Knot and Tonk: Nasty connectives on many-valued truth-tables for classical sentential logic

Abstract

Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this paper is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the problem of many-valued truthtables for classical sentential logic. I close by outlining the technicalities surrounding nasty connectives on many-valued truth-tables.