Critical Views of Infinity

The focus of the workshop are views of infinity that are critical of actual infinity. The literature presents us with a heterogeneous constellation of criticism of what is often called “Cantorian infinity”. This workshop will explore and compare a number of approaches to potentialism stemming from the history and contemporary mathematical practice. By comparing a number of approaches, we hope to better understand what are the perceived difficulties with actual infinity and which proposals have been put forth to overcome them. These include, for example, predicativist and constructivist approaches to mathematics and potentialist views of the set-theoretic universe in philosophy of mathematics.