Expressing consistency consistently

Abstract

In the paraconsistent tradition, it is fairly well-known how difficult it is to advance a theory containing a naive truth predicate together with a (classical, consistent) consistency operator. Recently, a number of theorists have risen up to the challenge by attempting to articulate such a theory. These theorists either tinker with the idea of semantic naivety, thereby imposing restrictions on the principles governing the truth predicate, or they substantially weaken the underlying syntax theory. My aim in this paper is to offer arguments against these two proposals.