Representing Counterparts

This paper presents and motivates a counterpart theoretic semantics for quantified modal logic based on a fleshed out account of Lewis’s notion of a ‘possibility.’ According to the account a possibility consists of a world and some haecceitistic information about how each possible individual gets represented de re. A semantics for quantified modal logic based on evaluating formulae at possibilities is developed. It is shown that this framework naturally accommodates an actuality operator, addressing recent objections to counterpart theory (see [2], [1]), and is equivalent to the more familiar Kripke semantics for quantified modal logic with an