  Unfortunately, the notion of topic neutrality is too vague to be of much help when it comes to the hard cases for which we need a principle of demarcation. Take arithmetic, for instance. Is it topic-neutral? Well, yes: anything can be counted, so the theorems of arithmetic will be useful in any field of inquiry. But then again, no: arithmetic has its own special subject matter, the natural numbers and the arithmetical relations that hold between them. The same can be said about set theory: on the one hand, anything we can reason about can be grouped into sets; on the other hand, set theory seems to be about a particular corner of the universe—the sets—and thus to have its own special “topic.” The general problem of which these two cases are instances might be called the antinomy of topic-neutrality. As George Boolos points out, the antinomy can be pressed all the way to paradigm cases of logical constants: “it might be said that logic is not so ‘topic-neutral’ as it is often made out to be: it can easily be said to be about the notions of negation, conjunction, identity, and the notions expressed by ‘all’ and ‘some’, among others …” (1975, 517). It is plausible to think that the source of the antinomy is the vagueness of the notion of topic neutrality, so let us consider some ways in which we might make this notion more precise.