First-order modal theories

This paper is part of a general programme of developing and investigating particular first-order modal theories. In the paper, a modal theory of propositions is constructed under the assumption that there are genuinely singular propositions, ie. ones that contain individuals as constituents. Various results on decidability, axiomatizability and definability are established.I should like to thank the members of a metaphysics seminar at Irvine, and Peter Woodruff in particular, for several helpful discussions on the topic of this paper.