Abstract

Models based on possible worlds have proved to be very useful in the interpretation of modal expressions. However, there is a difference in the way that mathematicians and philosophers may use such models. The mathematician constructs them to serve his own purposes and thereby determines their properties. The philosopher, on the other hand, does not have so much freedom. His objective, which is to achieve a better understanding of language, puts limits on this. Not everything can be stipulated. This fact is sometimes forgotten. An example of this is the almost unrestricted use of the notion of transworld identidy in philosophical explanations and discussions. The first objective of the article is to show that this unrestricted use is illegitimate. On the other hand, it would be important to maintain the possibility of using the notion. The second objective of the article is precisely to show how this can be achieved. The kind of structure which appears to be most appropriate to account for how modalities are applied to particulars is then made explicit, formal applications of the proposed model are briefly presented, and the conditions for the application of the notion of transworld identity in the interpretation of natural language are considered