We revisit a debate initiated some 15 years ago by Ray Elugardo and Robert Stainton about the domain of arguments. Our main result is that arguments are not exclusively sets of linguistic expressions. Instead, as we put it, some non-linguistic items have ‘logical form’. The crucial examples are arguments, both deductive and inductive, made with unembedded words and phrases. … subsentential expressions such as singular terms and predicates… cannot serve as premises or conclusions in inferences.