Analysis of alethic modality and the related notion of possible world have played important if not crucial role in the analytic philosophy of the 20th century. The mainstream in the theories of possible worlds, so called Actualism, is currently predominated by the theories, which define possible worlds as set-theoretical objects composed of propositions. Other theories are usually being dismissed by a set of rather standard criticisms. The aim of this paper is to show the problems that the propositional theories have to face and to argue that one of the alternative theories, namely Combinatorialism, provides much better basis for analysis of alethic modality than it is usually thought.
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