Abstractionism

The aim of this Element is to provide an overview of abstractionism in the philosophy of mathematics. We shall distinguish between mathematical abstractionism, which interprets mathematical theories on the basis of abstraction principles, and philosophical abstractionism, which attributes a philosophical significance to mathematical abstractionism. We shall then survey the main semantic, ontological and epistemological theses that are associated with philosophical abstractionism. We shall finally suggest that the most recent developments in the debate pull abstractionism in different directions.