Actualism and Potentialism: Konstanz 28th September 2023

There has been recent interest in intensional type theory, both as a framework to tackle metaphysical questions about modality, propositions, properties, and so on (e.g. Bacon and Dorr, ‘Classicism’) and as an alternative to set theory as a foundation of mathematics (e.g. Goodsell and Yli-Vakkuri, Logical Foundations). These type theorists typically adopt an ‘actualist’ attitude towards the type-theoretic hierarchy: quantifiers in each type are assumed to range over absolutely every entity of the appropriate type (e.g. type e quantifiers range over absolutely every individual). This talk considers a ‘potentialist’ alternative, which permits entities of arbitrary type to be nominalized as new individuals.