This introduction to modality places the emphasis on the metaphysics of modality rather than on the formal semetics of quantified modal logic. The text begins by introducing students to the "de re/de dicto" distinction, conventionalist and conceptualist theories of modality and some of the key problems in modality, particularly Quine's criticisms. It then moves on to explain how possible worlds provide a solution to many of the problems in modality and how possible worlds themselves have been used to analyse notions outside modality such as properties and propositions. Possible worlds introduce problems of their own and the book argues that to make progress with these problems a theory of possible worlds is required. The pros and cons of various theories of possible worlds are then examined in turn, including those of Lewis, Kripke, Adams, Stalnaker and Plantinga.
The possible worlds hypothesis as a means to explain modality is a little absurd. David Lewis purports that any world that is possible is real but that the world that we are in is the only "actual" world. This "actuality" is not something special to him but it is just actualized since we happen to be in this specific world (among the infinitely many other possible worlds). These other possible worlds are also spatio-temporally isolated and causally isolated from the "actual" world.
Joseph Melia pushes this into something he calls "ersatzism." Ersatz meaning some unreal reproduction of the original. So the possible worlds of Lewis become these Melian "ersatz possible worlds," which contain unreal reproductions of the members of other worlds. Melia makes the analogy to a bijection in that if we take the actual world to be a set that contains all of its elements then the other ersatz possible worlds as other sets wherein we can put all of their elements into a 1-1 correspondence to the elements of the actual world. But doesn't this undermine the very notion of ersatzism? Because the point of a bijection is that both sets are meant to be taken as real or actual or whatever other word might fit that description. It seems like a dubious analogy to make when referring to these other possible worlds.
In any case, David Lewis's original possible worlds hypothesis is incredibly Platonic since these other possible worlds; as both spatio-temporally and causally isolated; cannot truly be understood, just as the Platonic Forms are existent in the heavens. Melia's addition makes this whole hypothesis even more dangerously Platonic. Plato's notion of the Forms is that they exist as the perfect templates which the members of the world try to strive toward. But when the members of the world reproduce the Forms in the world as manifest parts of themselves, this reproduction is always a perversion. For example, Plato thought that when a parent had a child, the child was simply a less perfect, less ideal form of the parent. So this is in line with Melia's choice of using the word "ersatz" but it undermines the entire operation of the possible worlds hypothesis.
This book is not only an excellent introduction to the philosophy of modality, it’s explanations of models was the only explanations that had ever made sense to me. So good I have now taken up a study of model theory only made possible by this book. I think that the author should write an equivalent book on that subject.
My only disappointment with completing this book (twice) and this is my fault, not the authors, is that I am no closer to being able to give my own views on the subject of modality than before reading it. Every view seems to have too many good arguments against it.