The Problem

It seems to be an obvious truth that

1. (1) There could be something that doesn't actually exist.

That is, it seems to be obviously true that

1. (1a) ◊∃x(Actually ∼ (x exists)).

It is sufficient for the truth of (1) that there could be more people, or trees, or cars, than there actually are. It is also sufficient for the truth of (1) that there could be some people, or trees, or cars that are distinct from all those that actually exist. Do (1) and suchlike statements involve a commitment to possibilia, to things that possibly exist, but do not actually exist? If not, why not? And if so, what is the nature of the possibilia to which (1) and its ilk commit us? These simple little questions are at the tip of an iceberg.

We have to appreciate the size of the iceberg. Some years ago—more than a quarter of a century ago—I thought that there is no commitment to possibilia in this and suchlike statements. We can call this ‘the no-commitment view’. My reason for accepting the nocommitment view was that if one starts with an object language containing modal operators and an ‘Actually’ operator, one can give a truth-theory for this object language in a metalanguage that takes the modal operators as primitive.