Recombination unbound

Conclusion

The realisation that Forrest/Armstrong style cardinality arguments are not successful allowsus to have a simpler and more intuitive principle of recombination, and dispenses with the need to postulate mysterious necessities in order to guarantee a maximum size of worlds. As we have seen, examining the options for possibilia to form a proper class also raises new issues to do with the connection of possible worlds and classes, and may provide the motivation for various theoretical commitments that seemed previously to have no application outside pure mathematics (Should any proper classes have singletons? Should the individuals form a set?). While this essay has proceeded as a discussion primarily of Lewis' theory, it can be more generally applied — any theory of possible worlds that would wish to endorse something like the unrestricted principle of recombination and wishes to be able to talk about possibilia from more than one world simultaneously will need a modal class theory where the possibilia form a proper class rather than a set, for example. Nearly every theory of possible worlds can, and in my opinion should, take advantage of the unrestricted principle of recombination rather than limit the size of possible worlds.