Formal Methods in the Philosophy of Natural Science

Abstract

What is the proper place of formal methods in philosophy of natural science, or in philosophy more broadly speaking? The idea that philosophy should proceed formally (“more geometrico”, as in the title of Spinoza’s Ethica) has been around for some time, but both the attitude towards formal methods and the understanding of formal methods itself has changed. Mathematical logic has succeeded geometrical demonstration as the paradigm of formal precision, and in technical areas such as foundations of mathematics and logic, Frege’s and Russell’s logicist programmes indicate early peaks of the application of these methods. The idea of employing such formal-logical methods in philosophy more generally was championed by the logical empiricism of the 1920s and 1930s. Wrestling with the methodological foundations of their discipline in an attempt to exclude what they perceived to be nonsense, some at the time even sought recourse in a purely formal-logical foundation for philosophy. Frege’s student Carnap in his programmatic paper on “the old and the new logic” (Carnap, 1930, 26) put the matter thus: “To pursue philosophy means nothing but: clarifying the concepts and sentences of science by logical analysis.”