erences like S1 and S2. In both cases, we can recover as much of orthodox modal logic as we want by imposing such axioms (see section 9). From my point of view, Analysis F has one big advantage over Analysis E, namely the fact that it can very easily be extended to cover sentences in which plural terms and free variables occur in the scope of modal operators. All we need to do is to define 'RXY' to abbreviate the following conjunction: (i) for any x that is one of X, there is some y that is one of Y such that Rxy and (ii) for any y that is one of Y, there is some x that is one of X such that Rxy. We can then use Analysis F as it stands to analyse modal sentences involving plural terms: we simply allow the terms t1, . . . , tn to be plural as well as singular, understanding that the variables vi on the right-hand side should be made plural or singular according as the original terms ti were. 9 Constraints on counterpairings Since modal operators are context-dependent, the answer to the question what it is for some ordered pairs to be a counterpairing must vary from one context to another. But it is plausible that certain schematic principles involving modal operators are valid across all contexts; 17 these will correspond to constraints which all legitimate senses of 'counterpairing' must meet. The most central such principle is K: (K) (φ→ ψ)→ (φ→ ψ). This does not follow from Analysis F by itself. For example, '((Fa∧b = b) → Fa) → ((Fa ∧ b = b) → Fa)' is false if some counterpairings map a to objects that are not F, but none of these counterpairings have b in their domain. Given Analysis F, the most straightforward way to guarantee the truth of every instance of (K) is to lay it down as an axiom, true across all contexts, that counterpairings have universal domains: whenever R is a counterpairing, ∀x∃yRxy. It is easy to see that this validates (K). We don't, strictly speaking, need something quite this strong to validate (K). It would be enough, for example, if we stipulated that eve