  Although Carnap attended courses of Frege, his main ideas are based on Wittgenstein 1921. In the Tractatus, Wittgenstein introduced a precursor of possible world semantics. There are states of affairs, which can be identified with the set of all their truths, “(1.13) The facts in logical space are the world.” Presumably these facts are atomic, and can be varied independently, “(1.21) Each item can be the case or not the case while everything else remains the same.” Thus there are many possible states of affairs, among them the actual one, the real world. Objects, in some way, involve not only the actual state of affairs, but all possible ones, “(2.0123) If I know an object I also know all its possible occurrences in states of affairs. (Every one of these possibilities must be part of the nature of the object.) A new possibility cannot be discovered later.” It is from these ideas that Carnap developed his treatment.