The Epsilon-Reconstruction of Theories and Scientific Structuralism

Rudolf Carnap’s mature work on the logical reconstruction of scientific theories consists of two components. The first is the elimination of the theoretical vocabulary of a theory in terms of its Ramsification. The second is the reintroduction of the theoretical terms through explicit definitions in a language containing an epsilon operator. This paper investigates Carnap’s epsilon-reconstruction of theories in the context of pure mathematics. The main objective here is twofold: first, to specify the epsilon logic underlying his suggested definition of theoretical terms and a suitable choice semantics for it. Second, to analyze whether Carnap’s approach is compatible with a structuralist conception of mathematics.