Graham Leigh

Minimising disquotational truth

I present a new axiomatic theory of disquotational truth based on the theory of positive disquotation PUTB. Formulated in classical logic, PUTB restricts the T-schema to positive sentences and satisfies key epistemic desiderata (semantic conservativity and trustworthiness). It fares poorly, however, in proof-theoretic strength compared to reflective truth frameworks as the theory does not isolate a unique interpretation of truth. I will introduce a theory of positive disquotation which axiomatises the least fixed-point model without requiring additional resources. This is achieved by incorporating ill-founded reasoning under suitable soundness restrictions—applying the tools of cyclic proof theory to axiomatic theories of truth. The resulting theory is sound relative to the minimal fixed-point model and proves the same arithmetical theorems as the impredicative theory ID1. This work is joint with Pietro Brocci.