Logical Nihilism

Abstract

Much of the discussion in the philosophy of logic over the last decade has been devoted to the debate between logical monism and logical pluralism. But logical nihilism hasn’t been given nearly as much attention, even though the view has historical roots and is philosophically defensible. I present and defend a number of arguments in favor of logical nihilism. These arguments are grouped into two main families: arguments from diversity (§2) and arguments from expressive limitations (§3). These arguments are often simple syllogisms pointing to fundamental differences between natural languages and formal consequence relations. Many of the arguments involve familiar problems in the philosophy of logic. The arguments, taken individually, are interesting in their own right; they each highlight an important way in which the formal methods of logic can be seen to be inadequate to modeling natural language inference. But the arguments taken jointly are more significant; by presenting all the arguments together, we can build something of a cumulative case for logical nihilism. Of course, if any of these arguments are sound, then logical nihilism is correct. But the arguments reinforce one another, such that logical nihilism presents us with a unified view across a broad range of issues in philosophy of logic. I conclude (§4) by considering related philosophical issues and sketching a general outlook on logic and formal methods that is nihilist-friendly.