This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science.
Preface 1. Characterization 2. Axiomatization 3. A Mathematical Background 4. Criticism to the Axiomatic Method and its Defense 5. Axiomatization, and Scientific Theories 6. Models and Scientific Theories
Recent years have seen a surge of interest in the topics discussed by philosophers of mathematics and physics, particularly those relating to the way in which these disciplines intersect. Titles in this series cover a wide range of exciting and dynamic issues such as category theory, mathematical proofs, computability, emergence, time travel, quantum black holes, and string theory. Authors explore leading questions concerning new directions in the philosophy of mathematics and physics, with the aim of presenting clear, concise, and original monographs for an advanced audience.