Possibility offers a new analysis of the metaphysical concepts of possibility and necessity, one that does not rely on any sort of 'possible worlds'. The analysis proceeds from an account of the notion of a physical object and from the positing of properties and relations. It is motivated by considerations about how we actually speak of and think of objects. Michael Jubien discusses several closely related topics, including different purported varieties of possible worlds, the doctrine of 'essentialism', natural kind terms and alleged examples of necessity a posteriori. The book also offers a new theory of the functioning of proper names, both actual and fictional, and the discussion of natural kind terms and necessity a posteriori depends in part on this theory.