The models studied in modal logic are set theoretical structures. So one can regard the model theory of modal logic as a branch of set theory. The philosophical question arises: what is the connection between the set theoretical structures studied in the model theory and anything objective in virtue of which one can explain how a study of these structures can yield genuine insights into the principles and inferences of modal logic? One answer to this question is provided by the Modal Realist. Modal Realism is the doctrine that, besides the actual world one lives in, there exists other possible worlds. Modal Realism, in the full-blown sense of the term, maintains that these other possible worlds are not mere abstractions or descriptions.
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