 Technical matters aside, some philosophical issues are immediate. Firstly, how do we know in practice how many possible words there are? If we are talking about the number of possible worlds with respect to all possible sentences in English, then there will be infinitely many of them. Bar-Hillel and Carnap avoided this issue by talking exclusively about the semantic information encoded by sentences formulated in monadic predicate logic with a finite number of predicate letters. Where there are \(n\) predicate letters, there will be \(2^n\) possible objects, exhausting all possible predicate combinations. There will then be \(2^{2^n}\) possible worlds (“state descriptions” in Bar-Hillel and Carnap’s parlance), corresponding to all possible combinations of possible objects. Hintikka (1970, 1973), extended Bar-Hillel and Carnap’s theory of semantic information from monadic predicate logic to fully general predicate logic.