Carlo Nicolai


AHRC Research Grant

Properties, Paradox, and Circularity. A New, Type-Free Account

Co-Investigator: Salvatore Florio

Theorizing about the world requires a theory of propositions, properties, and relations (PPRs). Propositions are the entities to which the properties of being true, believed, desired, known apply. Natural properties and relations are the features of physical entities studied by natural science. Social properties and relations shape human interactions. The development of a satisfactory theory of PPRs lies at the foundation of scientific and philosophical enquiry. However, theories of propositions, properties, and relations are constrained by logical paradoxes: intuitive principles such as "To every predicate in language, there corresponds a property" are in fact inconsistent with the standard laws of logic. This is why a solid formal foundation for theories of PPRs is required. The project aims to provide a new formal and philosophical foundation to theories of propositions, properties, relations.
The most popular way of providing such a foundation arranges PPRs in hierarchies of logical types. The prominence of the typed approach is explained by some of its theoretical virtues: it is consistent with classical logic and it may achieve substantial mathematical strength. However, the typed approach misses out some important features of language and thought such as circularity and self-applicability. For instance, claims such as 'it's necessary that something is necessary' cannot be properly regimented in the typed setting. More generally, circular phenomena can be found in many theoretical contexts in philosophy (self-reference), computer science (streams, self-applicative programs), and mathematics (graphs, non-wellfounded sets). Circularity can also be found in natural language (self-predication). Such phenomena cannot be easily modelled in a typed theory of PPRs.
The project will analyse in detail extant theories of PPRs and develop the logic and philosophy of the type-free approach, a promising but underdeveloped approach to PPRs and their paradoxes.


The reading group will meet on Fridays, 12-14 in room 508, Philosophy Building, Strand Campus, King's College London.


The talks will be on Fridays, 12-14 in room 508, Philosophy Building, Strand Campus, King's College London.