If truth does not have any explanatory force, as some deflationists claim, the axioms for truth should not allow us to prove any new theorems that do not involve the truth predicate. Accordingly, Horsten (1995), Shapiro (1998) and Ketland (1999) have suggested that a deflationary axiomatization of truth should be at least conservative. The new axioms for truth are conservative if they do not imply any additional sentences (free of occurrences of the truth-predicate) that aren’t already provable without the truth axioms. Thus a non-conservative theory of truth adds new non-semantic content to a theory and has genuine explanatory power, contrary to many deflationist views. Certain natural theories of truth, however, fail to be conservative (see Section 3.3 below, Field 1999 and Shapiro 2002 for further discussion).