A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..

Let us begin with a piece of intellectual history. The story begins in a period encapsulating the second world war – say the ‘40’s, give and take a bit. Around then, it began to be argued with force that an expression – e.g., an English one – while it well might mean something, does not say anything, and notably no one thing in particular. The principal behind the argument was surely J.L. Austin, though, I would claim, the same point was (...) argued in a somewhat different way by Wittgenstein. The intended point was not merely a grammatical one: we say of an expression that it means such and such, but not that it says such and such. Be that as it may, the main point was quite substantive: typically, an English expression is such that, with its meaning fixed, there are a variety of distinct things to be said in using it on some production of it or other. (shrink)