 This argument turns on the notion of a conservative extension of a theory. Informally, a conservative extension of a theory is one that does not allow us to prove anything that could not be proved from the original, unextended theory. More formally, and applied to theories of truth, a truth theory, \(Tr\) is conservative over some theory \(T\) formulated in language \(L\) if and only if for every sentence \(\phi\) of \(L\) in which the truth predicate does not occur, if \(Tr \cup L \vdash \phi\), then \(L \vdash \phi\) (where ‘\(\vdash\)’ represents provability). Certain truth theories are conservative over arithmetic – e.g., theories that implicitly define truth using only the instances of some version of (ES) – and certain truth theories are not – e.g., Tarski’s (1935 [1956], 1944) compositional theory. Specifically, the addition of certain truth theories allows us to prove that arithmetic is consistent, something that we cannot do if we are confined to arithmetic itself.