The reader may wonder why I have left the discussion of type-free disquotation systems of truth until the end of the part on type-free theories, given that in the part on typed theories the disquotational theories come before all other typed theories.

In both parts I have roughly followed the strategy of discussing simpler and weaker theories first before proceeding to the stronger systems. But while typed disquotational theories such as TB and UTB are weaker than compositional theories such as CT and PT, type-free disquotational systems of truth are not necessarily weaker than type-free compositional theories. This is not to say that type-free disquotational theories are all very strong. Rather the type-free disquotational truth theories do not form a very homogenous class of theories: the strength of the consistent systems of type-free disquotation truth ranges from theories conservative over Peano arithmetic to theories of arbitrary strength, as will be shown below.

A reason for the disparity between type-free disquotational systems is that it is not always clear what the good systems are. Type-free disquotational system are not easily obtained by generalizing typed disquotational theories: generalizing the theory TB to a type-free theory is not as easy as generalizing CT to FS or PT to KF.