Counterfactuals without possible worlds

is true exactly when JI is derivable from 4 together with a suitable set of sentences S. Intuitively, S is to consist of sentences which (i) are in fact true and (ii) would also have been true, if contrary to fact, $ had been true. The second condition, which is strictly speaking a condition on S as a whole, Goodman referred to as the contenability of S with 4. The problem with (ii) as it stands is that it involves a counterfactual construction; any such account for the truthconditions of counterfactuals must, therefore, be circular. Furthermore, there does not appear to be a simple alternative characterisation of cotenability which is free from counterfactual constructions. Goodman himself thought that the only possible way to escape from this circularity would be to account for the truth-conditions of counterfactuals in terms of underlying natural laws; and a theory of lawlikeness which would include a solution of his socalled projection problem. Unfortunately, as Goodman himself emphasises, this would destroy his original claim to explicate the concept of law by reference to counterfactuals. Worse still, it now appears that the projection problem, which Goodman subsequently cameto see as the kernel of the problem of lawlikeness, can in its turn only be solved if we appeal to certain laws. Bob Stalnaker and David Lewis independently developed theories which, although they do not solve completely the problem of truth-conditions, say enough about it to clarify to a large extent the logic of conditionals. Stalnaker supposes that the circumstances in which we use a conditional (1) determine a function (f, say) which maps sentences onto alternative situations in which the sentences are true. The conditional (1) is true in