Hi-individuals and Where to Find Them—Towards a Hi-world Semantics for Quantified Modal Logic

If to be is to be the value of a bound variable, then the acknowledgment and denial of the existence of chairs amounts to a serious disagreement about the range of a quantifier. However, by resorting to the intrinsic hierarchical structure of hi-world semantics, we find that the varying of domains from worlds to worlds can actually be accommodated within a unified framework. With the introduction of a universal domain D of hi-individuals and an existence predicate E that serves as a realization operator, a new semantics for quantified modal logic is proposed. It allows individual variables to range over individuals in different levels of a hi-world, and is indifferent to the ontological debate about the existence of chairs.