Philosophy of Mathematics seminar

Laura Crosilla, Oslo

Predicativity as Invariance  

Predicativity imposes a constructivity requirement on mathematical definitions, which are to proceed as if the entities they define were constructed step-by-step and from below – or from within. At the beginning of the 20th century predicativity was discussed by some of the most prominent mathematicians of the time. In today’s mathematics it figures prominently in Proof Theory and in Constructive Set and Type Theories. Predicativity is often thought of as an injunction against vicious circular definitions, following Poincaré, Russell and Weyl. In this talk, I argue for the fruitfulness of a less well-known characterisation of predicativity also originating in Poincaré’s writings: “predicativity as invariance”. Its main advantage is that it allows for an expansion of predicativity. It also has the potential to unify classical and constructive variants of predicativity. Finally, it helps us understand the relation between predicativity and a number of themes that frequently emerge within the predicativist literature, such as forms of potentialism.