Mathematical Methods in Philosophy

Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician-philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant extent, have been driven by philosophical motivations and carried out by technically-minded philosophers. Mathematical logic continues to play an important role in contemporary philosophy, and mathematically trained philosophers continue to contribute to the literature in logic. For instance, modal logics were first investigated by philosophers, and now have important applications in computer science and mathematical linguistics. The theory and metatheory of formal systems was pioneered by philosophers and philosophically-minded mathematicians (Frege, Russell, Hilbert, Gödel, Tarski, among many others), and philosophers have continued to be significantly involved in the technical development of proof theory, and to a certain degree also in the development of model theory and set theory. On the other hand, philosophers use formal models to test the implications of their theories in tractable cases. Philosophical inquiry can also uncover new mathematical structures and problems, as with recent work on paradoxes about truth. Areas outside mathematical logic have also been important in recent philosophical work, e.g., probability and game theory in inductive logic, epistemology, and the philosophy of science. In fact, it seems that technical mathematical work is currently enjoying something of a renaissance in philosophy. The workshop on “Mathematical Methods in Philosophy” brought together eminent and emerging researchers who apply mathematical methods to current issues in philosophy. These mathematical methods come mainly from the fields of mathematical logic and probability theory, and the areas of application include philosophical logic, metaphysics, epistemology, the philosophy of mathematics, and the philosophy of science.