The philosophy of science and logic underwent a wide-ranging formal turn in the first half of the twentieth century. This shift is characterized by a new emphasis on formal methods and the adoption of a general formalist viewpoint towards the disciplines in question. Roughly put, formalism presented a novel methodological and epistemological stance: it is characterized by the use of non-representational forms of reasoning as well as the focus on the purely formal features of a field of inquiry, studied in abstraction from its traditional subject matter and from considerations about meaning or interpretation. As such, the position was often linked to a new understanding of the nature of scientific objectivity and rigor. Moreover, formalist positions not only dominated research at the time, but also led to fundamentally revised conceptions of logic, mathematics, and the philosophy of the exact sciences, determining the shape of these disciplines today.
The project will give an interdisciplinary study of early contributions to formalism in twentieth-century thought. This general objective will be addressed in terms of three interrelated projects. The first subproject is historical in character and aims at a historical reconstruction of the emergence of formalist thinking in nineteenth-century mathematics and neo-Kantian philosophy of science. On the mathematical side, the project will retrace several developments in projective geometry, symbolic algebra, and number theory (Peacock, Hankel, von Staudt) in the nineteenth century that contributed to a formalist conception of these fields. Regarding its philosophical roots, the focus will be on contributions to a formalist notion of scientific objectivity in the work of the Marburg school of neo-Kantianism (Ernst Cassirer, Paul Natorp). The second project will give a comparative study of different formal turns in logic, the foundations of mathematics, and philosophy of logical empiricism between 1920 and 1940. This includes research on the foundations of mathematics and the formality of logic by members of the Göttingen school (David Hilbert, Paul Bernays) as well as central contributions to a scientific formalism in logical empiricism (Rudolf Carnap, Moritz Schlick). The third project will analyze the philosophical implications of the formal turn for the subsequent shaping of these fields. The emergence of formalist thinking was closely related to the development of new theories of formal semantics in logic and philosophy. The aim will therefore be to connect the early contributions to formalism with contemporary debates on the philosophy of model theory and inferentialism as well as with the logical study of scientific theories.
