Model theory for modal logic - Part III existence and predication

This paper is concerned with the technical implications of a certain view connecting existence to predication. This is the view that in no possible world is there a genuine relation among the nonexistents of that world or between the nonexistents and the existents! The meaning of the term ‘genuine’ here may be variously explained. On an extreme interpretation, all relations are ‘genuine’, so that none of them are to relate non-existents. On a milder interpretation, the genuine relations are those that are simple or primitive in some absolute sense. But even without appeal to an absolute concept of simplicity, we can require that all relations should be analyzable in terms of some suitable set of relations, relating only existents to existents. In order to make our results applicable to the thesis, we shall suppose that the primitive non-logical predicates of our language correspond to the genuine relations, whatever they might be taken to be. Thus, the linguistic formulation of the thesis becomes that the primitive predicates of the language should only be true, in each world, of the existents of that world. Of course, the thesis might have been given a linguistic formulation, without any reference to relations, in the first place. The thesis is an instance of what has been called Actualism. This is the ontological doctrine that ascribes a special status to actual or existent objects. Another form of the doctrine, so-called World Actualism, says that the behaviour of nonexistents is supervenient upon the behaviour of the existents, that two possible worlds which agree in the latter respect cannot differ in the former respect. The present thesis, by contrast, might be called Redicate Acrualism . It should be clear that Predicate Actualism implies World Actualism, at least if the predicates used to describe the world are to express ‘genuine’ relations; for then there are no relationships involving nonexistents by which two worlds might be distinguished. On the other hand, World Actualism does not, as it stands, imply Predicate Actualism. For our purposes, it will be useful to distinguish two versions of the actualist doctrine for predicates. Under one, the primitive predicates do not