ation to treat sentences that contain occurrences of ↓i that are not within the scope of ↑i as expressing propositions in their own right. While '↓17 Mars is red' is meaningful-it makes a distinctive contribution to the meaning of larger sentences that embed it-its meaning, like that of the open sentence 'x is red', is not a matter of its expressing a particular proposition. Thus, 'What is it for it to be the case that ↓17 Mars is red?' doesn't look like a good question; our inability to answer it nontrivially does not amount to "taking ↓17 as primitive". The situation with ACT is, I suggest, similar. The semantic contribution of a sentence involving ACT is not properly thought of as a matter of its expressing a proposition, so the quest for an analysis of these sentences is misguided. (Of course we can use these sentences to assert propositions, just as we can use sentences with free variables to assert 50For operators that work in similar ways see, e.g., Vlach 1973, Fine 1977, Hodes 1984, Williamson MS. Under certain circumstances, the numerical subscripts can be dispensed with. But they are convenient, as they make the statement of the translation into LW easier. propositions.) Once we understand the sense in which everything that can be said using 'actually' can be said using '↑1' and '↓1', and we know how to analyse sentences using ↑1 and ↓1 in nonmodal terms, we have achieved everything the reductionist should want. 12 Surprising dependencies across Lewis-worlds Consider a very detailed qualitative property with just one instance in the whole of reality, which does not overlap our Lewis-world. Call the property 'F-ness' and its instance 'Felix'. Suppose that I could have been F, i.e. that Felix is one of my counterparts. Given the necessity of distinctness-a principle which, as we have seen, we must embrace if we want a reasonable logic for 'actually'-it is necessary that I am not Felix. Since the claim that exactly one thing is F is also necessary, being purely qualitative, it follows tha