The point of this appendix is to show that the truth predicate really is compatible with a wide array of logical systems. To make this point, we need to show that neither the classical logical setting nor the rich set-theoretic tools Tarski employs to define satisfaction are necessary for a truth predicate. This is what we have set out to do here.

There is one other interesting point to make. Tarski, and due to his influence, other philosophers and logicians too, have generally used as a criterion for a successful theory of truth that Tarski biconditionals be derivable from it. I want to turn this procedure on its head. My theory will contain the Tarski biconditional (as derivation rules) and some apparatus for referring to the sentences of the object-language (substitutional quantification). This will be taken as sufficient for a theory of truth. Anything further needed for a semantic theory of the object-language and for a description of the syntax of the objectlanguage must be evaluated on other grounds. Interestingly enough, however, it will turn out that in certain contexts (the sentential calculus) what I give will be sufficient for a semantic theory too, but this will not generally be the case. Syntax is another matter altogether. We will see that descriptions of proof procedures for language call for resources that go beyond what we supply here.

I will not be concerned with self-referential contexts, which raise an entirely distinct set of problems.