Recent Work in Relevant Logic

Abstract

But if A and B are utterly irrelevant to one another, many feel reluctant to call these inferences acceptable. Similarly for the validity of the corresponding material implications, often called ‘paradoxes’ of material implication. Relevant logic can be seen as the attempt to avoid these ‘paradoxes’. Relevant logic has a long history. Key early works include Anderson and Belnap 1962; 1963; 1975, and many important results appear in Routley et al. 1982. Those looking for a short introduction to relevant logics might look at Mares 2012 or Priest 2008. For a more detailed but still accessible introduction, there’s Dunn and Restall 2002; Mares 2004b; Priest 2008 and Read 1988. The aim of this article is to survey some of the most important work in the eld in the past ten years, in a way that I hope will be of interest to a philosophical audience. Much of this recent work has been of a formal nature. I will try to outline these technical developments, and convey something of their importance, with the minimum of technical jargon. A good deal of this recent technical work concerns how quanti ers should work in relevant logic. This is the topic of §2. §3 describes other advances in the recent technical literature. In §4, I discuss several recent attempts to give a philosophical interpretation of the most prominent semantics for relevant logic (the Routley-Meyer ternary relation semantics), and highlight some problems. These three sections may be read independently of one another. Those unfamiliar with the ternary relation semantics might like to read the introduction to §4, or consult Mares 2012, before going further.