FDE as the One True Logic

Abstract

The principal aim of this paper is to very briefly discuss one way in which FDE may be ‘the one true logic’ – an idea which neither Belnap nor Dunn have ever been keen to promote, but an idea which, properly understood, is worth having plainly on the table. After presenting the simple sense in which FDE may be plausibly thought of as the one true logic, I briefly rehearse a simple argument for thinking as much. (The argument is one I have advanced elsewhere (Beall, The simple argument for subclassical logic. In Juhl and Schechter (eds) Philosophical issues: philosophy of logic and inference (Annual Supplement to Noûs). Wiley, 2018, Forthcoming) but it seems especially appropriate to repeat in this volume.) There are two other aims of this paper, one of which is to keep the paper very short. The last but not least aim is to honor the pioneering work of Belnap and Dunn on FDE and its philosophical applications. Let me say from the start that the paper necessarily fails to achieve its last aim, not for lack of aiming or even for poorly aiming; rather, the honor that both Belnap and Dunn deserve for their work is not something that this paper – perhaps any paper – can reflect. By my lights, their work on the topic (both mathematical and philosophical) is what we should all aspire to do. Both logic and its philosophy are vastly better for their efforts. (I also want to explicitly record a small personal note to both Professor Belnap and Professor Dunn. Some people make a lot of their ‘intellectual heritage’ or ‘family line’ in PhDs and so forth. I’m not one of those people. Still, if one looks carefully beyond the exact letters of my ‘lineage’, one sees that I learned a lot of my logical background – though perhaps not logical proclivities – from Gary Hardegree, who gained much of his own logical background from Professor Dunn, who in turn gained valuable logical background from Professor Belnap. As a personal note to Nuel and Mike: thank you both. You remain, in so many ways, key sources in my intellectual development. (I’m sorry for the deviant turn that my own views have taken!))