The Value of the One Value: Exactly True Logic revisited

In this paper we re-assess the philosophical foundation of Exactly True Logic ( ℰ𝒯ℒ ), a competing variant of First Degree Entailment ( ℱ𝒟ℰ ). In order to do this, we first rebut an argument against it. As the argument appears in an interview with Nuel Belnap himself, one of the fathers of ℱ𝒟ℰ , we believe its provenance to be such that it needs to be taken seriously. We submit, however, that the argument ultimately fails, and that ℰ𝒯ℒ cannot easily be dismissed. We then proceed to give an overview of the research that was inspired by this logic over the last decade, thus providing further motivation for the study of ℰ𝒯ℒ and, more generally, of ℱ𝒟ℰ -related logics that result from semantical analyses alternative to Belnap’s canonical one. We focus, in particular, on philosophical questions that these developments raise.