Topic: Ontology&possible worlds
A paper by Allan Hazlett that I find intriguing:
Two Arguments in Defence of Impossible Worlds
I give two reasons to adopt etsatz impossible worlds as useful members of our ontology. The first is that such worlds are useful for accounting for truth in impossible fictions (including fictions that present themselves as fictional). The second is that such worlds are useful for accounting for the truth and falsity of safety and sensitivity conditionals, which we want an account of to explain our knowledge of mathematics and other necessary truths. Along the way I discuss a few bad reasons people have offered for believing in impossible worlds, and conclude with some remarks to dispell the worry that believing in impossible worlds will lead one to reject classical logic.
A brief comment on a part of the issues involved in the discussion of the paper above:
In talking about many worlds, one may start out with a number of concepts or definitions that will be used to make the propositions to be considered. In my mind, there are two ways to understand what the initial concepts or definitions are.
The first way is that those concepts or definitions constitute a kind of basic vocabulary. In this case, what one does by making a list of concepts or defintions is just to limit or circumscribe language. And it is just the language used, not the worlds that one talks about.
Alternatively, one may understand a defintion or a concept as a logic proposition; and as such it is true or false in a certain world or sets of worlds. Thus, if one limits the scope of his/her inquiry, considering only the worlds where the proposition one calls 'concept C' is true, of course, one get worlds out of that domain. But that does not make the worlds out of one's domain impossible.
Nevertheless, I of course agree with Allan when he claims that the idea of impossible worlds is usefull. Its utility is not in question for me, what is in question is how one can demonstrate such notion.
See also a paper of related interest by Edwin D. Mares.