify scientific knowledge and distinguish meaningful assertions from what he and other logical empiricists considered the meaningless doctrines of speculative metaphysics.12