Nonclassical theories of truth

This chapter gives a brief overview of theories of truth based on non-classical logics. It sticks to the most central motivation for such theories—the liar paradox—and focuses on a range of responses that have been made to this paradox. The chapter presents the paradox, and shows how it leads to trouble for classical logic. Then the chapter proceeds to lay out four families of response, which we call “paracomplete,” “paraconsistent,” “nontransitive,” and “noncontractive.” For each kind of theory, the chapter goes on to show how it can block paradoxical derivations, and gives references to sources that develop it.
more fully.