Relativism in Set Theory and Mathematics

According to the mathematical relativist, mathematical statements, if true, are relatively true only - that is, they are true relative to (i) the specifi cation of concepts and theories that characterize the relevant mathematical domain, (ii) the mathematical framework in which such mathematical truths are formulated, and (iii) the logic that is employed in the derivation of such truths. This chapter surveys mathematical relativism and its signifi cance. First, it clarifi es what mathematical relativism is not. It then examines a formulation of the view in which conceptual, structural, and logical relativity play a central role, but which still preserves the objectivity of mathematics. The implications of mathematical relativism for the ontology of mathematics are then considered. While some forms of Platonism and nominalism in mathematics are compatible with mathematical relativism, others are not. Finally, some remarks about the signifi cance of mathematical relativism conclude the chapter.