In the literature, predicativism is connected not only with the Vicious Circle Principle but also with the idea that certain totalities are inherently potential. To explain the connection between these two aspects of predicativism, we explore some approaches to predicativity within the modal framework for potentiality developed in Linnebo (2013) and Linnebo and Shapiro (2019). This puts predicativism into a more general framework and helps to sharpen some of its key theses.

In this paper we will investigate different axiomatic theories of truth that are minimal in some sense. One criterion for minimality will be conservativity over Peano Arithmetic. We will then give a more fine-grained characterization by investigating some interpretability relations. We will show that disquotational theories of truth, as well as compositional theories of truth with restricted induction are relatively interpretable in Peano Arithmetic. Furthermore, we will give an example of a theory of truth that is a conservative extension of (...) Peano Arithmetic but not interpretable in it. We will then use stricter versions of interpretations to compare weak theories of truth to subsystems of second-order arithmetic. (shrink)