Minimalism, Reference, and Paradoxes

The aim of this paper is to provide a minimalist axiomatic theory of truth based on the notion of reference. To do this, we first give sound and arithmetically simple notions of reference, self-reference, and well-foundedness for the language of first-order arithmetic extended with a truth predicate; a task that has been so far elusive in the literature. Then, we use the new notions to restrict the T-schema to sentences that exhibit "safe" reference patterns, confirming the widely accepted but never worked out idea that paradoxes can be characterised in terms of their underlying reference patterns. This results in a strong, ω-consistent, and well-motivated system of disquotational truth, as required by minimalism