 In trying to construct a definition of universal logical validity, it seems plausible to assume not only that the universe of discourse may contain an arbitrary number of elements and that predicates may be assigned any given interpretations in the actual world, but also that any combination of possible worlds may be associated with the real world with respect to some group of predicates. In other words, it is plausible to assume that no further restrictions need be placed on \(D, G\), and \(K\), except the standard one that \(D\) be non-empty. This assumption leads directly to our definition of universal validity. (1959a: 3) 