Abstract

We sometimes reason about logically incomplete sets of information that we take to resemble particular aspects of our world while differing from those aspects by being incomplete. This paper argues that there is a tension in this usual way of thinking about incompleteness: insofar as we take incomplete worlds to resemble ours, we have less grounds on which to assume that our world is logically complete. It is argued that the tension can be resolved by revising our notion of completeness. We may think of completeness, not as an absolute property that a world may have independently of other worlds, but as a relative property that worlds may have in relation to each other. The proposed relative notion preserves some of our usual ways of thinking about completeness and allows parallels to be drawn between the properties of logical completeness and logical consistency. A relative view of completeness has implications for attempts to align incomplete worlds with ours, and for the way we model our reasoning about incompleteness.