 The three inferences in this argument are all pretty clearly valid, and so the only question is whether the four basic premises—(1), (2), (4), and (5)—are true. And the nice thing about the way this argument is set up is that each of these premises is supposed to get rid of a different alternative to fictionalism. So the argument in (1)–(7) is actually a shell of a much longer argument that includes subarguments in favor of the basic premises and, hence, against the various alternatives to fictionalism.